% Proof 1 at 22.42 (+ 0.22) seconds.

% Length of proof is 770.

% Level of proof is 73.

% Maximum clause weight is 31.000.

% Given clauses 726.

1 R(R(R(C,A,B),A,B),A,B) = C # label(non_clause) # label(goal). [goal].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 C * ((x * y) * C) = (C * x) * (y * C). [assumption].

15 (C * x) * (y * C) = C * ((x * y) * C). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 R(x,y,z) = ((x * y) * z) / (y * z). [assumption].

18 ((x * y) * z) / (y * z) = R(x,y,z). [copy(17),flip(a)].

19 R(R(R(C,A,B),A,B),A,B) != C. [deny(1)].

20 (C * x) * (y * C) = C * (C * (x * y)). [back_rewrite(15),rewrite([16(9,R)])].

24 x / 0 = x. [para(3(a,1),6(a,1,1))].

29 0 / x = x'. [para(8(a,1),6(a,1,1))].

31 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([29(3)])].

32 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

33 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

35 x * (x' * y) = y. [back_rewrite(4),rewrite([32(1)])].

36 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

40 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

41 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

50 (x * C) / x = C. [para(16(a,1),6(a,1,1))].

52 C * (x / C) = x. [para(16(a,2),7(a,1))].

53 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

55 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

56 C * (x * x) = x * (x * C). [para(16(a,2),12(a,1))].

57 C * (x * x) = x * (C * x). [para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].

58 (x * (x * C)) * y = x * (C * (x * y)). [para(16(a,1),13(a,1,1,2))].

59 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

60 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

61 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

62 C * (x * (y * x)) = x * (y * (C * x)). [para(16(a,2),13(a,2,2,2)),rewrite([16(4,R)])].

66 R(x,y,z) * (y * z) = (x * y) * z. [para(18(a,1),7(a,1,1))].

67 R(x / y,y,z) = (x * z) / (y * z). [para(7(a,1),18(a,1,1,1)),flip(a)].

68 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(7(a,1),18(a,1,2))].

70 (x * y') * y = R(x,y',y). [para(8(a,1),18(a,1,2)),rewrite([24(5)])].

73 (x * y) * y' = R(x,y,y'). [para(9(a,1),18(a,1,2)),rewrite([24(5)])].

74 R(x',x * y,z) = (y * z) / ((x * y) * z). [para(10(a,1),18(a,1,1,1)),flip(a)].

80 (x * (y * (x * z))) / ((y * x) * z) = R(x,y * x,z). [para(13(a,1),18(a,1,1))].

82 ((x * C) * y) / (x * y) = R(C,x,y). [para(16(a,1),18(a,1,1,1))].

85 (C * (x * y)) / (y * C) = R(x,y,C). [para(16(a,2),18(a,1,1))].

86 (C * (x * y)) / (C * y) = R(x,y,C). [para(16(a,2),18(a,1,2)),rewrite([16(3,R)])].

88 C * (C * (x * (y / C))) = (C * x) * y. [para(7(a,1),20(a,1,2)),flip(a)].

96 C * (x * ((C * y) * x)) = x * (C * (C * (y * x))). [para(20(a,1),13(a,2,2)),rewrite([16(6,R)])].

98 (x * C) * (y * C) = C * (C * (x * y)). [para(16(a,1),20(a,1,1))].

99 (C * x) * (C * y) = C * (C * (x * y)). [para(16(a,2),20(a,1,2))].

105 x / C = C' * x. [para(52(a,1),10(a,1,2)),flip(a)].

109 C * (C * ((C' * x) * y)) = x * (y * C). [para(52(a,1),20(a,1,1)),rewrite([105(7)]),flip(a)].

110 C * (C * (x * (C' * y))) = (C * x) * y. [back_rewrite(88),rewrite([105(4)])].

111 x' * C = C * x'. [para(16(a,2),32(a,2)),rewrite([32(2)])].

112 (x / y)' = y / x. [para(7(a,1),33(a,1,2)),flip(a)].

115 x / (x * C) = C'. [para(16(a,1),33(a,1,2))].

116 C / (C * x) = x'. [para(16(a,2),33(a,1,2))].

121 x * (C * x') = C. [para(16(a,2),35(a,1,2))].

122 R(x,x' * y,z) = (y * z) / ((x' * y) * z). [para(35(a,1),18(a,1,1,1)),flip(a)].

128 C * (x * (C' * x)) = x * x. [para(53(a,1),13(a,2,2)),rewrite([16(6,R)])].

131 ((x * C') * (y * C)) / y = R(x,C',y * C). [para(53(a,1),18(a,1,2))].

136 (x / y) * (y / x) = 0. [para(112(a,1),8(a,1,1))].

138 (x * y) / ((z * x) * y) = R(z,x,y)'. [para(18(a,1),112(a,1,1)),flip(a)].

140 (C' * x)' = C / x. [para(105(a,1),112(a,1,1))].

141 R(x,x' * y,z) = R(x',y,z)'. [back_rewrite(122),rewrite([138(8)])].

142 R(x',x * y,z) = R(x,y,z)'. [back_rewrite(74),rewrite([138(7)])].

157 (C' * x) * (C / x) = 0. [para(105(a,1),136(a,1,1))].

158 (C / x) * (C' * x) = 0. [para(105(a,1),136(a,1,2))].

159 (C / x) * ((C' * x) * y) = y. [para(140(a,1),10(a,1,1))].

160 (C' * x) * ((C / x) * y) = y. [para(140(a,1),35(a,1,2,1))].

165 R(C',x,C / x) = (x * (C / x))'. [para(157(a,1),18(a,1,1)),rewrite([29(5)]),flip(a)].

167 x * (C * (C / x)) = C * C. [para(157(a,1),20(a,2,2,2)),rewrite([35(5),16(4,R),3(9)])].

170 (C * (C / x)) * x = C * C. [para(158(a,1),20(a,2,2,2)),rewrite([16(9,R),35(9),3(9)])].

172 x' / x = x' * x'. [para(8(a,1),36(a,1,1,2)),rewrite([3(3)])].

173 x / x' = x * x. [para(9(a,1),36(a,1,1,2)),rewrite([3(2)])].

177 (C * (x * C)) / x = C * C. [para(16(a,1),36(a,1,1,2))].

178 C' * (x * (C * x)) = x * x. [para(16(a,2),36(a,1,1,2)),rewrite([105(5)])].

181 (x * y) / (x' * y) = x * x. [para(35(a,1),36(a,1,1,2))].

188 (x * x)' = x' * x'. [para(173(a,1),112(a,1,1)),rewrite([172(4)])].

205 (C * (C * (x * y))) / (C * (C * y)) = R(x,C,y * C). [para(55(a,2),18(a,1,2)),rewrite([98(5)])].

212 (C * x)' = (x * C)'. [para(55(a,1),116(a,1,2)),rewrite([116(6)]),flip(a)].

219 (C * x)' * ((x * C) * y) = y. [para(212(a,2),10(a,1,1))].

220 (C * (x * x))' = (x * (x * C))'. [para(12(a,1),212(a,2,1))].

223 (C * x) * ((x * C)' * y) = y. [para(212(a,1),35(a,1,2,1))].

246 C * ((C' * x) * (C' * x)) = (C' * x) * x. [para(7(a,1),56(a,2,2)),rewrite([105(3),105(6),105(11)])].

275 (C * (x * x)) * y = x * (C * (x * y)). [para(57(a,2),13(a,1,1))].

310 C * (C / x') = x * (C * C). [para(167(a,1),35(a,1,2)),flip(a)].

320 (C * (C / x))' = x / (C * C). [para(170(a,1),33(a,1,2)),flip(a)].

377 (x * (x * y')) * y = R(x * x,y',y). [para(12(a,1),70(a,1,1))].

380 C * (x * C') = R(x,C',C). [para(70(a,1),16(a,2))].

384 C * (C * (x * (y * C'))) = (C * x) * R(y,C',C). [para(70(a,1),20(a,1,2)),flip(a)].

401 R(x,y,y') / y' = x * y. [para(73(a,1),6(a,1,1))].

409 (C * x) * C' = R(x,C,C'). [para(16(a,2),73(a,1,1))].

413 x' / R(y,x,x') = (y * x)'. [para(73(a,1),33(a,1,2))].

424 R(C,x * x,x' * x') = C. [para(56(a,1),73(a,1,1)),rewrite([188(5),58(7),35(5),121(4),188(5)]),flip(a)].

431 C' * (x * x) = x * (C' * x). [para(128(a,1),10(a,1,2))].

438 (C * x) * (x * y) = x * (x * (y * C)). [para(128(a,1),20(a,1,1)),rewrite([12(4),13(11),110(13)]),flip(a)].

439 (C * x) * x = C * (x * x). [para(128(a,1),20(a,2,2)),rewrite([16(7,R),35(7)])].

455 (x * C) * x = C * (x * x). [para(16(a,1),439(a,1,1))].

456 (x * (C * (x * y))) / (x * y) = R(C * x,x,y). [para(439(a,1),18(a,1,1,1)),rewrite([275(4)])].

460 (C' * x) * x = x * (C' * x). [para(35(a,1),439(a,1,1)),rewrite([246(13)]),flip(a)].

524 (C' * x) * (C' * x) = C' * (x * (C' * x)). [para(35(a,1),178(a,1,2,2)),rewrite([460(6)]),flip(a)].

536 (x * C) / (C' * x) = C * C. [para(16(a,1),181(a,1,1))].

555 (C * x) * y = (x * C) * y. [para(219(a,1),10(a,1,2)),rewrite([31(4)])].

579 R(C * x,y,z) = R(x * C,y,z). [para(555(a,1),18(a,1,1,1)),rewrite([18(6)]),flip(a)].

580 ((x * (C * y)) * z) / ((y * C) * z) = R(x,C * y,z). [para(555(a,1),18(a,1,2))].

624 ((C * (C / x')) * y) / (C * (C * y)) = R(x,C * C,y). [para(310(a,2),18(a,1,1,1)),rewrite([12(10)])].

626 ((x * y) * (C * C)) / (C * (C / y')) = R(x,y,C * C). [para(310(a,2),18(a,1,2))].

641 (x * (C * C)) * (C' * x') = R(C,C / x',C' * x'). [para(310(a,1),73(a,1,1)),rewrite([112(8),105(7),112(17),105(16)])].

648 (C * (C / x')) * y = (x * (C * C)) * y. [para(310(a,1),555(a,1,1)),rewrite([16(10,R)]),flip(a)].

666 (R(x,C',C) * y) / ((x * C') * y) = R(C,x * C',y). [para(380(a,1),18(a,1,1,1))].

686 R(C,C / x',C' * x') / (C' * x') = x * (C * C). [para(310(a,1),401(a,2)),rewrite([112(8),105(7),112(13),105(12)])].

703 R(x / y,y,z) = R(y / x,x,z)'. [para(7(a,1),142(a,1,2)),rewrite([112(2)])].

706 R(C',x * C,y) = R(C,x,y)'. [para(16(a,1),142(a,1,2))].

727 R(C',x * (C * C),y) = R(C,C / x',y)'. [para(310(a,1),142(a,1,2))].

749 C * (C * (x * (x * (x * (x * C))'))) = C. [para(220(a,1),121(a,1,2,2)),rewrite([99(10),12(8)])].

797 (x * (x * C))' = C' * (x' * x'). [para(56(a,1),413(a,2,1)),rewrite([188(2),188(7),424(9),105(5)]),flip(a)].

823 C * (C * (x * (x * (C' * (x' * x'))))) = C. [back_rewrite(749),rewrite([797(6)])].

853 x * (C' * (x' * x')) = C' * x'. [para(431(a,2),35(a,1,2))].

881 R(C,x,x') = C. [back_rewrite(823),rewrite([853(9),110(9),73(4)])].

888 x * (C / x) = C. [para(140(a,1),881(a,1,3)),rewrite([141(7),165(5),31(5)])].

892 C / x' = C * x. [para(881(a,1),401(a,1,1))].

893 (C * x)' = C' * x'. [para(881(a,1),413(a,1,2)),rewrite([105(3)]),flip(a)].

899 R(C',x * (C * C),y) = R(C,C * x,y)'. [back_rewrite(727),rewrite([892(11)])].

901 R(C,C * x,C' * x') / (C' * x') = x * (C * C). [back_rewrite(686),rewrite([892(4)])].

902 (x * (C * C)) * y = C * (x * (C * y)). [back_rewrite(648),rewrite([892(4),60(5)]),flip(a)].

906 R(C,C * x,C' * x') = C. [back_rewrite(641),rewrite([902(9),35(7),9(3),3(3),892(5)]),flip(a)].

914 ((x * y) * (C * C)) / (C * (C * y)) = R(x,y,C * C). [back_rewrite(626),rewrite([892(9)])].

916 R(x,C * C,y) = R(x,C * y,C). [back_rewrite(624),rewrite([892(4),60(5),86(10)]),flip(a)].

928 C * (C * x) = x * (C * C). [back_rewrite(310),rewrite([892(4)])].

977 x / (C * C) = C' * (C' * x). [back_rewrite(320),rewrite([893(5),112(5),105(4)]),flip(a)].

998 (x * C)' = C' * x'. [back_rewrite(212),rewrite([893(3)]),flip(a)].

1003 C / (C' * x') = x * (C * C). [back_rewrite(901),rewrite([906(8)])].

1004 R(x,C,y * C) = R(x,y,C * C). [back_rewrite(914),rewrite([928(5,R),205(10)])].

1049 (C * x) * ((C' * x') * y) = y. [back_rewrite(223),rewrite([998(5)])].

1062 C / x = x' * C. [para(888(a,1),10(a,1,2)),flip(a)].

1086 C * (x * C) = x * (C * C). [back_rewrite(1003),rewrite([1062(6),140(5),1062(3),31(2),16(4,R)])].

1135 (C' * x) * ((x' * C) * y) = y. [back_rewrite(160),rewrite([1062(5)])].

1136 (x' * C) * ((C' * x) * y) = y. [back_rewrite(159),rewrite([1062(2)])].

1139 (C' * x)' = x' * C. [back_rewrite(140),rewrite([1062(6)])].

1164 (C * (C * (x * y))) / (C * (y * C)) = R(x,y,C * C). [para(1086(a,2),18(a,1,2)),rewrite([928(5,R)])].

1244 R(x,C * C,C' * y) = R(x,y,C). [para(35(a,1),916(a,2,2))].

1246 R(x,C * (y * C),C) = R(x,C * C,C * y). [para(55(a,1),916(a,2,2)),flip(a)].

1247 R(x,C * (C * y),C) = R(x,C * C,y * C). [para(55(a,2),916(a,2,2)),flip(a)].

1248 R(x,y * (y * C),C) = R(x,C * C,y * y). [para(56(a,1),916(a,2,2)),flip(a)].

1258 R(x,C' * y,C * C) = R(x,C,y). [para(7(a,1),1004(a,1,3)),rewrite([105(4)]),flip(a)].

1262 R(x,C,C * y) = R(x,y,C * C). [para(16(a,2),1004(a,1,3))].

1265 R(x,y * C',C * C) = R(x,C,R(y,C',C)). [para(70(a,1),1004(a,1,3)),flip(a)].

1267 R(x,C * y,C * C) = R(x,C,C * (y * C)). [para(555(a,1),1004(a,1,3)),rewrite([16(5,R)]),flip(a)].

1281 (C' * x) * R(x',C,C') = C'. [para(73(a,1),1135(a,1,2))].

1348 R(x,C,y) * (y * C) = (x * C) * y. [para(16(a,1),66(a,1,2))].

1349 R(x,y,C) * (C * y) = C * (x * y). [para(16(a,2),66(a,1,2)),rewrite([16(8,R)])].

1353 R(x,y,y' * z) * z = (x * y) * (y' * z). [para(35(a,1),66(a,1,2))].

1389 R(x,y,C * C) * (C * (C * y)) = C * (C * (x * y)). [para(928(a,2),66(a,1,2)),rewrite([928(14,R)])].

1397 (x * C) * (C * y) = C * (C * (x * y)). [para(1262(a,1),66(a,1,1)),rewrite([1389(9)]),flip(a)].

1405 R((x / y) / z,z,y) = x / (z * y). [para(7(a,1),67(a,2,1))].

1416 (x * y) / (y * C) = R(C' * x,C,y). [para(16(a,1),67(a,2,2)),rewrite([105(2)]),flip(a)].

1423 R(C' / x,x,y * C) = y / (x * (y * C)). [para(53(a,1),67(a,2,1))].

1424 R(x / C',C',y * C) = (x * (y * C)) / y. [para(53(a,1),67(a,2,2))].

1427 (x * y) / (C * y) = R(C' * x,C,y). [para(105(a,1),67(a,1,1)),flip(a)].

1493 R(x / y,y,C * C) = (C * (C * x)) / (y * (C * C)). [para(928(a,2),67(a,2,1))].

1500 R(x / (C * y),C * C,y) = (x * C) / (C * (C * y)). [para(67(a,1),916(a,2)),rewrite([16(13,R)])].

1567 ((x' * C) * (x * y)) / y = R(C,x',x * y). [para(10(a,1),82(a,1,2))].

1569 (C * (C * ((C * x) * y))) / (C * (C * (x * y))) = R(C,C * x,y * C). [para(20(a,1),82(a,1,2)),rewrite([16(4,R),20(7)])].

1580 (C * (x * (C * ((C' * x') * y)))) / y = R(C,C * x,(C' * x') * y). [para(1049(a,1),82(a,1,2)),rewrite([16(4,R),60(10)])].

1582 (C * (x' * (C * ((C' * x) * y)))) / y = R(C,x' * C,(C' * x) * y). [para(1136(a,1),82(a,1,2)),rewrite([16(5,R),13(10)])].

1595 (C * (x * (C' * y))) / y = R(x,C' * y,C). [para(7(a,1),85(a,1,2)),rewrite([105(3),105(9)])].

1623 (C * ((x * y) * z)) / (C * (y * z)) = R(R(x,y,z),y * z,C). [para(66(a,1),85(a,1,1,2)),rewrite([16(7,R)])].

1641 (C * x) / (C * y) = (x * C) / (y * C). [para(67(a,1),86(a,2)),rewrite([7(3)])].

1652 R(x,C,C * (x' * y)) = R(x',y,C * C)'. [para(141(a,1),1004(a,2)),rewrite([16(5,R)])].

1781 (C * ((x * C) * y)) / (C * (y * C)) = R(R(x,C,y),y * C,C). [para(1348(a,1),85(a,1,1,2)),rewrite([16(9,R)])].

1804 R(R(x,y,C),C * y,C) = R(x,C,y * C). [para(1349(a,1),85(a,1,1,2)),rewrite([16(9,R),205(10)]),flip(a)].

1808 R(C' * (x / y),C,y) = x / (y * C). [para(16(a,1),1405(a,2,2)),rewrite([105(3)])].

1809 R((C' * x) / y,y,C) = x / (C * y). [para(16(a,2),1405(a,2,2)),rewrite([105(2)])].

1811 x / (C * y) = x / (y * C). [para(105(a,1),1405(a,1,1,1)),rewrite([1809(6)])].

1831 x / (C * (C * y)) = x / (y * (C * C)). [para(928(a,1),1405(a,2,2)),rewrite([105(5),1808(10),16(4,R)])].

1832 R((C' * (C' * x)) / y,y,C * C) = x / (C * (C * y)). [para(928(a,2),1405(a,2,2)),rewrite([977(4)])].

1849 (x / (C * y)) * (y * C) = x. [para(1405(a,1),1348(a,1,1)),rewrite([105(9),16(12,R),35(12),7(8)])].

1850 (x / (y * C)) * (C * y) = x. [para(1405(a,1),1349(a,1,1)),rewrite([105(9),7(12),35(11)])].

1851 (x * (C * y)) / (y * C) = x. [para(1811(a,1),6(a,1))].

1855 (C * x) / y = (x * C) / y. [para(1811(a,1),112(a,1,1)),rewrite([112(4)]),flip(a)].

1886 x * (C * y) = x * (y * C). [para(6(a,1),1849(a,1,1)),flip(a)].

1907 R(x / (C * y),y * C,C) = (C * x) / (C * (y * C)). [para(1849(a,1),85(a,1,1,2)),rewrite([16(6,R)]),flip(a)].

1923 R(x / (y * C),C * y,C) = (C * x) / (C * (C * y)). [para(1850(a,1),85(a,1,1,2)),rewrite([16(6,R)]),flip(a)].

1935 R(x,C * y,z) = R(x,y * C,z). [para(1851(a,1),67(a,1,1)),rewrite([580(11)]),flip(a)].

1965 ((x * y) * (C * z)) / (y * (z * C)) = R(x,y,C * z). [para(1886(a,1),18(a,1,2))].

1966 R(x,y,C * z) = R(x,y,z * C). [para(1886(a,2),18(a,1,1)),rewrite([1965(8)])].

2015 R(x,C * (C * y),z) = R(x,C * (y * C),z). [para(555(a,1),1935(a,2,2)),rewrite([16(9,R)])].

2137 x * ((y / (x * z)) * x) = (x * y) / z. [para(7(a,1),40(a,1,1,2)),flip(a)].

2139 x * ((x * y)' * x) = x / y. [para(8(a,1),40(a,1,1,2)),rewrite([3(2)]),flip(a)].

2140 (x * y) / x' = x * (y * x). [para(9(a,1),40(a,1,1,2,2)),rewrite([3(2)])].

2211 x * ((y / (C * x)) * x) = C' * (x * y). [para(1849(a,1),40(a,1,1,2)),rewrite([105(3)]),flip(a)].

2221 (x * y)' * x = x' * (x / y). [para(2139(a,1),10(a,1,2)),flip(a)].

2222 x' / (x * y) = x' * (y' * x'). [para(10(a,1),2139(a,1,2,1,1)),flip(a)].

2226 x * R(C',x',x) = C' * x. [para(16(a,2),2139(a,1,2,1,1)),rewrite([893(3),70(5),105(7)])].

2229 x / (x' * y) = x * (y' * x). [para(35(a,1),2139(a,1,2,1,1)),flip(a)].

2232 C' * R(x',C,C') = C' / x. [para(2139(a,1),105(a,2)),rewrite([1139(4),73(6),105(7)])].

2252 x * R(C' * C',x',x) = C' * (C' * x). [para(928(a,2),2139(a,1,2,1,1)),rewrite([893(5),893(5),377(8),977(12)])].

2278 C' * R(x,C,C') = C' * x. [para(53(a,1),2140(a,1,1)),rewrite([31(3),105(2),73(10)]),flip(a)].

2280 (x * (y * x))' = x' * (y' * x'). [para(2140(a,1),112(a,1,1)),rewrite([2222(6)])].

2331 C' / x = C' * x'. [back_rewrite(2232),rewrite([2278(8)]),flip(a)].

2357 R(C' * x',x,y * C) = y / (x * (y * C)). [back_rewrite(1423),rewrite([2331(3)])].

2359 R(C',x',x) = C'. [para(2331(a,1),7(a,1,1)),rewrite([70(5)])].

2361 x / C' = x * C. [para(2331(a,1),112(a,1,1)),rewrite([1139(5),31(2)]),flip(a)].

2369 C' * x = x * C'. [back_rewrite(2226),rewrite([2359(4)]),flip(a)].

2377 R(x * C,C',y * C) = (x * (y * C)) / y. [back_rewrite(1424),rewrite([2361(3)])].

2379 R(x,C,C') = x. [back_rewrite(409),rewrite([2369(5,R),10(5)]),flip(a)].

2383 R(C',x,x') = C'. [back_rewrite(1281),rewrite([2379(8),73(5)])].

2393 R(x,C',C) = x. [para(2369(a,1),10(a,1,2)),rewrite([31(3),380(5)])].

2394 x' * (C' * x) = C'. [para(2369(a,2),10(a,1,2))].

2399 (C' * (C' * x)) * y = C' * (x * (C' * y)). [para(2369(a,2),13(a,1,1,2))].

2408 x * (C' * x') = C'. [para(2369(a,2),35(a,1,2))].

2416 R(C,x * C',y) = R(C',x,y)'. [para(2369(a,1),142(a,1,2)),rewrite([31(3)])].

2418 (x * C')' = x' * C. [para(2369(a,1),413(a,2,1)),rewrite([2383(5),2361(4)]),flip(a)].

2421 (x * C') * ((x' * C) * y) = y. [para(2369(a,1),1135(a,1,1))].

2422 (x' * C) * ((x * C') * y) = y. [para(2369(a,1),1136(a,1,2,1))].

2427 (C' * x) * y = (x * C') * y. [para(2369(a,1),66(a,2,1)),rewrite([66(5)])].

2453 R(x,y * C',C * C) = R(x,C,y). [back_rewrite(1265),rewrite([2393(12)])].

2461 (x * y) / ((x * C') * y) = R(C',x,y)'. [back_rewrite(666),rewrite([2393(4),2416(11)])].

2465 C * (C * (x * (y * C'))) = (C * x) * y. [back_rewrite(384),rewrite([2393(14)])].

2466 C * (x * C') = x. [back_rewrite(380),rewrite([2393(9)])].

2504 R(x,C' * C',C) = x. [para(2408(a,1),86(a,1,2)),rewrite([2361(11),16(10,R),2465(10),2369(5,R),10(5)]),flip(a)].

2505 C * (x * (C' * C')) = x * C'. [para(2408(a,1),1349(a,1,2)),rewrite([2504(7)]),flip(a)].

2573 x' * (C' * (C' * x)) = R(C' * C',x',x). [para(928(a,2),2221(a,1,1,1)),rewrite([893(5),893(5),377(8),977(12)]),flip(a)].

2574 R(C' * C',x',x) = C' * C'. [para(1086(a,2),2221(a,1,1,1)),rewrite([2280(5),13(8),2394(7),977(10),2573(13)]),flip(a)].

2599 C' * (C' * x) = x * (C' * C') # label(flip_matches_hint). [back_rewrite(2252),rewrite([2574(7)]),flip(a)].

2678 (x' * C') * ((x * C) * y) = y. [para(31(a,1),2421(a,1,2,1,1))].

2702 (x' * C) * (((x * C') * y) * (x' * C)) = y / (C' * x). [para(2422(a,1),2140(a,1,1)),rewrite([998(4),31(4)]),flip(a)].

2714 ((x * (C' * y)) * z) / ((y * C') * z) = R(x,C' * y,z). [para(2427(a,1),18(a,1,2))].

2736 (C' * x) * (y * C) = (x * C') * (C * y). [para(2427(a,1),1886(a,1)),flip(a)].

2737 (C' * x) * (C * y) = (x * C') * (y * C). [para(2427(a,1),1886(a,2))].

2785 (x' * ((x * C) * y)) / y = R(C',x',(x * C) * y)'. [para(2678(a,1),82(a,1,2)),rewrite([16(6,R),2466(6),2416(15)])].

2804 C * (C * ((x * (C' * C')) * y)) = (x * C') * (y * C). [para(2505(a,1),20(a,1,1)),flip(a)].

2818 R(x,C * C,y * (C' * C')) = R(x,y * C',C). [para(2505(a,1),916(a,2,2))].

2819 R(x,y * (C' * C'),C * C) = R(x,C,y * C'). [para(2505(a,1),1262(a,1,3)),flip(a)].

2820 R(x,C,y * (C' * C')) * (y * C') = (x * C) * (y * (C' * C')). [para(2505(a,1),66(a,1,2))].

2836 (x * y) * x' = x * (y / x). [para(9(a,1),41(a,1,2,2)),rewrite([3(3)]),flip(a)].

2837 (x / y) * (y * z) = y' * ((y * x) * z). [para(41(a,1),10(a,1,2)),flip(a)].

2838 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),41(a,1,2,2)),flip(a)].

2846 C * ((C * x) * y) = x * (C * (C * y)). [para(41(a,1),20(a,2,2)),rewrite([105(3),35(5),16(4,R)]),flip(a)].

2849 (x * y) * (x' * z) = x * ((y / x) * z). [para(35(a,1),41(a,1,2,2)),flip(a)].

2850 (C' * x) * (y * C) = C' * ((x * C) * y). [para(53(a,1),41(a,1,2,2)),rewrite([2361(5)]),flip(a)].

2852 (x * y) * (C * x') = x * (C * (y / x)). [para(121(a,1),41(a,1,2,2)),rewrite([16(3,R)]),flip(a)].

2860 (x * (C * (x * C))) * y = x * (C * (C * (x * y))). [para(177(a,1),41(a,1,2,1)),rewrite([12(5)]),flip(a)].

2867 (C * x) * ((y / (C * x)) * (C * (x * x))) = ((C * x) * y) * x. [para(439(a,1),41(a,1,2,2))].

2876 (C' * x) * (x * (y * C)) = x * (x * y). [para(536(a,1),41(a,1,2,1)),rewrite([12(11),109(11),2850(13),455(12),10(13),12(9)])].

2916 x * ((C * y) * z) = x * ((y * C) * z). [para(41(a,1),1886(a,1,2)),rewrite([105(6),2838(10),2361(9),16(12,R),35(12)])].

2945 (x * C') * (y * C) = C' * ((x * C) * y). [back_rewrite(2737),rewrite([2838(6),2361(5)]),flip(a)].

2946 R(C',x',(x * C) * y)' = R(C,x',x * y). [back_rewrite(1567),rewrite([2838(5),1062(4),31(3),2785(6)])].

2959 (x * C') * (C * y) = C' * ((x * C) * y). [back_rewrite(2736),rewrite([2850(6)]),flip(a)].

2964 C * (C * ((x * (C' * C')) * y)) = C' * ((x * C) * y). [back_rewrite(2804),rewrite([2945(17)])].

2966 (C' * ((x * C) * y)) / y = R(x,C',y * C). [back_rewrite(131),rewrite([2945(6)])].

2967 (x' * ((x * C) * y)) / y = R(C,x',x * y). [back_rewrite(2785),rewrite([2946(14)])].

3007 (x * C) * R(y,x,C) = C * (x * y). [para(85(a,1),2836(a,2,2)),rewrite([1397(6),998(9),2849(11),105(7),10(8),2836(5),6(3)]),flip(a)].

3025 ((x * C') * y) * (x' * C) = (x * C') * (y / (x * C')). [para(2418(a,1),2836(a,1,2))].

3040 x / (C' * y) = x / (y * C'). [back_rewrite(2702),rewrite([3025(11),2422(12)]),flip(a)].

3091 (x * (C' * y)) / (y * C') = x. [para(3040(a,1),6(a,1))].

3125 (C * x) / (y * C') = (x * C) / (C' * y). [para(3040(a,1),1855(a,1))].

3150 R(x,C' * y,z) = R(x,y * C',z). [para(3091(a,1),67(a,1,1)),rewrite([2714(14)]),flip(a)].

3153 R(R(x,C' * y,C),y,C') = x. [para(3091(a,1),1405(a,2)),rewrite([2361(7),16(6,R),1595(7)])].

3202 R(R(x,y,C),y * C,C') = x. [para(53(a,1),3153(a,1,1,2))].

3245 C' * (x' * ((x * C) * y)) = R(y,x,C). [para(3007(a,1),10(a,1,2)),rewrite([998(3),2838(8),2361(6),2838(7),1062(6),31(5)])].

3260 C * (x * (C * R(y,C * x,C))) = C * ((C * x) * y). [para(555(a,1),3007(a,1,1)),rewrite([16(4,R),13(9)])].

3271 (C * (x * (C * R(y,x,C)))) / (C * (x * y)) = R(C,x * C,R(y,x,C)). [para(3007(a,1),82(a,1,2)),rewrite([16(4,R),13(7)])].

3514 R(x,y,C * (C * (C * z))) = R(x,y,C * (z * (C * C))). [para(60(a,1),1966(a,2,3))].

3540 x' * (C * (x * (y * x))) = y * (x * C). [para(61(a,2),10(a,1,2))].

3720 (C * (C * (x * (y * x)))) / (C * (y * (C * x))) = R(x,y * (C * x),C). [para(62(a,2),85(a,1,1,2)),rewrite([16(11,R)])].

4111 x / (C * (C * (y * y))) = x / (y * (C * (y * C))). [para(275(a,1),1811(a,2,2))].

4177 x' * (x' * (C * (x * y))) = (C * x') * y. [para(10(a,1),438(a,1,2)),rewrite([16(9,R)]),flip(a)].

4352 (x * C) / (y * x) = R(C' * y,C,x)'. [para(1416(a,1),112(a,1,1)),flip(a)].

4368 ((x * y) * z) / (C * (y * z)) = R(C' * R(x,y,z),C,y * z). [para(66(a,1),1416(a,1,1)),rewrite([16(5,R)])].

4397 (x * (C * (y * y))) / (y * (C * (y * C))) = R(C' * x,C,C * (y * y)). [para(275(a,1),1416(a,1,2))].

4433 (C * x) / (y * (C * C)) = (x * C) / (C * (C * y)). [para(928(a,1),1641(a,1,2)),rewrite([16(13,R)])].

4477 (C * (x * y)) / (C * (y * C)) = R(C' * R(x,y,C),C,y * C). [para(85(a,1),1808(a,1,1,2)),rewrite([16(16,R)]),flip(a)].

4489 R(C' * R(x * C,y,C),C,y * C) = R(R(x,C,y),y * C,C). [back_rewrite(1781),rewrite([4477(10)])].

4813 (x / (y * z)) * y = y' * ((y * x) / z). [para(2137(a,1),10(a,1,2)),flip(a)].

4814 (x' * y) / (x * z) = x' * ((y / z) * x'). [para(10(a,1),2137(a,1,2,1,2)),flip(a)].

4817 C * (C * (x / (C * y))) = (C * x) / y. [para(2137(a,1),16(a,1)),rewrite([16(8,R),16(10,R)]),flip(a)].

4822 (x * y) / (x' * z) = x * ((y / z) * x). [para(35(a,1),2137(a,1,2,1,2)),flip(a)].

4823 (C' * x) / (y * C) = C' * (C' * (x / y)). [para(53(a,1),2137(a,1,2,1,2)),rewrite([2369(6,R)]),flip(a)].

4857 C * (C * (x / (y * (C * C)))) = (C * x) / (C * y). [para(928(a,1),2137(a,1,2,1,2)),rewrite([16(8,R)])].

4873 (x * ((x * C) * y)) / y = x * (R(C,x,y) * x). [para(82(a,1),2137(a,1,2,1)),flip(a)].

4930 (C * (x * y)) / y = C * (C * R(C' * x,C,y)). [para(1427(a,1),2137(a,1,2,1)),rewrite([16(8,R)]),flip(a)].

4931 C' * (x * (C * y)) = C' * (x * (y * C)). [para(1641(a,2),2137(a,1,2,1)),rewrite([2211(7),105(11)])].

5088 (x * (C' * C')) / (C' * x) = C'. [para(2599(a,1),6(a,1,1))].

5111 (C' * x) * (x * (C' * C')) = C' * (C' * (x * (C' * x))). [para(2599(a,1),431(a,2,2)),rewrite([524(9)]),flip(a)].

5119 (x * (C' * C')) * y = C' * (x * (C' * y)). [para(2599(a,1),66(a,2,1)),rewrite([66(11),2399(7)]),flip(a)].

5161 C' * ((x * C) * y) = C * (x * (C' * y)). [back_rewrite(2964),rewrite([5119(9),35(10)]),flip(a)].

5180 R(x,C' * y,C) = R(x,C',y * C). [back_rewrite(2966),rewrite([5161(6),1595(7)])].

5182 (x * C') * (C * y) = C * (x * (C' * y)). [back_rewrite(2959),rewrite([5161(12)])].

5191 (C' * x) * (y * C) = C * (x * (C' * y)). [back_rewrite(2850),rewrite([5161(12)])].

5199 R(R(x,C',y * C),y,C') = x. [back_rewrite(3153),rewrite([5180(5)])].

5201 (C * (x * (C' * y))) / y = R(x,C',y * C). [back_rewrite(1595),rewrite([5180(12)])].

5250 ((x * y) * (C * (C * z))) / (C * ((C * y) * z)) = R(x,y,C * (C * z)). [para(2846(a,2),18(a,1,2))].

5288 R(x,y * (C * (C * z)),C) = R(x,C * C,(C * y) * z). [para(2846(a,1),916(a,2,2)),flip(a)].

5294 (x * y) * (C * (C * z)) = C * ((C * (x * y)) * z). [para(2846(a,2),66(a,2)),rewrite([66(11)])].

5306 (C * (x * ((C * y) * z))) / (y * (C * (C * z))) = R(x,(C * y) * z,C). [para(2846(a,1),86(a,1,2))].

5372 (C * ((C * x) * y)) / (C * (C * (C * y))) = R(C' * x,C,C * (C * y)). [para(2846(a,2),1416(a,1,1)),rewrite([16(11,R)])].

5374 (C * x) / (y * (C * (C * z))) = (x * C) / (C * ((C * y) * z)). [para(2846(a,1),1641(a,1,2)),rewrite([16(15,R)])].

5400 (C * ((C * (x * y)) * z)) / (C * ((C * y) * z)) = R(x,y,C * (C * z)). [back_rewrite(5250),rewrite([5294(6)])].

5435 C' * ((C * x) * y) = C * (x * (C' * y)). [para(2916(a,1),105(a,2)),rewrite([105(5),5161(12)])].

5500 (C * (x * ((C * y) * z))) / (C * ((y * C) * z)) = R(x,(y * C) * z,C). [para(2916(a,2),85(a,1,1,2)),rewrite([16(11,R)])].

5501 R(x,C * C,C * (y * (C' * z))) = R(x,(C * y) * z,C). [para(2916(a,1),1244(a,1,3)),rewrite([5161(9)])].

5558 (C * x) / (C * ((y * C) * z)) = (x * C) / (C * ((C * y) * z)). [para(2916(a,1),1641(a,1,2)),rewrite([16(15,R)])].

5593 R(x,y * C',C) = R(x,C',y * C). [para(3150(a,1),85(a,2)),rewrite([16(11,R),35(11),5201(7)]),flip(a)].

5603 R(x,C * C,y * (C' * C')) = R(x,C',y * C). [back_rewrite(2818),rewrite([5593(15)])].

5661 C' * ((C * x) / y) = C * (x / (C * y)). [para(4817(a,1),10(a,1,2))].

5678 (C * x) / (y * C') = C * (C * (x / y)). [para(3040(a,1),4817(a,2)),rewrite([35(7)]),flip(a)].

5685 C * (C * (x / (y * (C * (C * z))))) = (C * x) / ((C * y) * z). [para(2846(a,1),4817(a,1,2,2,2))].

5695 (x * C) / (C' * y) = C * (C * (x / y)). [back_rewrite(3125),rewrite([5678(6)]),flip(a)].

5704 R(x,C',C * (C * y)) = R(x,y,C). [para(10(a,1),5180(a,1,2)),rewrite([16(8,R)]),flip(a)].

5716 R(x,C * (y * (C' * z)),C) = R(x,C',C * ((C * y) * z)). [para(2916(a,1),5180(a,1,2)),rewrite([5161(6),16(15,R)])].

5727 R(x,y * (C * z),C) = R(x,y * (z * C),C). [para(59(a,1),5704(a,1,3,2)),rewrite([5704(10)]),flip(a)].

5759 (C * ((C' * x) * y)) / y = R(x,C,C' * y). [para(928(a,2),68(a,1,1)),rewrite([977(6),110(11),2849(6),105(3),977(11),1258(17)])].

5777 (C' * (x * (y * C))) / y = R(x,y * C,C'). [para(2369(a,2),68(a,1,1)),rewrite([2361(5),2361(10)])].

5829 C' * (x * (y * C)) = C * ((C' * x) * y). [para(109(a,1),10(a,1,2))].

5848 R(x,C * C,C * ((C' * y) * z)) = R(x,y * (z * C),C). [para(109(a,1),916(a,2,2))].

5877 R(x,C * ((C' * y) * z),C) = R(x,C',C * (y * (z * C))). [para(109(a,1),5704(a,1,3,2)),flip(a)].

5878 R(x,(C' * y) * z,C) = R(x,C',y * (z * C)). [para(109(a,1),5704(a,1,3)),flip(a)].

5879 R(x,y * C,C') = R(x,C,C' * y). [back_rewrite(5777),rewrite([5829(6),5759(7)]),flip(a)].

5882 C' * (x * (C * y)) = C * ((C' * x) * y). [back_rewrite(4931),rewrite([5829(12)])].

5892 R(R(x,y,C),C,C' * y) = x. [back_rewrite(3202),rewrite([5879(7)])].

5921 R(R(x,C * y,C),C,y) = x. [para(10(a,1),5892(a,1,3))].

6024 (x * C) * (C' * y) = C * ((C' * x) * y). [para(5879(a,1),66(a,1,1)),rewrite([2369(10,R),53(10),1353(6),2369(12,R),5829(12)])].

6028 R(x,C,y * (C' * C')) = R(x,y,C'). [para(2599(a,1),5879(a,2,3)),rewrite([16(5,R),35(5)]),flip(a)].

6043 (x * C) * (y * (C' * C')) = C' * (x * y). [back_rewrite(2820),rewrite([6028(8),66(7),2369(4,R)]),flip(a)].

6081 C' * (x * (C' * y))' = C * ((C * x) * y)'. [para(110(a,1),2221(a,1,1,1)),rewrite([16(6,R),1062(16),893(15),16(18,R),35(18)]),flip(a)].

6099 R(x,y * (C' * z),C) = R(x,C',(C * y) * z). [para(110(a,1),5704(a,1,3)),flip(a)].

6243 R(R(x,C',y * C),y,C) = R(x,C,y). [para(7(a,1),1804(a,2,3)),rewrite([105(2),5180(5),105(8),35(10)])].

6247 R(R(x,C * y,C),C * C,y * C) = R(x,C,C * (y * C)). [para(555(a,1),1804(a,2,3)),rewrite([1247(10),16(15,R)])].

6248 R(R(x,y * C,C),C * C,C * y) = R(x,C,C * (C * y)). [para(555(a,2),1804(a,2,3)),rewrite([1246(10),16(15,R)])].

6257 R((C' * x) / y,C,y * C) = (C * x) / (C * (C * y)). [para(1405(a,1),1804(a,1,1)),rewrite([1923(7),105(9)]),flip(a)].

6267 R(R(x,C,y * C),C,y) = R(x,y,C). [para(1804(a,1),5892(a,1,1)),rewrite([10(10)])].

6271 R(R(x,C',y * (y * C)),y * y,C) = R(x,C,y * y). [para(12(a,1),6243(a,1,1,3))].

6273 R(R(x,C',C * y),y,C) = R(x,C,y). [para(16(a,2),6243(a,1,1,3))].

6292 R(C * (x / (C * y)),C,y) = R(x / y,y,C). [para(1405(a,1),6273(a,1,1)),rewrite([10(5),2361(9),16(8,R)]),flip(a)].

6293 R(R(x,C',y * C'),C',y) = R(x,y,C'). [para(2505(a,1),6273(a,1,1,3)),rewrite([6099(14),2369(13,R),10(13),6028(17)])].

6295 R(R(x,C',C * (y * (z * C))),y * (C * z),C) = R(x,C,y * (C * z)). [para(59(a,1),6273(a,1,1,3))].

6299 R(R(x,C',y * (C * (C * z))),(C * y) * z,C) = R(x,C,(C * y) * z). [para(2846(a,1),6273(a,1,1,3))].

6301 R(R(x,C',C * ((C * y) * z)),(y * C) * z,C) = R(x,C,(y * C) * z). [para(2916(a,2),6273(a,1,1,3))].

6303 R(R(x,C',y * (z * C)),C',C * (y * (z * C))) = R(x,C,C * ((C' * y) * z)). [para(109(a,1),6273(a,1,1,3)),rewrite([5877(14)])].

6304 R(R(x,C',(C * y) * z),C',C * ((C * y) * z)) = R(x,C,C * (y * (C' * z))). [para(110(a,1),6273(a,1,1,3)),rewrite([5716(14)])].

6448 (C' * x') * (x * (C * (x * y))) = C * (x * (C' * y)). [para(115(a,1),2837(a,1,1)),rewrite([5161(6),998(9),455(13),275(14)]),flip(a)].

6492 (C' * x') * (x * y) = x' * ((x * C') * y). [para(2331(a,1),2837(a,1,1))].

6494 (x / y) * (C' * y) = y' * (C' * (y * x)). [para(2369(a,2),2837(a,1,2)),rewrite([2369(10,R)])].

6548 C * ((C' * x) * (C' * y)) = C' * (x * y). [para(2599(a,1),2837(a,1,2)),rewrite([2361(3),6043(9),31(7)]),flip(a)].

6552 (C' * x) * (y * (C * (C * z))) = C * (x * (C * (y * (C' * z)))). [para(2846(a,1),2837(a,1,2)),rewrite([105(2),5435(18),5435(16)])].

6559 (x / (C * y)) * (C * z) = C' * (((C * x) / y) * z). [para(4817(a,1),2837(a,2,2,1)),rewrite([105(7),10(8)])].

6562 (C' * x) * (y * (z * C)) = C * (x * ((C' * y) * z)). [para(109(a,1),2837(a,1,2)),rewrite([105(2),99(18),10(19)])].

6570 C * ((C' * x) * (x' * ((x * (C * y)) * x))) = ((C * x) * y) * x. [back_rewrite(2867),rewrite([6559(9),2837(9),2849(12),105(3)])].

6574 x' * (C * (x * (C' * (x * y)))) = C * (x * (C' * y)). [back_rewrite(6448),rewrite([6492(9),5182(8)])].

6611 C * (x * ((C' * x) * y)) = x * (x * y). [back_rewrite(2876),rewrite([6562(7)])].

6651 x * (C * (x * ((C' * x') * y))) = C * ((C' * x) * y). [para(115(a,1),2849(a,2,2,1)),rewrite([455(3),998(6),275(9),6024(15)])].

6652 (C * x') * (x * y) = x' * ((x * C) * y). [para(111(a,1),2849(a,1,1)),rewrite([31(5),1062(9),31(8)])].

6700 (C' * x) * (x' * y) = x * ((C' * x') * y). [para(2369(a,2),2849(a,1,1)),rewrite([2331(9)])].

6768 (C' * x) * (C' * y) = C' * (C' * (x * y)). [para(5088(a,1),2849(a,2,2,1)),rewrite([5111(10),1139(14),2399(15),5161(13),13(14),5882(13),

6700(12),6651(14),6548(11)]),flip(a)].

6783 C * (x * ((C' * x') * ((x * (C * y)) * x))) = ((C * x) * y) * x. [back_rewrite(6570),rewrite([6700(11)])].

6975 R(x,C',y * C) = R(x,y,C). [para(7(a,1),3245(a,1,2,2,1)),rewrite([105(4),1139(6),2838(7),1062(6),31(5),3245(8),105(4),5180(7)]),flip(a)]

.

6976 x' * ((x * C) * y) = C * R(y,x,C). [para(3245(a,1),10(a,1,2)),rewrite([31(3)]),flip(a)].

6977 C * (x' * ((x * C') * y)) = R(y,x * x,C). [para(12(a,1),3245(a,1,2,2,1)),rewrite([188(4),58(9),12(10),10(9),5882(8),6492(7)])].

6984 R(x,C * y,C) = R(x,y,C). [para(555(a,1),3245(a,1,2,2,1)),rewrite([893(5),16(10,R),13(11),2838(12),2361(8),2838(11),1062(8),31(7),1397(1

0),5882(12),2838(11),2361(9),2838(10),1062(9),31(8),6976(10),10(10),10(7)]),flip(a)].

6985 R(x,y * C,C) = R(x,y,C). [para(555(a,2),3245(a,1,2,2,1)),rewrite([998(5),16(10,R),60(11),2838(12),2361(8),2838(11),1062(8),31(7),1397(1

0),5882(12),2838(11),2361(9),2838(10),1062(9),31(8),6976(10),10(10),10(7)]),flip(a)].

6986 C * R(x,y,C) = R(x * C,y,C). [para(579(a,1),3245(a,2)),rewrite([1397(8),5882(10),2838(9),2361(7),2838(8),1062(7),31(6),6976(8),10(8)])]

.

6989 C' * R(x * C,y,C) = R(x,C * C,y). [para(916(a,2),3245(a,2)),rewrite([893(5),16(10,R),60(11),2838(12),2361(8),2838(11),1062(8),31(7),139

7(10),5882(12),2838(11),2361(9),2838(10),1062(9),31(8),6976(10),6986(9),35(11)])].

7008 R(x,R(y,z,C),C * C) = R(x,C,R(y * C,z,C)). [para(3245(a,1),1258(a,1,2)),rewrite([6976(12),6986(11)])].

7019 R(x,C * C,y) = R(x,y,C). [para(3245(a,1),2369(a,1)),rewrite([6976(7),6986(6),2369(9,R),6989(9)]),flip(a)].

7021 R(x * C,y,C)' = C' * R(x,y,C)'. [para(3245(a,1),2221(a,1,1,1)),rewrite([2369(6,R),31(9),6976(14),6986(13),2331(14),35(16)]),flip(a)].

7026 R(R(x,y,C),y,C) = R(x,y * y,C). [para(3007(a,1),3245(a,1,2,2)),rewrite([5882(8),6492(7),6977(8)]),flip(a)].

7027 x' * (C * (x * (C' * y))) = R(y,x * x,C). [para(58(a,1),3245(a,1,2,2,1)),rewrite([797(6),2860(14),6552(15),12(14),6574(13),10(13),1248(

13),7019(13)])].

7048 R(x,y * y,C) = R(x,C,y). [para(6243(a,1),3245(a,2)),rewrite([6975(10),3007(8),5882(8),6492(7),6977(8)])].

7068 R(x,C',y) = R(x,y,C). [back_rewrite(5603),rewrite([7019(10),6099(8),2369(7,R),10(7),6975(8)])].

7071 R(R(x,y,C),y,C') = x. [back_rewrite(5199),rewrite([6975(5)])].

7074 R(x,C' * y,C) = R(x,y,C). [back_rewrite(5180),rewrite([6975(10)])].

7078 (x * (y * C)) / y = R(x * C,y,C). [back_rewrite(2377),rewrite([6975(7)]),flip(a)].

7084 (C * x') * (x * y) = R(y * C,x,C). [back_rewrite(6652),rewrite([6976(10),6986(9)])].

7085 R(C,x',x * y) = R(y * C,x,C) / y. [back_rewrite(2967),rewrite([6976(5),6986(4)]),flip(a)].

7092 R(x,C,C * (y * C)) = R(x,C,y). [back_rewrite(6247),rewrite([6984(4),7019(8),6985(6),7026(4),7048(3)]),flip(a)].

7093 R(R(x,y,C),C,y) = x. [back_rewrite(5921),rewrite([6984(4)])].

7094 R(x,C',C * (y * (z * C))) = R(x,C',y * (z * C)). [back_rewrite(5877),rewrite([6984(8),5878(6)]),flip(a)].

7097 R(x,C',C * ((C * y) * z)) = R(x,C',(C * y) * z). [back_rewrite(5716),rewrite([6984(8),6099(6)]),flip(a)].

7100 C * (x * R(y * C,x,C)) = C * ((C * x) * y). [back_rewrite(3260),rewrite([6984(6),6986(5)])].

7102 R(x / (y * C),y,C) = (C * x) / (C * (C * y)). [back_rewrite(1923),rewrite([6984(7)])].

7104 R(x,C,y * C) = R(x,C,y). [back_rewrite(1804),rewrite([6984(6),7026(4),7048(3)]),flip(a)].

7113 R(x,C,C * (C * y)) = R(x,C,y). [back_rewrite(6248),rewrite([6985(4),7019(8),6984(6),7026(4),7048(3)]),flip(a)].

7114 R(R(x,C,y),y,C) = x. [back_rewrite(4489),rewrite([6989(7),7019(4),7104(6),7093(4),6985(6)]),flip(a)].

7115 R(x / (C * y),y,C) = (C * x) / (C * (y * C)). [back_rewrite(1907),rewrite([6985(7)])].

7126 R(R(C,x,y),x * y,C) = R(C,x * C,R(y,x,C)). [back_rewrite(3271),rewrite([6986(5),7100(7),1623(9)])].

7141 R(x,y * (z * C),C) = R(x,C',y * (z * C)). [back_rewrite(5848),rewrite([7019(10),6984(8),5878(6)]),flip(a)].

7142 R(x,(C * y) * z,C) = R(x,C',(C * y) * z). [back_rewrite(5501),rewrite([7019(10),6984(8),6099(6)]),flip(a)].

7144 R(x,y * (C * (C * z)),C) = R(x,C',(C * y) * z). [back_rewrite(5288),rewrite([7019(14),7142(12)])].

7160 R(x / (C * y),y,C) = (x * C) / (C * (C * y)). [back_rewrite(1500),rewrite([7019(7)])].

7164 R(x,C',y * (y * C)) = R(x,C,y). [back_rewrite(1248),rewrite([7141(5),7019(11),7048(9)])].

7171 R(x * y,C,x) = C * (x * (C' * y)). [back_rewrite(6574),rewrite([7027(9),7048(4)])].

7176 R(R(x,y,C),y,C) = R(x,C,y). [back_rewrite(7026),rewrite([7048(7)])].

7179 R(R(x,C,y),C,y) = R(x,C,y * y). [back_rewrite(6271),rewrite([7164(6),7048(5)])].

7201 R(x,C * y,C * C) = R(x,C,y). [back_rewrite(1267),rewrite([7092(12)])].

7202 R(R(x,C',y * (z * C)),C',y * (z * C)) = R(x,C,C * ((C' * y) * z)). [back_rewrite(6303),rewrite([7094(14)])].

7203 R(R(x,C',y * (z * C)),y * (C * z),C) = R(x,C,y * (C * z)). [back_rewrite(6295),rewrite([7094(8)])].

7208 R(R(x,C',(C * y) * z),C',(C * y) * z) = R(x,C,C * (y * (C' * z))). [back_rewrite(6304),rewrite([7097(14)])].

7209 R(R(x,C',(C * y) * z),(y * C) * z,C) = R(x,C,(y * C) * z). [back_rewrite(6301),rewrite([7097(8)])].

7215 R(x,C,y * y) = R(x,y,C). [back_rewrite(6267),rewrite([7104(4),7179(4)])].

7217 R((C' * x) / y,C,y) = (C * x) / (C * (C * y)). [back_rewrite(6257),rewrite([7104(8)])].

7236 R(x,y,C * C) = R(x,C,y). [back_rewrite(1004),rewrite([7104(4)]),flip(a)].

7240 (C * ((C * x) * y)) / (C * (C * (C * y))) = R(C' * x,C,y). [back_rewrite(5372),rewrite([7113(21)])].

7252 R(x,y * (C * z),C) = R(x,C',y * (z * C)). [back_rewrite(5727),rewrite([7141(10)])].

7258 R(R(x,C',y * (C * (C * z))),C',(C * y) * z) = R(x,C,(C * y) * z). [back_rewrite(6299),rewrite([7142(13)])].

7264 (C * (x * ((C * y) * z))) / (y * (C * (C * z))) = R(x,C',(C * y) * z). [back_rewrite(5306),rewrite([7142(17)])].

7272 R(R(x,C,y),C,y) = R(x,y,C). [back_rewrite(7179),rewrite([7215(7)])].

7294 R(x,C,C * (x' * y)) = R(x',C,y)'. [back_rewrite(1652),rewrite([7236(11)])].

7297 R(x,C,C * y) = R(x,C,y). [back_rewrite(7201),rewrite([7236(6)])].

7298 R(x,C,R(y * C,z,C)) = R(x,C,R(y,z,C)). [back_rewrite(7008),rewrite([7236(6)]),flip(a)].

7303 R(x,C,y * C') = R(x,y,C'). [back_rewrite(2819),rewrite([7236(10),6028(8)]),flip(a)].

7304 R(x,C,y) = R(x,y,C'). [back_rewrite(2453),rewrite([7236(7),7303(5)]),flip(a)].

7306 R((C' * (C' * x)) / y,C,y) = x / (C * (C * y)). [back_rewrite(1832),rewrite([7236(11)])].

7311 R(x / y,C,y) = (C * (C * x)) / (y * (C * C)). [back_rewrite(1493),rewrite([7236(5)])].

7316 R(x,C,C' * y) = R(x,C,y). [back_rewrite(1258),rewrite([7236(7)])].

7317 (C * (C * (x * y))) / (C * (y * C)) = R(x,C,y). [back_rewrite(1164),rewrite([7236(14)])].

7319 R(x,C,(C' * y) * z) = R(x,C,y * (C * z)). [back_rewrite(7203),rewrite([7252(11),7202(12),7297(8)])].

7321 R(x,C',y * (C * (C * z))) = R(x,C',(C * y) * z). [back_rewrite(7144),rewrite([7252(7),16(6,R)])].

7323 (C * (C * (x * (y * x)))) / (C * (y * (C * x))) = R(x,C',y * (x * C)). [back_rewrite(3720),rewrite([7252(17)])].

7340 R(x,C,x' * y) = R(x',C,y)'. [back_rewrite(7294),rewrite([7297(6)])].

7344 R(R(x,C',(C * y) * z),C',(C * y) * z) = R(x,C,y * (C' * z)). [back_rewrite(7208),rewrite([7297(20)])].

7368 (x * (C * (y * y))) / (y * (C * (y * C))) = R(C' * x,y,C). [back_rewrite(4397),rewrite([7297(18),7215(16)])].

7414 R(x,C,(C * y) * z) = R(x,C,y * (C' * z)). [back_rewrite(7258),rewrite([7321(8),7344(12)]),flip(a)].

7440 C * (R(x,C,y) * y) = x * (y * C). [para(7114(a,1),66(a,1,1)),rewrite([16(8,R)]),flip(a)].

7442 R(x / (C * y),y,C) = C' * (x / y). [para(1405(a,1),7114(a,1,1)),rewrite([105(8)])].

7443 C * (x * R(y,C,x)) = (x * C) * y. [para(7114(a,1),3007(a,1,2)),flip(a)].

7444 R(x / (y * C),y,C) = C' * (x / y). [para(1808(a,1),7114(a,1,1))].

7447 (x * C) / (C * (C * y)) = C' * (x / y). [back_rewrite(7160),rewrite([7442(5)]),flip(a)].

7448 (C * x) / (C * (y * C)) = C' * (x / y). [back_rewrite(7115),rewrite([7442(5)]),flip(a)].

7452 (C * x) / (C * (C * y)) = C' * (x / y). [back_rewrite(7102),rewrite([7444(5)]),flip(a)].

7456 (C * x) / (y * (C * C)) = C' * (x / y). [back_rewrite(4433),rewrite([7447(14)])].

7458 C * R(C' * x,C,y) = R(x,C,y). [back_rewrite(7317),rewrite([7448(10),5661(7),1427(5)])].

7465 C' * R(x,C,y) = R(C' * x,C,y). [back_rewrite(7240),rewrite([7452(12),1427(8),10(7)])].

7467 R((C' * x) / y,C,y) = C' * (x / y). [back_rewrite(7217),rewrite([7452(13)])].

7482 R(R(C,x,y),C,x * y) = R(C,C * x,y * C). [back_rewrite(1569),rewrite([7452(13),5661(10),4368(8),7458(10)])].

7483 R(x / y,C,y) = C * (x / (C * y)). [back_rewrite(7311),rewrite([7456(12),5661(9)])].

7487 (C * (x * y)) / y = C * R(x,C,y). [back_rewrite(4930),rewrite([7458(12)])].

7490 x / (C * (C * y)) = C' * ((C' * x) / y). [back_rewrite(7306),rewrite([7467(9)]),flip(a)].

7531 x / (y * (C * (y * C))) = C' * ((C' * x) / (y * y)). [back_rewrite(4111),rewrite([7490(6)]),flip(a)].

7538 x / (y * (C * C)) = C' * ((C' * x) / y). [back_rewrite(1831),rewrite([7490(5)]),flip(a)].

7561 C' * R(x,y,C) = R(C' * x,y,C). [back_rewrite(7368),rewrite([7531(10),5882(9),7487(11),7215(9),6986(9),16(7,R),35(7)])].

7571 (C * x) / (C * y) = C * ((C' * x) / y). [back_rewrite(4857),rewrite([7538(7),35(10)]),flip(a)].

7597 C * ((x * (y * x)) / (y * (C * x))) = R(x,C',y * (x * C)). [back_rewrite(7323),rewrite([7571(12),10(8)])].

7616 (x * C) / (C * ((C * y) * z)) = C * ((C' * x) / ((y * C) * z)). [back_rewrite(5558),rewrite([7571(8)]),flip(a)].

7618 C * ((C' * (x * ((C * y) * z))) / ((y * C) * z)) = R(x,(y * C) * z,C). [back_rewrite(5500),rewrite([7571(12)])].

7619 C * ((C * ((x * y) * (C' * z))) / ((C * y) * z)) = R(x,y,C * (C * z)). [back_rewrite(5400),rewrite([7571(12),5435(8)])].

7683 C * ((C' * (x * y)) / y) = R(x,y,C). [back_rewrite(86),rewrite([7571(6)])].

7700 (C * x) / (y * (C * (C * z))) = C * ((C' * x) / ((y * C) * z)). [back_rewrite(5374),rewrite([7616(16)])].

7713 R(x,(y * C) * z,C) = R(x,C',(C * y) * z). [back_rewrite(7264),rewrite([7700(12),7618(13)])].

7724 R(x,C,(y * C) * z) = R(x,C,y * (C' * z)). [back_rewrite(7209),rewrite([7713(11),7344(12)]),flip(a)].

7740 R(x',C',x * y) = R(x,y,C)'. [para(7068(a,2),142(a,1))].

7760 R(x,C',y * C') = R(x,y,C). [para(7068(a,2),3150(a,2)),rewrite([7074(5)]),flip(a)].

7761 R(R(x,C',y),C,y) = x. [para(7068(a,2),7093(a,1,1))].

7762 R(R(x,C,y),C',y) = x. [para(7068(a,2),7114(a,1))].

7769 R(R(x,y,C),C',y) = R(x,y,C'). [back_rewrite(6293),rewrite([7760(6)])].

7779 R(x / (y * C),y,C') = (C' * x) / y. [para(1405(a,1),7071(a,1,1)),rewrite([105(8)])].

7781 R(x,C,y)' = R(x,y,C')'. [para(7304(a,1),142(a,2,1)),rewrite([142(4)])].

7792 R(x,y,C') * (y * C) = (x * C) * y. [para(7304(a,1),1348(a,1,1))].

7794 R((x * C) / y,C,y) = x / (y * C'). [para(7304(a,2),1405(a,1)),rewrite([2361(3)])].

7809 R(C' * x,C,y) * y = x * (C' * y). [para(7762(a,1),66(a,1,1)),rewrite([2369(9,R),7465(9)]),flip(a)].

7815 R((x * C) / y,y,C) = C * (x / y). [para(6985(a,1),703(a,2,1)),rewrite([7444(10),1139(10),112(7),16(8,R)])].

7882 R(C' * x',x,y * C) = C' * R(x,y,C)'. [para(6975(a,1),703(a,2,1)),rewrite([2331(3),2361(10),7021(12)])].

7888 x / (y * (x * C)) = C' * R(y,x,C)'. [back_rewrite(2357),rewrite([7882(7)]),flip(a)].

8069 R(C' * x,C,y)' = C * R(x,y,C')'. [para(7781(a,1),2418(a,2,1)),rewrite([2369(5,R),7465(5),16(12,R)])].

8107 (x * C) / (y * x) = C * R(y,x,C')'. [back_rewrite(4352),rewrite([8069(10)])].

8178 (x * (C * y)) / y = R(x * C,y,C). [para(16(a,2),7078(a,1,1,2))].

8191 C * R(x,C,y) = R(x * C,C,y). [para(66(a,1),7078(a,1,1)),rewrite([16(3,R),7487(4),16(8,R),6986(8),7176(10)])].

8217 R(x * C,x * y,C) = R(C * x,x,y). [back_rewrite(456),rewrite([8178(6)])].

8220 (C * (x * y)) / y = R(x * C,C,y). [back_rewrite(7487),rewrite([8191(8)])].

8242 R(x,C,y) * R(x * C,C,y) = C * (R(x,C,y) * R(x,C,y)). [para(8191(a,1),57(a,2,2)),flip(a)].

8249 R(x * C,C,y)' = C' * R(x,C,y)'. [para(8191(a,1),413(a,2,1)),rewrite([881(10),105(5)]),flip(a)].

8277 C * R(x,y,C') = R(x * C,C,y). [para(7304(a,1),8191(a,1,2))].

8304 R(x,C,R(y,C,z) * z) * (y * (z * C)) = (x * C) * (R(y,C,z) * z). [para(7440(a,1),66(a,1,2))].

8309 C * (R(x,y,C) * y) = (x * C) * y. [para(1348(a,1),7440(a,2)),rewrite([7272(5)])].

8311 C * ((x / (C * y)) * y) = C * (y' * (C' * (y * x))). [para(1405(a,1),7440(a,1,2,1)),rewrite([105(9),5191(13),6494(12)])].

8313 (R(x,C,y) * (x * (y * C))) / y = C * (R(x,C,y) * R(x,C,y)). [para(7440(a,1),40(a,1,1,2)),rewrite([8191(13),8242(14)])].

8333 R(x * C,C,y) * y = C * (x * y). [para(7440(a,1),110(a,1,2)),rewrite([16(6,R),35(6),7316(9),8191(7)]),flip(a)].

8338 R(x,C,R(y,C,z) * z) = R(x,C,y * (z * C)). [para(7440(a,1),7297(a,1,3)),flip(a)].

8346 R(x,C,y * (z * C)) * (y * (z * C)) = (x * C) * (R(y,C,z) * z). [back_rewrite(8304),rewrite([8338(5)])].

8376 C * ((C' * x) * (y / x)) = C * (x * (y / (C * x))). [para(1405(a,1),7443(a,1,2,2)),rewrite([105(11),6024(13)]),flip(a)].

8403 R(x,C,y * R(z,C,y)) = R(x,C,y * (C' * z)). [para(7443(a,1),7297(a,1,3)),rewrite([7724(5)]),flip(a)].

8443 (C * (x / y)) * y = R(x * C,y,C). [para(7483(a,1),66(a,1,1)),rewrite([99(8),8311(7),110(10),7084(5),16(7,R)]),flip(a)].

8457 C * (C * ((C' * x) / y)) = x / (y * C'). [para(1855(a,1),7483(a,1,1)),rewrite([7794(5),7571(10)]),flip(a)].

8557 R(C' * x',C',(C * x) * y) = C' * R(x,y,C)'. [para(555(a,2),7740(a,1,3)),rewrite([998(3),7021(15)])].

8558 R(C * x,y,C)' = C' * R(x,y,C)'. [para(893(a,1),7740(a,1,1)),rewrite([8557(10)]),flip(a)].

8656 R(R(x,y,C'),C,y) = R(x,y,C). [para(7769(a,1),7761(a,1,1))].

8721 (C * (C * x)) / y = C * (x / (C' * y)). [para(7815(a,1),68(a,2)),rewrite([105(4),5695(6),105(7),2849(9),105(6),10(7),7(3),16(4,R),105(8

)])].

8830 R(x' * C,C,x * y) = C * R(x,y,C')'. [para(142(a,1),8277(a,1,2)),flip(a)].

8889 C * (x' * (C' * (x * y))) = R(y,x,C). [para(1405(a,1),8309(a,1,2,1)),rewrite([4813(5),105(5),105(10),16(14,R),8443(15),16(13,R),35(13)]

)].

8957 R(C * x,C,y) * y = C * (x * y). [para(16(a,2),8333(a,1,1,1))].

8972 C * ((C * (x * (C' * y))) / (x * y)) = R(C,R(x * C,C,y),y). [para(8333(a,1),82(a,1,2)),rewrite([16(6,R),8191(6),16(4,R),8957(7),7571(9)

,5161(7)])].

9018 R(C * (x * y),y,C) = (C * x) * y. [para(6(a,1),8443(a,1,1,2)),rewrite([16(6,R)]),flip(a)].

9023 R(C,x / y,y) = R(x * C,y,C) / x. [para(8443(a,1),18(a,1,1)),rewrite([7(6)]),flip(a)].

9111 R(C,R(C * x,C,y),y) = R(C,R(x * C,C,y),y). [para(8957(a,1),82(a,1,2)),rewrite([16(6,R),8191(6),16(4,R),8957(7),7571(9),5435(7),8972(10)

]),flip(a)].

9160 R(C * (x' * (x / y)),x,C) = (C * (x * y)') * x. [para(2221(a,1),9018(a,1,1,2))].

9224 R(x,C,x / y) = R(x,y,C). [para(7(a,1),7171(a,1,1)),rewrite([6494(9),8889(11)])].

9227 R(x,C,y') = R(x,y,C). [para(10(a,1),7171(a,1,1)),rewrite([8889(11)])].

9229 R(C * (x * y),C,x) = (C * x) * y. [para(7171(a,2),12(a,2,2)),rewrite([12(8),110(8),8191(8),16(6,R)]),flip(a)].

9254 R((x * C) * y,C,x) = x * (y * C). [para(555(a,1),7171(a,1,1)),rewrite([7297(7),2849(12),105(9),109(13)])].

9265 x * (C * ((C' * x') * y)) = R(y,C,x). [para(1049(a,1),7171(a,1,1)),rewrite([7297(4),2849(14),105(6),109(15),16(9,R)]),flip(a)].

9266 x' * (C * ((C' * x) * y)) = R(y,C,x'). [para(1136(a,1),7171(a,1,1)),rewrite([7104(5),6024(15),109(16),16(10,R)]),flip(a)].

9279 R(C * (x * y),C,R(x,y,C)) = (x * C) * y. [para(1349(a,1),7171(a,1,1)),rewrite([10(15),8309(12)])].

9301 R((x * C') * y,C,x) = C' * (x * y). [para(2427(a,1),7171(a,1,1)),rewrite([7316(9),6768(14),35(15)])].

9354 R(x,C,R(y * z,C,y)) = R(x,C,y * (C' * z)). [para(7171(a,2),7297(a,1,3))].

9366 R(R(x * C,y,C),C,x / y) = y' * (C * (y * x)). [para(8443(a,1),7171(a,1,1)),rewrite([7297(9),2849(15),105(12),109(16),2837(11),16(11,R)]

)].

9376 R(C,C * x,(C' * x') * y) = R(y * C,C,x) / y. [back_rewrite(1580),rewrite([9265(9),8191(4)]),flip(a)].

9379 R(C,x' * C,(C' * x) * y) = R(y * C,C,x') / y. [back_rewrite(1582),rewrite([9266(9),8191(5)]),flip(a)].

9383 R(x,y / z,C) = R(x,C,z / y). [para(112(a,1),9227(a,1,3)),flip(a)].

9384 R(x,C,y')' = R(x,y,C)'. [para(9227(a,1),142(a,2,1)),rewrite([142(5)])].

9386 R(C * x,y,C) = R(x * C,C,y'). [para(9227(a,1),579(a,1))].

9394 R(x,C,(x' * y)') = R(x',y,C)'. [para(9227(a,2),141(a,1))].

9409 R(R(x,C,y'),C,y) = x. [para(9227(a,2),7093(a,1,1))].

9412 R(x,C',y) = R(x,C,y'). [para(9227(a,2),7068(a,2))].

9414 R(x,y',C') = R(x,y,C). [para(9227(a,1),7304(a,1)),flip(a)].

9423 R(x,y',C) = R(x,y,C'). [para(9227(a,2),7769(a,1,1)),rewrite([9412(6),7272(6)])].

9451 R(x,(y * C) * z,C) = R(x,C,((C * y) * z)'). [back_rewrite(7713),rewrite([9412(11)])].

9462 R(x,y * (C' * z),C) = R(x,C,((C * y) * z)'). [back_rewrite(6099),rewrite([9412(12)])].

9481 C * ((x * (y * x)) / (y * (C * x))) = R(x,C,(y * (x * C))'). [back_rewrite(7597),rewrite([9412(14)])].

9489 R(x,(C' * y) * z,C) = R(x,C,(y * (z * C))'). [back_rewrite(5878),rewrite([9412(12)])].

9819 R(x * y,C,x) = R(x * y,y,C). [para(6(a,1),9224(a,1,3))].

9821 R(x,y * x,C) = R(x,C,y'). [para(33(a,1),9224(a,1,3)),flip(a)].

9845 R(R(x,y,C),C,y / x) = x. [para(9224(a,1),7114(a,1,1)),rewrite([9383(5)])].

9931 R(R(x,C,y'),C,y / x) = x. [para(9227(a,2),9845(a,1,1))].

9963 R(R(x * y,C,((x * C) * y)'),C,R(C,x,y)) = x * y. [para(82(a,1),9931(a,1,3))].

10000 R(x,R(y,z,u),C) = R(x,C,R(y,z,u)'). [para(18(a,1),9383(a,1,2)),rewrite([138(8)])].

10001 R(x,R(y,z,u),C') = R(x,C,R(y,z,u)). [para(18(a,1),9383(a,2,3)),rewrite([138(4),9423(4)])].

10003 R(x,y * z,C) = R(x,C,(y * z)'). [para(401(a,1),9383(a,1,2)),rewrite([413(8)])].

10004 R(x,y * z,C') = R(x,C,y * z). [para(401(a,1),9383(a,2,3)),rewrite([413(4),9423(4)])].

10015 R(x,C,R(C' * y,C,z)) = R(x,C,R(y,z,C')). [para(1416(a,1),9383(a,2,3)),rewrite([8107(4),10003(8),893(8),31(8),7316(8)]),flip(a)].

10030 R(x,C,(y * x)') = R(x,C,y'). [back_rewrite(9821),rewrite([10003(3)])].

10036 R(x,C,((C' * y) * z)') = R(x,C,(y * (z * C))'). [back_rewrite(9489),rewrite([10003(6)])].

10037 R(x,C,((C * y) * z)') = R(x,C,(y * (C' * z))'). [back_rewrite(9462),rewrite([10003(6)]),flip(a)].

10038 R(x,C,((y * C) * z)') = R(x,C,(y * (C' * z))'). [back_rewrite(9451),rewrite([10003(5),10037(12)])].

10065 R(x * C,C,(x * y)') = R(C * x,x,y). [back_rewrite(8217),rewrite([10003(5)])].

10071 R(R(C,x,y),C,(x * y)') = R(C,x * C,R(y,x,C)). [back_rewrite(7126),rewrite([10003(5)])].

10109 R(R(x * y,C,(x * (C' * y))'),C,R(C,x,y)) = x * y. [back_rewrite(9963),rewrite([10038(7)])].

10132 R((C' * x) * y,y,C) = C' * (x * y). [para(2427(a,1),9819(a,1,1)),rewrite([7316(9),9301(6)]),flip(a)].

10161 R(R(x * y,C,x),C,y) = x * y. [para(9819(a,2),7093(a,1,1))].

10170 x' * (C * (x * y)) = R(y * C,C,x). [para(8443(a,1),9819(a,1,1)),rewrite([7297(9),9366(7),8443(9),7176(11)])].

10187 x' * R(y * C,C,x) = (C * x') * y. [back_rewrite(4177),rewrite([10170(6)])].

10189 R(C * (x * y),C,y) = x * (y * C). [back_rewrite(3540),rewrite([10170(6),16(3,R)])].

10201 R(x',C,y / x)' = R(x,C,x * y). [para(2221(a,1),10030(a,1,3,1)),rewrite([9394(6),9383(4),31(9)])].

10207 R(x,C,(y * (C * x))') = R(x,C,y'). [para(60(a,1),10030(a,1,3,1)),rewrite([893(7),7316(9),893(12),893(12),7316(15),7316(12)])].

10223 R(R(x,C,y'),C,y * x) = x. [para(10030(a,1),7114(a,1,1)),rewrite([9423(7),10004(7)])].

10233 R(x,C,R(y,C,x)') = R(x,C,y'). [para(8333(a,1),10030(a,1,3,1)),rewrite([893(5),7316(7),10030(4),8249(9),7316(11)]),flip(a)].

10299 R(R(x,y,C),C,R(y,x,C)) = x. [para(8443(a,1),10223(a,1,3)),rewrite([893(5),112(5),7316(6),9224(3),7298(8)])].

10301 R(x,C,y * (C' * x)) = R(x,C,y). [para(9409(a,1),10223(a,1,1)),rewrite([31(4),8403(5),31(9)])].

10389 R(x,C,R(y,C,x')) = R(x,C,y). [para(7114(a,1),10299(a,1,1)),rewrite([10000(5),10233(6)])].

10396 R(R(x,y,C),C,R(y,C,x')) = x. [para(9227(a,2),10299(a,1,3))].

10412 R((x * C) * y,C,y) = C * (x * y). [para(1349(a,1),10161(a,1,1,1)),rewrite([9279(7),7297(7),1349(10)])].

10473 R(x',C,R(y,C,x)) = R(x',C,y). [para(31(a,1),10389(a,1,3,3))].

10482 R(x' * C,x,R(y,C,x'))' = R(C' * x,C,y). [para(10389(a,1),703(a,1)),rewrite([105(2),1062(7),105(11),1139(13),7104(13)]),flip(a)].

10483 R(x' * C,x,R(y,C,x')) = C * R(x,y,C')'. [para(10389(a,1),703(a,2,1)),rewrite([1062(2),105(6),1139(8),7104(8),105(9),8069(13)])].

10495 R(x,C,R(y,x,C')) = R(x,C,y). [para(7093(a,1),10389(a,1,3)),rewrite([9423(6)]),flip(a)].

10497 R(x,C,R(y,x,C)) = R(x,C,y). [para(7304(a,1),10389(a,1,3)),rewrite([9414(5)])].

10505 R(x,C,R(y,C,x)) = R(x,C,y). [para(9409(a,1),10389(a,1,3)),rewrite([31(6)]),flip(a)].

10512 C' * R(x,y,C') = R(C' * x,C,y). [back_rewrite(10482),rewrite([10483(7),893(7),31(7)])].

10524 R(R(x,C,y),C,R(y,x,C)') = x. [para(10497(a,1),7114(a,1,1)),rewrite([10000(6)])].

10529 R(x,C,y * x) = R(x,C,y). [para(9018(a,1),10497(a,1,3)),rewrite([7414(5),10301(6),7297(7)]),flip(a)].

10532 R(x,C,y / x) = R(x,C,y). [para(7(a,1),10529(a,1,3)),flip(a)].

10544 R((C' * x) * y,C,x') = R((C' * x) * y,C,y). [para(1136(a,1),10529(a,1,3)),rewrite([7104(15)]),flip(a)].

10561 R(C * x,C,y * x) = R(C * x,C,y). [para(99(a,1),10529(a,1,3)),rewrite([7297(9),7297(7),7297(11)])].

10588 R(x * y,C,x * (C' * y)) = R(x * y,C,R(C,x,y)). [para(82(a,1),10532(a,1,3)),rewrite([7724(11)]),flip(a)].

10685 R(R(x,y,C),C,R(y,C,x)) = x. [para(7093(a,1),10505(a,2)),rewrite([10497(7)])].

10693 R(x,C,x * (C' * y)) = R(x,C,x * y). [para(7171(a,1),10505(a,1,3)),rewrite([7297(8)])].

10698 R(x / y,C,R(y,C,x')) = R(x / y,C,y). [para(9931(a,1),10505(a,1,3)),flip(a)].

10707 R(R(x * y,C,x),C,R(y,C,x)) = x * y. [para(10161(a,1),10505(a,2)),rewrite([9354(9),10301(10)])].

10833 R(R(x,C,y),C,R(y,x,C)) = R(x,y,C). [para(10685(a,1),10505(a,1,3)),rewrite([7272(4)]),flip(a)].

10837 R(R(x',y,C),C,R(y,C,x)) = x'. [para(31(a,1),10396(a,1,3,3))].

11050 R((C * x) * y,x,C) = C * (x * y). [para(9229(a,1),7114(a,1,1))].

11055 (C * x) * R(y,C,x) = x * (y * C). [para(7443(a,1),9229(a,1,1)),rewrite([9254(5)]),flip(a)].

11061 ((C * x) * y) * x = C * ((x * y) * x). [para(9229(a,1),8957(a,1,1))].

11063 R(x * y,x,C) = C * ((C' * x) * y). [para(7171(a,2),9229(a,1,1)),rewrite([7272(5),2849(9),105(6)])].

11064 R(C * (x' * y),x,C) = (C * x') * y. [para(9229(a,1),9227(a,1)),flip(a)].

11077 C * (x * ((C' * x') * ((x * (C * y)) * x))) = C * ((x * y) * x). [back_rewrite(6783),rewrite([11061(16)])].

11079 (C * (x * y)') * x = (C * x') * (x / y). [back_rewrite(9160),rewrite([11064(7)]),flip(a)].

11133 x * (C * (x' * y)) = R(C * y,C,x'). [para(35(a,1),10189(a,1,1,2)),rewrite([10561(6),16(9,R)]),flip(a)].

11177 R(C * (x * y),y,C') = x * (y * C). [para(10189(a,1),7304(a,1)),flip(a)].

11333 R(R(R(x,C,y)',y,C),C,R(y,C,x)) = R(x,C,y)'. [para(10505(a,1),10837(a,1,3))].

11397 C * (x * ((C' * x') * y)) = R(y,x,C). [para(35(a,1),11050(a,1,1)),rewrite([893(6)]),flip(a)].

11431 R(x * (y * C),x,C) = (x * C) * y. [para(7443(a,1),11050(a,2)),rewrite([11055(5)])].

11447 R((x * (C * y)) * x,x,C) = C * ((x * y) * x). [back_rewrite(11077),rewrite([11397(12)])].

11516 R(x * (C * y),x,C) = (x * C) * y. [para(16(a,2),11431(a,1,1,2))].

11524 (C * (x / (C * y))) * y = R(x,C,y). [para(1849(a,1),11431(a,1,1)),rewrite([9383(5),10532(5),7297(4),16(7,R)]),flip(a)].

11530 R((x * C) * y,x,C') = x * (y * C). [para(11431(a,1),7071(a,1,1))].

11539 R(x,C,x * (y * C)) = R(x,C,x * y). [para(11431(a,1),10497(a,1,3)),rewrite([7724(5),10693(6)]),flip(a)].

11625 (C' * (x * y)) / y = R(C' * x,y,C). [para(7683(a,1),10(a,1,2)),rewrite([7561(5)]),flip(a)].

11656 R(x,C,(y * (x * C))') = R(x,C,y'). [para(62(a,2),7683(a,1,2,1,2)),rewrite([10(8),9481(8),10003(11),10207(12)])].

11665 (R(x,y,C) * y) / (C' * (x * y)) = R(C,R(C' * x,y,C),y). [para(7683(a,1),68(a,1,1,1)),rewrite([11625(14)])].

11673 x * R(y,C,x) = R(x * y,C,x). [para(2852(a,1),7683(a,1,2,1,2)),rewrite([5882(8),8376(8),7571(11),8457(13),4822(9),2361(6),16(5,R),11524

(6),10003(9),893(9),31(9),7316(9)])].

11682 R(x,y,C) * y = R(x * y,y,C). [para(7683(a,1),8443(a,1,1)),rewrite([16(9,R),35(9)])].

11748 R(x * y,y,C) / (C' * (x * y)) = R(C,R(C' * x,y,C),y). [back_rewrite(11665),rewrite([11682(3)])].

11865 ((x * C) * y) * x = C * ((x * y) * x). [para(11516(a,1),11682(a,1,1)),rewrite([11447(10)])].

11866 R(x,C,y) * y = R(x * y,C,y). [para(11682(a,1),11682(a,2,1)),rewrite([7176(4),7176(8)])].

11907 R(x * (y * (z * C)),C,y * (z * C)) = (x * C) * R(y * z,C,z). [back_rewrite(8346),rewrite([11866(9),11866(14)])].

11912 R(x,C,R(y * z,C,z)) = R(x,C,y * (z * C)). [back_rewrite(8338),rewrite([11866(4)])].

11940 R((C' * x) * y,C,y) = x * (C' * y). [back_rewrite(7809),rewrite([11866(6)])].

11945 R((C' * x) * y,C,x') = x * (C' * y). [back_rewrite(10544),rewrite([11940(13)])].

11954 (R(x,C,y) * R(x * y,C,y)) / y = R(x,C,y) * R(x,C,y). [para(11866(a,1),36(a,1,1,2))].

11964 (C * (x * y)) / R(x * y,C,y) = R(C,R(x,C,y),y). [para(11866(a,1),82(a,1,2)),rewrite([16(4,R),8191(4),11866(5),10412(5)])].

12002 R(x,y,C') * y = R(x * y,C,y). [para(7304(a,1),11866(a,1,1))].

12024 R(x,C,y) * R(y,C,x) = x * y. [para(10505(a,1),11866(a,1,1)),rewrite([11673(8),10707(12)])].

12046 (x * y) / R(y,C,x) = R(x,C,y). [para(12024(a,1),6(a,1,1))].

12114 R(x * y,C,y) = x * R(y,x,C). [para(7093(a,1),12024(a,1,2)),rewrite([10497(4),11866(3)])].

12120 R(x,y,C) * R(y,C,x) = R(x * y,C,y). [para(8656(a,1),12024(a,1,1)),rewrite([10495(7),12002(9)])].

12138 (x / y) * R(y,C,x') = R(x,C,y). [para(9931(a,1),12024(a,1,2)),rewrite([10698(6),11866(4),7(2)]),flip(a)].

12212 x / (y * (C' * x)) = C * R(y,C,x)'. [para(1136(a,1),12046(a,1,1)),rewrite([7104(9),11945(7),7319(14),8830(13),10004(11),7297(10)])].

12254 R(x * y,y,C) / R(y,C,x) = x. [para(7093(a,1),12046(a,2)),rewrite([11682(3),10497(7)])].

12289 R(x * y,C,y) / R(y,x,C) = x. [para(10685(a,1),12046(a,2)),rewrite([12120(5),10833(9)])].

12351 R(C,R(x,C,y),y) = R(C,x,R(y,x,C)). [para(12114(a,2),82(a,1,2)),rewrite([3007(5),11964(7)])].

12425 x * R(y,x,C) = R(x * y,C,x'). [para(12114(a,1),10532(a,2)),rewrite([33(4)]),flip(a)].

12440 (x * C) * R(x * y,C,y) = x * ((x * C) * y). [para(11431(a,1),12114(a,2,2)),rewrite([11907(9)])].

12609 R(x,y,C) / R(y,C,x) = x / y. [para(7(a,1),12254(a,1,1,1)),rewrite([10532(5)])].

12614 R(x,C,y) / R(y' * x,C,y) = y. [para(35(a,1),12254(a,1,1,1)),rewrite([10003(4),10030(5),31(3)])].

12737 R(x * y,y,C') / R(y,x,C) = x. [para(7304(a,1),12289(a,1,1))].

12790 (x / y) * R(y,C,x) = R(x,y,C). [para(12609(a,1),7(a,1,1))].

12798 R((x * C) * y,C,(x * y)') / R(x * y,C,R(C,x,y)) = R(C,x,y). [para(82(a,1),12609(a,2)),rewrite([10003(6),7724(13),10588(14)])].

13040 x * (y' * R(y,C,x)) = R(x',y,C)'. [para(141(a,1),12790(a,2)),rewrite([2229(3),13(8),11673(6),35(4)])].

13411 x * (y' * R(y,C,x')) = R(x',C,y)'. [para(7171(a,1),12138(a,1,2)),rewrite([2229(3),13(11),11133(9),35(6),7340(10)])].

13772 x * R(y,C,x') = R(x * y,C,x'). [para(9227(a,2),12425(a,1,2))].

14189 R(C,R(x,y,C'),y * C) = R(C,x * C,y). [para(7792(a,1),82(a,1,2)),rewrite([16(5,R),8277(5),1348(7),16(4,R),13(5),80(9)]),flip(a)].

14413 (x * (y * C)) * x = (x * y) * (x * C). [para(11530(a,1),12002(a,1,1)),rewrite([11865(8),10189(10)])].

14649 R(C,R(x * C,C,y),y) = R(C,C * x,R(y,C,x')). [para(579(a,1),12351(a,1,2)),rewrite([10003(13),893(13),7316(15)])].

14673 R(C,R(x,C,y),C' * y) = R(C,x,R(C' * y,x,C)). [para(7316(a,1),12351(a,1,2))].

14681 R(C,R(x,C,y),y) = R(C,x,R(y,C,x')). [para(9227(a,2),12351(a,2,3))].

14703 R(C,R(x,y,C),y) = R(C,x,R(y,C,x)). [para(10685(a,1),12351(a,1,2)),rewrite([10000(13),10524(14)]),flip(a)].

14729 x' * R(y,C,x) = R(x' * y,C,x). [para(31(a,1),13772(a,1,2,3)),rewrite([31(9)])].

14785 R(x' * (y * C),C,x) = (C * x') * y. [back_rewrite(10187),rewrite([14729(6)])].

14910 (C * x') * (x / y) = x' * ((C * x) / y). [para(16(a,2),4813(a,2,2,1)),rewrite([1062(3),16(4,R),11079(5)])].

14944 C' * (x / (C' * y)) = C * ((C' * x) / y). [para(4813(a,1),928(a,2)),rewrite([12(6),7490(7),35(10),188(10),12(15),8721(16),12(18),10(17

)]),flip(a)].

14954 x' * ((x * ((x * C) * y)) / y) = R(C,x,y) * x. [para(82(a,1),4813(a,1,1)),flip(a)].

14971 C * ((C' * x) / y) = C * ((x * C') / y). [para(2369(a,1),4813(a,2,2,1)),rewrite([2369(7,R),14944(7),31(9)])].

15120 (C * (x * y)') * x = x' * ((C * x) / y). [back_rewrite(11079),rewrite([14910(10)])].

15249 R(x,C,y) * R(x * y,C,y) = C * (R(x,C,y) * (x * (C' * y))). [para(11866(a,1),6611(a,2,2)),rewrite([7465(8),11866(9),11940(9)]),flip(a)]

.

15352 (C * x) / ((C * y) * z) = C' * (x / (y * (C' * z))). [para(110(a,1),7571(a,1,2)),rewrite([4814(17),2369(17,R),35(19)])].

15411 R(x,y,C * (C * z)) = R(x,y,C' * z). [back_rewrite(7619),rewrite([15352(12),18(13),35(9)]),flip(a)].

15412 C * (C * (x / (y * (C * (C * z))))) = C' * (x / (y * (C' * z))). [back_rewrite(5685),rewrite([15352(16)])].

15436 R(x,y,C * (z * (C * C))) = R(x,y,z). [back_rewrite(3514),rewrite([15411(7),10(5)]),flip(a)].

15445 R(x,y,C' * (C' * z)) = R(x,y,C * z). [para(7(a,1),15436(a,1,3,2)),rewrite([977(7)]),flip(a)].

15499 R(C,R(x,C,y),y) = R(C,x,R(C * (C * (y * C)),x,C)). [para(12351(a,2),15436(a,2)),rewrite([928(8,R),6986(7),6986(8),16(6,R),6986(9),16(7

,R)]),flip(a)].

15527 (C' * (x * (x * (y * C)))) / y = R(x * x,y,C'). [para(36(a,1),7779(a,1,1)),flip(a)].

15642 R(x,C,R(C * y,z,C)) = R(x,C,R(y,z,C)). [para(8558(a,1),9423(a,1,2)),rewrite([10003(8),1139(8),31(5),16(5,R),6986(5),7298(6),10001(11)]

),flip(a)].

15733 x * (C * (C * (x' * y))) = R(C * (y * C),C,x). [para(9265(a,1),98(a,2,2,2)),rewrite([16(11,R),109(11),2849(7),1062(2),98(6),8191(12),8

191(13),16(11,R)])].

15877 R(x,C,(x * (y * C))') = R(x,C' * x,y). [para(7(a,1),10065(a,1,1)),rewrite([105(3),10036(7),105(9),35(11),105(8)])].

16542 x * (x * (y' * R(y,x,C))) = R(x' * x',y,C)'. [para(13040(a,1),12(a,1)),rewrite([188(2),7215(10)]),flip(a)].

16613 x * (y' * R(y,x,C')) = R(x',y,C)'. [para(7304(a,1),13040(a,1,2,2))].

16806 R(x,y,C' * ((C' * z) * u)) = R(x,y,z * (u * C)). [para(109(a,1),15411(a,1,3)),flip(a)].

16807 R(x,y,C * ((C * z) * u)) = R(x,y,z * (C' * u)). [para(110(a,1),15411(a,1,3,2)),rewrite([10(15)])].

16823 R(C,R(x,C,y),C' * y) = R(C,x,R(C * (C * y),x,C)). [para(15411(a,1),12351(a,1,2)),rewrite([7316(6),15411(8)])].

17162 R(C,R(C * (x * C),C,y),y) = R(C,C * (x * C),R(y,C,x')). [para(2015(a,2),12351(a,2,3)),rewrite([10003(19),893(19),893(19),15445(22),729

7(18)])].

17280 R(C,R(x * C,C,y),y) = R(C',x,C' * y)'. [para(2846(a,2),2461(a,1,1)),rewrite([5294(13),2466(11),7571(9),5435(7),8972(10),15411(13)])].

17293 R(C,R(C' * x,y,C),y) = R(C',R(x,y,C),y)'. [para(11682(a,1),2461(a,1,1)),rewrite([2369(8,R),7561(8),11682(9),10132(9),11748(8)])].

17326 R(C,C * x,R(y,C,x')) = R(C',x,C' * y)'. [back_rewrite(14649),rewrite([17280(6)]),flip(a)].

17327 R(C,R(C * x,C,y),y) = R(C',x,C' * y)'. [back_rewrite(9111),rewrite([17280(12)])].

17329 R(x * y,y,C) / (C' * (x * y)) = R(C',R(x,y,C),y)'. [back_rewrite(11748),rewrite([17293(15)])].

17336 R(C,C * (x * C),R(y,C,x')) = R(C,x,C' * y). [back_rewrite(17162),rewrite([17327(8),706(8),31(7)]),flip(a)].

17387 C' * (x * (x * (y * C))) = C * (x * (C' * (x * y))). [para(438(a,1),5435(a,1,2))].

17396 (C * (x * (C' * (x * y)))) / y = R(x * x,y,C'). [back_rewrite(15527),rewrite([17387(7)])].

17523 (C * ((C' * x) * y)) * x' = C * (x * (y / (C * x))). [para(6024(a,1),2852(a,1,1)),rewrite([998(10),35(12),4823(17),35(19),6024(15),837

6(15)])].

17939 R(x,C,y') / y = R(x / y,y,C). [para(9266(a,1),2140(a,1,1)),rewrite([31(5),17523(13),10170(12),16(9,R),6292(11)])].

18620 R(x' * x',C,y)' = x * R(x',y,C)'. [para(13411(a,1),12(a,1)),rewrite([188(2),188(10),7215(12),9423(10),16613(12)])].

18666 x * (y' * R(y,x,C)) = R(x',C,y)'. [para(7304(a,1),13411(a,1,2,2)),rewrite([9414(5)])].

18707 R(x' * R(x,C,y),C,y) / R(R(y,C,x)',C,y) = y. [para(13411(a,1),12614(a,1,2,1)),rewrite([31(4),31(8)])].

18715 R(x' * R(x,C,y),C,y) = y * R(y,C,x)'. [para(13411(a,1),9265(a,1,2,2)),rewrite([1139(6),31(3),8249(6),35(8),1139(11),31(8),7104(9)]),fl

ip(a)].

18734 R(x' * x',y,C)' = x * R(x',C,y)'. [back_rewrite(16542),rewrite([18666(5)]),flip(a)].

18735 R(x,C,R(x,C,y)') = x. [back_rewrite(18707),rewrite([18715(6),12046(10)])].

18761 R(x,C,R(x,C,y)) = x. [para(18735(a,1),7114(a,1,1)),rewrite([9423(5),10001(5)])].

18765 R(x * y,C,(x * (C' * y))') = x * y. [para(7171(a,1),18735(a,1,3,1)),rewrite([893(9),6081(10),7297(9),10037(7)])].

18780 R(R(x,C,y),C,x) = R(x,C,y). [para(18735(a,1),12138(a,1,2)),rewrite([7(4)]),flip(a)].

18801 R(x * y,C,R(C,x,y)) = x * y. [back_rewrite(10109),rewrite([18765(8)])].

18805 R(R(C,x,y),C,(x * y)') = R(C,x,y). [back_rewrite(12798),rewrite([18801(12),17939(9),82(5),10003(5)])].

18807 R(C,x * C,R(y,x,C)) = R(C,x,y). [back_rewrite(10071),rewrite([18805(6)]),flip(a)].

18819 R(x,C,R(x,y,C)) = x. [para(7215(a,1),18761(a,1,3))].

18899 R(R(x * C,C,y),C,x) = R(C * x,C,y). [para(579(a,1),18780(a,1,1)),rewrite([7297(8)])].

18913 R(R(C * x,y,C),C,x) = R(x * C,C,y'). [para(9386(a,2),18780(a,1,1)),rewrite([7104(8)])].

19092 R(C,C * x,y * C) = R(C,x,y). [para(18801(a,1),10685(a,1,3)),rewrite([10003(5),18805(6),7482(5)])].

19134 R(C,C * x,y) = R(C,x,C' * y). [para(7(a,1),19092(a,1,3)),rewrite([105(7)])].

19136 R(C,x,y * C) = R(C',x,y)'. [para(35(a,1),19092(a,1,2)),rewrite([141(9)])].

19137 R(C,x,C * y) = R(C',x,y)'. [para(555(a,2),19092(a,1,3)),rewrite([16(7,R),15411(8),19134(7),15445(8),19136(8)])].

19138 R(C,x * C,y) = R(C,x,C' * y). [para(1086(a,1),19092(a,1,2)),rewrite([19136(8),899(7),19134(4),31(7)]),flip(a)].

19159 R(C,x,R(C' * (C' * y),C,x')) = R(C,x,C' * y). [back_rewrite(17336),rewrite([19134(9),7465(9),19138(10),7465(10)])].

19160 R(C,x,R(C' * y,C,x')) = R(C',x,C' * y)'. [back_rewrite(17326),rewrite([19134(7),7465(7)])].

19167 R(C,x,x' * (y * C)) = R(y * C,C,x) / y. [back_rewrite(9376),rewrite([19134(9),16806(10)])].

19178 R(C',R(x,y,C'),y)' = R(C,x,C' * y). [back_rewrite(14189),rewrite([19136(7),19138(11)])].

19207 R(C,x,R(C' * y,x,C)) = R(C,x,y). [back_rewrite(18807),rewrite([19138(6),7561(6)])].

19210 R(C,x',x * (y * C)) = R(y * C,C,x') / y. [back_rewrite(9379),rewrite([19138(9),16806(10)])].

19214 R(C',x,C * y)' = R(C,x,C' * y). [back_rewrite(19159),rewrite([19160(11),15445(9)])].

19217 R(C,R(x,C,y),C' * y) = R(C,x,y). [back_rewrite(14673),rewrite([19207(14)])].

19226 R(C,x,R(C * (C * y),x,C)) = R(C,x,y). [back_rewrite(16823),rewrite([19217(7)]),flip(a)].

19227 R(C,R(x,C,y),y) = R(C',x,y)'. [back_rewrite(15499),rewrite([19226(14),19136(8)])].

19237 R(C,x,R(y,C,x')) = R(C',x,y)'. [back_rewrite(14681),rewrite([19227(4)]),flip(a)].

19314 R(C',x,(y * C) * z)' = R(C,x,y * (C' * z)). [para(2916(a,2),19137(a,1,3)),rewrite([16807(7)]),flip(a)].

19320 R(C,x,R(y * z,y,C)) = R(C',x,(C' * y) * z)'. [para(11063(a,2),19137(a,1,3))].

19325 R(C,x',x * (C' * y)) = R(C,x',x * y). [back_rewrite(2946),rewrite([19314(8)])].

19352 R(C',R(x,y,C),y)' = R(C,x,y). [para(7093(a,1),19227(a,1,2)),flip(a)].

19354 R(C,R(x,y,C),y) = R(C,x,C' * y). [para(8656(a,1),19227(a,1,2)),rewrite([19178(11)])].

19394 R(x * y,y,C) / (C' * (x * y)) = R(C,x,y). [back_rewrite(17329),rewrite([19352(14)])].

19399 R(C,x,R(y,C,x)) = R(C,x,C' * y). [back_rewrite(14703),rewrite([19354(4)]),flip(a)].

19476 R(C,x,(C * x') * y) = R(C,x,C' * (x' * y)). [para(9229(a,1),19237(a,1,3)),rewrite([19214(14)])].

19598 R(C',x,(C' * x') * y)' = R(C,x,C' * (x' * y)). [para(14785(a,1),19399(a,1,3)),rewrite([19476(6),5829(15),19137(16)]),flip(a)].

19712 R(C',x,R(y * z,y,C))' = R(C,x,y * (z * C)). [para(11063(a,2),19214(a,1,1,3)),rewrite([16806(16)])].

19817 R(C,(C' * x) / y,y) = R(x,y,C) / (C' * x). [para(14971(a,1),68(a,1,1,1)),rewrite([8443(7),16(5,R),2466(5)]),flip(a)].

19922 R(x,C' * x,y) = R(x,C,(x * y)'). [para(15877(a,1),10030(a,2)),rewrite([14413(5),11656(7)]),flip(a)].

20164 R(R(C * x,y,C),x,C') = R(x * C,C,y'). [para(18913(a,1),7304(a,1)),flip(a)].

20769 R(x,C,y / (x * ((x * C) * y))) = R(x',C,R(C,x,y)')'. [para(4873(a,2),19922(a,2,3,1)),rewrite([19922(7),2280(6),7340(9),10529(8),112(14

)]),flip(a)].

20906 R(x,C,x * y) * (x * (y * C)) = x * ((x * C) * y). [para(12440(a,1),66(a,2)),rewrite([11912(5),11539(5),8191(8),16(6,R),10189(8)])].

21041 R(R(x * C,y,C),x,C') = R(x * C,C,y'). [para(16(a,1),20164(a,1,1,1))].

21047 R(R(C * x,y,C),x,C) = R(C * x,C,y'). [para(20164(a,1),8656(a,1,1)),rewrite([18899(7)]),flip(a)].

21051 R(R(x * C,y,C),x,C) = R(C * x,C,y'). [para(16(a,1),21047(a,1,1,1))].

21070 R(C * x,C,y') / x = R(C * x,y,C) / x. [para(21047(a,1),12609(a,1,1)),rewrite([15642(11),18819(9)])].

21227 R(C * (C * (x / y)),C,x) = C * ((C * x) / y). [para(2221(a,1),96(a,2,2,2,2)),rewrite([15120(6),35(7),15733(13),16(9,R)]),flip(a)].

21301 C * R(x,C,y)' = R(C * x',C,y). [para(138(a,1),21227(a,2,2)),rewrite([33(6),998(5),35(7)]),flip(a)].

21349 R(x,C,y')' = R(x',y,C). [para(7888(a,1),21227(a,2,2)),rewrite([16(6,R),15412(10),12212(7),21301(7),7465(8),10(6),7272(5),10003(10),893

(10),7316(12),35(12)]),flip(a)].

21473 R(x,C,y / (x * ((x * C) * y))) = R(x,C,R(C,x,y)'). [back_rewrite(20769),rewrite([21349(14),31(9),10000(11)])].

21810 R(x,y,C)' = R(x',y,C). [back_rewrite(9384),rewrite([21349(4)]),flip(a)].

22272 x * R(x',C,y)' = R(x * x,y,C). [back_rewrite(18734),rewrite([21810(6),188(4),31(2),31(2)]),flip(a)].

22279 R(x' * x',C,y)' = x * R(x,y,C). [back_rewrite(18620),rewrite([21810(10),31(8)])].

22534 R(R(x,C,y)',y,C) = x'. [para(7114(a,1),21810(a,1,1)),flip(a)].

22537 R(x,y,C')' = R(x',y,C'). [para(9423(a,1),21810(a,1,1)),rewrite([9423(8)])].

22615 R(x,C,y)' = R(x',C,y). [back_rewrite(11333),rewrite([22534(5),10473(5)]),flip(a)].

22910 R(x,C,x * y) = R(x,C,y). [back_rewrite(10201),rewrite([22615(5),31(2),10532(3)]),flip(a)].

23001 x * R(x,y,C) = R(x * x,C,y). [back_rewrite(22279),rewrite([22615(6),188(4),31(2),31(2)]),flip(a)].

23005 x * R(x,C,y) = R(x * x,y,C). [back_rewrite(22272),rewrite([22615(4),31(2)])].

23593 R(x,C,y) * (x * (y * C)) = x * ((x * C) * y). [back_rewrite(20906),rewrite([22910(3)])].

23696 C * (R(x,C,y) * R(x,C,y)) = (x * ((x * C) * y)) / y. [back_rewrite(8313),rewrite([23593(6)]),flip(a)].

23727 R(x,C,y) * R(x * C,C,y) = (x * ((x * C) * y)) / y. [back_rewrite(8242),rewrite([23696(14)])].

23845 C' * (R(x',C,y) * R(x',C,y)) = y / (x * ((x * C) * y)). [para(22615(a,1),797(a,2,2,1)),rewrite([16(6,R),8191(6),23727(7),112(6),22615(

13)]),flip(a)].

23994 R(x,C,R(x * x,y,C)) = x. [para(18761(a,1),22910(a,2)),rewrite([23005(4)])].

23995 R(x,C,R(x * x,C,y)) = x. [para(18819(a,1),22910(a,2)),rewrite([23001(4)])].

24047 R(x,C,R(x * x,y,C')) = x. [para(9423(a,1),23994(a,1,3))].

24343 R(x,C,R(x' * x',y,C')) = x. [para(24047(a,1),7114(a,1,1)),rewrite([10000(6),22537(6),188(3)])].

24468 x' * R(x * x,C,y) = R(x,y,C). [para(23001(a,1),10(a,1,2))].

25503 x' * R(C * (x * x),C,y) = R(x * C,y,C). [para(24468(a,1),1349(a,2,2)),rewrite([10000(6),22615(6),188(4),23995(8),8191(6),16(4,R),6986(

11)])].

26280 R(x,C,y) * (x * (C' * y)) = x * (C' * (x * y)). [para(15445(a,1),23593(a,1,1)),rewrite([7297(4),16(10,R),35(10),6024(16),6768(15),35(1

6)])].

26300 R(x,C,y) * R(x * y,C,y) = C * (x * (C' * (x * y))). [back_rewrite(15249),rewrite([26280(14)])].

26304 R(x,C,y) * R(x,C,y) = R(x * x,y,C'). [back_rewrite(11954),rewrite([26300(6),17396(8)]),flip(a)].

26308 x / (y * ((y * C) * x)) = R(C' * (y' * y'),C,x). [back_rewrite(23845),rewrite([26304(9),10512(9)]),flip(a)].

26312 (x * ((x * C) * y)) / y = R(C * (x * x),C,y). [back_rewrite(23696),rewrite([26304(6),8277(6),16(3,R)]),flip(a)].

26344 R(x,C,R(C,x,y)') = x. [back_rewrite(21473),rewrite([26308(6),10015(10),24343(8)]),flip(a)].

26384 R(x * C,y,C) = R(C,x,y) * x. [back_rewrite(14954),rewrite([26312(6),25503(7)])].

26411 R(x,C,R(C,x,y)) = x. [para(26344(a,1),7114(a,1,1)),rewrite([9423(5),10001(5)])].

26594 R(x * C,y,C) / x = R(C,x,y). [para(26384(a,2),6(a,1,1))].

26663 R(C * x,C,y') / x = R(C,x,y). [para(26384(a,2),12254(a,1,1,1)),rewrite([21051(6),26411(9)])].

26671 R(x * C,C,y') / x = R(C,x,y). [para(26384(a,2),12737(a,1,1,1)),rewrite([21041(7),10000(9),26344(10)])].

26706 R(C,x / y,y) = R(C,x,y). [back_rewrite(9023),rewrite([26594(8)])].

26707 R(C,x',x * y) = R(C,y,x). [back_rewrite(7085),rewrite([26594(9)])].

26711 R(C * x,y,C) / x = R(C,x,y). [back_rewrite(21070),rewrite([26663(6)]),flip(a)].

26714 R(C,x,C' * y) = R(C,x,y). [back_rewrite(19210),rewrite([26707(6),19138(4),26671(11)])].

26718 R(x,y,C) / (C' * x) = R(C',x,y)'. [back_rewrite(19817),rewrite([26706(6),141(5)]),flip(a)].

26723 R(C',x,y)' = R(C,x,y). [back_rewrite(19325),rewrite([26707(7),141(5),26707(8)])].

26812 R(C,x,(C' * x') * y) = R(C,x,x' * y). [back_rewrite(19598),rewrite([26723(9),26714(14)])].

26886 R(C,x * C,y) = R(C,x,y). [back_rewrite(19138),rewrite([26714(9)])].

26896 R(C,x * y,y) = R(C,x,y). [back_rewrite(19394),rewrite([26718(8),26723(5)])].

26970 R(C,x,(C' * y) * z) = R(C,x,y * (z * C)). [back_rewrite(19712),rewrite([26723(7),19320(5),26723(8)])].

27131 R(C,x,x' * (y * C)) = R(C,x,x' * y). [back_rewrite(26812),rewrite([26970(7)])].

27180 R(C,x,x' * y) = R(y * C,C,x) / y. [back_rewrite(19167),rewrite([27131(6)])].

27183 R(C,x,y * x) = R(C,x,y). [para(10(a,1),26896(a,1,2)),rewrite([26707(7)])].

27186 R(C,x,x' * y) = R(C,y,x'). [para(35(a,1),26896(a,1,2)),rewrite([27183(4)]),flip(a)].

27248 R(x * C,C,y) / x = R(C,x,y'). [back_rewrite(27180),rewrite([27186(4)]),flip(a)].

27557 R(C,x,y') = R(C,y,x). [para(141(a,1),26711(a,1,1)),rewrite([893(3),21810(7),1139(5),31(2),26594(5),893(6),26970(9),27186(8),26886(7)])

,flip(a)].

27623 R(C,x * y,y') = R(C,y,x). [para(27557(a,2),27183(a,1))].

27792 (x * (y * C)) / (x * y) = R(C,y,x). [para(27623(a,1),26711(a,2)),rewrite([9423(6),11177(6)])].

27896 R(R(C,x,y),x,y) = R(C,y,x). [para(27792(a,1),1405(a,2)),rewrite([7078(4),26594(5)])].

27922 R(R(C,B,A),A,B) != C. [back_rewrite(19),rewrite([27896(7)])].

27946 R(R(C,A,B'),A,B) != C. [para(27557(a,2),27922(a,1,1))].

28677 R(R(C,x,y'),x,y) = C. [para(50(a,1),1405(a,2)),rewrite([16(3,R),8220(4),27248(5)])].

28678 $F. [resolve(28677,a,27946,a)].

============================== end of proof ==========================

% Proof 1 at 1619.31 (+ 9.59) seconds.

% Length of proof is 1889.

% Level of proof is 111.

% Maximum clause weight is 36.000.

% Given clauses 26101.

1 R(R(R(C,A,B),A,B),A,B) = C # label(non_clause) # label(goal). [goal].

2 0 * x = x. [assumption].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 A * ((x * y) * A) = (A * x) * (y * A). [assumption].

15 (A * x) * (y * A) = A * ((x * y) * A). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 R(x,y,z) = ((x * y) * z) / (y * z). [assumption].

18 ((x * y) * z) / (y * z) = R(x,y,z). [copy(17),flip(a)].

19 R(R(R(C,A,B),A,B),A,B) != C. [deny(1)].

22 x / x = 0. [para(2(a,1),6(a,1,1))].

23 x / 0 = x. [para(3(a,1),6(a,1,1))].

26 0' = 0. [para(8(a,1),3(a,1)),flip(a)].

28 0 / x = x'. [para(8(a,1),6(a,1,1))].

30 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([28(3)])].

31 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

32 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

34 x * (x' * y) = y. [back_rewrite(4),rewrite([31(1)])].

35 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

39 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

40 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

45 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(12(a,1),13(a,1,1,2)),rewrite([12(7)])].

47 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [para(13(a,1),13(a,1,1,2)),rewrite([13(9)])].

49 (A * x) * A = A * (x * A). [para(2(a,1),15(a,1,2)),rewrite([3(7)])].

50 (A * ((x * y) * A)) / (y * A) = A * x. [para(15(a,1),6(a,1,1))].

51 A * ((x * (y / A)) * A) = (A * x) * y. [para(7(a,1),15(a,1,2)),flip(a)].

53 A * ((A' * x) * A) = x * A. [para(9(a,1),15(a,1,1)),rewrite([2(4)]),flip(a)].

54 (A * x)' * (A * ((x * y) * A)) = y * A. [para(15(a,1),10(a,1,2))].

56 (A * x) * (y * (y * A)) = A * ((x * (y * y)) * A). [para(12(a,1),15(a,1,2))].

57 ((x * A) * (A * ((y * x) * A))) * z = (x * A) * ((A * y) * ((x * A) * z)). [para(15(a,1),13(a,1,1,2))].

58 A * (((x * A) * y) * A) = A * (x * (A * (y * A))). [para(15(a,1),13(a,1))].

59 (A * x) * (y * (z * (y * A))) = A * ((x * (y * (z * y))) * A). [para(13(a,1),15(a,1,2))].

60 (x * C) / x = C. [para(16(a,1),6(a,1,1))].

62 C * (x / C) = x. [para(16(a,2),7(a,1))].

63 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

64 x' * (C * x) = C. [para(16(a,2),10(a,1,2))].

65 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

66 C * (x * x) = x * (x * C). [para(16(a,2),12(a,1))].

67 C * (x * x) = x * (C * x). [para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].

68 (x * (x * C)) * y = x * (C * (x * y)). [para(16(a,1),13(a,1,1,2))].

69 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

70 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

71 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

72 C * (x * (y * x)) = x * (y * (C * x)). [para(16(a,2),13(a,2,2,2)),rewrite([16(4,R)])].

73 (A * x) * (A * C) = A * ((x * C) * A). [para(16(a,1),15(a,1,2))].

76 R(x,0,y) = x. [para(2(a,1),18(a,1,2)),rewrite([3(2),6(2)]),flip(a)].

77 R(x,y,0) = x. [para(3(a,1),18(a,1,1)),rewrite([3(3),6(2)]),flip(a)].

78 R(x,y,z) * (y * z) = (x * y) * z. [para(18(a,1),7(a,1,1))].

79 R(x / y,y,z) = (x * z) / (y * z). [para(7(a,1),18(a,1,1,1)),flip(a)].

80 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(7(a,1),18(a,1,2))].

81 R(x',x,y) = x'. [para(8(a,1),18(a,1,1,1)),rewrite([2(2),32(2)]),flip(a)].

82 (x * y') * y = R(x,y',y). [para(8(a,1),18(a,1,2)),rewrite([23(5)])].

85 (x * y) * y' = R(x,y,y'). [para(9(a,1),18(a,1,2)),rewrite([23(5)])].

86 R(x',x * y,z) = (y * z) / ((x * y) * z). [para(10(a,1),18(a,1,1,1)),flip(a)].

87 ((x * y') * (y * z)) / z = R(x,y',y * z). [para(10(a,1),18(a,1,2))].

88 ((x * (x * y)) * z) / (y * z) = R(x * x,y,z). [para(12(a,1),18(a,1,1,1))].

89 R(x,x,y) = x. [para(12(a,1),18(a,1,1)),rewrite([6(4)]),flip(a)].

90 ((x * (y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(12(a,1),18(a,1,2))].

91 ((x * (y * (x * z))) * u) / (z * u) = R(x * (y * x),z,u). [para(13(a,1),18(a,1,1,1))].

92 (x * (y * (x * z))) / ((y * x) * z) = R(x,y * x,z). [para(13(a,1),18(a,1,1))].

93 ((x * (y * (z * y))) * u) / (y * (z * (y * u))) = R(x,y * (z * y),u). [para(13(a,1),18(a,1,2))].

94 (A * ((x * y) * (A * z))) / ((y * A) * z) = R(A * x,y * A,z). [para(15(a,1),18(a,1,1,1)),rewrite([13(6)])].

95 (A * ((x * y) * A)) / (x * (y * A)) = R(A,x,y * A). [para(15(a,1),18(a,1,1))].

96 ((x * (A * y)) * (z * A)) / (A * ((y * z) * A)) = R(x,A * y,z * A). [para(15(a,1),18(a,1,2))].

97 ((x * C) * y) / (x * y) = R(C,x,y). [para(16(a,1),18(a,1,1,1))].

100 (C * (x * y)) / (y * C) = R(x,y,C). [para(16(a,2),18(a,1,1))].

101 (C * (x * y)) / (C * y) = R(x,y,C). [para(16(a,2),18(a,1,2)),rewrite([16(3,R)])].

103 x' * C = C * x'. [para(16(a,2),31(a,2)),rewrite([31(2)])].

104 (x / y)' = y / x. [para(7(a,1),32(a,1,2)),flip(a)].

105 x / (y * (y * x)) = (y * y)'. [para(12(a,1),32(a,1,2))].

106 x / (y * (z * (y * x))) = (y * (z * y))'. [para(13(a,1),32(a,1,2))].

108 x / (x * C) = C'. [para(16(a,1),32(a,1,2))].

109 C / (C * x) = x'. [para(16(a,2),32(a,1,2))].

112 (x * (y * (x * C))) / (x * (y * x)) = C. [para(13(a,1),60(a,1,1))].

113 x / C = C' * x. [para(62(a,1),10(a,1,2)),flip(a)].

120 A * (((A' * x) * y) * A) = x * (y * A). [para(34(a,1),15(a,1,1)),flip(a)].

122 x * (C * x') = C. [para(16(a,2),34(a,1,2))].

123 R(x,x' * y,z) = (y * z) / ((x' * y) * z). [para(34(a,1),18(a,1,1,1)),flip(a)].

124 R(x,y,(x * y)' * z) = z / (y * ((x * y)' * z)). [para(34(a,1),18(a,1,1)),flip(a)].

125 ((x * y) * (y' * z)) / z = R(x,y,y' * z). [para(34(a,1),18(a,1,2))].

126 C' * (x * (x * C)) = x * x. [para(12(a,1),63(a,1,2))].

127 (x * C) * (C' * ((x * C) * y)) = ((x * C) * x) * y. [para(63(a,1),13(a,1,1,2)),flip(a)].

128 C * (x * (C' * x)) = x * x. [para(63(a,1),13(a,2,2)),rewrite([16(6,R)])].

129 C' * (x * (y * (x * C))) = x * (y * x). [para(13(a,1),63(a,1,2))].

130 (x * y) / ((x * C) * y) = R(C',x * C,y). [para(63(a,1),18(a,1,1,1))].

131 ((x * C') * (y * C)) / y = R(x,C',y * C). [para(63(a,1),18(a,1,2))].

132 (C * x) * (x' * ((C * x) * y)) = C * (x * (C * y)). [para(64(a,1),13(a,1,1,2)),rewrite([16(4,R),70(5)]),flip(a)].

133 R(x',C * x,y) = (C * y) / ((C * x) * y). [para(64(a,1),18(a,1,1,1)),flip(a)].

136 (x / y) * (y / x) = 0. [para(104(a,1),8(a,1,1))].

137 (x / y) * ((y / x) * z) = z. [para(104(a,1),10(a,1,1))].

138 (x * y) / ((z * x) * y) = R(z,x,y)'. [para(18(a,1),104(a,1,1)),flip(a)].

140 (x / y) * (C * (y / x)) = C. [para(104(a,1),64(a,1,1))].

141 R(x,x' * y,z) = R(x',y,z)'. [back_rewrite(123),rewrite([138(8)])].

142 R(x',x * y,z) = R(x,y,z)'. [back_rewrite(86),rewrite([138(7)])].

143 ((x / y) * x) / y = (x / y) * (x / y). [para(7(a,1),35(a,1,1,2))].

144 x' / x = x' * x'. [para(8(a,1),35(a,1,1,2)),rewrite([3(3)])].

145 x / x' = x * x. [para(9(a,1),35(a,1,1,2)),rewrite([3(2)])].

150 (A * (x * (A * (x * A)))) / A = (A * x) * (A * x). [para(15(a,1),35(a,1,1)),rewrite([13(6)])].

151 (C * (x * C)) / x = C * C. [para(16(a,1),35(a,1,1,2))].

152 C' * (x * (C * x)) = x * x. [para(16(a,2),35(a,1,1,2)),rewrite([113(5)])].

153 (x * y) / (x' * y) = x * x. [para(34(a,1),35(a,1,1,2))].

155 (x' * C) / (C * x) = x' * x'. [para(64(a,1),35(a,1,1,2))].

158 (C' * x)' = C / x. [para(34(a,1),109(a,1,2)),flip(a)].

162 A * (((C * A') * x) * A) = C * (x * A). [para(122(a,1),15(a,1,1)),flip(a)].

165 C' * ((x * y) * (C * y')) = R(x,y,C * y'). [para(122(a,1),18(a,1,2)),rewrite([113(7)])].

172 (x * x)' = x' * x'. [para(145(a,1),104(a,1,1)),rewrite([144(4)])].

176 x / (y * (y * x)) = y' * y'. [back_rewrite(105),rewrite([172(5)])].

177 x' * (C * x') = C * (x' * x'). [para(103(a,1),12(a,2,2)),rewrite([16(5,R)]),flip(a)].

181 A * ((x' * C) * A) = A * ((C * x') * A). [para(103(a,1),15(a,2,2,1)),rewrite([16(6),73(7)])].

182 (x * (y / z)) * (z / y) = R(x,y / z,z / y). [para(136(a,1),18(a,1,2)),rewrite([23(6)])].

183 (C' * x) * (C / x) = 0. [para(113(a,1),136(a,1,1))].

184 (C / x) * (C' * x) = 0. [para(113(a,1),136(a,1,2))].

185 (C / x) * ((C' * x) * y) = y. [para(158(a,1),10(a,1,1))].

191 ((x / y) * (z * x)) / y = (x / y) * (z * (x / y)). [para(7(a,1),39(a,1,1,2,2))].

192 x * ((y / (x * z)) * x) = (x * y) / z. [para(7(a,1),39(a,1,1,2)),flip(a)].

193 (x' * y) / x = x' * (y * x'). [para(8(a,1),39(a,1,1,2,2)),rewrite([3(3)])].

194 x * ((x * y)' * x) = x / y. [para(8(a,1),39(a,1,1,2)),rewrite([3(2)]),flip(a)].

195 (x * y) / x' = x * (y * x). [para(9(a,1),39(a,1,1,2,2)),rewrite([3(2)])].

198 (x * (y * (y * (x * z)))) / z = x * (y * (y * x)). [para(12(a,1),39(a,1,1,2)),rewrite([12(7)])].

200 (x * (y * (z * (y * (x * u))))) / u = x * (y * (z * (y * x))). [para(13(a,1),39(a,1,1,2)),rewrite([13(9)])].

201 ((A * x) * (y * (A * ((x * z) * A)))) / (z * A) = (A * x) * (y * (A * x)). [para(15(a,1),39(a,1,1,2,2))].

202 (x * (A * ((y * x) * A))) / A = x * ((A * y) * x). [para(15(a,1),39(a,1,1,2))].

203 (C * (x * (y * C))) / y = C * (x * C). [para(16(a,1),39(a,1,1,2,2))].

208 C' * (x * x) = x * (C' * x). [para(63(a,1),39(a,1,1,2)),rewrite([113(3)])].

210 (C * C) / x = C * (x' * C). [para(64(a,1),39(a,1,1,2))].

224 (x * (C' * y)) * (C / y) = R(x,C' * y,C / y). [para(183(a,1),18(a,1,2)),rewrite([23(9)])].

226 (x * (C / y)) * (C' * y) = R(x,C / y,C' * y). [para(184(a,1),18(a,1,2)),rewrite([23(9)])].

230 (x / y) * ((z / (x / y)) * x) = ((x / y) * z) * y. [para(7(a,1),40(a,1,2,2))].

231 (x' * y) * x = x' * (y / x'). [para(8(a,1),40(a,1,2,2)),rewrite([3(5)]),flip(a)].

232 (x * y) * x' = x * (y / x). [para(9(a,1),40(a,1,2,2)),rewrite([3(3)]),flip(a)].

233 (x / y) * (y * z) = y' * ((y * x) * z). [para(40(a,1),10(a,1,2)),flip(a)].

234 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),40(a,1,2,2)),flip(a)].

240 (x / C') * y = (C * x) * y. [para(40(a,1),16(a,1)),rewrite([113(5),234(9),16(12,R),34(12)]),flip(a)].

242 (C * x) * y = (x * C) * y. [para(16(a,1),40(a,2,1)),rewrite([113(3),234(7),240(7),34(8)])].

246 (x * y) * (x' * z) = x * ((y / x) * z). [para(34(a,1),40(a,1,2,2)),flip(a)].

247 (C' * x) * (y * C) = C' * ((C * x) * y). [para(63(a,1),40(a,1,2,2)),rewrite([240(6)]),flip(a)].

248 (x' * y) * (C * x) = x' * (C * (y / x')). [para(64(a,1),40(a,1,2,2)),rewrite([16(5,R)]),flip(a)].

249 (x * y) * (C * x') = x * (C * (y / x)). [para(122(a,1),40(a,1,2,2)),rewrite([16(3,R)]),flip(a)].

250 (C * x) * (C / x) = C * C. [para(122(a,1),40(a,1,2)),rewrite([113(7),158(9)]),flip(a)].

256 x / A' = x * A. [back_rewrite(53),rewrite([231(6),34(8)])].

259 R(x,A',A) = x. [para(256(a,1),6(a,1)),rewrite([82(5)])].

260 R(x,A,A') = x. [para(256(a,1),7(a,1,1)),rewrite([85(5)])].

261 (x * A)' = A' / x. [para(256(a,1),104(a,1,1))].

263 (x * A) * (A' / x) = 0. [para(256(a,1),136(a,1,1))].

266 A' / (x / A) = x'. [para(7(a,1),261(a,1,1)),flip(a)].

267 (A' / x) * ((x * A) * y) = y. [para(261(a,1),10(a,1,1))].

269 (x * (y * (x * A)))' = A' / (x * (y * x)). [para(13(a,1),261(a,1,1))].

270 (A * C)' = C' * A'. [para(16(a,1),261(a,1,1)),rewrite([113(8)])].

273 (A' / x) * (C * (x * A)) = C. [para(261(a,1),64(a,1,1))].

291 x' * (x / A) = A'. [para(266(a,1),7(a,1,1))].

293 x / A = x * A'. [para(291(a,1),10(a,1,2)),rewrite([30(2)]),flip(a)].

294 R(A,x',x) = A. [para(291(a,1),15(a,2,2,1)),rewrite([293(5),82(8),259(7),82(4),8(8),3(6)])].

295 ((x * y') * (y * A')) * A = R(x,y',y * A'). [para(291(a,1),18(a,1,2)),rewrite([293(4),256(9),293(11)])].

297 (x * (A * ((y * x) * A))) * A' = x * ((A * y) * x). [back_rewrite(202),rewrite([293(8)])].

298 A * ((x * (A * (x * A))) * A') = (A * x) * (A * x). [back_rewrite(150),rewrite([293(9),232(10),293(8)])].

299 A * ((x * (y * A')) * A) = (A * x) * y. [back_rewrite(51),rewrite([293(3)])].

300 R(A,x,x') = A. [para(30(a,1),294(a,1,2))].

301 R(A,x / y,y / x) = A. [para(104(a,1),294(a,1,2))].

302 R(A,C / x,C' * x) = A. [para(158(a,1),294(a,1,2))].

333 (x * A')' = A / x. [para(293(a,1),104(a,1,1))].

335 (x * A') * (A / x) = 0. [para(293(a,1),136(a,1,1))].

336 (x * (y * (x * A))) * A' = x * (y * x). [para(293(a,1),39(a,1))].

337 (A * x) * (A * x) = A * (x * (A * x)). [back_rewrite(298),rewrite([336(9)]),flip(a)].

393 (x * (x * A)) * (A' / (x * x)) = 0. [para(12(a,1),263(a,1,1))].

397 (x * (y * A)) * (A' / y) = R(x,y * A,A' / y). [para(263(a,1),18(a,1,2)),rewrite([23(9)])].

400 (C' * A') * ((A * C) * x) = x. [para(270(a,1),10(a,1,1))].

402 (A * C) * ((C' * A') * x) = x. [para(270(a,1),34(a,1,2,1))].

415 (x * (y * (z * (z * (y * x))))) * u = x * (y * (z * (z * (y * (x * u))))). [para(45(a,1),13(a,1,1,2)),rewrite([45(11)])].

419 A * (((x * (x * A)) * y) * A) = A * (x * (x * (A * (y * A)))). [para(45(a,1),15(a,1)),flip(a)].

422 C * (x * (y * (y * x))) = x * (y * (y * (x * C))). [para(45(a,1),16(a,2))].

423 (x * (C * (x * C))) * y = x * (C * (C * (x * y))). [para(16(a,1),45(a,1,1,2,2))].

424 C * (x * (x * (C * y))) = C * (x * (x * (y * C))). [para(16(a,1),45(a,2,2,2,2)),rewrite([45(6)])].

428 (x * (y * (y * (x * z)))) / ((y * (y * x)) * z) = R(x,y * (y * x),z). [para(45(a,1),18(a,1,1))].

444 C * (x * (x * (y' * C))) = C * (x * (x * (C * y'))). [para(103(a,2),45(a,2,2,2,2)),rewrite([45(7)]),flip(a)].

458 (x * (x * A')) * (A / (x * x)) = 0. [para(12(a,1),335(a,1,1))].

461 (x * (y * A')) * (A / y) = R(x,y * A',A / y). [para(335(a,1),18(a,1,2)),rewrite([23(9)])].

465 (A * (A * (x * A))) * y = A * ((A * x) * (A * y)). [para(49(a,1),13(a,1,1,2))].

467 (A * x) * (A * (y * A)) = A * ((x * (A * y)) * A). [para(49(a,1),15(a,1,2))].

468 (A * (x * (A * y))) / (A * y) = R(A * x,A,y). [para(49(a,1),18(a,1,1,1)),rewrite([13(5)])].

469 R(A,x,A) = A. [para(49(a,1),18(a,1,1)),rewrite([6(7)]),flip(a)].

470 ((x * (A * y)) * A) / (A * (y * A)) = R(x,A * y,A). [para(49(a,1),18(a,1,2))].

471 A / (A * (x * A)) = (A * x)'. [para(49(a,1),32(a,1,2))].

473 (A * (x * A))' = A' / (A * x). [para(49(a,1),261(a,1,1))].

474 A * (x * (A * (A' / (A * x)))) = 0. [para(49(a,1),263(a,1,1)),rewrite([13(10)])].

484 (C * (x * (C * y))) / ((C * x) * y) = R(C,C * x,y). [para(65(a,1),18(a,1,1,1)),rewrite([13(5)])].

493 (C * x)' = (x * C)'. [para(65(a,1),109(a,1,2)),rewrite([109(6)]),flip(a)].

514 A * (((x * (y * (x * A))) * z) * A) = A * (x * (y * (x * (A * (z * A))))). [para(47(a,1),15(a,1)),flip(a)].

518 (x * (C * (y * (x * C)))) * z = x * (C * (y * (C * (x * z)))). [para(16(a,1),47(a,1,1,2,2,2))].

523 (x * (y * (z * (y * (x * u))))) / ((y * (z * (y * x))) * u) = R(x,y * (z * (y * x)),u). [para(47(a,1),18(a,1,1))].

528 x' * ((y / x') * (z * (x * ((x' * y) * u)))) = (x' * ((y / x') * (z * y))) * u. [para(34(a,1),47(a,1,1,2,2,2)),rewrite([234(5),234(16)])

,flip(a)].

529 C' * (x * (y * (z * (y * (x * C))))) = x * (y * (z * (y * x))). [para(47(a,1),63(a,1,2))].

531 C * (x * (C' * (x * (C * y)))) = (C * (x * x)) * y. [para(63(a,1),47(a,1,1,2,2)),flip(a)].

532 C * (x * (C' * (y * (C' * x)))) = x * (C' * (y * x)). [para(63(a,1),47(a,2,2,2,2)),rewrite([16(10,R)])].

534 x * (C * (x' * (C * (x * y)))) = (x * (C * C)) * y. [para(64(a,1),47(a,1,1,2,2)),flip(a)].

540 x * (C * (y * (z * y))) = x * (y * (z * (y * C))). [para(122(a,1),47(a,2,2,2,2,2)),rewrite([249(8),39(5)])].

568 (C * x) * (x * C)' = 0. [para(493(a,1),9(a,1,2))].

573 (C * (x * (y * x)))' = (x * (y * (x * C)))'. [para(13(a,1),493(a,2,1))].

619 (A * (x * A)) / (y * A) = A * (x / y). [para(7(a,1),50(a,1,1,2,1))].

620 (A * A) / (x * A) = A * x'. [para(8(a,1),50(a,1,1,2,1)),rewrite([2(4)])].

659 x * (y * (C * (x * x))) = x * (y * (x * (x * C))). [para(66(a,2),13(a,2,2,2)),rewrite([13(5)]),flip(a)].

670 x * (C * (x' * x')) = x' * C. [para(66(a,2),34(a,1,2))].

698 (C * (x * x)) * y = x * (C * (x * y)). [para(67(a,2),13(a,1,1))].

727 C * (x * (C' * (x * (C * y)))) = x * (C * (x * y)). [back_rewrite(531),rewrite([698(13)])].

743 ((x * (A * y)') * (A * ((y * z) * A))) / (z * A) = R(x,(A * y)',A * ((y * z) * A)). [para(54(a,1),18(a,1,2))].

749 A / x = A * x'. [para(54(a,1),39(a,1,1,2)),rewrite([619(8),32(3),194(10)]),flip(a)].

762 A * (A' / (A * x)) = (A * x)'. [back_rewrite(471),rewrite([749(6),473(6)])].

765 (x * (y * A')) * (A * y') = R(x,y * A',A * y'). [back_rewrite(461),rewrite([749(6),749(13)])].

768 (x * (x * A')) * (A * (x' * x')) = 0. [back_rewrite(458),rewrite([749(7),172(7)])].

783 (x * A') * (A * x') = 0. [back_rewrite(335),rewrite([749(5)])].

784 (x * A')' = A * x'. [back_rewrite(333),rewrite([749(6)])].

785 A * (x * (A * x)') = 0. [back_rewrite(474),rewrite([762(8)])].

786 A * (A' / x) = x'. [para(749(a,1),32(a,1)),rewrite([261(4)])].

788 A * (C' * A') = C'. [para(749(a,1),108(a,1)),rewrite([270(5)])].

789 C' * A = A * C'. [para(749(a,1),113(a,1)),flip(a)].

790 (A * x') * (x * A') = 0. [para(749(a,1),136(a,1,1)),rewrite([293(5)])].

794 A' / x = A' * x'. [para(786(a,1),10(a,1,2)),flip(a)].

807 (x * (y * A)) * (A' * y') = R(x,y * A,A' * y'). [back_rewrite(397),rewrite([794(6),794(13)])].

809 (x * (x * A)) * (A' * (x' * x')) = 0. [back_rewrite(393),rewrite([794(7),172(7)])].

817 (A' * x') * (C * (x * A)) = C. [back_rewrite(273),rewrite([794(3)])].

820 (x * (y * (x * A)))' = A' * (x * (y * x))'. [back_rewrite(269),rewrite([794(10)])].

822 (A' * x') * ((x * A) * y) = y. [back_rewrite(267),rewrite([794(3)])].

824 (x * A)' = A' * x'. [back_rewrite(261),rewrite([794(6)])].

825 C * (A * C') = A. [para(789(a,1),10(a,1,2)),rewrite([30(3)])].

827 (A * x) * (A * C') = A * ((x * C') * A). [para(789(a,1),15(a,1,2))].

836 ((x * C) * (A * C')) * A' = R(x,C,A * C'). [para(825(a,1),18(a,1,2)),rewrite([293(9)])].

858 (x * (A * ((y * (x * x)) * A))) / (x * A) = x * ((A * y) * x). [para(56(a,1),39(a,1,1,2))].

880 x * (A * x)' = A'. [para(785(a,1),10(a,1,2)),rewrite([3(4)]),flip(a)].

882 R(x,A * x,(A * x)') = x. [para(785(a,1),13(a,2,2)),rewrite([85(7),3(8)])].

889 (A * x)' = x' * A'. [para(880(a,1),10(a,1,2)),flip(a)].

893 R(A',x,x') = A'. [para(34(a,1),880(a,1,2,1)),rewrite([85(5)])].

895 x' * ((A' * x) * (y * (x * ((x' * A') * z)))) = (x' * ((A' * x) * (y * A'))) * z. [para(880(a,1),47(a,1,1,2,2,2)),rewrite([889(3),234(9)

,794(5),30(5),889(13),889(17),234(23),794(15),30(15)]),flip(a)].

899 R(x,A * x,x' * A') = x. [back_rewrite(882),rewrite([889(5)])].

913 ((x * (y' * A')) * (A * ((y * z) * A))) / (z * A) = R(x,y' * A',A * ((y * z) * A)). [back_rewrite(743),rewrite([889(3),889(17)])].

945 ((x * C) * A) * ((A * C') * (((x * C) * A) * y)) = (((x * C) * A) * (A * (x * A))) * y. [para(63(a,1),57(a,1,1,2,2,1)),flip(a)].

953 (A * C') * (A * x) = A * (A * (x * C')). [para(183(a,1),57(a,2,2,2)),rewrite([789(4),467(12),293(15),249(17),293(14),85(15),260(14),34(1

1),789(11),3(15)]),flip(a)].

971 (A * C) * (A * x) = A * (A * (x * C)). [para(568(a,1),57(a,2,2,2)),rewrite([16(3),467(10),889(14),13(16),788(14),232(10),113(8),34(10),1

6(9),3(13)]),flip(a)].

987 R(A',x',x) = A'. [para(30(a,1),893(a,1,3))].

1000 C' * A' = A' * C'. [para(788(a,1),10(a,1,2)),flip(a)].

1001 A' * ((A * C') * ((A' * C') * x)) = ((A' * C') * C') * x. [para(788(a,1),13(a,1,1,2)),rewrite([1000(5),1000(14),1000(20),234(23),256(16

),789(15)]),flip(a)].

1012 (A * C) * ((A' * C') * x) = x. [back_rewrite(402),rewrite([1000(8)])].

1014 (A' * C') * ((A * C) * x) = x. [back_rewrite(400),rewrite([1000(5)])].

1016 (A' * x')' = x * A. [para(794(a,1),104(a,1,1)),rewrite([256(8)])].

1017 (A' * x') * (x * A) = 0. [para(794(a,1),136(a,1,1)),rewrite([256(7)])].

1021 ((x * A) * y) * A = x * (A * (y * A)). [para(58(a,1),10(a,1,2)),rewrite([10(10)]),flip(a)].

1023 (A * (x * (A * (y * A)))) * z = A * (((x * A) * y) * (A * z)). [para(58(a,1),13(a,1,1))].

1026 (A * (((x * A) * y) * (A * z))) / ((x * (A * (y * A))) * z) = R(A,x * (A * (y * A)),z). [para(58(a,1),18(a,1,1,1)),rewrite([1023(8),102

1(13),1021(21)])].

1032 A * (((x * (y * (z * (y * (x * A))))) * u) * A) = A * (x * (y * (z * (y * (x * (A * (u * A))))))). [para(47(a,1),58(a,1,2,1,1)),rewrite

([47(21)])].

1052 (x' * A') * (A * x) = 0. [para(889(a,1),8(a,1,1))].

1053 (A * x) * (x' * A') = 0. [para(889(a,1),9(a,1,2))].

1058 (x' * A') * (C * (A * x)) = C. [para(889(a,1),64(a,1,1))].

1065 R(A,A * x,x' * A') = A. [para(889(a,1),300(a,1,3))].

1071 (A' * x)' = x' * A. [para(30(a,1),1016(a,1,1,2))].

1079 A * ((x * ((y * A') * (z * (y * A')))) * A) = (A * x) * ((y * A') * (z * y)). [para(7(a,1),59(a,1,2,2,2)),rewrite([293(4),293(11),293(1

4)]),flip(a)].

1089 (A * ((x * (y * (z * y))) * (A * u))) / ((y * (z * (y * A))) * u) = R(A * x,y * (z * (y * A)),u). [para(59(a,1),18(a,1,1,1)),rewrite([1

3(8)])].

1127 (A * x) * (C' * (y * (A * C'))) = A * ((x * (C' * (y * C'))) * A). [para(789(a,1),59(a,1,2,2,2))].

1136 (x' * A) * (A' * x) = 0. [para(1071(a,1),8(a,1,1))].

1137 (A' * x) * (x' * A) = 0. [para(1071(a,1),9(a,1,2))].

1140 (A' * x) * ((x' * A) * y) = y. [para(1071(a,1),34(a,1,2,1))].

1177 (x / y) * (C * ((y / x) * (C * ((x / y) * z)))) = ((x / y) * (C * C)) * z. [para(140(a,1),47(a,1,1,2,2)),flip(a)].

1185 C * (x * (x * C)) = x * (C * (x * C)). [para(68(a,1),16(a,2))].

1268 R(C * x,y,z) = R(x * C,y,z). [para(242(a,1),18(a,1,1,1)),rewrite([18(6)]),flip(a)].

1276 ((x * C) * (y * ((C * x) * z))) / z = (C * x) * (y * (C * x)). [para(242(a,1),39(a,1,1))].

1277 (C * x) * (y * (C * x)) = (x * C) * (y * (x * C)). [para(242(a,2),39(a,1,1,2,2)),rewrite([1276(8)])].

1292 (x * ((C * y) * (z * ((y * C) * x)))) * u = x * ((C * y) * (z * ((C * y) * (x * u)))). [para(242(a,1),47(a,1,1,2,2,2))].

1336 (C * x)' * (C * C) = C / x. [para(250(a,1),10(a,1,2))].

1338 (x * C) * (C / x) = C * C. [para(16(a,1),250(a,1,1))].

1343 x * (C / (C' * x)) = C * C. [para(34(a,1),250(a,1,1))].

1358 x * (C * y) = x * (y * C). [para(69(a,1),10(a,1,2)),rewrite([10(8)]),flip(a)].

1382 C * (x * C) = x * (C * C). [para(69(a,2),39(a,1,1)),rewrite([113(8),10(9)]),flip(a)].

1411 C * ((C * x) * (C * y)) = C * ((x * C) * (y * C)). [para(242(a,1),69(a,2,2))].

1419 C * (C * (C * x)') = C / x. [back_rewrite(1336),rewrite([1382(7,R),16(6,R)])].

1420 (x / y) * (C * ((y / x) * (C * ((x / y) * z)))) = C * ((x / y) * (C * z)). [back_rewrite(1177),rewrite([1382(15,R),16(14,R),70(16)])].

1449 ((x * (C * (C * y))) * z) / (C * (y * (C * z))) = R(x,C * (C * y),z). [para(70(a,1),18(a,1,2))].

1452 C * (C * x) = x * (C * C). [para(70(a,1),63(a,1,2)),rewrite([10(9)]),flip(a)].

1472 (C * (x * (A * C)))' = A' * (C * (C * x))'. [para(70(a,1),824(a,1,1)),rewrite([16(4)])].

1511 C' * x = x * C'. [para(8(a,1),71(a,2,2,2)),rewrite([34(8),3(7)]),flip(a)].

1512 x' * (C * (x * (y * x))) = y * (x * C). [para(71(a,2),10(a,1,2))].

1518 A * ((C * (x * (y * x))) * A) = A * ((x * (y * (x * C))) * A). [para(71(a,1),15(a,2,2,1)),rewrite([13(7),59(8)])].

1522 ((C * (x * (y * x))) * z) / ((y * (x * C)) * z) = R(x,y * (x * C),z). [para(71(a,2),18(a,1,1,1))].

1527 x * (C * (x' * (y * x'))) = y * (x' * C). [para(71(a,2),34(a,1,2))].

1534 (C * (x * C))' = (x * (C * C))'. [para(71(a,2),109(a,1,2)),rewrite([109(8)])].

1538 (x * C')' = C / x. [para(71(a,2),158(a,1,1)),rewrite([34(8),16(9,R),9(9),3(7)])].

1626 A' * ((A * C') * ((A' * C') * x)) = C' * (A' * (C' * x)). [back_rewrite(1001),rewrite([1511(22,R),13(23)])].

1659 C * (x * C') = x. [para(1511(a,1),10(a,1,2)),rewrite([30(3)])].

1660 x' * (C' * x) = C'. [para(1511(a,2),10(a,1,2))].

1663 (x * (x * C')) * y = x * (C' * (x * y)). [para(1511(a,1),13(a,1,1,2))].

1664 C' * (x * (C' * y)) = C' * (x * (y * C')). [para(1511(a,1),13(a,2,2,2)),rewrite([13(7)])].

1665 (C' * (C' * x)) * y = C' * (x * (C' * y)). [para(1511(a,2),13(a,1,1,2))].

1666 C' * (x * (y * x)) = x * (y * (x * C')). [para(1511(a,2),13(a,1))].

1672 (C' * (x * y)) / (y * C') = R(x,y,C'). [para(1511(a,2),18(a,1,1))].

1673 (C' * (x * y)) / (C' * y) = R(x,y,C'). [para(1511(a,2),18(a,1,2)),rewrite([1511(4,R)])].

1674 x / (x * C') = C. [para(1511(a,1),32(a,1,2)),rewrite([30(7)])].

1676 x * (C' * x') = C'. [para(1511(a,2),34(a,1,2))].

1684 (C' * (x * (C' * x))) * y = C' * (x * (x * (C' * y))). [para(1511(a,2),45(a,1,1,2,2))].

1690 C' * (x * (y * (z * (y * x)))) = x * (y * (z * (y * (x * C')))). [para(1511(a,2),47(a,1))].

1698 C * (x * (x * C')) = x * x. [para(1511(a,1),71(a,1,2,2)),rewrite([63(11)])].

1699 x / C' = C * x. [para(7(a,1),1659(a,1,2)),flip(a)].

1701 C * (x * (y * (x * C'))) = x * (y * x). [para(13(a,1),1659(a,1,2))].

1702 (x * y) / ((x * C') * y) = R(C,x * C',y). [para(1659(a,1),18(a,1,1,1))].

1703 ((x * C) * (y * C')) / y = R(x,C,y * C'). [para(1659(a,1),18(a,1,2))].

1711 C * (x * (y * (z * (y * (x * C'))))) = x * (y * (z * (y * x))). [para(47(a,1),1659(a,1,2))].

1724 (C * x)' = C' / x. [para(1699(a,1),104(a,1,1))].

1730 (C' / x) * ((C * x) * y) = y. [para(1699(a,1),137(a,1,2,1))].

1736 (x * (C * C))' = C' / (x * C). [back_rewrite(1534),rewrite([1724(5)]),flip(a)].

1755 C' / (x * (A * C)) = A' * (C' / (C * x)). [back_rewrite(1472),rewrite([1724(7),1724(14)])].

1769 C * (C * (C' / x)) = C / x. [back_rewrite(1419),rewrite([1724(5)])].

1824 (x * (y * (x * C)))' = C' / (x * (y * x)). [back_rewrite(573),rewrite([1724(5)]),flip(a)].

1828 (x * C)' = C' / x. [back_rewrite(493),rewrite([1724(3)]),flip(a)].

1872 x * (y' * C) = x * (C * y'). [para(72(a,2),34(a,1,2)),rewrite([1527(7)])].

1930 (C / x) * ((x * C') * y) = y. [para(1538(a,1),10(a,1,1))].

1934 (x * C') * ((C / x) * y) = y. [para(1538(a,1),34(a,1,2,1))].

1952 C' / (C * x) = C' / (x * C). [para(242(a,1),1828(a,1,1)),rewrite([16(4,R),1724(5)]),flip(a)].

1957 (A * ((x * C) * A)) / (x * (A * C)) = R(A,x,A * C). [para(73(a,1),18(a,1,1))].

1960 A * ((C * (A' * x)) * A) = x * (A * C). [para(34(a,1),73(a,1,1)),rewrite([16(10,R)]),flip(a)].

1991 R(x',C' * x,y) = (C' * y) / ((C' * x) * y). [para(1660(a,1),18(a,1,1,1)),flip(a)].

2000 x * (C' * (x' * (C' * (x * y)))) = (x * (C' * C')) * y. [para(1660(a,1),47(a,1,1,2,2)),flip(a)].

2007 (x' * A) * (C' * (A' * x)) = C'. [para(1071(a,1),1660(a,1,1))].

2023 (x * A') * (C' * (A * x')) = C'. [para(784(a,1),1676(a,1,2,2))].

2035 R(x,y / z,z) * y = (x * (y / z)) * z. [para(7(a,1),78(a,1,2))].

2036 R(x,y,z)' * ((x * y) * z) = y * z. [para(78(a,1),10(a,1,2))].

2037 R(x,y',y * z) * z = (x * y') * (y * z). [para(10(a,1),78(a,1,2))].

2041 R(x,C,y) * (y * C) = (x * C) * y. [para(16(a,1),78(a,1,2))].

2042 R(x,y,C) * (C * y) = C * (x * y). [para(16(a,2),78(a,1,2)),rewrite([16(8,R)])].

2043 (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u). [para(78(a,1),18(a,1,1,1))].

2044 ((x * R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u). [para(78(a,1),18(a,1,2))].

2045 R(x,y,y' * z) * z = (x * y) * (y' * z). [para(34(a,1),78(a,1,2))].

2048 (R(x,y,z) * ((x * y) * z)) / (y * z) = R(x,y,z) * R(x,y,z). [para(78(a,1),35(a,1,1,2))].

2051 (x * ((y * x) * z)) / z = x * (R(y,x,z) * x). [para(78(a,1),39(a,1,1,2))].

2071 ((C * x) * y) * z = ((x * C) * y) * z. [para(242(a,1),78(a,2,1)),rewrite([78(5)])].

2084 R(x,y,C') * (C' * y) = C' * (x * y). [para(1511(a,2),78(a,1,2)),rewrite([1511(11,R)])].

2092 R(x,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u). [para(78(a,1),78(a,1,2))].

2104 R((x / y) / z,z,y) = x / (z * y). [para(7(a,1),79(a,2,1))].

2105 R(x / (y / z),y / z,z) = (x * z) / y. [para(7(a,1),79(a,2,2))].

2107 R(x / y',y',y) = x * y. [para(8(a,1),79(a,2,2)),rewrite([23(7)])].

2108 R(x / y,y,x') = (y * x')'. [para(9(a,1),79(a,2,1)),rewrite([28(7)])].

2109 R(x / y,y,y') = x * y'. [para(9(a,1),79(a,2,2)),rewrite([23(7)])].

2110 R(x' / y,y,x * z) = z / (y * (x * z)). [para(10(a,1),79(a,2,1))].

2111 R(x / y',y',y * z) = (x * (y * z)) / z. [para(10(a,1),79(a,2,2))].

2118 R(C / x,x,y) = (y * C) / (x * y). [para(16(a,1),79(a,2,1))].

2119 (x * y) / (y * C) = R(C' * x,C,y). [para(16(a,1),79(a,2,2)),rewrite([113(2)]),flip(a)].

2120 R(x / y,y,C) = (C * x) / (y * C). [para(16(a,2),79(a,2,1))].

2124 R(C' / x,x,y * C) = y / (x * (y * C)). [para(63(a,1),79(a,2,1))].

2128 R(x / y,y,z)' = (y * z) / (x * z). [para(79(a,2),104(a,1,1))].

2130 (x * y) / (C * y) = R(C' * x,C,y). [para(113(a,1),79(a,1,1)),flip(a)].

2143 (x * y) / (A' * y) = R(x * A,A',y). [para(256(a,1),79(a,1,1)),flip(a)].

2144 (x * y) / (A * y) = R(x * A',A,y). [para(293(a,1),79(a,1,1)),flip(a)].

2149 R((A * x) / y,y,A) = A * (x / y). [para(49(a,1),79(a,2,1)),rewrite([619(12)])].

2150 R(x / (A * y),A * y,A) = (x * A) / (A * (y * A)). [para(49(a,1),79(a,2,2))].

2180 R((C * x) / y,y,z) = ((x * C) * z) / (y * z). [para(242(a,1),79(a,2,1))].

2182 R((x * C) / y,y,z) = ((C * x) * z) / (y * z). [para(242(a,2),79(a,2,1))].

2190 R((C * (C * x)) / y,y,z) = (C * (x * (C * z))) / (y * z). [para(70(a,1),79(a,2,1))].

2195 (x * (y * (z * C))) / (C * (z * (y * z))) = R(x / z,z,y * (z * C)). [para(71(a,2),79(a,2,2)),flip(a)].

2197 (x * y) / (y * C') = R(C * x,C',y). [para(1511(a,1),79(a,2,2)),rewrite([1699(3)]),flip(a)].

2198 R(x / y,y,C') = (C' * x) / (y * C'). [para(1511(a,2),79(a,2,1))].

2217 R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z)). [para(78(a,1),79(a,2,1))].

2232 ((x * (y * (x * (z / u)))) * u) / z = R(x * (y * x),z / u,u). [para(13(a,1),80(a,1,1,1))].

2233 (A * (((x / (y * A)) * y) * A)) / x = R(A,x / (y * A),y * A). [para(15(a,1),80(a,1,1))].

2234 (C * (x * (C' * y))) / y = R(x,C' * y,C). [para(16(a,2),80(a,1,1)),rewrite([113(3),113(9)])].

2235 x / ((y * (x / z)) * z) = R(y,x / z,z)'. [para(80(a,1),104(a,1,1)),flip(a)].

2236 C' * ((x * (C / y)) * y) = R(x,C / y,y). [para(80(a,1),113(a,1)),flip(a)].

2239 ((x * (A' * y')) * y) * A = R(x,A' * y',y). [para(80(a,1),256(a,1)),rewrite([794(3),794(8)]),flip(a)].

2242 ((x * (y * A')) * A) / y = R(x,y * A',A). [para(293(a,1),80(a,1,1,1,2)),rewrite([293(9)])].

2249 (C' * (x * (C * y))) / y = R(x,C * y,C'). [para(1511(a,2),80(a,1,1)),rewrite([1699(5),1699(10)])].

2260 (A * ((x * A') * (y * x))) * x' = A * ((x * A') * y). [para(783(a,1),47(a,2,2,2,2)),rewrite([82(9),259(8),3(15)])].

2273 (x * y')' * R(x,y',y) = y. [para(82(a,1),10(a,1,2))].

2275 x * ((y * x') * (x * z)) = (x * R(y,x',x)) * z. [para(82(a,1),13(a,1,1,2)),flip(a)].

2276 (x * (y * (x * z'))) * z = R(x * (y * x),z',z). [para(13(a,1),82(a,1,1))].

2277 R(x,C',C) = x. [para(82(a,1),16(a,2)),rewrite([1659(5)]),flip(a)].

2279 (R(x,y',y) * z) / (y * z) = R(x * y',y,z). [para(82(a,1),18(a,1,1,1))].

2285 (x * (y' * y')) * (y * y) = R(x,y' * y',y * y). [para(172(a,1),82(a,1,1,2)),rewrite([172(8)])].

2292 (x * (A * y')) * (y * A') = R(x,A * y',y * A'). [para(784(a,1),82(a,1,1,2)),rewrite([784(12)])].

2294 (x * (A' * y')) * (y * A) = R(x,A' * y',y * A). [para(824(a,1),82(a,1,1,2)),rewrite([824(11)])].

2301 R(x,C,C') = x. [para(82(a,1),1511(a,2)),rewrite([30(5),63(5),30(3)]),flip(a)].

2306 R(x,y * z',z) * R(y,z',z) = (x * (y * z')) * z. [para(82(a,1),78(a,1,2))].

2321 (A * (C / x)) * ((C' * x) * A') = 0. [para(158(a,1),790(a,1,1,2))].

2419 R(x,y,y') / y' = x * y. [para(85(a,1),6(a,1,1))].

2420 (x * y)' * R(x,y,y') = y'. [para(85(a,1),10(a,1,2))].

2421 (x * (x * y)) * y' = R(x * x,y,y'). [para(12(a,1),85(a,1,1))].

2424 (x * (y * (x * z))) * z' = R(x * (y * x),z,z'). [para(13(a,1),85(a,1,1))].

2466 R(x,y * z,z') * R(y,z,z') = (x * (y * z)) * z'. [para(85(a,1),78(a,1,2))].

2467 R(R(x,y,z),y * z,(y * z)') = ((x * y) * z) * (y * z)'. [para(78(a,1),85(a,1,1)),flip(a)].

2537 R(A,x',x * A) = A. [para(15(a,1),87(a,1,1)),rewrite([8(3),2(4),293(5),12(6),9(5),3(3)]),flip(a)].

2542 x / ((y * z') * (z * x)) = R(y,z',z * x)'. [para(87(a,1),104(a,1,1)),flip(a)].

2546 R(x,C',y' * C) = R(x,C',C * y'). [para(103(a,2),87(a,1,1,2)),rewrite([131(9)])].

2569 R(A,x',x * (y * (x * A))) = R(A,y,x * A). [para(59(a,1),87(a,1,1)),rewrite([10(5),95(9)]),flip(a)].

2585 R(x,C,C' * y) = R(x,C,y * C'). [para(1511(a,1),87(a,1,1,2)),rewrite([30(3),1703(7),30(8)]),flip(a)].

2586 (C' * ((C * x) * y)) / y = R(x,C',C * y). [para(1511(a,2),87(a,1,1,1)),rewrite([234(6),1699(5)])].

2596 R(x,C,C' * (C' / x)) = C' / (C' / x). [para(1676(a,1),87(a,1,1)),rewrite([30(5),1828(5),30(9),30(12),1828(12)]),flip(a)].

2600 (R(x,y,y') * (y * z)) / z = R(x * y,y',y * z). [para(82(a,1),87(a,1,1,1)),rewrite([30(2),30(7)])].

2603 R(A,A * x',x) = A. [para(7(a,1),2537(a,1,3)),rewrite([293(3),784(5)])].

2622 R(A,A * x,x') = A. [para(30(a,1),2603(a,1,2,2))].

2655 ((x * (x * y)) * (y' * z)) / z = R(x * x,y,y' * z). [para(34(a,1),88(a,1,2))].

2723 (x * (C' * (x * y))) / (y * C') = R(x * x,C',y). [para(1511(a,1),88(a,1,2)),rewrite([1663(5)])].

2777 R(A * A,x,x') = A * A. [para(2622(a,1),78(a,1,1)),rewrite([85(5),300(4),2421(9)]),flip(a)].

2808 ((x * (C' * C')) * (y * C)) / (C' * y) = R(x,C' * C',y * C). [para(63(a,1),90(a,1,2,2))].

2809 C * (C * (x * (C' * C'))) = R(x,C' * C',C). [para(63(a,1),90(a,1,2)),rewrite([16(8,R),1699(11)])].

2814 C' * (C' * (x * (C * C))) = R(x,C * C,C'). [para(122(a,1),90(a,1,2)),rewrite([1511(7,R),113(9)])].

2875 (((x * y) * y) * z) / (y * (y * z)) = R(R(x,y,y),y * y,z). [para(78(a,1),90(a,1,1,1))].

2918 (A' * (C / x)) * ((C' * x) * A) = 0. [para(158(a,1),1017(a,1,1,2))].

3043 R(x * (C' * x),y,z) = R(x * (x * C'),y,z). [para(1511(a,1),91(a,2,1,2)),rewrite([91(8)])].

3115 (A * ((x' * A') * (y * x'))) * x = A * ((x' * A') * y). [para(1052(a,1),47(a,2,2,2,2)),rewrite([82(11),259(10),3(17)])].

3160 A * ((x * (A' * y)) * A) = A * ((x * A') * (y * A)). [para(1136(a,1),59(a,2,2,1,2,2)),rewrite([231(13),256(13),1140(15),246(8),293(3),3

(14)]),flip(a)].

3173 A * ((C * A') * (x * A)) = x * (A * C). [back_rewrite(1960),rewrite([3160(9)])].

3176 (x' * y) / R(y,x',x) = R(x',y * x',x). [para(8(a,1),92(a,1,1,2,2)),rewrite([3(3),82(5)])].

3185 (C * (x * (y * C))) / ((x * C) * y) = R(C,x * C,y). [para(16(a,1),92(a,1,1,2,2))].

3187 (x * (y * (C * x))) / (C * (y * x)) = R(x,y * x,C). [para(16(a,2),92(a,1,1,2,2)),rewrite([16(7,R)])].

3189 (x * (y * (x * C))) / (C * (y * x)) = R(x,y * x,C). [para(16(a,2),92(a,1,2))].

3190 (x * (y * z)) / ((y * x) * (x' * z)) = R(x,y * x,x' * z). [para(34(a,1),92(a,1,1,2,2))].

3196 (C * (x * (C * y))) / (C * y) = R(C * x,C,y). [para(64(a,1),92(a,1,2,1)),rewrite([132(8),64(14)])].

3197 ((x * y) * z) / (y * (x * (y * z))) = R(y,x * y,z)'. [para(92(a,1),104(a,1,1)),flip(a)].

3198 (x * (y * C)) / ((y * x) * (C * x')) = R(x,y * x,C * x'). [para(122(a,1),92(a,1,1,2,2))].

3201 R(C,x' * C,y) = R(C,C * x',y). [para(103(a,1),92(a,1,2,1)),rewrite([484(11)]),flip(a)].

3213 R(x,A * x,A) = x. [para(49(a,1),92(a,1,2)),rewrite([6(10)]),flip(a)].

3252 R(x,(C * y) * x,z) = R(x,(y * C) * x,z). [para(242(a,1),92(a,2,2)),rewrite([92(10)])].

3365 R(x,C * (C * y),z) = R(x,C * (y * C),z). [para(16(a,2),93(a,1,1,1,2,2)),rewrite([1449(12)])].

3366 (C * (x * (y * (z * y)))) / (y * (z * (y * C))) = R(x,y * (z * y),C). [para(16(a,2),93(a,1,1))].

3414 R(x,C * (y * y),z) = R(x,y * (C * y),z). [para(67(a,2),93(a,2,2)),rewrite([93(10)]),flip(a)].

3446 (C * ((C * x) * (C * y))) / (C * (x * (C * y))) = R(C,C * (x * C),y). [para(69(a,2),93(a,1,1,1)),rewrite([70(7)])].

3468 R(x,C' * (C' * y),z) = R(x,C' * (y * C'),z). [para(1511(a,2),93(a,2,2,2)),rewrite([93(16)]),flip(a)].

3563 (A * ((x * C) * (A * y))) / ((x * A) * y) = R(A * C,x * A,y). [para(16(a,1),94(a,1,1,2,1))].

3565 (A * ((x * y) * (A * C))) / (C * (y * A)) = R(A * x,y * A,C). [para(16(a,2),94(a,1,1,2,2)),rewrite([16(5),16(11,R)])].

3673 R(x,A' * x,x' * A) = x. [para(1137(a,1),92(a,1,2)),rewrite([34(6),8(4),3(2),23(2)]),flip(a)].

3710 x * (C * (C * x')) = C * C. [para(68(a,1),1338(a,1,1)),rewrite([176(10),246(9),151(5),12(5)])].

3728 (A * (x * A)) / (y' * ((y * x) * A)) = R(A,x / y,y * A). [para(7(a,1),95(a,1,1,2,1)),rewrite([233(8)])].

3729 R(A,x / y,y * A) = R(A,y',(y * x) * A). [para(10(a,1),95(a,1,1,2,1)),rewrite([3728(10)])].

3730 R(A,x,x * A) = A. [para(12(a,1),95(a,1,1,2)),rewrite([6(9)]),flip(a)].

3737 (A * (x * A)) / (C' * ((x * C) * A)) = R(A,C',(x * C) * A). [para(63(a,1),95(a,1,1,2,1))].

3762 R(A,x,(C * y) * A) = R(A,x,(y * C) * A). [para(242(a,1),95(a,2,3)),rewrite([95(13)])].

3773 (A * ((x * C') * A)) / (x * (A * C')) = R(A,x,A * C'). [para(1511(a,1),95(a,1,2,2)),rewrite([1511(18)])].

3782 A * ((R(x,y,A) * y) / (x * y)) = R(A,R(x,y,A),y * A). [para(78(a,1),95(a,1,2)),rewrite([619(11)])].

3791 (A * (x * A)) / (y' * ((y * x) * A)) = R(A,y',(y * x) * A). [back_rewrite(3728),rewrite([3729(15)])].

3792 R(A,x * A',x) = A. [para(7(a,1),3730(a,1,3)),rewrite([293(3)])].

3816 (A * (x * A')) * x = A * ((x * A') * x). [para(3792(a,1),78(a,1,1)),flip(a)].

3865 R(x,A * y,(C * z) * A) = R(x,A * y,(z * C) * A). [para(242(a,1),96(a,2,3)),rewrite([96(16)])].

3921 (A * ((C * x) * A)) / (A * (x * A)) = R(C,A,x * A). [para(15(a,1),97(a,1,1))].

3923 (x * ((C / x) * y)) / y = R(C,x,x' * y). [para(34(a,1),97(a,1,2)),rewrite([246(5)])].

3925 R(C',x * C,y) = R(C,x,y)'. [para(97(a,1),104(a,1,1)),rewrite([130(8)]),flip(a)].

3947 (x * y) / ((x * C) * y) = R(C,x,y)'. [back_rewrite(130),rewrite([3925(10)])].

3951 (x * (y * C)) / (C * y) = x. [para(1358(a,1),6(a,1,1))].

3952 (x * (C * y)) / (y * C) = x. [para(1358(a,2),6(a,1,1))].

3953 (x / (C * y)) * (y * C) = x. [para(1358(a,1),7(a,1))].

3954 (x / (y * C)) * (C * y) = x. [para(1358(a,2),7(a,1))].

3960 ((x * y) * (C * z)) / (y * (z * C)) = R(x,y,C * z). [para(1358(a,1),18(a,1,2))].

3961 R(x,y,C * z) = R(x,y,z * C). [para(1358(a,2),18(a,1,1)),rewrite([3960(8)])].

3983 x * (C * (C * y)) = x * (C * (y * C)). [para(242(a,1),1358(a,2,2)),rewrite([16(9,R)])].

4032 (C * x) / (C * (y * x)) = R(y,x,C)'. [para(10(a,1),100(a,1,1,2)),rewrite([16(5,R),142(10)])].

4034 R(x',C * x,C) = x'. [para(64(a,1),100(a,1,1,2)),rewrite([16(7,R),210(8),1724(6),16(8,R),1769(9),109(4)]),flip(a)].

4035 (x * C) / (C * (y * x)) = R(y,x,C)'. [para(100(a,1),104(a,1,1)),flip(a)].

4052 (C * (x * (C * (C * y)))) / (C * (y * (C * C))) = R(x,C * (C * y),C). [para(70(a,1),100(a,1,2))].

4058 (C * ((x * y) * z)) / (C * (y * z)) = R(R(x,y,z),y * z,C). [para(78(a,1),100(a,1,1,2)),rewrite([16(7,R)])].

4066 R(R(C,x,C * y),x * (C * y),C) = R(C,C * (x * C),y). [back_rewrite(3446),rewrite([4058(13)])].

4089 (C * (x * (y * (C * z)))) / (C * (y * (z * C))) = R(x,y * (C * z),C). [para(69(a,1),101(a,1,2))].

4090 (C * (x * (y * (z * C)))) / (C * (y * (C * z))) = R(x,y * (z * C),C). [para(69(a,2),101(a,1,2))].

4097 R(C / x,x,C) = C / x. [para(34(a,1),4034(a,1,2)),rewrite([158(4),158(8)])].

4111 x' * (C * (C * x)) = C * C. [para(4034(a,1),78(a,1,1)),rewrite([16(5,R),64(10)])].

4115 C / (C' * x) = C * (x' * C). [para(4097(a,1),80(a,2)),rewrite([113(3),113(7),7(9),210(4),113(8)]),flip(a)].

4117 x * (C * (x' * C)) = C * C. [back_rewrite(1343),rewrite([4115(5)])].

4118 (x * (C * C)) / (x * C) = C. [para(1382(a,1),6(a,1,1))].

4120 C' * (x * (C * C)) = x * C. [para(1382(a,1),10(a,1,2))].

4123 (x * (C * C)) * y = C * (x * (C * y)). [para(1382(a,1),13(a,1,1))].

4130 R(x,C * C,y) = R(x,C * y,C). [para(1382(a,2),18(a,1,1,1)),rewrite([13(5),12(9),101(10)]),flip(a)].

4131 (C * (C * (x * y))) / (y * (C * C)) = R(x,y,C * C). [para(1382(a,2),18(a,1,1)),rewrite([16(4,R)])].

4132 (C * (C * (x * y))) / (C * (y * C)) = R(x,y,C * C). [para(1382(a,2),18(a,1,2)),rewrite([1382(5,R),16(4,R)])].

4134 C / (x * (C * C)) = C' / x. [para(1382(a,1),109(a,1,2)),rewrite([1828(9)])].

4177 R(x,C' * C',C * C) = R(x,C' * C',C). [para(1382(a,2),82(a,1)),rewrite([172(5),16(9,R),2809(10),172(11)]),flip(a)].

4190 R(x,C * (y * C),C) = R(x,C * C,y * C). [para(1382(a,1),90(a,1,2,2)),rewrite([4123(7),3366(14)])].

4228 R(x,C * C,C) = R(x,C,C * C). [para(1382(a,2),100(a,1,1,2)),rewrite([16(11,R),4131(12)]),flip(a)].

4231 R(x,C * C,C') = x. [back_rewrite(2814),rewrite([4120(9),63(5)]),flip(a)].

4243 x * (C * (x' * (C * (x * y)))) = C * (x * (C * y)). [back_rewrite(534),rewrite([4123(13)])].

4256 (x * (y * x))' = x' / (x * y). [para(9(a,1),106(a,1,2,2,2)),rewrite([3(3)]),flip(a)].

4269 C' / (C * x) = x' / (C * C). [para(122(a,1),106(a,1,2,2)),rewrite([4256(10)]),flip(a)].

4273 C / (x * C') = C * (x' * C). [para(158(a,1),106(a,2)),rewrite([106(8),4256(7),30(3),4115(5)]),flip(a)].

4326 x / (C' * (y * (x * C'))) = C * (y' * C). [para(1511(a,1),106(a,1,2,2,2)),rewrite([4256(15),30(11),4115(13)])].

4339 x / (C' * C') = C * (x * C). [para(1660(a,1),106(a,1,2,2)),rewrite([4256(14),30(9),4115(12),30(9)])].

4372 (x * (y * (x * A)))' = A' * (x' / (x * y)). [back_rewrite(820),rewrite([4256(10)])].

4419 x / (C * C) = C' * (x * C'). [para(4231(a,1),79(a,1)),rewrite([1511(13,R),1382(13,R),16(12,R),9(12),3(10),113(9)])].

4422 C' / (C * x) = C' * (x' * C'). [back_rewrite(4269),rewrite([4419(10)])].

4460 C' / (x * C) = C' * (x' * C'). [back_rewrite(1952),rewrite([4422(5)]),flip(a)].

4463 C' / (x * (A * C)) = A' * (C' * (x' * C')). [back_rewrite(1755),rewrite([4422(14)])].

4469 (x * (C * C))' = C' * (x' * C'). [back_rewrite(1736),rewrite([4460(10)])].

4524 (x * (C * C)) / (C * x) = C. [para(1452(a,1),6(a,1,1))].

4529 (C * (C * (x * y))) / (C * (C * y)) = R(x,y,C * C). [para(1452(a,2),18(a,1,2)),rewrite([1382(5,R),16(4,R)])].

4530 (C * x) / (x * (C * C)) = C'. [para(1452(a,1),32(a,1,2))].

4537 (x * (x * (C * C))) * y = x * (C * (C * (x * y))). [para(1452(a,1),45(a,1,1,2))].

4565 R(x,C * (C * y),C) = R(x,C * C,C * y). [para(1452(a,1),90(a,1,2,2)),rewrite([4123(7),4052(14)])].

4606 ((A' * x) * y) * A = A' * (x * (y * A)). [para(120(a,1),10(a,1,2)),flip(a)].

4610 (x * (A' * y)) * A = (x * A') * (y * A). [para(13(a,1),120(a,1,2,1)),rewrite([231(10),256(10),34(11)])].

4627 A * ((A' * C') * (x * A)) = x * (A * C'). [para(1511(a,1),120(a,2,2)),rewrite([1511(7,R),4610(9),1511(6)])].

4638 (C * x) * (A * C) = C * (C * (x * A)). [para(1382(a,2),120(a,1,2,1,1)),rewrite([16(6,R),70(8),4610(10),3173(11),12(12)])].

4657 R(x,y,(x * y)' * z)' = (y * ((x * y)' * z)) / z. [para(124(a,2),104(a,1,1))].

4658 R(x,C,C * (C' / x)) = C' / (C' / x). [para(124(a,2),109(a,1)),rewrite([1828(4),16(6,R),1828(10),16(12,R),1724(13)])].

4687 x / (y * ((y' * A') * x)) = R(A,y,(y' * A') * x). [para(889(a,1),124(a,1,3,1)),rewrite([889(10)]),flip(a)].

4727 R(x',C' * x,C * y) = y / (C' * ((C * x) * y)). [para(1660(a,1),124(a,1,3,1,1)),rewrite([30(7),1660(15),30(13),234(13),1699(12)])].

4751 C' / (C' / x) = C / (C / x). [para(1382(a,1),124(a,2,2)),rewrite([1828(4),16(6,R),4658(7),1828(10),1382(14,R),16(13,R),1769(14)])].

4759 R(x,C,C' * (C' / x)) = C / (C / x). [back_rewrite(2596),rewrite([4751(14)])].

4833 R(A * x,A,A' * y) = (A * (x * y)) / y. [para(49(a,1),125(a,1,1,1)),rewrite([246(8),293(5),85(6),260(5)]),flip(a)].

4849 R(A,x,x' * (y * (x' * A))) = R(A,y,x' * A). [para(59(a,1),125(a,1,1)),rewrite([34(6),95(11)]),flip(a)].

4883 R(x,C * C,C' * (C' * y)) = R(x,C' * y,C). [para(1382(a,2),125(a,1,1,1)),rewrite([172(8),12(10),246(11),113(5),63(6),2234(7),172(12),12(

14)]),flip(a)].

4996 R(x,C' * C',C) = x. [para(126(a,1),90(a,1,2)),rewrite([16(10,R),9(10),3(8),4339(12),16(9,R),2809(10),16(16,R),9(16),77(14)])].

5026 R(x,C' * C',C * C) = x. [back_rewrite(4177),rewrite([4996(16)])].

5028 C * (x * (C' * C')) = x * C'. [para(4996(a,1),78(a,1,1)),rewrite([16(7,R),34(7),16(11,R)]),flip(a)].

5089 ((x * C) * x) * ((C' / x) * y) = (x * C) * (C' * y). [para(34(a,1),127(a,1,2,2)),rewrite([1828(12)]),flip(a)].

5225 R(x,C * C,y * (C' * y)) = R(x,y * y,C). [para(128(a,1),90(a,1,2,2)),rewrite([4123(9),128(7),101(8)]),flip(a)].

5303 C * (C * (x / (y * C))) = (C * x) / y. [para(3954(a,1),39(a,1,1,2)),rewrite([16(9,R)]),flip(a)].

5317 R(x,(y * C) / z,z) * (C * y) = (x * ((y * C) / z)) * z. [para(80(a,1),3954(a,1,1))].

5373 C' * (x * (C * (y * x))) = x * (R(y,x,C) * x). [para(78(a,1),129(a,1,2,2)),rewrite([16(5,R)])].

5427 x / ((y * C') * (x * C)) = R(y,C',x * C)'. [para(131(a,1),104(a,1,1)),flip(a)].

5530 R(C,x,x' * ((C * x) * y)) = R(C,C * x,y). [para(132(a,1),18(a,1,1)),rewrite([34(11),484(9)]),flip(a)].

5677 (C * x) / ((C * y) * x) = R(y,C,x)'. [para(16(a,1),133(a,1,2)),rewrite([142(4)]),flip(a)].

5679 R(x',C * x,y) = R(x,C,y)'. [para(16(a,1),133(a,2,2,1)),rewrite([138(10)])].

5680 R(x,C * x',y) = R(x',C,y)'. [para(30(a,1),133(a,1,1)),rewrite([5677(11)])].

5691 (C * (C * C)) / (C * (C * (C * x))) = R(x,C,C * C)'. [para(66(a,2),133(a,2,1)),rewrite([5679(7),1382(17,R),16(16,R)]),flip(a)].

5715 C' * (C / x) = C * (C' / x). [para(1676(a,1),133(a,2,2)),rewrite([1724(8),5679(10),4759(8),104(5),113(4),1724(11),34(13),1699(11)])].

5745 (x * C) / (C' * x) = C * C. [para(16(a,1),153(a,1,1))].

5853 (C / x) * (C * x) = C * C. [para(1382(a,2),185(a,1,2)),rewrite([16(8,R),34(8)])].

5938 (C * (C * C)) / x = C * (C * (C / x)). [para(5853(a,1),39(a,1,1,2)),rewrite([16(11,R)])].

5981 R(x,C,C * C)' = x'. [back_rewrite(5691),rewrite([5938(12),109(10),1724(7),4422(7),34(10),1659(6)]),flip(a)].

5991 R(x,C,C * C) = x. [para(5981(a,1),30(a,1,1)),rewrite([30(2)]),flip(a)].

5993 R(x,C * C,C) = x. [back_rewrite(4228),rewrite([5991(10)])].

6041 (x * C') / ((y * C') * x) = R(y,C',x)'. [para(1511(a,1),138(a,1,1))].

6042 R(C,x * C',y) = R(C',x,y)'. [para(1511(a,1),138(a,1,2,1)),rewrite([1702(6)])].

6044 (C' * x) / ((C' * y) * x) = R(y,C',x)'. [para(1511(a,2),138(a,1,2,1))].

6114 (x * y) / ((x * C') * y) = R(C',x,y)'. [back_rewrite(1702),rewrite([6042(11)])].

6116 R(x',C' * x,y) = R(x,C',y)'. [back_rewrite(1991),rewrite([6044(13)])].

6129 x / (C' * ((C * y) * x)) = R(y,C',C * x)'. [back_rewrite(4727),rewrite([6116(7)]),flip(a)].

6130 C * (x * (C * C)) = x * (C * (C * C)). [para(5993(a,1),78(a,1,1)),rewrite([16(5,R),16(12,R)]),flip(a)].

6173 (x * y)' * x = x' * (x / y). [para(194(a,1),10(a,1,2)),flip(a)].

6174 x' / (x * y) = x' * (y' * x'). [para(10(a,1),194(a,1,2,1,1)),flip(a)].

6180 x / (x' * y) = x * (y' * x). [para(34(a,1),194(a,1,2,1,1)),flip(a)].

6182 x / (C * x') = x * (C' * x). [para(122(a,1),194(a,1,2,1,1)),flip(a)].

6204 (x * C') / (y * x) = x / (y * (x * C)). [para(71(a,2),194(a,1,2,1,1)),rewrite([1724(5),192(7)])].

6208 (A * x) / (A * C) = A * (C' * (x * A')). [para(73(a,1),194(a,1,2,1,1)),rewrite([4256(9),6174(9),1828(7),13(14),10(12),7(8),246(8),293(3

),1511(7,R)]),flip(a)].

6240 C / (x * (C' * x)) = C * (C * (x' * x')). [para(128(a,1),194(a,1,2,1,1)),rewrite([172(3),16(6,R)]),flip(a)].

6248 C' / (x * (C * x)) = C' * (C' * (x' * x')). [para(152(a,1),194(a,1,2,1,1)),rewrite([172(4),1511(8,R)]),flip(a)].

6313 (x * (y * (x * A)))' = A' * (x' * (y' * x')). [back_rewrite(4372),rewrite([6174(10)])].

6360 (x * (y * x))' = x' * (y' * x'). [back_rewrite(4256),rewrite([6174(6)])].

6379 R(x,C',y * C)' = R(x,C',y)'. [back_rewrite(6041),rewrite([6204(8),5427(7)])].

6410 x / ((y * C') * (x * C)) = R(y,C',x)'. [back_rewrite(5427),rewrite([6379(13)])].

6450 R(x / y,y,z) = R(y / x,x,z)'. [para(7(a,1),142(a,1,2)),rewrite([104(2)])].

6459 R(A' * x',(x * A) * y,z) = R(x * A,y,z)'. [para(824(a,1),142(a,1,1))].

6466 R(x',C * (x * (y * x)),z) = R(x,y * (x * C),z)'. [para(71(a,2),142(a,1,2))].

6469 R(C / x,(x * C') * y,z) = R(x * C',y,z)'. [para(1538(a,1),142(a,1,1))].

6475 R(x',C * (C * x),y) = R(x,C * C,y)'. [para(1452(a,2),142(a,1,2))].

6502 x / (C' / x) = (x * C) * x. [para(63(a,1),195(a,2,2)),rewrite([1511(5,R),63(5),1828(3)])].

6518 x / (C / x) = (x * C') * x. [para(1659(a,1),195(a,2,2)),rewrite([16(5,R),1659(5),1538(4)])].

6554 (x * A) * (x * A) = x * (A * (x * A)). [para(143(a,1),256(a,1)),rewrite([256(3),256(5),256(8),1021(10)])].

6610 (x / y) * (y / (x / y)) = x * (y / x). [para(7(a,1),232(a,1,1)),rewrite([104(2)]),flip(a)].

6618 x' * ((x / y) * x') = (x * y)'. [para(232(a,1),32(a,1,2)),rewrite([6174(4),104(3)])].

6638 ((C * x) * y) * (C' / x) = (x * C) * (y / (C * x)). [para(242(a,1),232(a,2)),rewrite([1724(6)])].

6639 (x * C) * (y / (C * x)) = (x * C) * (y / (x * C)). [para(242(a,2),232(a,1,1)),rewrite([1828(6),6638(7)])].

6645 ((x * C') * y) * (C / x) = (x * C') * (y / (x * C')). [para(1538(a,1),232(a,1,2))].

6658 (x * (y / x)) * x = R(x * y,x',x). [para(232(a,1),82(a,1,1))].

6741 (A * A) / x = A * (A * x'). [para(7(a,1),620(a,1,2)),rewrite([293(7),784(9)])].

6745 R(x,A,A)' = x'. [para(824(a,1),620(a,2,2)),rewrite([138(8),34(10)])].

6792 R(x,A,A) = x. [para(6745(a,1),30(a,1,1)),rewrite([30(2)]),flip(a)].

6793 (x * A) * A = x * (A * A). [para(6792(a,1),78(a,1,1)),flip(a)].

6823 (x * (A * A)) * A' = x * A. [para(6793(a,1),6(a,1,1)),rewrite([293(6)])].

6824 (x * A') * (A * A) = x * A. [para(7(a,1),6793(a,1,1)),rewrite([293(4)]),flip(a)].

6830 (A * x) * (y * (A * A)) = A * ((x * (y * A)) * A). [para(6793(a,1),15(a,1,2))].

6831 A * ((x * (A * A)) * A) = A * (x * (A * (A * A))). [para(6793(a,1),15(a,2,2,1)),rewrite([13(8)]),flip(a)].

6850 R(x,A' * A',A * A) = x. [para(82(a,1),6793(a,2)),rewrite([172(4),4610(8),8(7),3(5),82(5),259(4),172(4)]),flip(a)].

6875 (x * (A * A)) * A = (x * A) * (A * A). [para(6793(a,1),6793(a,1,1))].

6893 A * ((x * A) * (A * A)) = A * (x * (A * (A * A))). [back_rewrite(6831),rewrite([6875(7)])].

7049 R(A' * x,x,x') = A' * x. [para(34(a,1),899(a,1,2)),rewrite([1071(7),85(9),260(8)])].

7181 ((C * A') * x) * A = A' * (C * (x * A)). [para(162(a,1),10(a,1,2)),flip(a)].

7183 C * ((x * (C * A')) * A) = A * ((C * A') * (x * C)). [para(13(a,1),162(a,1,2)),rewrite([82(11),259(10)]),flip(a)].

7191 (C * (x * (A * (x * A)))) * y = (x * A) * (C * ((x * A) * y)). [para(162(a,1),57(a,1,1,2)),rewrite([67(7,R),6554(6),122(16)])].

7511 R(A * x,A,C * A') = C' * (A * (C * x)). [para(49(a,1),165(a,1,2,1)),rewrite([249(11),293(8),85(9),260(8)]),flip(a)].

7609 R(x,C * C,C * (C' / y)) = R(x,C / y,C). [para(1769(a,1),90(a,1,2,2)),rewrite([4123(10),1769(8),101(10)]),flip(a)].

7775 ((x * (C' * y)) * z) / ((y * C') * z) = R(x,C' * y,z). [para(1930(a,1),87(a,1,1,2)),rewrite([104(3),113(2),104(13),113(12),1930(20)])].

7790 R(C' * x,y,z) = R(x * C',y,z). [para(1930(a,1),142(a,1,2)),rewrite([104(3),113(2),6469(11),30(10)])].

7791 x / (C' * y) = x / (y * C'). [para(1930(a,1),195(a,1,1)),rewrite([104(3),113(2),6645(13),1930(15)])].

7806 ((x * C') * x) * ((C / x) * y) = (x * C') * (C * y). [para(1934(a,1),68(a,2,2,2)),rewrite([16(8,R),1659(8)])].

7944 R(A * x,x',x) = A * x. [para(749(a,1),2107(a,1,1)),rewrite([30(3)])].

7967 R(A * x',x,x') = A * x'. [para(30(a,1),7944(a,1,2))].

8265 R(A * x,x,x') = A * x. [para(10(a,1),3673(a,1,2)),rewrite([889(5),82(8),259(7)])].

8298 (A * x) / x' = (A * x) * x. [para(8265(a,1),2419(a,1,1))].

8522 (x * (y / z))' * R(x,y / z,z / y) = z / y. [para(182(a,1),10(a,1,2))].

8765 x / (C * (y * (C' * x))) = R(y,C' * x,C)'. [para(4111(a,1),124(a,1,3,1,1)),rewrite([172(9),12(11),6475(12),4883(10),4111(16),172(14),12

(16),246(17),113(11),10(12)]),flip(a)].

8823 C * (x * (C' * (y * x))) = x * (C' * (y * (x * C))). [para(4120(a,1),47(a,2,2,2,2)),rewrite([1382(12,R),16(11,R),532(11)])].

8831 (x * (y * (C * C))) / (y * C) = R(C * x,C',y * (C * C)). [para(4120(a,1),79(a,2,2)),rewrite([1699(3)]),flip(a)].

8843 R(A,C',C * (x * (A * C))) = R(A,x,A * C). [para(4120(a,1),95(a,1,1,2,1)),rewrite([4123(14),16(12),10(15),1957(11),4123(14),16(12)]),fli

p(a)].

8897 (C * x) * (y * (C * x)) = C * ((C * x) * (y * x)). [para(191(a,1),1699(a,1)),rewrite([1699(3),1699(5),1699(10)])].

9118 (x * C) * (y * (x * C)) = C * ((C * x) * (y * x)). [back_rewrite(1277),rewrite([8897(6)]),flip(a)].

9194 C' / (x * (C' * C')) = C / x. [para(82(a,1),4134(a,1,2)),rewrite([172(5),5026(10),172(8)]),flip(a)].

9200 (x / (y * z)) * y = y' * ((y * x) / z). [para(192(a,1),10(a,1,2)),flip(a)].

9201 (x' * y) / (x * z) = x' * ((y / z) * x'). [para(10(a,1),192(a,1,2,1,2)),flip(a)].

9203 x * ((y / (x * z)) * (x * u)) = ((x * y) / z) * u. [para(192(a,1),13(a,1,1)),flip(a)].

9204 (A * x) * ((y / (A * ((x * z) * A))) * (A * x)) = ((A * x) * y) / (z * A). [para(15(a,1),192(a,1,2,1,2))].

9205 C * (C * (x / (C * y))) = (C * x) / y. [para(192(a,1),16(a,1)),rewrite([16(8,R),16(10,R)]),flip(a)].

9207 (x * y) / (x' * z) = x * ((y / z) * x). [para(34(a,1),192(a,1,2,1,2)),flip(a)].

9211 (x' * y) / (C * x) = x' * ((C' * y) * x'). [para(64(a,1),192(a,1,2,1,2)),rewrite([113(3)]),flip(a)].

9220 (A * x) * ((y / (A * (x * A))) * (A * x)) = ((A * x) * y) * A'. [para(49(a,1),192(a,1,2,1,2)),rewrite([293(16)])].

9233 A * (((A' * x) / y) * A) = x / (A' * y). [para(192(a,1),1071(a,1,1)),rewrite([104(5),9200(11),30(7),889(11),104(9),9200(11),30(7),49(12

)]),flip(a)].

9295 (x * (C * y)) / z = (x * (y * C)) / z. [para(1358(a,1),192(a,2,1)),rewrite([9200(5),34(7)])].

9327 (C * (x' * C)) / x = C * (C * (x' * x')). [para(155(a,1),192(a,1,2,1)),rewrite([16(6,R)]),flip(a)].

9339 (C * x) / (C * (C' / y)) = C * (C * (x / (C / y))). [para(1769(a,1),192(a,1,2,1,2)),rewrite([16(6,R)]),flip(a)].

9366 R(A,x / (y * A),y * A) = R(A,y',y * x). [back_rewrite(2233),rewrite([9200(5),293(5),299(10),87(6)]),flip(a)].

9418 (A' * x) * A' = A' * (x * A'). [para(193(a,1),293(a,1)),flip(a)].

9954 (A * x) * (y * (A * x)) = A * (x * ((y * A) * x)). [para(9(a,1),201(a,1,1,2,2,2,1)),rewrite([2(6),6830(7),619(11),195(6)]),flip(a)].

9956 (A * x) * x = A * (x * x). [para(10(a,1),201(a,1,1,2)),rewrite([15(6),619(9),35(4),10(10)]),flip(a)].

10077 ((A * C) * (x * (A * ((C / y) * A)))) / ((C * (C' / y)) * A) = C * (A * ((C * x) * A)). [para(1769(a,1),201(a,1,1,2,2,2,1)),rewrite([9

118(27),16(23),15(26)])].

10113 A * (x * ((A' * ((A * y) / (x * A))) * x)) = ((A * x) * y) * A'. [back_rewrite(9220),rewrite([9954(11),9200(8)])].

10114 A * (x * ((A' * ((A * y) / ((x * z) * A))) * x)) = ((A * x) * y) / (z * A). [back_rewrite(9204),rewrite([9954(12),9200(9)])].

10140 (A * x) / x' = A * (x * x). [back_rewrite(8298),rewrite([9956(7)])].

10163 (x * (A * (x * x))) * y = x * ((A * x) * (x * y)). [para(9956(a,1),13(a,1,1,2))].

10200 (A * (x * x)) * x' = A * x. [para(9956(a,1),85(a,1,1)),rewrite([8265(9)])].

10224 R(A,A * x,x * A) = A. [para(9956(a,1),95(a,1,1,2,1)),rewrite([49(6),12(5),15(12),12(11),6(13)]),flip(a)].

10225 R(A,x,A * (A * A)) = A. [para(9956(a,1),95(a,1,2,2)),rewrite([6875(7),6893(8),6(15),12(7)]),flip(a)].

10253 (A * (x * x)) * (x' * A') = A * (x * A'). [para(9956(a,1),232(a,1,1)),rewrite([889(6),32(13),232(13),293(11)])].

10315 (C * (x * (y * C))) * y' = R(C * (x * C),y,y'). [para(203(a,1),2109(a,1,1)),flip(a)].

10318 R(A,A * (x * A'),x) = A. [para(7(a,1),10224(a,1,3)),rewrite([293(4)])].

10321 R(A,x,A' * (x * A)) = A. [para(34(a,1),10224(a,1,2)),rewrite([231(6),256(6)])].

10333 R(A',x,A * (A * A))' = A. [para(10225(a,1),141(a,1)),flip(a)].

10413 (A * (A * (x * A'))) * x = A * (A * ((x * A') * x)). [para(10318(a,1),78(a,1,1)),rewrite([3816(7)]),flip(a)].

10426 A * ((x * A') * (x * A)) = A * (x * (A' * (x * A))). [para(10321(a,1),78(a,1,1)),rewrite([246(16),293(11)]),flip(a)].

10466 (C' * (x * x)) * y = x * (C' * (x * y)). [para(208(a,2),13(a,1,1))].

10514 (x * y) * (C' * (x * y)) = C' * ((x * y) * (x * y)). [para(208(a,2),78(a,2)),rewrite([78(11)])].

10697 R(x,C * C,C' * y) = R(x,y,C). [para(5745(a,1),80(a,1,1,1,2)),rewrite([4123(8),34(6),100(6),5745(8)]),flip(a)].

10978 R(A * (A * x),x',x) = A * (A * x). [para(6741(a,1),2107(a,1,1)),rewrite([30(4),12(10)])].

11157 R(x * A,A',A') = x * A. [para(6824(a,1),2107(a,2)),rewrite([172(7),2143(9),172(11),6850(16)])].

11160 A * ((x * A') * x) = A * (x * (A' * x)). [para(6824(a,1),198(a,1,1,2,2)),rewrite([10426(8),293(10),232(11),293(9),2424(10),260(9),82(1

5),259(14)]),flip(a)].

11173 (A * (A * (x * A'))) * x = A * (A * (x * (A' * x))). [back_rewrite(10413),rewrite([11160(15)])].

11197 x / (A' * A') = x * (A * A). [para(6850(a,1),79(a,1)),rewrite([12(19),10(18),8(14),23(12)])].

11248 (x * (A' * C')) * (A * C) = R(x,A' * C',A * C). [para(256(a,1),224(a,1,2)),rewrite([1511(5),16(9),1511(15),256(19),16(18)])].

11364 (x * (A * C)) * (A' * C') = R(x,A * C,A' * C'). [para(256(a,1),226(a,1,1,2)),rewrite([16(3),1511(9),256(14),16(13),1511(18)])].

11560 (C * x) * (y * C') = C * ((C' * x) * y). [para(1674(a,1),230(a,1,1)),rewrite([1674(5),113(3),1674(10)]),flip(a)].

11880 (x * y) / (y' * (x / y')) = R(y',x,y)'. [para(231(a,1),138(a,1,2))].

11954 (x * A) * (A' * y) = A * ((A' * x) * y). [para(256(a,1),233(a,1,1)),rewrite([30(9)])].

11955 (x * A') * (A * y) = A' * ((A * x) * y). [para(293(a,1),233(a,1,1))].

11964 (A * x') * (x * y) = x' * ((x * A) * y). [para(749(a,1),233(a,1,1))].

11967 (A' * x') * (x * y) = x' * ((x * A') * y). [para(794(a,1),233(a,1,1))].

11983 (x / y) * (C' * y) = y' * (C' * (y * x)). [para(1511(a,2),233(a,1,2)),rewrite([1511(10,R)])].

12018 (A' * x) * (x' * (A * x)) = x. [para(1052(a,1),233(a,2,2)),rewrite([794(4),30(4),30(10),3(10)])].

12145 (x * C) * (C' * y) = C * ((C' * x) * y). [para(6502(a,1),233(a,1,1)),rewrite([5089(8),104(10),1699(9),7(12),246(12),113(9)])].

12146 (x * C') * (C * y) = C' * ((C * x) * y). [para(6518(a,1),233(a,1,1)),rewrite([7806(8),104(9),113(8),7(12),234(12),1699(11)])].

12157 (A * (x * x)) * (x' * y) = x * ((x' * (A * x)) * y). [para(10140(a,1),233(a,1,1)),rewrite([30(8)])].

12159 R(x,x * A',A * x') = x. [para(10200(a,1),233(a,2,2)),rewrite([293(3),12(4),765(8),10(12)])].

12281 x * ((x' * (A * x)) * A') = A * (x * A'). [back_rewrite(10253),rewrite([12157(8)])].

12312 R(A',x,A * (A * A)) = A'. [para(10333(a,1),30(a,1,1)),flip(a)].

12314 (A' * ((A * x) * y)) / y = R(x,A',A * y). [para(10333(a,1),125(a,1,1,2,1)),rewrite([12312(8),11955(6),12312(15),12312(17),30(12)])].

12316 C' * (A' * (C * (A * x))) = R(x,A',A * C). [para(10333(a,1),165(a,1,2,2,2)),rewrite([12312(10),16(8),11955(9),16(8,R),12312(18),12312(

21),30(16),16(15)])].

12478 R(x,A',A') = x. [para(7(a,1),11157(a,1,1)),rewrite([293(7),82(10),259(9)])].

12481 (x * A') * A' = x * (A' * A'). [para(12478(a,1),78(a,1,1)),flip(a)].

13604 (x * y) * (C' * x') = x * (C' * (y / x)). [para(1511(a,2),246(a,1,2)),rewrite([1511(10,R)])].

13683 x * (C * (x' * (x' * (C * y)))) = C * (C * (x' * y)). [para(4117(a,1),246(a,1,1)),rewrite([12(6),9327(12),70(14),12(13)]),flip(a)].

13836 (x * C') * (y * C) = C' * ((C * x) * y). [para(71(a,2),247(a,1,1)),rewrite([34(8),16(13,R),9(13),3(11)])].

13901 R(x,C',C * y)' = R(x,C',y)'. [back_rewrite(6410),rewrite([13836(6),6129(7)])].

14542 (A' * (C / x)) * (C * ((C' * x) * A)) = C. [para(158(a,1),817(a,1,1,2))].

14578 C' * (x' * (C * (x * A))) = R(A',x',C * (x * A))'. [para(817(a,1),138(a,1,2)),rewrite([113(8)])].

14784 x / (C * ((A' * C') * x)) = R(A,C,(A' * C') * x). [para(1012(a,1),18(a,1,1))].

14792 A * (C * (A * ((A' * C') * (x * C')))) = C' * (A * x). [para(1012(a,1),59(a,2,2,1)),rewrite([231(17),256(17),1511(16),10(17),68(15),46

10(24),1511(23),11955(24),1511(23,R),34(25)])].

14812 (C * ((A' * C') * x)) / x = R(A,C,(A' * C') * x)'. [para(1012(a,1),138(a,1,2))].

14813 C * (A * (C * ((A' * C') * (x * A)))) = x / (A' * C'). [para(1012(a,1),195(a,1,1)),rewrite([1828(4),293(4),1511(5),9118(20),16(10),460

6(18),246(19),293(11),246(18),113(13),1511(14)]),flip(a)].

14841 C' * ((A * C) * (x * (A * (A * C)))) = A * ((x * (A * C)) * A). [para(1014(a,1),59(a,2,2,1)),rewrite([34(7),49(10),16(9)])].

14844 C' * ((C * A') * (C * (A * ((C * x) * A)))) = x * (A * (C * C)). [para(71(a,2),1014(a,1,2)),rewrite([9118(14),16(10),15(13),12146(16),

16(21,R),1382(21)])].

14858 (A * (x * A)) / ((A' * C') * (((A * C) * x) * A)) = R(A',C',((A * C) * x) * A)'. [para(1014(a,1),95(a,1,1,2,1)),rewrite([141(30)])].

15067 (A * (C * C)) / x = C * (A * (C * x')). [para(1058(a,1),200(a,1,1,2,2)),rewrite([16(15),11955(16),16(15,R),4243(18)])].

16312 (C' * ((C * x) * A')) * A = R(x,C',C * A'). [para(16(a,1),295(a,1,1,2)),rewrite([16(7,R),12146(8)])].

16328 A' * (C' * (A * (x * C))) = R(x,C,A' * C'). [para(1511(a,1),295(a,1,1,2)),rewrite([30(3),4610(10),1511(9),11955(10),1511(9,R),30(13),1

511(16)])].

16405 (x * (A * (y * A))) * A' = x * ((A * (y / x)) * x). [para(7(a,1),297(a,1,1,2,2,1))].

16451 (C' * (A * ((C' * x) * A))) * A' = C' * (C' * (A * x)). [para(1511(a,2),297(a,1,1,2,2,1)),rewrite([1511(20,R)])].

16520 (x * A') * ((A * y) * (x * A')) = x * (y * (x * A')). [para(233(a,1),297(a,1,1)),rewrite([293(6),15(11),2276(10),259(9),10(7),13(5),29

3(7),293(12)]),flip(a)].

16598 (x * (y * A')) * A = A' * ((A * x) * y). [para(299(a,1),10(a,1,2)),flip(a)].

16618 (A * R(x,y,A')) * y = A * (x * y). [para(78(a,1),299(a,1,2,1)),rewrite([82(7),259(6)]),flip(a)].

16636 (A * (x / y)) * y = y' * ((y * A) * x). [para(233(a,1),299(a,1,2,1)),rewrite([16598(9),11964(8),34(10)]),flip(a)].

16641 C * (A * (A * x)) = A * ((A * C) * x). [para(248(a,1),299(a,1,2,1)),rewrite([30(4),30(6),293(5),49(10),16598(9),34(10),30(10),16(12,R)

]),flip(a)].

16657 A' * (C' * ((A * C) * x)) = R(x,C',C * A'). [back_rewrite(16312),rewrite([16598(10),12146(9),16(7)])].

16666 C * (A' * (C * (A * x))) = A * ((C * A') * (x * C)). [back_rewrite(7183),rewrite([16598(8),16(7,R)])].

16667 R(x,y * A',A) = R(x,A',A * y). [back_rewrite(2242),rewrite([16598(6),12314(7)]),flip(a)].

16673 (x * (A * (y * A))) * A' = (x * A) * y. [back_rewrite(16405),rewrite([16636(12),34(14)])].

16741 (A * C') * (C' * x) = C' * (C' * (A * x)). [back_rewrite(16451),rewrite([16673(13),1511(4)])].

16760 (x * A) * (y * x) = x * ((A * y) * x). [back_rewrite(297),rewrite([16673(9)])].

17618 R(A,x,A * x) = A. [para(337(a,1),18(a,1,1)),rewrite([6(9)]),flip(a)].

17677 R(A',x,x)' = A. [para(34(a,1),17618(a,1,3)),rewrite([141(5)])].

17686 R(A',x,x) = A'. [para(17677(a,1),30(a,1,1)),flip(a)].

17687 (A' * x) * x = A' * (x * x). [para(17686(a,1),78(a,1,1)),flip(a)].

18273 C * (x * (C' * (C' * (x * (C * y))))) = x * (x * y). [para(63(a,1),415(a,1,1,2,2,2)),rewrite([128(6),12(2)]),flip(a)].

18478 R(x,y,C * (z * z)) = R(x,y,z * (z * C)). [para(12(a,1),3961(a,2,3))].

18492 R(x,y,z' * (C * z')) = R(x,y,C * (z' * z')). [para(177(a,2),3961(a,1,3)),rewrite([16(11,R)])].

18592 R(x,C * C,y) = R(x,y * C,C). [para(16(a,1),4130(a,2,2))].

18597 R(x,y * (C * y),C) = R(x,C * C,y * y). [para(67(a,1),4130(a,2,2)),flip(a)].

18634 A * ((C * (A * (C * x))) * A) = A * (C * (C * (A * (x * A)))). [para(16(a,1),419(a,1,2,1,1,2)),rewrite([1382(6),4123(7)])].

19215 C' * ((C * A') * (C * x)) = A' * (A' * ((A * C) * x)). [para(1014(a,1),423(a,2,2,2,2)),rewrite([16(13,R),1659(13),12146(10),12481(9),1

0(10),12(10),12146(20)]),flip(a)].

19271 A' * (C * (C * (A * (x * A)))) = x * (A * (C * C)). [back_rewrite(14844),rewrite([19215(16),467(14),18634(14),10(15)])].

19360 R(x,x * (C * y),C) = R(x,x * (y * C),C). [para(424(a,1),100(a,1,1)),rewrite([16(11,R),4090(12)]),flip(a)].

20219 R(x,A * (A * x),A) = x. [para(49(a,1),428(a,1,2)),rewrite([49(12),6(14)]),flip(a)].

20246 R(x',A * (x * A),A') = x'. [para(1053(a,1),428(a,1,1,2,2)),rewrite([3(5),85(10),300(9),49(8),232(11),293(9),85(10),260(9),6(7),85(8),3

00(7),49(6)]),flip(a)].

21297 (x / y) * ((y / x) / x) = y' * (y / x). [para(7(a,1),6173(a,1,1,1)),rewrite([104(5)]),flip(a)].

21527 x * (C' * (x * ((C * x') * y))) = (C' / x') * (R(C,x',x) * y). [para(6182(a,1),233(a,1,1)),rewrite([13(9),1724(13),82(17)])].

21540 R(x,x * (y' * C),C) = R(x,x * (C * y'),C). [para(444(a,1),100(a,1,1)),rewrite([16(13,R),4089(14)]),flip(a)].

21843 R(A' * x',x',x) = A' * x'. [para(30(a,1),7049(a,1,3))].

21939 (x * (C' * y)) / (y * C') = x. [para(7791(a,1),6(a,1))].

21941 (x / (y * C')) * (C' * y) = x. [para(7791(a,1),7(a,1,1))].

22323 R(A * (C / x),C' * x,C / x) = A * (C / x). [para(158(a,1),7967(a,1,1,2)),rewrite([158(11),158(15)])].

22775 ((A * C) * x) * A = C * (A * (x * A)). [para(122(a,1),467(a,1,1)),rewrite([11955(14),231(16),256(16),34(17)]),flip(a)].

22782 R(A * x,A,A * (x * A)) = A * x. [para(467(a,1),92(a,1,1)),rewrite([45(8),49(15),49(14),468(16),3213(16)])].

22786 C * (C * (A * (x * A))) = A * (C * ((x * C) * A)). [para(3710(a,1),467(a,1,1)),rewrite([12(8),70(18),16666(18),49(20),7181(19),34(20)]

)].

22790 R(A',C',A * (x * A))' = R(A,C',(C * x) * A). [back_rewrite(14858),rewrite([22775(15),12146(16),11955(15),15(14),10(15),3791(12),22775(

18),13901(20)]),flip(a)].

22791 C * ((x * C) * A) = x * (A * (C * C)). [back_rewrite(19271),rewrite([22786(10),10(11)])].

22849 ((x' * (A * x)) * y) / (x * y) = R(A' * x,x' * (A * x),y)'. [para(12018(a,1),138(a,1,2,1))].

22850 R(A' * x,x' * (A * x),y)' = R(x' * A,x,y). [para(12018(a,1),142(a,1,2)),rewrite([1071(4)]),flip(a)].

22863 ((x' * (A * x)) * y) / (x * y) = R(x' * A,x,y). [back_rewrite(22849),rewrite([22850(16)])].

22986 (A * ((x * C) * (A * A))) / (A * (A * C)) = R(A * x,A * C,A). [para(73(a,1),470(a,1,1,1)),rewrite([13(8),16(12)])].

22987 R(R(x,A,y),A * y,A) = x. [para(78(a,1),470(a,1,1,1)),rewrite([1021(5),6(10)]),flip(a)].

23049 R(R(x,A,A' * y),y,A) = x. [para(34(a,1),22987(a,1,2))].

23050 R(R(x,A,C * A'),C,A) = x. [para(122(a,1),22987(a,1,2))].

23055 R(R(x,A,C * y),A * (y * C),A) = x. [para(1358(a,1),22987(a,1,2))].

23148 R((x * (A' * y)) / y,y,A) = x * A'. [para(79(a,1),23049(a,1,1)),rewrite([34(9),293(9)])].

23162 A * ((x * (A * C)) * A) = A * (C * (x * (A * A))). [para(128(a,1),514(a,2,2,2,2)),rewrite([16(5),1511(10,R),10(10)])].

23168 C' * ((A * C) * (x * (A * (A * C)))) = A * (C * (x * (A * A))). [back_rewrite(14841),rewrite([23162(21)])].

23319 C * (x * (C * (y * x))) = x * (C * (y * (x * C))). [para(518(a,1),1659(a,1,2)),rewrite([1659(7)])].

23765 R(x,x * A,A' * x') = x. [para(17687(a,1),2273(a,1,1,1)),rewrite([1071(7),172(4),30(2),30(2),12(3),21843(9),807(8)])].

24137 (x * C) * (A * C) = C * (C * (x * A)). [para(181(a,1),528(a,1,2,2,2)),rewrite([256(6),16(5),82(12),259(11),9118(10),16(6),15(9),1512(1

1),4638(6),256(12),16(11),231(17),256(17),22775(16),1512(17)]),flip(a)].

24356 R(A * x,A * x',A') = A * x. [para(6173(a,1),20246(a,1,2,2)),rewrite([889(3),784(5),30(3),749(7),10(9),889(11),784(13),30(11)])].

24502 x * (C' * y) = x * (y * C'). [para(8(a,1),540(a,2,2,2,2)),rewrite([34(8),3(8)]),flip(a)].

24745 R(x,C' * y,z) = R(x,y * C',z). [para(21939(a,1),79(a,1,1)),rewrite([7775(14)]),flip(a)].

24793 (x * (C' * C')) * y = C' * (x * (C' * y)). [para(21941(a,1),529(a,1,2,2,2)),rewrite([1511(14,R),63(14),11983(14),2000(17)]),flip(a)].

24807 R(x,C' * C',y * C) = R(x,y,C'). [back_rewrite(2808),rewrite([24793(9),63(7),1673(8)]),flip(a)].

25344 (A * x) / (y * A) = A * ((x * A') / y). [para(7(a,1),619(a,1,1,2)),rewrite([293(8)])].

25345 (A * (x * A)) / y = A * (x / (y * A')). [para(7(a,1),619(a,1,2)),rewrite([293(8)])].

25346 (x * A) / (A * (y * A)) = (x / y) * A'. [para(619(a,1),104(a,1,1)),rewrite([889(4),104(2)]),flip(a)].

25369 (x * A) / (y * A) = A * ((A' * x) / y). [para(231(a,1),619(a,1,1,2)),rewrite([256(6),34(7)])].

25390 ((A * x) * y) / (z * A) = A * ((x * (y * A')) / z). [back_rewrite(10114),rewrite([25344(9),10(11),9200(7),34(9)]),flip(a)].

25391 ((A * x) * y) * A' = A * (x * (y * A')). [back_rewrite(10113),rewrite([25344(8),10(10),7(6)]),flip(a)].

25402 A * R(C * A',A,x) = R(C,A,x * A). [back_rewrite(3921),rewrite([25345(11),232(10),293(8),85(9),260(8),2144(6)])].

25408 A * ((x * C') / ((x * (A * C')) * A')) = R(A,x,A * C'). [back_rewrite(3773),rewrite([25345(13)])].

25411 A * (x / ((C' * ((x * C) * A)) * A')) = R(A,C',(x * C) * A). [back_rewrite(3737),rewrite([25345(12)])].

25428 R(x / (A * y),A * y,A) = (x / y) * A'. [back_rewrite(2150),rewrite([25346(14)])].

25429 ((x * (A * y)) / y) * A' = R(x,A * y,A). [back_rewrite(470),rewrite([25346(10)])].

25430 C * (A * ((C * x) * A)) = A * (C * (C * (x * A))). [back_rewrite(10077),rewrite([25390(19),16673(12),9339(14),6(11)]),flip(a)].

25535 (x * C) * (y * C') = C * ((C' * x) * y). [para(24502(a,1),242(a,2)),rewrite([246(6),113(3)]),flip(a)].

25653 (C * ((C' * x) * A)) * A' = R(x,C,A * C'). [back_rewrite(836),rewrite([25535(7)])].

26799 R(A * R(x,C,A),A,C) = A * x. [para(2041(a,1),468(a,1,1,2)),rewrite([6208(10),85(10),260(9),63(6)]),flip(a)].

26804 R(A * x,A * C,A) = A * R(x,C,A). [para(26799(a,1),22987(a,1,1))].

26806 (A * ((x * C) * (A * A))) / (A * (A * C)) = A * R(x,C,A). [back_rewrite(22986),rewrite([26804(21)])].

26808 R(x,C' * y,C) * y = C * (x * (C' * y)). [para(34(a,1),2042(a,1,2))].

26813 R(R(x,y,C),C * y,C) = R(x,y,C * C). [para(2042(a,1),100(a,1,1,2)),rewrite([16(9,R),4529(10)]),flip(a)].

26848 R((x / y) * A',A,y) = x / (A * y). [para(293(a,1),2104(a,1,1))].

26849 x / (A * (y * A)) = ((x * A') / y) * A'. [para(49(a,1),2104(a,2,2)),rewrite([293(2),25428(10)]),flip(a)].

26864 R(R(x,C * y,C'),y,C) = x. [para(3952(a,1),2104(a,2)),rewrite([113(5),2249(7)])].

26923 R(x / y,y,A) = A * ((A' * x) / y). [para(2104(a,1),23049(a,1,1)),rewrite([34(5),293(9),9200(10),30(6)])].

26935 R(R(x,C' * y,C),y,C') = x. [para(21939(a,1),2104(a,2)),rewrite([1699(7),2234(7)])].

26987 R(R(x,y,C'),C' * y,C) = x. [para(34(a,1),26864(a,1,1,2))].

26994 R(R(x,y,C'),y * C',C) = x. [para(1659(a,1),26864(a,1,1,2))].

26997 R((x * C') / y,y,C) = x / (C * y). [para(79(a,1),26864(a,1,1)),rewrite([1511(8,R),10(8)])].

27013 R(x,A * C,C') = R(x,A * C,A). [para(26864(a,1),22987(a,1,1)),rewrite([16(8)]),flip(a)].

27045 R(R(x,y,C),C * y,C') = x. [para(10(a,1),26935(a,1,1,2))].

27046 R(R(x,y,C),y * C,C') = x. [para(63(a,1),26935(a,1,1,2))].

27047 R(R(x,y * C',C),y,C') = x. [para(71(a,2),26935(a,1,1,2)),rewrite([34(8),16(9,R),9(9),3(7)])].

27190 R(R(x,y,C')',C' * (x * y),C) = x'. [para(26987(a,1),142(a,2,1)),rewrite([2084(11)])].

27450 R(C' * x,C,y) = R(C / x,x,y)'. [para(2118(a,2),104(a,1,1)),rewrite([2119(8)]),flip(a)].

27522 (C * x) / (A * C) = R(x * A',A,C). [para(293(a,1),2120(a,1,1)),flip(a)].

27544 (C * ((x * C) * y)) / (C * (x * y)) = R(R(C,x,y),x * y,C). [para(97(a,1),2120(a,1,1)),rewrite([16(13,R)]),flip(a)].

28599 R(x',A * x,x') = x'. [para(768(a,1),523(a,1,1,2,2)),rewrite([3(4),765(12),12159(11),85(7),300(6),293(5),85(6),260(5),765(11),12159(10)

]),flip(a)].

28602 R(x,A * x',x) = x. [para(30(a,1),28599(a,1,1)),rewrite([30(5),30(6)])].

28627 (x * (A * x')) * x = x * A. [para(28602(a,1),78(a,1,1)),rewrite([82(4),294(3)]),flip(a)].

28631 (x * A) / x = x * (A * x'). [para(28627(a,1),6(a,1,1))].

29173 R(x / (A * C),A * C,A' * C') = x * (A' * C'). [para(3954(a,1),807(a,1,1)),rewrite([16(13)]),flip(a)].

29284 R(x',A' * x,x') = x'. [para(809(a,1),523(a,1,1,2,2)),rewrite([3(5),807(14),23765(13),85(9),893(8),256(7),82(6),259(5),807(12),23765(11

)]),flip(a)].

29288 R(x,A' * x',x) = x. [para(30(a,1),29284(a,1,1)),rewrite([30(6),30(7)])].

29312 (x * (A' * x')) * x = x * A'. [para(29288(a,1),78(a,1,1)),rewrite([82(5),987(4)]),flip(a)].

29558 (x * C) / (y * x) = R(C' * y,C,x)'. [para(6450(a,1),2118(a,1)),rewrite([113(2)]),flip(a)].

29750 (x / y) * x' = x * (x * y)'. [para(6618(a,1),10(a,1,2)),rewrite([30(2)]),flip(a)].

29766 (x * y)' * (x * z) = x' * ((x / y) * z). [para(6618(a,1),234(a,1,1)),rewrite([29750(8),195(10),6173(8),34(9)])].

29801 (x * y) * ((x * y) * y)' = x * (x * y)'. [para(6(a,1),29750(a,1,1)),flip(a)].

29968 R(C / x,x * (C' * C'),y) = R(x * C',C',y)'. [para(9194(a,1),6450(a,1,1)),rewrite([1699(18),5028(17)])].

29976 C * (C * (A * (C' * (x * C')))) = R(A * x,A,C). [para(3953(a,1),858(a,1,1,2,2,1)),rewrite([16(9),27522(10),232(7),293(5),85(6),260(5),

4419(11),16(16,R)]),flip(a)].

29977 C * (C * (A * (C' * x))) = A * ((x * A) * (C * A')). [para(247(a,1),858(a,1,1,2,2,1)),rewrite([16(8,R),10(9),25430(8),16(11),6208(12),

70(12),10(13),16(17,R)]),flip(a)].

29983 A * (((x * C') * A) * (C * A')) = R(A * x,A,C). [back_rewrite(29976),rewrite([29977(12)])].

30507 A * (C * ((A' * C') * (A' * (C * x)))) = (C * A') * x. [para(1012(a,1),895(a,1,2,2)),rewrite([1538(6),256(4),16(3),1538(17),256(15),16

(14),232(17),293(15),122(17),1663(14),246(15),293(4),246(14),113(6),1511(7),1538(21),256(19),16(18),232(32),293(30),122(32),16(28,R),1698(28)

,246(24),293(19),12481(23),670(24),16(19,R)])].

30642 A * ((A' * (x * y)) / y) = R(x,A',A * (y * A)). [para(2(a,1),913(a,1,1,2,2,1)),rewrite([26(2),2(4),11955(8),15(7),10(8),25369(6),26(9)

,2(11),2(12)])].

30644 (C' * (A * ((C * x) * A))) / (x * A) = R(A,x,A * C). [para(1660(a,1),913(a,1,1,1)),rewrite([30(15),1511(18),141(25),22790(24),70(21),1

6(19),8843(22)])].

31134 A * (A * (C' * (A' * x))) = (A * C') * x. [para(34(a,1),953(a,1,2)),rewrite([1511(13,R)]),flip(a)].

31303 (A * (A * (x * C))) / (A * x) = A * C. [para(971(a,1),6(a,1,1))].

31306 A * (A * (C * (A' * x))) = (A * C) * x. [para(34(a,1),971(a,1,2)),rewrite([16(11,R)]),flip(a)].

31403 R(x,A,x * A) = x. [para(34(a,1),22782(a,1,1)),rewrite([231(7),256(7),34(8),34(9)])].

31427 R(A * x',x,x) = A * x'. [para(31403(a,1),6450(a,2,1)),rewrite([749(2),293(5),82(8),259(7),293(6),784(8)])].

31452 R(A * x,x',x') = A * x. [para(30(a,1),31427(a,1,1,2)),rewrite([30(8)])].

31492 (A * x) * (x' * x') = A * x'. [para(31452(a,1),78(a,1,1)),rewrite([85(10),300(9)])].

31535 (C * (x * A)) * A = x * (A * (A * C)). [para(16(a,1),1021(a,2,2,2)),rewrite([16(4,R)])].

31670 R(A,x * (A * (y * A)),A') = A. [para(9(a,1),1026(a,1,1,2,2)),rewrite([3(6),16673(13),6(9)]),flip(a)].

31678 R(A,x,A') = A. [para(7(a,1),31670(a,1,2))].

31681 R(A',x,A')' = A. [para(31678(a,1),141(a,1)),flip(a)].

31686 R(A',x,A') = A'. [para(31681(a,1),30(a,1,1)),flip(a)].

32001 R(A * x,A,x' * A') = A * x. [para(24356(a,1),18(a,2)),rewrite([25391(9),232(7),293(5),232(15),293(13),468(16)])].

32154 A * ((x * (y * (A' * A'))) * A) = (A * x) * (y * A'). [para(8(a,1),1079(a,2,2,2)),rewrite([10(9),12481(7),3(18)])].

32157 C' * ((A * C) * (x * C)) = C * (A * x). [para(1730(a,1),1079(a,1,2,1)),rewrite([16598(8),16(7,R),34(9),256(10),1511(9),1663(18),21527(

18),256(9),1511(8),259(13),12146(13),16(9)]),flip(a)].

32241 R(x,A * C,A) * A = C' * (x * (A * C)). [para(27013(a,1),78(a,1,1)),rewrite([1511(11,R),63(11),1511(14,R)])].

32245 x / (A * (A * C)) = (C' * (x * A')) * A'. [para(2104(a,1),27013(a,2)),rewrite([293(2),27013(13),25428(12),113(5),49(14),16(13)]),flip(

a)].

32247 C' * ((A * C) * x) = A * R(x,C,A). [back_rewrite(26806),rewrite([32245(14),232(13),293(11),6823(12),16673(12),1511(4),13836(7),16(5)])

].

32248 A * R(x * C,C,A) = C * (A * x). [back_rewrite(32157),rewrite([32247(9)])].

32251 A * R(x * (A * (A * C)),C,A) = A * (C * (x * (A * A))). [back_rewrite(23168),rewrite([32247(13)])].

32253 R(x,C',C * A') = R(x,C,A). [back_rewrite(16657),rewrite([32247(9),10(8)]),flip(a)].

32258 C' * ((C * x) * A') = R(x,C,A) * A'. [para(32253(a,1),78(a,1,1)),rewrite([10(10),12146(14)]),flip(a)].

32259 A' * (C * (A * x)) = R(C * x,C,A). [para(32253(a,1),79(a,1)),rewrite([1699(3),10(17),256(13),16598(12),16(11,R)]),flip(a)].

32260 (x * (C' * (x * (C * A')))) * A = R(x * x,C,A). [para(32253(a,1),88(a,2)),rewrite([1663(9),10(16),256(12)])].

32272 C' * R(C * x,C,A) = R(x,A',A * C). [back_rewrite(12316),rewrite([32259(9)])].

32638 R(A,C,C' * (x * (A * C'))) = R(A,x,A * C'). [para(1127(a,1),87(a,1,1)),rewrite([30(4),34(9),25345(13),25408(14),30(10)]),flip(a)].

32639 C' * ((C * x) * A) = C * (x * (A * C')). [para(3710(a,1),1127(a,1,1)),rewrite([12(12),34(11),246(21),113(15),10(16),4610(18),3173(19),

13836(14)]),flip(a)].

32704 C * (A * R(x,C,A)) = (A * C) * x. [para(29312(a,1),945(a,1,1,1)),rewrite([82(6),259(5),1659(12),16(9,R),82(11),259(10),12146(8),16(6),

32247(8),1659(14),16(11,R),82(13),259(12),1659(16),8(13),3(11),16(10)])].

33146 C' * (x * (C * (C * (x * y)))) = x * (x * (C * y)). [para(1185(a,1),233(a,2,2,1)),rewrite([113(5),126(6),12(4),423(12)]),flip(a)].

33478 R(x,A,x') = x. [para(34(a,1),32001(a,1,1)),rewrite([1071(5),85(7),260(6),34(8)])].

33724 (C * (A * x)) / R(x * C,C,A) = A. [para(32248(a,1),6(a,1,1))].

33725 C * (A * (C' * x)) = A * R(x,C,A). [para(7(a,1),32248(a,1,2,1)),rewrite([113(9)]),flip(a)].

33730 A * R(C * x,C,A) = C * (A * x). [para(16(a,2),32248(a,1,2,1))].

33760 A * R(x * (A * C'),C,A) = A * (C' * (x * A)). [para(532(a,1),32248(a,2)),rewrite([1511(7),16(11,R),34(11)])].

33764 R(C * (A * x),A,C) = A * (x * C). [para(32248(a,1),26799(a,1,1))].

33780 A * ((x * A) * (C * A')) = (A * C) * x. [back_rewrite(29977),rewrite([33725(8),32704(7)]),flip(a)].

33788 C * ((A * C') * x) = R(A * x,A,C). [back_rewrite(29983),rewrite([33780(12),25535(7),1511(5)])].

33891 ((A * C) * x) / (A * R(x,C,A)) = C. [para(32704(a,1),6(a,1,1))].

33892 (A * R(x,C,A)) / ((A * C) * x) = C'. [para(32704(a,1),32(a,1,2))].

33904 (A * C) * (x * C) = C * (C * (A * x)). [para(1358(a,1),32704(a,2)),rewrite([33730(8)]),flip(a)].

33905 (A * C) * (C * x) = C * (C * (A * x)). [para(1358(a,2),32704(a,2)),rewrite([32248(8)]),flip(a)].

34236 A * (C * (A' * x)) = R(C * x,A,C). [para(34(a,1),33764(a,1,1,2)),rewrite([16(11,R)]),flip(a)].

34237 R(A * (x * (A * C)),A,C) = A * (C * (x * A)). [para(71(a,1),33764(a,1,1)),rewrite([16(14,R)])].

34252 A * R(C * x,A,C) = (A * C) * x. [back_rewrite(31306),rewrite([34236(8)])].

34415 A' * ((A * C) * x) = R(C * x,A,C). [para(34252(a,1),10(a,1,2))].

34420 A * R(x,A,C) = R(A * x,A,C). [para(34(a,1),34252(a,1,2,1)),rewrite([12145(12),1511(10),33788(12)])].

34431 R(A * (C * x),A,C) = (A * C) * x. [para(242(a,2),34252(a,2)),rewrite([34420(7),16(10)])].

34454 R(A * (x * C),A,C) = (A * C) * x. [para(1268(a,1),34252(a,1,2)),rewrite([34420(7)])].

34496 R(A * x,A,C) / R(x,A,C) = A. [para(34420(a,1),6(a,1,1))].

34497 A' * R(A * x,A,C) = R(x,A,C). [para(34420(a,1),10(a,1,2))].

34500 R(x,A,C) / R(A * x,A,C) = A'. [para(34420(a,1),32(a,1,2))].

34578 R(A * (x * C'),A,C) / R(C' * x,A,C) = A. [para(24502(a,1),34496(a,1,1,1))].

34581 (A * x) / R(R(x,C,A),A,C) = A. [para(26799(a,1),34496(a,1,1))].

34603 A * (x / R(R(x,C,A),A,C)) = A. [para(34581(a,1),2149(a,1,1)),rewrite([469(9)]),flip(a)].

34613 x / R(R(x,C,A),A,C) = 0. [para(34603(a,1),10(a,1,2)),rewrite([8(4)]),flip(a)].

34635 R(R(x,C,A),A,C) = x. [para(34613(a,1),7(a,1,1)),rewrite([2(8)])].

34640 C * (R(x,C,A) * A) = x * (A * C). [para(34635(a,1),78(a,1,1)),rewrite([16(11,R)]),flip(a)].

34641 R(x,A * C,A) = R(x,C,A). [para(34635(a,1),22987(a,1,1))].

34642 R(x,A,C * A') = R(x,A,C). [para(23049(a,1),34635(a,1,1)),rewrite([16(8,R)]),flip(a)].

34643 R(x / (A * C),A,C) = C' * (x * A'). [para(2104(a,1),34635(a,1,1)),rewrite([16(3),293(9),113(12)])].

34644 R(A * (C' * x),A,C) = C' * (A * x). [para(2149(a,1),34635(a,1,1)),rewrite([113(3),113(12)])].

34647 C' * (x * (A * C)) = R(x,C,A) * A. [back_rewrite(32241),rewrite([34641(5)]),flip(a)].

34650 R(x,A * C,C') = R(x,C,A). [back_rewrite(27013),rewrite([34641(11)])].

34651 A * R(x,C,A) = R(A * x,C,A). [back_rewrite(26804),rewrite([34641(7)]),flip(a)].

34653 R(R(x,A,C),C,A) = x. [back_rewrite(23050),rewrite([34642(6)])].

34655 C' * (A * (C * x)) = R(A * x,A,C). [back_rewrite(7511),rewrite([34642(8)]),flip(a)].

34671 R(A * x,C,A) / ((A * C) * x) = C'. [back_rewrite(33892),rewrite([34651(5)])].

34672 ((A * C) * x) / R(A * x,C,A) = C. [back_rewrite(33891),rewrite([34651(9)])].

34678 R(A * (x * (A * C')),C,A) = A * (C' * (x * A)). [back_rewrite(33760),rewrite([34651(10)])].

34680 R(A * (C * x),C,A) = C * (A * x). [back_rewrite(33730),rewrite([34651(7)])].

34683 C * (A * (C' * x)) = R(A * x,C,A). [back_rewrite(33725),rewrite([34651(12)])].

34684 C * R(A * x,C,A) = (A * C) * x. [back_rewrite(32704),rewrite([34651(6)])].

34689 R(A * (x * (A * (A * C))),C,A) = A * (C * (x * (A * A))). [back_rewrite(32251),rewrite([34651(11)])].

34692 C' * ((A * C) * x) = R(A * x,C,A). [back_rewrite(32247),rewrite([34651(12)])].

34695 (C * R(x,A,C)) * A = x * (A * C). [para(34653(a,1),78(a,1,1)),rewrite([16(3),16(9,R)]),flip(a)].

34696 R(x / (A * C),C,A) = (C' * x) * A'. [para(2104(a,1),34653(a,1,1)),rewrite([113(9),293(12)])].

34697 R(R(A * x',x,C)',C,A) = x * A'. [para(6450(a,1),34653(a,1,1)),rewrite([749(2),293(11)])].

34702 (x * A) * (C * A') = C * R(x,A,C). [para(34642(a,1),78(a,1,1)),rewrite([122(9),16(5,R)]),flip(a)].

34703 C' * (x * (C * A')) = R(x * A',A,C). [para(34642(a,1),79(a,1)),rewrite([293(2),122(17),113(13)]),flip(a)].

34704 C' * (A * (x * C)) = R(A * x,A,C). [para(34642(a,1),468(a,2)),rewrite([122(7),122(10),113(6)])].

34708 A * (C * R(x,A,C)) = (A * C) * x. [back_rewrite(33780),rewrite([34702(8)])].

34711 (x * R(x * A',A,C)) * A = R(x * x,C,A). [back_rewrite(32260),rewrite([34703(8)])].

34714 R(x,C,A' * C') = R(x,A,C). [back_rewrite(16328),rewrite([34704(9),34497(8)]),flip(a)].

34719 A' * R(A * x,C,A) = R(x,C,A). [para(34651(a,1),10(a,1,2))].

34727 A * ((C * R(x,C,A)) * A) = (C * (A * x)) * A. [para(34651(a,1),73(a,1,1)),rewrite([2041(9),16(4,R),16(12,R)]),flip(a)].

34734 R(A * x,C,A) * A' = A * (R(x,C,A) * A'). [para(34651(a,1),232(a,1,1)),rewrite([293(14)])].

34762 R(A * (C' * x),C,A) = R(A * (x * C'),C,A). [para(24502(a,1),34651(a,2,1)),rewrite([34651(8)])].

34773 R(A * (C' * x),C,A) = A * R(C / x,x,A)'. [para(6450(a,1),34651(a,1,2)),rewrite([113(10)]),flip(a)].

34789 C * ((C' * x) * A') = R(x,A,C) * A'. [para(34714(a,1),78(a,1,1)),rewrite([1659(10),25535(14)]),flip(a)].

34790 A' * (C' * (A * x)) = R(C' * x,A,C). [para(34714(a,1),79(a,1)),rewrite([113(2),1659(19),256(15),4610(14),1511(13),11955(14),1511(13,R)

]),flip(a)].

34839 C * (C * (A * (C' / x))) = R(A * (C / x),A,C). [para(1769(a,1),34431(a,1,1,2)),rewrite([33905(16)]),flip(a)].

34841 R(R(C * x,A,C),A,C) = A * ((C * A') * x). [para(246(a,1),34431(a,2)),rewrite([34236(7),293(12)])].

34843 R((A * C) * x,C,A) = A * (C * x). [para(34431(a,1),22987(a,1,1)),rewrite([34641(9)])].

34855 A' * R(x,A,C) = R(A' * x,A,C). [para(34(a,1),34497(a,1,2,1))].

34858 R(x * (A * C),A,C) = C * (x * A). [para(71(a,2),34497(a,1,2,1)),rewrite([33764(11),16(7,R),10(9)]),flip(a)].

34869 R(x * (x * (A * C)),A,C) = C * (x * (x * A)). [para(422(a,2),34497(a,1,2,1)),rewrite([33764(12),16(8,R),10(10)]),flip(a)].

34938 (x * (A * C)) / (R(x,C,A) * A) = C. [para(34640(a,1),6(a,1,1))].

34967 C' * R(C * x,A,C) = C * R(C' * x,A,C). [para(2104(a,1),34640(a,1,2,1)),rewrite([16(4),9200(7),113(7),34790(9),293(10),113(13),247(18),

16598(17),34415(17)]),flip(a)].

34981 (C * (A * x)) * A = A * (C * (x * A)). [para(34640(a,1),34431(a,1,1,2)),rewrite([34237(9),15(15),34727(15)]),flip(a)].

34996 R(C,R(A * x,C,A),y) = R(C',(A * C) * x,y)'. [para(34672(a,1),6450(a,1,1)),rewrite([34671(17)])].

35014 C * (A * (x * (C' * C'))) = R(A * (x * C'),C,A). [para(5028(a,1),34680(a,1,1,2)),flip(a)].

35019 A * ((C * A') * x) = C * R(x,C,A). [para(34(a,1),34684(a,1,2,1)),rewrite([246(12),293(9)]),flip(a)].

35056 (A * C) * R(x,A,C) = C * (A * x). [para(34420(a,1),34684(a,1,2,1)),rewrite([34653(9)]),flip(a)].

35060 R(R(C * x,A,C),A,C) = C * R(x,C,A). [back_rewrite(34841),rewrite([35019(15)])].

35068 C * R(x * A,C,A) = x * (A * C). [back_rewrite(3173),rewrite([35019(9)])].

35073 (x * (A * C)) * A' = C * R(x,A,C). [para(34695(a,1),6(a,1,1)),rewrite([293(6)])].

35139 C * R(x,A,C) = R(C * x,A,C). [para(34708(a,1),10(a,1,2)),rewrite([34415(7)]),flip(a)].

35142 C * (A * ((A * C) * x)) = A * (C * (A * (x * C))). [para(34708(a,1),45(a,2,2,2)),rewrite([16641(7),16(6,R),1382(6),4537(11),34420(8),3

5139(9),33764(9)]),flip(a)].

35147 R(R(C,A,x),A * x,C) = R(C,A * C,R(x,A,C)). [para(34708(a,1),92(a,1,1,2)),rewrite([35056(13),27544(11)])].

35148 R(C,A,R(C * x,A,C)) = R(C,A * C,x). [para(34708(a,1),97(a,1,2)),rewrite([35139(8),35056(9),92(11),35139(12)]),flip(a)].

35156 ((A * C) * x)' * A = R(C * x,A,C)'. [para(34708(a,1),2420(a,1,1,1)),rewrite([35139(11),35139(16),300(18),35139(12)])].

35166 (A * C) * R(x,C,A) = A * (C * x). [para(26864(a,1),34708(a,1,2,2)),rewrite([16(10),34650(13)]),flip(a)].

35183 R(R(A,C,x),C * x,C) = A. [para(34708(a,1),33724(a,1,1,2)),rewrite([35139(11),16(13,R),35139(13),34653(16),4058(11)])].

35186 R((A * C) * x,A,C) = C * (A * x). [para(34708(a,1),34431(a,1,1)),rewrite([35056(14)])].

35205 (x * (A * C)) * A' = R(C * x,A,C). [back_rewrite(35073),rewrite([35139(12)])].

35208 C' * R(C * x,A,C) = R(x,A,C). [back_rewrite(34967),rewrite([35139(16),34(13)])].

35210 (x * A) * (C * A') = R(C * x,A,C). [back_rewrite(34702),rewrite([35139(12)])].

35211 R(C * x,A,C) * A = x * (A * C). [back_rewrite(34695),rewrite([35139(5)])].

35218 R(R(A,C,C' * x),x,C) = A. [para(34(a,1),35183(a,1,2))].

35225 C * ((A * C) * x) = A * (C * (C * x)). [para(35183(a,1),78(a,1,1)),rewrite([16(5,R),78(12),16(12,R)]),flip(a)].

35227 R(R(A,C,C * x),C * C,x * C) = A. [para(1358(a,1),35183(a,1,2)),rewrite([4190(11)])].

35263 R(A,C,C' * (C' * x)) = R(A,x,C'). [para(35218(a,1),26935(a,1,1)),flip(a)].

35264 R(A,C * x,C') = R(A,C,C' * x). [para(35218(a,1),27045(a,1,1))].

35265 R(A,x * C,C') = R(A,C,C' * x). [para(35218(a,1),27046(a,1,1))].

35275 R(x,A,C) / R(C * x,A,C) = C'. [para(35139(a,1),32(a,1,2))].

35278 C / R(C * x,A,C) = R(x,A,C)'. [para(35139(a,1),109(a,1,2))].

35282 R(C * x,A,C)' = C' / R(x,A,C). [para(35139(a,1),1724(a,1,1))].

35305 R(x,R(C * y,A,C),C) = R(x,C * C,R(y,A,C)). [para(35139(a,1),4130(a,2,2)),flip(a)].

35330 R(C * R(x,C,A),A,C) = C * x. [para(26864(a,1),35139(a,1,2)),rewrite([16(6),34650(9)]),flip(a)].

35353 ((A * C) * x)' * A = C' / R(x,A,C). [back_rewrite(35156),rewrite([35282(13)])].

35393 C * R(x,C,A) = R(C * x,C,A). [para(35330(a,1),22987(a,1,1)),rewrite([34641(7)]),flip(a)].

35396 R(C * (A * x),C,A) = (A * C) * x. [para(34684(a,1),35330(a,2)),rewrite([35393(10),35393(7),34635(13)])].

35401 R(C * (x * A),C,A) = x * (A * C). [back_rewrite(35068),rewrite([35393(7)])].

35402 R(R(C * x,A,C),A,C) = R(C * x,C,A). [back_rewrite(35060),rewrite([35393(13)])].

35403 A * ((C * A') * x) = R(C * x,C,A). [back_rewrite(35019),rewrite([35393(12)])].

35418 R(x,A',A * C) = R(x,C,A). [para(35393(a,1),10(a,1,2)),rewrite([32272(8)])].

35420 R(x,C,A)' * R(C * x,C,A) = C. [para(35393(a,1),64(a,1,2))].

35451 R(x,R(C * y,C,A),C) = R(x,C * C,R(y,C,A)). [para(35393(a,1),4130(a,2,2)),flip(a)].

35473 C * (x / (A * C)) = R(x * A',C,A). [para(2104(a,1),35393(a,1,2)),rewrite([16(4),293(9),113(12),34(14)])].

35482 C * R(C / x,x,A)' = R(x,C,A). [para(6450(a,1),35393(a,1,2)),rewrite([113(10),34(12)])].

35494 C' * R(C * x,C,A) = R(x,C,A). [back_rewrite(32272),rewrite([35418(14)])].

35506 R(x,C,A) * A = R(x * A,C,A). [para(35418(a,1),79(a,1)),rewrite([256(3),10(15),113(11),34647(12)]),flip(a)].

35531 (x * (A * C)) / R(x * A,C,A) = C. [back_rewrite(34938),rewrite([35506(9)])].

35541 C' * (x * (A * C)) = R(x * A,C,A). [back_rewrite(34647),rewrite([35506(12)])].

35572 R(x * A,C,A) * A' = R(x,C,A). [para(35506(a,1),6(a,1,1)),rewrite([293(7)])].

35582 A * ((x * C) / R(A * x,C,A)) = C. [para(35506(a,1),112(a,1,2,2)),rewrite([2041(8),34651(13),25345(14),34734(13),35572(12),34651(8)])].

35605 R(R(x,A,C) * A,C,A) = x * A. [para(23049(a,1),35506(a,1,1)),rewrite([16(7,R),34642(8)]),flip(a)].

35642 R(x * (A * C),C,A) = (x * C) * A. [para(242(a,1),35605(a,2)),rewrite([35211(7)])].

35647 R(x,A,C) * A = R(x * A,A,C). [para(35605(a,1),34635(a,1,1)),flip(a)].

35648 R((C * x) * A,A,C) = x * (A * C). [back_rewrite(35211),rewrite([35647(7)])].

35658 R(x,A,C)' * R(x * A,A,C) = A. [para(35647(a,1),10(a,1,2))].

35704 R(A * x',x,C)' * A = R(x,A,C). [para(6450(a,1),35647(a,1,1)),rewrite([749(2),293(10),82(13),259(12)])].

35718 A' * R(x,C,A) = R(A' * x,C,A). [para(34(a,1),34719(a,1,2,1))].

35724 R(x * (A * (A * C)),C,A) = C * (x * (A * A)). [para(659(a,1),34719(a,1,2,1)),rewrite([34689(13),10(11),66(11)]),flip(a)].

35726 R(A' * (C * x),C,A) = R(C * (A' * x),A,C). [para(34719(a,1),727(a,2,2,2)),rewrite([35393(14),35396(14),34415(12),35208(11),34855(7),35

139(8),35393(15),35718(16)]),flip(a)].

35776 A * (C * ((A' * C') * x)) = R(x,C,A). [para(34(a,1),34843(a,1,1)),rewrite([1828(9),293(9),1511(10)]),flip(a)].

35783 R(C * (A' * x),A,C) = (C * A') * x. [back_rewrite(30507),rewrite([35776(15),35726(8)])].

35784 x / (A' * C') = x * (A * C). [back_rewrite(14813),rewrite([35776(13),35393(7),35401(7)]),flip(a)].

35790 R(x,A' * C',A * C) = x. [para(35784(a,1),6(a,1)),rewrite([11248(10)])].

35791 R(x,A * C,A' * C') = x. [para(35784(a,1),7(a,1,1)),rewrite([11364(10)])].

35792 R(x,A',C') = R(x,A,C). [para(35784(a,1),18(a,1)),rewrite([1511(6,R),247(10),16598(9),34415(9),35208(8)]),flip(a)].

35803 C * (x * (A * C')) = R(x * A,A,C). [para(35784(a,1),79(a,2)),rewrite([256(3),35792(7),13836(12),32639(12)]),flip(a)].

35827 (x * (A' * C')) * (A * C) = x. [back_rewrite(11248),rewrite([35790(19)])].

35828 x / (A * C) = x * (A' * C'). [back_rewrite(29173),rewrite([35791(13)])].

35829 (x * (A * C)) * (A' * C') = x. [back_rewrite(11364),rewrite([35791(19)])].

35837 C' * ((C * x) * A) = R(x * A,A,C). [back_rewrite(32639),rewrite([35803(14)])].

35840 C * (x * (A' * C')) = R(x * A',C,A). [back_rewrite(35473),rewrite([35828(5)])].

35841 R(x * (A' * C'),C,A) = (C' * x) * A'. [back_rewrite(34696),rewrite([35828(4)])].

35842 R(x * (A' * C'),A,C) = C' * (x * A'). [back_rewrite(34643),rewrite([35828(4)])].

35846 R(x,A,C) * A' = R(x * A',A,C). [back_rewrite(27522),rewrite([35828(6),11560(8),34789(8)])].

35857 C * ((C' * x) * A') = R(x * A',A,C). [back_rewrite(34789),rewrite([35846(14)])].

35863 R(R(x,A' * C',C),A,C) = x. [para(35792(a,1),26935(a,1)),rewrite([1511(5)])].

35879 (x * (A' * C'))' = (A * C) / x. [para(35827(a,1),32(a,1,2)),flip(a)].

35956 R(x,A' * C',C) = R(x,C,A). [para(35863(a,1),22987(a,1,1)),rewrite([34641(5)]),flip(a)].

35958 R(x,C,A) * A' = R(x * A',C,A). [para(35956(a,1),78(a,1,1)),rewrite([16(10,R),1659(10),16(14,R),35840(14)])].

35959 A * (C' * (A' * x)) = R(C' * x,C,A). [para(79(a,1),35956(a,2)),rewrite([113(2),35956(10),16(11),35828(12),11954(14),1511(13,R)]),flip(

a)].

35970 C' * ((C * x) * A') = R(x * A',C,A). [back_rewrite(32258),rewrite([35958(14)])].

35972 R(A * (C' * x),C,A) = (A * C') * x. [back_rewrite(31134),rewrite([35959(9),34651(8)])].

35976 A * R(C / x,x,A)' = (A * C') * x. [back_rewrite(34773),rewrite([35972(8)]),flip(a)].

35977 R(A * (x * C'),C,A) = (A * C') * x. [back_rewrite(34762),rewrite([35972(8)]),flip(a)].

35978 C * (A * (x * (C' * C'))) = (A * C') * x. [back_rewrite(35014),rewrite([35977(18)])].

35983 R(R(x * A,A,C),A,C) = C * ((C' * x) * A). [para(247(a,1),34858(a,1,1)),rewrite([35837(7)])].

35986 (C * (A * x)) / R(x,A,C) = A * C. [para(35056(a,1),6(a,1,1))].

35987 (C * (A * x)) / R(C * x,A,C) = R(A,C,R(x,A,C)). [para(35056(a,1),18(a,1,1)),rewrite([35139(9)])].

35988 R(x,A,C) / (C * (A * x)) = A' * C'. [para(35056(a,1),32(a,1,2)),rewrite([1828(12),293(12),1511(13)])].

35990 (C * (A * x)) / R(A * x,A,C) = R(C,A,R(x,A,C)). [para(35056(a,1),97(a,1,1)),rewrite([34420(9)])].

36014 (A * C) * (x * (A' * C')) = A * (x * A'). [para(2104(a,1),35166(a,1,2)),rewrite([16(6),35828(7),293(14),113(17),34(19)])].

36015 (A * C) * R(C / x,x,A)' = A * x. [para(6450(a,1),35166(a,1,2)),rewrite([113(13),34(15)])].

36019 C * (A * ((A' * C') * x)) = R(x,A,C). [para(34(a,1),35186(a,1,1)),rewrite([1828(9),293(9),1511(10)]),flip(a)].

36025 R(A * (x * C'),A,C) = C' * (A * x). [back_rewrite(14792),rewrite([36019(14),34420(8)])].

36036 (C' * (A * x)) / R(C' * x,A,C) = A. [back_rewrite(34578),rewrite([36025(8)])].

36039 C' * R(x,A,C) = R(C' * x,A,C). [para(34(a,1),35208(a,1,2,1))].

36055 R(R(x,A,C),A,C) = R(x,C,A). [para(35139(a,1),35208(a,1,2,1)),rewrite([35402(10),35494(8)]),flip(a)].

36056 C * ((C' * x) * A) = R(x * A,C,A). [back_rewrite(35983),rewrite([36055(8)]),flip(a)].

36057 R(x,C,A * C') = R(x,C,A). [back_rewrite(25653),rewrite([36056(7),35958(8),85(5),260(4)]),flip(a)].

36059 (A' * (C / x)) * R(x * A,C,A) = C. [back_rewrite(14542),rewrite([36056(12)])].

36060 R(C * (x * A),A,C) = (x * C) * A. [para(36055(a,1),78(a,1,1)),rewrite([2041(7),35647(9),16(11,R),35139(11)]),flip(a)].

36062 R(R(x,C,A),C,A) = R(x,A,C). [para(36055(a,1),22987(a,1,1)),rewrite([34641(8)])].

36074 R(C' * (x * A'),A,C) = (C' * x) * A'. [para(2104(a,1),36062(a,1,1)),rewrite([16(3),35828(4),35841(9),293(8),113(11)]),flip(a)].

36146 R(C' * x,A,C)' = C / R(x,A,C). [para(34(a,1),35278(a,1,2,1)),flip(a)].

36151 R(x * C',A,C)' = C / R(x,A,C). [para(1659(a,1),35278(a,1,2,1)),flip(a)].

36152 R(x * C,A,C)' = C' / R(x,A,C). [para(1358(a,1),35278(a,1,2,1)),rewrite([35278(9),35282(12)])].

36228 R(C * (x * (A * A)),C,A) = (x * A) * (A * C). [para(6793(a,1),35401(a,1,1,2))].

36230 (x * (A * C)) * A = C * (x * (A * A)). [para(35401(a,1),35506(a,1,1)),rewrite([31535(12),35724(15)])].

36271 R(C / x,x,A) * R(x,C,A) = C. [para(6450(a,1),35420(a,1,1,1)),rewrite([30(6),113(7),34(9)])].

36275 R(C / x,x,A) = C / R(x,C,A). [para(36271(a,1),6(a,1,1)),flip(a)].

36286 R(C' * x,C,A)' = C / R(x,C,A). [para(36275(a,1),18(a,2)),rewrite([7(3),16(3),29558(6)])].

36298 C' * R(x,C,A) = R(C' * x,C,A). [para(36275(a,1),138(a,2,1)),rewrite([7(5),16(5),35828(6),11954(8),1511(7,R),35959(8),104(12),113(11)])

,flip(a)].

36417 ((x * C) * A) / R(x * A,A,C) = C. [para(2041(a,1),35531(a,1,1)),rewrite([35506(9),36062(12)])].

36468 (x * C) / R(A * x,C,A) = C * A'. [para(35582(a,1),10(a,1,2)),rewrite([16(4,R)]),flip(a)].

36478 R(A,C,(A' * C') * x) = R(A',C,C' * x)'. [para(35582(a,1),124(a,1,3,1,1)),rewrite([36468(9),5680(9),36468(16),36468(21),122(18),246(16)

,113(13),1511(14),14784(17)]),flip(a)].

36489 A * (R(C * x,A,C) / (A * x)) = C. [para(34420(a,1),35582(a,1,2,2,1)),rewrite([16(6,R),35139(6),34653(14)])].

36491 (C * ((A' * C') * x)) / x = R(A',C,C' * x). [back_rewrite(14812),rewrite([36478(18),30(18)])].

36529 (x * C) * (A * A) = (x * A) * (A * C). [para(35642(a,1),35506(a,1,1)),rewrite([6793(6),36230(12),36228(15)])].

36575 R(A * x',x,C) * R(x,A,C) = A. [para(6450(a,1),35658(a,1,1,1)),rewrite([749(2),30(7),293(7),82(10),259(9)])].

36738 R(x * A,A,C) / ((x * C) * A) = C'. [para(36060(a,1),35275(a,1,2))].

36895 R(C * x,A,C) / (A * x) = C * A'. [para(36489(a,1),10(a,1,2)),rewrite([16(4,R)]),flip(a)].

36901 R(A,C,R(x,A,C)) = R(A',C,A * x)'. [para(36489(a,1),80(a,1,1,1)),rewrite([35987(10),36895(15),5680(14)])].

36925 R(A * x,x',C) * R(x',A,C) = A. [para(30(a,1),36575(a,1,1,1,2))].

37480 C * (C * (C * (A * x))) = A * (C * (C * (C * x))). [para(35986(a,1),1420(a,1,1)),rewrite([35988(12),35986(18),35225(15),234(16),256(11

),1511(10),12146(15),16(11),33905(14),10(15),32259(11),35393(10),35166(11),35986(17),33905(15)]),flip(a)].

37565 (C' * x) * (A * C') = C' * (C' * (x * A)). [para(2007(a,1),1032(a,1,2,1,1,2,2)),rewrite([24793(10),4610(12),1511(6),4627(13),8(17),10(

23),2(20),34(21)])].

37576 C' * (C' * (A' * (C * x))) = (A' * C') * x. [para(2023(a,1),1292(a,2,2,2,2)),rewrite([16(10,R),1511(13,R),10(13),37565(16),16598(14),1

22(12),11560(21),1511(19),10(22)])].

37818 (C * x) * (A * A) = (x * A) * (A * C). [para(2071(a,1),6793(a,1)),rewrite([6793(6),36529(6)]),flip(a)].

38078 x / (y * (x * C)) = R(C * y,C',x)'. [para(63(a,1),2128(a,2,1)),rewrite([1699(3),6379(8)]),flip(a)].

38079 R(C' / x,x,y * C)' = (x * (y * C)) / y. [para(63(a,1),2128(a,2,2))].

38179 A * (x * (A * C'))' = C / R(x,C,A). [para(36057(a,1),2128(a,1,1)),rewrite([113(2),36286(7),1659(11),749(12)]),flip(a)].

38181 (x * C') / (y * x) = R(C * y,C',x)'. [back_rewrite(6204),rewrite([38078(9)])].

38182 R(C' / x,x,y * C) = R(C * x,C',y)'. [back_rewrite(2124),rewrite([38078(10)])].

38184 (x * (y * C)) / y = R(C * x,C',y). [back_rewrite(38079),rewrite([38182(6),30(7)]),flip(a)].

38193 R(C' * x,C,C' * y) = (x * (C' * y)) / y. [para(34(a,1),2130(a,1,2)),flip(a)].

38295 R(A * (C / x),(C' * x) * A',y) = A * (C / x). [para(2321(a,1),18(a,1,1,1)),rewrite([2(2),32(8),784(7),158(5)]),flip(a)].

38296 C / R(x * A',A,C) = A * (C / x). [para(2321(a,1),100(a,1,1,2)),rewrite([3(3),16(9,R),35857(9),38295(20)])].

38626 R(C' * (x * A),C,A) = (C' * x) * A. [para(2918(a,1),129(a,2,2)),rewrite([16(19,R),36056(19),36059(18),16(9,R),36056(9),36298(8),3(15)]

)].

39165 R(x,C * A',A * C') = x. [para(1527(a,1),827(a,1,1)),rewrite([16(4,R),765(10),1511(21,R),10(21),13(18),8(16),3(14),34(14)])].

39194 x / (C * A') = x * (A * C'). [para(39165(a,1),79(a,1)),rewrite([11955(19),1511(18,R),63(18),8(14),23(12)])].

39196 R(x,A * C',C * A') = x. [para(39194(a,1),7(a,1,1)),rewrite([2292(10)])].

39197 R(x,C,A') = R(x,A,C). [para(39194(a,1),18(a,1)),rewrite([11955(10),1511(9,R),34704(9),34855(8),10(5)]),flip(a)].

39198 (x * (A * C'))' = (C * A') / x. [para(39194(a,1),104(a,1,1))].

39206 C * (A' * ((A * C') * x)) = R(x,A',C). [para(39194(a,1),101(a,1)),rewrite([11560(10),16598(9)])].

39226 R(C' * (x * A),A,C) = x * (A * C'). [para(39194(a,1),2104(a,2)),rewrite([256(3),113(4),39197(9)])].

39247 R(C' * x,A,C) = R(C / x,x,A')'. [para(39194(a,1),2128(a,2)),rewrite([11955(14),1511(13,R),34790(14)]),flip(a)].

39248 A * ((C * A') / x) = C / R(x,C,A). [back_rewrite(38179),rewrite([39198(7)])].

39252 R(x,A,C) * (C * A') = (x * C) * A'. [para(39197(a,1),78(a,1,1))].

39253 R(C / x,x,A') = C / R(x,A,C). [para(39197(a,1),6450(a,2,1)),rewrite([113(7),36146(12)])].

39255 x / (A * C') = x * (C * A'). [para(39196(a,1),79(a,1)),rewrite([249(19),293(16),1511(17),1659(18),9(14),23(12)])].

39260 R(x,C,A) = R(x,A,C'). [para(39255(a,1),18(a,1)),rewrite([1511(5,R),234(10),1699(7),35970(10),85(5),260(4)])].

39261 (x * (C * A'))' = (A * C') / x. [para(39255(a,1),104(a,1,1))].

39307 A * ((C * A') / x) = C / R(x,A,C'). [back_rewrite(39248),rewrite([39260(11)])].

39337 R(C' * (x * A),A,C') = (C' * x) * A. [back_rewrite(38626),rewrite([39260(8)])].

39492 C' * R(x,A,C') = R(C' * x,A,C'). [back_rewrite(36298),rewrite([39260(5),39260(13)])].

39497 R(C' * x,A,C')' = C / R(x,A,C'). [back_rewrite(36286),rewrite([39260(6),39260(12)])].

39500 R(C / x,x,A) = C / R(x,A,C'). [back_rewrite(36275),rewrite([39260(8)])].

39501 R(C / x,x,A) * R(x,A,C') = C. [back_rewrite(36271),rewrite([39260(7)])].

39535 R(R(x,A,C'),A,C') = R(x,A,C). [back_rewrite(36062),rewrite([39260(3),39260(7)])].

39539 C * ((C' * x) * A) = R(x * A,A,C'). [back_rewrite(36056),rewrite([39260(12)])].

39540 R(R(x,A,C),A,C) = R(x,A,C'). [back_rewrite(36055),rewrite([39260(9)])].

39548 R(A * (x * C'),A,C') = (A * C') * x. [back_rewrite(35977),rewrite([39260(8)])].

39550 R(A * (C' * x),A,C') = (A * C') * x. [back_rewrite(35972),rewrite([39260(8)])].

39562 R(x,A,C') * A' = R(x * A',A,C'). [back_rewrite(35958),rewrite([39260(3),39260(13)])].

39570 C * (x * (A' * C')) = R(x * A',A,C'). [back_rewrite(35840),rewrite([39260(14)])].

39587 A' * R(x,A,C') = R(A' * x,A,C'). [back_rewrite(35718),rewrite([39260(5),39260(13)])].

39631 C' * (x * (A * C)) = R(x * A,A,C'). [back_rewrite(35541),rewrite([39260(12)])].

39651 R(x,A,C') * A = R(x * A,A,C'). [back_rewrite(35506),rewrite([39260(3),39260(11)])].

39659 C * R(C / x,x,A)' = R(x,A,C'). [back_rewrite(35482),rewrite([39260(10)])].

39662 R(x,R(C * y,A,C'),C) = R(x,C * C,R(y,A,C')). [back_rewrite(35451),rewrite([39260(5),39260(14)])].

39686 A * ((C * A') * x) = R(C * x,A,C'). [back_rewrite(35403),rewrite([39260(12)])].

39687 R(C * (x * A),A,C') = x * (A * C). [back_rewrite(35401),rewrite([39260(7)])].

39691 R(C * (A * x),A,C') = (A * C) * x. [back_rewrite(35396),rewrite([39260(7)])].

39692 C * R(x,A,C') = R(C * x,A,C'). [back_rewrite(35393),rewrite([39260(4),39260(11)])].

39698 (A * C) * R(x,A,C') = A * (C * x). [back_rewrite(35166),rewrite([39260(6)])].

39708 R(C,R(A * x,A,C'),y) = R(C',(A * C) * x,y)'. [back_rewrite(34996),rewrite([39260(6)])].

39739 (x * R(x * A',A,C)) * A = R(x * x,A,C'). [back_rewrite(34711),rewrite([39260(13)])].

39741 R(R(A * x',x,C)',A,C') = x * A'. [back_rewrite(34697),rewrite([39260(9)])].

39743 C' * ((A * C) * x) = R(A * x,A,C'). [back_rewrite(34692),rewrite([39260(12)])].

39748 C * (A * (C' * x)) = R(A * x,A,C'). [back_rewrite(34683),rewrite([39260(12)])].

39750 R(A * (C * x),A,C') = C * (A * x). [back_rewrite(34680),rewrite([39260(7)])].

39752 R(A * (x * (A * C')),A,C') = A * (C' * (x * A)). [back_rewrite(34678),rewrite([39260(10)])].

39761 R(R(x,A,C),A,C') = x. [back_rewrite(34653),rewrite([39260(6)])].

39762 A * R(x,A,C') = R(A * x,A,C'). [back_rewrite(34651),rewrite([39260(4),39260(11)])].

39763 R(x,A * C,C') = R(x,A,C'). [back_rewrite(34650),rewrite([39260(9)])].

39765 R(x,A * C,A) = R(x,A,C'). [back_rewrite(34641),rewrite([39260(8)])].

39766 R(R(x,A,C'),A,C) = x. [back_rewrite(34635),rewrite([39260(3)])].

39783 A' * (C * (A * x)) = R(C * x,A,C'). [back_rewrite(32259),rewrite([39260(12)])].

39784 R(x,C',C * A') = R(x,A,C'). [back_rewrite(32253),rewrite([39260(10)])].

39791 R(x,A,C') * (A * C) = (x * C) * A. [para(39260(a,1),78(a,1,1)),rewrite([16(7)])].

39797 R(x,A * C',A) = R(x,A,C). [para(39761(a,1),22987(a,1,1))].

39948 R(C / x,x,A') * R(x,A,C) = C. [para(39253(a,2),7(a,1,1))].

39958 R(C / (x * A'),x * A',A') = A * (C / x). [para(79(a,1),39253(a,2,2)),rewrite([293(3),293(7),35828(18),25535(20),35857(20),38296(19)])]

.

39985 C / R(A * x',x,C)' = A * (C / x). [para(6450(a,1),39253(a,2,2)),rewrite([293(3),293(7),39958(11),749(7)]),flip(a)].

40041 R(R(C / x,x,A),R(x,A,C'),A') = C / x. [para(39500(a,2),39253(a,1,1)),rewrite([39766(19)])].

40046 R(x,A,C) * (A * C') = (C' * x) * A. [para(39535(a,1),78(a,1,1)),rewrite([39651(14),1511(17,R),39492(17),39337(17)])].

40047 R(x,C',A)' = R(x,A,C)'. [para(39535(a,1),138(a,2,1)),rewrite([39651(10),1511(13,R),39492(13),39337(13),38181(10),34(5)])].

40055 R(x,C',A) = R(x,A,C). [para(40047(a,1),30(a,1,1)),rewrite([30(5)]),flip(a)].

40093 R(C' / x,x,A) = C' / R(x,A,C). [para(40047(a,1),6450(a,2)),rewrite([1699(8),35282(11)])].

40108 R(C * x,A,C) = R(C' / x,x,A)'. [para(40055(a,1),6450(a,1)),rewrite([1699(3)])].

40146 C * R(C / x,x,A')' = R(x,A,C). [para(39948(a,1),10(a,1,2)),rewrite([16(8,R)])].

40565 R(x,A * C,C)' = R(x',A,C). [para(9956(a,1),4035(a,1,1)),rewrite([15067(12),1724(10),4463(10),34236(15),34(10),35139(9),1659(6)]),flip(

a)].

40584 R(x,A * C,C) = R(x',A,C)'. [para(40565(a,1),30(a,1,1)),flip(a)].

40585 C * (A * (C * (C' / x))) = R((A * C) / x,A,C). [para(79(a,1),40565(a,1,1)),rewrite([16(7,R),1382(7),104(9),15067(8),1828(6),35828(13),

35879(16)])].

41068 R(x,C,A * C) = R(x,A,C * C). [para(4638(a,1),2119(a,1,1)),rewrite([16(11,R),1382(11),4131(12),10(10)]),flip(a)].

41078 A' * ((A * C') * x) = R(C' * x,A,C'). [para(34(a,1),1626(a,1,2,2)),rewrite([1538(20),256(18),16(17),39743(19),39587(19),10(15),39492(1

5)])].

41080 C' * (A' * (C * x)) = R(A' * x,A,C'). [para(3983(a,1),1626(a,1,2,2)),rewrite([12146(16),16741(17),39686(15),39492(15),10(11),39492(11)

,63(7),39587(7),10(18)]),flip(a)].

41082 R(x,A',C) = R(x,A,C'). [back_rewrite(39206),rewrite([41078(9),39692(9),34(5)]),flip(a)].

41083 R(C' * (A' * x),A,C') = (A' * C') * x. [back_rewrite(37576),rewrite([41080(10),39492(10)])].

41347 R(A * (C / x),A,C) = (A * C) / x. [para(749(a,1),5303(a,1,2,2)),rewrite([1828(6),34839(9),16(10)])].

41403 R(x,A,C)' = R(x',A,C). [para(138(a,1),41347(a,2)),rewrite([16(6,R),109(7),824(4),34(6)]),flip(a)].

41424 R((A * C) / x,A,C) = R(A * (C / x),A,C'). [para(41347(a,1),39540(a,1,1))].

41449 R(x,A * C,C) = R(x,A,C). [back_rewrite(40584),rewrite([41403(10),30(7)])].

41508 C' / R(x,A,C) = R(C' / x,A,C). [back_rewrite(36152),rewrite([41403(6),1828(3)]),flip(a)].

41509 C / R(x,A,C) = R(C / x,A,C). [back_rewrite(36151),rewrite([41403(7),1538(4)]),flip(a)].

41537 C * (A * (C * (C' / x))) = R(A * (C / x),A,C'). [back_rewrite(40585),rewrite([41424(16)])].

41540 R(C' / x,A,C) = R(C' / x,x,A). [back_rewrite(40093),rewrite([41508(11)]),flip(a)].

41564 ((A * C) * x)' * A = R(C' / x,A,C). [back_rewrite(35353),rewrite([41508(13)])].

41586 R(C / (x * A'),A,C) = A * (C / x). [back_rewrite(38296),rewrite([41509(8)])].

41601 R(x',A,C) * R(x,A,C) = 0. [para(41403(a,1),8(a,1,1))].

41653 R(A * (C / x),A,C') = C / (x * A'). [para(35879(a,1),41403(a,2,1)),rewrite([35842(9),158(7),41424(12)]),flip(a)].

41658 R(x,A,C')' = R(x',A,C'). [para(39540(a,1),41403(a,1,1)),rewrite([41403(9),39540(12)])].

41661 C * (A * (C * (C' / x))) = C / (x * A'). [back_rewrite(41537),rewrite([41653(17)])].

41701 C / R(x,A,C') = R(C / x,A,C'). [back_rewrite(39497),rewrite([41658(8),158(4)]),flip(a)].

41766 A * ((C * A') / x) = R(C / x,A,C'). [back_rewrite(39307),rewrite([41701(13)])].

41793 x / (A * (C * C)) = C' * ((C' * x) * A'). [para(41449(a,1),2104(a,1)),rewrite([113(2),35828(7),35842(12),16(14,R),1382(14)]),flip(a)].

41878 (C * (x * A)) * A' = R(C * x,A,C'). [para(4638(a,1),1672(a,1,1,2)),rewrite([10(9),1511(10,R),63(10),293(6),39763(15)])].

41992 R(x',A,C') * (R(x,A,C') * y) = y. [para(41658(a,1),10(a,1,1))].

42015 R(A * (C' / x),A,C') = (A * C') / x. [para(2104(a,1),41658(a,1,1)),rewrite([39255(5),39261(6),1699(8),293(9),784(11),1724(9)]),flip(a)

].

42363 C' * (x * ((A * C) * x)) = x * R(A * x,A,C). [para(1012(a,1),1690(a,1,2,2)),rewrite([25535(23),1511(21),33788(23),1012(23)])].

42812 C' * (A * ((C * x) * A)) = R(A * (x * A),A,C'). [para(31492(a,1),1711(a,1,2,2,2,2)),rewrite([39743(13),39752(12),39748(9),1511(19,R),6

3(19),15(16)]),flip(a)].

42814 R(A * (x * A),A,C') / (x * A) = R(A,x,A * C). [back_rewrite(30644),rewrite([42812(9)])].

43633 R(x,C',y * C) = R(x,C',y). [para(6379(a,1),30(a,1,1)),rewrite([30(5)]),flip(a)].

43653 R(x,C',C * y') = R(x,C',y'). [back_rewrite(2546),rewrite([43633(6)]),flip(a)].

43654 R(x,C',A') = R(x,A,C'). [back_rewrite(39784),rewrite([43653(7)])].

43661 R(x,C',C' * y) = R(x,C',y). [para(7(a,1),43633(a,1,3)),rewrite([113(7)]),flip(a)].

43663 R(x,C',C * y) = R(x,C',y). [para(16(a,2),43633(a,1,3))].

43665 R(x,C',y * (C * C)) = R(x,C',y). [para(70(a,1),43633(a,1,3)),rewrite([43663(9),43663(14),43663(12)])].

43671 R(C * (x / (y * C)),C',y) = x / y. [para(43633(a,1),2104(a,1)),rewrite([1699(6),63(13)])].

43685 R(A,C',x * (A * C)) = R(A,x,A * C). [back_rewrite(8843),rewrite([43663(10)])].

43688 (C' * ((C * x) * y)) / y = R(x,C',y). [back_rewrite(2586),rewrite([43663(12)])].

43690 (x * (y * (C * C))) / (y * C) = R(C * x,C',y). [back_rewrite(8831),rewrite([43665(17)])].

43706 (x * (C * y)) / y = R(C * x,C',y). [para(43663(a,1),79(a,1)),rewrite([1699(3),10(13)]),flip(a)].

43793 C' * ((x * C) * A) = R(x * A,A,C). [para(36417(a,1),6610(a,1,1)),rewrite([36417(16),113(8),36039(9),39226(9),35803(7),36738(19),1511(1

2,R)]),flip(a)].

43802 R(A,C',(x * C) * A) = A * (x / R(x,A,C)). [back_rewrite(25411),rewrite([43793(8),35846(9),85(6),260(5)]),flip(a)].

44206 (A * (A * C)) / x = A * (C / (x * A')). [para(6741(a,1),9205(a,1,2,2)),rewrite([1724(7),16641(10),35142(11),16(8,R),41661(10),66(12)])

,flip(a)].

44414 R(A * C,C',A * x) = R(A * C,A,x). [para(9295(a,1),468(a,1)),rewrite([16(5,R),43706(9),16(3)])].

44469 C * ((A' * C') * x) = R(A' * x,A,C'). [para(9418(a,1),100(a,1,1,2)),rewrite([16(12,R),39194(13),11560(13),4610(12),1511(6),82(11),259(

10),41082(15)])].

44480 R(C * (A' * x),A,C') = A' * (x * C). [para(9418(a,1),1518(a,1,2,1,2,2)),rewrite([4610(14),13(13),8(11),3(9),39686(10),16(19,R),231(23)

,256(23),16598(22),34(19),34(19)])].

44481 C' * ((C * A') * x) = R(A' * x,A,C). [para(9418(a,1),1672(a,1,1,2)),rewrite([35784(15),247(13),4610(12),82(11),259(10),35792(16)])].

44485 R(A' * x,A,C') / x = R(A',C,C' * x). [back_rewrite(36491),rewrite([44469(8)])].

45738 (A * (x * y)) / y = A * R(x,y,A'). [para(16618(a,1),6(a,1,1))].

45777 R(x,C * C,R(A * y,A,C)) = R(x,A * (y * C),C). [para(16618(a,1),18592(a,2,2)),rewrite([39197(8),34420(8)])].

45820 (A * (C / x)) * R(x,A,C') = A * C. [para(39501(a,1),16618(a,2,2)),rewrite([40041(12)])].

45835 R(x,C',R(A * y,A,C)) = R(x,C',A * (y * C)). [para(16618(a,1),43633(a,1,3)),rewrite([39197(14),34420(14)]),flip(a)].

45843 R(A * x,A,A' * y) = A * R(x,y,A'). [back_rewrite(4833),rewrite([45738(11)])].

45845 A * R(x,A * y,A') = R(A * x,A,y). [back_rewrite(468),rewrite([45738(8)])].

45883 R(x,A',A * (y * A)) = R(x,y,A). [para(7(a,1),16667(a,1,2)),rewrite([256(8)]),flip(a)].

45891 R(x / (y * A'),A',A * y) = (x * A) / y. [para(16667(a,1),79(a,1)),rewrite([82(16),259(15)])].

45892 R(C * x,A,C) / x = R(C,A',A * x). [para(16667(a,1),97(a,2)),rewrite([16(5,R),16598(7),34415(7),82(10),259(9)])].

45903 R((x * A') / y,y,A) = x / (y * A). [para(16667(a,1),6450(a,2,1)),rewrite([45891(15),104(10)])].

45910 R(x,A' * y,A) = R(x,A',y * A). [para(6658(a,1),16667(a,1,2)),rewrite([30(6),260(7),256(13),34(14)])].

45912 A * ((A' * (x * y)) / y) = R(x,y,A). [back_rewrite(30642),rewrite([45883(14)])].

45993 A * R(C * A',C',x) = R(C,x,A). [para(45883(a,1),97(a,2)),rewrite([16(4,R),11955(9),15(8),10(9),10(11),25369(7),43706(7)])].

46045 (x * ((A * y) * x)) / (y * x) = x * A. [para(16760(a,1),6(a,1,1))].

46681 R(x,y * A,A') * y = (x * (y * A)) * A'. [para(256(a,1),2035(a,1,1,2)),rewrite([256(9)])].

46726 C' * (x * (A * (C * C))) = (x * C) * A. [para(22791(a,1),10(a,1,2))].

46729 C * ((C * x) * A) = x * (A * (C * C)). [para(16(a,2),22791(a,1,2,1))].

46732 x * (C * ((x' * C) * A)) = A * (C * C). [para(22791(a,2),34(a,1,2))].

46773 C * (x * (x * A)) = x * ((x * C) * A). [para(22791(a,2),1663(a,1)),rewrite([16(7,R),1698(7),12(4),46726(14)])].

46836 R(R(x,y,A'),A',A * y) = x. [para(16667(a,1),2043(a,2)),rewrite([82(6),259(5),82(6),259(5),6(2)]),flip(a)].

46896 R(R(x,y * A,A'),y,A) = x. [para(46836(a,1),45883(a,1)),flip(a)].

46898 R(A,R(x,A,C),A * C) = R(A,x * A,C). [para(73(a,1),2044(a,1,1)),rewrite([16(6,R),35139(6),35647(8),35648(8),16(10,R),3189(11)]),flip(a)

].

47215 R(x,A,C * C) = R(x,A,C'). [para(24137(a,1),18(a,1,1)),rewrite([1382(11),41793(12),10(11),41878(9),39492(9),10(5),41068(9)]),flip(a)].

47631 R(R(x,A * y,A),A,y) = x. [para(6(a,1),26848(a,2)),rewrite([25429(7)])].

47659 R(R(x,y,A),A,A' * y) = x. [para(34(a,1),47631(a,1,1,2))].

47700 A * ((A' * R(x,y,A)) * y) = x * y. [para(47631(a,1),2045(a,1,1)),rewrite([34(6),11954(9)]),flip(a)].

47701 R(x,A * (y * A),A') = R(x,A,y). [para(46896(a,1),47631(a,1,1)),rewrite([49(6)]),flip(a)].

47780 A * R(x / y,y,A') = (A * x) / y. [para(2149(a,1),47659(a,1,1)),rewrite([45843(8)])].

47797 R(R(x,A',A * y),A,A' * (y * A')) = x. [para(16667(a,1),47659(a,1,1))].

47800 R(x,y * A,A') = R(x,A,A' * y). [para(46896(a,1),47659(a,1,1)),flip(a)].

47803 (x * (y * A)) * A' = A * ((A' * x) * y). [back_rewrite(46681),rewrite([47800(5),2045(6),11954(6)]),flip(a)].

47811 (x * (y * (C * C))) / (C * y) = R(C * x,C',y). [para(4530(a,1),2105(a,1,1,2)),rewrite([1699(3),4530(9),43665(9)]),flip(a)].

47886 x / (C' * (y * x)) = R(y * C',C',x)'. [para(9194(a,1),2110(a,1,1)),rewrite([29968(11),43663(8),24793(16),10(14)]),flip(a)].

47920 R(A * x,x',x * y) = A * R(x,y,A'). [para(749(a,1),2111(a,1,1)),rewrite([30(3),45738(9)])].

47936 R(A * R(x,y,A'),y,A) = A * x. [para(2111(a,2),2149(a,1,1)),rewrite([749(3),30(3),47920(5),6(10)])].

47951 (x * (C * (C * y))) / (y * C) = R(C * x,C',y). [para(3983(a,2),2111(a,2,1)),rewrite([1699(3),43663(9),43633(7)]),flip(a)].

48002 R(x,A * y,A') = R(x,A,y * A'). [para(7(a,1),47701(a,1,2,2)),rewrite([293(8)])].

48004 (x * (A * (A * x))) / (A * x) = R(x * A,A,x). [para(47701(a,1),92(a,2)),rewrite([85(8),260(7),16760(5),12(4),232(12),293(10),85(11),26

0(10)])].

48025 A * R(x,A,y * A') = R(A * x,A,y). [back_rewrite(45845),rewrite([48002(6)])].

48331 R(x / y,y,A) / ((A' * x) / y) = A. [para(26923(a,2),6(a,1,1))].

48341 R(x / y,y,A) * A = x / (A' * y). [para(26923(a,2),49(a,1,1)),rewrite([9233(13)])].

48343 R(C',x,A)' = R(C,x,A). [para(1674(a,1),26923(a,1,1)),rewrite([6042(6),2197(13),45993(14)])].

48346 A * R(A' * x',x,y) = R(x,y,A)'. [para(79(a,2),26923(a,2,2)),rewrite([32(2),142(4),794(7)]),flip(a)].

48348 R(x / y,y,A) * (y / (A' * x)) = A. [para(26923(a,2),85(a,1,1)),rewrite([104(8),104(18),301(18)])].

48353 R(C,x * C,A) = R(C,x,A). [para(4118(a,1),26923(a,1,1)),rewrite([43690(16),45993(14)])].

48355 R(C,C * x,A) = R(C,x,A). [para(4524(a,1),26923(a,1,1)),rewrite([47811(16),45993(14)])].

48409 R(C,x,A)' = R(C',x,A). [para(48343(a,1),30(a,1,1))].

48509 R(R(C,x,A),A,A' * (x * C)) = C. [para(48353(a,1),47659(a,1,1))].

48518 R(C,R(C * x,A,C),A) = R(C,R(x,A,C),A). [para(35139(a,1),48355(a,1,2))].

48527 R(C',C' * x,A) = R(C',x,A). [para(141(a,1),48409(a,1,1)),rewrite([48343(5),48409(4)]),flip(a)].

48595 R(R(C,x,A),A,A' * (C' * x)) = C. [para(1665(a,1),48509(a,1,3,2)),rewrite([141(9),48527(7),48343(5),16(12,R),9(12),3(10)])].

48717 R(A * C,A',x)' = R(A' * C',C,x). [para(256(a,1),27450(a,2,1,1)),rewrite([1511(5),16(10)]),flip(a)].

49082 R(A * C,A * x,C) = R(A * C,A,x). [para(31303(a,1),2120(a,1,1)),rewrite([16641(15),33904(14),16(19,R),43706(20),16(10),43663(17),44414(

15)])].

49254 R(R(x,C',y),y,C) = R(x,C,y). [para(2182(a,2),26997(a,2)),rewrite([1511(6,R),43688(7),113(9),63(10)])].

49255 C * (R(x,C',y) * y) = (x * C) * y. [para(49254(a,1),78(a,1,1)),rewrite([2041(5),16(9,R)]),flip(a)].

49266 R(R(x,C,y),y * C,C') = R(x,C',y). [para(49254(a,1),27046(a,1,1))].

49487 (x * y) / (y * y) = R(x / y,y,y). [para(63(a,1),2195(a,1,1,2)),rewrite([128(7),63(9)])].

49492 R(C * R(x,C,y),C',y) = x * C. [para(2041(a,1),2197(a,1,1)),rewrite([1511(8,R),63(8),6(4),43633(11)]),flip(a)].

49513 (x * x) / (y * x) = R(y / x,x,x)'. [para(49487(a,1),104(a,1,1)),flip(a)].

49540 (C' * (x * y)) / y = R(C' * x,C',y). [para(2119(a,1),2198(a,1,1)),rewrite([49266(10),1511(15,R),63(15)]),flip(a)].

49556 R(x,C,y) * y = C * ((C' * x) * y). [para(49492(a,1),78(a,1,1)),rewrite([12145(6),1511(13,R),10(13)]),flip(a)].

49576 R(C * R(x,C,y),C,y) = R(x * C,y,C). [para(49492(a,1),49254(a,1,1)),flip(a)].

49829 R(A,C,x * C) = R(A,x,C * C). [para(33904(a,1),18(a,1,1)),rewrite([4132(11)]),flip(a)].

49846 R(A * x,A,C) / x = R(A,C,x * C'). [para(49829(a,2),80(a,2)),rewrite([4419(5),1382(12,R),16(11,R),39748(11),39548(10),33788(7),4419(12)

,16(16,R),34(16)])].

49939 (C * A') * (x * C) = C * (C * (A' * x)). [para(424(a,2),34236(a,1,2)),rewrite([13683(12),35783(17)]),flip(a)].

50112 C * (A' * (C' * x)) = R(A' * x,A,C). [para(35205(a,1),532(a,2,2,2)),rewrite([1511(14),35829(15),36039(18),10(15),34855(14)])].

50126 (C * A') * R(x,A,C) = A' * (x * C). [para(35210(a,1),532(a,2,2,2)),rewrite([10(16),85(12),260(11),246(9),113(6),1511(7),44469(9),39692

(9),44480(9),36039(17),10(14)]),flip(a)].

50130 (x * A) * R(x,A,C) = x * R(A * x,A,C). [para(35210(a,1),1663(a,2,2,2)),rewrite([1511(7,R),10514(8),6554(7),234(13),1699(10),7191(12),8

5(10),260(9),16760(7),42363(8),36039(16),10(13)]),flip(a)].

50131 A' * (C * (C * x)) = C * ((C * A') * x). [para(35210(a,1),1701(a,2,2)),rewrite([1511(14,R),10(14),85(10),260(9),50126(17),16(13,R)]),f

lip(a)].

50143 R(A * C,C',x) = R(A * C,x,C). [para(35225(a,1),100(a,1,1)),rewrite([47951(9),16(3)])].

50149 (x * C) / (A * (C * (C * x))) = R(A * C,x,C)'. [para(35225(a,1),4035(a,1,2))].

50160 R(A * C,x,C)' = R(A' * C',A,x). [para(50143(a,1),138(a,2,1)),rewrite([1511(9,R),63(9),2144(6),1511(5)]),flip(a)].

50161 R(A * C,C',x)' = R(A' * C',A,x). [para(50143(a,2),138(a,2,1)),rewrite([16(8,R),35225(8),50149(9),50160(6)]),flip(a)].

50183 R(A,x * (C * C),C') = R(A,C,x). [para(1382(a,1),35264(a,1,2)),rewrite([63(15)])].

50221 (C * ((x * C') * y)) / y = R(x,C,C' * y). [para(49254(a,1),2234(a,2)),rewrite([43661(7),78(8)])].

50314 R(A',x',C * (x * A))' = R(A,x',x * C). [para(15(a,1),2236(a,1,2)),rewrite([9200(8),293(8),16598(12),11964(11),16(10,R),34(13),14578(9)

,9366(17)])].

50321 C' * (x' * (C * (x * A))) = R(A,x',x * C). [back_rewrite(14578),rewrite([50314(18)])].

50360 R(C,A,R(C / x,x,A)') = R(C',A,x)'. [para(36015(a,1),97(a,1,1)),rewrite([35976(9),6114(8)]),flip(a)].

50385 (x * A') * ((A * y) * x) = x * (y * x). [para(2239(a,1),57(a,2,2,2)),rewrite([16598(8),232(7),293(5),10(8),32154(14),16520(10),2276(7)

,259(6),16598(10),232(9),293(7),10(10),16667(14),9(13),77(11)]),flip(a)].

50386 R(x,A' * x,x') = x. [para(232(a,1),2239(a,1,1)),rewrite([30(4),6(4),82(5),259(4),30(4)]),flip(a)].

50394 R(A * x,x,x' * A') = A * x. [para(10(a,1),50386(a,1,2)),rewrite([889(5)])].

50402 (x * (A * y)) * A' = (x * A) * (y * A'). [para(50394(a,1),2092(a,1,1,2)),rewrite([34(7),48002(5),9956(8),12157(13),12281(13),78(11),50

394(13),34(14)]),flip(a)].

50834 R(x,y * (z * A'),A) = R(x,A',(A * y) * z). [para(2275(a,1),16667(a,2,3)),rewrite([11955(6),9418(9),25391(8),10(9),259(13)])].

50838 (A * x) / R(C * x,A,C) = A * C'. [para(36895(a,1),104(a,1,1)),rewrite([784(5)]),flip(a)].

50850 R(A * x,x',C) = R(A * x,A,C). [para(36925(a,1),6(a,1,1)),rewrite([749(6),41403(6),30(3),34420(5)]),flip(a)].

50869 R(x,A,C) / R(A * x,x',C) = A'. [para(50850(a,2),34500(a,1,2))].

50894 A' * R(A * x,x',C) = R(x,A,C). [para(50850(a,2),34855(a,1,2)),rewrite([10(13)])].

50923 (C * (x * y)) / y = C * (C * R(x * C',C,y)). [para(2279(a,1),9205(a,1,2,2)),rewrite([2277(14)]),flip(a)].

51083 R(A,C,x * (C' * C')) = R(A,x,C'). [para(2285(a,1),50183(a,1,2)),rewrite([24807(10),2301(5)]),flip(a)].

51238 R(C * x,A * A,C) = R(C * x,A,C'). [para(37818(a,1),100(a,1,1,2)),rewrite([16(13,R),66(13),32245(14),10315(13),16(7,R),260(12),10(9),47

803(7),16(5,R),39686(7)]),flip(a)].

51251 A * (C' / (x * A)) = R(C' / x,A,C'). [para(37818(a,1),4032(a,1,2,2)),rewrite([66(5),44206(14),10315(13),16(7,R),260(12),109(9),1724(6)

,51238(14),41658(14),1724(10)])].

51388 R(R(A * C,C',x),x,A) = A * C. [para(38184(a,1),2149(a,1,1)),rewrite([16(3),60(12)])].

51401 A * R(C,x,A') = R(A * C,C',x). [para(51388(a,1),47659(a,1,1)),rewrite([45843(8)])].

51402 R(R(A * C,x,C),x,A) = A * C. [para(50143(a,1),51388(a,1,1))].

51533 (A' * C') * ((A * C) / x) = C * (C' / x). [para(6173(a,1),39687(a,2)),rewrite([41564(8),35139(8),39761(12),1828(9),293(9),1511(10)]),f

lip(a)].

51540 R(C,R(C * x,A,C'),A) = R(C,R(x,A,C'),A). [para(39692(a,1),48355(a,1,2))].

51576 R(C,R(x,A,C'),A * C) = R(C,x,A). [para(39791(a,1),97(a,1,2)),rewrite([16(6,R),39692(6),39791(10),16(4,R),70(6),16(4),3185(11),48353(5)

]),flip(a)].

51669 R(R(A',C,A * x)',C * C,R(x,A,C)) = A. [para(40146(a,1),35227(a,1,1,3)),rewrite([36901(6),16(18,R),40146(18)])].

51839 (A * C) / (x * A') = A * (A * (C / x)). [para(41586(a,1),34420(a,1,2)),rewrite([41347(16)]),flip(a)].

52422 R(A,x * A,C) = R(A,C',x * A). [para(2042(a,1),2569(a,1,3,2)),rewrite([43663(10),43663(8),16(13),46898(14)]),flip(a)].

52430 R(A,C * x,A * C) = R(A,C',x * A). [para(1411(a,1),2569(a,1,3)),rewrite([24137(10),43663(12),43663(10),43663(8),16(12)]),flip(a)].

52450 R(A,C',x) = R(A,x,C). [para(7(a,1),52422(a,1,2)),rewrite([293(8),82(11),259(10)]),flip(a)].

52456 R(A,A * x,C) = R(A,C',A * x). [para(6658(a,1),52422(a,1,2)),rewrite([259(7),293(11),16598(15),12(14),10(15)])].

52457 R(A,R(x,A,C),C) = R(A,C',R(x,A,C)). [para(35704(a,1),52422(a,1,2)),rewrite([35704(17)])].

52465 R(A,C',x) * (x * C) = C * (A * x). [para(52450(a,2),78(a,1,1)),rewrite([16(11,R)])].

52466 R(A * x,A,C') / x = R(A,C',x). [para(52450(a,2),80(a,2)),rewrite([113(3),16(7,R),39748(7),113(12),43661(14)])].

52468 R(A,C',x)' = R(A,x,C)'. [para(52450(a,1),138(a,2,1)),rewrite([138(9)])].

52469 R(A,C',A' * x) = R(A',x,C)'. [para(52450(a,2),141(a,1))].

52471 R(A,C * C,x) = R(A,C',x). [para(52450(a,2),4130(a,2)),rewrite([43663(11)])].

52479 R(A,C' * x,C) = R(A,C',x). [para(52450(a,1),43661(a,1))].

52483 R(R(A,x,C),x,C) = R(A,C,x). [para(52450(a,1),49254(a,1,1))].

52485 R(A,C',x * A) = R(A,x,A * C). [back_rewrite(42814),rewrite([52466(11)])].

52515 R(A,x,C)' * R(A,C',x) = 0. [para(52468(a,1),8(a,1,1))].

52516 R(A,C',x)' * R(A,x,C) = 0. [para(52468(a,2),8(a,1,1))].

52519 R(A,x,C)' * (R(A,C',x) * y) = y. [para(52468(a,1),10(a,1,1))].

52589 C * (R(A,x,C) * x) = (A * C) * x. [para(52483(a,1),78(a,1,1)),rewrite([2041(6),16(10,R)]),flip(a)].

52597 x / R(A * x,A,C) = R(A,C,C' * x)'. [para(52483(a,1),2235(a,2,1)),rewrite([113(3),52479(6),113(6),78(8),16(7,R),33788(7),113(10)])].

52618 (x * R(A,y,C)) / R(A,C',y) = x. [para(52515(a,1),87(a,1,1,2)),rewrite([30(5),3(6),30(14),52515(21),77(14)])].

52632 R(A,C',x) / (y * R(A,x,C)) = y'. [para(52515(a,1),2542(a,1,2,2)),rewrite([30(9),3(10),30(14),52515(21),77(14)])].

52692 (x' * ((x * A) * y)) / y = R(A,x',x * y). [para(7967(a,1),2600(a,1,1,1)),rewrite([11964(5),82(10),294(9)])].

52696 R(A,C',(x * C) * A) = R(A,C',x * A). [para(242(a,1),52485(a,1,3)),rewrite([52430(15)])].

52698 R(A,C',R(C' * x,A,C)) = R(A,C',x). [para(52485(a,2),80(a,2)),rewrite([35828(5),73(12),16(9,R),39570(9),39651(10),82(6),259(5),39762(6)

,52466(7),35828(11),4610(15),1511(14),11955(15),1511(14,R),34790(15)]),flip(a)].

52711 A * (x / R(x,A,C)) = R(A,C',x * A). [back_rewrite(43802),rewrite([52696(8)]),flip(a)].

52756 R(A * x,A,C') = R(A,x,C) * x. [para(52589(a,1),10(a,1,2)),rewrite([39743(7)])].

52813 R(A,x,C) / R(A,C',x) = 0. [para(2(a,1),52618(a,1,1))].

52814 x * R(A,C',y) = x * R(A,y,C). [para(52618(a,1),7(a,1,1))].

52820 R(A,C',x) * y = R(A,x,C) * y. [para(52618(a,1),6610(a,2,2)),rewrite([52632(9),52632(14),195(7),10(7)]),flip(a)].

52828 (x * R(A,C',y)) / R(A,y,C) = x. [para(52813(a,1),80(a,1,1,1,2)),rewrite([3(2),52813(17),76(15)])].

52863 R(R(A,x,C) * x,A,C) = A * x. [para(52756(a,1),22987(a,1,1)),rewrite([39797(10)])].

52888 R(A' * (R(A,x,C) * x),A,C) = x. [para(52863(a,1),34855(a,1,2)),rewrite([10(5)]),flip(a)].

52934 R(A,C',x)' * A = R(A,x,C)' * A. [para(52814(a,1),1071(a,1,1)),rewrite([1071(7)]),flip(a)].

53037 R(A,C',x)' * (R(A,x,C) * y) = y. [para(52820(a,1),10(a,1,2))].

53097 A' * (R(A,x,C) * x) = R(x,A,C'). [para(52888(a,1),22987(a,1,1)),rewrite([39765(5)]),flip(a)].

53360 R(R(C * x,A,C') / x,x,A) = C. [para(60(a,1),45903(a,2)),rewrite([16(4,R),47803(7),16(5,R),39686(7)])].

53388 R(C * x,A,C') / x = R(C,A,A' * x). [para(53360(a,1),47659(a,1,1)),flip(a)].

53390 R(R(C,A * C,x),(A * C) * x,A) = C. [para(35225(a,1),53360(a,1,1,1,1)),rewrite([39750(10),92(11)])].

53400 R(A * (A * x),A,C) / x = R(A * A,C',x). [para(34655(a,1),2723(a,1,1,2)),rewrite([34420(7),1511(12,R),10(12),43663(16)])].

53413 (A' * (x * y)) / y = A' * R(x,y,A). [para(45912(a,1),10(a,1,2)),flip(a)].

53418 R(x * A,A,x) * A' = x. [para(20219(a,1),45912(a,2)),rewrite([9201(14),48004(11),34(12)])].

53443 A * (R(x,A,C') / x) = R(R(A,x,C),x,A). [para(52756(a,2),45912(a,1,2,1,2)),rewrite([39587(10),10(6)])].

53450 R(x * A,A,x) = x * A. [para(53418(a,1),6(a,1,1)),rewrite([256(3)]),flip(a)].

53458 x / R(C * x,A,C') = R(C,A,A' * x)'. [para(53418(a,1),3947(a,1,1)),rewrite([53450(4),16(4,R),47803(7),16(5,R),39686(7),53450(12),47800(

13)])].

53553 A * R(A * C',C',x)' = R(C,A * x,A). [para(124(a,1),45993(a,1,2)),rewrite([1511(10,R),10(10),30(6),47886(7),1511(18,R),10(18),30(14)])]

.

53574 R((C * (A * x)) / x,x,C) = A * C. [para(46045(a,1),2120(a,2)),rewrite([16(4,R),16(10)])].

53964 R(A * A,C' * x,C) = R(A * A,C',x). [para(46729(a,2),2655(a,1,1,1)),rewrite([16(4),49(6),16(5),16641(7),16(6,R),1382(6),172(11),12(13),

4537(14),39748(12),39550(11),33788(8),34420(7),53400(8),172(16),12(18),10697(19)]),flip(a)].

53968 x' * (C * (x * (x * A))) = (x * C) * A. [para(46773(a,2),10(a,1,2))].

54084 (A' * R(x,y,A)) * y = A' * (x * y). [para(47700(a,1),10(a,1,2)),flip(a)].

54117 R(R(x,y,A)',A,A' * (x * y)) = x'. [para(47700(a,1),2110(a,2,2)),rewrite([1071(6),293(7),85(8),260(7),54084(10),32(11)])].

54121 R(A * C,x,C) * x = A * (C * x). [para(51402(a,1),47700(a,1,2,1,2)),rewrite([10(7)]),flip(a)].

54123 R(A,x * y,C) = R(A,C',x * y). [para(47700(a,1),52456(a,1,2)),rewrite([54084(14),34(13)])].

54127 R(C' * R(A * C,x,C),C,x) = A. [para(54121(a,1),2119(a,1,1)),rewrite([3952(7)]),flip(a)].

54136 R(A,R(x,A,C'),C) = R(A,C',R(x,A,C')). [para(39659(a,1),54123(a,1,2)),rewrite([39659(17)])].

54235 R(x,A,A' * (y * A')) = R(x,y,A'). [para(7(a,1),47800(a,1,2)),rewrite([293(8)]),flip(a)].

54249 R(R(x,A',A * y),y,A') = x. [back_rewrite(47797),rewrite([54235(13)])].

54261 R(R(x,A',y),A' * y,A') = x. [para(34(a,1),54249(a,1,1,3))].

54262 R((x * (A * y)) / y,y,A') = x * A. [para(79(a,1),54249(a,1,1)),rewrite([10(8),256(10)])].

54281 R(x,A,y) * A = R(x * A,y,A'). [para(2217(a,1),54249(a,1,1)),rewrite([10(8),6(4),256(10)]),flip(a)].

54382 R(x * A,y,A') * A' = R(x,A,y). [para(54281(a,1),6(a,1,1)),rewrite([293(7)])].

54383 R(x,A,y)' * R(x * A,y,A') = A. [para(54281(a,1),10(a,1,2))].

54384 R(x * A,y,A')' = A' * R(x,A,y)'. [para(54281(a,1),824(a,1,1))].

54397 R(A * x',x,y)' * A = R(x,y,A'). [para(6450(a,1),54281(a,1,1)),rewrite([749(2),293(9),82(12),259(11)])].

54476 R(A * x,A,y * A) = A * R(x,A,y). [para(48002(a,1),1089(a,2)),rewrite([9(10),3(8),232(16),293(14),47803(15),231(14),256(14),34(15),2684

9(12),232(10),293(8),50402(9),85(8),260(7),45738(6),232(10),293(8),54382(9),47803(14),231(13),256(13),34(14)]),flip(a)].

54690 R(x,y,A) * A = R(x * A,A',y). [para(6(a,1),48341(a,1,1,1)),rewrite([2143(9)])].

54713 x / (A' * (y * A')) = ((x * A) / y) * A. [para(16667(a,1),48341(a,1,1)),rewrite([45891(9)]),flip(a)].

54842 R(R(C,A * (x * C),A),A,R(x,A,C)) = C. [para(34704(a,1),48595(a,1,3,2)),rewrite([34855(16),10(13)])].

54877 R(x',A * A,x) = x'. [para(10978(a,1),3176(a,1,2)),rewrite([6(11),2421(8),2777(7)]),flip(a)].

54896 R(x / y,A * A,y / x) = x / y. [para(104(a,1),54877(a,1,1)),rewrite([104(8)])].

54963 R(C,A * C,R(C / x,x,A)') = R(C,A,x). [para(36015(a,1),3185(a,1,2)),rewrite([16(9,R),39659(9),39762(7),39692(8),39691(8),2144(7),232(6)

,293(4),122(6)]),flip(a)].

54977 (A * x) / R(x,A,C) = R(A,C',x). [para(2294(a,1),3187(a,1,1,2)),rewrite([16(9),35790(10),4610(11),1511(10),11955(11),1511(10,R),34790(1

1),35139(10),34(7),4610(15),1511(14),11955(15),1511(14,R),34790(15),52457(15),52698(16)])].

55055 R(x,A,C) / (A * x) = R(A,C',x)'. [para(35827(a,1),3197(a,1,2,2)),rewrite([4610(8),1511(7),11955(8),1511(7,R),34790(8),16(8,R),35139(8)

,34(5),4610(15),1511(14),11955(15),1511(14,R),34790(15),52457(15),52698(16)])].

55062 R(A * C,C',x * A') = R(A * C,x,A'). [para(35827(a,1),3198(a,1,2,1)),rewrite([16(11,R),39570(11),39698(11),1828(12),293(12),1511(13),16

59(14),43706(11),16(3),35827(22),1828(17),293(17),1511(18),1659(19)])].

55087 R(A,C',x) * R(x,A,C) = A * x. [para(54977(a,1),7(a,1,1))].

55091 R(A,C',R(x,A,C')) = R(A,C',x). [para(26864(a,1),54977(a,1,2)),rewrite([16(4),39763(7),39762(6),52466(7),16(10),39763(13)]),flip(a)].

55094 R(A,C',R(x,A,C)) = R(A,C',x). [para(54977(a,1),43671(a,2)),rewrite([16(8,R),35139(8),50838(9),1659(6)])].

55096 R(A,R(x,A,C'),C) = R(A,C',x). [back_rewrite(54136),rewrite([55091(15)])].

55097 R(A,R(x,A,C),C) = R(A,C',x). [back_rewrite(52457),rewrite([55094(13)])].

55164 R(A,C',x)' * (A * x) = R(x,A,C). [para(55087(a,1),10(a,1,2))].

55169 R(A,x,C) * R(x,A,C) = A * x. [para(52450(a,1),55087(a,1,1))].

55171 R(A,x,C)' * (A * x) = R(x,A,C). [para(55169(a,1),10(a,1,2))].

55177 R(R(A,x,C),R(x,A,C),C') = A. [para(55169(a,1),1672(a,1,1,2)),rewrite([1511(11,R),36039(11),36036(12)]),flip(a)].

55179 R(R(A,x,C)',A * x,C') = A'. [para(55177(a,1),142(a,2,1)),rewrite([55169(11)])].

55236 R(A' * x,A,C) = R(A',x,C) * x. [para(34(a,1),55171(a,1,2)),rewrite([141(6),30(6)]),flip(a)].

55237 A * (R(A,x,C)' * A) = R(A,C,x * C'). [para(55171(a,1),39(a,1,1,2)),rewrite([34420(5),49846(6)]),flip(a)].

55242 R(R(A',x,C),x,C') = A'. [para(34(a,1),55179(a,1,2)),rewrite([141(6),30(6)])].

55264 R(A',C * x,C) = R(A',x,C). [para(55242(a,1),26864(a,1,1)),flip(a)].

55266 R(A',C' * x,C) = R(A',x,C). [para(55242(a,1),26987(a,1,1))].

55267 R(A',x * C',C) = R(A',x,C). [para(55242(a,1),26994(a,1,1))].

55276 R(A',C * C,x) = R(A',x,C). [para(55264(a,1),4130(a,2))].

55288 R(A' * x,A,C) / x = R(A',x,C). [para(55276(a,1),125(a,2)),rewrite([1382(6,R),16(5,R),172(10),12(12),246(13),113(7),10(8),50112(8),172(

13),12(15),55266(17),55266(14)])].

55297 R(A',R(x,A,C'),C) = R(A',x,C). [para(2260(a,1),55267(a,1,2)),rewrite([39686(9),39662(10),55276(10),49939(18),142(21),4565(18),52471(18

),43663(17),52469(15),30(14)])].

55372 R(A,R(x,A,C),A * C) = R(A,C',x * A). [para(49255(a,1),2569(a,1,3)),rewrite([16(8),24137(9),43663(10),43663(8),16(12),43633(13),40055(1

1),16(13)]),flip(a)].

55373 R(C * R(x,C',y),C,y) = x * C. [para(49255(a,1),3196(a,1,1)),rewrite([6(8),43663(8)]),flip(a)].

55387 C * (C * R(x,C,y)) = R(C * (x * C),C,y). [para(49492(a,1),55373(a,1,1,2)),rewrite([16(12,R)]),flip(a)].

55396 R(C * (x / y),C,y) = (C * x) / y. [para(43671(a,1),55373(a,1,1,2)),rewrite([16(12,R),5303(12)])].

55403 (C * (x * y)) / y = R(C * x,C,y). [back_rewrite(50923),rewrite([55387(13),16(10,R),1659(10)])].

55407 R(R(A * C,C,x),x,C) = A * C. [back_rewrite(53574),rewrite([55403(5),16(3)])].

55419 R(x,C,C' * y) = R(x,C,y). [back_rewrite(50221),rewrite([55403(7),1659(5)]),flip(a)].

55431 x / R(A * x,A,C) = R(A,C,x)'. [back_rewrite(52597),rewrite([55419(12)])].

55437 R(A' * x,A,C') / x = R(A',C,x). [back_rewrite(44485),rewrite([55419(15)])].

55440 (x * (C' * y)) / y = R(C' * x,C,y). [back_rewrite(38193),rewrite([55419(8)]),flip(a)].

55441 R(A,C,(A' * C') * x) = R(A',C,x)'. [back_rewrite(36478),rewrite([55419(16)])].

55443 R(A,x * C,C') = R(A,C,x). [back_rewrite(35265),rewrite([55419(12)])].

55445 R(A,C,x) = R(A,x,C'). [back_rewrite(35263),rewrite([55419(9),55419(6)])].

55447 R(R(A,C,x),x,C) = A. [back_rewrite(35218),rewrite([55419(6)])].

55448 R(A,C,x * (A * C')) = R(A,x,A * C'). [back_rewrite(32638),rewrite([55419(11)])].

55455 R(x,C,y * C') = R(x,C,y). [back_rewrite(2585),rewrite([55419(5)]),flip(a)].

55468 A * (R(A,x,C)' * A) = R(A,C,x). [back_rewrite(55237),rewrite([55455(14)])].

55472 R(A * x,A,C) / x = R(A,C,x). [back_rewrite(49846),rewrite([55455(12)])].

55492 R(A,C,C * x) = R(A,C,x). [para(55445(a,2),80(a,2)),rewrite([1699(4),1511(7,R),34655(7),55472(6),1699(8)]),flip(a)].

55495 R(A,C' * x,C') = R(A,C,x). [para(55445(a,1),125(a,2)),rewrite([12145(7),1511(5),33788(7),55472(6)]),flip(a)].

55496 R(A,C,x)' = R(A,x,C')'. [para(55445(a,1),138(a,2,1)),rewrite([138(7)])].

55497 R(A,C,A' * x) = R(A',x,C')'. [para(55445(a,2),141(a,1))].

55506 R(A,C,x * (A * C)) = A * (x / R(x,A,C')). [para(55445(a,2),1522(a,2)),rewrite([1511(9,R),10(9),1511(11,R),39631(11),25345(11),39562(10

),85(6),260(5)]),flip(a)].

55507 R(A * x,A,C) = R(A,C,x) * x. [para(55445(a,2),2035(a,1,1)),rewrite([1699(5),55492(5),1699(8),1511(11,R),34655(11)]),flip(a)].

55511 R(A,x,C * C) = R(A,C,x). [para(55445(a,1),49829(a,1)),rewrite([55443(6)]),flip(a)].

55560 R(A * x,A,C) = R(A,x,C') * x. [para(55511(a,1),2306(a,1,1)),rewrite([172(6),51083(9),172(8),24807(13),2301(8),172(10),1382(17,R),16(16

,R),35978(16),33788(12)]),flip(a)].

55562 R(x,C,C * y) = R(x,C,y). [para(10(a,1),55419(a,1,3)),flip(a)].

55563 R(x,C,y * C) = R(x,C,y). [para(63(a,1),55419(a,1,3)),flip(a)].

55564 R(x,C,y * (y * C)) = R(x,C,y * y). [para(126(a,1),55419(a,1,3)),flip(a)].

55568 R(x,C,C' / y) = R(x,C,C / y). [para(5715(a,1),55419(a,1,3)),rewrite([55562(7)])].

55579 R(x,C,R(A * y,A,C)) = R(x,C,A * (C * y)). [para(34655(a,1),55419(a,1,3))].

55580 R(x,C,R(y * A,A,C)) = R(x,C,(C * y) * A). [para(35837(a,1),55419(a,1,3))].

55613 R(x,C,y * (C * (y * C))) = R(x,C,y * y). [para(1185(a,1),55562(a,1,3)),rewrite([55564(12)])].

55615 R(x,C,R(C * y,A,C)) = R(x,C,R(y,A,C)). [para(35139(a,1),55562(a,1,3))].

55621 R(x,C,(A * C') * y) = R(x,C,A * (C * y)). [para(33788(a,1),55562(a,1,3)),rewrite([55579(7)]),flip(a)].

55622 R(x,C,(C * y) * A) = R(x,C,y * (A * C')). [para(35803(a,1),55562(a,1,3)),rewrite([55580(7)])].

55642 R(A,C,x)' * R(A * x,A,C) = x. [para(55443(a,1),2036(a,1,1,1)),rewrite([1511(11,R),34704(11),1511(15,R),63(15)])].

55687 R(A,C,x)' * R(A,x,C') = 0. [para(55496(a,2),8(a,1,1))].

55793 R(A * C,C,x) = R(A * C,x,C'). [para(55407(a,1),26935(a,1,1)),rewrite([55419(14)]),flip(a)].

55811 A * (R(x,A,C) / x) = R(R(A,C,x),x,A). [para(55472(a,1),26923(a,1,1)),rewrite([34855(14),10(11)]),flip(a)].

55815 (A * x) / R(x,A,C') = R(A,C,R(x,A,C')). [para(39762(a,1),55472(a,1,1,1)),rewrite([39766(9)])].

55817 R(R(A,C,x),x,A) = R(A,C,x * A). [para(55472(a,1),45903(a,2)),rewrite([35846(10),232(7),293(5),85(6),260(5),55472(6)])].

55818 A * R(R(A,C,x),x,A') = R(A * A,C',x). [para(55472(a,1),47780(a,1,2,1)),rewrite([34420(15),53400(16)])].

55819 R(A,C,x * A) / (R(x,A,C) / x) = A. [para(55472(a,1),48331(a,1,1,1)),rewrite([55817(5),34855(13),10(10)])].

55820 R(A,C,x * A) * (x / R(x,A,C)) = A. [para(55472(a,1),48348(a,1,1,1)),rewrite([55817(5),34855(13),10(10)])].

55821 A * (R(x,A,C) / x) = R(A,C,x * A). [back_rewrite(55811),rewrite([55817(11)])].

55842 R(A,x',C') = R(A,C,x'). [para(1872(a,1),55495(a,1,2)),rewrite([10(7),55563(11)])].

55849 R(A,x / y,C') = R(A,C,x / y). [para(104(a,1),55842(a,1,2)),rewrite([104(9)])].

55856 R(A',x,C')' * (A' * x) = R(x,A,C). [para(34(a,1),55507(a,1,1)),rewrite([55497(9)]),flip(a)].

55902 R(A,C,x) * x = R(A * x,x',C). [para(55507(a,1),50850(a,2)),flip(a)].

55903 R(A,R(A * x,x',C),C) = R(A,C',A * x). [para(55507(a,1),55097(a,1,2)),rewrite([55902(5)])].

55941 R(R(A,C,x)',R(A,x,C'),y)' = R(A,C,x). [para(55687(a,1),141(a,1,2)),rewrite([76(5)]),flip(a)].

55942 R(A,C,x) * y = R(A,x,C') * y. [para(55687(a,1),2036(a,1,2,1)),rewrite([55941(10),2(5)])].

56033 R(x,C' * y,C) = R(x,y,C). [para(2234(a,1),55396(a,2)),rewrite([55440(6),49576(9),16(5,R),34(5)]),flip(a)].

56039 R(A * A,C',x) = R(A * A,x,C). [back_rewrite(53964),rewrite([56033(8)]),flip(a)].

56053 R(R(x,y,C')',x * y,C) = x'. [back_rewrite(27190),rewrite([56033(10)])].

56054 R(R(x,y,C'),y,C) = x. [back_rewrite(26987),rewrite([56033(8)])].

56055 R(R(x,y,C),y,C') = x. [back_rewrite(26935),rewrite([56033(5)])].

56056 R(x,y,C) * y = C * (x * (C' * y)). [back_rewrite(26808),rewrite([56033(5)])].

56057 x / (C * (y * (C' * x))) = R(y,x,C)'. [back_rewrite(8765),rewrite([56033(12)])].

56064 R(x,C * y,C') = R(x,y,C'). [para(56054(a,1),27045(a,1,1))].

56065 R(x,C * y,C) = R(x,y,C). [para(27045(a,1),56054(a,1,1))].

56066 R(x,y * C,C') = R(x,y,C'). [para(56054(a,1),27046(a,1,1))].

56067 R(x,y * C,C) = R(x,y,C). [para(27046(a,1),56054(a,1,1))].

56069 R(x,y * C',C) = R(x,y,C). [para(27047(a,1),56054(a,1,1)),flip(a)].

56087 R(x,C * C,y) = R(x,y,C). [para(56054(a,1),2875(a,2,1)),rewrite([2301(4),16(4,R),13(5),101(10),56065(4)]),flip(a)].

56154 R(R(x,y,C),y,C) = R(x,y,C * C). [back_rewrite(26813),rewrite([56065(6)])].

56185 R(R(A',C,A * x)',R(x,A,C),C) = A. [back_rewrite(51669),rewrite([56087(14)])].

56188 R(x,R(A * y,A,C),C) = R(x,A * (y * C),C). [back_rewrite(45777),rewrite([56087(9)])].

56208 R(x,R(C * y,A,C),C) = R(x,R(y,A,C),C). [back_rewrite(35305),rewrite([56087(14)])].

56217 R(x,y * (C * y),C) = R(x,y * y,C). [back_rewrite(18597),rewrite([56087(10)])].

56219 R(x,C' / y,C) = R(x,C / y,C). [back_rewrite(7609),rewrite([56087(9),56065(7)])].

56226 R(x,y * (C' * y),C) = R(x,y * y,C). [back_rewrite(5225),rewrite([56087(8)])].

56288 R(x,(A * C') * y,C) = R(x,A * (y * C),C). [para(33788(a,1),56065(a,1,2)),rewrite([56188(7)]),flip(a)].

56316 R(x,R(C' * y,A,C),C) = R(x,R(y,A,C),C). [para(36039(a,1),56033(a,1,2))].

56354 R(x,C' * y,C') = R(x,y,C'). [para(34(a,1),56064(a,1,2)),flip(a)].

56458 R(A,x,C)' * A = A' * R(A,C,x). [para(55468(a,1),10(a,1,2)),flip(a)].

56482 R(A,C,x) * A' = A * R(A,x,C)'. [para(55468(a,1),2466(a,2,1)),rewrite([56458(7),141(10),31686(8),30(3),260(9)]),flip(a)].

56485 A * (R(A,C',x)' * A) = R(A,C,x). [para(52450(a,2),55468(a,1,2,1,1))].

56492 R(A',C,A * x)' = R(A,C,x). [para(55097(a,1),55468(a,1,2,1,1)),rewrite([56485(9),36901(9)]),flip(a)].

56493 R(A,C,R(x,A,C')) = R(A,C,x). [para(55096(a,1),55468(a,1,2,1,1)),rewrite([56485(9)]),flip(a)].

56496 R(A,C',x)' * A = A' * R(A,C,x). [back_rewrite(52934),rewrite([56458(13)])].

56499 R(R(A,C,x),R(x,A,C),C) = A. [back_rewrite(56185),rewrite([56492(7)])].

56502 R(A,C,R(x,A,C)) = R(A,C,x). [back_rewrite(36901),rewrite([56492(13)])].

56503 (A * x) / R(x,A,C') = R(A,C,x). [back_rewrite(55815),rewrite([56493(14)])].

56521 R(R(A,C,x),R(x * C',A,C),C) = A. [para(7790(a,1),56499(a,1,2)),rewrite([55419(6)])].

56536 R(A,R(x,A,C),C') = R(A,C,x). [para(56499(a,1),56055(a,1,1))].

56539 R(A,C,A * (x * C)) = R(A,C,A * x). [para(33764(a,1),56502(a,1,3)),rewrite([55562(14)])].

56540 R(A,C,(A * C) * x) = R(A,C,A * (C * x)). [para(34431(a,1),56502(a,1,3))].

56541 R(A,C,A * (C * x)) = R(A,C,A * x). [para(34454(a,1),56502(a,1,3)),rewrite([56540(7),56539(14)])].

56542 R(A,C,x * (A * C)) = R(A,C,x * A). [para(34858(a,1),56502(a,1,3)),rewrite([55562(7)]),flip(a)].

56548 R(A,C,(x * C) * A') = R(A,C,x * A'). [para(2182(a,1),56502(a,1,3)),rewrite([16(6,R),35828(10),11560(12),10(8),55562(8),293(12)]),flip(

a)].

56550 R(A,C,x * (C * A')) = R(A,C,x * A'). [para(2190(a,1),56502(a,1,3)),rewrite([35828(12),11560(14),4120(10),55562(10),56548(8),293(14),70

(15),55562(16)]),flip(a)].

56556 R(A,C,R(C' / x,x,A)) = R(A,C,C / x). [para(41540(a,1),56502(a,1,3)),rewrite([55568(14)])].

56568 R(A,C,(A * C) * x) = R(A,C,A * x). [back_rewrite(56540),rewrite([56541(14)])].

56569 A * (x / R(x,A,C')) = R(A,C,x * A). [back_rewrite(55506),rewrite([56542(7)]),flip(a)].

56579 R(A',C,A * x) = R(A,C,x)'. [para(56492(a,1),30(a,1,1)),flip(a)].

56636 R(A',C,R(x,A,C)) = R(A',x,C'). [para(34236(a,1),56579(a,1,3)),rewrite([55615(9),55562(15),55497(13),30(14)])].

56675 R(A,C,x) * R(x,A,C) = R(A * x,A,C'). [para(34420(a,1),55560(a,1,1)),rewrite([56154(8),47215(7),56536(13)]),flip(a)].

56698 R(A,x,C') * x = R(A * x,x',C). [para(55560(a,1),50850(a,2)),flip(a)].

56700 R(A,C',A * (x * C)) = R(A,C',A * x). [para(55560(a,2),54123(a,2,3)),rewrite([56698(6),55903(8),45835(15)]),flip(a)].

56717 R(A * C,x * A,C) = R(A * C,C',x * A). [para(16(a,2),3563(a,1,1,2,2)),rewrite([16(6),24137(7),16(12,R),43706(13),16(3),43663(10)]),flip

(a)].

56720 R(A',x,C') * R(x,A,C) = A' * x. [para(34(a,1),55642(a,1,2,1)),rewrite([55497(6),30(7)])].

56730 R(A * C,x,C') * x = C * (A * x). [para(55793(a,1),2045(a,1,1)),rewrite([56354(9),16(12,R),1382(12),4123(16),34(14)])].

56755 R(R(A,C,x),R(x,A,C'),A) = R(A,C,x * A). [para(56493(a,1),55817(a,1,1)),rewrite([54281(17),43654(18),56493(18)])].

56770 R(A,x * y,C') = R(A,C,x * y). [para(2419(a,1),55849(a,1,2)),rewrite([2419(11)])].

56966 R(A * A,x,C * C) = R(A * A,C,x). [para(56039(a,1),49254(a,1,1)),rewrite([56154(7)])].

56991 R(R(x',A,C'),x * A,C) = x'. [para(41658(a,1),56053(a,1,1))].

57114 R(x,y * C',C * C) = R(x,y,C * C). [para(56154(a,1),24745(a,2)),rewrite([56069(5),56033(7),56154(4)]),flip(a)].

57296 R(A,C,x * A) / (x / R(x,A,C')) = A. [para(56503(a,1),48331(a,1,1,1)),rewrite([56755(9),10(10)])].

57367 R(A,C',(C' * x) * A) = R(A,x,A * C). [para(35139(a,1),3729(a,2,3,1)),rewrite([113(6),36039(7),16(10),55372(11),54281(19),39197(20),356

48(19),43685(17)])].

57392 R(R(x,A,C'),x' * A,C) = x. [para(30(a,1),56991(a,1,1,1)),rewrite([30(11)])].

57400 R(R(A,x,C) * x,x',C) = A * x. [para(52756(a,1),57392(a,1,1)),rewrite([889(7),82(10),259(9)])].

58268 R(x,C,(y * C) * A) = R(x,C,y * (A * C')). [para(122(a,1),3865(a,1,2)),rewrite([55622(6),122(13)]),flip(a)].

58301 A * R(C * A',x,A') = R(C,A,A' * x). [para(3923(a,1),45738(a,1)),rewrite([293(10)]),flip(a)].

58811 R(A,x,C) * x = R(A * x,x',C'). [para(57400(a,1),56055(a,1,1)),flip(a)].

58812 A' * R(A * x,x',C') = R(x,A,C'). [back_rewrite(53097),rewrite([58811(6)])].

58971 R(A * (A * x),A,C') / x = R(A * A,C,x). [para(56039(a,1),4058(a,2,1)),rewrite([1511(7,R),10466(8),39748(9),34(13),56033(19),56154(16),

56966(16)])].

59577 x * (R(x,y,C)' * x) = R(x,y,C'). [para(4243(a,1),1672(a,1,1,2)),rewrite([10(8),1511(13,R),10(13),9207(9),4032(6),56064(15),141(13),560

64(12),142(10),30(10)])].

59709 R(A * C,C',x) / R(C,x,A') = A. [para(51401(a,1),6(a,1,1))].

59717 R(C,x,A')' = R(C',x,A'). [para(51401(a,1),2420(a,1,1,1)),rewrite([50161(7),300(18),54281(9),231(7),256(7),1511(6),10(7)]),flip(a)].

59733 R(C',x,A')' = R(C,x,A'). [para(59717(a,1),30(a,1,1))].

59749 R(C',x * C',A') = R(C',x,A'). [para(6042(a,1),59717(a,1,1)),rewrite([59733(6),59717(5)]),flip(a)].

59752 R(C,A,A' * x)' = R(C',A,A' * x). [para(59717(a,1),2235(a,2)),rewrite([256(4),47803(7),16(5,R),39686(7),53458(7),256(12),47800(14)])].

59759 x / R(C * x,A,C') = R(C',A,A' * x). [back_rewrite(53458),rewrite([59752(14)])].

59762 R(C,C * x,A') = R(C,x,A'). [para(141(a,1),59733(a,1,1)),rewrite([30(3),59717(5),59733(6),30(8)]),flip(a)].

59763 R(C,x * C,A') = R(C,x,A'). [para(3925(a,1),59733(a,1,1)),rewrite([59717(5),59733(6)]),flip(a)].

59782 R(C,A,A * (x * C)) = R(C,A,A * x). [para(465(a,1),59763(a,1,2)),rewrite([73(8),48002(12),232(11),293(9),85(10),260(9),48002(17),232(16

),293(14),85(15),260(14)])].

59797 R(C,R(x,A,C),A) = R(C,x,A * C). [para(47631(a,1),51576(a,1,2)),rewrite([39797(12)]),flip(a)].

59803 R(C,C * x,A * C) = R(C,x,A * C). [back_rewrite(48518),rewrite([59797(8),59797(13)])].

59807 R(C,A * (x * C),A) = R(C,A * x,A * C). [para(33764(a,1),59797(a,1,2)),rewrite([59803(16)])].

59816 R(R(C,A * x,A * C),A,R(x,A,C)) = C. [back_rewrite(54842),rewrite([59807(7)])].

60017 R(R(A,C',x),x,A) = R(A,C',x * A). [para(52466(a,1),45903(a,2)),rewrite([39562(11),232(7),293(5),85(6),260(5),52466(7)])].

60018 A * R(R(A,C',x),x,A') = R(A * A,C,x). [para(52466(a,1),47780(a,1,2,1)),rewrite([39762(17),58971(18)])].

60262 R(A' * x,A',A * y) = A' * R(x,y,A). [para(4606(a,1),80(a,1,1)),rewrite([293(4),82(7),259(6),53413(5),293(10),16667(13)]),flip(a)].

60416 R(A' * R(x,y,A),y,A') = A' * x. [para(3115(a,1),54262(a,2)),rewrite([12(10),34(11),13(9),10(7),53413(5),12(15),34(16)])].

60724 R(A',C',x)' = R(A',x,C)'. [para(1664(a,1),4687(a,1,2)),rewrite([30(8),11560(13),1511(11),44469(13),39492(13),41083(13),138(10),30(12),

246(17),113(14),1511(15),44469(17),55091(17),52469(13)])].

60745 R(A',C',x) = R(A',x,C). [para(60724(a,1),30(a,1,1)),rewrite([30(6)]),flip(a)].

60761 R(A',C',A * x) = R(A,x,C)'. [para(60745(a,2),141(a,1)),rewrite([30(7),30(10)])].

60795 R(x,y,A') * A' = R(x * A',A,y). [para(7(a,1),54382(a,1,1,1)),rewrite([293(8)])].

60889 R(C,A,x)' * R(A * C,x,A') = A. [para(16(a,1),54383(a,1,2,1))].

60905 R(A,x * (C * A'),A * C') = R(A,C,x). [para(226(a,1),4849(a,1,3,2)),rewrite([293(7),1511(12),39165(13),55419(6),293(7),1511(13)]),flip(

a)].

60935 A * R(A' * x,A,y) = R(x,A,y * A). [para(34(a,1),54476(a,1,1)),flip(a)].

61131 (R(x,A,C) / x) * A' = R(A,x,A * C)'. [para(52485(a,1),55055(a,2,1)),rewrite([26849(10),35846(8),85(5),260(4)])].

61140 R(x,A,C) / x = A' * R(A,C,x * A). [para(55164(a,1),2111(a,2,1)),rewrite([256(8),56496(7),60262(11),55817(7)]),flip(a)].

61156 A * (R(A',x,C) * x) = R(x,A,C). [para(55236(a,1),34420(a,1,2)),rewrite([34(12)])].

61184 R(A,x / y,y) = R(A,y',y * x). [para(61156(a,1),2232(a,2,1)),rewrite([81(6),10(7),16636(4),52692(6),89(8)]),flip(a)].

61193 R(A,x',x * (y * x)) = R(A,y,x). [para(6(a,1),61184(a,1,2)),flip(a)].

61281 R(A,(x * y)',x) = R(A,x',x / y). [para(6173(a,1),61193(a,1,3,2)),rewrite([34(6)]),flip(a)].

61386 R(R(x,A,C) / x,x,A) = A * R(A',x,C). [para(55288(a,1),2149(a,2,2)),rewrite([34420(8),34(5)])].

61405 R(A',R(x,A,C),C) = R(A',x,C). [para(39535(a,1),55297(a,1,2)),rewrite([55297(15)])].

61450 (R(x,A,C) / x) / R(A,C,x * A) = A'. [para(55819(a,1),104(a,1,1)),flip(a)].

61454 (x / R(x,A,C)) * A' = R(A,C,x * A)'. [para(55820(a,1),32(a,1,2)),rewrite([293(6)])].

61460 R(A,C,x * A) * x = R(A * x,A,C). [para(55821(a,1),2035(a,2,1)),rewrite([61184(6),2037(11),11964(8),50130(7),10(8)]),flip(a)].

61461 R(A,x',x * R(x,A,C))' = A'. [para(55821(a,1),2235(a,1,2,1)),rewrite([61460(9),34500(9),61184(8)]),flip(a)].

61466 R(A,x',x * R(x,A,C)) = A. [para(61461(a,1),30(a,1,1)),rewrite([30(3)]),flip(a)].

61494 R(A,C',x) * x = R(A * x,x',C'). [para(56056(a,2),52465(a,2)),rewrite([43661(7),16(9,R),34(9),58811(9)])].

61601 R(A,C,x)' * A = A' * R(A,x,C). [para(56458(a,1),824(a,1,1)),rewrite([1071(7),30(13)])].

61651 R(A',R(x,A,C'),C') = R(A',C,x). [para(47631(a,1),56636(a,1,3)),rewrite([39765(11)]),flip(a)].

61917 R(R(A * C,x,C') * A',A,x) = C. [para(56730(a,1),2144(a,1,1)),rewrite([6(7)]),flip(a)].

62195 R(x,y,C)' * x = x' * R(x,y,C'). [para(59577(a,1),10(a,1,2)),flip(a)].

62196 x * (R(x',y,C) * x) = R(x',y,C')'. [para(141(a,1),59577(a,1,2,1,1)),rewrite([30(5),141(10)])].

62198 x * (R(x',A,C') * x) = R(x,A,C). [para(35792(a,1),59577(a,2)),rewrite([41082(4),41658(5)])].

62231 R(A * C,x,C) / R(C,x,A') = A. [para(50143(a,1),59709(a,1,1))].

62236 R(C,x,A') / R(A * C,x,C) = A'. [para(62231(a,1),104(a,1,1)),flip(a)].

62238 R(A * C,x,C) * A' = R(C,A,x * A). [para(62231(a,1),6610(a,1,1)),rewrite([62231(15),293(7),60795(8),25402(8),62236(20)]),flip(a)].

62251 R(C,A * C,x) = R(C,A,x). [para(34(a,1),59782(a,2,3)),rewrite([16(8,R),34236(9),35148(8)])].

62260 R(C',A,x)' = R(C,A,x). [back_rewrite(54963),rewrite([62251(10),50360(8)])].

62261 R(R(C,A,x),(A * C) * x,A) = C. [back_rewrite(53390),rewrite([62251(5)])].

62263 R(R(C,A,x),A * x,C) = R(C,A,R(x,A,C)). [back_rewrite(35147),rewrite([62251(15)])].

62267 R(C,A,R(C / x,x,A)') = R(C,A,x). [back_rewrite(50360),rewrite([62260(13)])].

62270 R(C,A,R(x,A,C)) = R(C,A,C' * x). [para(62251(a,1),3190(a,2)),rewrite([12145(11),1511(9),33788(11),35990(10)])].

62271 R(R(C,A,x),A * x,C) = R(C,A,C' * x). [back_rewrite(62263),rewrite([62270(13)])].

62276 R(C,A,x)' = R(C',A,x). [para(62260(a,1),30(a,1,1))].

62301 R(R(C',A,x),A,R(C,A,x)) = R(C',A,x). [para(62260(a,1),33478(a,1,3))].

62316 R(C',A,x) * R(A * C,x,A') = A. [back_rewrite(60889),rewrite([62276(4)])].

62378 R(C,A * (C * C),x) = R(C,A,x). [para(5530(a,1),62251(a,1)),rewrite([1382(6),1828(13),293(13),1511(14),1382(19),4123(20),12146(21),1195

5(20),33905(19),50131(20),11955(19),34415(19),35139(18),36039(19),10(16),62270(15),10(14)])].

62379 R(R(C,A,x),C * (A * (C * x)),A) = C. [para(5530(a,1),62261(a,1,1)),rewrite([16(4),62251(5),16(11),34415(13),35056(12)])].

62384 R(C,C * (A * (C * C)),x) = R(C,A,x). [para(62378(a,1),5530(a,1)),rewrite([4469(8),10163(18),33905(17),37480(18),13(19),34655(17),34431

(15),33905(12),50131(13),11955(12),34415(12),35139(11),36039(12),10(9),62270(8),10(7)]),flip(a)].

62988 R(A,C,x * A) = R(A,C,x). [para(61460(a,1),6(a,1,1)),rewrite([55472(6)]),flip(a)].

62991 R(A,x,A * C') = R(A,C,x). [para(61460(a,1),3951(a,1,1)),rewrite([34454(7),2130(7),63(6),58268(10),55448(11)]),flip(a)].

63011 (x / R(x,A,C)) * A' = R(A,C,x)'. [back_rewrite(61454),rewrite([62988(12)])].

63012 (R(x,A,C) / x) / R(A,C,x) = A'. [back_rewrite(61450),rewrite([62988(9)])].

63013 R(x,A,C) / x = A' * R(A,C,x). [back_rewrite(61140),rewrite([62988(11)])].

63021 R(A,C,x) / (x / R(x,A,C')) = A. [back_rewrite(57296),rewrite([62988(5)])].

63030 A * (x / R(x,A,C')) = R(A,C,x). [back_rewrite(56569),rewrite([62988(12)])].

63032 R(A,C,x * (A * C)) = R(A,C,x). [back_rewrite(56542),rewrite([62988(12)])].

63035 A * (R(x,A,C) / x) = R(A,C,x). [back_rewrite(55821),rewrite([62988(11)])].

63036 R(A,C,x) * (x / R(x,A,C)) = A. [back_rewrite(55820),rewrite([62988(5)])].

63046 R(A,C,x * A') = R(A,C,x). [back_rewrite(60905),rewrite([62991(11),56550(8)])].

63062 R(A,C,x * (A * C')) = R(A,C,x). [back_rewrite(55448),rewrite([62991(14)])].

63070 R(A,C,x * (C * A')) = R(A,C,x). [back_rewrite(56550),rewrite([63046(14)])].

63150 R(A,C,x * (A' * C')) = R(A,C,x). [para(1665(a,1),63046(a,1,3)),rewrite([1511(9),55419(12),55419(18),55419(15)])].

63153 R(R(A,C,x),x * A',C) = A. [para(63046(a,1),55447(a,1,1))].

63166 R(R(A,C,x),(C' * x) * A',C) = A. [para(63046(a,1),56521(a,1,1)),rewrite([1511(9,R),36074(12)])].

63222 R(A,C,((A * C) * x)') = R(A,C,C / x). [para(6173(a,1),63032(a,1,3)),rewrite([1828(6),293(6),1511(7),51533(12),55562(8),55568(6)]),flip

(a)].

63253 A * ((R(x,A,C) / x) * A) = R(A,C,x) * A. [para(63035(a,1),49(a,1,1)),flip(a)].

63283 R(A,x,C) * (R(x,A,C) / x) = A. [para(63036(a,1),2260(a,1,1,2,2)),rewrite([63011(8),61601(7),34(8),104(8),63011(16),8(17),3(11)])].

63353 R(A,C',x * A) = R(A,x,C). [para(63283(a,1),6(a,1,1)),rewrite([749(6),104(6),52711(6)])].

63369 R(R(A,C',x),x,A) = R(A,x,C). [back_rewrite(60017),rewrite([63353(12)])].

63373 R(A,x,A * C) = R(A,x,C). [back_rewrite(57367),rewrite([63353(9),56033(6)]),flip(a)].

63379 A * (x / R(x,A,C)) = R(A,x,C). [back_rewrite(52711),rewrite([63353(12)])].

63380 (R(x,A,C) / x) * A' = R(A,x,C)'. [back_rewrite(61131),rewrite([63373(12)])].

63424 R(R(A,x,C),x,A) = R(A,x,C). [para(63369(a,1),18(a,2)),rewrite([61494(5),25369(11),58812(10),53443(7)])].

63440 A * (R(x,A,C') / x) = R(A,x,C). [back_rewrite(53443),rewrite([63424(12)])].

63543 A * ((x / R(x,A,C)) * A) = R(A,x,C) * A. [para(63379(a,1),49(a,1,1)),flip(a)].

63688 R(A',R(A,C,x),x) = A'. [para(63012(a,1),2104(a,1,1)),rewrite([55902(13),50869(15)])].

63689 (x / R(x,A,C')) / R(A,C,x) = A'. [para(47631(a,1),63012(a,1,1,1)),rewrite([39765(5),39765(12),56493(12)])].

63693 (A' * R(A,C,x)) * x = R(x,A,C). [para(63688(a,1),78(a,1,1)),rewrite([55902(6),50894(8)]),flip(a)].

63767 A' * R(A,C,x) = A * R(A',x,C). [para(63013(a,1),45903(a,2)),rewrite([35846(8),85(5),260(4),61386(6),62988(13)]),flip(a)].

63768 R(x,A,C) / x = A * R(A',x,C). [para(63013(a,1),54896(a,2)),rewrite([54896(12),63767(10)])].

63769 x / R(x,A,C') = A * R(A',x,C). [para(56054(a,1),63013(a,1,1)),rewrite([56493(14),63767(11)])].

63780 R(A,A * R(A',x,C),x) = A. [para(63013(a,1),61184(a,1,2)),rewrite([63767(7),61466(15)])].

63784 A * (A * R(A',x,C)) = R(A,C,x). [para(63013(a,1),63035(a,1,2)),rewrite([63767(7)])].

63794 (A * R(A',x,C)) * x = R(x,A,C). [back_rewrite(63693),rewrite([63767(6)])].

63867 R(A,C,((C * A') * x)') = R(A,C,C / x). [para(6173(a,1),63070(a,1,3)),rewrite([784(7),55621(13),56541(12),41766(9),56493(9)]),flip(a)].

64059 A' * R(A,x,C') = A * R(A',x,C). [para(63440(a,1),6173(a,1,1,1)),rewrite([62195(6),749(16),104(16),63030(16),63767(13)])].

64145 R(A,C,x) * A = A * R(A',x,C')'. [para(63768(a,2),15(a,2,2,1)),rewrite([12(10),62196(9),63253(16)]),flip(a)].

64147 x / R(x,A,C) = A * R(A',x,C'). [para(63768(a,1),104(a,1,1)),rewrite([889(7),62195(8),30(3)]),flip(a)].

64150 (R(x,A,C) / x) * A = R(A',x,C')'. [para(63768(a,2),49(a,1,1)),rewrite([62196(14)])].

64163 (x / R(x,A,C)) * A = R(A',x,C)'. [para(63768(a,2),2420(a,1,1,1)),rewrite([104(5),300(15)])].

64171 A * (A * R(A',x,C')) = R(A,x,C). [para(63768(a,2),29750(a,2,2,1)),rewrite([749(6),232(10),293(8),62195(9),30(4),104(15),63379(15)])].

64211 R(A,x,C) * A = A * R(A',x,C)'. [back_rewrite(63543),rewrite([64163(7)]),flip(a)].

64238 A * (A * R(A,x,C)') = R(A,C,A * x). [para(141(a,1),63784(a,1,2,2)),rewrite([30(5),30(13)])].

64256 (A * R(A',x,C')) * R(x,A,C) = x. [para(63794(a,1),10(a,1,2)),rewrite([889(7),62195(8),30(3)])].

64273 R(R(A,C,x),x,A') = R(A,C,x). [para(63794(a,1),54262(a,1,1,1)),rewrite([55472(6),142(13),49(14),62195(13),64059(14),63784(14)])].

64276 A * R(A,C,x) = R(A * A,C',x). [back_rewrite(55818),rewrite([64273(7)])].

64488 A' * R(A,x,C) = A * R(A',x,C'). [para(52519(a,1),6313(a,1,1)),rewrite([62195(6),64059(7),889(7),62195(8),30(3),30(14),30(22),52516(21)

,3(14)]),flip(a)].

64958 R(A * C,x,C') * A' = R(C,A * x,A). [para(61917(a,1),22987(a,1,1)),flip(a)].

64963 R(C,A * x,A * C) = R(C,A * x,A). [para(61917(a,1),23055(a,1,1)),rewrite([59807(7),56064(15),64958(16)])].

64968 R(R(C,A * x,A),A,C * (C * x)) = C. [para(3365(a,1),61917(a,1,1,1)),rewrite([56064(10),56066(8),64958(9)])].

64978 R(R(C,A * x,A),A,R(x,A,C)) = C. [back_rewrite(59816),rewrite([64963(7)])].

65025 R(R(C,(A * C) * x,A),A,x) = C. [para(47631(a,1),64978(a,1,3)),rewrite([39765(7),39762(7),39708(9),48343(9)])].

65034 R(C,R(x,A,C'),A) = R(C,x,A). [para(65025(a,1),23049(a,1,1)),rewrite([246(11),293(8),39686(11),51540(12)]),flip(a)].

65045 R(C,x,A * C) = R(C,x,A). [para(39535(a,1),65034(a,1,2)),rewrite([59797(6),65034(12)])].

65063 R(C,R(x,A,C),A) = R(C,x,A). [back_rewrite(59797),rewrite([65045(11)])].

65293 R(x,A,C') * x' = x * R(x',A,C). [para(62198(a,1),34(a,1,2)),rewrite([30(7)]),flip(a)].

65295 R(x',A,C) * x = x' * R(x,A,C'). [para(62198(a,1),231(a,1,1)),rewrite([30(8),65293(12),195(13),62196(12),41658(12),30(8)])].

65305 A' * R(A * C,x,C) = R(C,x,A'). [para(62236(a,1),7(a,1,1))].

65327 R(R(x,A,y)',(x * A) * y,A) = x'. [para(6459(a,1),47936(a,1,1,2)),rewrite([54384(7),34(8),34(14)])].

65330 R(C,A,R(x,A,C')) = R(C,A,x * C). [para(32(a,1),62267(a,1,3,1,1)),rewrite([142(7),39260(5),41658(7),41658(8),30(4)])].

65336 R(C,A,C' * (C' * x)) = R(C,A,x * C). [para(49254(a,1),62270(a,1,3)),rewrite([39260(5),65330(7),40055(13),36039(13),62270(14)]),flip(a)

].

65338 R(C,A,C' * (x * C')) = R(C,A,x * C). [para(5373(a,2),62270(a,2,3)),rewrite([2277(6),62270(9),1659(20),65336(18)])].

65399 R(C,A,C * (C * (C * x))) = R(C,A,x). [para(62379(a,1),47659(a,1,1)),rewrite([39783(11),65330(11),16(8,R)])].

65570 R(A,C,x)' * (A * A) = R(A',x,C)'. [para(63011(a,1),2143(a,1,1)),rewrite([11197(10),64163(14),12478(18)])].

66395 R(A,x,C)' * (A * A) = R(A',x,C')'. [para(63380(a,1),2143(a,1,1)),rewrite([11197(10),64150(14),12478(19)])].

66586 (x / R(x,A,C')) * A = R(A',x,C')'. [para(63689(a,1),6610(a,1,1)),rewrite([63689(14),256(8),64145(7),10(11),63021(20)]),flip(a)].

66621 R(x,A,C) / x = x / R(x,A,C'). [para(63769(a,2),63768(a,2))].

66643 R(x,A,C') / x = x / R(x,A,C). [para(66621(a,1),104(a,1,1)),rewrite([104(6)])].

66653 (x / R(x,A,C)) * x = R(x,A,C'). [para(66643(a,1),7(a,1,1))].

66682 R(R(A,C',x),x,A') = R(A,x,C). [para(66653(a,1),54262(a,1,1,1)),rewrite([52466(7),64163(17),142(13),30(12)])].

66684 A * R(A,x,C) = R(A * A,C,x). [back_rewrite(60018),rewrite([66682(8)])].

66779 A' * R(A * A,C,x) = R(A,x,C). [para(66684(a,1),10(a,1,2))].

66947 x / R(x,A,C) = A * R(A',C,x). [para(47631(a,1),64147(a,1,2)),rewrite([39765(5),66643(5),39765(12),61651(14)])].

66959 (x / R(x,A,C)) / R(A',C,x) = A. [para(66947(a,2),6(a,1,1))].

66960 (A * R(A',C,x)) * R(x,A,C) = x. [para(66947(a,1),7(a,1,1))].

66961 A * (A * R(A',C,x)) = R(A,x,C). [para(66947(a,2),12(a,2,2)),rewrite([12(8),63379(14)])].

66962 R(A',C,x) / (x / R(x,A,C)) = A'. [para(66947(a,2),32(a,1,2))].

66971 A * (R(A',C,x) * A') = R(A,C,x)'. [para(66947(a,2),232(a,1,1)),rewrite([63011(7),293(11)]),flip(a)].

66988 R(A,x,C) * R(A',C,x)' = A * A. [para(66947(a,2),2421(a,1,1,2)),rewrite([63379(6),2777(22)])].

67034 R(A',C,x) * A = A' * R(A',x,C)'. [para(66959(a,1),6610(a,2,2)),rewrite([66962(9),66962(15),256(9),64163(8)]),flip(a)].

67044 A * (A * R(A,C,x)') = R(A,C',A * x). [para(124(a,1),66961(a,1,2,2)),rewrite([16(7,R),784(8),33788(9),55431(8),16(13,R),784(14),56288(1

6),54123(15),56700(16)])].

67045 R(A',C,x)' * A' = A * R(A',x,C). [para(66961(a,1),2420(a,1,1,1)),rewrite([889(18),1065(20),62195(6),64059(7),889(13)]),flip(a)].

67087 R(A,R(A',x,C'),R(x,A,C)) = A. [para(64256(a,1),18(a,1,1)),rewrite([56720(9),32(4),30(3)]),flip(a)].

67103 R(A,R(A',C,x),x) = A. [para(47631(a,1),67087(a,1,3)),rewrite([39765(8),61651(10)])].

67124 R(A,R(A,C,x)',A * x) = A. [para(56579(a,1),67103(a,1,2))].

67192 R(A,R(A,C,x)',R(A * x,A,C')) = A. [para(39762(a,1),67124(a,1,3)),rewrite([56493(8)])].

67447 R(R(C,A * (x * (C' * C')),A),A,x) = C. [para(5028(a,1),64968(a,1,3,2)),rewrite([1659(17)])].

67577 R(C,A,C * (x * (C * C))) = R(C,A,x). [para(70(a,1),65330(a,2,3)),rewrite([65330(11),16(8,R),65399(9)]),flip(a)].

67980 R(A,C',x)' * (A * A) = R(A',C,x)'. [para(66988(a,1),53037(a,1,2))].

68103 R(C,A,x * (C' * C')) = R(C,A,C * x). [para(82(a,1),67577(a,1,3,2)),rewrite([172(7),57114(12),43633(9),2277(7),172(11)]),flip(a)].

68105 R(C,A,x * (C * (C * C))) = R(C,A,x). [para(6130(a,1),67577(a,1,3))].

68207 R(C,A,R(A,C,x)) = R(C,A,R(A,x,C')). [para(55942(a,1),68105(a,1,3)),rewrite([68105(13)]),flip(a)].

68496 R(A,x / y,C) = R(A,C',x / y). [para(8522(a,1),54123(a,1,2)),rewrite([8522(14)])].

68498 R(A,R(x,y,z),C) = R(A,C',R(x,y,z)). [para(18(a,1),68496(a,1,2)),rewrite([18(11)])].

68806 ((x * y) / z) * x' = x * (y / (x * z)). [para(9(a,1),9203(a,1,2,2)),rewrite([3(4)]),flip(a)].

69136 R(C,R(x,A,C),C * A') = R(C,x,A'). [para(39252(a,1),97(a,1,2)),rewrite([16(5,R),35139(5),39252(10),16(4,R),70(7),92(13),59763(6)]),flip

(a)].

69200 (A * (A * (C / x))) * (x * A') = A * C. [para(39985(a,1),45820(a,1,1,2)),rewrite([39741(16)])].

69820 A' * R(A * x,A,y) = R(x,A,y * A'). [para(48025(a,1),10(a,1,2))].

69983 R(R(C,A,C * x),A * x,C) = R(C,A,x). [para(11173(a,1),4066(a,2,2,2)),rewrite([122(8),62251(7),122(12),33905(11),56065(13),56065(11),16(

18,R),3710(20),62384(18)])].

70139 ((A * x) * y) / (y * (x * y)) = A * y'. [para(50385(a,1),32(a,1,2)),rewrite([784(10)])].

70533 x * R(A,x',x * C) = R(x * A,A,C). [para(11964(a,1),8823(a,2,2,2)),rewrite([82(7),294(6),1511(5),35803(7),16(12,R),50321(14)]),flip(a)]

.

70548 ((x * C) * A) / (C * x) = x * (A * x'). [para(53968(a,1),9211(a,1,1)),rewrite([10(16),232(13),28631(11),10(14)])].

70549 x' * R(x * A,A,C) = R(A,x',x * C). [para(53968(a,1),10466(a,2,2,2)),rewrite([234(12),1699(8),698(11),10(9),50321(9),43793(13)]),flip(a

)].

70855 R(x,y * (x * C),C) = R(x,y * x,C). [para(6466(a,1),56057(a,2,1)),rewrite([10(13),10(9),101(8),30(10)]),flip(a)].

70861 R(x,R(y,x,C) * x,C) = R(x,y * x,C). [para(78(a,1),70855(a,1,2)),rewrite([16(3,R),56065(5)]),flip(a)].

71842 R(x,A,y * A) / R(A' * x,A,y) = A. [para(60935(a,1),6(a,1,1))].

72109 x * (R(x,y,C')' * x) = R(x,y,C). [para(62195(a,1),32(a,1,2)),rewrite([6180(6),30(10)])].

72128 R(x,y,C')' * x = x' * R(x,y,C). [para(72109(a,1),10(a,1,2)),flip(a)].

72130 R(x,y,C') * x' = x * R(x,y,C)'. [para(72109(a,1),29750(a,2,2,1)),rewrite([72128(5),6180(5),62195(4),34(6)])].

72970 R(A',C,x) * A' = A' * R(A,C,x)'. [para(66971(a,1),10(a,1,2)),flip(a)].

73440 (C' * (x * y)) * x' = x * (y / (C * x)). [para(16(a,2),68806(a,2,2,2)),rewrite([113(3)])].

73629 R(C,R(x,A,C'),A') = R(C,x,C * A'). [para(47631(a,1),69136(a,1,2)),rewrite([39765(12)]),flip(a)].

73819 R(R(C,A,x * C),A * x,C) = R(C,A,x). [para(16(a,1),69983(a,1,1,3))].

73883 R(R(A,x,y) / y,y,x * y) = A * y'. [para(70139(a,1),2104(a,2)),rewrite([18(5)])].

73897 x * (x * ((x' * C) * A)) = C * (x * A). [para(46732(a,1),18273(a,1,2,2,2,2)),rewrite([4120(11),63(7)]),flip(a)].

73978 R(x * A,A,C) / R(A,x',x * C) = x. [para(70533(a,1),6(a,1,1))].

73979 x * R(A,x',C * x) = R(x * A,A,C). [para(16(a,2),70533(a,1,2,3))].

73981 x * R(x' * A,A,C) = R(A,x,x' * C). [para(70533(a,1),34(a,1,2)),rewrite([30(10)])].

73991 (C' * x) * (A * (C / x)) = x * (A * x'). [para(7(a,1),70548(a,1,1,1)),rewrite([113(5),34(7),28631(3),113(6),113(10),158(12)]),flip(a)]

.

73992 (C * x) * (A * (C' / x)) = x * (A * x'). [para(16(a,2),70548(a,1,1,1)),rewrite([28631(7),1724(6)])].

74120 A * R(C,A,x * C) = A * R(C,A,x). [para(73(a,1),70861(a,2,2)),rewrite([56067(10),78(12),49(7),16(9,R),56065(11),49082(9),54476(7),49082

(16),54476(14)]),flip(a)].

74121 R(A * C,R(x,A,C),C) = R(A * C,x,C). [para(35827(a,1),70861(a,2,2)),rewrite([56067(14),35842(12),247(13),16598(12),34415(12),36039(11),

10(8)])].

74131 R(C,A,x * C) = R(C,A,x). [para(74120(a,1),10(a,1,2)),rewrite([10(8)]),flip(a)].

74138 R(C,A,C' * x) = R(C,A,x). [back_rewrite(73819),rewrite([74131(5),62271(7)])].

74145 R(C,A,x * C') = R(C,A,x). [back_rewrite(65338),rewrite([74138(9),74131(11)])].

74158 R(C,A,R(x,A,C)) = R(C,A,x). [back_rewrite(62270),rewrite([74138(12)])].

74162 R(C,A,x * (x * C)) = R(C,A,x * x). [para(12(a,1),74131(a,1,3))].

74163 R(C,A,C * x) = R(C,A,x). [para(16(a,2),74131(a,1,3))].

74165 R(R(C,A,x),A * (x * C),A) = C. [para(74131(a,1),22987(a,1,1))].

74167 R(C,A,x * (C' * x)) = R(C,A,x * x). [para(1684(a,1),74131(a,1,3)),rewrite([16(8,R),9(8),3(6),74138(7),74138(14)]),flip(a)].

74184 R(C,A,x * (C' * C')) = R(C,A,x). [back_rewrite(68103),rewrite([74163(14)])].

74215 R(C',A,C' * x) = R(C',A,x). [para(74138(a,1),62276(a,1,1)),rewrite([62276(4)]),flip(a)].

74225 R(C',A,x * C') = R(C',A,x). [para(74145(a,1),62276(a,1,1)),rewrite([62276(4)]),flip(a)].

74235 R(R(C',A,x),C * (A * x),A) = C'. [para(74158(a,1),65327(a,1,1,1)),rewrite([62276(4),16(7),35056(11)])].

74256 R(R(C,x,A'),A',C * (A * x)) = C. [para(54235(a,1),74165(a,1,1)),rewrite([16(13,R),1527(14),16(8,R),50834(11),16(10,R)])].

74313 R(R(C',A,A' * x),C * x,A) = C'. [para(34(a,1),74235(a,1,2,2))].

74336 R(C,C * x,C * A') = R(C,x,A'). [para(74256(a,1),54261(a,1,1)),rewrite([39783(8),73629(10)])].

74372 R(C,x,C * A') = R(C,x,A'). [para(34(a,1),74336(a,1,2)),rewrite([141(13),59733(12)])].

74376 R(C',x,C * A')' = R(C,x,A'). [para(3468(a,1),74336(a,2)),rewrite([34(9),141(9),141(18),59749(16),59733(14)])].

74377 R(C,R(x,A,C'),A') = R(C,x,A'). [back_rewrite(73629),rewrite([74372(14)])].

74386 R(C',x,C * A') = R(C',x,A'). [para(74376(a,1),30(a,1,1)),rewrite([59717(5)]),flip(a)].

74387 R(C',R(x,A,C'),A') = R(C',x,A'). [para(74377(a,1),59717(a,1,1)),rewrite([59717(5)]),flip(a)].

74398 R(C',A,A' * x) * (C * x) = R(x,A,C). [para(74386(a,1),5317(a,1,1)),rewrite([39194(9),25535(9),39539(9),74387(11),47800(7),39194(19),25

535(19),39539(19),39492(19),39337(19),35210(20),34(15)])].

75299 R(A * x',x,R(x,A,C)) = A * x'. [para(63780(a,1),73883(a,1,1,1)),rewrite([749(2),63794(10)])].

75395 R(x,R(x,A,C),A') = x. [para(75299(a,1),54397(a,1,1,1)),rewrite([889(4),30(2),82(5),259(4)]),flip(a)].

75404 R(x,A,R(A' * (x * A'),A,C)) = x. [para(75395(a,1),54235(a,2)),rewrite([35846(9),34855(10)])].

75546 R(x,R(x * A',A,C),A) = x. [para(75404(a,1),22987(a,1,1)),rewrite([34420(11),34(8)])].

75551 x * R(x,A,C) = R(x * x,A,C'). [para(75546(a,1),78(a,1,1)),rewrite([54281(8),82(5),259(4),39197(4),39739(13)])].

75553 x' * R(x * x,A,C') = R(x,A,C). [para(75546(a,1),2036(a,1,1,1)),rewrite([39739(10),54281(15),82(12),259(11),39197(11)])].

75673 x * R(x' * x',A,C') = R(x',A,C). [para(75551(a,1),34(a,1,2))].

75888 x' * (C * (x * A)) = x * ((x' * C) * A). [para(73897(a,1),10(a,1,2))].

75890 x' * ((x * C) * A) = x * (C * (x' * A)). [para(73897(a,1),34(a,1,2)),rewrite([30(9)]),flip(a)].

76040 R(x * A,A,C) / R(A,x',C * x) = x. [para(16(a,2),73978(a,1,2,3))].

76044 R(A,x',C * x) / R(x * A,A,C) = x'. [para(73979(a,1),32(a,1,2))].

76108 R(A * C,A,x * C) = R(A * C,A,x). [para(33764(a,1),74121(a,1,2)),rewrite([49082(9),56065(16),49082(14)])].

76109 R(A * C,(A * C) * x,C) = R(A * C,A,x). [para(34454(a,1),74121(a,1,2)),rewrite([49082(18),76108(16)])].

76113 R(C' * R(A * C,x,C),C,R(x,A,C)) = A. [para(74121(a,1),54127(a,1,1,2))].

76117 R(A * C,A,C' * x) = R(A * C,A,x). [para(34644(a,1),74121(a,1,2)),rewrite([56033(10),49082(7),49082(15)]),flip(a)].

76119 R(A * C,A,C * x) = R(A * C,A,x). [para(16(a,2),76108(a,1,3))].

76160 R(R(C',A,A' * (x * C')),x,A) = C'. [para(1659(a,1),74313(a,1,2))].

78147 (x * (A * x')) / (C / x) = (C' * x) * A. [para(22323(a,1),2051(a,2,2,1)),rewrite([226(11),302(10),73991(8),226(18),302(17)])].

78782 R((C * x) * A,C / x,C) = x * (A * C). [para(56219(a,1),22863(a,2)),rewrite([104(4),1699(3),73992(8),16(6,R),16(11,R),9339(12),78147(9)

,39539(8),39692(8),39687(8),104(8),1699(7)]),flip(a)].

78797 R(x * A,x',C) = R(x * A,A,C). [para(34(a,1),78782(a,1,1,1)),rewrite([6180(7),56065(9),56067(7),247(12),35837(12)])].

78801 R(x' * A,A,C) = R(x' * A,x,C). [para(30(a,1),78797(a,1,2)),flip(a)].

79141 (A * R(A',C,x)) * x' = R(x',A,C). [para(66960(a,1),29801(a,1,1)),rewrite([66960(10),75551(4),41658(6),172(2),75673(8),66960(20)]),flip

(a)].

79149 R(R(A,x,C),x' * A,C) = A. [para(79141(a,1),3565(a,1,1,2,1)),rewrite([78(9),16(6,R),6(13),66961(9)]),flip(a)].

79175 R(A,C,x') = R(A,x,C). [para(79149(a,1),56055(a,1,1)),rewrite([56770(7),62988(6)])].

79183 R(A,x',C) = R(A,C,x). [para(30(a,1),79175(a,1,3)),flip(a)].

79185 R(A,C,C / x) = R(A,x,C). [para(158(a,1),79175(a,1,3)),rewrite([56033(11)])].

79190 R(A',x,C)' = R(A,C,x'). [para(1071(a,1),79175(a,1,3)),rewrite([62988(6),141(10)]),flip(a)].

79193 R(A,C,x')' = R(A,x,C)'. [para(79175(a,1),138(a,2,1)),rewrite([138(9)])].

79202 R(A,C',x) = R(A,C,x'). [para(41403(a,1),79175(a,1,3)),rewrite([56502(7),68498(10),55094(11)]),flip(a)].

79358 R(A,x,C) / (x' / R(x',A,C')) = A. [para(79175(a,1),63021(a,1,1))].

79428 R(A * A,C',x') = R(A * A,C,x). [para(79175(a,1),64276(a,1,2)),rewrite([66684(5)]),flip(a)].

79542 (x' / R(x',A,C')) / R(A,x,C) = A'. [para(79175(a,1),63689(a,1,2))].

79553 A * R(A',x',C) = A * R(A',x,C'). [para(79175(a,1),63767(a,1,2)),rewrite([64488(6)]),flip(a)].

79853 R(A,C,A * x) = R(A,C,x). [para(79175(a,2),64238(a,1,2,2,1)),rewrite([67044(9),79202(7),889(6),30(4),63046(6)]),flip(a)].

79909 R(A',x,C')' = R(A,C,x). [para(79175(a,1),65570(a,1,1,1)),rewrite([66395(8),79190(12),30(10)])].

80145 R(A,C,((C * A') * x)') = R(A,x,C). [back_rewrite(63867),rewrite([79185(14)])].

80148 R(A,C,((A * C) * x)') = R(A,x,C). [back_rewrite(63222),rewrite([79185(13)])].

80164 R(A,C,R(C' / x,x,A)) = R(A,x,C). [back_rewrite(56556),rewrite([79185(13)])].

80224 R(A',C,x) * A = A * R(A',x,C'). [back_rewrite(67034),rewrite([79190(13),63767(13),79553(13)])].

80229 R(A,C,x)' * (A * A) = R(A,C,x'). [back_rewrite(65570),rewrite([79190(13)])].

80232 R(A,x,C) * A = R(A * A,C,x). [back_rewrite(64211),rewrite([79190(11),64276(11),79428(12)])].

80349 R(A',C,x)' = R(A,C,x). [back_rewrite(67980),rewrite([79202(4),80229(9),30(4)]),flip(a)].

80388 R(A,x * y,C) = R(A,C,(x * y)'). [back_rewrite(54123),rewrite([79202(9)])].

80423 (x * R(A,C,y')) / R(A,y,C) = x. [back_rewrite(52828),rewrite([79202(4)])].

80502 R(A,C,(A * C) * x) = R(A,C,x). [back_rewrite(56568),rewrite([79853(12)])].

80511 (x / R(x,A,C')) * A = R(A,C,x). [back_rewrite(66586),rewrite([79909(13)])].

80538 R(A,C,x) * (A' * x) = R(x,A,C). [back_rewrite(55856),rewrite([79909(6)])].

80541 R(A,C,A' * x) = R(A,C,x). [back_rewrite(55497),rewrite([79909(12)])].

80569 A * R(A,x,C)' = A * R(A',x,C). [back_rewrite(67045),rewrite([80349(5),56482(6)])].

80589 R(A,C,(A' * C') * x) = R(A,C,x). [back_rewrite(55441),rewrite([80349(14)])].

80621 R(A,C,x) * A' = A * R(A',x,C). [back_rewrite(56482),rewrite([80569(12)])].

80646 R(A,x',C) = R(A,x,C'). [para(79183(a,2),55445(a,1))].

80654 R(A,C,x)' = R(A',C,x). [para(79183(a,2),4657(a,1,1)),rewrite([1828(5),293(5),1511(6),80646(10),56770(10),80589(9),1828(9),293(9),1511(

10),44469(12),55437(12)])].

80655 R(A,x,C')' = R(A',C,x). [para(79183(a,1),60761(a,2,1)),rewrite([60761(8),80646(4),80654(9)])].

80992 R(A,R(A',C,x),R(A * x,A,C')) = A. [para(79183(a,2),67192(a,1,2,1)),rewrite([80646(5),80655(6)])].

81202 R(A,x,C)' = R(A',C,x'). [back_rewrite(79193),rewrite([80654(5)]),flip(a)].

81213 R(A',C,x) * A' = A' * R(A',C,x). [back_rewrite(72970),rewrite([80654(13)])].

81529 R(A',C,x') = R(A',x,C). [para(79202(a,1),4657(a,1,1)),rewrite([1538(7),293(5),80145(9),81202(4),1538(12),293(10),44481(13),55288(12)])

].

81582 R(A,C,x / R(x,A,C)) = R(A,C,R(A,x,C)). [para(63379(a,1),79853(a,1,3)),flip(a)].

81648 R(A,C,R(A',C,x)) = R(A,C,R(A,x,C)). [para(66947(a,2),79853(a,1,3)),rewrite([81582(7)]),flip(a)].

82073 R(A',x,C') * A = A * R(A',x,C'). [para(79190(a,1),72130(a,2,2)),rewrite([30(8),63767(14),79553(14)])].

82374 R(A',x',C) = R(A',C,x). [para(30(a,1),81529(a,1,3)),flip(a)].

82382 R(A',C',x) = R(A',C,x'). [para(81529(a,2),60745(a,2))].

82672 R(A',x',C) = R(A',x,C'). [para(41403(a,1),82374(a,1,2)),rewrite([61405(8),56636(12)])].

83016 C * (x * R(y,x,C)) = x * (y * C). [para(23319(a,2),13604(a,1,1)),rewrite([246(11),113(7),73440(10),101(7),203(13),10(12)])].

84018 C' * (x * (y * C)) = x * R(y,x,C). [para(83016(a,1),10(a,1,2))].

84026 x * (C * R(A,C,x)) = C * (x * A). [para(55447(a,1),83016(a,1,2,2)),rewrite([16(9,R)]),flip(a)].

84029 (x * A') * (C * R(A,C,x)) = C * x. [para(63153(a,1),83016(a,1,2,2)),rewrite([82(6),259(5),16(10,R)]),flip(a)].

84248 x * ((x' * C) * A) = C * R(A,C,x). [para(84026(a,1),10(a,1,2)),rewrite([75888(6)])].

84250 x * (C * (x' * A)) = C * R(A,C,x'). [para(84026(a,1),34(a,1,2))].

84254 R(A,x,C * x') = R(A,C,x'). [para(84026(a,1),4687(a,1,2,2)),rewrite([63046(8),82(13),259(12),122(10),113(8),10(9),63046(17),84029(16)])

,flip(a)].

84270 x' * ((x * C) * A) = C * R(A,C,x'). [back_rewrite(75890),rewrite([84250(12)])].

84284 R(A,x,x' * C) = R(A,C,x'). [para(16(a,1),84254(a,1,3))].

84285 R(A,x',C * x) = R(A,C,x). [para(30(a,1),84254(a,1,3,2)),rewrite([30(9)])].

84290 x * R(x' * A,A,C) = R(A,C,x'). [back_rewrite(73981),rewrite([84284(12)])].

84292 R(A,C,x) / R(x * A,A,C) = x'. [back_rewrite(76044),rewrite([84285(5)])].

84293 R(x * A,A,C) / R(A,C,x) = x. [back_rewrite(76040),rewrite([84285(10)])].

84295 R(x * A,A,C) = x * R(A,C,x). [back_rewrite(73979),rewrite([84285(5)]),flip(a)].

84296 R(A,x',x * C) = R(A,C,x). [para(16(a,1),84285(a,1,3))].

84302 x' * R(x * A,A,C) = R(A,C,x). [back_rewrite(70549),rewrite([84296(12)])].

84320 R(x,A,C) / R(A,C,x) = x * A'. [para(7(a,1),84293(a,1,1,1)),rewrite([293(7),63046(9),293(9)])].

84333 (x * A') * R(A,C,x) = R(x,A,C). [para(7(a,1),84295(a,1,1)),rewrite([293(5),293(10),63046(12)]),flip(a)].

84389 R(x',A,C') * (x * A) = R(A,C,x). [para(84295(a,2),41992(a,1,2)),rewrite([54281(11),43654(12),56054(14),56493(15)])].

84429 x * R(A,C,x) = R(x * A,x',C). [para(84295(a,1),78797(a,2)),flip(a)].

84582 R(A,C,x) / R(x,A,C) = A * x'. [para(7(a,1),84292(a,1,2,1)),rewrite([293(4),63046(6),293(9),784(11)])].

84591 R(A,C,x * x) = R(A,C,x'). [para(423(a,1),84302(a,1,2,1)),rewrite([1824(6),6248(6),1665(20),36039(18),33146(15),16(8),34869(13),12(11),

53968(10),84270(8),10(9),55613(12)]),flip(a)].

84959 R(A,x * A',R(A,C,x)) = A. [para(84320(a,1),61184(a,1,2)),rewrite([80654(13),56675(20),80992(20)])].

84984 R(A,C * x,R(A,C,x)) = A. [para(3762(a,1),84959(a,1,3)),rewrite([85(8),260(7),58268(10),63062(11)])].

85208 R(A,C * (A' * x),R(A,C,x)) = A. [para(80541(a,1),84984(a,1,3))].

87436 R(A,x,C) / R(x',A,C) = A * x. [para(79175(a,1),84582(a,1,1)),rewrite([30(11)])].

88180 R(A',x * A',R(A,C,x))' = A. [para(1666(a,2),85208(a,1,2,2)),rewrite([34(12),63150(16),141(11)])].

88966 x * (A * R(A',x,C)) = R(x,A,C). [para(88180(a,1),2036(a,1,1)),rewrite([13(11),63767(9),34(12),84333(14)])].

89235 x * (x / R(x,A,C')) = R(x,A,C). [para(63769(a,2),88966(a,1,2))].

89369 x / R(x,A,C') = x' * R(x,A,C). [para(89235(a,1),10(a,1,2)),flip(a)].

89390 (x' * R(x,A,C)) * A = R(A,C,x). [back_rewrite(80511),rewrite([89369(5)])].

89394 (x * R(x',A,C)) / R(A,x,C) = A'. [back_rewrite(79542),rewrite([89369(7),30(2)])].

89398 R(A,x,C) / (x * R(x',A,C)) = A. [back_rewrite(79358),rewrite([89369(10),30(5)])].

89424 R(x,A,C) / x = x' * R(x,A,C). [back_rewrite(66621),rewrite([89369(9)])].

89563 R(x',R(x,A,C),A) = x'. [para(89390(a,1),18(a,1,1)),rewrite([54281(8),39197(9),84292(9)]),flip(a)].

89587 R(A,x',R(x * A,A,C)) = A. [para(89563(a,1),3782(a,1,2,1,1)),rewrite([22(12),3(3),89563(8),54281(8),39197(9)]),flip(a)].

89609 R(A,R(x',A,C'),x * A) = A. [para(41658(a,1),89587(a,1,2)),rewrite([54281(12),43654(13),56054(15)])].

89676 R(x,A,R(A,C,x))' = x'. [para(89609(a,1),73883(a,1,1,1)),rewrite([32(4),84389(11),142(7),824(10),34(12)])].

89680 R(x,A,R(A,C,x)) = x. [para(89676(a,1),30(a,1,1)),rewrite([30(2)]),flip(a)].

89711 R(x * A,R(A,C,x),A') = x * A. [para(89680(a,1),54281(a,1,1)),flip(a)].

89858 A * (x * R(x',A,C)) = R(A,x,C). [para(89398(a,1),7(a,1,1))].

89862 R(A,x,R(x',A,C)) = A. [para(89398(a,1),2104(a,2)),rewrite([87436(8),6(3)])].

89864 (x * R(x',A,C)) * A = R(A,x,C). [para(89398(a,1),6610(a,2,2)),rewrite([89394(9),89394(14),256(8),80232(7),66779(8)]),flip(a)].

89868 R(A,x',R(x,A,C)) = A. [para(30(a,1),89862(a,1,3,1))].

90077 (x' * R(x,A,C))' = x / R(x,A,C). [para(89424(a,1),104(a,1,1))].

90115 R(x,R(A,C,x),A') = x. [para(7(a,1),89711(a,1,1)),rewrite([293(4),63046(6),293(8),82(11),259(10)])].

90123 R(x,R(x' * A,x,C),A') = x. [para(90115(a,1),141(a,2,1)),rewrite([84429(6),30(5),30(10)])].

90381 R(x,R(x' * A,A,C),A') = x. [para(78801(a,2),90123(a,1,2))].

90477 R(x,R(x',A,C),R(x,A,C)) = x. [para(90381(a,1),2467(a,1,1)),rewrite([35846(9),85(6),260(5),35846(13),85(10),260(9),41403(9),30(6),84290

(15),80621(15),82672(14),35846(24),85(21),260(20),41403(20),30(17),64256(19)])].

90483 (x * R(x',A,C)) * R(x,A,C) = x. [para(90477(a,1),18(a,2)),rewrite([41601(17),23(11)])].

91038 x / R(x,A,C) = x * R(x',A,C). [para(90483(a,1),6(a,1,1))].

91054 (x' * R(x,A,C))' = x * R(x',A,C). [back_rewrite(90077),rewrite([91038(10)])].

92301 x * R(A * C,x,C) = (x * C) * A. [para(9956(a,1),84018(a,1,2,2)),rewrite([46726(9)]),flip(a)].

92303 (x * R(y,x,C)) / y = R(x,y,C'). [para(84018(a,1),1672(a,1,1)),rewrite([1511(8,R),63(8),56066(9)])].

92320 C * R(A,C,x) = R(A * C,x',C). [para(92301(a,1),34(a,1,2)),rewrite([84248(6)])].

92324 R(A * C,C',x * A) = R(A * C,x,C). [para(92301(a,1),822(a,1,2)),rewrite([16(8,R),31535(10),11967(11),11955(10),73(9),10(10),84270(6),92

320(6),30(5),56717(12)]),flip(a)].

92356 R(A * C,x * A,C) = R(A * C,x,C). [back_rewrite(56717),rewrite([92324(15)])].

92507 R(A * C,x',C) / R(A,C,x) = C. [para(92320(a,1),6(a,1,1))].

92514 C * R(A,x,C) = R(A * C,x,C). [para(40108(a,2),92320(a,2,2)),rewrite([80164(9),56208(15),74121(13)])].

92518 R(A * C,x * x,C) = R(A * C,x',C). [para(18492(a,1),92320(a,1,2)),rewrite([55562(9),84591(7),30(5),92320(5),6360(15),30(11),30(13),5622

6(15)]),flip(a)].

92519 R(A * C,A,x) = R(A * C,x,C). [para(80148(a,1),92320(a,1,2)),rewrite([92514(5),30(14),76109(14)]),flip(a)].

92520 R(A * C,x,C) / R(A,x,C) = C. [para(92320(a,1),80423(a,1,1)),rewrite([30(5)])].

92537 C' * R(A * C,x,C) = R(A,x,C). [para(92514(a,1),10(a,1,2))].

92538 C / R(A * C,x,C) = R(A',C,x'). [para(92514(a,1),109(a,1,2)),rewrite([81202(11)])].

92548 R(R(A,x,C),C,R(x,A,C)) = A. [back_rewrite(76113),rewrite([92537(8)])].

92680 R(R(A,x,C),C,x * A') = A. [para(2180(a,1),92548(a,1,3)),rewrite([293(5),80388(8),784(8),1724(6),79853(8),55568(6),79185(5),16(8,R),358

28(12),13(14),1659(12),55562(10)])].

92828 R(A * C,x,A') = R(A * C,x,C). [para(92680(a,1),49492(a,1,1,2)),rewrite([16(3),55062(9),16(11,R),92514(11)])].

92842 R(C',A,x) * R(A * C,x,C) = A. [back_rewrite(62316),rewrite([92828(10)])].

92846 R(A * C,C',x) = R(A * C,A,x). [para(92519(a,2),18(a,2)),rewrite([16(6,R),35225(6),47951(9),16(3)])].

92849 R(A * C,A,x) * x = A * (x * C). [para(92519(a,2),2035(a,1,1)),rewrite([113(6),76117(8),113(11),12145(13),1511(11),33788(13),16(13,R),3

5139(13),33764(13)])].

92852 A * R(C,A,x) = R(A * C,x,C). [para(92519(a,2),3252(a,1)),rewrite([4638(10),76119(11),76119(9),54476(7),24137(14),56065(16),56065(14),9

2356(12)])].

92853 R(A * C,A,A * x) = R(A * C,A,x). [para(92519(a,2),49082(a,1))].

92854 R(A * C,A,x * x) = R(A * C,x',C). [para(92519(a,2),3414(a,1)),rewrite([76119(8),56217(14),92518(12)])].

92865 R(C,A,x * A') = R(C,x,A'). [para(92519(a,2),65305(a,1,2)),rewrite([69820(8)])].

92871 R(A * C,A,x) * A' = R(C,A,x * A). [para(92519(a,2),62238(a,1,1))].

92873 R(A * C,x,C) / R(C,A,x) = A. [para(92519(a,1),71842(a,1,1)),rewrite([92356(7),10(11)])].

92879 x * R(A * C,A,x) = (x * C) * A. [para(92519(a,2),84018(a,2,2)),rewrite([16(7,R),1382(7),46726(9)]),flip(a)].

92885 A * R(C,x,A') = R(A * C,A,x). [back_rewrite(51401),rewrite([92846(12)])].

92892 R(A * C,A,x) / R(A,x,C) = C. [para(19360(a,1),92520(a,1,2)),rewrite([49082(9),76119(7),80388(12),889(12),1828(10),63046(14),55568(11),

79185(10)])].

92893 R(A * C,A,x') / R(A,C,x) = C. [para(21540(a,1),92520(a,1,1)),rewrite([33905(10),56065(12),56065(10),49082(8),33904(14),56065(16),56065

(14),80388(12),889(12),30(10),63046(12)])].

93042 R(C,A,x) = R(C,x,A'). [para(92852(a,1),10(a,1,2)),rewrite([65305(8)]),flip(a)].

93056 R(C,A,x * A) = R(C,A,x). [para(92852(a,1),11880(a,1,1)),rewrite([62276(9),62276(14),749(15),62260(15),92852(14),92842(15),293(7),62238

(8),62276(9),62301(14),62260(10)])].

93078 R(A * C,A,x) * A' = R(C,A,x). [back_rewrite(92871),rewrite([93056(13)])].

93094 R(A * C,x,C) * A' = R(C,A,x). [back_rewrite(62238),rewrite([93056(13)])].

93102 A * R(C * A',A,x) = R(C,A,x). [back_rewrite(25402),rewrite([93056(13)])].

93103 R(R(R(C,B,A'),A,B),A,B) != C. [para(93042(a,1),19(a,1,1,1))].

93106 R(C,A,A' * x) = R(C,A,x). [para(93042(a,2),80(a,2)),rewrite([256(4),47803(7),16(5,R),39686(7),53388(7),256(11),93056(11)])].

93109 R(C,A' * x,A') = R(C,A,x). [para(93042(a,1),125(a,2)),rewrite([16(3),246(7),293(4),39686(7),53388(7),93106(6)]),flip(a)].

93111 R(R(C,A,x),x,A) = C. [para(93042(a,1),23049(a,1,1)),rewrite([93109(7)])].

93113 R(C,x',A') = R(C,A,x'). [para(93042(a,2),3201(a,1)),rewrite([74131(6),59762(11)]),flip(a)].

93114 R(C * x,A,C') = R(C,A,x) * x. [para(93042(a,2),2035(a,1,1)),rewrite([256(5),93056(5),256(8),47803(11),16(9,R),39686(11)]),flip(a)].

93119 R(C',A,A' * x) = R(C',A,x). [para(93042(a,2),2235(a,2,1)),rewrite([256(4),47803(7),16(5,R),39686(7),59759(7),256(12),93056(12),62276(1

1)])].

93121 R(C,x * A',A') = R(C,x,A'). [para(93042(a,1),48002(a,2)),rewrite([48002(6),92865(6)]),flip(a)].

93122 R(C,A,A * x) = R(C,x,A'). [para(93042(a,2),48002(a,1)),rewrite([92865(11)])].

93135 R(R(C,x,A'),(A * C) * x,A) = C. [para(93042(a,1),62261(a,1,1))].

93169 R(C,A,x) * A' = R(C * A',A,x). [para(93042(a,2),60795(a,1,1))].

93189 R(C,x * (C' * C'),A') = R(C,A,x). [para(93042(a,1),74184(a,1))].

93235 A * R(C * A',x,A') = R(C,A,x). [back_rewrite(58301),rewrite([93106(15)])].

93237 R(C * x,A,C') / x = R(C,A,x). [back_rewrite(53388),rewrite([93106(13)])].

93241 R(R(C',A,x),x,A) = C'. [back_rewrite(76160),rewrite([93119(10),74225(7)])].

93246 R(C',A,x) * (C * x) = R(x,A,C). [back_rewrite(74398),rewrite([93119(7)])].

93278 A' * R(C,A,x) = R(C * A',x,A'). [para(93111(a,1),60416(a,1,1,2)),rewrite([16(4,R)]),flip(a)].

93439 R(C,A,R(C',A,x) * x) = R(C,A,x). [para(93241(a,1),54117(a,1,1,1)),rewrite([30(3),93106(11),62260(13)])].

93520 R(R(C,A,x),x,C) = R(C,A,x). [para(93106(a,1),4058(a,2,1)),rewrite([16(4),246(8),293(5),39686(8),39692(8),34(14),93237(11),74163(5),34(

11)]),flip(a)].

93536 R(C,x / y,A') = R(C,A,x / y). [para(104(a,1),93113(a,1,2)),rewrite([104(9)])].

93558 R(C,A,R(A',C,x)) = R(C,A,R(A,x,C)). [para(66961(a,1),93122(a,1,3)),rewrite([48002(16),81213(15),93106(16)]),flip(a)].

93660 R(x,R(C,A,x),C') = x. [para(93520(a,1),92303(a,1,1,2)),rewrite([6(8)]),flip(a)].

93717 R(A,x,C) / R(A * C,A,x) = C'. [para(92892(a,1),104(a,1,1)),flip(a)].

93718 C' * R(A * C,A,x) = R(A,x,C). [para(92892(a,1),6610(a,1,1)),rewrite([92892(13),113(6),34(8),93717(17),1511(11,R)]),flip(a)].

93733 R(C * A',C,x) * A = R(C,A,x). [para(93109(a,1),18(a,2)),rewrite([9418(14),54713(15),82(10),259(9),55403(6)])].

94091 C' * R(A,x,C) = R(A * C',C',x). [para(92846(a,1),2051(a,2,2,1)),rewrite([1511(8,R),63(8),49540(6),1511(4),1511(17,R),93718(17)]),flip(

a)].

94095 R(R(C,A',A * x),x,A) = R(C,A,x). [para(92849(a,1),23148(a,1,1,1)),rewrite([16(6,R),34236(7),45892(6),45843(16),92885(14),93078(16)])].

94104 (x * R(C,A,x)) * A = C * (x * A). [para(92879(a,1),16598(a,2,2)),rewrite([92853(7),93078(8),16(12,R),34981(14),10(15)])].

94148 R(C,A,x * x) = R(C,A,x'). [para(18478(a,1),93078(a,2)),rewrite([76119(8),92854(6),93094(9),74162(10)]),flip(a)].

94170 R(C,A,x * (C' * x)) = R(C,A,x'). [back_rewrite(74167),rewrite([94148(11)])].

94254 (A * C) / R(C,A,x) = R(A,x,C'). [para(93094(a,1),51839(a,1,2)),rewrite([92538(16),66961(16),80646(11)])].

94255 R(A,x,C') * R(C,A,x) = A * C. [para(93094(a,1),69200(a,1,2)),rewrite([92538(9),66961(9),80646(4)])].

94424 R(R(C,A,x) * x,A,C) = C * x. [para(93114(a,1),22987(a,1,1)),rewrite([39797(10)])].

94539 R(A,(R(C,A,x) * x)',C * x) = A. [para(94424(a,1),89868(a,1,3))].

94568 R(C,x * (A' * C'),A') = R(C,A,x). [para(24793(a,1),93121(a,1,2)),rewrite([1511(8),141(13),59733(12),93189(20)])].

94573 R(R(C,A,x),A * (x * A'),A) = C. [para(6639(a,1),93135(a,1,2)),rewrite([16(4),35828(5),94568(10),35828(10),36014(13)])].

94623 R(C / x,x,A')' = R(C',A,x) * x. [para(39247(a,1),93246(a,2)),rewrite([74215(7),34(9)]),flip(a)].

94665 C * (R(C',A,x) * x) = R(x,A,C). [back_rewrite(40146),rewrite([94623(7)])].

94788 R(C,R(x,y,z),A') = R(C,A,R(x,y,z)). [para(18(a,1),93536(a,1,2)),rewrite([18(11)])].

94827 R(C * A',C,x) = R(C * A',A,x). [para(93733(a,1),6(a,1,1)),rewrite([293(5),93169(6)]),flip(a)].

94932 R(C * x,A,C') = x * R(C,A,x). [para(94104(a,1),6(a,1,1)),rewrite([293(6),47803(7),16(5,R),39686(7)])].

94938 R(x * R(C,A,x),A,C) = C * x. [para(94104(a,1),100(a,1,1,2)),rewrite([35828(10),11560(12),10(8),85(6),260(5)]),flip(a)].

94943 A * (x * R(C,A,x))' = (A * C') / x. [para(94104(a,1),49513(a,1,2)),rewrite([6741(8),1724(7),51251(8),39762(9),42015(9),293(11),6792(15

),784(13)]),flip(a)].

94964 R(C,x * R(C,A,x),A) = R(C,x,A). [para(94938(a,1),65063(a,1,2)),rewrite([48355(5)]),flip(a)].

95031 R(A,C,R(C,A,x)) = R(A,C,R(A,x,C)). [para(94254(a,1),61281(a,2,3)),rewrite([63373(13),80646(11),56770(11),80502(10),1828(11),293(11),15

11(12),141(17),82382(15),80655(14),80349(15),81648(13)])].

95039 R(A',C,x) * (A * C) = R(C,A,x). [para(94255(a,1),10(a,1,2)),rewrite([80655(5)])].

95183 R(A,(R(C,A,x) * x)',x * C) = A. [para(16(a,1),94539(a,1,3))].

95198 R(R(C,A,R(A,C,x')),R(A,x,C),A) = C. [para(62195(a,1),94573(a,1,2,2)),rewrite([79190(7),30(11),64171(16)])].

95239 R(C * x,A,C') / R(C,A,x) = x. [para(94932(a,2),6(a,1,1))].

95246 (C / x) * R(x,A,C') = R(C,A,x). [para(94932(a,2),185(a,1,2)),rewrite([34(7),74138(13)])].

95254 x * (C' * R(C,A,x)) = R(x,A,C'). [para(94932(a,2),2084(a,2,2)),rewrite([93660(6),39492(16),10(12)])].

95319 R(C,A,x) * x = x * R(C,A,x). [para(94932(a,1),93114(a,1)),flip(a)].

95324 R(A,(x * R(C,A,x))',x * C) = A. [back_rewrite(95183),rewrite([95319(5)])].

96300 R(C,x * (C' * C'),A) = R(C,x,A). [para(74184(a,1),94964(a,1,2,2)),rewrite([24793(11),95254(10),39492(8),65034(10),141(6),48343(5)]),fl

ip(a)].

96317 (A * C) * R(A',x,C') = R(C,A,x). [para(95039(a,1),39687(a,2)),rewrite([80224(7),39691(13)])].

96384 x / R(C,A,x) = R(C',A,x) * x. [para(94665(a,1),95239(a,1,1,1)),rewrite([56055(7),93439(8)])].

96398 C * (x' * R(x,A,C')) = R(C,A,x). [para(4273(a,1),95246(a,1,1)),rewrite([13(13),39692(11),1659(7),74145(14)])].

96402 R(C / x,A,C) * x = R(C,A,x). [para(41509(a,1),95246(a,1,1)),rewrite([56055(12),74158(12)])].

96403 C * (x' * R(x,A,C)) = R(C,A,x'). [para(3043(a,1),95246(a,1,2)),rewrite([6240(6),70(16),39692(14),1698(10),12(10),75553(9),94170(14)])]

.

96748 R(x',R(x,A,C'),C)' = x. [para(96402(a,1),3187(a,1,1,2)),rewrite([74163(5),109(9),65295(10),96398(12),6(8),109(4),65295(5),141(8)]),fli

p(a)].

96769 R(x',R(x,A,C'),C) = x'. [para(96748(a,1),30(a,1,1)),flip(a)].

96774 R(x,R(x',A,C'),C) = x. [para(30(a,1),96769(a,1,1)),rewrite([30(9)])].

96784 R(R(x,A,C),x',C) = R(x,A,C). [para(41403(a,1),96774(a,1,2,1)),rewrite([56055(11)])].

97196 R(x',R(x,A,C),C') = x'. [para(96784(a,1),92303(a,1,1,2)),rewrite([6(9)]),flip(a)].

97200 R(x',R(x,A,C),C) = x'. [para(97196(a,1),56054(a,1,1))].

97246 R(C / x,R(x,A,C),C) = C / x. [para(158(a,1),97200(a,1,1)),rewrite([56316(10),158(11)])].

97332 R(C / x,R(x,A,C),C') = C / x. [para(97246(a,1),56055(a,1,1))].

97448 R(A,C,x * R(x',A,C)) = A. [para(95324(a,1),4058(a,2,1)),rewrite([94943(8),233(9),16(9,R),35803(9),84302(8),92320(5),29766(15),96384(12

),16(15,R),94665(15),96403(13),92873(11),29766(10),96384(7),16(10,R),94665(10),80388(9),91054(9)]),flip(a)].

97466 R(R(A,x,C),A,C) = R(A,x,C). [para(97448(a,1),49556(a,1,1)),rewrite([89858(7),1511(8),33788(15),89858(10)]),flip(a)].

97467 R(A,C,R(A,x,C)) = A. [para(97448(a,1),62988(a,2)),rewrite([89864(9)])].

97487 R(A,C,R(C,A,x)) = A. [back_rewrite(95031),rewrite([97467(12)])].

97502 R(A,C,R(C,A * x,A)) = A. [para(97467(a,1),63166(a,1,1)),rewrite([94091(7),80388(13),784(13),53553(12)])].

97518 R(C,A,R(A,x,C')) = C. [para(97467(a,1),92893(a,1,2)),rewrite([81202(8),293(12),93078(13),93558(8),80646(6)])].

97521 R(C,A,R(A,C,x)) = C. [back_rewrite(68207),rewrite([97518(13)])].

97522 R(C,R(A,x,C),A) = C. [back_rewrite(95198),rewrite([97521(7)])].

97567 R(R(C,A,x),A,C) = R(C,A,x). [para(97487(a,1),80538(a,1,1)),rewrite([93278(7),93235(9)]),flip(a)].

97651 R(C,A,R(A',x,C')) = C. [para(97522(a,1),47659(a,1,1)),rewrite([64488(8),93122(10),94788(9)])].

98084 R(A,C,R(C,x,A)) = A. [para(34(a,1),97502(a,1,3,2))].

98112 R(A,C,R(A * C,A',x)) = A. [para(98084(a,1),62988(a,2)),rewrite([54690(7),16(5)])].

98296 C' * R(C,A,x) = A * R(A',x,C'). [para(97651(a,1),2036(a,1,1,1)),rewrite([16(5),96317(11)])].

98926 R(C,A,x) * (A * C') = R(A,x,C). [para(97567(a,1),40046(a,1,1)),rewrite([98296(14),49(17),82073(16),64171(17)])].

99077 R(C,A,R(A' * C',C,x)) = C. [para(98112(a,1),92507(a,1,2)),rewrite([48717(10),293(14),93094(15)])].

99906 R(C,A,x) / R(C',x,A) = C * C. [para(99077(a,1),2048(a,1,1,1)),rewrite([16(4),35225(13),55387(12),16(9,R),1659(9),94827(7),93102(8),483

46(12),48409(7),99077(18),99077(19)])].

101159 R(A * C',C',x)' = C / R(A,x,C). [para(97466(a,1),97332(a,1,2)),rewrite([2108(11),1511(6,R),94091(6)])].

101160 A * (C / R(A,x,C)) = R(C,A * x,A). [back_rewrite(53553),rewrite([101159(9)])].

101563 C * (C * R(C',A,x)) = R(C,A * x,A). [para(98926(a,1),4326(a,1,2,2)),rewrite([94091(7),749(9),101159(9),101160(7),62276(10),16(12,R)])

,flip(a)].

101787 R(C',x,A) / R(C,A,x) = C' * C'. [para(99906(a,1),104(a,1,1)),rewrite([172(4)]),flip(a)].

101793 R(C,A * x,A) = R(C,x,A). [para(99906(a,1),21297(a,1,2,1)),rewrite([101787(8),210(13),48343(11),16(11,R),12(13),10(12),10(8),62276(7),

99906(15),1382(11,R),16(10,R),101563(11)]),flip(a)].

101804 A * (C / R(A,x,C)) = R(C,x,A). [back_rewrite(101160),rewrite([101793(12)])].

101823 R(R(C,x,A),A,x) = C. [back_rewrite(67447),rewrite([101793(11),96300(9)])].

101859 R(C,A',x * A) = R(C,x,A). [para(101823(a,1),23049(a,1,1)),rewrite([45910(9)]),flip(a)].

101866 R(R(C,A',x),x,A') = C. [para(101823(a,1),54235(a,1)),rewrite([45910(10),82(9),259(8)]),flip(a)].

101954 R(C,A',A * x) = R(C,A',x). [para(101866(a,1),46836(a,1,1))].

101975 R(R(C,A',x),x,A) = R(C,A,x). [back_rewrite(94095),rewrite([101954(6)])].

102088 A * (C / R(A,C,x')) = R(C,x,A). [para(141(a,1),101804(a,1,2,2)),rewrite([79190(7),45910(14),101859(14)])].

102092 R(C,A',x) = R(C,x,A). [para(16667(a,1),101804(a,2)),rewrite([80388(8),784(8),79853(8),102088(8),101954(9)]),flip(a)].

102154 R(R(C,A',x),A,x) = C. [para(102092(a,2),47631(a,1,1)),rewrite([101954(6)])].

102642 R(R(C,x,A'),A,x) = R(C,A',x). [para(101975(a,1),47631(a,1,1)),rewrite([93122(5),101954(12)])].

102652 $F. [back_rewrite(93103),rewrite([102642(8),102154(8)]),xx(a)].

============================== end of proof ==========================

1 R(R(R(C,A,B),A,B),A,B) = C # label(non_clause) # label(goal). [goal].

2 0 * x = x. [assumption].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 B * ((x * y) * B) = (B * x) * (y * B). [assumption].

15 (B * x) * (y * B) = B * ((x * y) * B). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 R(x,y,z) = ((x * y) * z) / (y * z). [assumption].

18 ((x * y) * z) / (y * z) = R(x,y,z). [copy(17),flip(a)].

19 R(R(R(C,A,B),A,B),A,B) != C. [deny(1)].

22 x / x = 0. [para(2(a,1),6(a,1,1))].

23 x / 0 = x. [para(3(a,1),6(a,1,1))].

26 0' = 0. [para(8(a,1),3(a,1)),flip(a)].

28 0 / x = x'. [para(8(a,1),6(a,1,1))].

30 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([28(3)])].

31 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

32 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

34 x * (x' * y) = y. [back_rewrite(4),rewrite([31(1)])].

35 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

39 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

40 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

45 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(12(a,1),13(a,1,1,2)),rewrite([12(7)])].

47 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [para(13(a,1),13(a,1,1,2)),rewrite([13(9)])].

49 (B * x) * B = B * (x * B). [para(2(a,1),15(a,1,2)),rewrite([3(7)])].

50 (B * ((x * y) * B)) / (y * B) = B * x. [para(15(a,1),6(a,1,1))].

51 B * ((x * (y / B)) * B) = (B * x) * y. [para(7(a,1),15(a,1,2)),flip(a)].

53 B * ((B' * x) * B) = x * B. [para(9(a,1),15(a,1,1)),rewrite([2(4)]),flip(a)].

54 (B * x)' * (B * ((x * y) * B)) = y * B. [para(15(a,1),10(a,1,2))].

56 (B * x) * (y * (y * B)) = B * ((x * (y * y)) * B). [para(12(a,1),15(a,1,2))].

57 ((x * B) * (B * ((y * x) * B))) * z = (x * B) * ((B * y) * ((x * B) * z)). [para(15(a,1),13(a,1,1,2))].

58 B * (((x * B) * y) * B) = B * (x * (B * (y * B))). [para(15(a,1),13(a,1))].

59 (B * x) * (y * (z * (y * B))) = B * ((x * (y * (z * y))) * B). [para(13(a,1),15(a,1,2))].

60 (x * C) / x = C. [para(16(a,1),6(a,1,1))].

62 C * (x / C) = x. [para(16(a,2),7(a,1))].

63 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

64 x' * (C * x) = C. [para(16(a,2),10(a,1,2))].

65 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

66 C * (x * x) = x * (x * C). [para(16(a,2),12(a,1))].

67 C * (x * x) = x * (C * x). [para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].

68 (x * (x * C)) * y = x * (C * (x * y)). [para(16(a,1),13(a,1,1,2))].

69 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

70 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

71 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

72 C * (x * (y * x)) = x * (y * (C * x)). [para(16(a,2),13(a,2,2,2)),rewrite([16(4,R)])].

73 (B * x) * (B * C) = B * ((x * C) * B). [para(16(a,1),15(a,1,2))].

76 R(x,0,y) = x. [para(2(a,1),18(a,1,2)),rewrite([3(2),6(2)]),flip(a)].

77 R(x,y,0) = x. [para(3(a,1),18(a,1,1)),rewrite([3(3),6(2)]),flip(a)].

78 R(x,y,z) * (y * z) = (x * y) * z. [para(18(a,1),7(a,1,1))].

79 R(x / y,y,z) = (x * z) / (y * z). [para(7(a,1),18(a,1,1,1)),flip(a)].

80 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(7(a,1),18(a,1,2))].

81 R(x',x,y) = x'. [para(8(a,1),18(a,1,1,1)),rewrite([2(2),32(2)]),flip(a)].

82 (x * y') * y = R(x,y',y). [para(8(a,1),18(a,1,2)),rewrite([23(5)])].

85 (x * y) * y' = R(x,y,y'). [para(9(a,1),18(a,1,2)),rewrite([23(5)])].

86 R(x',x * y,z) = (y * z) / ((x * y) * z). [para(10(a,1),18(a,1,1,1)),flip(a)].

87 ((x * y') * (y * z)) / z = R(x,y',y * z). [para(10(a,1),18(a,1,2))].

88 ((x * (x * y)) * z) / (y * z) = R(x * x,y,z). [para(12(a,1),18(a,1,1,1))].

89 R(x,x,y) = x. [para(12(a,1),18(a,1,1)),rewrite([6(4)]),flip(a)].

90 ((x * (y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(12(a,1),18(a,1,2))].

91 ((x * (y * (x * z))) * u) / (z * u) = R(x * (y * x),z,u). [para(13(a,1),18(a,1,1,1))].

92 (x * (y * (x * z))) / ((y * x) * z) = R(x,y * x,z). [para(13(a,1),18(a,1,1))].

93 ((x * (y * (z * y))) * u) / (y * (z * (y * u))) = R(x,y * (z * y),u). [para(13(a,1),18(a,1,2))].

94 (B * ((x * y) * (B * z))) / ((y * B) * z) = R(B * x,y * B,z). [para(15(a,1),18(a,1,1,1)),rewrite([13(6)])].

95 (B * ((x * y) * B)) / (x * (y * B)) = R(B,x,y * B). [para(15(a,1),18(a,1,1))].

96 ((x * (B * y)) * (z * B)) / (B * ((y * z) * B)) = R(x,B * y,z * B). [para(15(a,1),18(a,1,2))].

97 ((x * C) * y) / (x * y) = R(C,x,y). [para(16(a,1),18(a,1,1,1))].

100 (C * (x * y)) / (y * C) = R(x,y,C). [para(16(a,2),18(a,1,1))].

101 (C * (x * y)) / (C * y) = R(x,y,C). [para(16(a,2),18(a,1,2)),rewrite([16(3,R)])].

103 x' * C = C * x'. [para(16(a,2),31(a,2)),rewrite([31(2)])].

104 (x / y)' = y / x. [para(7(a,1),32(a,1,2)),flip(a)].

105 x / (y * (y * x)) = (y * y)'. [para(12(a,1),32(a,1,2))].

106 x / (y * (z * (y * x))) = (y * (z * y))'. [para(13(a,1),32(a,1,2))].

108 x / (x * C) = C'. [para(16(a,1),32(a,1,2))].

109 C / (C * x) = x'. [para(16(a,2),32(a,1,2))].

112 (x * (y * (x * C))) / (x * (y * x)) = C. [para(13(a,1),60(a,1,1))].

113 x / C = C' * x. [para(62(a,1),10(a,1,2)),flip(a)].

120 B * (((B' * x) * y) * B) = x * (y * B). [para(34(a,1),15(a,1,1)),flip(a)].

122 x * (C * x') = C. [para(16(a,2),34(a,1,2))].

123 R(x,x' * y,z) = (y * z) / ((x' * y) * z). [para(34(a,1),18(a,1,1,1)),flip(a)].

124 R(x,y,(x * y)' * z) = z / (y * ((x * y)' * z)). [para(34(a,1),18(a,1,1)),flip(a)].

125 ((x * y) * (y' * z)) / z = R(x,y,y' * z). [para(34(a,1),18(a,1,2))].

126 C' * (x * (x * C)) = x * x. [para(12(a,1),63(a,1,2))].

127 (x * C) * (C' * ((x * C) * y)) = ((x * C) * x) * y. [para(63(a,1),13(a,1,1,2)),flip(a)].

128 C * (x * (C' * x)) = x * x. [para(63(a,1),13(a,2,2)),rewrite([16(6,R)])].

129 C' * (x * (y * (x * C))) = x * (y * x). [para(13(a,1),63(a,1,2))].

130 (x * y) / ((x * C) * y) = R(C',x * C,y). [para(63(a,1),18(a,1,1,1))].

131 ((x * C') * (y * C)) / y = R(x,C',y * C). [para(63(a,1),18(a,1,2))].

132 (C * x) * (x' * ((C * x) * y)) = C * (x * (C * y)). [para(64(a,1),13(a,1,1,2)),rewrite([16(4,R),70(5)]),flip(a)].

133 R(x',C * x,y) = (C * y) / ((C * x) * y). [para(64(a,1),18(a,1,1,1)),flip(a)].

136 (x / y) * (y / x) = 0. [para(104(a,1),8(a,1,1))].

137 (x / y) * ((y / x) * z) = z. [para(104(a,1),10(a,1,1))].

138 (x * y) / ((z * x) * y) = R(z,x,y)'. [para(18(a,1),104(a,1,1)),flip(a)].

140 (x / y) * (C * (y / x)) = C. [para(104(a,1),64(a,1,1))].

141 R(x,x' * y,z) = R(x',y,z)'. [back_rewrite(123),rewrite([138(8)])].

142 R(x',x * y,z) = R(x,y,z)'. [back_rewrite(86),rewrite([138(7)])].

143 ((x / y) * x) / y = (x / y) * (x / y). [para(7(a,1),35(a,1,1,2))].

144 x' / x = x' * x'. [para(8(a,1),35(a,1,1,2)),rewrite([3(3)])].

145 x / x' = x * x. [para(9(a,1),35(a,1,1,2)),rewrite([3(2)])].

150 (B * (x * (B * (x * B)))) / B = (B * x) * (B * x). [para(15(a,1),35(a,1,1)),rewrite([13(6)])].

151 (C * (x * C)) / x = C * C. [para(16(a,1),35(a,1,1,2))].

152 C' * (x * (C * x)) = x * x. [para(16(a,2),35(a,1,1,2)),rewrite([113(5)])].

153 (x * y) / (x' * y) = x * x. [para(34(a,1),35(a,1,1,2))].

155 (x' * C) / (C * x) = x' * x'. [para(64(a,1),35(a,1,1,2))].

158 (C' * x)' = C / x. [para(34(a,1),109(a,1,2)),flip(a)].

162 B * (((C * B') * x) * B) = C * (x * B). [para(122(a,1),15(a,1,1)),flip(a)].

165 C' * ((x * y) * (C * y')) = R(x,y,C * y'). [para(122(a,1),18(a,1,2)),rewrite([113(7)])].

172 (x * x)' = x' * x'. [para(145(a,1),104(a,1,1)),rewrite([144(4)])].

176 x / (y * (y * x)) = y' * y'. [back_rewrite(105),rewrite([172(5)])].

177 x' * (C * x') = C * (x' * x'). [para(103(a,1),12(a,2,2)),rewrite([16(5,R)]),flip(a)].

181 B * ((x' * C) * B) = B * ((C * x') * B). [para(103(a,1),15(a,2,2,1)),rewrite([16(6),73(7)])].

182 (x * (y / z)) * (z / y) = R(x,y / z,z / y). [para(136(a,1),18(a,1,2)),rewrite([23(6)])].

183 (C' * x) * (C / x) = 0. [para(113(a,1),136(a,1,1))].

184 (C / x) * (C' * x) = 0. [para(113(a,1),136(a,1,2))].

185 (C / x) * ((C' * x) * y) = y. [para(158(a,1),10(a,1,1))].

191 ((x / y) * (z * x)) / y = (x / y) * (z * (x / y)). [para(7(a,1),39(a,1,1,2,2))].

192 x * ((y / (x * z)) * x) = (x * y) / z. [para(7(a,1),39(a,1,1,2)),flip(a)].

193 (x' * y) / x = x' * (y * x'). [para(8(a,1),39(a,1,1,2,2)),rewrite([3(3)])].

194 x * ((x * y)' * x) = x / y. [para(8(a,1),39(a,1,1,2)),rewrite([3(2)]),flip(a)].

195 (x * y) / x' = x * (y * x). [para(9(a,1),39(a,1,1,2,2)),rewrite([3(2)])].

198 (x * (y * (y * (x * z)))) / z = x * (y * (y * x)). [para(12(a,1),39(a,1,1,2)),rewrite([12(7)])].

200 (x * (y * (z * (y * (x * u))))) / u = x * (y * (z * (y * x))). [para(13(a,1),39(a,1,1,2)),rewrite([13(9)])].

201 ((B * x) * (y * (B * ((x * z) * B)))) / (z * B) = (B * x) * (y * (B * x)). [para(15(a,1),39(a,1,1,2,2))].

202 (x * (B * ((y * x) * B))) / B = x * ((B * y) * x). [para(15(a,1),39(a,1,1,2))].

203 (C * (x * (y * C))) / y = C * (x * C). [para(16(a,1),39(a,1,1,2,2))].

208 C' * (x * x) = x * (C' * x). [para(63(a,1),39(a,1,1,2)),rewrite([113(3)])].

210 (C * C) / x = C * (x' * C). [para(64(a,1),39(a,1,1,2))].

224 (x * (C' * y)) * (C / y) = R(x,C' * y,C / y). [para(183(a,1),18(a,1,2)),rewrite([23(9)])].

226 (x * (C / y)) * (C' * y) = R(x,C / y,C' * y). [para(184(a,1),18(a,1,2)),rewrite([23(9)])].

230 (x / y) * ((z / (x / y)) * x) = ((x / y) * z) * y. [para(7(a,1),40(a,1,2,2))].

231 (x' * y) * x = x' * (y / x'). [para(8(a,1),40(a,1,2,2)),rewrite([3(5)]),flip(a)].

232 (x * y) * x' = x * (y / x). [para(9(a,1),40(a,1,2,2)),rewrite([3(3)]),flip(a)].

233 (x / y) * (y * z) = y' * ((y * x) * z). [para(40(a,1),10(a,1,2)),flip(a)].

234 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),40(a,1,2,2)),flip(a)].

240 (x / C') * y = (C * x) * y. [para(40(a,1),16(a,1)),rewrite([113(5),234(9),16(12,R),34(12)]),flip(a)].

242 (C * x) * y = (x * C) * y. [para(16(a,1),40(a,2,1)),rewrite([113(3),234(7),240(7),34(8)])].

246 (x * y) * (x' * z) = x * ((y / x) * z). [para(34(a,1),40(a,1,2,2)),flip(a)].

247 (C' * x) * (y * C) = C' * ((C * x) * y). [para(63(a,1),40(a,1,2,2)),rewrite([240(6)]),flip(a)].

248 (x' * y) * (C * x) = x' * (C * (y / x')). [para(64(a,1),40(a,1,2,2)),rewrite([16(5,R)]),flip(a)].

249 (x * y) * (C * x') = x * (C * (y / x)). [para(122(a,1),40(a,1,2,2)),rewrite([16(3,R)]),flip(a)].

250 (C * x) * (C / x) = C * C. [para(122(a,1),40(a,1,2)),rewrite([113(7),158(9)]),flip(a)].

256 x / B' = x * B. [back_rewrite(53),rewrite([231(6),34(8)])].

259 R(x,B',B) = x. [para(256(a,1),6(a,1)),rewrite([82(5)])].

260 R(x,B,B') = x. [para(256(a,1),7(a,1,1)),rewrite([85(5)])].

261 (x * B)' = B' / x. [para(256(a,1),104(a,1,1))].

263 (x * B) * (B' / x) = 0. [para(256(a,1),136(a,1,1))].

266 B' / (x / B) = x'. [para(7(a,1),261(a,1,1)),flip(a)].

267 (B' / x) * ((x * B) * y) = y. [para(261(a,1),10(a,1,1))].

269 (x * (y * (x * B)))' = B' / (x * (y * x)). [para(13(a,1),261(a,1,1))].

270 (B * C)' = C' * B'. [para(16(a,1),261(a,1,1)),rewrite([113(8)])].

273 (B' / x) * (C * (x * B)) = C. [para(261(a,1),64(a,1,1))].

291 x' * (x / B) = B'. [para(266(a,1),7(a,1,1))].

293 x / B = x * B'. [para(291(a,1),10(a,1,2)),rewrite([30(2)]),flip(a)].

294 R(B,x',x) = B. [para(291(a,1),15(a,2,2,1)),rewrite([293(5),82(8),259(7),82(4),8(8),3(6)])].

295 ((x * y') * (y * B')) * B = R(x,y',y * B'). [para(291(a,1),18(a,1,2)),rewrite([293(4),256(9),293(11)])].

297 (x * (B * ((y * x) * B))) * B' = x * ((B * y) * x). [back_rewrite(202),rewrite([293(8)])].

298 B * ((x * (B * (x * B))) * B') = (B * x) * (B * x). [back_rewrite(150),rewrite([293(9),232(10),293(8)])].

299 B * ((x * (y * B')) * B) = (B * x) * y. [back_rewrite(51),rewrite([293(3)])].

300 R(B,x,x') = B. [para(30(a,1),294(a,1,2))].

301 R(B,x / y,y / x) = B. [para(104(a,1),294(a,1,2))].

302 R(B,C / x,C' * x) = B. [para(158(a,1),294(a,1,2))].

333 (x * B')' = B / x. [para(293(a,1),104(a,1,1))].

335 (x * B') * (B / x) = 0. [para(293(a,1),136(a,1,1))].

336 (x * (y * (x * B))) * B' = x * (y * x). [para(293(a,1),39(a,1))].

337 (B * x) * (B * x) = B * (x * (B * x)). [back_rewrite(298),rewrite([336(9)]),flip(a)].

393 (x * (x * B)) * (B' / (x * x)) = 0. [para(12(a,1),263(a,1,1))].

397 (x * (y * B)) * (B' / y) = R(x,y * B,B' / y). [para(263(a,1),18(a,1,2)),rewrite([23(9)])].

400 (C' * B') * ((B * C) * x) = x. [para(270(a,1),10(a,1,1))].

402 (B * C) * ((C' * B') * x) = x. [para(270(a,1),34(a,1,2,1))].

415 (x * (y * (z * (z * (y * x))))) * u = x * (y * (z * (z * (y * (x * u))))). [para(45(a,1),13(a,1,1,2)),rewrite([45(11)])].

419 B * (((x * (x * B)) * y) * B) = B * (x * (x * (B * (y * B)))). [para(45(a,1),15(a,1)),flip(a)].

422 C * (x * (y * (y * x))) = x * (y * (y * (x * C))). [para(45(a,1),16(a,2))].

423 (x * (C * (x * C))) * y = x * (C * (C * (x * y))). [para(16(a,1),45(a,1,1,2,2))].

424 C * (x * (x * (C * y))) = C * (x * (x * (y * C))). [para(16(a,1),45(a,2,2,2,2)),rewrite([45(6)])].

428 (x * (y * (y * (x * z)))) / ((y * (y * x)) * z) = R(x,y * (y * x),z). [para(45(a,1),18(a,1,1))].

444 C * (x * (x * (y' * C))) = C * (x * (x * (C * y'))). [para(103(a,2),45(a,2,2,2,2)),rewrite([45(7)]),flip(a)].

458 (x * (x * B')) * (B / (x * x)) = 0. [para(12(a,1),335(a,1,1))].

461 (x * (y * B')) * (B / y) = R(x,y * B',B / y). [para(335(a,1),18(a,1,2)),rewrite([23(9)])].

465 (B * (B * (x * B))) * y = B * ((B * x) * (B * y)). [para(49(a,1),13(a,1,1,2))].

467 (B * x) * (B * (y * B)) = B * ((x * (B * y)) * B). [para(49(a,1),15(a,1,2))].

468 (B * (x * (B * y))) / (B * y) = R(B * x,B,y). [para(49(a,1),18(a,1,1,1)),rewrite([13(5)])].

469 R(B,x,B) = B. [para(49(a,1),18(a,1,1)),rewrite([6(7)]),flip(a)].

470 ((x * (B * y)) * B) / (B * (y * B)) = R(x,B * y,B). [para(49(a,1),18(a,1,2))].

471 B / (B * (x * B)) = (B * x)'. [para(49(a,1),32(a,1,2))].

473 (B * (x * B))' = B' / (B * x). [para(49(a,1),261(a,1,1))].

474 B * (x * (B * (B' / (B * x)))) = 0. [para(49(a,1),263(a,1,1)),rewrite([13(10)])].

484 (C * (x * (C * y))) / ((C * x) * y) = R(C,C * x,y). [para(65(a,1),18(a,1,1,1)),rewrite([13(5)])].

493 (C * x)' = (x * C)'. [para(65(a,1),109(a,1,2)),rewrite([109(6)]),flip(a)].

514 B * (((x * (y * (x * B))) * z) * B) = B * (x * (y * (x * (B * (z * B))))). [para(47(a,1),15(a,1)),flip(a)].

518 (x * (C * (y * (x * C)))) * z = x * (C * (y * (C * (x * z)))). [para(16(a,1),47(a,1,1,2,2,2))].

523 (x * (y * (z * (y * (x * u))))) / ((y * (z * (y * x))) * u) = R(x,y * (z * (y * x)),u). [para(47(a,1),18(a,1,1))].

528 x' * ((y / x') * (z * (x * ((x' * y) * u)))) = (x' * ((y / x') * (z * y))) * u. [para(34(a,1),47(a,1,1,2,2,2)),rewrite([234(5),234(16)])

,flip(a)].

529 C' * (x * (y * (z * (y * (x * C))))) = x * (y * (z * (y * x))). [para(47(a,1),63(a,1,2))].

531 C * (x * (C' * (x * (C * y)))) = (C * (x * x)) * y. [para(63(a,1),47(a,1,1,2,2)),flip(a)].

532 C * (x * (C' * (y * (C' * x)))) = x * (C' * (y * x)). [para(63(a,1),47(a,2,2,2,2)),rewrite([16(10,R)])].

534 x * (C * (x' * (C * (x * y)))) = (x * (C * C)) * y. [para(64(a,1),47(a,1,1,2,2)),flip(a)].

540 x * (C * (y * (z * y))) = x * (y * (z * (y * C))). [para(122(a,1),47(a,2,2,2,2,2)),rewrite([249(8),39(5)])].

568 (C * x) * (x * C)' = 0. [para(493(a,1),9(a,1,2))].

573 (C * (x * (y * x)))' = (x * (y * (x * C)))'. [para(13(a,1),493(a,2,1))].

619 (B * (x * B)) / (y * B) = B * (x / y). [para(7(a,1),50(a,1,1,2,1))].

620 (B * B) / (x * B) = B * x'. [para(8(a,1),50(a,1,1,2,1)),rewrite([2(4)])].

659 x * (y * (C * (x * x))) = x * (y * (x * (x * C))). [para(66(a,2),13(a,2,2,2)),rewrite([13(5)]),flip(a)].

670 x * (C * (x' * x')) = x' * C. [para(66(a,2),34(a,1,2))].

698 (C * (x * x)) * y = x * (C * (x * y)). [para(67(a,2),13(a,1,1))].

727 C * (x * (C' * (x * (C * y)))) = x * (C * (x * y)). [back_rewrite(531),rewrite([698(13)])].

743 ((x * (B * y)') * (B * ((y * z) * B))) / (z * B) = R(x,(B * y)',B * ((y * z) * B)). [para(54(a,1),18(a,1,2))].

749 B / x = B * x'. [para(54(a,1),39(a,1,1,2)),rewrite([619(8),32(3),194(10)]),flip(a)].

762 B * (B' / (B * x)) = (B * x)'. [back_rewrite(471),rewrite([749(6),473(6)])].

765 (x * (y * B')) * (B * y') = R(x,y * B',B * y'). [back_rewrite(461),rewrite([749(6),749(13)])].

768 (x * (x * B')) * (B * (x' * x')) = 0. [back_rewrite(458),rewrite([749(7),172(7)])].

783 (x * B') * (B * x') = 0. [back_rewrite(335),rewrite([749(5)])].

784 (x * B')' = B * x'. [back_rewrite(333),rewrite([749(6)])].

785 B * (x * (B * x)') = 0. [back_rewrite(474),rewrite([762(8)])].

786 B * (B' / x) = x'. [para(749(a,1),32(a,1)),rewrite([261(4)])].

788 B * (C' * B') = C'. [para(749(a,1),108(a,1)),rewrite([270(5)])].

789 C' * B = B * C'. [para(749(a,1),113(a,1)),flip(a)].

790 (B * x') * (x * B') = 0. [para(749(a,1),136(a,1,1)),rewrite([293(5)])].

794 B' / x = B' * x'. [para(786(a,1),10(a,1,2)),flip(a)].

807 (x * (y * B)) * (B' * y') = R(x,y * B,B' * y'). [back_rewrite(397),rewrite([794(6),794(13)])].

809 (x * (x * B)) * (B' * (x' * x')) = 0. [back_rewrite(393),rewrite([794(7),172(7)])].

817 (B' * x') * (C * (x * B)) = C. [back_rewrite(273),rewrite([794(3)])].

820 (x * (y * (x * B)))' = B' * (x * (y * x))'. [back_rewrite(269),rewrite([794(10)])].

822 (B' * x') * ((x * B) * y) = y. [back_rewrite(267),rewrite([794(3)])].

824 (x * B)' = B' * x'. [back_rewrite(261),rewrite([794(6)])].

825 C * (B * C') = B. [para(789(a,1),10(a,1,2)),rewrite([30(3)])].

827 (B * x) * (B * C') = B * ((x * C') * B). [para(789(a,1),15(a,1,2))].

836 ((x * C) * (B * C')) * B' = R(x,C,B * C'). [para(825(a,1),18(a,1,2)),rewrite([293(9)])].

858 (x * (B * ((y * (x * x)) * B))) / (x * B) = x * ((B * y) * x). [para(56(a,1),39(a,1,1,2))].

880 x * (B * x)' = B'. [para(785(a,1),10(a,1,2)),rewrite([3(4)]),flip(a)].

882 R(x,B * x,(B * x)') = x. [para(785(a,1),13(a,2,2)),rewrite([85(7),3(8)])].

889 (B * x)' = x' * B'. [para(880(a,1),10(a,1,2)),flip(a)].

893 R(B',x,x') = B'. [para(34(a,1),880(a,1,2,1)),rewrite([85(5)])].

895 x' * ((B' * x) * (y * (x * ((x' * B') * z)))) = (x' * ((B' * x) * (y * B'))) * z. [para(880(a,1),47(a,1,1,2,2,2)),rewrite([889(3),234(9)

,794(5),30(5),889(13),889(17),234(23),794(15),30(15)]),flip(a)].

899 R(x,B * x,x' * B') = x. [back_rewrite(882),rewrite([889(5)])].

913 ((x * (y' * B')) * (B * ((y * z) * B))) / (z * B) = R(x,y' * B',B * ((y * z) * B)). [back_rewrite(743),rewrite([889(3),889(17)])].

945 ((x * C) * B) * ((B * C') * (((x * C) * B) * y)) = (((x * C) * B) * (B * (x * B))) * y. [para(63(a,1),57(a,1,1,2,2,1)),flip(a)].

953 (B * C') * (B * x) = B * (B * (x * C')). [para(183(a,1),57(a,2,2,2)),rewrite([789(4),467(12),293(15),249(17),293(14),85(15),260(14),34(1

1),789(11),3(15)]),flip(a)].

971 (B * C) * (B * x) = B * (B * (x * C)). [para(568(a,1),57(a,2,2,2)),rewrite([16(3),467(10),889(14),13(16),788(14),232(10),113(8),34(10),1

6(9),3(13)]),flip(a)].

987 R(B',x',x) = B'. [para(30(a,1),893(a,1,3))].

1000 C' * B' = B' * C'. [para(788(a,1),10(a,1,2)),flip(a)].

1001 B' * ((B * C') * ((B' * C') * x)) = ((B' * C') * C') * x. [para(788(a,1),13(a,1,1,2)),rewrite([1000(5),1000(14),1000(20),234(23),256(16

),789(15)]),flip(a)].

1012 (B * C) * ((B' * C') * x) = x. [back_rewrite(402),rewrite([1000(8)])].

1014 (B' * C') * ((B * C) * x) = x. [back_rewrite(400),rewrite([1000(5)])].

1016 (B' * x')' = x * B. [para(794(a,1),104(a,1,1)),rewrite([256(8)])].

1017 (B' * x') * (x * B) = 0. [para(794(a,1),136(a,1,1)),rewrite([256(7)])].

1021 ((x * B) * y) * B = x * (B * (y * B)). [para(58(a,1),10(a,1,2)),rewrite([10(10)]),flip(a)].

1023 (B * (x * (B * (y * B)))) * z = B * (((x * B) * y) * (B * z)). [para(58(a,1),13(a,1,1))].

1026 (B * (((x * B) * y) * (B * z))) / ((x * (B * (y * B))) * z) = R(B,x * (B * (y * B)),z). [para(58(a,1),18(a,1,1,1)),rewrite([1023(8),102

1(13),1021(21)])].

1032 B * (((x * (y * (z * (y * (x * B))))) * u) * B) = B * (x * (y * (z * (y * (x * (B * (u * B))))))). [para(47(a,1),58(a,1,2,1,1)),rewrite

([47(21)])].

1052 (x' * B') * (B * x) = 0. [para(889(a,1),8(a,1,1))].

1053 (B * x) * (x' * B') = 0. [para(889(a,1),9(a,1,2))].

1058 (x' * B') * (C * (B * x)) = C. [para(889(a,1),64(a,1,1))].

1065 R(B,B * x,x' * B') = B. [para(889(a,1),300(a,1,3))].

1071 (B' * x)' = x' * B. [para(30(a,1),1016(a,1,1,2))].

1079 B * ((x * ((y * B') * (z * (y * B')))) * B) = (B * x) * ((y * B') * (z * y)). [para(7(a,1),59(a,1,2,2,2)),rewrite([293(4),293(11),293(1

4)]),flip(a)].

1089 (B * ((x * (y * (z * y))) * (B * u))) / ((y * (z * (y * B))) * u) = R(B * x,y * (z * (y * B)),u). [para(59(a,1),18(a,1,1,1)),rewrite([1

3(8)])].

1127 (B * x) * (C' * (y * (B * C'))) = B * ((x * (C' * (y * C'))) * B). [para(789(a,1),59(a,1,2,2,2))].

1136 (x' * B) * (B' * x) = 0. [para(1071(a,1),8(a,1,1))].

1137 (B' * x) * (x' * B) = 0. [para(1071(a,1),9(a,1,2))].

1140 (B' * x) * ((x' * B) * y) = y. [para(1071(a,1),34(a,1,2,1))].

1177 (x / y) * (C * ((y / x) * (C * ((x / y) * z)))) = ((x / y) * (C * C)) * z. [para(140(a,1),47(a,1,1,2,2)),flip(a)].

1185 C * (x * (x * C)) = x * (C * (x * C)). [para(68(a,1),16(a,2))].

1268 R(C * x,y,z) = R(x * C,y,z). [para(242(a,1),18(a,1,1,1)),rewrite([18(6)]),flip(a)].

1276 ((x * C) * (y * ((C * x) * z))) / z = (C * x) * (y * (C * x)). [para(242(a,1),39(a,1,1))].

1277 (C * x) * (y * (C * x)) = (x * C) * (y * (x * C)). [para(242(a,2),39(a,1,1,2,2)),rewrite([1276(8)])].

1292 (x * ((C * y) * (z * ((y * C) * x)))) * u = x * ((C * y) * (z * ((C * y) * (x * u)))). [para(242(a,1),47(a,1,1,2,2,2))].

1336 (C * x)' * (C * C) = C / x. [para(250(a,1),10(a,1,2))].

1338 (x * C) * (C / x) = C * C. [para(16(a,1),250(a,1,1))].

1343 x * (C / (C' * x)) = C * C. [para(34(a,1),250(a,1,1))].

1358 x * (C * y) = x * (y * C). [para(69(a,1),10(a,1,2)),rewrite([10(8)]),flip(a)].

1382 C * (x * C) = x * (C * C). [para(69(a,2),39(a,1,1)),rewrite([113(8),10(9)]),flip(a)].

1411 C * ((C * x) * (C * y)) = C * ((x * C) * (y * C)). [para(242(a,1),69(a,2,2))].

1419 C * (C * (C * x)') = C / x. [back_rewrite(1336),rewrite([1382(7,R),16(6,R)])].

1420 (x / y) * (C * ((y / x) * (C * ((x / y) * z)))) = C * ((x / y) * (C * z)). [back_rewrite(1177),rewrite([1382(15,R),16(14,R),70(16)])].

1449 ((x * (C * (C * y))) * z) / (C * (y * (C * z))) = R(x,C * (C * y),z). [para(70(a,1),18(a,1,2))].

1452 C * (C * x) = x * (C * C). [para(70(a,1),63(a,1,2)),rewrite([10(9)]),flip(a)].

1472 (C * (x * (B * C)))' = B' * (C * (C * x))'. [para(70(a,1),824(a,1,1)),rewrite([16(4)])].

1511 C' * x = x * C'. [para(8(a,1),71(a,2,2,2)),rewrite([34(8),3(7)]),flip(a)].

1512 x' * (C * (x * (y * x))) = y * (x * C). [para(71(a,2),10(a,1,2))].

1518 B * ((C * (x * (y * x))) * B) = B * ((x * (y * (x * C))) * B). [para(71(a,1),15(a,2,2,1)),rewrite([13(7),59(8)])].

1522 ((C * (x * (y * x))) * z) / ((y * (x * C)) * z) = R(x,y * (x * C),z). [para(71(a,2),18(a,1,1,1))].

1527 x * (C * (x' * (y * x'))) = y * (x' * C). [para(71(a,2),34(a,1,2))].

1534 (C * (x * C))' = (x * (C * C))'. [para(71(a,2),109(a,1,2)),rewrite([109(8)])].

1538 (x * C')' = C / x. [para(71(a,2),158(a,1,1)),rewrite([34(8),16(9,R),9(9),3(7)])].

1626 B' * ((B * C') * ((B' * C') * x)) = C' * (B' * (C' * x)). [back_rewrite(1001),rewrite([1511(22,R),13(23)])].

1659 C * (x * C') = x. [para(1511(a,1),10(a,1,2)),rewrite([30(3)])].

1660 x' * (C' * x) = C'. [para(1511(a,2),10(a,1,2))].

1663 (x * (x * C')) * y = x * (C' * (x * y)). [para(1511(a,1),13(a,1,1,2))].

1664 C' * (x * (C' * y)) = C' * (x * (y * C')). [para(1511(a,1),13(a,2,2,2)),rewrite([13(7)])].

1665 (C' * (C' * x)) * y = C' * (x * (C' * y)). [para(1511(a,2),13(a,1,1,2))].

1666 C' * (x * (y * x)) = x * (y * (x * C')). [para(1511(a,2),13(a,1))].

1672 (C' * (x * y)) / (y * C') = R(x,y,C'). [para(1511(a,2),18(a,1,1))].

1673 (C' * (x * y)) / (C' * y) = R(x,y,C'). [para(1511(a,2),18(a,1,2)),rewrite([1511(4,R)])].

1674 x / (x * C') = C. [para(1511(a,1),32(a,1,2)),rewrite([30(7)])].

1676 x * (C' * x') = C'. [para(1511(a,2),34(a,1,2))].

1684 (C' * (x * (C' * x))) * y = C' * (x * (x * (C' * y))). [para(1511(a,2),45(a,1,1,2,2))].

1690 C' * (x * (y * (z * (y * x)))) = x * (y * (z * (y * (x * C')))). [para(1511(a,2),47(a,1))].

1698 C * (x * (x * C')) = x * x. [para(1511(a,1),71(a,1,2,2)),rewrite([63(11)])].

1699 x / C' = C * x. [para(7(a,1),1659(a,1,2)),flip(a)].

1701 C * (x * (y * (x * C'))) = x * (y * x). [para(13(a,1),1659(a,1,2))].

1702 (x * y) / ((x * C') * y) = R(C,x * C',y). [para(1659(a,1),18(a,1,1,1))].

1703 ((x * C) * (y * C')) / y = R(x,C,y * C'). [para(1659(a,1),18(a,1,2))].

1711 C * (x * (y * (z * (y * (x * C'))))) = x * (y * (z * (y * x))). [para(47(a,1),1659(a,1,2))].

1724 (C * x)' = C' / x. [para(1699(a,1),104(a,1,1))].

1730 (C' / x) * ((C * x) * y) = y. [para(1699(a,1),137(a,1,2,1))].

1736 (x * (C * C))' = C' / (x * C). [back_rewrite(1534),rewrite([1724(5)]),flip(a)].

1755 C' / (x * (B * C)) = B' * (C' / (C * x)). [back_rewrite(1472),rewrite([1724(7),1724(14)])].

1769 C * (C * (C' / x)) = C / x. [back_rewrite(1419),rewrite([1724(5)])].

1824 (x * (y * (x * C)))' = C' / (x * (y * x)). [back_rewrite(573),rewrite([1724(5)]),flip(a)].

1828 (x * C)' = C' / x. [back_rewrite(493),rewrite([1724(3)]),flip(a)].

1872 x * (y' * C) = x * (C * y'). [para(72(a,2),34(a,1,2)),rewrite([1527(7)])].

1930 (C / x) * ((x * C') * y) = y. [para(1538(a,1),10(a,1,1))].

1934 (x * C') * ((C / x) * y) = y. [para(1538(a,1),34(a,1,2,1))].

1952 C' / (C * x) = C' / (x * C). [para(242(a,1),1828(a,1,1)),rewrite([16(4,R),1724(5)]),flip(a)].

1957 (B * ((x * C) * B)) / (x * (B * C)) = R(B,x,B * C). [para(73(a,1),18(a,1,1))].

1960 B * ((C * (B' * x)) * B) = x * (B * C). [para(34(a,1),73(a,1,1)),rewrite([16(10,R)]),flip(a)].

1991 R(x',C' * x,y) = (C' * y) / ((C' * x) * y). [para(1660(a,1),18(a,1,1,1)),flip(a)].

2000 x * (C' * (x' * (C' * (x * y)))) = (x * (C' * C')) * y. [para(1660(a,1),47(a,1,1,2,2)),flip(a)].

2007 (x' * B) * (C' * (B' * x)) = C'. [para(1071(a,1),1660(a,1,1))].

2023 (x * B') * (C' * (B * x')) = C'. [para(784(a,1),1676(a,1,2,2))].

2035 R(x,y / z,z) * y = (x * (y / z)) * z. [para(7(a,1),78(a,1,2))].

2036 R(x,y,z)' * ((x * y) * z) = y * z. [para(78(a,1),10(a,1,2))].

2037 R(x,y',y * z) * z = (x * y') * (y * z). [para(10(a,1),78(a,1,2))].

2041 R(x,C,y) * (y * C) = (x * C) * y. [para(16(a,1),78(a,1,2))].

2042 R(x,y,C) * (C * y) = C * (x * y). [para(16(a,2),78(a,1,2)),rewrite([16(8,R)])].

2043 (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u). [para(78(a,1),18(a,1,1,1))].

2044 ((x * R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u). [para(78(a,1),18(a,1,2))].

2045 R(x,y,y' * z) * z = (x * y) * (y' * z). [para(34(a,1),78(a,1,2))].

2048 (R(x,y,z) * ((x * y) * z)) / (y * z) = R(x,y,z) * R(x,y,z). [para(78(a,1),35(a,1,1,2))].

2051 (x * ((y * x) * z)) / z = x * (R(y,x,z) * x). [para(78(a,1),39(a,1,1,2))].

2071 ((C * x) * y) * z = ((x * C) * y) * z. [para(242(a,1),78(a,2,1)),rewrite([78(5)])].

2084 R(x,y,C') * (C' * y) = C' * (x * y). [para(1511(a,2),78(a,1,2)),rewrite([1511(11,R)])].

2092 R(x,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u). [para(78(a,1),78(a,1,2))].

2104 R((x / y) / z,z,y) = x / (z * y). [para(7(a,1),79(a,2,1))].

2105 R(x / (y / z),y / z,z) = (x * z) / y. [para(7(a,1),79(a,2,2))].

2107 R(x / y',y',y) = x * y. [para(8(a,1),79(a,2,2)),rewrite([23(7)])].

2108 R(x / y,y,x') = (y * x')'. [para(9(a,1),79(a,2,1)),rewrite([28(7)])].

2109 R(x / y,y,y') = x * y'. [para(9(a,1),79(a,2,2)),rewrite([23(7)])].

2110 R(x' / y,y,x * z) = z / (y * (x * z)). [para(10(a,1),79(a,2,1))].

2111 R(x / y',y',y * z) = (x * (y * z)) / z. [para(10(a,1),79(a,2,2))].

2118 R(C / x,x,y) = (y * C) / (x * y). [para(16(a,1),79(a,2,1))].

2119 (x * y) / (y * C) = R(C' * x,C,y). [para(16(a,1),79(a,2,2)),rewrite([113(2)]),flip(a)].

2120 R(x / y,y,C) = (C * x) / (y * C). [para(16(a,2),79(a,2,1))].

2124 R(C' / x,x,y * C) = y / (x * (y * C)). [para(63(a,1),79(a,2,1))].

2128 R(x / y,y,z)' = (y * z) / (x * z). [para(79(a,2),104(a,1,1))].

2130 (x * y) / (C * y) = R(C' * x,C,y). [para(113(a,1),79(a,1,1)),flip(a)].

2143 (x * y) / (B' * y) = R(x * B,B',y). [para(256(a,1),79(a,1,1)),flip(a)].

2144 (x * y) / (B * y) = R(x * B',B,y). [para(293(a,1),79(a,1,1)),flip(a)].

2149 R((B * x) / y,y,B) = B * (x / y). [para(49(a,1),79(a,2,1)),rewrite([619(12)])].

2150 R(x / (B * y),B * y,B) = (x * B) / (B * (y * B)). [para(49(a,1),79(a,2,2))].

2180 R((C * x) / y,y,z) = ((x * C) * z) / (y * z). [para(242(a,1),79(a,2,1))].

2182 R((x * C) / y,y,z) = ((C * x) * z) / (y * z). [para(242(a,2),79(a,2,1))].

2190 R((C * (C * x)) / y,y,z) = (C * (x * (C * z))) / (y * z). [para(70(a,1),79(a,2,1))].

2195 (x * (y * (z * C))) / (C * (z * (y * z))) = R(x / z,z,y * (z * C)). [para(71(a,2),79(a,2,2)),flip(a)].

2197 (x * y) / (y * C') = R(C * x,C',y). [para(1511(a,1),79(a,2,2)),rewrite([1699(3)]),flip(a)].

2198 R(x / y,y,C') = (C' * x) / (y * C'). [para(1511(a,2),79(a,2,1))].

2217 R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z)). [para(78(a,1),79(a,2,1))].

2232 ((x * (y * (x * (z / u)))) * u) / z = R(x * (y * x),z / u,u). [para(13(a,1),80(a,1,1,1))].

2233 (B * (((x / (y * B)) * y) * B)) / x = R(B,x / (y * B),y * B). [para(15(a,1),80(a,1,1))].

2234 (C * (x * (C' * y))) / y = R(x,C' * y,C). [para(16(a,2),80(a,1,1)),rewrite([113(3),113(9)])].

2235 x / ((y * (x / z)) * z) = R(y,x / z,z)'. [para(80(a,1),104(a,1,1)),flip(a)].

2236 C' * ((x * (C / y)) * y) = R(x,C / y,y). [para(80(a,1),113(a,1)),flip(a)].

2239 ((x * (B' * y')) * y) * B = R(x,B' * y',y). [para(80(a,1),256(a,1)),rewrite([794(3),794(8)]),flip(a)].

2242 ((x * (y * B')) * B) / y = R(x,y * B',B). [para(293(a,1),80(a,1,1,1,2)),rewrite([293(9)])].

2249 (C' * (x * (C * y))) / y = R(x,C * y,C'). [para(1511(a,2),80(a,1,1)),rewrite([1699(5),1699(10)])].

2260 (B * ((x * B') * (y * x))) * x' = B * ((x * B') * y). [para(783(a,1),47(a,2,2,2,2)),rewrite([82(9),259(8),3(15)])].

2273 (x * y')' * R(x,y',y) = y. [para(82(a,1),10(a,1,2))].

2275 x * ((y * x') * (x * z)) = (x * R(y,x',x)) * z. [para(82(a,1),13(a,1,1,2)),flip(a)].

2276 (x * (y * (x * z'))) * z = R(x * (y * x),z',z). [para(13(a,1),82(a,1,1))].

2277 R(x,C',C) = x. [para(82(a,1),16(a,2)),rewrite([1659(5)]),flip(a)].

2279 (R(x,y',y) * z) / (y * z) = R(x * y',y,z). [para(82(a,1),18(a,1,1,1))].

2285 (x * (y' * y')) * (y * y) = R(x,y' * y',y * y). [para(172(a,1),82(a,1,1,2)),rewrite([172(8)])].

2292 (x * (B * y')) * (y * B') = R(x,B * y',y * B'). [para(784(a,1),82(a,1,1,2)),rewrite([784(12)])].

2294 (x * (B' * y')) * (y * B) = R(x,B' * y',y * B). [para(824(a,1),82(a,1,1,2)),rewrite([824(11)])].

2301 R(x,C,C') = x. [para(82(a,1),1511(a,2)),rewrite([30(5),63(5),30(3)]),flip(a)].

2306 R(x,y * z',z) * R(y,z',z) = (x * (y * z')) * z. [para(82(a,1),78(a,1,2))].

2321 (B * (C / x)) * ((C' * x) * B') = 0. [para(158(a,1),790(a,1,1,2))].

2419 R(x,y,y') / y' = x * y. [para(85(a,1),6(a,1,1))].

2420 (x * y)' * R(x,y,y') = y'. [para(85(a,1),10(a,1,2))].

2421 (x * (x * y)) * y' = R(x * x,y,y'). [para(12(a,1),85(a,1,1))].

2424 (x * (y * (x * z))) * z' = R(x * (y * x),z,z'). [para(13(a,1),85(a,1,1))].

2466 R(x,y * z,z') * R(y,z,z') = (x * (y * z)) * z'. [para(85(a,1),78(a,1,2))].

2467 R(R(x,y,z),y * z,(y * z)') = ((x * y) * z) * (y * z)'. [para(78(a,1),85(a,1,1)),flip(a)].

2537 R(B,x',x * B) = B. [para(15(a,1),87(a,1,1)),rewrite([8(3),2(4),293(5),12(6),9(5),3(3)]),flip(a)].

2542 x / ((y * z') * (z * x)) = R(y,z',z * x)'. [para(87(a,1),104(a,1,1)),flip(a)].

2546 R(x,C',y' * C) = R(x,C',C * y'). [para(103(a,2),87(a,1,1,2)),rewrite([131(9)])].

2569 R(B,x',x * (y * (x * B))) = R(B,y,x * B). [para(59(a,1),87(a,1,1)),rewrite([10(5),95(9)]),flip(a)].

2585 R(x,C,C' * y) = R(x,C,y * C'). [para(1511(a,1),87(a,1,1,2)),rewrite([30(3),1703(7),30(8)]),flip(a)].

2586 (C' * ((C * x) * y)) / y = R(x,C',C * y). [para(1511(a,2),87(a,1,1,1)),rewrite([234(6),1699(5)])].

2596 R(x,C,C' * (C' / x)) = C' / (C' / x). [para(1676(a,1),87(a,1,1)),rewrite([30(5),1828(5),30(9),30(12),1828(12)]),flip(a)].

2600 (R(x,y,y') * (y * z)) / z = R(x * y,y',y * z). [para(82(a,1),87(a,1,1,1)),rewrite([30(2),30(7)])].

2603 R(B,B * x',x) = B. [para(7(a,1),2537(a,1,3)),rewrite([293(3),784(5)])].

2622 R(B,B * x,x') = B. [para(30(a,1),2603(a,1,2,2))].

2655 ((x * (x * y)) * (y' * z)) / z = R(x * x,y,y' * z). [para(34(a,1),88(a,1,2))].

2723 (x * (C' * (x * y))) / (y * C') = R(x * x,C',y). [para(1511(a,1),88(a,1,2)),rewrite([1663(5)])].

2777 R(B * B,x,x') = B * B. [para(2622(a,1),78(a,1,1)),rewrite([85(5),300(4),2421(9)]),flip(a)].

2808 ((x * (C' * C')) * (y * C)) / (C' * y) = R(x,C' * C',y * C). [para(63(a,1),90(a,1,2,2))].

2809 C * (C * (x * (C' * C'))) = R(x,C' * C',C). [para(63(a,1),90(a,1,2)),rewrite([16(8,R),1699(11)])].

2814 C' * (C' * (x * (C * C))) = R(x,C * C,C'). [para(122(a,1),90(a,1,2)),rewrite([1511(7,R),113(9)])].

2875 (((x * y) * y) * z) / (y * (y * z)) = R(R(x,y,y),y * y,z). [para(78(a,1),90(a,1,1,1))].

2918 (B' * (C / x)) * ((C' * x) * B) = 0. [para(158(a,1),1017(a,1,1,2))].

3043 R(x * (C' * x),y,z) = R(x * (x * C'),y,z). [para(1511(a,1),91(a,2,1,2)),rewrite([91(8)])].

3115 (B * ((x' * B') * (y * x'))) * x = B * ((x' * B') * y). [para(1052(a,1),47(a,2,2,2,2)),rewrite([82(11),259(10),3(17)])].

3160 B * ((x * (B' * y)) * B) = B * ((x * B') * (y * B)). [para(1136(a,1),59(a,2,2,1,2,2)),rewrite([231(13),256(13),1140(15),246(8),293(3),3

(14)]),flip(a)].

3173 B * ((C * B') * (x * B)) = x * (B * C). [back_rewrite(1960),rewrite([3160(9)])].

3176 (x' * y) / R(y,x',x) = R(x',y * x',x). [para(8(a,1),92(a,1,1,2,2)),rewrite([3(3),82(5)])].

3185 (C * (x * (y * C))) / ((x * C) * y) = R(C,x * C,y). [para(16(a,1),92(a,1,1,2,2))].

3187 (x * (y * (C * x))) / (C * (y * x)) = R(x,y * x,C). [para(16(a,2),92(a,1,1,2,2)),rewrite([16(7,R)])].

3189 (x * (y * (x * C))) / (C * (y * x)) = R(x,y * x,C). [para(16(a,2),92(a,1,2))].

3190 (x * (y * z)) / ((y * x) * (x' * z)) = R(x,y * x,x' * z). [para(34(a,1),92(a,1,1,2,2))].

3196 (C * (x * (C * y))) / (C * y) = R(C * x,C,y). [para(64(a,1),92(a,1,2,1)),rewrite([132(8),64(14)])].

3197 ((x * y) * z) / (y * (x * (y * z))) = R(y,x * y,z)'. [para(92(a,1),104(a,1,1)),flip(a)].

3198 (x * (y * C)) / ((y * x) * (C * x')) = R(x,y * x,C * x'). [para(122(a,1),92(a,1,1,2,2))].

3201 R(C,x' * C,y) = R(C,C * x',y). [para(103(a,1),92(a,1,2,1)),rewrite([484(11)]),flip(a)].

3213 R(x,B * x,B) = x. [para(49(a,1),92(a,1,2)),rewrite([6(10)]),flip(a)].

3252 R(x,(C * y) * x,z) = R(x,(y * C) * x,z). [para(242(a,1),92(a,2,2)),rewrite([92(10)])].

3365 R(x,C * (C * y),z) = R(x,C * (y * C),z). [para(16(a,2),93(a,1,1,1,2,2)),rewrite([1449(12)])].

3366 (C * (x * (y * (z * y)))) / (y * (z * (y * C))) = R(x,y * (z * y),C). [para(16(a,2),93(a,1,1))].

3414 R(x,C * (y * y),z) = R(x,y * (C * y),z). [para(67(a,2),93(a,2,2)),rewrite([93(10)]),flip(a)].

3446 (C * ((C * x) * (C * y))) / (C * (x * (C * y))) = R(C,C * (x * C),y). [para(69(a,2),93(a,1,1,1)),rewrite([70(7)])].

3468 R(x,C' * (C' * y),z) = R(x,C' * (y * C'),z). [para(1511(a,2),93(a,2,2,2)),rewrite([93(16)]),flip(a)].

3563 (B * ((x * C) * (B * y))) / ((x * B) * y) = R(B * C,x * B,y). [para(16(a,1),94(a,1,1,2,1))].

3565 (B * ((x * y) * (B * C))) / (C * (y * B)) = R(B * x,y * B,C). [para(16(a,2),94(a,1,1,2,2)),rewrite([16(5),16(11,R)])].

3673 R(x,B' * x,x' * B) = x. [para(1137(a,1),92(a,1,2)),rewrite([34(6),8(4),3(2),23(2)]),flip(a)].

3710 x * (C * (C * x')) = C * C. [para(68(a,1),1338(a,1,1)),rewrite([176(10),246(9),151(5),12(5)])].

3728 (B * (x * B)) / (y' * ((y * x) * B)) = R(B,x / y,y * B). [para(7(a,1),95(a,1,1,2,1)),rewrite([233(8)])].

3729 R(B,x / y,y * B) = R(B,y',(y * x) * B). [para(10(a,1),95(a,1,1,2,1)),rewrite([3728(10)])].

3730 R(B,x,x * B) = B. [para(12(a,1),95(a,1,1,2)),rewrite([6(9)]),flip(a)].

3737 (B * (x * B)) / (C' * ((x * C) * B)) = R(B,C',(x * C) * B). [para(63(a,1),95(a,1,1,2,1))].

3762 R(B,x,(C * y) * B) = R(B,x,(y * C) * B). [para(242(a,1),95(a,2,3)),rewrite([95(13)])].

3773 (B * ((x * C') * B)) / (x * (B * C')) = R(B,x,B * C'). [para(1511(a,1),95(a,1,2,2)),rewrite([1511(18)])].

3782 B * ((R(x,y,B) * y) / (x * y)) = R(B,R(x,y,B),y * B). [para(78(a,1),95(a,1,2)),rewrite([619(11)])].

3791 (B * (x * B)) / (y' * ((y * x) * B)) = R(B,y',(y * x) * B). [back_rewrite(3728),rewrite([3729(15)])].

3792 R(B,x * B',x) = B. [para(7(a,1),3730(a,1,3)),rewrite([293(3)])].

3816 (B * (x * B')) * x = B * ((x * B') * x). [para(3792(a,1),78(a,1,1)),flip(a)].

3865 R(x,B * y,(C * z) * B) = R(x,B * y,(z * C) * B). [para(242(a,1),96(a,2,3)),rewrite([96(16)])].

3921 (B * ((C * x) * B)) / (B * (x * B)) = R(C,B,x * B). [para(15(a,1),97(a,1,1))].

3923 (x * ((C / x) * y)) / y = R(C,x,x' * y). [para(34(a,1),97(a,1,2)),rewrite([246(5)])].

3925 R(C',x * C,y) = R(C,x,y)'. [para(97(a,1),104(a,1,1)),rewrite([130(8)]),flip(a)].

3947 (x * y) / ((x * C) * y) = R(C,x,y)'. [back_rewrite(130),rewrite([3925(10)])].

3951 (x * (y * C)) / (C * y) = x. [para(1358(a,1),6(a,1,1))].

3952 (x * (C * y)) / (y * C) = x. [para(1358(a,2),6(a,1,1))].

3953 (x / (C * y)) * (y * C) = x. [para(1358(a,1),7(a,1))].

3954 (x / (y * C)) * (C * y) = x. [para(1358(a,2),7(a,1))].

3960 ((x * y) * (C * z)) / (y * (z * C)) = R(x,y,C * z). [para(1358(a,1),18(a,1,2))].

3961 R(x,y,C * z) = R(x,y,z * C). [para(1358(a,2),18(a,1,1)),rewrite([3960(8)])].

3983 x * (C * (C * y)) = x * (C * (y * C)). [para(242(a,1),1358(a,2,2)),rewrite([16(9,R)])].

4032 (C * x) / (C * (y * x)) = R(y,x,C)'. [para(10(a,1),100(a,1,1,2)),rewrite([16(5,R),142(10)])].

4034 R(x',C * x,C) = x'. [para(64(a,1),100(a,1,1,2)),rewrite([16(7,R),210(8),1724(6),16(8,R),1769(9),109(4)]),flip(a)].

4035 (x * C) / (C * (y * x)) = R(y,x,C)'. [para(100(a,1),104(a,1,1)),flip(a)].

4052 (C * (x * (C * (C * y)))) / (C * (y * (C * C))) = R(x,C * (C * y),C). [para(70(a,1),100(a,1,2))].

4058 (C * ((x * y) * z)) / (C * (y * z)) = R(R(x,y,z),y * z,C). [para(78(a,1),100(a,1,1,2)),rewrite([16(7,R)])].

4066 R(R(C,x,C * y),x * (C * y),C) = R(C,C * (x * C),y). [back_rewrite(3446),rewrite([4058(13)])].

4089 (C * (x * (y * (C * z)))) / (C * (y * (z * C))) = R(x,y * (C * z),C). [para(69(a,1),101(a,1,2))].

4090 (C * (x * (y * (z * C)))) / (C * (y * (C * z))) = R(x,y * (z * C),C). [para(69(a,2),101(a,1,2))].

4097 R(C / x,x,C) = C / x. [para(34(a,1),4034(a,1,2)),rewrite([158(4),158(8)])].

4111 x' * (C * (C * x)) = C * C. [para(4034(a,1),78(a,1,1)),rewrite([16(5,R),64(10)])].

4115 C / (C' * x) = C * (x' * C). [para(4097(a,1),80(a,2)),rewrite([113(3),113(7),7(9),210(4),113(8)]),flip(a)].

4117 x * (C * (x' * C)) = C * C. [back_rewrite(1343),rewrite([4115(5)])].

4118 (x * (C * C)) / (x * C) = C. [para(1382(a,1),6(a,1,1))].

4120 C' * (x * (C * C)) = x * C. [para(1382(a,1),10(a,1,2))].

4123 (x * (C * C)) * y = C * (x * (C * y)). [para(1382(a,1),13(a,1,1))].

4130 R(x,C * C,y) = R(x,C * y,C). [para(1382(a,2),18(a,1,1,1)),rewrite([13(5),12(9),101(10)]),flip(a)].

4131 (C * (C * (x * y))) / (y * (C * C)) = R(x,y,C * C). [para(1382(a,2),18(a,1,1)),rewrite([16(4,R)])].

4132 (C * (C * (x * y))) / (C * (y * C)) = R(x,y,C * C). [para(1382(a,2),18(a,1,2)),rewrite([1382(5,R),16(4,R)])].

4134 C / (x * (C * C)) = C' / x. [para(1382(a,1),109(a,1,2)),rewrite([1828(9)])].

4177 R(x,C' * C',C * C) = R(x,C' * C',C). [para(1382(a,2),82(a,1)),rewrite([172(5),16(9,R),2809(10),172(11)]),flip(a)].

4190 R(x,C * (y * C),C) = R(x,C * C,y * C). [para(1382(a,1),90(a,1,2,2)),rewrite([4123(7),3366(14)])].

4228 R(x,C * C,C) = R(x,C,C * C). [para(1382(a,2),100(a,1,1,2)),rewrite([16(11,R),4131(12)]),flip(a)].

4231 R(x,C * C,C') = x. [back_rewrite(2814),rewrite([4120(9),63(5)]),flip(a)].

4243 x * (C * (x' * (C * (x * y)))) = C * (x * (C * y)). [back_rewrite(534),rewrite([4123(13)])].

4256 (x * (y * x))' = x' / (x * y). [para(9(a,1),106(a,1,2,2,2)),rewrite([3(3)]),flip(a)].

4269 C' / (C * x) = x' / (C * C). [para(122(a,1),106(a,1,2,2)),rewrite([4256(10)]),flip(a)].

4273 C / (x * C') = C * (x' * C). [para(158(a,1),106(a,2)),rewrite([106(8),4256(7),30(3),4115(5)]),flip(a)].

4326 x / (C' * (y * (x * C'))) = C * (y' * C). [para(1511(a,1),106(a,1,2,2,2)),rewrite([4256(15),30(11),4115(13)])].

4339 x / (C' * C') = C * (x * C). [para(1660(a,1),106(a,1,2,2)),rewrite([4256(14),30(9),4115(12),30(9)])].

4372 (x * (y * (x * B)))' = B' * (x' / (x * y)). [back_rewrite(820),rewrite([4256(10)])].

4419 x / (C * C) = C' * (x * C'). [para(4231(a,1),79(a,1)),rewrite([1511(13,R),1382(13,R),16(12,R),9(12),3(10),113(9)])].

4422 C' / (C * x) = C' * (x' * C'). [back_rewrite(4269),rewrite([4419(10)])].

4460 C' / (x * C) = C' * (x' * C'). [back_rewrite(1952),rewrite([4422(5)]),flip(a)].

4463 C' / (x * (B * C)) = B' * (C' * (x' * C')). [back_rewrite(1755),rewrite([4422(14)])].

4469 (x * (C * C))' = C' * (x' * C'). [back_rewrite(1736),rewrite([4460(10)])].

4524 (x * (C * C)) / (C * x) = C. [para(1452(a,1),6(a,1,1))].

4529 (C * (C * (x * y))) / (C * (C * y)) = R(x,y,C * C). [para(1452(a,2),18(a,1,2)),rewrite([1382(5,R),16(4,R)])].

4530 (C * x) / (x * (C * C)) = C'. [para(1452(a,1),32(a,1,2))].

4537 (x * (x * (C * C))) * y = x * (C * (C * (x * y))). [para(1452(a,1),45(a,1,1,2))].

4565 R(x,C * (C * y),C) = R(x,C * C,C * y). [para(1452(a,1),90(a,1,2,2)),rewrite([4123(7),4052(14)])].

4606 ((B' * x) * y) * B = B' * (x * (y * B)). [para(120(a,1),10(a,1,2)),flip(a)].

4610 (x * (B' * y)) * B = (x * B') * (y * B). [para(13(a,1),120(a,1,2,1)),rewrite([231(10),256(10),34(11)])].

4627 B * ((B' * C') * (x * B)) = x * (B * C'). [para(1511(a,1),120(a,2,2)),rewrite([1511(7,R),4610(9),1511(6)])].

4638 (C * x) * (B * C) = C * (C * (x * B)). [para(1382(a,2),120(a,1,2,1,1)),rewrite([16(6,R),70(8),4610(10),3173(11),12(12)])].

4657 R(x,y,(x * y)' * z)' = (y * ((x * y)' * z)) / z. [para(124(a,2),104(a,1,1))].

4658 R(x,C,C * (C' / x)) = C' / (C' / x). [para(124(a,2),109(a,1)),rewrite([1828(4),16(6,R),1828(10),16(12,R),1724(13)])].

4687 x / (y * ((y' * B') * x)) = R(B,y,(y' * B') * x). [para(889(a,1),124(a,1,3,1)),rewrite([889(10)]),flip(a)].

4727 R(x',C' * x,C * y) = y / (C' * ((C * x) * y)). [para(1660(a,1),124(a,1,3,1,1)),rewrite([30(7),1660(15),30(13),234(13),1699(12)])].

4751 C' / (C' / x) = C / (C / x). [para(1382(a,1),124(a,2,2)),rewrite([1828(4),16(6,R),4658(7),1828(10),1382(14,R),16(13,R),1769(14)])].

4759 R(x,C,C' * (C' / x)) = C / (C / x). [back_rewrite(2596),rewrite([4751(14)])].

4833 R(B * x,B,B' * y) = (B * (x * y)) / y. [para(49(a,1),125(a,1,1,1)),rewrite([246(8),293(5),85(6),260(5)]),flip(a)].

4849 R(B,x,x' * (y * (x' * B))) = R(B,y,x' * B). [para(59(a,1),125(a,1,1)),rewrite([34(6),95(11)]),flip(a)].

4883 R(x,C * C,C' * (C' * y)) = R(x,C' * y,C). [para(1382(a,2),125(a,1,1,1)),rewrite([172(8),12(10),246(11),113(5),63(6),2234(7),172(12),12(

14)]),flip(a)].

4996 R(x,C' * C',C) = x. [para(126(a,1),90(a,1,2)),rewrite([16(10,R),9(10),3(8),4339(12),16(9,R),2809(10),16(16,R),9(16),77(14)])].

5026 R(x,C' * C',C * C) = x. [back_rewrite(4177),rewrite([4996(16)])].

5028 C * (x * (C' * C')) = x * C'. [para(4996(a,1),78(a,1,1)),rewrite([16(7,R),34(7),16(11,R)]),flip(a)].

5089 ((x * C) * x) * ((C' / x) * y) = (x * C) * (C' * y). [para(34(a,1),127(a,1,2,2)),rewrite([1828(12)]),flip(a)].

5225 R(x,C * C,y * (C' * y)) = R(x,y * y,C). [para(128(a,1),90(a,1,2,2)),rewrite([4123(9),128(7),101(8)]),flip(a)].

5303 C * (C * (x / (y * C))) = (C * x) / y. [para(3954(a,1),39(a,1,1,2)),rewrite([16(9,R)]),flip(a)].

5317 R(x,(y * C) / z,z) * (C * y) = (x * ((y * C) / z)) * z. [para(80(a,1),3954(a,1,1))].

5373 C' * (x * (C * (y * x))) = x * (R(y,x,C) * x). [para(78(a,1),129(a,1,2,2)),rewrite([16(5,R)])].

5427 x / ((y * C') * (x * C)) = R(y,C',x * C)'. [para(131(a,1),104(a,1,1)),flip(a)].

5530 R(C,x,x' * ((C * x) * y)) = R(C,C * x,y). [para(132(a,1),18(a,1,1)),rewrite([34(11),484(9)]),flip(a)].

5677 (C * x) / ((C * y) * x) = R(y,C,x)'. [para(16(a,1),133(a,1,2)),rewrite([142(4)]),flip(a)].

5679 R(x',C * x,y) = R(x,C,y)'. [para(16(a,1),133(a,2,2,1)),rewrite([138(10)])].

5680 R(x,C * x',y) = R(x',C,y)'. [para(30(a,1),133(a,1,1)),rewrite([5677(11)])].

5691 (C * (C * C)) / (C * (C * (C * x))) = R(x,C,C * C)'. [para(66(a,2),133(a,2,1)),rewrite([5679(7),1382(17,R),16(16,R)]),flip(a)].

5715 C' * (C / x) = C * (C' / x). [para(1676(a,1),133(a,2,2)),rewrite([1724(8),5679(10),4759(8),104(5),113(4),1724(11),34(13),1699(11)])].

5745 (x * C) / (C' * x) = C * C. [para(16(a,1),153(a,1,1))].

5853 (C / x) * (C * x) = C * C. [para(1382(a,2),185(a,1,2)),rewrite([16(8,R),34(8)])].

5938 (C * (C * C)) / x = C * (C * (C / x)). [para(5853(a,1),39(a,1,1,2)),rewrite([16(11,R)])].

5981 R(x,C,C * C)' = x'. [back_rewrite(5691),rewrite([5938(12),109(10),1724(7),4422(7),34(10),1659(6)]),flip(a)].

5991 R(x,C,C * C) = x. [para(5981(a,1),30(a,1,1)),rewrite([30(2)]),flip(a)].

5993 R(x,C * C,C) = x. [back_rewrite(4228),rewrite([5991(10)])].

6041 (x * C') / ((y * C') * x) = R(y,C',x)'. [para(1511(a,1),138(a,1,1))].

6042 R(C,x * C',y) = R(C',x,y)'. [para(1511(a,1),138(a,1,2,1)),rewrite([1702(6)])].

6044 (C' * x) / ((C' * y) * x) = R(y,C',x)'. [para(1511(a,2),138(a,1,2,1))].

6114 (x * y) / ((x * C') * y) = R(C',x,y)'. [back_rewrite(1702),rewrite([6042(11)])].

6116 R(x',C' * x,y) = R(x,C',y)'. [back_rewrite(1991),rewrite([6044(13)])].

6129 x / (C' * ((C * y) * x)) = R(y,C',C * x)'. [back_rewrite(4727),rewrite([6116(7)]),flip(a)].

6130 C * (x * (C * C)) = x * (C * (C * C)). [para(5993(a,1),78(a,1,1)),rewrite([16(5,R),16(12,R)]),flip(a)].

6173 (x * y)' * x = x' * (x / y). [para(194(a,1),10(a,1,2)),flip(a)].

6174 x' / (x * y) = x' * (y' * x'). [para(10(a,1),194(a,1,2,1,1)),flip(a)].

6180 x / (x' * y) = x * (y' * x). [para(34(a,1),194(a,1,2,1,1)),flip(a)].

6182 x / (C * x') = x * (C' * x). [para(122(a,1),194(a,1,2,1,1)),flip(a)].

6204 (x * C') / (y * x) = x / (y * (x * C)). [para(71(a,2),194(a,1,2,1,1)),rewrite([1724(5),192(7)])].

6208 (B * x) / (B * C) = B * (C' * (x * B')). [para(73(a,1),194(a,1,2,1,1)),rewrite([4256(9),6174(9),1828(7),13(14),10(12),7(8),246(8),293(3

),1511(7,R)]),flip(a)].

6240 C / (x * (C' * x)) = C * (C * (x' * x')). [para(128(a,1),194(a,1,2,1,1)),rewrite([172(3),16(6,R)]),flip(a)].

6248 C' / (x * (C * x)) = C' * (C' * (x' * x')). [para(152(a,1),194(a,1,2,1,1)),rewrite([172(4),1511(8,R)]),flip(a)].

6313 (x * (y * (x * B)))' = B' * (x' * (y' * x')). [back_rewrite(4372),rewrite([6174(10)])].

6360 (x * (y * x))' = x' * (y' * x'). [back_rewrite(4256),rewrite([6174(6)])].

6379 R(x,C',y * C)' = R(x,C',y)'. [back_rewrite(6041),rewrite([6204(8),5427(7)])].

6410 x / ((y * C') * (x * C)) = R(y,C',x)'. [back_rewrite(5427),rewrite([6379(13)])].

6450 R(x / y,y,z) = R(y / x,x,z)'. [para(7(a,1),142(a,1,2)),rewrite([104(2)])].

6459 R(B' * x',(x * B) * y,z) = R(x * B,y,z)'. [para(824(a,1),142(a,1,1))].

6466 R(x',C * (x * (y * x)),z) = R(x,y * (x * C),z)'. [para(71(a,2),142(a,1,2))].

6469 R(C / x,(x * C') * y,z) = R(x * C',y,z)'. [para(1538(a,1),142(a,1,1))].

6475 R(x',C * (C * x),y) = R(x,C * C,y)'. [para(1452(a,2),142(a,1,2))].

6502 x / (C' / x) = (x * C) * x. [para(63(a,1),195(a,2,2)),rewrite([1511(5,R),63(5),1828(3)])].

6518 x / (C / x) = (x * C') * x. [para(1659(a,1),195(a,2,2)),rewrite([16(5,R),1659(5),1538(4)])].

6554 (x * B) * (x * B) = x * (B * (x * B)). [para(143(a,1),256(a,1)),rewrite([256(3),256(5),256(8),1021(10)])].

6610 (x / y) * (y / (x / y)) = x * (y / x). [para(7(a,1),232(a,1,1)),rewrite([104(2)]),flip(a)].

6618 x' * ((x / y) * x') = (x * y)'. [para(232(a,1),32(a,1,2)),rewrite([6174(4),104(3)])].

6638 ((C * x) * y) * (C' / x) = (x * C) * (y / (C * x)). [para(242(a,1),232(a,2)),rewrite([1724(6)])].

6639 (x * C) * (y / (C * x)) = (x * C) * (y / (x * C)). [para(242(a,2),232(a,1,1)),rewrite([1828(6),6638(7)])].

6645 ((x * C') * y) * (C / x) = (x * C') * (y / (x * C')). [para(1538(a,1),232(a,1,2))].

6658 (x * (y / x)) * x = R(x * y,x',x). [para(232(a,1),82(a,1,1))].

6741 (B * B) / x = B * (B * x'). [para(7(a,1),620(a,1,2)),rewrite([293(7),784(9)])].

6745 R(x,B,B)' = x'. [para(824(a,1),620(a,2,2)),rewrite([138(8),34(10)])].

6792 R(x,B,B) = x. [para(6745(a,1),30(a,1,1)),rewrite([30(2)]),flip(a)].

6793 (x * B) * B = x * (B * B). [para(6792(a,1),78(a,1,1)),flip(a)].

6823 (x * (B * B)) * B' = x * B. [para(6793(a,1),6(a,1,1)),rewrite([293(6)])].

6824 (x * B') * (B * B) = x * B. [para(7(a,1),6793(a,1,1)),rewrite([293(4)]),flip(a)].

6830 (B * x) * (y * (B * B)) = B * ((x * (y * B)) * B). [para(6793(a,1),15(a,1,2))].

6831 B * ((x * (B * B)) * B) = B * (x * (B * (B * B))). [para(6793(a,1),15(a,2,2,1)),rewrite([13(8)]),flip(a)].

6850 R(x,B' * B',B * B) = x. [para(82(a,1),6793(a,2)),rewrite([172(4),4610(8),8(7),3(5),82(5),259(4),172(4)]),flip(a)].

6875 (x * (B * B)) * B = (x * B) * (B * B). [para(6793(a,1),6793(a,1,1))].

6893 B * ((x * B) * (B * B)) = B * (x * (B * (B * B))). [back_rewrite(6831),rewrite([6875(7)])].

7049 R(B' * x,x,x') = B' * x. [para(34(a,1),899(a,1,2)),rewrite([1071(7),85(9),260(8)])].

7181 ((C * B') * x) * B = B' * (C * (x * B)). [para(162(a,1),10(a,1,2)),flip(a)].

7183 C * ((x * (C * B')) * B) = B * ((C * B') * (x * C)). [para(13(a,1),162(a,1,2)),rewrite([82(11),259(10)]),flip(a)].

7191 (C * (x * (B * (x * B)))) * y = (x * B) * (C * ((x * B) * y)). [para(162(a,1),57(a,1,1,2)),rewrite([67(7,R),6554(6),122(16)])].

7511 R(B * x,B,C * B') = C' * (B * (C * x)). [para(49(a,1),165(a,1,2,1)),rewrite([249(11),293(8),85(9),260(8)]),flip(a)].

7609 R(x,C * C,C * (C' / y)) = R(x,C / y,C). [para(1769(a,1),90(a,1,2,2)),rewrite([4123(10),1769(8),101(10)]),flip(a)].

7775 ((x * (C' * y)) * z) / ((y * C') * z) = R(x,C' * y,z). [para(1930(a,1),87(a,1,1,2)),rewrite([104(3),113(2),104(13),113(12),1930(20)])].

7790 R(C' * x,y,z) = R(x * C',y,z). [para(1930(a,1),142(a,1,2)),rewrite([104(3),113(2),6469(11),30(10)])].

7791 x / (C' * y) = x / (y * C'). [para(1930(a,1),195(a,1,1)),rewrite([104(3),113(2),6645(13),1930(15)])].

7806 ((x * C') * x) * ((C / x) * y) = (x * C') * (C * y). [para(1934(a,1),68(a,2,2,2)),rewrite([16(8,R),1659(8)])].

7944 R(B * x,x',x) = B * x. [para(749(a,1),2107(a,1,1)),rewrite([30(3)])].

7967 R(B * x',x,x') = B * x'. [para(30(a,1),7944(a,1,2))].

8265 R(B * x,x,x') = B * x. [para(10(a,1),3673(a,1,2)),rewrite([889(5),82(8),259(7)])].

8298 (B * x) / x' = (B * x) * x. [para(8265(a,1),2419(a,1,1))].

8522 (x * (y / z))' * R(x,y / z,z / y) = z / y. [para(182(a,1),10(a,1,2))].

8765 x / (C * (y * (C' * x))) = R(y,C' * x,C)'. [para(4111(a,1),124(a,1,3,1,1)),rewrite([172(9),12(11),6475(12),4883(10),4111(16),172(14),12

(16),246(17),113(11),10(12)]),flip(a)].

8823 C * (x * (C' * (y * x))) = x * (C' * (y * (x * C))). [para(4120(a,1),47(a,2,2,2,2)),rewrite([1382(12,R),16(11,R),532(11)])].

8831 (x * (y * (C * C))) / (y * C) = R(C * x,C',y * (C * C)). [para(4120(a,1),79(a,2,2)),rewrite([1699(3)]),flip(a)].

8843 R(B,C',C * (x * (B * C))) = R(B,x,B * C). [para(4120(a,1),95(a,1,1,2,1)),rewrite([4123(14),16(12),10(15),1957(11),4123(14),16(12)]),fli

p(a)].

8897 (C * x) * (y * (C * x)) = C * ((C * x) * (y * x)). [para(191(a,1),1699(a,1)),rewrite([1699(3),1699(5),1699(10)])].

9118 (x * C) * (y * (x * C)) = C * ((C * x) * (y * x)). [back_rewrite(1277),rewrite([8897(6)]),flip(a)].

9194 C' / (x * (C' * C')) = C / x. [para(82(a,1),4134(a,1,2)),rewrite([172(5),5026(10),172(8)]),flip(a)].

9200 (x / (y * z)) * y = y' * ((y * x) / z). [para(192(a,1),10(a,1,2)),flip(a)].

9201 (x' * y) / (x * z) = x' * ((y / z) * x'). [para(10(a,1),192(a,1,2,1,2)),flip(a)].

9203 x * ((y / (x * z)) * (x * u)) = ((x * y) / z) * u. [para(192(a,1),13(a,1,1)),flip(a)].

9204 (B * x) * ((y / (B * ((x * z) * B))) * (B * x)) = ((B * x) * y) / (z * B). [para(15(a,1),192(a,1,2,1,2))].

9205 C * (C * (x / (C * y))) = (C * x) / y. [para(192(a,1),16(a,1)),rewrite([16(8,R),16(10,R)]),flip(a)].

9207 (x * y) / (x' * z) = x * ((y / z) * x). [para(34(a,1),192(a,1,2,1,2)),flip(a)].

9211 (x' * y) / (C * x) = x' * ((C' * y) * x'). [para(64(a,1),192(a,1,2,1,2)),rewrite([113(3)]),flip(a)].

9220 (B * x) * ((y / (B * (x * B))) * (B * x)) = ((B * x) * y) * B'. [para(49(a,1),192(a,1,2,1,2)),rewrite([293(16)])].

9233 B * (((B' * x) / y) * B) = x / (B' * y). [para(192(a,1),1071(a,1,1)),rewrite([104(5),9200(11),30(7),889(11),104(9),9200(11),30(7),49(12

)]),flip(a)].

9295 (x * (C * y)) / z = (x * (y * C)) / z. [para(1358(a,1),192(a,2,1)),rewrite([9200(5),34(7)])].

9327 (C * (x' * C)) / x = C * (C * (x' * x')). [para(155(a,1),192(a,1,2,1)),rewrite([16(6,R)]),flip(a)].

9339 (C * x) / (C * (C' / y)) = C * (C * (x / (C / y))). [para(1769(a,1),192(a,1,2,1,2)),rewrite([16(6,R)]),flip(a)].

9366 R(B,x / (y * B),y * B) = R(B,y',y * x). [back_rewrite(2233),rewrite([9200(5),293(5),299(10),87(6)]),flip(a)].

9418 (B' * x) * B' = B' * (x * B'). [para(193(a,1),293(a,1)),flip(a)].

9954 (B * x) * (y * (B * x)) = B * (x * ((y * B) * x)). [para(9(a,1),201(a,1,1,2,2,2,1)),rewrite([2(6),6830(7),619(11),195(6)]),flip(a)].

9956 (B * x) * x = B * (x * x). [para(10(a,1),201(a,1,1,2)),rewrite([15(6),619(9),35(4),10(10)]),flip(a)].

10077 ((B * C) * (x * (B * ((C / y) * B)))) / ((C * (C' / y)) * B) = C * (B * ((C * x) * B)). [para(1769(a,1),201(a,1,1,2,2,2,1)),rewrite([9

118(27),16(23),15(26)])].

10113 B * (x * ((B' * ((B * y) / (x * B))) * x)) = ((B * x) * y) * B'. [back_rewrite(9220),rewrite([9954(11),9200(8)])].

10114 B * (x * ((B' * ((B * y) / ((x * z) * B))) * x)) = ((B * x) * y) / (z * B). [back_rewrite(9204),rewrite([9954(12),9200(9)])].

10140 (B * x) / x' = B * (x * x). [back_rewrite(8298),rewrite([9956(7)])].

10163 (x * (B * (x * x))) * y = x * ((B * x) * (x * y)). [para(9956(a,1),13(a,1,1,2))].

10200 (B * (x * x)) * x' = B * x. [para(9956(a,1),85(a,1,1)),rewrite([8265(9)])].

10224 R(B,B * x,x * B) = B. [para(9956(a,1),95(a,1,1,2,1)),rewrite([49(6),12(5),15(12),12(11),6(13)]),flip(a)].

10225 R(B,x,B * (B * B)) = B. [para(9956(a,1),95(a,1,2,2)),rewrite([6875(7),6893(8),6(15),12(7)]),flip(a)].

10253 (B * (x * x)) * (x' * B') = B * (x * B'). [para(9956(a,1),232(a,1,1)),rewrite([889(6),32(13),232(13),293(11)])].

10315 (C * (x * (y * C))) * y' = R(C * (x * C),y,y'). [para(203(a,1),2109(a,1,1)),flip(a)].

10318 R(B,B * (x * B'),x) = B. [para(7(a,1),10224(a,1,3)),rewrite([293(4)])].

10321 R(B,x,B' * (x * B)) = B. [para(34(a,1),10224(a,1,2)),rewrite([231(6),256(6)])].

10333 R(B',x,B * (B * B))' = B. [para(10225(a,1),141(a,1)),flip(a)].

10413 (B * (B * (x * B'))) * x = B * (B * ((x * B') * x)). [para(10318(a,1),78(a,1,1)),rewrite([3816(7)]),flip(a)].

10426 B * ((x * B') * (x * B)) = B * (x * (B' * (x * B))). [para(10321(a,1),78(a,1,1)),rewrite([246(16),293(11)]),flip(a)].

10466 (C' * (x * x)) * y = x * (C' * (x * y)). [para(208(a,2),13(a,1,1))].

10514 (x * y) * (C' * (x * y)) = C' * ((x * y) * (x * y)). [para(208(a,2),78(a,2)),rewrite([78(11)])].

10697 R(x,C * C,C' * y) = R(x,y,C). [para(5745(a,1),80(a,1,1,1,2)),rewrite([4123(8),34(6),100(6),5745(8)]),flip(a)].

10978 R(B * (B * x),x',x) = B * (B * x). [para(6741(a,1),2107(a,1,1)),rewrite([30(4),12(10)])].

11157 R(x * B,B',B') = x * B. [para(6824(a,1),2107(a,2)),rewrite([172(7),2143(9),172(11),6850(16)])].

11160 B * ((x * B') * x) = B * (x * (B' * x)). [para(6824(a,1),198(a,1,1,2,2)),rewrite([10426(8),293(10),232(11),293(9),2424(10),260(9),82(1

5),259(14)]),flip(a)].

11173 (B * (B * (x * B'))) * x = B * (B * (x * (B' * x))). [back_rewrite(10413),rewrite([11160(15)])].

11197 x / (B' * B') = x * (B * B). [para(6850(a,1),79(a,1)),rewrite([12(19),10(18),8(14),23(12)])].

11248 (x * (B' * C')) * (B * C) = R(x,B' * C',B * C). [para(256(a,1),224(a,1,2)),rewrite([1511(5),16(9),1511(15),256(19),16(18)])].

11364 (x * (B * C)) * (B' * C') = R(x,B * C,B' * C'). [para(256(a,1),226(a,1,1,2)),rewrite([16(3),1511(9),256(14),16(13),1511(18)])].

11560 (C * x) * (y * C') = C * ((C' * x) * y). [para(1674(a,1),230(a,1,1)),rewrite([1674(5),113(3),1674(10)]),flip(a)].

11880 (x * y) / (y' * (x / y')) = R(y',x,y)'. [para(231(a,1),138(a,1,2))].

11954 (x * B) * (B' * y) = B * ((B' * x) * y). [para(256(a,1),233(a,1,1)),rewrite([30(9)])].

11955 (x * B') * (B * y) = B' * ((B * x) * y). [para(293(a,1),233(a,1,1))].

11964 (B * x') * (x * y) = x' * ((x * B) * y). [para(749(a,1),233(a,1,1))].

11967 (B' * x') * (x * y) = x' * ((x * B') * y). [para(794(a,1),233(a,1,1))].

11983 (x / y) * (C' * y) = y' * (C' * (y * x)). [para(1511(a,2),233(a,1,2)),rewrite([1511(10,R)])].

12018 (B' * x) * (x' * (B * x)) = x. [para(1052(a,1),233(a,2,2)),rewrite([794(4),30(4),30(10),3(10)])].

12145 (x * C) * (C' * y) = C * ((C' * x) * y). [para(6502(a,1),233(a,1,1)),rewrite([5089(8),104(10),1699(9),7(12),246(12),113(9)])].

12146 (x * C') * (C * y) = C' * ((C * x) * y). [para(6518(a,1),233(a,1,1)),rewrite([7806(8),104(9),113(8),7(12),234(12),1699(11)])].

12157 (B * (x * x)) * (x' * y) = x * ((x' * (B * x)) * y). [para(10140(a,1),233(a,1,1)),rewrite([30(8)])].

12159 R(x,x * B',B * x') = x. [para(10200(a,1),233(a,2,2)),rewrite([293(3),12(4),765(8),10(12)])].

12281 x * ((x' * (B * x)) * B') = B * (x * B'). [back_rewrite(10253),rewrite([12157(8)])].

12312 R(B',x,B * (B * B)) = B'. [para(10333(a,1),30(a,1,1)),flip(a)].

12314 (B' * ((B * x) * y)) / y = R(x,B',B * y). [para(10333(a,1),125(a,1,1,2,1)),rewrite([12312(8),11955(6),12312(15),12312(17),30(12)])].

12316 C' * (B' * (C * (B * x))) = R(x,B',B * C). [para(10333(a,1),165(a,1,2,2,2)),rewrite([12312(10),16(8),11955(9),16(8,R),12312(18),12312(

21),30(16),16(15)])].

12478 R(x,B',B') = x. [para(7(a,1),11157(a,1,1)),rewrite([293(7),82(10),259(9)])].

12481 (x * B') * B' = x * (B' * B'). [para(12478(a,1),78(a,1,1)),flip(a)].

13604 (x * y) * (C' * x') = x * (C' * (y / x)). [para(1511(a,2),246(a,1,2)),rewrite([1511(10,R)])].

13683 x * (C * (x' * (x' * (C * y)))) = C * (C * (x' * y)). [para(4117(a,1),246(a,1,1)),rewrite([12(6),9327(12),70(14),12(13)]),flip(a)].

13836 (x * C') * (y * C) = C' * ((C * x) * y). [para(71(a,2),247(a,1,1)),rewrite([34(8),16(13,R),9(13),3(11)])].

13901 R(x,C',C * y)' = R(x,C',y)'. [back_rewrite(6410),rewrite([13836(6),6129(7)])].

14542 (B' * (C / x)) * (C * ((C' * x) * B)) = C. [para(158(a,1),817(a,1,1,2))].

14578 C' * (x' * (C * (x * B))) = R(B',x',C * (x * B))'. [para(817(a,1),138(a,1,2)),rewrite([113(8)])].

14784 x / (C * ((B' * C') * x)) = R(B,C,(B' * C') * x). [para(1012(a,1),18(a,1,1))].

14792 B * (C * (B * ((B' * C') * (x * C')))) = C' * (B * x). [para(1012(a,1),59(a,2,2,1)),rewrite([231(17),256(17),1511(16),10(17),68(15),46

10(24),1511(23),11955(24),1511(23,R),34(25)])].

14812 (C * ((B' * C') * x)) / x = R(B,C,(B' * C') * x)'. [para(1012(a,1),138(a,1,2))].

14813 C * (B * (C * ((B' * C') * (x * B)))) = x / (B' * C'). [para(1012(a,1),195(a,1,1)),rewrite([1828(4),293(4),1511(5),9118(20),16(10),460

6(18),246(19),293(11),246(18),113(13),1511(14)]),flip(a)].

14841 C' * ((B * C) * (x * (B * (B * C)))) = B * ((x * (B * C)) * B). [para(1014(a,1),59(a,2,2,1)),rewrite([34(7),49(10),16(9)])].

14844 C' * ((C * B') * (C * (B * ((C * x) * B)))) = x * (B * (C * C)). [para(71(a,2),1014(a,1,2)),rewrite([9118(14),16(10),15(13),12146(16),

16(21,R),1382(21)])].

14858 (B * (x * B)) / ((B' * C') * (((B * C) * x) * B)) = R(B',C',((B * C) * x) * B)'. [para(1014(a,1),95(a,1,1,2,1)),rewrite([141(30)])].

15067 (B * (C * C)) / x = C * (B * (C * x')). [para(1058(a,1),200(a,1,1,2,2)),rewrite([16(15),11955(16),16(15,R),4243(18)])].

16312 (C' * ((C * x) * B')) * B = R(x,C',C * B'). [para(16(a,1),295(a,1,1,2)),rewrite([16(7,R),12146(8)])].

16328 B' * (C' * (B * (x * C))) = R(x,C,B' * C'). [para(1511(a,1),295(a,1,1,2)),rewrite([30(3),4610(10),1511(9),11955(10),1511(9,R),30(13),1

511(16)])].

16405 (x * (B * (y * B))) * B' = x * ((B * (y / x)) * x). [para(7(a,1),297(a,1,1,2,2,1))].

16451 (C' * (B * ((C' * x) * B))) * B' = C' * (C' * (B * x)). [para(1511(a,2),297(a,1,1,2,2,1)),rewrite([1511(20,R)])].

16520 (x * B') * ((B * y) * (x * B')) = x * (y * (x * B')). [para(233(a,1),297(a,1,1)),rewrite([293(6),15(11),2276(10),259(9),10(7),13(5),29

3(7),293(12)]),flip(a)].

16598 (x * (y * B')) * B = B' * ((B * x) * y). [para(299(a,1),10(a,1,2)),flip(a)].

16618 (B * R(x,y,B')) * y = B * (x * y). [para(78(a,1),299(a,1,2,1)),rewrite([82(7),259(6)]),flip(a)].

16636 (B * (x / y)) * y = y' * ((y * B) * x). [para(233(a,1),299(a,1,2,1)),rewrite([16598(9),11964(8),34(10)]),flip(a)].

16641 C * (B * (B * x)) = B * ((B * C) * x). [para(248(a,1),299(a,1,2,1)),rewrite([30(4),30(6),293(5),49(10),16598(9),34(10),30(10),16(12,R)

]),flip(a)].

16657 B' * (C' * ((B * C) * x)) = R(x,C',C * B'). [back_rewrite(16312),rewrite([16598(10),12146(9),16(7)])].

16666 C * (B' * (C * (B * x))) = B * ((C * B') * (x * C)). [back_rewrite(7183),rewrite([16598(8),16(7,R)])].

16667 R(x,y * B',B) = R(x,B',B * y). [back_rewrite(2242),rewrite([16598(6),12314(7)]),flip(a)].

16673 (x * (B * (y * B))) * B' = (x * B) * y. [back_rewrite(16405),rewrite([16636(12),34(14)])].

16741 (B * C') * (C' * x) = C' * (C' * (B * x)). [back_rewrite(16451),rewrite([16673(13),1511(4)])].

16760 (x * B) * (y * x) = x * ((B * y) * x). [back_rewrite(297),rewrite([16673(9)])].

17618 R(B,x,B * x) = B. [para(337(a,1),18(a,1,1)),rewrite([6(9)]),flip(a)].

17677 R(B',x,x)' = B. [para(34(a,1),17618(a,1,3)),rewrite([141(5)])].

17686 R(B',x,x) = B'. [para(17677(a,1),30(a,1,1)),flip(a)].

17687 (B' * x) * x = B' * (x * x). [para(17686(a,1),78(a,1,1)),flip(a)].

18273 C * (x * (C' * (C' * (x * (C * y))))) = x * (x * y). [para(63(a,1),415(a,1,1,2,2,2)),rewrite([128(6),12(2)]),flip(a)].

18478 R(x,y,C * (z * z)) = R(x,y,z * (z * C)). [para(12(a,1),3961(a,2,3))].

18492 R(x,y,z' * (C * z')) = R(x,y,C * (z' * z')). [para(177(a,2),3961(a,1,3)),rewrite([16(11,R)])].

18592 R(x,C * C,y) = R(x,y * C,C). [para(16(a,1),4130(a,2,2))].

18597 R(x,y * (C * y),C) = R(x,C * C,y * y). [para(67(a,1),4130(a,2,2)),flip(a)].

18634 B * ((C * (B * (C * x))) * B) = B * (C * (C * (B * (x * B)))). [para(16(a,1),419(a,1,2,1,1,2)),rewrite([1382(6),4123(7)])].

19215 C' * ((C * B') * (C * x)) = B' * (B' * ((B * C) * x)). [para(1014(a,1),423(a,2,2,2,2)),rewrite([16(13,R),1659(13),12146(10),12481(9),1

0(10),12(10),12146(20)]),flip(a)].

19271 B' * (C * (C * (B * (x * B)))) = x * (B * (C * C)). [back_rewrite(14844),rewrite([19215(16),467(14),18634(14),10(15)])].

19360 R(x,x * (C * y),C) = R(x,x * (y * C),C). [para(424(a,1),100(a,1,1)),rewrite([16(11,R),4090(12)]),flip(a)].

20219 R(x,B * (B * x),B) = x. [para(49(a,1),428(a,1,2)),rewrite([49(12),6(14)]),flip(a)].

20246 R(x',B * (x * B),B') = x'. [para(1053(a,1),428(a,1,1,2,2)),rewrite([3(5),85(10),300(9),49(8),232(11),293(9),85(10),260(9),6(7),85(8),3

00(7),49(6)]),flip(a)].

21297 (x / y) * ((y / x) / x) = y' * (y / x). [para(7(a,1),6173(a,1,1,1)),rewrite([104(5)]),flip(a)].

21527 x * (C' * (x * ((C * x') * y))) = (C' / x') * (R(C,x',x) * y). [para(6182(a,1),233(a,1,1)),rewrite([13(9),1724(13),82(17)])].

21540 R(x,x * (y' * C),C) = R(x,x * (C * y'),C). [para(444(a,1),100(a,1,1)),rewrite([16(13,R),4089(14)]),flip(a)].

21843 R(B' * x',x',x) = B' * x'. [para(30(a,1),7049(a,1,3))].

21939 (x * (C' * y)) / (y * C') = x. [para(7791(a,1),6(a,1))].

21941 (x / (y * C')) * (C' * y) = x. [para(7791(a,1),7(a,1,1))].

22323 R(B * (C / x),C' * x,C / x) = B * (C / x). [para(158(a,1),7967(a,1,1,2)),rewrite([158(11),158(15)])].

22775 ((B * C) * x) * B = C * (B * (x * B)). [para(122(a,1),467(a,1,1)),rewrite([11955(14),231(16),256(16),34(17)]),flip(a)].

22782 R(B * x,B,B * (x * B)) = B * x. [para(467(a,1),92(a,1,1)),rewrite([45(8),49(15),49(14),468(16),3213(16)])].

22786 C * (C * (B * (x * B))) = B * (C * ((x * C) * B)). [para(3710(a,1),467(a,1,1)),rewrite([12(8),70(18),16666(18),49(20),7181(19),34(20)]

)].

22790 R(B',C',B * (x * B))' = R(B,C',(C * x) * B). [back_rewrite(14858),rewrite([22775(15),12146(16),11955(15),15(14),10(15),3791(12),22775(

18),13901(20)]),flip(a)].

22791 C * ((x * C) * B) = x * (B * (C * C)). [back_rewrite(19271),rewrite([22786(10),10(11)])].

22849 ((x' * (B * x)) * y) / (x * y) = R(B' * x,x' * (B * x),y)'. [para(12018(a,1),138(a,1,2,1))].

22850 R(B' * x,x' * (B * x),y)' = R(x' * B,x,y). [para(12018(a,1),142(a,1,2)),rewrite([1071(4)]),flip(a)].

22863 ((x' * (B * x)) * y) / (x * y) = R(x' * B,x,y). [back_rewrite(22849),rewrite([22850(16)])].

22986 (B * ((x * C) * (B * B))) / (B * (B * C)) = R(B * x,B * C,B). [para(73(a,1),470(a,1,1,1)),rewrite([13(8),16(12)])].

22987 R(R(x,B,y),B * y,B) = x. [para(78(a,1),470(a,1,1,1)),rewrite([1021(5),6(10)]),flip(a)].

23049 R(R(x,B,B' * y),y,B) = x. [para(34(a,1),22987(a,1,2))].

23050 R(R(x,B,C * B'),C,B) = x. [para(122(a,1),22987(a,1,2))].

23055 R(R(x,B,C * y),B * (y * C),B) = x. [para(1358(a,1),22987(a,1,2))].

23148 R((x * (B' * y)) / y,y,B) = x * B'. [para(79(a,1),23049(a,1,1)),rewrite([34(9),293(9)])].

23162 B * ((x * (B * C)) * B) = B * (C * (x * (B * B))). [para(128(a,1),514(a,2,2,2,2)),rewrite([16(5),1511(10,R),10(10)])].

23168 C' * ((B * C) * (x * (B * (B * C)))) = B * (C * (x * (B * B))). [back_rewrite(14841),rewrite([23162(21)])].

23319 C * (x * (C * (y * x))) = x * (C * (y * (x * C))). [para(518(a,1),1659(a,1,2)),rewrite([1659(7)])].

23765 R(x,x * B,B' * x') = x. [para(17687(a,1),2273(a,1,1,1)),rewrite([1071(7),172(4),30(2),30(2),12(3),21843(9),807(8)])].

24137 (x * C) * (B * C) = C * (C * (x * B)). [para(181(a,1),528(a,1,2,2,2)),rewrite([256(6),16(5),82(12),259(11),9118(10),16(6),15(9),1512(1

1),4638(6),256(12),16(11),231(17),256(17),22775(16),1512(17)]),flip(a)].

24356 R(B * x,B * x',B') = B * x. [para(6173(a,1),20246(a,1,2,2)),rewrite([889(3),784(5),30(3),749(7),10(9),889(11),784(13),30(11)])].

24502 x * (C' * y) = x * (y * C'). [para(8(a,1),540(a,2,2,2,2)),rewrite([34(8),3(8)]),flip(a)].

24745 R(x,C' * y,z) = R(x,y * C',z). [para(21939(a,1),79(a,1,1)),rewrite([7775(14)]),flip(a)].

24793 (x * (C' * C')) * y = C' * (x * (C' * y)). [para(21941(a,1),529(a,1,2,2,2)),rewrite([1511(14,R),63(14),11983(14),2000(17)]),flip(a)].

24807 R(x,C' * C',y * C) = R(x,y,C'). [back_rewrite(2808),rewrite([24793(9),63(7),1673(8)]),flip(a)].

25344 (B * x) / (y * B) = B * ((x * B') / y). [para(7(a,1),619(a,1,1,2)),rewrite([293(8)])].

25345 (B * (x * B)) / y = B * (x / (y * B')). [para(7(a,1),619(a,1,2)),rewrite([293(8)])].

25346 (x * B) / (B * (y * B)) = (x / y) * B'. [para(619(a,1),104(a,1,1)),rewrite([889(4),104(2)]),flip(a)].

25369 (x * B) / (y * B) = B * ((B' * x) / y). [para(231(a,1),619(a,1,1,2)),rewrite([256(6),34(7)])].

25390 ((B * x) * y) / (z * B) = B * ((x * (y * B')) / z). [back_rewrite(10114),rewrite([25344(9),10(11),9200(7),34(9)]),flip(a)].

25391 ((B * x) * y) * B' = B * (x * (y * B')). [back_rewrite(10113),rewrite([25344(8),10(10),7(6)]),flip(a)].

25402 B * R(C * B',B,x) = R(C,B,x * B). [back_rewrite(3921),rewrite([25345(11),232(10),293(8),85(9),260(8),2144(6)])].

25408 B * ((x * C') / ((x * (B * C')) * B')) = R(B,x,B * C'). [back_rewrite(3773),rewrite([25345(13)])].

25411 B * (x / ((C' * ((x * C) * B)) * B')) = R(B,C',(x * C) * B). [back_rewrite(3737),rewrite([25345(12)])].

25428 R(x / (B * y),B * y,B) = (x / y) * B'. [back_rewrite(2150),rewrite([25346(14)])].

25429 ((x * (B * y)) / y) * B' = R(x,B * y,B). [back_rewrite(470),rewrite([25346(10)])].

25430 C * (B * ((C * x) * B)) = B * (C * (C * (x * B))). [back_rewrite(10077),rewrite([25390(19),16673(12),9339(14),6(11)]),flip(a)].

25535 (x * C) * (y * C') = C * ((C' * x) * y). [para(24502(a,1),242(a,2)),rewrite([246(6),113(3)]),flip(a)].

25653 (C * ((C' * x) * B)) * B' = R(x,C,B * C'). [back_rewrite(836),rewrite([25535(7)])].

26799 R(B * R(x,C,B),B,C) = B * x. [para(2041(a,1),468(a,1,1,2)),rewrite([6208(10),85(10),260(9),63(6)]),flip(a)].

26804 R(B * x,B * C,B) = B * R(x,C,B). [para(26799(a,1),22987(a,1,1))].

26806 (B * ((x * C) * (B * B))) / (B * (B * C)) = B * R(x,C,B). [back_rewrite(22986),rewrite([26804(21)])].

26808 R(x,C' * y,C) * y = C * (x * (C' * y)). [para(34(a,1),2042(a,1,2))].

26813 R(R(x,y,C),C * y,C) = R(x,y,C * C). [para(2042(a,1),100(a,1,1,2)),rewrite([16(9,R),4529(10)]),flip(a)].

26848 R((x / y) * B',B,y) = x / (B * y). [para(293(a,1),2104(a,1,1))].

26849 x / (B * (y * B)) = ((x * B') / y) * B'. [para(49(a,1),2104(a,2,2)),rewrite([293(2),25428(10)]),flip(a)].

26864 R(R(x,C * y,C'),y,C) = x. [para(3952(a,1),2104(a,2)),rewrite([113(5),2249(7)])].

26923 R(x / y,y,B) = B * ((B' * x) / y). [para(2104(a,1),23049(a,1,1)),rewrite([34(5),293(9),9200(10),30(6)])].

26935 R(R(x,C' * y,C),y,C') = x. [para(21939(a,1),2104(a,2)),rewrite([1699(7),2234(7)])].

26987 R(R(x,y,C'),C' * y,C) = x. [para(34(a,1),26864(a,1,1,2))].

26994 R(R(x,y,C'),y * C',C) = x. [para(1659(a,1),26864(a,1,1,2))].

26997 R((x * C') / y,y,C) = x / (C * y). [para(79(a,1),26864(a,1,1)),rewrite([1511(8,R),10(8)])].

27013 R(x,B * C,C') = R(x,B * C,B). [para(26864(a,1),22987(a,1,1)),rewrite([16(8)]),flip(a)].

27045 R(R(x,y,C),C * y,C') = x. [para(10(a,1),26935(a,1,1,2))].

27046 R(R(x,y,C),y * C,C') = x. [para(63(a,1),26935(a,1,1,2))].

27047 R(R(x,y * C',C),y,C') = x. [para(71(a,2),26935(a,1,1,2)),rewrite([34(8),16(9,R),9(9),3(7)])].

27190 R(R(x,y,C')',C' * (x * y),C) = x'. [para(26987(a,1),142(a,2,1)),rewrite([2084(11)])].

27450 R(C' * x,C,y) = R(C / x,x,y)'. [para(2118(a,2),104(a,1,1)),rewrite([2119(8)]),flip(a)].

27522 (C * x) / (B * C) = R(x * B',B,C). [para(293(a,1),2120(a,1,1)),flip(a)].

27544 (C * ((x * C) * y)) / (C * (x * y)) = R(R(C,x,y),x * y,C). [para(97(a,1),2120(a,1,1)),rewrite([16(13,R)]),flip(a)].

28599 R(x',B * x,x') = x'. [para(768(a,1),523(a,1,1,2,2)),rewrite([3(4),765(12),12159(11),85(7),300(6),293(5),85(6),260(5),765(11),12159(10)

]),flip(a)].

28602 R(x,B * x',x) = x. [para(30(a,1),28599(a,1,1)),rewrite([30(5),30(6)])].

28627 (x * (B * x')) * x = x * B. [para(28602(a,1),78(a,1,1)),rewrite([82(4),294(3)]),flip(a)].

28631 (x * B) / x = x * (B * x'). [para(28627(a,1),6(a,1,1))].

29173 R(x / (B * C),B * C,B' * C') = x * (B' * C'). [para(3954(a,1),807(a,1,1)),rewrite([16(13)]),flip(a)].

29284 R(x',B' * x,x') = x'. [para(809(a,1),523(a,1,1,2,2)),rewrite([3(5),807(14),23765(13),85(9),893(8),256(7),82(6),259(5),807(12),23765(11

)]),flip(a)].

29288 R(x,B' * x',x) = x. [para(30(a,1),29284(a,1,1)),rewrite([30(6),30(7)])].

29312 (x * (B' * x')) * x = x * B'. [para(29288(a,1),78(a,1,1)),rewrite([82(5),987(4)]),flip(a)].

29558 (x * C) / (y * x) = R(C' * y,C,x)'. [para(6450(a,1),2118(a,1)),rewrite([113(2)]),flip(a)].

29750 (x / y) * x' = x * (x * y)'. [para(6618(a,1),10(a,1,2)),rewrite([30(2)]),flip(a)].

29766 (x * y)' * (x * z) = x' * ((x / y) * z). [para(6618(a,1),234(a,1,1)),rewrite([29750(8),195(10),6173(8),34(9)])].

29801 (x * y) * ((x * y) * y)' = x * (x * y)'. [para(6(a,1),29750(a,1,1)),flip(a)].

29968 R(C / x,x * (C' * C'),y) = R(x * C',C',y)'. [para(9194(a,1),6450(a,1,1)),rewrite([1699(18),5028(17)])].

29976 C * (C * (B * (C' * (x * C')))) = R(B * x,B,C). [para(3953(a,1),858(a,1,1,2,2,1)),rewrite([16(9),27522(10),232(7),293(5),85(6),260(5),

4419(11),16(16,R)]),flip(a)].

29977 C * (C * (B * (C' * x))) = B * ((x * B) * (C * B')). [para(247(a,1),858(a,1,1,2,2,1)),rewrite([16(8,R),10(9),25430(8),16(11),6208(12),

70(12),10(13),16(17,R)]),flip(a)].

29983 B * (((x * C') * B) * (C * B')) = R(B * x,B,C). [back_rewrite(29976),rewrite([29977(12)])].

30507 B * (C * ((B' * C') * (B' * (C * x)))) = (C * B') * x. [para(1012(a,1),895(a,1,2,2)),rewrite([1538(6),256(4),16(3),1538(17),256(15),16

(14),232(17),293(15),122(17),1663(14),246(15),293(4),246(14),113(6),1511(7),1538(21),256(19),16(18),232(32),293(30),122(32),16(28,R),1698(28)

,246(24),293(19),12481(23),670(24),16(19,R)])].

30642 B * ((B' * (x * y)) / y) = R(x,B',B * (y * B)). [para(2(a,1),913(a,1,1,2,2,1)),rewrite([26(2),2(4),11955(8),15(7),10(8),25369(6),26(9)

,2(11),2(12)])].

30644 (C' * (B * ((C * x) * B))) / (x * B) = R(B,x,B * C). [para(1660(a,1),913(a,1,1,1)),rewrite([30(15),1511(18),141(25),22790(24),70(21),1

6(19),8843(22)])].

31134 B * (B * (C' * (B' * x))) = (B * C') * x. [para(34(a,1),953(a,1,2)),rewrite([1511(13,R)]),flip(a)].

31303 (B * (B * (x * C))) / (B * x) = B * C. [para(971(a,1),6(a,1,1))].

31306 B * (B * (C * (B' * x))) = (B * C) * x. [para(34(a,1),971(a,1,2)),rewrite([16(11,R)]),flip(a)].

31403 R(x,B,x * B) = x. [para(34(a,1),22782(a,1,1)),rewrite([231(7),256(7),34(8),34(9)])].

31427 R(B * x',x,x) = B * x'. [para(31403(a,1),6450(a,2,1)),rewrite([749(2),293(5),82(8),259(7),293(6),784(8)])].

31452 R(B * x,x',x') = B * x. [para(30(a,1),31427(a,1,1,2)),rewrite([30(8)])].

31492 (B * x) * (x' * x') = B * x'. [para(31452(a,1),78(a,1,1)),rewrite([85(10),300(9)])].

31535 (C * (x * B)) * B = x * (B * (B * C)). [para(16(a,1),1021(a,2,2,2)),rewrite([16(4,R)])].

31670 R(B,x * (B * (y * B)),B') = B. [para(9(a,1),1026(a,1,1,2,2)),rewrite([3(6),16673(13),6(9)]),flip(a)].

31678 R(B,x,B') = B. [para(7(a,1),31670(a,1,2))].

31681 R(B',x,B')' = B. [para(31678(a,1),141(a,1)),flip(a)].

31686 R(B',x,B') = B'. [para(31681(a,1),30(a,1,1)),flip(a)].

32001 R(B * x,B,x' * B') = B * x. [para(24356(a,1),18(a,2)),rewrite([25391(9),232(7),293(5),232(15),293(13),468(16)])].

32154 B * ((x * (y * (B' * B'))) * B) = (B * x) * (y * B'). [para(8(a,1),1079(a,2,2,2)),rewrite([10(9),12481(7),3(18)])].

32157 C' * ((B * C) * (x * C)) = C * (B * x). [para(1730(a,1),1079(a,1,2,1)),rewrite([16598(8),16(7,R),34(9),256(10),1511(9),1663(18),21527(

18),256(9),1511(8),259(13),12146(13),16(9)]),flip(a)].

32241 R(x,B * C,B) * B = C' * (x * (B * C)). [para(27013(a,1),78(a,1,1)),rewrite([1511(11,R),63(11),1511(14,R)])].

32245 x / (B * (B * C)) = (C' * (x * B')) * B'. [para(2104(a,1),27013(a,2)),rewrite([293(2),27013(13),25428(12),113(5),49(14),16(13)]),flip(

a)].

32247 C' * ((B * C) * x) = B * R(x,C,B). [back_rewrite(26806),rewrite([32245(14),232(13),293(11),6823(12),16673(12),1511(4),13836(7),16(5)])

].

32248 B * R(x * C,C,B) = C * (B * x). [back_rewrite(32157),rewrite([32247(9)])].

32251 B * R(x * (B * (B * C)),C,B) = B * (C * (x * (B * B))). [back_rewrite(23168),rewrite([32247(13)])].

32253 R(x,C',C * B') = R(x,C,B). [back_rewrite(16657),rewrite([32247(9),10(8)]),flip(a)].

32258 C' * ((C * x) * B') = R(x,C,B) * B'. [para(32253(a,1),78(a,1,1)),rewrite([10(10),12146(14)]),flip(a)].

32259 B' * (C * (B * x)) = R(C * x,C,B). [para(32253(a,1),79(a,1)),rewrite([1699(3),10(17),256(13),16598(12),16(11,R)]),flip(a)].

32260 (x * (C' * (x * (C * B')))) * B = R(x * x,C,B). [para(32253(a,1),88(a,2)),rewrite([1663(9),10(16),256(12)])].

32272 C' * R(C * x,C,B) = R(x,B',B * C). [back_rewrite(12316),rewrite([32259(9)])].

32638 R(B,C,C' * (x * (B * C'))) = R(B,x,B * C'). [para(1127(a,1),87(a,1,1)),rewrite([30(4),34(9),25345(13),25408(14),30(10)]),flip(a)].

32639 C' * ((C * x) * B) = C * (x * (B * C')). [para(3710(a,1),1127(a,1,1)),rewrite([12(12),34(11),246(21),113(15),10(16),4610(18),3173(19),

13836(14)]),flip(a)].

32704 C * (B * R(x,C,B)) = (B * C) * x. [para(29312(a,1),945(a,1,1,1)),rewrite([82(6),259(5),1659(12),16(9,R),82(11),259(10),12146(8),16(6),

32247(8),1659(14),16(11,R),82(13),259(12),1659(16),8(13),3(11),16(10)])].

33146 C' * (x * (C * (C * (x * y)))) = x * (x * (C * y)). [para(1185(a,1),233(a,2,2,1)),rewrite([113(5),126(6),12(4),423(12)]),flip(a)].

33478 R(x,B,x') = x. [para(34(a,1),32001(a,1,1)),rewrite([1071(5),85(7),260(6),34(8)])].

33724 (C * (B * x)) / R(x * C,C,B) = B. [para(32248(a,1),6(a,1,1))].

33725 C * (B * (C' * x)) = B * R(x,C,B). [para(7(a,1),32248(a,1,2,1)),rewrite([113(9)]),flip(a)].

33730 B * R(C * x,C,B) = C * (B * x). [para(16(a,2),32248(a,1,2,1))].

33760 B * R(x * (B * C'),C,B) = B * (C' * (x * B)). [para(532(a,1),32248(a,2)),rewrite([1511(7),16(11,R),34(11)])].

33764 R(C * (B * x),B,C) = B * (x * C). [para(32248(a,1),26799(a,1,1))].

33780 B * ((x * B) * (C * B')) = (B * C) * x. [back_rewrite(29977),rewrite([33725(8),32704(7)]),flip(a)].

33788 C * ((B * C') * x) = R(B * x,B,C). [back_rewrite(29983),rewrite([33780(12),25535(7),1511(5)])].

33891 ((B * C) * x) / (B * R(x,C,B)) = C. [para(32704(a,1),6(a,1,1))].

33892 (B * R(x,C,B)) / ((B * C) * x) = C'. [para(32704(a,1),32(a,1,2))].

33904 (B * C) * (x * C) = C * (C * (B * x)). [para(1358(a,1),32704(a,2)),rewrite([33730(8)]),flip(a)].

33905 (B * C) * (C * x) = C * (C * (B * x)). [para(1358(a,2),32704(a,2)),rewrite([32248(8)]),flip(a)].

34236 B * (C * (B' * x)) = R(C * x,B,C). [para(34(a,1),33764(a,1,1,2)),rewrite([16(11,R)]),flip(a)].

34237 R(B * (x * (B * C)),B,C) = B * (C * (x * B)). [para(71(a,1),33764(a,1,1)),rewrite([16(14,R)])].

34252 B * R(C * x,B,C) = (B * C) * x. [back_rewrite(31306),rewrite([34236(8)])].

34415 B' * ((B * C) * x) = R(C * x,B,C). [para(34252(a,1),10(a,1,2))].

34420 B * R(x,B,C) = R(B * x,B,C). [para(34(a,1),34252(a,1,2,1)),rewrite([12145(12),1511(10),33788(12)])].

34431 R(B * (C * x),B,C) = (B * C) * x. [para(242(a,2),34252(a,2)),rewrite([34420(7),16(10)])].

34454 R(B * (x * C),B,C) = (B * C) * x. [para(1268(a,1),34252(a,1,2)),rewrite([34420(7)])].

34496 R(B * x,B,C) / R(x,B,C) = B. [para(34420(a,1),6(a,1,1))].

34497 B' * R(B * x,B,C) = R(x,B,C). [para(34420(a,1),10(a,1,2))].

34500 R(x,B,C) / R(B * x,B,C) = B'. [para(34420(a,1),32(a,1,2))].

34578 R(B * (x * C'),B,C) / R(C' * x,B,C) = B. [para(24502(a,1),34496(a,1,1,1))].

34581 (B * x) / R(R(x,C,B),B,C) = B. [para(26799(a,1),34496(a,1,1))].

34603 B * (x / R(R(x,C,B),B,C)) = B. [para(34581(a,1),2149(a,1,1)),rewrite([469(9)]),flip(a)].

34613 x / R(R(x,C,B),B,C) = 0. [para(34603(a,1),10(a,1,2)),rewrite([8(4)]),flip(a)].

34635 R(R(x,C,B),B,C) = x. [para(34613(a,1),7(a,1,1)),rewrite([2(8)])].

34640 C * (R(x,C,B) * B) = x * (B * C). [para(34635(a,1),78(a,1,1)),rewrite([16(11,R)]),flip(a)].

34641 R(x,B * C,B) = R(x,C,B). [para(34635(a,1),22987(a,1,1))].

34642 R(x,B,C * B') = R(x,B,C). [para(23049(a,1),34635(a,1,1)),rewrite([16(8,R)]),flip(a)].

34643 R(x / (B * C),B,C) = C' * (x * B'). [para(2104(a,1),34635(a,1,1)),rewrite([16(3),293(9),113(12)])].

34644 R(B * (C' * x),B,C) = C' * (B * x). [para(2149(a,1),34635(a,1,1)),rewrite([113(3),113(12)])].

34647 C' * (x * (B * C)) = R(x,C,B) * B. [back_rewrite(32241),rewrite([34641(5)]),flip(a)].

34650 R(x,B * C,C') = R(x,C,B). [back_rewrite(27013),rewrite([34641(11)])].

34651 B * R(x,C,B) = R(B * x,C,B). [back_rewrite(26804),rewrite([34641(7)]),flip(a)].

34653 R(R(x,B,C),C,B) = x. [back_rewrite(23050),rewrite([34642(6)])].

34655 C' * (B * (C * x)) = R(B * x,B,C). [back_rewrite(7511),rewrite([34642(8)]),flip(a)].

34671 R(B * x,C,B) / ((B * C) * x) = C'. [back_rewrite(33892),rewrite([34651(5)])].

34672 ((B * C) * x) / R(B * x,C,B) = C. [back_rewrite(33891),rewrite([34651(9)])].

34678 R(B * (x * (B * C')),C,B) = B * (C' * (x * B)). [back_rewrite(33760),rewrite([34651(10)])].

34680 R(B * (C * x),C,B) = C * (B * x). [back_rewrite(33730),rewrite([34651(7)])].

34683 C * (B * (C' * x)) = R(B * x,C,B). [back_rewrite(33725),rewrite([34651(12)])].

34684 C * R(B * x,C,B) = (B * C) * x. [back_rewrite(32704),rewrite([34651(6)])].

34689 R(B * (x * (B * (B * C))),C,B) = B * (C * (x * (B * B))). [back_rewrite(32251),rewrite([34651(11)])].

34692 C' * ((B * C) * x) = R(B * x,C,B). [back_rewrite(32247),rewrite([34651(12)])].

34695 (C * R(x,B,C)) * B = x * (B * C). [para(34653(a,1),78(a,1,1)),rewrite([16(3),16(9,R)]),flip(a)].

34696 R(x / (B * C),C,B) = (C' * x) * B'. [para(2104(a,1),34653(a,1,1)),rewrite([113(9),293(12)])].

34697 R(R(B * x',x,C)',C,B) = x * B'. [para(6450(a,1),34653(a,1,1)),rewrite([749(2),293(11)])].

34702 (x * B) * (C * B') = C * R(x,B,C). [para(34642(a,1),78(a,1,1)),rewrite([122(9),16(5,R)]),flip(a)].

34703 C' * (x * (C * B')) = R(x * B',B,C). [para(34642(a,1),79(a,1)),rewrite([293(2),122(17),113(13)]),flip(a)].

34704 C' * (B * (x * C)) = R(B * x,B,C). [para(34642(a,1),468(a,2)),rewrite([122(7),122(10),113(6)])].

34708 B * (C * R(x,B,C)) = (B * C) * x. [back_rewrite(33780),rewrite([34702(8)])].

34711 (x * R(x * B',B,C)) * B = R(x * x,C,B). [back_rewrite(32260),rewrite([34703(8)])].

34714 R(x,C,B' * C') = R(x,B,C). [back_rewrite(16328),rewrite([34704(9),34497(8)]),flip(a)].

34719 B' * R(B * x,C,B) = R(x,C,B). [para(34651(a,1),10(a,1,2))].

34727 B * ((C * R(x,C,B)) * B) = (C * (B * x)) * B. [para(34651(a,1),73(a,1,1)),rewrite([2041(9),16(4,R),16(12,R)]),flip(a)].

34734 R(B * x,C,B) * B' = B * (R(x,C,B) * B'). [para(34651(a,1),232(a,1,1)),rewrite([293(14)])].

34762 R(B * (C' * x),C,B) = R(B * (x * C'),C,B). [para(24502(a,1),34651(a,2,1)),rewrite([34651(8)])].

34773 R(B * (C' * x),C,B) = B * R(C / x,x,B)'. [para(6450(a,1),34651(a,1,2)),rewrite([113(10)]),flip(a)].

34789 C * ((C' * x) * B') = R(x,B,C) * B'. [para(34714(a,1),78(a,1,1)),rewrite([1659(10),25535(14)]),flip(a)].

34790 B' * (C' * (B * x)) = R(C' * x,B,C). [para(34714(a,1),79(a,1)),rewrite([113(2),1659(19),256(15),4610(14),1511(13),11955(14),1511(13,R)

]),flip(a)].

34839 C * (C * (B * (C' / x))) = R(B * (C / x),B,C). [para(1769(a,1),34431(a,1,1,2)),rewrite([33905(16)]),flip(a)].

34841 R(R(C * x,B,C),B,C) = B * ((C * B') * x). [para(246(a,1),34431(a,2)),rewrite([34236(7),293(12)])].

34843 R((B * C) * x,C,B) = B * (C * x). [para(34431(a,1),22987(a,1,1)),rewrite([34641(9)])].

34855 B' * R(x,B,C) = R(B' * x,B,C). [para(34(a,1),34497(a,1,2,1))].

34858 R(x * (B * C),B,C) = C * (x * B). [para(71(a,2),34497(a,1,2,1)),rewrite([33764(11),16(7,R),10(9)]),flip(a)].

34869 R(x * (x * (B * C)),B,C) = C * (x * (x * B)). [para(422(a,2),34497(a,1,2,1)),rewrite([33764(12),16(8,R),10(10)]),flip(a)].

34938 (x * (B * C)) / (R(x,C,B) * B) = C. [para(34640(a,1),6(a,1,1))].

34967 C' * R(C * x,B,C) = C * R(C' * x,B,C). [para(2104(a,1),34640(a,1,2,1)),rewrite([16(4),9200(7),113(7),34790(9),293(10),113(13),247(18),

16598(17),34415(17)]),flip(a)].

34981 (C * (B * x)) * B = B * (C * (x * B)). [para(34640(a,1),34431(a,1,1,2)),rewrite([34237(9),15(15),34727(15)]),flip(a)].

34996 R(C,R(B * x,C,B),y) = R(C',(B * C) * x,y)'. [para(34672(a,1),6450(a,1,1)),rewrite([34671(17)])].

35014 C * (B * (x * (C' * C'))) = R(B * (x * C'),C,B). [para(5028(a,1),34680(a,1,1,2)),flip(a)].

35019 B * ((C * B') * x) = C * R(x,C,B). [para(34(a,1),34684(a,1,2,1)),rewrite([246(12),293(9)]),flip(a)].

35056 (B * C) * R(x,B,C) = C * (B * x). [para(34420(a,1),34684(a,1,2,1)),rewrite([34653(9)]),flip(a)].

35060 R(R(C * x,B,C),B,C) = C * R(x,C,B). [back_rewrite(34841),rewrite([35019(15)])].

35068 C * R(x * B,C,B) = x * (B * C). [back_rewrite(3173),rewrite([35019(9)])].

35073 (x * (B * C)) * B' = C * R(x,B,C). [para(34695(a,1),6(a,1,1)),rewrite([293(6)])].

35139 C * R(x,B,C) = R(C * x,B,C). [para(34708(a,1),10(a,1,2)),rewrite([34415(7)]),flip(a)].

35142 C * (B * ((B * C) * x)) = B * (C * (B * (x * C))). [para(34708(a,1),45(a,2,2,2)),rewrite([16641(7),16(6,R),1382(6),4537(11),34420(8),3

5139(9),33764(9)]),flip(a)].

35147 R(R(C,B,x),B * x,C) = R(C,B * C,R(x,B,C)). [para(34708(a,1),92(a,1,1,2)),rewrite([35056(13),27544(11)])].

35148 R(C,B,R(C * x,B,C)) = R(C,B * C,x). [para(34708(a,1),97(a,1,2)),rewrite([35139(8),35056(9),92(11),35139(12)]),flip(a)].

35156 ((B * C) * x)' * B = R(C * x,B,C)'. [para(34708(a,1),2420(a,1,1,1)),rewrite([35139(11),35139(16),300(18),35139(12)])].

35166 (B * C) * R(x,C,B) = B * (C * x). [para(26864(a,1),34708(a,1,2,2)),rewrite([16(10),34650(13)]),flip(a)].

35183 R(R(B,C,x),C * x,C) = B. [para(34708(a,1),33724(a,1,1,2)),rewrite([35139(11),16(13,R),35139(13),34653(16),4058(11)])].

35186 R((B * C) * x,B,C) = C * (B * x). [para(34708(a,1),34431(a,1,1)),rewrite([35056(14)])].

35205 (x * (B * C)) * B' = R(C * x,B,C). [back_rewrite(35073),rewrite([35139(12)])].

35208 C' * R(C * x,B,C) = R(x,B,C). [back_rewrite(34967),rewrite([35139(16),34(13)])].

35210 (x * B) * (C * B') = R(C * x,B,C). [back_rewrite(34702),rewrite([35139(12)])].

35211 R(C * x,B,C) * B = x * (B * C). [back_rewrite(34695),rewrite([35139(5)])].

35218 R(R(B,C,C' * x),x,C) = B. [para(34(a,1),35183(a,1,2))].

35225 C * ((B * C) * x) = B * (C * (C * x)). [para(35183(a,1),78(a,1,1)),rewrite([16(5,R),78(12),16(12,R)]),flip(a)].

35227 R(R(B,C,C * x),C * C,x * C) = B. [para(1358(a,1),35183(a,1,2)),rewrite([4190(11)])].

35263 R(B,C,C' * (C' * x)) = R(B,x,C'). [para(35218(a,1),26935(a,1,1)),flip(a)].

35264 R(B,C * x,C') = R(B,C,C' * x). [para(35218(a,1),27045(a,1,1))].

35265 R(B,x * C,C') = R(B,C,C' * x). [para(35218(a,1),27046(a,1,1))].

35275 R(x,B,C) / R(C * x,B,C) = C'. [para(35139(a,1),32(a,1,2))].

35278 C / R(C * x,B,C) = R(x,B,C)'. [para(35139(a,1),109(a,1,2))].

35282 R(C * x,B,C)' = C' / R(x,B,C). [para(35139(a,1),1724(a,1,1))].

35305 R(x,R(C * y,B,C),C) = R(x,C * C,R(y,B,C)). [para(35139(a,1),4130(a,2,2)),flip(a)].

35330 R(C * R(x,C,B),B,C) = C * x. [para(26864(a,1),35139(a,1,2)),rewrite([16(6),34650(9)]),flip(a)].

35353 ((B * C) * x)' * B = C' / R(x,B,C). [back_rewrite(35156),rewrite([35282(13)])].

35393 C * R(x,C,B) = R(C * x,C,B). [para(35330(a,1),22987(a,1,1)),rewrite([34641(7)]),flip(a)].

35396 R(C * (B * x),C,B) = (B * C) * x. [para(34684(a,1),35330(a,2)),rewrite([35393(10),35393(7),34635(13)])].

35401 R(C * (x * B),C,B) = x * (B * C). [back_rewrite(35068),rewrite([35393(7)])].

35402 R(R(C * x,B,C),B,C) = R(C * x,C,B). [back_rewrite(35060),rewrite([35393(13)])].

35403 B * ((C * B') * x) = R(C * x,C,B). [back_rewrite(35019),rewrite([35393(12)])].

35418 R(x,B',B * C) = R(x,C,B). [para(35393(a,1),10(a,1,2)),rewrite([32272(8)])].

35420 R(x,C,B)' * R(C * x,C,B) = C. [para(35393(a,1),64(a,1,2))].

35451 R(x,R(C * y,C,B),C) = R(x,C * C,R(y,C,B)). [para(35393(a,1),4130(a,2,2)),flip(a)].

35473 C * (x / (B * C)) = R(x * B',C,B). [para(2104(a,1),35393(a,1,2)),rewrite([16(4),293(9),113(12),34(14)])].

35482 C * R(C / x,x,B)' = R(x,C,B). [para(6450(a,1),35393(a,1,2)),rewrite([113(10),34(12)])].

35494 C' * R(C * x,C,B) = R(x,C,B). [back_rewrite(32272),rewrite([35418(14)])].

35506 R(x,C,B) * B = R(x * B,C,B). [para(35418(a,1),79(a,1)),rewrite([256(3),10(15),113(11),34647(12)]),flip(a)].

35531 (x * (B * C)) / R(x * B,C,B) = C. [back_rewrite(34938),rewrite([35506(9)])].

35541 C' * (x * (B * C)) = R(x * B,C,B). [back_rewrite(34647),rewrite([35506(12)])].

35572 R(x * B,C,B) * B' = R(x,C,B). [para(35506(a,1),6(a,1,1)),rewrite([293(7)])].

35582 B * ((x * C) / R(B * x,C,B)) = C. [para(35506(a,1),112(a,1,2,2)),rewrite([2041(8),34651(13),25345(14),34734(13),35572(12),34651(8)])].

35605 R(R(x,B,C) * B,C,B) = x * B. [para(23049(a,1),35506(a,1,1)),rewrite([16(7,R),34642(8)]),flip(a)].

35642 R(x * (B * C),C,B) = (x * C) * B. [para(242(a,1),35605(a,2)),rewrite([35211(7)])].

35647 R(x,B,C) * B = R(x * B,B,C). [para(35605(a,1),34635(a,1,1)),flip(a)].

35648 R((C * x) * B,B,C) = x * (B * C). [back_rewrite(35211),rewrite([35647(7)])].

35658 R(x,B,C)' * R(x * B,B,C) = B. [para(35647(a,1),10(a,1,2))].

35704 R(B * x',x,C)' * B = R(x,B,C). [para(6450(a,1),35647(a,1,1)),rewrite([749(2),293(10),82(13),259(12)])].

35718 B' * R(x,C,B) = R(B' * x,C,B). [para(34(a,1),34719(a,1,2,1))].

35724 R(x * (B * (B * C)),C,B) = C * (x * (B * B)). [para(659(a,1),34719(a,1,2,1)),rewrite([34689(13),10(11),66(11)]),flip(a)].

35726 R(B' * (C * x),C,B) = R(C * (B' * x),B,C). [para(34719(a,1),727(a,2,2,2)),rewrite([35393(14),35396(14),34415(12),35208(11),34855(7),35

139(8),35393(15),35718(16)]),flip(a)].

35776 B * (C * ((B' * C') * x)) = R(x,C,B). [para(34(a,1),34843(a,1,1)),rewrite([1828(9),293(9),1511(10)]),flip(a)].

35783 R(C * (B' * x),B,C) = (C * B') * x. [back_rewrite(30507),rewrite([35776(15),35726(8)])].

35784 x / (B' * C') = x * (B * C). [back_rewrite(14813),rewrite([35776(13),35393(7),35401(7)]),flip(a)].

35790 R(x,B' * C',B * C) = x. [para(35784(a,1),6(a,1)),rewrite([11248(10)])].

35791 R(x,B * C,B' * C') = x. [para(35784(a,1),7(a,1,1)),rewrite([11364(10)])].

35792 R(x,B',C') = R(x,B,C). [para(35784(a,1),18(a,1)),rewrite([1511(6,R),247(10),16598(9),34415(9),35208(8)]),flip(a)].

35803 C * (x * (B * C')) = R(x * B,B,C). [para(35784(a,1),79(a,2)),rewrite([256(3),35792(7),13836(12),32639(12)]),flip(a)].

35827 (x * (B' * C')) * (B * C) = x. [back_rewrite(11248),rewrite([35790(19)])].

35828 x / (B * C) = x * (B' * C'). [back_rewrite(29173),rewrite([35791(13)])].

35829 (x * (B * C)) * (B' * C') = x. [back_rewrite(11364),rewrite([35791(19)])].

35837 C' * ((C * x) * B) = R(x * B,B,C). [back_rewrite(32639),rewrite([35803(14)])].

35840 C * (x * (B' * C')) = R(x * B',C,B). [back_rewrite(35473),rewrite([35828(5)])].

35841 R(x * (B' * C'),C,B) = (C' * x) * B'. [back_rewrite(34696),rewrite([35828(4)])].

35842 R(x * (B' * C'),B,C) = C' * (x * B'). [back_rewrite(34643),rewrite([35828(4)])].

35846 R(x,B,C) * B' = R(x * B',B,C). [back_rewrite(27522),rewrite([35828(6),11560(8),34789(8)])].

35857 C * ((C' * x) * B') = R(x * B',B,C). [back_rewrite(34789),rewrite([35846(14)])].

35863 R(R(x,B' * C',C),B,C) = x. [para(35792(a,1),26935(a,1)),rewrite([1511(5)])].

35879 (x * (B' * C'))' = (B * C) / x. [para(35827(a,1),32(a,1,2)),flip(a)].

35956 R(x,B' * C',C) = R(x,C,B). [para(35863(a,1),22987(a,1,1)),rewrite([34641(5)]),flip(a)].

35958 R(x,C,B) * B' = R(x * B',C,B). [para(35956(a,1),78(a,1,1)),rewrite([16(10,R),1659(10),16(14,R),35840(14)])].

35959 B * (C' * (B' * x)) = R(C' * x,C,B). [para(79(a,1),35956(a,2)),rewrite([113(2),35956(10),16(11),35828(12),11954(14),1511(13,R)]),flip(

a)].

35970 C' * ((C * x) * B') = R(x * B',C,B). [back_rewrite(32258),rewrite([35958(14)])].

35972 R(B * (C' * x),C,B) = (B * C') * x. [back_rewrite(31134),rewrite([35959(9),34651(8)])].

35976 B * R(C / x,x,B)' = (B * C') * x. [back_rewrite(34773),rewrite([35972(8)]),flip(a)].

35977 R(B * (x * C'),C,B) = (B * C') * x. [back_rewrite(34762),rewrite([35972(8)]),flip(a)].

35978 C * (B * (x * (C' * C'))) = (B * C') * x. [back_rewrite(35014),rewrite([35977(18)])].

35983 R(R(x * B,B,C),B,C) = C * ((C' * x) * B). [para(247(a,1),34858(a,1,1)),rewrite([35837(7)])].

35986 (C * (B * x)) / R(x,B,C) = B * C. [para(35056(a,1),6(a,1,1))].

35987 (C * (B * x)) / R(C * x,B,C) = R(B,C,R(x,B,C)). [para(35056(a,1),18(a,1,1)),rewrite([35139(9)])].

35988 R(x,B,C) / (C * (B * x)) = B' * C'. [para(35056(a,1),32(a,1,2)),rewrite([1828(12),293(12),1511(13)])].

35990 (C * (B * x)) / R(B * x,B,C) = R(C,B,R(x,B,C)). [para(35056(a,1),97(a,1,1)),rewrite([34420(9)])].

36014 (B * C) * (x * (B' * C')) = B * (x * B'). [para(2104(a,1),35166(a,1,2)),rewrite([16(6),35828(7),293(14),113(17),34(19)])].

36015 (B * C) * R(C / x,x,B)' = B * x. [para(6450(a,1),35166(a,1,2)),rewrite([113(13),34(15)])].

36019 C * (B * ((B' * C') * x)) = R(x,B,C). [para(34(a,1),35186(a,1,1)),rewrite([1828(9),293(9),1511(10)]),flip(a)].

36025 R(B * (x * C'),B,C) = C' * (B * x). [back_rewrite(14792),rewrite([36019(14),34420(8)])].

36036 (C' * (B * x)) / R(C' * x,B,C) = B. [back_rewrite(34578),rewrite([36025(8)])].

36039 C' * R(x,B,C) = R(C' * x,B,C). [para(34(a,1),35208(a,1,2,1))].

36055 R(R(x,B,C),B,C) = R(x,C,B). [para(35139(a,1),35208(a,1,2,1)),rewrite([35402(10),35494(8)]),flip(a)].

36056 C * ((C' * x) * B) = R(x * B,C,B). [back_rewrite(35983),rewrite([36055(8)]),flip(a)].

36057 R(x,C,B * C') = R(x,C,B). [back_rewrite(25653),rewrite([36056(7),35958(8),85(5),260(4)]),flip(a)].

36059 (B' * (C / x)) * R(x * B,C,B) = C. [back_rewrite(14542),rewrite([36056(12)])].

36060 R(C * (x * B),B,C) = (x * C) * B. [para(36055(a,1),78(a,1,1)),rewrite([2041(7),35647(9),16(11,R),35139(11)]),flip(a)].

36062 R(R(x,C,B),C,B) = R(x,B,C). [para(36055(a,1),22987(a,1,1)),rewrite([34641(8)])].

36074 R(C' * (x * B'),B,C) = (C' * x) * B'. [para(2104(a,1),36062(a,1,1)),rewrite([16(3),35828(4),35841(9),293(8),113(11)]),flip(a)].

36146 R(C' * x,B,C)' = C / R(x,B,C). [para(34(a,1),35278(a,1,2,1)),flip(a)].

36151 R(x * C',B,C)' = C / R(x,B,C). [para(1659(a,1),35278(a,1,2,1)),flip(a)].

36152 R(x * C,B,C)' = C' / R(x,B,C). [para(1358(a,1),35278(a,1,2,1)),rewrite([35278(9),35282(12)])].

36228 R(C * (x * (B * B)),C,B) = (x * B) * (B * C). [para(6793(a,1),35401(a,1,1,2))].

36230 (x * (B * C)) * B = C * (x * (B * B)). [para(35401(a,1),35506(a,1,1)),rewrite([31535(12),35724(15)])].

36271 R(C / x,x,B) * R(x,C,B) = C. [para(6450(a,1),35420(a,1,1,1)),rewrite([30(6),113(7),34(9)])].

36275 R(C / x,x,B) = C / R(x,C,B). [para(36271(a,1),6(a,1,1)),flip(a)].

36286 R(C' * x,C,B)' = C / R(x,C,B). [para(36275(a,1),18(a,2)),rewrite([7(3),16(3),29558(6)])].

36298 C' * R(x,C,B) = R(C' * x,C,B). [para(36275(a,1),138(a,2,1)),rewrite([7(5),16(5),35828(6),11954(8),1511(7,R),35959(8),104(12),113(11)])

,flip(a)].

36417 ((x * C) * B) / R(x * B,B,C) = C. [para(2041(a,1),35531(a,1,1)),rewrite([35506(9),36062(12)])].

36468 (x * C) / R(B * x,C,B) = C * B'. [para(35582(a,1),10(a,1,2)),rewrite([16(4,R)]),flip(a)].

36478 R(B,C,(B' * C') * x) = R(B',C,C' * x)'. [para(35582(a,1),124(a,1,3,1,1)),rewrite([36468(9),5680(9),36468(16),36468(21),122(18),246(16)

,113(13),1511(14),14784(17)]),flip(a)].

36489 B * (R(C * x,B,C) / (B * x)) = C. [para(34420(a,1),35582(a,1,2,2,1)),rewrite([16(6,R),35139(6),34653(14)])].

36491 (C * ((B' * C') * x)) / x = R(B',C,C' * x). [back_rewrite(14812),rewrite([36478(18),30(18)])].

36529 (x * C) * (B * B) = (x * B) * (B * C). [para(35642(a,1),35506(a,1,1)),rewrite([6793(6),36230(12),36228(15)])].

36575 R(B * x',x,C) * R(x,B,C) = B. [para(6450(a,1),35658(a,1,1,1)),rewrite([749(2),30(7),293(7),82(10),259(9)])].

36738 R(x * B,B,C) / ((x * C) * B) = C'. [para(36060(a,1),35275(a,1,2))].

36895 R(C * x,B,C) / (B * x) = C * B'. [para(36489(a,1),10(a,1,2)),rewrite([16(4,R)]),flip(a)].

36901 R(B,C,R(x,B,C)) = R(B',C,B * x)'. [para(36489(a,1),80(a,1,1,1)),rewrite([35987(10),36895(15),5680(14)])].

36925 R(B * x,x',C) * R(x',B,C) = B. [para(30(a,1),36575(a,1,1,1,2))].

37480 C * (C * (C * (B * x))) = B * (C * (C * (C * x))). [para(35986(a,1),1420(a,1,1)),rewrite([35988(12),35986(18),35225(15),234(16),256(11

),1511(10),12146(15),16(11),33905(14),10(15),32259(11),35393(10),35166(11),35986(17),33905(15)]),flip(a)].

37565 (C' * x) * (B * C') = C' * (C' * (x * B)). [para(2007(a,1),1032(a,1,2,1,1,2,2)),rewrite([24793(10),4610(12),1511(6),4627(13),8(17),10(

23),2(20),34(21)])].

37576 C' * (C' * (B' * (C * x))) = (B' * C') * x. [para(2023(a,1),1292(a,2,2,2,2)),rewrite([16(10,R),1511(13,R),10(13),37565(16),16598(14),1

22(12),11560(21),1511(19),10(22)])].

37818 (C * x) * (B * B) = (x * B) * (B * C). [para(2071(a,1),6793(a,1)),rewrite([6793(6),36529(6)]),flip(a)].

38078 x / (y * (x * C)) = R(C * y,C',x)'. [para(63(a,1),2128(a,2,1)),rewrite([1699(3),6379(8)]),flip(a)].

38079 R(C' / x,x,y * C)' = (x * (y * C)) / y. [para(63(a,1),2128(a,2,2))].

38179 B * (x * (B * C'))' = C / R(x,C,B). [para(36057(a,1),2128(a,1,1)),rewrite([113(2),36286(7),1659(11),749(12)]),flip(a)].

38181 (x * C') / (y * x) = R(C * y,C',x)'. [back_rewrite(6204),rewrite([38078(9)])].

38182 R(C' / x,x,y * C) = R(C * x,C',y)'. [back_rewrite(2124),rewrite([38078(10)])].

38184 (x * (y * C)) / y = R(C * x,C',y). [back_rewrite(38079),rewrite([38182(6),30(7)]),flip(a)].

38193 R(C' * x,C,C' * y) = (x * (C' * y)) / y. [para(34(a,1),2130(a,1,2)),flip(a)].

38295 R(B * (C / x),(C' * x) * B',y) = B * (C / x). [para(2321(a,1),18(a,1,1,1)),rewrite([2(2),32(8),784(7),158(5)]),flip(a)].

38296 C / R(x * B',B,C) = B * (C / x). [para(2321(a,1),100(a,1,1,2)),rewrite([3(3),16(9,R),35857(9),38295(20)])].

38626 R(C' * (x * B),C,B) = (C' * x) * B. [para(2918(a,1),129(a,2,2)),rewrite([16(19,R),36056(19),36059(18),16(9,R),36056(9),36298(8),3(15)]

)].

39165 R(x,C * B',B * C') = x. [para(1527(a,1),827(a,1,1)),rewrite([16(4,R),765(10),1511(21,R),10(21),13(18),8(16),3(14),34(14)])].

39194 x / (C * B') = x * (B * C'). [para(39165(a,1),79(a,1)),rewrite([11955(19),1511(18,R),63(18),8(14),23(12)])].

39196 R(x,B * C',C * B') = x. [para(39194(a,1),7(a,1,1)),rewrite([2292(10)])].

39197 R(x,C,B') = R(x,B,C). [para(39194(a,1),18(a,1)),rewrite([11955(10),1511(9,R),34704(9),34855(8),10(5)]),flip(a)].

39198 (x * (B * C'))' = (C * B') / x. [para(39194(a,1),104(a,1,1))].

39206 C * (B' * ((B * C') * x)) = R(x,B',C). [para(39194(a,1),101(a,1)),rewrite([11560(10),16598(9)])].

39226 R(C' * (x * B),B,C) = x * (B * C'). [para(39194(a,1),2104(a,2)),rewrite([256(3),113(4),39197(9)])].

39247 R(C' * x,B,C) = R(C / x,x,B')'. [para(39194(a,1),2128(a,2)),rewrite([11955(14),1511(13,R),34790(14)]),flip(a)].

39248 B * ((C * B') / x) = C / R(x,C,B). [back_rewrite(38179),rewrite([39198(7)])].

39252 R(x,B,C) * (C * B') = (x * C) * B'. [para(39197(a,1),78(a,1,1))].

39253 R(C / x,x,B') = C / R(x,B,C). [para(39197(a,1),6450(a,2,1)),rewrite([113(7),36146(12)])].

39255 x / (B * C') = x * (C * B'). [para(39196(a,1),79(a,1)),rewrite([249(19),293(16),1511(17),1659(18),9(14),23(12)])].

39260 R(x,C,B) = R(x,B,C'). [para(39255(a,1),18(a,1)),rewrite([1511(5,R),234(10),1699(7),35970(10),85(5),260(4)])].

39261 (x * (C * B'))' = (B * C') / x. [para(39255(a,1),104(a,1,1))].

39307 B * ((C * B') / x) = C / R(x,B,C'). [back_rewrite(39248),rewrite([39260(11)])].

39337 R(C' * (x * B),B,C') = (C' * x) * B. [back_rewrite(38626),rewrite([39260(8)])].

39492 C' * R(x,B,C') = R(C' * x,B,C'). [back_rewrite(36298),rewrite([39260(5),39260(13)])].

39497 R(C' * x,B,C')' = C / R(x,B,C'). [back_rewrite(36286),rewrite([39260(6),39260(12)])].

39500 R(C / x,x,B) = C / R(x,B,C'). [back_rewrite(36275),rewrite([39260(8)])].

39501 R(C / x,x,B) * R(x,B,C') = C. [back_rewrite(36271),rewrite([39260(7)])].

39535 R(R(x,B,C'),B,C') = R(x,B,C). [back_rewrite(36062),rewrite([39260(3),39260(7)])].

39539 C * ((C' * x) * B) = R(x * B,B,C'). [back_rewrite(36056),rewrite([39260(12)])].

39540 R(R(x,B,C),B,C) = R(x,B,C'). [back_rewrite(36055),rewrite([39260(9)])].

39548 R(B * (x * C'),B,C') = (B * C') * x. [back_rewrite(35977),rewrite([39260(8)])].

39550 R(B * (C' * x),B,C') = (B * C') * x. [back_rewrite(35972),rewrite([39260(8)])].

39562 R(x,B,C') * B' = R(x * B',B,C'). [back_rewrite(35958),rewrite([39260(3),39260(13)])].

39570 C * (x * (B' * C')) = R(x * B',B,C'). [back_rewrite(35840),rewrite([39260(14)])].

39587 B' * R(x,B,C') = R(B' * x,B,C'). [back_rewrite(35718),rewrite([39260(5),39260(13)])].

39631 C' * (x * (B * C)) = R(x * B,B,C'). [back_rewrite(35541),rewrite([39260(12)])].

39651 R(x,B,C') * B = R(x * B,B,C'). [back_rewrite(35506),rewrite([39260(3),39260(11)])].

39659 C * R(C / x,x,B)' = R(x,B,C'). [back_rewrite(35482),rewrite([39260(10)])].

39662 R(x,R(C * y,B,C'),C) = R(x,C * C,R(y,B,C')). [back_rewrite(35451),rewrite([39260(5),39260(14)])].

39686 B * ((C * B') * x) = R(C * x,B,C'). [back_rewrite(35403),rewrite([39260(12)])].

39687 R(C * (x * B),B,C') = x * (B * C). [back_rewrite(35401),rewrite([39260(7)])].

39691 R(C * (B * x),B,C') = (B * C) * x. [back_rewrite(35396),rewrite([39260(7)])].

39692 C * R(x,B,C') = R(C * x,B,C'). [back_rewrite(35393),rewrite([39260(4),39260(11)])].

39698 (B * C) * R(x,B,C') = B * (C * x). [back_rewrite(35166),rewrite([39260(6)])].

39708 R(C,R(B * x,B,C'),y) = R(C',(B * C) * x,y)'. [back_rewrite(34996),rewrite([39260(6)])].

39739 (x * R(x * B',B,C)) * B = R(x * x,B,C'). [back_rewrite(34711),rewrite([39260(13)])].

39741 R(R(B * x',x,C)',B,C') = x * B'. [back_rewrite(34697),rewrite([39260(9)])].

39743 C' * ((B * C) * x) = R(B * x,B,C'). [back_rewrite(34692),rewrite([39260(12)])].

39748 C * (B * (C' * x)) = R(B * x,B,C'). [back_rewrite(34683),rewrite([39260(12)])].

39750 R(B * (C * x),B,C') = C * (B * x). [back_rewrite(34680),rewrite([39260(7)])].

39752 R(B * (x * (B * C')),B,C') = B * (C' * (x * B)). [back_rewrite(34678),rewrite([39260(10)])].

39761 R(R(x,B,C),B,C') = x. [back_rewrite(34653),rewrite([39260(6)])].

39762 B * R(x,B,C') = R(B * x,B,C'). [back_rewrite(34651),rewrite([39260(4),39260(11)])].

39763 R(x,B * C,C') = R(x,B,C'). [back_rewrite(34650),rewrite([39260(9)])].

39765 R(x,B * C,B) = R(x,B,C'). [back_rewrite(34641),rewrite([39260(8)])].

39766 R(R(x,B,C'),B,C) = x. [back_rewrite(34635),rewrite([39260(3)])].

39783 B' * (C * (B * x)) = R(C * x,B,C'). [back_rewrite(32259),rewrite([39260(12)])].

39784 R(x,C',C * B') = R(x,B,C'). [back_rewrite(32253),rewrite([39260(10)])].

39791 R(x,B,C') * (B * C) = (x * C) * B. [para(39260(a,1),78(a,1,1)),rewrite([16(7)])].

39797 R(x,B * C',B) = R(x,B,C). [para(39761(a,1),22987(a,1,1))].

39948 R(C / x,x,B') * R(x,B,C) = C. [para(39253(a,2),7(a,1,1))].

39958 R(C / (x * B'),x * B',B') = B * (C / x). [para(79(a,1),39253(a,2,2)),rewrite([293(3),293(7),35828(18),25535(20),35857(20),38296(19)])]

.

39985 C / R(B * x',x,C)' = B * (C / x). [para(6450(a,1),39253(a,2,2)),rewrite([293(3),293(7),39958(11),749(7)]),flip(a)].

40041 R(R(C / x,x,B),R(x,B,C'),B') = C / x. [para(39500(a,2),39253(a,1,1)),rewrite([39766(19)])].

40046 R(x,B,C) * (B * C') = (C' * x) * B. [para(39535(a,1),78(a,1,1)),rewrite([39651(14),1511(17,R),39492(17),39337(17)])].

40047 R(x,C',B)' = R(x,B,C)'. [para(39535(a,1),138(a,2,1)),rewrite([39651(10),1511(13,R),39492(13),39337(13),38181(10),34(5)])].

40055 R(x,C',B) = R(x,B,C). [para(40047(a,1),30(a,1,1)),rewrite([30(5)]),flip(a)].

40093 R(C' / x,x,B) = C' / R(x,B,C). [para(40047(a,1),6450(a,2)),rewrite([1699(8),35282(11)])].

40108 R(C * x,B,C) = R(C' / x,x,B)'. [para(40055(a,1),6450(a,1)),rewrite([1699(3)])].

40146 C * R(C / x,x,B')' = R(x,B,C). [para(39948(a,1),10(a,1,2)),rewrite([16(8,R)])].

40565 R(x,B * C,C)' = R(x',B,C). [para(9956(a,1),4035(a,1,1)),rewrite([15067(12),1724(10),4463(10),34236(15),34(10),35139(9),1659(6)]),flip(

a)].

40584 R(x,B * C,C) = R(x',B,C)'. [para(40565(a,1),30(a,1,1)),flip(a)].

40585 C * (B * (C * (C' / x))) = R((B * C) / x,B,C). [para(79(a,1),40565(a,1,1)),rewrite([16(7,R),1382(7),104(9),15067(8),1828(6),35828(13),

35879(16)])].

41068 R(x,C,B * C) = R(x,B,C * C). [para(4638(a,1),2119(a,1,1)),rewrite([16(11,R),1382(11),4131(12),10(10)]),flip(a)].

41078 B' * ((B * C') * x) = R(C' * x,B,C'). [para(34(a,1),1626(a,1,2,2)),rewrite([1538(20),256(18),16(17),39743(19),39587(19),10(15),39492(1

5)])].

41080 C' * (B' * (C * x)) = R(B' * x,B,C'). [para(3983(a,1),1626(a,1,2,2)),rewrite([12146(16),16741(17),39686(15),39492(15),10(11),39492(11)

,63(7),39587(7),10(18)]),flip(a)].

41082 R(x,B',C) = R(x,B,C'). [back_rewrite(39206),rewrite([41078(9),39692(9),34(5)]),flip(a)].

41083 R(C' * (B' * x),B,C') = (B' * C') * x. [back_rewrite(37576),rewrite([41080(10),39492(10)])].

41347 R(B * (C / x),B,C) = (B * C) / x. [para(749(a,1),5303(a,1,2,2)),rewrite([1828(6),34839(9),16(10)])].

41403 R(x,B,C)' = R(x',B,C). [para(138(a,1),41347(a,2)),rewrite([16(6,R),109(7),824(4),34(6)]),flip(a)].

41424 R((B * C) / x,B,C) = R(B * (C / x),B,C'). [para(41347(a,1),39540(a,1,1))].

41449 R(x,B * C,C) = R(x,B,C). [back_rewrite(40584),rewrite([41403(10),30(7)])].

41508 C' / R(x,B,C) = R(C' / x,B,C). [back_rewrite(36152),rewrite([41403(6),1828(3)]),flip(a)].

41509 C / R(x,B,C) = R(C / x,B,C). [back_rewrite(36151),rewrite([41403(7),1538(4)]),flip(a)].

41537 C * (B * (C * (C' / x))) = R(B * (C / x),B,C'). [back_rewrite(40585),rewrite([41424(16)])].

41540 R(C' / x,B,C) = R(C' / x,x,B). [back_rewrite(40093),rewrite([41508(11)]),flip(a)].

41564 ((B * C) * x)' * B = R(C' / x,B,C). [back_rewrite(35353),rewrite([41508(13)])].

41586 R(C / (x * B'),B,C) = B * (C / x). [back_rewrite(38296),rewrite([41509(8)])].

41601 R(x',B,C) * R(x,B,C) = 0. [para(41403(a,1),8(a,1,1))].

41653 R(B * (C / x),B,C') = C / (x * B'). [para(35879(a,1),41403(a,2,1)),rewrite([35842(9),158(7),41424(12)]),flip(a)].

41658 R(x,B,C')' = R(x',B,C'). [para(39540(a,1),41403(a,1,1)),rewrite([41403(9),39540(12)])].

41661 C * (B * (C * (C' / x))) = C / (x * B'). [back_rewrite(41537),rewrite([41653(17)])].

41701 C / R(x,B,C') = R(C / x,B,C'). [back_rewrite(39497),rewrite([41658(8),158(4)]),flip(a)].

41766 B * ((C * B') / x) = R(C / x,B,C'). [back_rewrite(39307),rewrite([41701(13)])].

41793 x / (B * (C * C)) = C' * ((C' * x) * B'). [para(41449(a,1),2104(a,1)),rewrite([113(2),35828(7),35842(12),16(14,R),1382(14)]),flip(a)].

41878 (C * (x * B)) * B' = R(C * x,B,C'). [para(4638(a,1),1672(a,1,1,2)),rewrite([10(9),1511(10,R),63(10),293(6),39763(15)])].

41992 R(x',B,C') * (R(x,B,C') * y) = y. [para(41658(a,1),10(a,1,1))].

42015 R(B * (C' / x),B,C') = (B * C') / x. [para(2104(a,1),41658(a,1,1)),rewrite([39255(5),39261(6),1699(8),293(9),784(11),1724(9)]),flip(a)

].

42363 C' * (x * ((B * C) * x)) = x * R(B * x,B,C). [para(1012(a,1),1690(a,1,2,2)),rewrite([25535(23),1511(21),33788(23),1012(23)])].

42812 C' * (B * ((C * x) * B)) = R(B * (x * B),B,C'). [para(31492(a,1),1711(a,1,2,2,2,2)),rewrite([39743(13),39752(12),39748(9),1511(19,R),6

3(19),15(16)]),flip(a)].

42814 R(B * (x * B),B,C') / (x * B) = R(B,x,B * C). [back_rewrite(30644),rewrite([42812(9)])].

43633 R(x,C',y * C) = R(x,C',y). [para(6379(a,1),30(a,1,1)),rewrite([30(5)]),flip(a)].

43653 R(x,C',C * y') = R(x,C',y'). [back_rewrite(2546),rewrite([43633(6)]),flip(a)].

43654 R(x,C',B') = R(x,B,C'). [back_rewrite(39784),rewrite([43653(7)])].

43661 R(x,C',C' * y) = R(x,C',y). [para(7(a,1),43633(a,1,3)),rewrite([113(7)]),flip(a)].

43663 R(x,C',C * y) = R(x,C',y). [para(16(a,2),43633(a,1,3))].

43665 R(x,C',y * (C * C)) = R(x,C',y). [para(70(a,1),43633(a,1,3)),rewrite([43663(9),43663(14),43663(12)])].

43671 R(C * (x / (y * C)),C',y) = x / y. [para(43633(a,1),2104(a,1)),rewrite([1699(6),63(13)])].

43685 R(B,C',x * (B * C)) = R(B,x,B * C). [back_rewrite(8843),rewrite([43663(10)])].

43688 (C' * ((C * x) * y)) / y = R(x,C',y). [back_rewrite(2586),rewrite([43663(12)])].

43690 (x * (y * (C * C))) / (y * C) = R(C * x,C',y). [back_rewrite(8831),rewrite([43665(17)])].

43706 (x * (C * y)) / y = R(C * x,C',y). [para(43663(a,1),79(a,1)),rewrite([1699(3),10(13)]),flip(a)].

43793 C' * ((x * C) * B) = R(x * B,B,C). [para(36417(a,1),6610(a,1,1)),rewrite([36417(16),113(8),36039(9),39226(9),35803(7),36738(19),1511(1

2,R)]),flip(a)].

43802 R(B,C',(x * C) * B) = B * (x / R(x,B,C)). [back_rewrite(25411),rewrite([43793(8),35846(9),85(6),260(5)]),flip(a)].

44206 (B * (B * C)) / x = B * (C / (x * B')). [para(6741(a,1),9205(a,1,2,2)),rewrite([1724(7),16641(10),35142(11),16(8,R),41661(10),66(12)])

,flip(a)].

44414 R(B * C,C',B * x) = R(B * C,B,x). [para(9295(a,1),468(a,1)),rewrite([16(5,R),43706(9),16(3)])].

44469 C * ((B' * C') * x) = R(B' * x,B,C'). [para(9418(a,1),100(a,1,1,2)),rewrite([16(12,R),39194(13),11560(13),4610(12),1511(6),82(11),259(

10),41082(15)])].

44480 R(C * (B' * x),B,C') = B' * (x * C). [para(9418(a,1),1518(a,1,2,1,2,2)),rewrite([4610(14),13(13),8(11),3(9),39686(10),16(19,R),231(23)

,256(23),16598(22),34(19),34(19)])].

44481 C' * ((C * B') * x) = R(B' * x,B,C). [para(9418(a,1),1672(a,1,1,2)),rewrite([35784(15),247(13),4610(12),82(11),259(10),35792(16)])].

44485 R(B' * x,B,C') / x = R(B',C,C' * x). [back_rewrite(36491),rewrite([44469(8)])].

45738 (B * (x * y)) / y = B * R(x,y,B'). [para(16618(a,1),6(a,1,1))].

45777 R(x,C * C,R(B * y,B,C)) = R(x,B * (y * C),C). [para(16618(a,1),18592(a,2,2)),rewrite([39197(8),34420(8)])].

45820 (B * (C / x)) * R(x,B,C') = B * C. [para(39501(a,1),16618(a,2,2)),rewrite([40041(12)])].

45835 R(x,C',R(B * y,B,C)) = R(x,C',B * (y * C)). [para(16618(a,1),43633(a,1,3)),rewrite([39197(14),34420(14)]),flip(a)].

45843 R(B * x,B,B' * y) = B * R(x,y,B'). [back_rewrite(4833),rewrite([45738(11)])].

45845 B * R(x,B * y,B') = R(B * x,B,y). [back_rewrite(468),rewrite([45738(8)])].

45883 R(x,B',B * (y * B)) = R(x,y,B). [para(7(a,1),16667(a,1,2)),rewrite([256(8)]),flip(a)].

45891 R(x / (y * B'),B',B * y) = (x * B) / y. [para(16667(a,1),79(a,1)),rewrite([82(16),259(15)])].

45892 R(C * x,B,C) / x = R(C,B',B * x). [para(16667(a,1),97(a,2)),rewrite([16(5,R),16598(7),34415(7),82(10),259(9)])].

45903 R((x * B') / y,y,B) = x / (y * B). [para(16667(a,1),6450(a,2,1)),rewrite([45891(15),104(10)])].

45910 R(x,B' * y,B) = R(x,B',y * B). [para(6658(a,1),16667(a,1,2)),rewrite([30(6),260(7),256(13),34(14)])].

45912 B * ((B' * (x * y)) / y) = R(x,y,B). [back_rewrite(30642),rewrite([45883(14)])].

45993 B * R(C * B',C',x) = R(C,x,B). [para(45883(a,1),97(a,2)),rewrite([16(4,R),11955(9),15(8),10(9),10(11),25369(7),43706(7)])].

46045 (x * ((B * y) * x)) / (y * x) = x * B. [para(16760(a,1),6(a,1,1))].

46681 R(x,y * B,B') * y = (x * (y * B)) * B'. [para(256(a,1),2035(a,1,1,2)),rewrite([256(9)])].

46726 C' * (x * (B * (C * C))) = (x * C) * B. [para(22791(a,1),10(a,1,2))].

46729 C * ((C * x) * B) = x * (B * (C * C)). [para(16(a,2),22791(a,1,2,1))].

46732 x * (C * ((x' * C) * B)) = B * (C * C). [para(22791(a,2),34(a,1,2))].

46773 C * (x * (x * B)) = x * ((x * C) * B). [para(22791(a,2),1663(a,1)),rewrite([16(7,R),1698(7),12(4),46726(14)])].

46836 R(R(x,y,B'),B',B * y) = x. [para(16667(a,1),2043(a,2)),rewrite([82(6),259(5),82(6),259(5),6(2)]),flip(a)].

46896 R(R(x,y * B,B'),y,B) = x. [para(46836(a,1),45883(a,1)),flip(a)].

46898 R(B,R(x,B,C),B * C) = R(B,x * B,C). [para(73(a,1),2044(a,1,1)),rewrite([16(6,R),35139(6),35647(8),35648(8),16(10,R),3189(11)]),flip(a)

].

47215 R(x,B,C * C) = R(x,B,C'). [para(24137(a,1),18(a,1,1)),rewrite([1382(11),41793(12),10(11),41878(9),39492(9),10(5),41068(9)]),flip(a)].

47631 R(R(x,B * y,B),B,y) = x. [para(6(a,1),26848(a,2)),rewrite([25429(7)])].

47659 R(R(x,y,B),B,B' * y) = x. [para(34(a,1),47631(a,1,1,2))].

47700 B * ((B' * R(x,y,B)) * y) = x * y. [para(47631(a,1),2045(a,1,1)),rewrite([34(6),11954(9)]),flip(a)].

47701 R(x,B * (y * B),B') = R(x,B,y). [para(46896(a,1),47631(a,1,1)),rewrite([49(6)]),flip(a)].

47780 B * R(x / y,y,B') = (B * x) / y. [para(2149(a,1),47659(a,1,1)),rewrite([45843(8)])].

47797 R(R(x,B',B * y),B,B' * (y * B')) = x. [para(16667(a,1),47659(a,1,1))].

47800 R(x,y * B,B') = R(x,B,B' * y). [para(46896(a,1),47659(a,1,1)),flip(a)].

47803 (x * (y * B)) * B' = B * ((B' * x) * y). [back_rewrite(46681),rewrite([47800(5),2045(6),11954(6)]),flip(a)].

47811 (x * (y * (C * C))) / (C * y) = R(C * x,C',y). [para(4530(a,1),2105(a,1,1,2)),rewrite([1699(3),4530(9),43665(9)]),flip(a)].

47886 x / (C' * (y * x)) = R(y * C',C',x)'. [para(9194(a,1),2110(a,1,1)),rewrite([29968(11),43663(8),24793(16),10(14)]),flip(a)].

47920 R(B * x,x',x * y) = B * R(x,y,B'). [para(749(a,1),2111(a,1,1)),rewrite([30(3),45738(9)])].

47936 R(B * R(x,y,B'),y,B) = B * x. [para(2111(a,2),2149(a,1,1)),rewrite([749(3),30(3),47920(5),6(10)])].

47951 (x * (C * (C * y))) / (y * C) = R(C * x,C',y). [para(3983(a,2),2111(a,2,1)),rewrite([1699(3),43663(9),43633(7)]),flip(a)].

48002 R(x,B * y,B') = R(x,B,y * B'). [para(7(a,1),47701(a,1,2,2)),rewrite([293(8)])].

48004 (x * (B * (B * x))) / (B * x) = R(x * B,B,x). [para(47701(a,1),92(a,2)),rewrite([85(8),260(7),16760(5),12(4),232(12),293(10),85(11),26

0(10)])].

48025 B * R(x,B,y * B') = R(B * x,B,y). [back_rewrite(45845),rewrite([48002(6)])].

48331 R(x / y,y,B) / ((B' * x) / y) = B. [para(26923(a,2),6(a,1,1))].

48341 R(x / y,y,B) * B = x / (B' * y). [para(26923(a,2),49(a,1,1)),rewrite([9233(13)])].

48343 R(C',x,B)' = R(C,x,B). [para(1674(a,1),26923(a,1,1)),rewrite([6042(6),2197(13),45993(14)])].

48346 B * R(B' * x',x,y) = R(x,y,B)'. [para(79(a,2),26923(a,2,2)),rewrite([32(2),142(4),794(7)]),flip(a)].

48348 R(x / y,y,B) * (y / (B' * x)) = B. [para(26923(a,2),85(a,1,1)),rewrite([104(8),104(18),301(18)])].

48353 R(C,x * C,B) = R(C,x,B). [para(4118(a,1),26923(a,1,1)),rewrite([43690(16),45993(14)])].

48355 R(C,C * x,B) = R(C,x,B). [para(4524(a,1),26923(a,1,1)),rewrite([47811(16),45993(14)])].

48409 R(C,x,B)' = R(C',x,B). [para(48343(a,1),30(a,1,1))].

48509 R(R(C,x,B),B,B' * (x * C)) = C. [para(48353(a,1),47659(a,1,1))].

48518 R(C,R(C * x,B,C),B) = R(C,R(x,B,C),B). [para(35139(a,1),48355(a,1,2))].

48527 R(C',C' * x,B) = R(C',x,B). [para(141(a,1),48409(a,1,1)),rewrite([48343(5),48409(4)]),flip(a)].

48595 R(R(C,x,B),B,B' * (C' * x)) = C. [para(1665(a,1),48509(a,1,3,2)),rewrite([141(9),48527(7),48343(5),16(12,R),9(12),3(10)])].

48717 R(B * C,B',x)' = R(B' * C',C,x). [para(256(a,1),27450(a,2,1,1)),rewrite([1511(5),16(10)]),flip(a)].

49082 R(B * C,B * x,C) = R(B * C,B,x). [para(31303(a,1),2120(a,1,1)),rewrite([16641(15),33904(14),16(19,R),43706(20),16(10),43663(17),44414(

15)])].

49254 R(R(x,C',y),y,C) = R(x,C,y). [para(2182(a,2),26997(a,2)),rewrite([1511(6,R),43688(7),113(9),63(10)])].

49255 C * (R(x,C',y) * y) = (x * C) * y. [para(49254(a,1),78(a,1,1)),rewrite([2041(5),16(9,R)]),flip(a)].

49266 R(R(x,C,y),y * C,C') = R(x,C',y). [para(49254(a,1),27046(a,1,1))].

49487 (x * y) / (y * y) = R(x / y,y,y). [para(63(a,1),2195(a,1,1,2)),rewrite([128(7),63(9)])].

49492 R(C * R(x,C,y),C',y) = x * C. [para(2041(a,1),2197(a,1,1)),rewrite([1511(8,R),63(8),6(4),43633(11)]),flip(a)].

49513 (x * x) / (y * x) = R(y / x,x,x)'. [para(49487(a,1),104(a,1,1)),flip(a)].

49540 (C' * (x * y)) / y = R(C' * x,C',y). [para(2119(a,1),2198(a,1,1)),rewrite([49266(10),1511(15,R),63(15)]),flip(a)].

49556 R(x,C,y) * y = C * ((C' * x) * y). [para(49492(a,1),78(a,1,1)),rewrite([12145(6),1511(13,R),10(13)]),flip(a)].

49576 R(C * R(x,C,y),C,y) = R(x * C,y,C). [para(49492(a,1),49254(a,1,1)),flip(a)].

49829 R(B,C,x * C) = R(B,x,C * C). [para(33904(a,1),18(a,1,1)),rewrite([4132(11)]),flip(a)].

49846 R(B * x,B,C) / x = R(B,C,x * C'). [para(49829(a,2),80(a,2)),rewrite([4419(5),1382(12,R),16(11,R),39748(11),39548(10),33788(7),4419(12)

,16(16,R),34(16)])].

49939 (C * B') * (x * C) = C * (C * (B' * x)). [para(424(a,2),34236(a,1,2)),rewrite([13683(12),35783(17)]),flip(a)].

50112 C * (B' * (C' * x)) = R(B' * x,B,C). [para(35205(a,1),532(a,2,2,2)),rewrite([1511(14),35829(15),36039(18),10(15),34855(14)])].

50126 (C * B') * R(x,B,C) = B' * (x * C). [para(35210(a,1),532(a,2,2,2)),rewrite([10(16),85(12),260(11),246(9),113(6),1511(7),44469(9),39692

(9),44480(9),36039(17),10(14)]),flip(a)].

50130 (x * B) * R(x,B,C) = x * R(B * x,B,C). [para(35210(a,1),1663(a,2,2,2)),rewrite([1511(7,R),10514(8),6554(7),234(13),1699(10),7191(12),8

5(10),260(9),16760(7),42363(8),36039(16),10(13)]),flip(a)].

50131 B' * (C * (C * x)) = C * ((C * B') * x). [para(35210(a,1),1701(a,2,2)),rewrite([1511(14,R),10(14),85(10),260(9),50126(17),16(13,R)]),f

lip(a)].

50143 R(B * C,C',x) = R(B * C,x,C). [para(35225(a,1),100(a,1,1)),rewrite([47951(9),16(3)])].

50149 (x * C) / (B * (C * (C * x))) = R(B * C,x,C)'. [para(35225(a,1),4035(a,1,2))].

50160 R(B * C,x,C)' = R(B' * C',B,x). [para(50143(a,1),138(a,2,1)),rewrite([1511(9,R),63(9),2144(6),1511(5)]),flip(a)].

50161 R(B * C,C',x)' = R(B' * C',B,x). [para(50143(a,2),138(a,2,1)),rewrite([16(8,R),35225(8),50149(9),50160(6)]),flip(a)].

50183 R(B,x * (C * C),C') = R(B,C,x). [para(1382(a,1),35264(a,1,2)),rewrite([63(15)])].

50221 (C * ((x * C') * y)) / y = R(x,C,C' * y). [para(49254(a,1),2234(a,2)),rewrite([43661(7),78(8)])].

50314 R(B',x',C * (x * B))' = R(B,x',x * C). [para(15(a,1),2236(a,1,2)),rewrite([9200(8),293(8),16598(12),11964(11),16(10,R),34(13),14578(9)

,9366(17)])].

50321 C' * (x' * (C * (x * B))) = R(B,x',x * C). [back_rewrite(14578),rewrite([50314(18)])].

50360 R(C,B,R(C / x,x,B)') = R(C',B,x)'. [para(36015(a,1),97(a,1,1)),rewrite([35976(9),6114(8)]),flip(a)].

50385 (x * B') * ((B * y) * x) = x * (y * x). [para(2239(a,1),57(a,2,2,2)),rewrite([16598(8),232(7),293(5),10(8),32154(14),16520(10),2276(7)

,259(6),16598(10),232(9),293(7),10(10),16667(14),9(13),77(11)]),flip(a)].

50386 R(x,B' * x,x') = x. [para(232(a,1),2239(a,1,1)),rewrite([30(4),6(4),82(5),259(4),30(4)]),flip(a)].

50394 R(B * x,x,x' * B') = B * x. [para(10(a,1),50386(a,1,2)),rewrite([889(5)])].

50402 (x * (B * y)) * B' = (x * B) * (y * B'). [para(50394(a,1),2092(a,1,1,2)),rewrite([34(7),48002(5),9956(8),12157(13),12281(13),78(11),50

394(13),34(14)]),flip(a)].

50834 R(x,y * (z * B'),B) = R(x,B',(B * y) * z). [para(2275(a,1),16667(a,2,3)),rewrite([11955(6),9418(9),25391(8),10(9),259(13)])].

50838 (B * x) / R(C * x,B,C) = B * C'. [para(36895(a,1),104(a,1,1)),rewrite([784(5)]),flip(a)].

50850 R(B * x,x',C) = R(B * x,B,C). [para(36925(a,1),6(a,1,1)),rewrite([749(6),41403(6),30(3),34420(5)]),flip(a)].

50869 R(x,B,C) / R(B * x,x',C) = B'. [para(50850(a,2),34500(a,1,2))].

50894 B' * R(B * x,x',C) = R(x,B,C). [para(50850(a,2),34855(a,1,2)),rewrite([10(13)])].

50923 (C * (x * y)) / y = C * (C * R(x * C',C,y)). [para(2279(a,1),9205(a,1,2,2)),rewrite([2277(14)]),flip(a)].

51083 R(B,C,x * (C' * C')) = R(B,x,C'). [para(2285(a,1),50183(a,1,2)),rewrite([24807(10),2301(5)]),flip(a)].

51238 R(C * x,B * B,C) = R(C * x,B,C'). [para(37818(a,1),100(a,1,1,2)),rewrite([16(13,R),66(13),32245(14),10315(13),16(7,R),260(12),10(9),47

803(7),16(5,R),39686(7)]),flip(a)].

51251 B * (C' / (x * B)) = R(C' / x,B,C'). [para(37818(a,1),4032(a,1,2,2)),rewrite([66(5),44206(14),10315(13),16(7,R),260(12),109(9),1724(6)

,51238(14),41658(14),1724(10)])].

51388 R(R(B * C,C',x),x,B) = B * C. [para(38184(a,1),2149(a,1,1)),rewrite([16(3),60(12)])].

51401 B * R(C,x,B') = R(B * C,C',x). [para(51388(a,1),47659(a,1,1)),rewrite([45843(8)])].

51402 R(R(B * C,x,C),x,B) = B * C. [para(50143(a,1),51388(a,1,1))].

51533 (B' * C') * ((B * C) / x) = C * (C' / x). [para(6173(a,1),39687(a,2)),rewrite([41564(8),35139(8),39761(12),1828(9),293(9),1511(10)]),f

lip(a)].

51540 R(C,R(C * x,B,C'),B) = R(C,R(x,B,C'),B). [para(39692(a,1),48355(a,1,2))].

51576 R(C,R(x,B,C'),B * C) = R(C,x,B). [para(39791(a,1),97(a,1,2)),rewrite([16(6,R),39692(6),39791(10),16(4,R),70(6),16(4),3185(11),48353(5)

]),flip(a)].

51669 R(R(B',C,B * x)',C * C,R(x,B,C)) = B. [para(40146(a,1),35227(a,1,1,3)),rewrite([36901(6),16(18,R),40146(18)])].

51839 (B * C) / (x * B') = B * (B * (C / x)). [para(41586(a,1),34420(a,1,2)),rewrite([41347(16)]),flip(a)].

52422 R(B,x * B,C) = R(B,C',x * B). [para(2042(a,1),2569(a,1,3,2)),rewrite([43663(10),43663(8),16(13),46898(14)]),flip(a)].

52430 R(B,C * x,B * C) = R(B,C',x * B). [para(1411(a,1),2569(a,1,3)),rewrite([24137(10),43663(12),43663(10),43663(8),16(12)]),flip(a)].

52450 R(B,C',x) = R(B,x,C). [para(7(a,1),52422(a,1,2)),rewrite([293(8),82(11),259(10)]),flip(a)].

52456 R(B,B * x,C) = R(B,C',B * x). [para(6658(a,1),52422(a,1,2)),rewrite([259(7),293(11),16598(15),12(14),10(15)])].

52457 R(B,R(x,B,C),C) = R(B,C',R(x,B,C)). [para(35704(a,1),52422(a,1,2)),rewrite([35704(17)])].

52465 R(B,C',x) * (x * C) = C * (B * x). [para(52450(a,2),78(a,1,1)),rewrite([16(11,R)])].

52466 R(B * x,B,C') / x = R(B,C',x). [para(52450(a,2),80(a,2)),rewrite([113(3),16(7,R),39748(7),113(12),43661(14)])].

52468 R(B,C',x)' = R(B,x,C)'. [para(52450(a,1),138(a,2,1)),rewrite([138(9)])].

52469 R(B,C',B' * x) = R(B',x,C)'. [para(52450(a,2),141(a,1))].

52471 R(B,C * C,x) = R(B,C',x). [para(52450(a,2),4130(a,2)),rewrite([43663(11)])].

52479 R(B,C' * x,C) = R(B,C',x). [para(52450(a,1),43661(a,1))].

52483 R(R(B,x,C),x,C) = R(B,C,x). [para(52450(a,1),49254(a,1,1))].

52485 R(B,C',x * B) = R(B,x,B * C). [back_rewrite(42814),rewrite([52466(11)])].

52515 R(B,x,C)' * R(B,C',x) = 0. [para(52468(a,1),8(a,1,1))].

52516 R(B,C',x)' * R(B,x,C) = 0. [para(52468(a,2),8(a,1,1))].

52519 R(B,x,C)' * (R(B,C',x) * y) = y. [para(52468(a,1),10(a,1,1))].

52589 C * (R(B,x,C) * x) = (B * C) * x. [para(52483(a,1),78(a,1,1)),rewrite([2041(6),16(10,R)]),flip(a)].

52597 x / R(B * x,B,C) = R(B,C,C' * x)'. [para(52483(a,1),2235(a,2,1)),rewrite([113(3),52479(6),113(6),78(8),16(7,R),33788(7),113(10)])].

52618 (x * R(B,y,C)) / R(B,C',y) = x. [para(52515(a,1),87(a,1,1,2)),rewrite([30(5),3(6),30(14),52515(21),77(14)])].

52632 R(B,C',x) / (y * R(B,x,C)) = y'. [para(52515(a,1),2542(a,1,2,2)),rewrite([30(9),3(10),30(14),52515(21),77(14)])].

52692 (x' * ((x * B) * y)) / y = R(B,x',x * y). [para(7967(a,1),2600(a,1,1,1)),rewrite([11964(5),82(10),294(9)])].

52696 R(B,C',(x * C) * B) = R(B,C',x * B). [para(242(a,1),52485(a,1,3)),rewrite([52430(15)])].

52698 R(B,C',R(C' * x,B,C)) = R(B,C',x). [para(52485(a,2),80(a,2)),rewrite([35828(5),73(12),16(9,R),39570(9),39651(10),82(6),259(5),39762(6)

,52466(7),35828(11),4610(15),1511(14),11955(15),1511(14,R),34790(15)]),flip(a)].

52711 B * (x / R(x,B,C)) = R(B,C',x * B). [back_rewrite(43802),rewrite([52696(8)]),flip(a)].

52756 R(B * x,B,C') = R(B,x,C) * x. [para(52589(a,1),10(a,1,2)),rewrite([39743(7)])].

52813 R(B,x,C) / R(B,C',x) = 0. [para(2(a,1),52618(a,1,1))].

52814 x * R(B,C',y) = x * R(B,y,C). [para(52618(a,1),7(a,1,1))].

52820 R(B,C',x) * y = R(B,x,C) * y. [para(52618(a,1),6610(a,2,2)),rewrite([52632(9),52632(14),195(7),10(7)]),flip(a)].

52828 (x * R(B,C',y)) / R(B,y,C) = x. [para(52813(a,1),80(a,1,1,1,2)),rewrite([3(2),52813(17),76(15)])].

52863 R(R(B,x,C) * x,B,C) = B * x. [para(52756(a,1),22987(a,1,1)),rewrite([39797(10)])].

52888 R(B' * (R(B,x,C) * x),B,C) = x. [para(52863(a,1),34855(a,1,2)),rewrite([10(5)]),flip(a)].

52934 R(B,C',x)' * B = R(B,x,C)' * B. [para(52814(a,1),1071(a,1,1)),rewrite([1071(7)]),flip(a)].

53037 R(B,C',x)' * (R(B,x,C) * y) = y. [para(52820(a,1),10(a,1,2))].

53097 B' * (R(B,x,C) * x) = R(x,B,C'). [para(52888(a,1),22987(a,1,1)),rewrite([39765(5)]),flip(a)].

53360 R(R(C * x,B,C') / x,x,B) = C. [para(60(a,1),45903(a,2)),rewrite([16(4,R),47803(7),16(5,R),39686(7)])].

53388 R(C * x,B,C') / x = R(C,B,B' * x). [para(53360(a,1),47659(a,1,1)),flip(a)].

53390 R(R(C,B * C,x),(B * C) * x,B) = C. [para(35225(a,1),53360(a,1,1,1,1)),rewrite([39750(10),92(11)])].

53400 R(B * (B * x),B,C) / x = R(B * B,C',x). [para(34655(a,1),2723(a,1,1,2)),rewrite([34420(7),1511(12,R),10(12),43663(16)])].

53413 (B' * (x * y)) / y = B' * R(x,y,B). [para(45912(a,1),10(a,1,2)),flip(a)].

53418 R(x * B,B,x) * B' = x. [para(20219(a,1),45912(a,2)),rewrite([9201(14),48004(11),34(12)])].

53443 B * (R(x,B,C') / x) = R(R(B,x,C),x,B). [para(52756(a,2),45912(a,1,2,1,2)),rewrite([39587(10),10(6)])].

53450 R(x * B,B,x) = x * B. [para(53418(a,1),6(a,1,1)),rewrite([256(3)]),flip(a)].

53458 x / R(C * x,B,C') = R(C,B,B' * x)'. [para(53418(a,1),3947(a,1,1)),rewrite([53450(4),16(4,R),47803(7),16(5,R),39686(7),53450(12),47800(

13)])].

53553 B * R(B * C',C',x)' = R(C,B * x,B). [para(124(a,1),45993(a,1,2)),rewrite([1511(10,R),10(10),30(6),47886(7),1511(18,R),10(18),30(14)])]

.

53574 R((C * (B * x)) / x,x,C) = B * C. [para(46045(a,1),2120(a,2)),rewrite([16(4,R),16(10)])].

53964 R(B * B,C' * x,C) = R(B * B,C',x). [para(46729(a,2),2655(a,1,1,1)),rewrite([16(4),49(6),16(5),16641(7),16(6,R),1382(6),172(11),12(13),

4537(14),39748(12),39550(11),33788(8),34420(7),53400(8),172(16),12(18),10697(19)]),flip(a)].

53968 x' * (C * (x * (x * B))) = (x * C) * B. [para(46773(a,2),10(a,1,2))].

54084 (B' * R(x,y,B)) * y = B' * (x * y). [para(47700(a,1),10(a,1,2)),flip(a)].

54117 R(R(x,y,B)',B,B' * (x * y)) = x'. [para(47700(a,1),2110(a,2,2)),rewrite([1071(6),293(7),85(8),260(7),54084(10),32(11)])].

54121 R(B * C,x,C) * x = B * (C * x). [para(51402(a,1),47700(a,1,2,1,2)),rewrite([10(7)]),flip(a)].

54123 R(B,x * y,C) = R(B,C',x * y). [para(47700(a,1),52456(a,1,2)),rewrite([54084(14),34(13)])].

54127 R(C' * R(B * C,x,C),C,x) = B. [para(54121(a,1),2119(a,1,1)),rewrite([3952(7)]),flip(a)].

54136 R(B,R(x,B,C'),C) = R(B,C',R(x,B,C')). [para(39659(a,1),54123(a,1,2)),rewrite([39659(17)])].

54235 R(x,B,B' * (y * B')) = R(x,y,B'). [para(7(a,1),47800(a,1,2)),rewrite([293(8)]),flip(a)].

54249 R(R(x,B',B * y),y,B') = x. [back_rewrite(47797),rewrite([54235(13)])].

54261 R(R(x,B',y),B' * y,B') = x. [para(34(a,1),54249(a,1,1,3))].

54262 R((x * (B * y)) / y,y,B') = x * B. [para(79(a,1),54249(a,1,1)),rewrite([10(8),256(10)])].

54281 R(x,B,y) * B = R(x * B,y,B'). [para(2217(a,1),54249(a,1,1)),rewrite([10(8),6(4),256(10)]),flip(a)].

54382 R(x * B,y,B') * B' = R(x,B,y). [para(54281(a,1),6(a,1,1)),rewrite([293(7)])].

54383 R(x,B,y)' * R(x * B,y,B') = B. [para(54281(a,1),10(a,1,2))].

54384 R(x * B,y,B')' = B' * R(x,B,y)'. [para(54281(a,1),824(a,1,1))].

54397 R(B * x',x,y)' * B = R(x,y,B'). [para(6450(a,1),54281(a,1,1)),rewrite([749(2),293(9),82(12),259(11)])].

54476 R(B * x,B,y * B) = B * R(x,B,y). [para(48002(a,1),1089(a,2)),rewrite([9(10),3(8),232(16),293(14),47803(15),231(14),256(14),34(15),2684

9(12),232(10),293(8),50402(9),85(8),260(7),45738(6),232(10),293(8),54382(9),47803(14),231(13),256(13),34(14)]),flip(a)].

54690 R(x,y,B) * B = R(x * B,B',y). [para(6(a,1),48341(a,1,1,1)),rewrite([2143(9)])].

54713 x / (B' * (y * B')) = ((x * B) / y) * B. [para(16667(a,1),48341(a,1,1)),rewrite([45891(9)]),flip(a)].

54842 R(R(C,B * (x * C),B),B,R(x,B,C)) = C. [para(34704(a,1),48595(a,1,3,2)),rewrite([34855(16),10(13)])].

54877 R(x',B * B,x) = x'. [para(10978(a,1),3176(a,1,2)),rewrite([6(11),2421(8),2777(7)]),flip(a)].

54896 R(x / y,B * B,y / x) = x / y. [para(104(a,1),54877(a,1,1)),rewrite([104(8)])].

54963 R(C,B * C,R(C / x,x,B)') = R(C,B,x). [para(36015(a,1),3185(a,1,2)),rewrite([16(9,R),39659(9),39762(7),39692(8),39691(8),2144(7),232(6)

,293(4),122(6)]),flip(a)].

54977 (B * x) / R(x,B,C) = R(B,C',x). [para(2294(a,1),3187(a,1,1,2)),rewrite([16(9),35790(10),4610(11),1511(10),11955(11),1511(10,R),34790(1

1),35139(10),34(7),4610(15),1511(14),11955(15),1511(14,R),34790(15),52457(15),52698(16)])].

55055 R(x,B,C) / (B * x) = R(B,C',x)'. [para(35827(a,1),3197(a,1,2,2)),rewrite([4610(8),1511(7),11955(8),1511(7,R),34790(8),16(8,R),35139(8)

,34(5),4610(15),1511(14),11955(15),1511(14,R),34790(15),52457(15),52698(16)])].

55062 R(B * C,C',x * B') = R(B * C,x,B'). [para(35827(a,1),3198(a,1,2,1)),rewrite([16(11,R),39570(11),39698(11),1828(12),293(12),1511(13),16

59(14),43706(11),16(3),35827(22),1828(17),293(17),1511(18),1659(19)])].

55087 R(B,C',x) * R(x,B,C) = B * x. [para(54977(a,1),7(a,1,1))].

55091 R(B,C',R(x,B,C')) = R(B,C',x). [para(26864(a,1),54977(a,1,2)),rewrite([16(4),39763(7),39762(6),52466(7),16(10),39763(13)]),flip(a)].

55094 R(B,C',R(x,B,C)) = R(B,C',x). [para(54977(a,1),43671(a,2)),rewrite([16(8,R),35139(8),50838(9),1659(6)])].

55096 R(B,R(x,B,C'),C) = R(B,C',x). [back_rewrite(54136),rewrite([55091(15)])].

55097 R(B,R(x,B,C),C) = R(B,C',x). [back_rewrite(52457),rewrite([55094(13)])].

55164 R(B,C',x)' * (B * x) = R(x,B,C). [para(55087(a,1),10(a,1,2))].

55169 R(B,x,C) * R(x,B,C) = B * x. [para(52450(a,1),55087(a,1,1))].

55171 R(B,x,C)' * (B * x) = R(x,B,C). [para(55169(a,1),10(a,1,2))].

55177 R(R(B,x,C),R(x,B,C),C') = B. [para(55169(a,1),1672(a,1,1,2)),rewrite([1511(11,R),36039(11),36036(12)]),flip(a)].

55179 R(R(B,x,C)',B * x,C') = B'. [para(55177(a,1),142(a,2,1)),rewrite([55169(11)])].

55236 R(B' * x,B,C) = R(B',x,C) * x. [para(34(a,1),55171(a,1,2)),rewrite([141(6),30(6)]),flip(a)].

55237 B * (R(B,x,C)' * B) = R(B,C,x * C'). [para(55171(a,1),39(a,1,1,2)),rewrite([34420(5),49846(6)]),flip(a)].

55242 R(R(B',x,C),x,C') = B'. [para(34(a,1),55179(a,1,2)),rewrite([141(6),30(6)])].

55264 R(B',C * x,C) = R(B',x,C). [para(55242(a,1),26864(a,1,1)),flip(a)].

55266 R(B',C' * x,C) = R(B',x,C). [para(55242(a,1),26987(a,1,1))].

55267 R(B',x * C',C) = R(B',x,C). [para(55242(a,1),26994(a,1,1))].

55276 R(B',C * C,x) = R(B',x,C). [para(55264(a,1),4130(a,2))].

55288 R(B' * x,B,C) / x = R(B',x,C). [para(55276(a,1),125(a,2)),rewrite([1382(6,R),16(5,R),172(10),12(12),246(13),113(7),10(8),50112(8),172(

13),12(15),55266(17),55266(14)])].

55297 R(B',R(x,B,C'),C) = R(B',x,C). [para(2260(a,1),55267(a,1,2)),rewrite([39686(9),39662(10),55276(10),49939(18),142(21),4565(18),52471(18

),43663(17),52469(15),30(14)])].

55372 R(B,R(x,B,C),B * C) = R(B,C',x * B). [para(49255(a,1),2569(a,1,3)),rewrite([16(8),24137(9),43663(10),43663(8),16(12),43633(13),40055(1

1),16(13)]),flip(a)].

55373 R(C * R(x,C',y),C,y) = x * C. [para(49255(a,1),3196(a,1,1)),rewrite([6(8),43663(8)]),flip(a)].

55387 C * (C * R(x,C,y)) = R(C * (x * C),C,y). [para(49492(a,1),55373(a,1,1,2)),rewrite([16(12,R)]),flip(a)].

55396 R(C * (x / y),C,y) = (C * x) / y. [para(43671(a,1),55373(a,1,1,2)),rewrite([16(12,R),5303(12)])].

55403 (C * (x * y)) / y = R(C * x,C,y). [back_rewrite(50923),rewrite([55387(13),16(10,R),1659(10)])].

55407 R(R(B * C,C,x),x,C) = B * C. [back_rewrite(53574),rewrite([55403(5),16(3)])].

55419 R(x,C,C' * y) = R(x,C,y). [back_rewrite(50221),rewrite([55403(7),1659(5)]),flip(a)].

55431 x / R(B * x,B,C) = R(B,C,x)'. [back_rewrite(52597),rewrite([55419(12)])].

55437 R(B' * x,B,C') / x = R(B',C,x). [back_rewrite(44485),rewrite([55419(15)])].

55440 (x * (C' * y)) / y = R(C' * x,C,y). [back_rewrite(38193),rewrite([55419(8)]),flip(a)].

55441 R(B,C,(B' * C') * x) = R(B',C,x)'. [back_rewrite(36478),rewrite([55419(16)])].

55443 R(B,x * C,C') = R(B,C,x). [back_rewrite(35265),rewrite([55419(12)])].

55445 R(B,C,x) = R(B,x,C'). [back_rewrite(35263),rewrite([55419(9),55419(6)])].

55447 R(R(B,C,x),x,C) = B. [back_rewrite(35218),rewrite([55419(6)])].

55448 R(B,C,x * (B * C')) = R(B,x,B * C'). [back_rewrite(32638),rewrite([55419(11)])].

55455 R(x,C,y * C') = R(x,C,y). [back_rewrite(2585),rewrite([55419(5)]),flip(a)].

55468 B * (R(B,x,C)' * B) = R(B,C,x). [back_rewrite(55237),rewrite([55455(14)])].

55472 R(B * x,B,C) / x = R(B,C,x). [back_rewrite(49846),rewrite([55455(12)])].

55492 R(B,C,C * x) = R(B,C,x). [para(55445(a,2),80(a,2)),rewrite([1699(4),1511(7,R),34655(7),55472(6),1699(8)]),flip(a)].

55495 R(B,C' * x,C') = R(B,C,x). [para(55445(a,1),125(a,2)),rewrite([12145(7),1511(5),33788(7),55472(6)]),flip(a)].

55496 R(B,C,x)' = R(B,x,C')'. [para(55445(a,1),138(a,2,1)),rewrite([138(7)])].

55497 R(B,C,B' * x) = R(B',x,C')'. [para(55445(a,2),141(a,1))].

55506 R(B,C,x * (B * C)) = B * (x / R(x,B,C')). [para(55445(a,2),1522(a,2)),rewrite([1511(9,R),10(9),1511(11,R),39631(11),25345(11),39562(10

),85(6),260(5)]),flip(a)].

55507 R(B * x,B,C) = R(B,C,x) * x. [para(55445(a,2),2035(a,1,1)),rewrite([1699(5),55492(5),1699(8),1511(11,R),34655(11)]),flip(a)].

55511 R(B,x,C * C) = R(B,C,x). [para(55445(a,1),49829(a,1)),rewrite([55443(6)]),flip(a)].

55560 R(B * x,B,C) = R(B,x,C') * x. [para(55511(a,1),2306(a,1,1)),rewrite([172(6),51083(9),172(8),24807(13),2301(8),172(10),1382(17,R),16(16

,R),35978(16),33788(12)]),flip(a)].

55562 R(x,C,C * y) = R(x,C,y). [para(10(a,1),55419(a,1,3)),flip(a)].

55563 R(x,C,y * C) = R(x,C,y). [para(63(a,1),55419(a,1,3)),flip(a)].

55564 R(x,C,y * (y * C)) = R(x,C,y * y). [para(126(a,1),55419(a,1,3)),flip(a)].

55568 R(x,C,C' / y) = R(x,C,C / y). [para(5715(a,1),55419(a,1,3)),rewrite([55562(7)])].

55579 R(x,C,R(B * y,B,C)) = R(x,C,B * (C * y)). [para(34655(a,1),55419(a,1,3))].

55580 R(x,C,R(y * B,B,C)) = R(x,C,(C * y) * B). [para(35837(a,1),55419(a,1,3))].

55613 R(x,C,y * (C * (y * C))) = R(x,C,y * y). [para(1185(a,1),55562(a,1,3)),rewrite([55564(12)])].

55615 R(x,C,R(C * y,B,C)) = R(x,C,R(y,B,C)). [para(35139(a,1),55562(a,1,3))].

55621 R(x,C,(B * C') * y) = R(x,C,B * (C * y)). [para(33788(a,1),55562(a,1,3)),rewrite([55579(7)]),flip(a)].

55622 R(x,C,(C * y) * B) = R(x,C,y * (B * C')). [para(35803(a,1),55562(a,1,3)),rewrite([55580(7)])].

55642 R(B,C,x)' * R(B * x,B,C) = x. [para(55443(a,1),2036(a,1,1,1)),rewrite([1511(11,R),34704(11),1511(15,R),63(15)])].

55687 R(B,C,x)' * R(B,x,C') = 0. [para(55496(a,2),8(a,1,1))].

55793 R(B * C,C,x) = R(B * C,x,C'). [para(55407(a,1),26935(a,1,1)),rewrite([55419(14)]),flip(a)].

55811 B * (R(x,B,C) / x) = R(R(B,C,x),x,B). [para(55472(a,1),26923(a,1,1)),rewrite([34855(14),10(11)]),flip(a)].

55815 (B * x) / R(x,B,C') = R(B,C,R(x,B,C')). [para(39762(a,1),55472(a,1,1,1)),rewrite([39766(9)])].

55817 R(R(B,C,x),x,B) = R(B,C,x * B). [para(55472(a,1),45903(a,2)),rewrite([35846(10),232(7),293(5),85(6),260(5),55472(6)])].

55818 B * R(R(B,C,x),x,B') = R(B * B,C',x). [para(55472(a,1),47780(a,1,2,1)),rewrite([34420(15),53400(16)])].

55819 R(B,C,x * B) / (R(x,B,C) / x) = B. [para(55472(a,1),48331(a,1,1,1)),rewrite([55817(5),34855(13),10(10)])].

55820 R(B,C,x * B) * (x / R(x,B,C)) = B. [para(55472(a,1),48348(a,1,1,1)),rewrite([55817(5),34855(13),10(10)])].

55821 B * (R(x,B,C) / x) = R(B,C,x * B). [back_rewrite(55811),rewrite([55817(11)])].

55842 R(B,x',C') = R(B,C,x'). [para(1872(a,1),55495(a,1,2)),rewrite([10(7),55563(11)])].

55849 R(B,x / y,C') = R(B,C,x / y). [para(104(a,1),55842(a,1,2)),rewrite([104(9)])].

55856 R(B',x,C')' * (B' * x) = R(x,B,C). [para(34(a,1),55507(a,1,1)),rewrite([55497(9)]),flip(a)].

55902 R(B,C,x) * x = R(B * x,x',C). [para(55507(a,1),50850(a,2)),flip(a)].

55903 R(B,R(B * x,x',C),C) = R(B,C',B * x). [para(55507(a,1),55097(a,1,2)),rewrite([55902(5)])].

55941 R(R(B,C,x)',R(B,x,C'),y)' = R(B,C,x). [para(55687(a,1),141(a,1,2)),rewrite([76(5)]),flip(a)].

55942 R(B,C,x) * y = R(B,x,C') * y. [para(55687(a,1),2036(a,1,2,1)),rewrite([55941(10),2(5)])].

56033 R(x,C' * y,C) = R(x,y,C). [para(2234(a,1),55396(a,2)),rewrite([55440(6),49576(9),16(5,R),34(5)]),flip(a)].

56039 R(B * B,C',x) = R(B * B,x,C). [back_rewrite(53964),rewrite([56033(8)]),flip(a)].

56053 R(R(x,y,C')',x * y,C) = x'. [back_rewrite(27190),rewrite([56033(10)])].

56054 R(R(x,y,C'),y,C) = x. [back_rewrite(26987),rewrite([56033(8)])].

56055 R(R(x,y,C),y,C') = x. [back_rewrite(26935),rewrite([56033(5)])].

56056 R(x,y,C) * y = C * (x * (C' * y)). [back_rewrite(26808),rewrite([56033(5)])].

56057 x / (C * (y * (C' * x))) = R(y,x,C)'. [back_rewrite(8765),rewrite([56033(12)])].

56064 R(x,C * y,C') = R(x,y,C'). [para(56054(a,1),27045(a,1,1))].

56065 R(x,C * y,C) = R(x,y,C). [para(27045(a,1),56054(a,1,1))].

56066 R(x,y * C,C') = R(x,y,C'). [para(56054(a,1),27046(a,1,1))].

56067 R(x,y * C,C) = R(x,y,C). [para(27046(a,1),56054(a,1,1))].

56069 R(x,y * C',C) = R(x,y,C). [para(27047(a,1),56054(a,1,1)),flip(a)].

56087 R(x,C * C,y) = R(x,y,C). [para(56054(a,1),2875(a,2,1)),rewrite([2301(4),16(4,R),13(5),101(10),56065(4)]),flip(a)].

56154 R(R(x,y,C),y,C) = R(x,y,C * C). [back_rewrite(26813),rewrite([56065(6)])].

56185 R(R(B',C,B * x)',R(x,B,C),C) = B. [back_rewrite(51669),rewrite([56087(14)])].

56188 R(x,R(B * y,B,C),C) = R(x,B * (y * C),C). [back_rewrite(45777),rewrite([56087(9)])].

56208 R(x,R(C * y,B,C),C) = R(x,R(y,B,C),C). [back_rewrite(35305),rewrite([56087(14)])].

56217 R(x,y * (C * y),C) = R(x,y * y,C). [back_rewrite(18597),rewrite([56087(10)])].

56219 R(x,C' / y,C) = R(x,C / y,C). [back_rewrite(7609),rewrite([56087(9),56065(7)])].

56226 R(x,y * (C' * y),C) = R(x,y * y,C). [back_rewrite(5225),rewrite([56087(8)])].

56288 R(x,(B * C') * y,C) = R(x,B * (y * C),C). [para(33788(a,1),56065(a,1,2)),rewrite([56188(7)]),flip(a)].

56316 R(x,R(C' * y,B,C),C) = R(x,R(y,B,C),C). [para(36039(a,1),56033(a,1,2))].

56354 R(x,C' * y,C') = R(x,y,C'). [para(34(a,1),56064(a,1,2)),flip(a)].

56458 R(B,x,C)' * B = B' * R(B,C,x). [para(55468(a,1),10(a,1,2)),flip(a)].

56482 R(B,C,x) * B' = B * R(B,x,C)'. [para(55468(a,1),2466(a,2,1)),rewrite([56458(7),141(10),31686(8),30(3),260(9)]),flip(a)].

56485 B * (R(B,C',x)' * B) = R(B,C,x). [para(52450(a,2),55468(a,1,2,1,1))].

56492 R(B',C,B * x)' = R(B,C,x). [para(55097(a,1),55468(a,1,2,1,1)),rewrite([56485(9),36901(9)]),flip(a)].

56493 R(B,C,R(x,B,C')) = R(B,C,x). [para(55096(a,1),55468(a,1,2,1,1)),rewrite([56485(9)]),flip(a)].

56496 R(B,C',x)' * B = B' * R(B,C,x). [back_rewrite(52934),rewrite([56458(13)])].

56499 R(R(B,C,x),R(x,B,C),C) = B. [back_rewrite(56185),rewrite([56492(7)])].

56502 R(B,C,R(x,B,C)) = R(B,C,x). [back_rewrite(36901),rewrite([56492(13)])].

56503 (B * x) / R(x,B,C') = R(B,C,x). [back_rewrite(55815),rewrite([56493(14)])].

56521 R(R(B,C,x),R(x * C',B,C),C) = B. [para(7790(a,1),56499(a,1,2)),rewrite([55419(6)])].

56536 R(B,R(x,B,C),C') = R(B,C,x). [para(56499(a,1),56055(a,1,1))].

56539 R(B,C,B * (x * C)) = R(B,C,B * x). [para(33764(a,1),56502(a,1,3)),rewrite([55562(14)])].

56540 R(B,C,(B * C) * x) = R(B,C,B * (C * x)). [para(34431(a,1),56502(a,1,3))].

56541 R(B,C,B * (C * x)) = R(B,C,B * x). [para(34454(a,1),56502(a,1,3)),rewrite([56540(7),56539(14)])].

56542 R(B,C,x * (B * C)) = R(B,C,x * B). [para(34858(a,1),56502(a,1,3)),rewrite([55562(7)]),flip(a)].

56548 R(B,C,(x * C) * B') = R(B,C,x * B'). [para(2182(a,1),56502(a,1,3)),rewrite([16(6,R),35828(10),11560(12),10(8),55562(8),293(12)]),flip(

a)].

56550 R(B,C,x * (C * B')) = R(B,C,x * B'). [para(2190(a,1),56502(a,1,3)),rewrite([35828(12),11560(14),4120(10),55562(10),56548(8),293(14),70

(15),55562(16)]),flip(a)].

56556 R(B,C,R(C' / x,x,B)) = R(B,C,C / x). [para(41540(a,1),56502(a,1,3)),rewrite([55568(14)])].

56568 R(B,C,(B * C) * x) = R(B,C,B * x). [back_rewrite(56540),rewrite([56541(14)])].

56569 B * (x / R(x,B,C')) = R(B,C,x * B). [back_rewrite(55506),rewrite([56542(7)]),flip(a)].

56579 R(B',C,B * x) = R(B,C,x)'. [para(56492(a,1),30(a,1,1)),flip(a)].

56636 R(B',C,R(x,B,C)) = R(B',x,C'). [para(34236(a,1),56579(a,1,3)),rewrite([55615(9),55562(15),55497(13),30(14)])].

56675 R(B,C,x) * R(x,B,C) = R(B * x,B,C'). [para(34420(a,1),55560(a,1,1)),rewrite([56154(8),47215(7),56536(13)]),flip(a)].

56698 R(B,x,C') * x = R(B * x,x',C). [para(55560(a,1),50850(a,2)),flip(a)].

56700 R(B,C',B * (x * C)) = R(B,C',B * x). [para(55560(a,2),54123(a,2,3)),rewrite([56698(6),55903(8),45835(15)]),flip(a)].

56717 R(B * C,x * B,C) = R(B * C,C',x * B). [para(16(a,2),3563(a,1,1,2,2)),rewrite([16(6),24137(7),16(12,R),43706(13),16(3),43663(10)]),flip

(a)].

56720 R(B',x,C') * R(x,B,C) = B' * x. [para(34(a,1),55642(a,1,2,1)),rewrite([55497(6),30(7)])].

56730 R(B * C,x,C') * x = C * (B * x). [para(55793(a,1),2045(a,1,1)),rewrite([56354(9),16(12,R),1382(12),4123(16),34(14)])].

56755 R(R(B,C,x),R(x,B,C'),B) = R(B,C,x * B). [para(56493(a,1),55817(a,1,1)),rewrite([54281(17),43654(18),56493(18)])].

56770 R(B,x * y,C') = R(B,C,x * y). [para(2419(a,1),55849(a,1,2)),rewrite([2419(11)])].

56966 R(B * B,x,C * C) = R(B * B,C,x). [para(56039(a,1),49254(a,1,1)),rewrite([56154(7)])].

56991 R(R(x',B,C'),x * B,C) = x'. [para(41658(a,1),56053(a,1,1))].

57114 R(x,y * C',C * C) = R(x,y,C * C). [para(56154(a,1),24745(a,2)),rewrite([56069(5),56033(7),56154(4)]),flip(a)].

57296 R(B,C,x * B) / (x / R(x,B,C')) = B. [para(56503(a,1),48331(a,1,1,1)),rewrite([56755(9),10(10)])].

57367 R(B,C',(C' * x) * B) = R(B,x,B * C). [para(35139(a,1),3729(a,2,3,1)),rewrite([113(6),36039(7),16(10),55372(11),54281(19),39197(20),356

48(19),43685(17)])].

57392 R(R(x,B,C'),x' * B,C) = x. [para(30(a,1),56991(a,1,1,1)),rewrite([30(11)])].

57400 R(R(B,x,C) * x,x',C) = B * x. [para(52756(a,1),57392(a,1,1)),rewrite([889(7),82(10),259(9)])].

58268 R(x,C,(y * C) * B) = R(x,C,y * (B * C')). [para(122(a,1),3865(a,1,2)),rewrite([55622(6),122(13)]),flip(a)].

58301 B * R(C * B',x,B') = R(C,B,B' * x). [para(3923(a,1),45738(a,1)),rewrite([293(10)]),flip(a)].

58811 R(B,x,C) * x = R(B * x,x',C'). [para(57400(a,1),56055(a,1,1)),flip(a)].

58812 B' * R(B * x,x',C') = R(x,B,C'). [back_rewrite(53097),rewrite([58811(6)])].

58971 R(B * (B * x),B,C') / x = R(B * B,C,x). [para(56039(a,1),4058(a,2,1)),rewrite([1511(7,R),10466(8),39748(9),34(13),56033(19),56154(16),

56966(16)])].

59577 x * (R(x,y,C)' * x) = R(x,y,C'). [para(4243(a,1),1672(a,1,1,2)),rewrite([10(8),1511(13,R),10(13),9207(9),4032(6),56064(15),141(13),560

64(12),142(10),30(10)])].

59709 R(B * C,C',x) / R(C,x,B') = B. [para(51401(a,1),6(a,1,1))].

59717 R(C,x,B')' = R(C',x,B'). [para(51401(a,1),2420(a,1,1,1)),rewrite([50161(7),300(18),54281(9),231(7),256(7),1511(6),10(7)]),flip(a)].

59733 R(C',x,B')' = R(C,x,B'). [para(59717(a,1),30(a,1,1))].

59749 R(C',x * C',B') = R(C',x,B'). [para(6042(a,1),59717(a,1,1)),rewrite([59733(6),59717(5)]),flip(a)].

59752 R(C,B,B' * x)' = R(C',B,B' * x). [para(59717(a,1),2235(a,2)),rewrite([256(4),47803(7),16(5,R),39686(7),53458(7),256(12),47800(14)])].

59759 x / R(C * x,B,C') = R(C',B,B' * x). [back_rewrite(53458),rewrite([59752(14)])].

59762 R(C,C * x,B') = R(C,x,B'). [para(141(a,1),59733(a,1,1)),rewrite([30(3),59717(5),59733(6),30(8)]),flip(a)].

59763 R(C,x * C,B') = R(C,x,B'). [para(3925(a,1),59733(a,1,1)),rewrite([59717(5),59733(6)]),flip(a)].

59782 R(C,B,B * (x * C)) = R(C,B,B * x). [para(465(a,1),59763(a,1,2)),rewrite([73(8),48002(12),232(11),293(9),85(10),260(9),48002(17),232(16

),293(14),85(15),260(14)])].

59797 R(C,R(x,B,C),B) = R(C,x,B * C). [para(47631(a,1),51576(a,1,2)),rewrite([39797(12)]),flip(a)].

59803 R(C,C * x,B * C) = R(C,x,B * C). [back_rewrite(48518),rewrite([59797(8),59797(13)])].

59807 R(C,B * (x * C),B) = R(C,B * x,B * C). [para(33764(a,1),59797(a,1,2)),rewrite([59803(16)])].

59816 R(R(C,B * x,B * C),B,R(x,B,C)) = C. [back_rewrite(54842),rewrite([59807(7)])].

60017 R(R(B,C',x),x,B) = R(B,C',x * B). [para(52466(a,1),45903(a,2)),rewrite([39562(11),232(7),293(5),85(6),260(5),52466(7)])].

60018 B * R(R(B,C',x),x,B') = R(B * B,C,x). [para(52466(a,1),47780(a,1,2,1)),rewrite([39762(17),58971(18)])].

60262 R(B' * x,B',B * y) = B' * R(x,y,B). [para(4606(a,1),80(a,1,1)),rewrite([293(4),82(7),259(6),53413(5),293(10),16667(13)]),flip(a)].

60416 R(B' * R(x,y,B),y,B') = B' * x. [para(3115(a,1),54262(a,2)),rewrite([12(10),34(11),13(9),10(7),53413(5),12(15),34(16)])].

60724 R(B',C',x)' = R(B',x,C)'. [para(1664(a,1),4687(a,1,2)),rewrite([30(8),11560(13),1511(11),44469(13),39492(13),41083(13),138(10),30(12),

246(17),113(14),1511(15),44469(17),55091(17),52469(13)])].

60745 R(B',C',x) = R(B',x,C). [para(60724(a,1),30(a,1,1)),rewrite([30(6)]),flip(a)].

60761 R(B',C',B * x) = R(B,x,C)'. [para(60745(a,2),141(a,1)),rewrite([30(7),30(10)])].

60795 R(x,y,B') * B' = R(x * B',B,y). [para(7(a,1),54382(a,1,1,1)),rewrite([293(8)])].

60889 R(C,B,x)' * R(B * C,x,B') = B. [para(16(a,1),54383(a,1,2,1))].

60905 R(B,x * (C * B'),B * C') = R(B,C,x). [para(226(a,1),4849(a,1,3,2)),rewrite([293(7),1511(12),39165(13),55419(6),293(7),1511(13)]),flip(

a)].

60935 B * R(B' * x,B,y) = R(x,B,y * B). [para(34(a,1),54476(a,1,1)),flip(a)].

61131 (R(x,B,C) / x) * B' = R(B,x,B * C)'. [para(52485(a,1),55055(a,2,1)),rewrite([26849(10),35846(8),85(5),260(4)])].

61140 R(x,B,C) / x = B' * R(B,C,x * B). [para(55164(a,1),2111(a,2,1)),rewrite([256(8),56496(7),60262(11),55817(7)]),flip(a)].

61156 B * (R(B',x,C) * x) = R(x,B,C). [para(55236(a,1),34420(a,1,2)),rewrite([34(12)])].

61184 R(B,x / y,y) = R(B,y',y * x). [para(61156(a,1),2232(a,2,1)),rewrite([81(6),10(7),16636(4),52692(6),89(8)]),flip(a)].

61193 R(B,x',x * (y * x)) = R(B,y,x). [para(6(a,1),61184(a,1,2)),flip(a)].

61281 R(B,(x * y)',x) = R(B,x',x / y). [para(6173(a,1),61193(a,1,3,2)),rewrite([34(6)]),flip(a)].

61386 R(R(x,B,C) / x,x,B) = B * R(B',x,C). [para(55288(a,1),2149(a,2,2)),rewrite([34420(8),34(5)])].

61405 R(B',R(x,B,C),C) = R(B',x,C). [para(39535(a,1),55297(a,1,2)),rewrite([55297(15)])].

61450 (R(x,B,C) / x) / R(B,C,x * B) = B'. [para(55819(a,1),104(a,1,1)),flip(a)].

61454 (x / R(x,B,C)) * B' = R(B,C,x * B)'. [para(55820(a,1),32(a,1,2)),rewrite([293(6)])].

61460 R(B,C,x * B) * x = R(B * x,B,C). [para(55821(a,1),2035(a,2,1)),rewrite([61184(6),2037(11),11964(8),50130(7),10(8)]),flip(a)].

61461 R(B,x',x * R(x,B,C))' = B'. [para(55821(a,1),2235(a,1,2,1)),rewrite([61460(9),34500(9),61184(8)]),flip(a)].

61466 R(B,x',x * R(x,B,C)) = B. [para(61461(a,1),30(a,1,1)),rewrite([30(3)]),flip(a)].

61494 R(B,C',x) * x = R(B * x,x',C'). [para(56056(a,2),52465(a,2)),rewrite([43661(7),16(9,R),34(9),58811(9)])].

61601 R(B,C,x)' * B = B' * R(B,x,C). [para(56458(a,1),824(a,1,1)),rewrite([1071(7),30(13)])].

61651 R(B',R(x,B,C'),C') = R(B',C,x). [para(47631(a,1),56636(a,1,3)),rewrite([39765(11)]),flip(a)].

61917 R(R(B * C,x,C') * B',B,x) = C. [para(56730(a,1),2144(a,1,1)),rewrite([6(7)]),flip(a)].

62195 R(x,y,C)' * x = x' * R(x,y,C'). [para(59577(a,1),10(a,1,2)),flip(a)].

62196 x * (R(x',y,C) * x) = R(x',y,C')'. [para(141(a,1),59577(a,1,2,1,1)),rewrite([30(5),141(10)])].

62198 x * (R(x',B,C') * x) = R(x,B,C). [para(35792(a,1),59577(a,2)),rewrite([41082(4),41658(5)])].

62231 R(B * C,x,C) / R(C,x,B') = B. [para(50143(a,1),59709(a,1,1))].

62236 R(C,x,B') / R(B * C,x,C) = B'. [para(62231(a,1),104(a,1,1)),flip(a)].

62238 R(B * C,x,C) * B' = R(C,B,x * B). [para(62231(a,1),6610(a,1,1)),rewrite([62231(15),293(7),60795(8),25402(8),62236(20)]),flip(a)].

62251 R(C,B * C,x) = R(C,B,x). [para(34(a,1),59782(a,2,3)),rewrite([16(8,R),34236(9),35148(8)])].

62260 R(C',B,x)' = R(C,B,x). [back_rewrite(54963),rewrite([62251(10),50360(8)])].

62261 R(R(C,B,x),(B * C) * x,B) = C. [back_rewrite(53390),rewrite([62251(5)])].

62263 R(R(C,B,x),B * x,C) = R(C,B,R(x,B,C)). [back_rewrite(35147),rewrite([62251(15)])].

62267 R(C,B,R(C / x,x,B)') = R(C,B,x). [back_rewrite(50360),rewrite([62260(13)])].

62270 R(C,B,R(x,B,C)) = R(C,B,C' * x). [para(62251(a,1),3190(a,2)),rewrite([12145(11),1511(9),33788(11),35990(10)])].

62271 R(R(C,B,x),B * x,C) = R(C,B,C' * x). [back_rewrite(62263),rewrite([62270(13)])].

62276 R(C,B,x)' = R(C',B,x). [para(62260(a,1),30(a,1,1))].

62301 R(R(C',B,x),B,R(C,B,x)) = R(C',B,x). [para(62260(a,1),33478(a,1,3))].

62316 R(C',B,x) * R(B * C,x,B') = B. [back_rewrite(60889),rewrite([62276(4)])].

62378 R(C,B * (C * C),x) = R(C,B,x). [para(5530(a,1),62251(a,1)),rewrite([1382(6),1828(13),293(13),1511(14),1382(19),4123(20),12146(21),1195

5(20),33905(19),50131(20),11955(19),34415(19),35139(18),36039(19),10(16),62270(15),10(14)])].

62379 R(R(C,B,x),C * (B * (C * x)),B) = C. [para(5530(a,1),62261(a,1,1)),rewrite([16(4),62251(5),16(11),34415(13),35056(12)])].

62384 R(C,C * (B * (C * C)),x) = R(C,B,x). [para(62378(a,1),5530(a,1)),rewrite([4469(8),10163(18),33905(17),37480(18),13(19),34655(17),34431

(15),33905(12),50131(13),11955(12),34415(12),35139(11),36039(12),10(9),62270(8),10(7)]),flip(a)].

62988 R(B,C,x * B) = R(B,C,x). [para(61460(a,1),6(a,1,1)),rewrite([55472(6)]),flip(a)].

62991 R(B,x,B * C') = R(B,C,x). [para(61460(a,1),3951(a,1,1)),rewrite([34454(7),2130(7),63(6),58268(10),55448(11)]),flip(a)].

63011 (x / R(x,B,C)) * B' = R(B,C,x)'. [back_rewrite(61454),rewrite([62988(12)])].

63012 (R(x,B,C) / x) / R(B,C,x) = B'. [back_rewrite(61450),rewrite([62988(9)])].

63013 R(x,B,C) / x = B' * R(B,C,x). [back_rewrite(61140),rewrite([62988(11)])].

63021 R(B,C,x) / (x / R(x,B,C')) = B. [back_rewrite(57296),rewrite([62988(5)])].

63030 B * (x / R(x,B,C')) = R(B,C,x). [back_rewrite(56569),rewrite([62988(12)])].

63032 R(B,C,x * (B * C)) = R(B,C,x). [back_rewrite(56542),rewrite([62988(12)])].

63035 B * (R(x,B,C) / x) = R(B,C,x). [back_rewrite(55821),rewrite([62988(11)])].

63036 R(B,C,x) * (x / R(x,B,C)) = B. [back_rewrite(55820),rewrite([62988(5)])].

63046 R(B,C,x * B') = R(B,C,x). [back_rewrite(60905),rewrite([62991(11),56550(8)])].

63062 R(B,C,x * (B * C')) = R(B,C,x). [back_rewrite(55448),rewrite([62991(14)])].

63070 R(B,C,x * (C * B')) = R(B,C,x). [back_rewrite(56550),rewrite([63046(14)])].

63150 R(B,C,x * (B' * C')) = R(B,C,x). [para(1665(a,1),63046(a,1,3)),rewrite([1511(9),55419(12),55419(18),55419(15)])].

63153 R(R(B,C,x),x * B',C) = B. [para(63046(a,1),55447(a,1,1))].

63166 R(R(B,C,x),(C' * x) * B',C) = B. [para(63046(a,1),56521(a,1,1)),rewrite([1511(9,R),36074(12)])].

63222 R(B,C,((B * C) * x)') = R(B,C,C / x). [para(6173(a,1),63032(a,1,3)),rewrite([1828(6),293(6),1511(7),51533(12),55562(8),55568(6)]),flip

(a)].

63253 B * ((R(x,B,C) / x) * B) = R(B,C,x) * B. [para(63035(a,1),49(a,1,1)),flip(a)].

63283 R(B,x,C) * (R(x,B,C) / x) = B. [para(63036(a,1),2260(a,1,1,2,2)),rewrite([63011(8),61601(7),34(8),104(8),63011(16),8(17),3(11)])].

63353 R(B,C',x * B) = R(B,x,C). [para(63283(a,1),6(a,1,1)),rewrite([749(6),104(6),52711(6)])].

63369 R(R(B,C',x),x,B) = R(B,x,C). [back_rewrite(60017),rewrite([63353(12)])].

63373 R(B,x,B * C) = R(B,x,C). [back_rewrite(57367),rewrite([63353(9),56033(6)]),flip(a)].

63379 B * (x / R(x,B,C)) = R(B,x,C). [back_rewrite(52711),rewrite([63353(12)])].

63380 (R(x,B,C) / x) * B' = R(B,x,C)'. [back_rewrite(61131),rewrite([63373(12)])].

63424 R(R(B,x,C),x,B) = R(B,x,C). [para(63369(a,1),18(a,2)),rewrite([61494(5),25369(11),58812(10),53443(7)])].

63440 B * (R(x,B,C') / x) = R(B,x,C). [back_rewrite(53443),rewrite([63424(12)])].

63543 B * ((x / R(x,B,C)) * B) = R(B,x,C) * B. [para(63379(a,1),49(a,1,1)),flip(a)].

63688 R(B',R(B,C,x),x) = B'. [para(63012(a,1),2104(a,1,1)),rewrite([55902(13),50869(15)])].

63689 (x / R(x,B,C')) / R(B,C,x) = B'. [para(47631(a,1),63012(a,1,1,1)),rewrite([39765(5),39765(12),56493(12)])].

63693 (B' * R(B,C,x)) * x = R(x,B,C). [para(63688(a,1),78(a,1,1)),rewrite([55902(6),50894(8)]),flip(a)].

63767 B' * R(B,C,x) = B * R(B',x,C). [para(63013(a,1),45903(a,2)),rewrite([35846(8),85(5),260(4),61386(6),62988(13)]),flip(a)].

63768 R(x,B,C) / x = B * R(B',x,C). [para(63013(a,1),54896(a,2)),rewrite([54896(12),63767(10)])].

63769 x / R(x,B,C') = B * R(B',x,C). [para(56054(a,1),63013(a,1,1)),rewrite([56493(14),63767(11)])].

63780 R(B,B * R(B',x,C),x) = B. [para(63013(a,1),61184(a,1,2)),rewrite([63767(7),61466(15)])].

63784 B * (B * R(B',x,C)) = R(B,C,x). [para(63013(a,1),63035(a,1,2)),rewrite([63767(7)])].

63794 (B * R(B',x,C)) * x = R(x,B,C). [back_rewrite(63693),rewrite([63767(6)])].

63867 R(B,C,((C * B') * x)') = R(B,C,C / x). [para(6173(a,1),63070(a,1,3)),rewrite([784(7),55621(13),56541(12),41766(9),56493(9)]),flip(a)].

64059 B' * R(B,x,C') = B * R(B',x,C). [para(63440(a,1),6173(a,1,1,1)),rewrite([62195(6),749(16),104(16),63030(16),63767(13)])].

64145 R(B,C,x) * B = B * R(B',x,C')'. [para(63768(a,2),15(a,2,2,1)),rewrite([12(10),62196(9),63253(16)]),flip(a)].

64147 x / R(x,B,C) = B * R(B',x,C'). [para(63768(a,1),104(a,1,1)),rewrite([889(7),62195(8),30(3)]),flip(a)].

64150 (R(x,B,C) / x) * B = R(B',x,C')'. [para(63768(a,2),49(a,1,1)),rewrite([62196(14)])].

64163 (x / R(x,B,C)) * B = R(B',x,C)'. [para(63768(a,2),2420(a,1,1,1)),rewrite([104(5),300(15)])].

64171 B * (B * R(B',x,C')) = R(B,x,C). [para(63768(a,2),29750(a,2,2,1)),rewrite([749(6),232(10),293(8),62195(9),30(4),104(15),63379(15)])].

64211 R(B,x,C) * B = B * R(B',x,C)'. [back_rewrite(63543),rewrite([64163(7)]),flip(a)].

64238 B * (B * R(B,x,C)') = R(B,C,B * x). [para(141(a,1),63784(a,1,2,2)),rewrite([30(5),30(13)])].

64256 (B * R(B',x,C')) * R(x,B,C) = x. [para(63794(a,1),10(a,1,2)),rewrite([889(7),62195(8),30(3)])].

64273 R(R(B,C,x),x,B') = R(B,C,x). [para(63794(a,1),54262(a,1,1,1)),rewrite([55472(6),142(13),49(14),62195(13),64059(14),63784(14)])].

64276 B * R(B,C,x) = R(B * B,C',x). [back_rewrite(55818),rewrite([64273(7)])].

64488 B' * R(B,x,C) = B * R(B',x,C'). [para(52519(a,1),6313(a,1,1)),rewrite([62195(6),64059(7),889(7),62195(8),30(3),30(14),30(22),52516(21)

,3(14)]),flip(a)].

64958 R(B * C,x,C') * B' = R(C,B * x,B). [para(61917(a,1),22987(a,1,1)),flip(a)].

64963 R(C,B * x,B * C) = R(C,B * x,B). [para(61917(a,1),23055(a,1,1)),rewrite([59807(7),56064(15),64958(16)])].

64968 R(R(C,B * x,B),B,C * (C * x)) = C. [para(3365(a,1),61917(a,1,1,1)),rewrite([56064(10),56066(8),64958(9)])].

64978 R(R(C,B * x,B),B,R(x,B,C)) = C. [back_rewrite(59816),rewrite([64963(7)])].

65025 R(R(C,(B * C) * x,B),B,x) = C. [para(47631(a,1),64978(a,1,3)),rewrite([39765(7),39762(7),39708(9),48343(9)])].

65034 R(C,R(x,B,C'),B) = R(C,x,B). [para(65025(a,1),23049(a,1,1)),rewrite([246(11),293(8),39686(11),51540(12)]),flip(a)].

65045 R(C,x,B * C) = R(C,x,B). [para(39535(a,1),65034(a,1,2)),rewrite([59797(6),65034(12)])].

65063 R(C,R(x,B,C),B) = R(C,x,B). [back_rewrite(59797),rewrite([65045(11)])].

65293 R(x,B,C') * x' = x * R(x',B,C). [para(62198(a,1),34(a,1,2)),rewrite([30(7)]),flip(a)].

65295 R(x',B,C) * x = x' * R(x,B,C'). [para(62198(a,1),231(a,1,1)),rewrite([30(8),65293(12),195(13),62196(12),41658(12),30(8)])].

65305 B' * R(B * C,x,C) = R(C,x,B'). [para(62236(a,1),7(a,1,1))].

65327 R(R(x,B,y)',(x * B) * y,B) = x'. [para(6459(a,1),47936(a,1,1,2)),rewrite([54384(7),34(8),34(14)])].

65330 R(C,B,R(x,B,C')) = R(C,B,x * C). [para(32(a,1),62267(a,1,3,1,1)),rewrite([142(7),39260(5),41658(7),41658(8),30(4)])].

65336 R(C,B,C' * (C' * x)) = R(C,B,x * C). [para(49254(a,1),62270(a,1,3)),rewrite([39260(5),65330(7),40055(13),36039(13),62270(14)]),flip(a)

].

65338 R(C,B,C' * (x * C')) = R(C,B,x * C). [para(5373(a,2),62270(a,2,3)),rewrite([2277(6),62270(9),1659(20),65336(18)])].

65399 R(C,B,C * (C * (C * x))) = R(C,B,x). [para(62379(a,1),47659(a,1,1)),rewrite([39783(11),65330(11),16(8,R)])].

65570 R(B,C,x)' * (B * B) = R(B',x,C)'. [para(63011(a,1),2143(a,1,1)),rewrite([11197(10),64163(14),12478(18)])].

66395 R(B,x,C)' * (B * B) = R(B',x,C')'. [para(63380(a,1),2143(a,1,1)),rewrite([11197(10),64150(14),12478(19)])].

66586 (x / R(x,B,C')) * B = R(B',x,C')'. [para(63689(a,1),6610(a,1,1)),rewrite([63689(14),256(8),64145(7),10(11),63021(20)]),flip(a)].

66621 R(x,B,C) / x = x / R(x,B,C'). [para(63769(a,2),63768(a,2))].

66643 R(x,B,C') / x = x / R(x,B,C). [para(66621(a,1),104(a,1,1)),rewrite([104(6)])].

66653 (x / R(x,B,C)) * x = R(x,B,C'). [para(66643(a,1),7(a,1,1))].

66682 R(R(B,C',x),x,B') = R(B,x,C). [para(66653(a,1),54262(a,1,1,1)),rewrite([52466(7),64163(17),142(13),30(12)])].

66684 B * R(B,x,C) = R(B * B,C,x). [back_rewrite(60018),rewrite([66682(8)])].

66779 B' * R(B * B,C,x) = R(B,x,C). [para(66684(a,1),10(a,1,2))].

66947 x / R(x,B,C) = B * R(B',C,x). [para(47631(a,1),64147(a,1,2)),rewrite([39765(5),66643(5),39765(12),61651(14)])].

66959 (x / R(x,B,C)) / R(B',C,x) = B. [para(66947(a,2),6(a,1,1))].

66960 (B * R(B',C,x)) * R(x,B,C) = x. [para(66947(a,1),7(a,1,1))].

66961 B * (B * R(B',C,x)) = R(B,x,C). [para(66947(a,2),12(a,2,2)),rewrite([12(8),63379(14)])].

66962 R(B',C,x) / (x / R(x,B,C)) = B'. [para(66947(a,2),32(a,1,2))].

66971 B * (R(B',C,x) * B') = R(B,C,x)'. [para(66947(a,2),232(a,1,1)),rewrite([63011(7),293(11)]),flip(a)].

66988 R(B,x,C) * R(B',C,x)' = B * B. [para(66947(a,2),2421(a,1,1,2)),rewrite([63379(6),2777(22)])].

67034 R(B',C,x) * B = B' * R(B',x,C)'. [para(66959(a,1),6610(a,2,2)),rewrite([66962(9),66962(15),256(9),64163(8)]),flip(a)].

67044 B * (B * R(B,C,x)') = R(B,C',B * x). [para(124(a,1),66961(a,1,2,2)),rewrite([16(7,R),784(8),33788(9),55431(8),16(13,R),784(14),56288(1

6),54123(15),56700(16)])].

67045 R(B',C,x)' * B' = B * R(B',x,C). [para(66961(a,1),2420(a,1,1,1)),rewrite([889(18),1065(20),62195(6),64059(7),889(13)]),flip(a)].

67087 R(B,R(B',x,C'),R(x,B,C)) = B. [para(64256(a,1),18(a,1,1)),rewrite([56720(9),32(4),30(3)]),flip(a)].

67103 R(B,R(B',C,x),x) = B. [para(47631(a,1),67087(a,1,3)),rewrite([39765(8),61651(10)])].

67124 R(B,R(B,C,x)',B * x) = B. [para(56579(a,1),67103(a,1,2))].

67192 R(B,R(B,C,x)',R(B * x,B,C')) = B. [para(39762(a,1),67124(a,1,3)),rewrite([56493(8)])].

67447 R(R(C,B * (x * (C' * C')),B),B,x) = C. [para(5028(a,1),64968(a,1,3,2)),rewrite([1659(17)])].

67577 R(C,B,C * (x * (C * C))) = R(C,B,x). [para(70(a,1),65330(a,2,3)),rewrite([65330(11),16(8,R),65399(9)]),flip(a)].

67980 R(B,C',x)' * (B * B) = R(B',C,x)'. [para(66988(a,1),53037(a,1,2))].

68103 R(C,B,x * (C' * C')) = R(C,B,C * x). [para(82(a,1),67577(a,1,3,2)),rewrite([172(7),57114(12),43633(9),2277(7),172(11)]),flip(a)].

68105 R(C,B,x * (C * (C * C))) = R(C,B,x). [para(6130(a,1),67577(a,1,3))].

68207 R(C,B,R(B,C,x)) = R(C,B,R(B,x,C')). [para(55942(a,1),68105(a,1,3)),rewrite([68105(13)]),flip(a)].

68496 R(B,x / y,C) = R(B,C',x / y). [para(8522(a,1),54123(a,1,2)),rewrite([8522(14)])].

68498 R(B,R(x,y,z),C) = R(B,C',R(x,y,z)). [para(18(a,1),68496(a,1,2)),rewrite([18(11)])].

68806 ((x * y) / z) * x' = x * (y / (x * z)). [para(9(a,1),9203(a,1,2,2)),rewrite([3(4)]),flip(a)].

69136 R(C,R(x,B,C),C * B') = R(C,x,B'). [para(39252(a,1),97(a,1,2)),rewrite([16(5,R),35139(5),39252(10),16(4,R),70(7),92(13),59763(6)]),flip

(a)].

69200 (B * (B * (C / x))) * (x * B') = B * C. [para(39985(a,1),45820(a,1,1,2)),rewrite([39741(16)])].

69820 B' * R(B * x,B,y) = R(x,B,y * B'). [para(48025(a,1),10(a,1,2))].

69983 R(R(C,B,C * x),B * x,C) = R(C,B,x). [para(11173(a,1),4066(a,2,2,2)),rewrite([122(8),62251(7),122(12),33905(11),56065(13),56065(11),16(

18,R),3710(20),62384(18)])].

70139 ((B * x) * y) / (y * (x * y)) = B * y'. [para(50385(a,1),32(a,1,2)),rewrite([784(10)])].

70533 x * R(B,x',x * C) = R(x * B,B,C). [para(11964(a,1),8823(a,2,2,2)),rewrite([82(7),294(6),1511(5),35803(7),16(12,R),50321(14)]),flip(a)]

.

70548 ((x * C) * B) / (C * x) = x * (B * x'). [para(53968(a,1),9211(a,1,1)),rewrite([10(16),232(13),28631(11),10(14)])].

70549 x' * R(x * B,B,C) = R(B,x',x * C). [para(53968(a,1),10466(a,2,2,2)),rewrite([234(12),1699(8),698(11),10(9),50321(9),43793(13)]),flip(a

)].

70855 R(x,y * (x * C),C) = R(x,y * x,C). [para(6466(a,1),56057(a,2,1)),rewrite([10(13),10(9),101(8),30(10)]),flip(a)].

70861 R(x,R(y,x,C) * x,C) = R(x,y * x,C). [para(78(a,1),70855(a,1,2)),rewrite([16(3,R),56065(5)]),flip(a)].

71842 R(x,B,y * B) / R(B' * x,B,y) = B. [para(60935(a,1),6(a,1,1))].

72109 x * (R(x,y,C')' * x) = R(x,y,C). [para(62195(a,1),32(a,1,2)),rewrite([6180(6),30(10)])].

72128 R(x,y,C')' * x = x' * R(x,y,C). [para(72109(a,1),10(a,1,2)),flip(a)].

72130 R(x,y,C') * x' = x * R(x,y,C)'. [para(72109(a,1),29750(a,2,2,1)),rewrite([72128(5),6180(5),62195(4),34(6)])].

72970 R(B',C,x) * B' = B' * R(B,C,x)'. [para(66971(a,1),10(a,1,2)),flip(a)].

73440 (C' * (x * y)) * x' = x * (y / (C * x)). [para(16(a,2),68806(a,2,2,2)),rewrite([113(3)])].

73629 R(C,R(x,B,C'),B') = R(C,x,C * B'). [para(47631(a,1),69136(a,1,2)),rewrite([39765(12)]),flip(a)].

73819 R(R(C,B,x * C),B * x,C) = R(C,B,x). [para(16(a,1),69983(a,1,1,3))].

73883 R(R(B,x,y) / y,y,x * y) = B * y'. [para(70139(a,1),2104(a,2)),rewrite([18(5)])].

73897 x * (x * ((x' * C) * B)) = C * (x * B). [para(46732(a,1),18273(a,1,2,2,2,2)),rewrite([4120(11),63(7)]),flip(a)].

73978 R(x * B,B,C) / R(B,x',x * C) = x. [para(70533(a,1),6(a,1,1))].

73979 x * R(B,x',C * x) = R(x * B,B,C). [para(16(a,2),70533(a,1,2,3))].

73981 x * R(x' * B,B,C) = R(B,x,x' * C). [para(70533(a,1),34(a,1,2)),rewrite([30(10)])].

73991 (C' * x) * (B * (C / x)) = x * (B * x'). [para(7(a,1),70548(a,1,1,1)),rewrite([113(5),34(7),28631(3),113(6),113(10),158(12)]),flip(a)]

.

73992 (C * x) * (B * (C' / x)) = x * (B * x'). [para(16(a,2),70548(a,1,1,1)),rewrite([28631(7),1724(6)])].

74120 B * R(C,B,x * C) = B * R(C,B,x). [para(73(a,1),70861(a,2,2)),rewrite([56067(10),78(12),49(7),16(9,R),56065(11),49082(9),54476(7),49082

(16),54476(14)]),flip(a)].

74121 R(B * C,R(x,B,C),C) = R(B * C,x,C). [para(35827(a,1),70861(a,2,2)),rewrite([56067(14),35842(12),247(13),16598(12),34415(12),36039(11),

10(8)])].

74131 R(C,B,x * C) = R(C,B,x). [para(74120(a,1),10(a,1,2)),rewrite([10(8)]),flip(a)].

74138 R(C,B,C' * x) = R(C,B,x). [back_rewrite(73819),rewrite([74131(5),62271(7)])].

74145 R(C,B,x * C') = R(C,B,x). [back_rewrite(65338),rewrite([74138(9),74131(11)])].

74158 R(C,B,R(x,B,C)) = R(C,B,x). [back_rewrite(62270),rewrite([74138(12)])].

74162 R(C,B,x * (x * C)) = R(C,B,x * x). [para(12(a,1),74131(a,1,3))].

74163 R(C,B,C * x) = R(C,B,x). [para(16(a,2),74131(a,1,3))].

74165 R(R(C,B,x),B * (x * C),B) = C. [para(74131(a,1),22987(a,1,1))].

74167 R(C,B,x * (C' * x)) = R(C,B,x * x). [para(1684(a,1),74131(a,1,3)),rewrite([16(8,R),9(8),3(6),74138(7),74138(14)]),flip(a)].

74184 R(C,B,x * (C' * C')) = R(C,B,x). [back_rewrite(68103),rewrite([74163(14)])].

74215 R(C',B,C' * x) = R(C',B,x). [para(74138(a,1),62276(a,1,1)),rewrite([62276(4)]),flip(a)].

74225 R(C',B,x * C') = R(C',B,x). [para(74145(a,1),62276(a,1,1)),rewrite([62276(4)]),flip(a)].

74235 R(R(C',B,x),C * (B * x),B) = C'. [para(74158(a,1),65327(a,1,1,1)),rewrite([62276(4),16(7),35056(11)])].

74256 R(R(C,x,B'),B',C * (B * x)) = C. [para(54235(a,1),74165(a,1,1)),rewrite([16(13,R),1527(14),16(8,R),50834(11),16(10,R)])].

74313 R(R(C',B,B' * x),C * x,B) = C'. [para(34(a,1),74235(a,1,2,2))].

74336 R(C,C * x,C * B') = R(C,x,B'). [para(74256(a,1),54261(a,1,1)),rewrite([39783(8),73629(10)])].

74372 R(C,x,C * B') = R(C,x,B'). [para(34(a,1),74336(a,1,2)),rewrite([141(13),59733(12)])].

74376 R(C',x,C * B')' = R(C,x,B'). [para(3468(a,1),74336(a,2)),rewrite([34(9),141(9),141(18),59749(16),59733(14)])].

74377 R(C,R(x,B,C'),B') = R(C,x,B'). [back_rewrite(73629),rewrite([74372(14)])].

74386 R(C',x,C * B') = R(C',x,B'). [para(74376(a,1),30(a,1,1)),rewrite([59717(5)]),flip(a)].

74387 R(C',R(x,B,C'),B') = R(C',x,B'). [para(74377(a,1),59717(a,1,1)),rewrite([59717(5)]),flip(a)].

74398 R(C',B,B' * x) * (C * x) = R(x,B,C). [para(74386(a,1),5317(a,1,1)),rewrite([39194(9),25535(9),39539(9),74387(11),47800(7),39194(19),25

535(19),39539(19),39492(19),39337(19),35210(20),34(15)])].

75299 R(B * x',x,R(x,B,C)) = B * x'. [para(63780(a,1),73883(a,1,1,1)),rewrite([749(2),63794(10)])].

75395 R(x,R(x,B,C),B') = x. [para(75299(a,1),54397(a,1,1,1)),rewrite([889(4),30(2),82(5),259(4)]),flip(a)].

75404 R(x,B,R(B' * (x * B'),B,C)) = x. [para(75395(a,1),54235(a,2)),rewrite([35846(9),34855(10)])].

75546 R(x,R(x * B',B,C),B) = x. [para(75404(a,1),22987(a,1,1)),rewrite([34420(11),34(8)])].

75551 x * R(x,B,C) = R(x * x,B,C'). [para(75546(a,1),78(a,1,1)),rewrite([54281(8),82(5),259(4),39197(4),39739(13)])].

75553 x' * R(x * x,B,C') = R(x,B,C). [para(75546(a,1),2036(a,1,1,1)),rewrite([39739(10),54281(15),82(12),259(11),39197(11)])].

75673 x * R(x' * x',B,C') = R(x',B,C). [para(75551(a,1),34(a,1,2))].

75888 x' * (C * (x * B)) = x * ((x' * C) * B). [para(73897(a,1),10(a,1,2))].

75890 x' * ((x * C) * B) = x * (C * (x' * B)). [para(73897(a,1),34(a,1,2)),rewrite([30(9)]),flip(a)].

76040 R(x * B,B,C) / R(B,x',C * x) = x. [para(16(a,2),73978(a,1,2,3))].

76044 R(B,x',C * x) / R(x * B,B,C) = x'. [para(73979(a,1),32(a,1,2))].

76108 R(B * C,B,x * C) = R(B * C,B,x). [para(33764(a,1),74121(a,1,2)),rewrite([49082(9),56065(16),49082(14)])].

76109 R(B * C,(B * C) * x,C) = R(B * C,B,x). [para(34454(a,1),74121(a,1,2)),rewrite([49082(18),76108(16)])].

76113 R(C' * R(B * C,x,C),C,R(x,B,C)) = B. [para(74121(a,1),54127(a,1,1,2))].

76117 R(B * C,B,C' * x) = R(B * C,B,x). [para(34644(a,1),74121(a,1,2)),rewrite([56033(10),49082(7),49082(15)]),flip(a)].

76119 R(B * C,B,C * x) = R(B * C,B,x). [para(16(a,2),76108(a,1,3))].

76160 R(R(C',B,B' * (x * C')),x,B) = C'. [para(1659(a,1),74313(a,1,2))].

78147 (x * (B * x')) / (C / x) = (C' * x) * B. [para(22323(a,1),2051(a,2,2,1)),rewrite([226(11),302(10),73991(8),226(18),302(17)])].

78782 R((C * x) * B,C / x,C) = x * (B * C). [para(56219(a,1),22863(a,2)),rewrite([104(4),1699(3),73992(8),16(6,R),16(11,R),9339(12),78147(9)

,39539(8),39692(8),39687(8),104(8),1699(7)]),flip(a)].

78797 R(x * B,x',C) = R(x * B,B,C). [para(34(a,1),78782(a,1,1,1)),rewrite([6180(7),56065(9),56067(7),247(12),35837(12)])].

78801 R(x' * B,B,C) = R(x' * B,x,C). [para(30(a,1),78797(a,1,2)),flip(a)].

79141 (B * R(B',C,x)) * x' = R(x',B,C). [para(66960(a,1),29801(a,1,1)),rewrite([66960(10),75551(4),41658(6),172(2),75673(8),66960(20)]),flip

(a)].

79149 R(R(B,x,C),x' * B,C) = B. [para(79141(a,1),3565(a,1,1,2,1)),rewrite([78(9),16(6,R),6(13),66961(9)]),flip(a)].

79175 R(B,C,x') = R(B,x,C). [para(79149(a,1),56055(a,1,1)),rewrite([56770(7),62988(6)])].

79183 R(B,x',C) = R(B,C,x). [para(30(a,1),79175(a,1,3)),flip(a)].

79185 R(B,C,C / x) = R(B,x,C). [para(158(a,1),79175(a,1,3)),rewrite([56033(11)])].

79190 R(B',x,C)' = R(B,C,x'). [para(1071(a,1),79175(a,1,3)),rewrite([62988(6),141(10)]),flip(a)].

79193 R(B,C,x')' = R(B,x,C)'. [para(79175(a,1),138(a,2,1)),rewrite([138(9)])].

79202 R(B,C',x) = R(B,C,x'). [para(41403(a,1),79175(a,1,3)),rewrite([56502(7),68498(10),55094(11)]),flip(a)].

79358 R(B,x,C) / (x' / R(x',B,C')) = B. [para(79175(a,1),63021(a,1,1))].

79428 R(B * B,C',x') = R(B * B,C,x). [para(79175(a,1),64276(a,1,2)),rewrite([66684(5)]),flip(a)].

79542 (x' / R(x',B,C')) / R(B,x,C) = B'. [para(79175(a,1),63689(a,1,2))].

79553 B * R(B',x',C) = B * R(B',x,C'). [para(79175(a,1),63767(a,1,2)),rewrite([64488(6)]),flip(a)].

79853 R(B,C,B * x) = R(B,C,x). [para(79175(a,2),64238(a,1,2,2,1)),rewrite([67044(9),79202(7),889(6),30(4),63046(6)]),flip(a)].

79909 R(B',x,C')' = R(B,C,x). [para(79175(a,1),65570(a,1,1,1)),rewrite([66395(8),79190(12),30(10)])].

80145 R(B,C,((C * B') * x)') = R(B,x,C). [back_rewrite(63867),rewrite([79185(14)])].

80148 R(B,C,((B * C) * x)') = R(B,x,C). [back_rewrite(63222),rewrite([79185(13)])].

80164 R(B,C,R(C' / x,x,B)) = R(B,x,C). [back_rewrite(56556),rewrite([79185(13)])].

80224 R(B',C,x) * B = B * R(B',x,C'). [back_rewrite(67034),rewrite([79190(13),63767(13),79553(13)])].

80229 R(B,C,x)' * (B * B) = R(B,C,x'). [back_rewrite(65570),rewrite([79190(13)])].

80232 R(B,x,C) * B = R(B * B,C,x). [back_rewrite(64211),rewrite([79190(11),64276(11),79428(12)])].

80349 R(B',C,x)' = R(B,C,x). [back_rewrite(67980),rewrite([79202(4),80229(9),30(4)]),flip(a)].

80388 R(B,x * y,C) = R(B,C,(x * y)'). [back_rewrite(54123),rewrite([79202(9)])].

80423 (x * R(B,C,y')) / R(B,y,C) = x. [back_rewrite(52828),rewrite([79202(4)])].

80502 R(B,C,(B * C) * x) = R(B,C,x). [back_rewrite(56568),rewrite([79853(12)])].

80511 (x / R(x,B,C')) * B = R(B,C,x). [back_rewrite(66586),rewrite([79909(13)])].

80538 R(B,C,x) * (B' * x) = R(x,B,C). [back_rewrite(55856),rewrite([79909(6)])].

80541 R(B,C,B' * x) = R(B,C,x). [back_rewrite(55497),rewrite([79909(12)])].

80569 B * R(B,x,C)' = B * R(B',x,C). [back_rewrite(67045),rewrite([80349(5),56482(6)])].

80589 R(B,C,(B' * C') * x) = R(B,C,x). [back_rewrite(55441),rewrite([80349(14)])].

80621 R(B,C,x) * B' = B * R(B',x,C). [back_rewrite(56482),rewrite([80569(12)])].

80646 R(B,x',C) = R(B,x,C'). [para(79183(a,2),55445(a,1))].

80654 R(B,C,x)' = R(B',C,x). [para(79183(a,2),4657(a,1,1)),rewrite([1828(5),293(5),1511(6),80646(10),56770(10),80589(9),1828(9),293(9),1511(

10),44469(12),55437(12)])].

80655 R(B,x,C')' = R(B',C,x). [para(79183(a,1),60761(a,2,1)),rewrite([60761(8),80646(4),80654(9)])].

80992 R(B,R(B',C,x),R(B * x,B,C')) = B. [para(79183(a,2),67192(a,1,2,1)),rewrite([80646(5),80655(6)])].

81202 R(B,x,C)' = R(B',C,x'). [back_rewrite(79193),rewrite([80654(5)]),flip(a)].

81213 R(B',C,x) * B' = B' * R(B',C,x). [back_rewrite(72970),rewrite([80654(13)])].

81529 R(B',C,x') = R(B',x,C). [para(79202(a,1),4657(a,1,1)),rewrite([1538(7),293(5),80145(9),81202(4),1538(12),293(10),44481(13),55288(12)])

].

81582 R(B,C,x / R(x,B,C)) = R(B,C,R(B,x,C)). [para(63379(a,1),79853(a,1,3)),flip(a)].

81648 R(B,C,R(B',C,x)) = R(B,C,R(B,x,C)). [para(66947(a,2),79853(a,1,3)),rewrite([81582(7)]),flip(a)].

82073 R(B',x,C') * B = B * R(B',x,C'). [para(79190(a,1),72130(a,2,2)),rewrite([30(8),63767(14),79553(14)])].

82374 R(B',x',C) = R(B',C,x). [para(30(a,1),81529(a,1,3)),flip(a)].

82382 R(B',C',x) = R(B',C,x'). [para(81529(a,2),60745(a,2))].

82672 R(B',x',C) = R(B',x,C'). [para(41403(a,1),82374(a,1,2)),rewrite([61405(8),56636(12)])].

83016 C * (x * R(y,x,C)) = x * (y * C). [para(23319(a,2),13604(a,1,1)),rewrite([246(11),113(7),73440(10),101(7),203(13),10(12)])].

84018 C' * (x * (y * C)) = x * R(y,x,C). [para(83016(a,1),10(a,1,2))].

84026 x * (C * R(B,C,x)) = C * (x * B). [para(55447(a,1),83016(a,1,2,2)),rewrite([16(9,R)]),flip(a)].

84029 (x * B') * (C * R(B,C,x)) = C * x. [para(63153(a,1),83016(a,1,2,2)),rewrite([82(6),259(5),16(10,R)]),flip(a)].

84248 x * ((x' * C) * B) = C * R(B,C,x). [para(84026(a,1),10(a,1,2)),rewrite([75888(6)])].

84250 x * (C * (x' * B)) = C * R(B,C,x'). [para(84026(a,1),34(a,1,2))].

84254 R(B,x,C * x') = R(B,C,x'). [para(84026(a,1),4687(a,1,2,2)),rewrite([63046(8),82(13),259(12),122(10),113(8),10(9),63046(17),84029(16)])

,flip(a)].

84270 x' * ((x * C) * B) = C * R(B,C,x'). [back_rewrite(75890),rewrite([84250(12)])].

84284 R(B,x,x' * C) = R(B,C,x'). [para(16(a,1),84254(a,1,3))].

84285 R(B,x',C * x) = R(B,C,x). [para(30(a,1),84254(a,1,3,2)),rewrite([30(9)])].

84290 x * R(x' * B,B,C) = R(B,C,x'). [back_rewrite(73981),rewrite([84284(12)])].

84292 R(B,C,x) / R(x * B,B,C) = x'. [back_rewrite(76044),rewrite([84285(5)])].

84293 R(x * B,B,C) / R(B,C,x) = x. [back_rewrite(76040),rewrite([84285(10)])].

84295 R(x * B,B,C) = x * R(B,C,x). [back_rewrite(73979),rewrite([84285(5)]),flip(a)].

84296 R(B,x',x * C) = R(B,C,x). [para(16(a,1),84285(a,1,3))].

84302 x' * R(x * B,B,C) = R(B,C,x). [back_rewrite(70549),rewrite([84296(12)])].

84320 R(x,B,C) / R(B,C,x) = x * B'. [para(7(a,1),84293(a,1,1,1)),rewrite([293(7),63046(9),293(9)])].

84333 (x * B') * R(B,C,x) = R(x,B,C). [para(7(a,1),84295(a,1,1)),rewrite([293(5),293(10),63046(12)]),flip(a)].

84389 R(x',B,C') * (x * B) = R(B,C,x). [para(84295(a,2),41992(a,1,2)),rewrite([54281(11),43654(12),56054(14),56493(15)])].

84429 x * R(B,C,x) = R(x * B,x',C). [para(84295(a,1),78797(a,2)),flip(a)].

84582 R(B,C,x) / R(x,B,C) = B * x'. [para(7(a,1),84292(a,1,2,1)),rewrite([293(4),63046(6),293(9),784(11)])].

84591 R(B,C,x * x) = R(B,C,x'). [para(423(a,1),84302(a,1,2,1)),rewrite([1824(6),6248(6),1665(20),36039(18),33146(15),16(8),34869(13),12(11),

53968(10),84270(8),10(9),55613(12)]),flip(a)].

84959 R(B,x * B',R(B,C,x)) = B. [para(84320(a,1),61184(a,1,2)),rewrite([80654(13),56675(20),80992(20)])].

84984 R(B,C * x,R(B,C,x)) = B. [para(3762(a,1),84959(a,1,3)),rewrite([85(8),260(7),58268(10),63062(11)])].

85208 R(B,C * (B' * x),R(B,C,x)) = B. [para(80541(a,1),84984(a,1,3))].

87436 R(B,x,C) / R(x',B,C) = B * x. [para(79175(a,1),84582(a,1,1)),rewrite([30(11)])].

88180 R(B',x * B',R(B,C,x))' = B. [para(1666(a,2),85208(a,1,2,2)),rewrite([34(12),63150(16),141(11)])].

88966 x * (B * R(B',x,C)) = R(x,B,C). [para(88180(a,1),2036(a,1,1)),rewrite([13(11),63767(9),34(12),84333(14)])].

89235 x * (x / R(x,B,C')) = R(x,B,C). [para(63769(a,2),88966(a,1,2))].

89369 x / R(x,B,C') = x' * R(x,B,C). [para(89235(a,1),10(a,1,2)),flip(a)].

89390 (x' * R(x,B,C)) * B = R(B,C,x). [back_rewrite(80511),rewrite([89369(5)])].

89394 (x * R(x',B,C)) / R(B,x,C) = B'. [back_rewrite(79542),rewrite([89369(7),30(2)])].

89398 R(B,x,C) / (x * R(x',B,C)) = B. [back_rewrite(79358),rewrite([89369(10),30(5)])].

89424 R(x,B,C) / x = x' * R(x,B,C). [back_rewrite(66621),rewrite([89369(9)])].

89563 R(x',R(x,B,C),B) = x'. [para(89390(a,1),18(a,1,1)),rewrite([54281(8),39197(9),84292(9)]),flip(a)].

89587 R(B,x',R(x * B,B,C)) = B. [para(89563(a,1),3782(a,1,2,1,1)),rewrite([22(12),3(3),89563(8),54281(8),39197(9)]),flip(a)].

89609 R(B,R(x',B,C'),x * B) = B. [para(41658(a,1),89587(a,1,2)),rewrite([54281(12),43654(13),56054(15)])].

89676 R(x,B,R(B,C,x))' = x'. [para(89609(a,1),73883(a,1,1,1)),rewrite([32(4),84389(11),142(7),824(10),34(12)])].

89680 R(x,B,R(B,C,x)) = x. [para(89676(a,1),30(a,1,1)),rewrite([30(2)]),flip(a)].

89711 R(x * B,R(B,C,x),B') = x * B. [para(89680(a,1),54281(a,1,1)),flip(a)].

89858 B * (x * R(x',B,C)) = R(B,x,C). [para(89398(a,1),7(a,1,1))].

89862 R(B,x,R(x',B,C)) = B. [para(89398(a,1),2104(a,2)),rewrite([87436(8),6(3)])].

89864 (x * R(x',B,C)) * B = R(B,x,C). [para(89398(a,1),6610(a,2,2)),rewrite([89394(9),89394(14),256(8),80232(7),66779(8)]),flip(a)].

89868 R(B,x',R(x,B,C)) = B. [para(30(a,1),89862(a,1,3,1))].

90077 (x' * R(x,B,C))' = x / R(x,B,C). [para(89424(a,1),104(a,1,1))].

90115 R(x,R(B,C,x),B') = x. [para(7(a,1),89711(a,1,1)),rewrite([293(4),63046(6),293(8),82(11),259(10)])].

90123 R(x,R(x' * B,x,C),B') = x. [para(90115(a,1),141(a,2,1)),rewrite([84429(6),30(5),30(10)])].

90381 R(x,R(x' * B,B,C),B') = x. [para(78801(a,2),90123(a,1,2))].

90477 R(x,R(x',B,C),R(x,B,C)) = x. [para(90381(a,1),2467(a,1,1)),rewrite([35846(9),85(6),260(5),35846(13),85(10),260(9),41403(9),30(6),84290

(15),80621(15),82672(14),35846(24),85(21),260(20),41403(20),30(17),64256(19)])].

90483 (x * R(x',B,C)) * R(x,B,C) = x. [para(90477(a,1),18(a,2)),rewrite([41601(17),23(11)])].

91038 x / R(x,B,C) = x * R(x',B,C). [para(90483(a,1),6(a,1,1))].

91054 (x' * R(x,B,C))' = x * R(x',B,C). [back_rewrite(90077),rewrite([91038(10)])].

92301 x * R(B * C,x,C) = (x * C) * B. [para(9956(a,1),84018(a,1,2,2)),rewrite([46726(9)]),flip(a)].

92303 (x * R(y,x,C)) / y = R(x,y,C'). [para(84018(a,1),1672(a,1,1)),rewrite([1511(8,R),63(8),56066(9)])].

92320 C * R(B,C,x) = R(B * C,x',C). [para(92301(a,1),34(a,1,2)),rewrite([84248(6)])].

92324 R(B * C,C',x * B) = R(B * C,x,C). [para(92301(a,1),822(a,1,2)),rewrite([16(8,R),31535(10),11967(11),11955(10),73(9),10(10),84270(6),92

320(6),30(5),56717(12)]),flip(a)].

92356 R(B * C,x * B,C) = R(B * C,x,C). [back_rewrite(56717),rewrite([92324(15)])].

92507 R(B * C,x',C) / R(B,C,x) = C. [para(92320(a,1),6(a,1,1))].

92514 C * R(B,x,C) = R(B * C,x,C). [para(40108(a,2),92320(a,2,2)),rewrite([80164(9),56208(15),74121(13)])].

92518 R(B * C,x * x,C) = R(B * C,x',C). [para(18492(a,1),92320(a,1,2)),rewrite([55562(9),84591(7),30(5),92320(5),6360(15),30(11),30(13),5622

6(15)]),flip(a)].

92519 R(B * C,B,x) = R(B * C,x,C). [para(80148(a,1),92320(a,1,2)),rewrite([92514(5),30(14),76109(14)]),flip(a)].

92520 R(B * C,x,C) / R(B,x,C) = C. [para(92320(a,1),80423(a,1,1)),rewrite([30(5)])].

92537 C' * R(B * C,x,C) = R(B,x,C). [para(92514(a,1),10(a,1,2))].

92538 C / R(B * C,x,C) = R(B',C,x'). [para(92514(a,1),109(a,1,2)),rewrite([81202(11)])].

92548 R(R(B,x,C),C,R(x,B,C)) = B. [back_rewrite(76113),rewrite([92537(8)])].

92680 R(R(B,x,C),C,x * B') = B. [para(2180(a,1),92548(a,1,3)),rewrite([293(5),80388(8),784(8),1724(6),79853(8),55568(6),79185(5),16(8,R),358

28(12),13(14),1659(12),55562(10)])].

92828 R(B * C,x,B') = R(B * C,x,C). [para(92680(a,1),49492(a,1,1,2)),rewrite([16(3),55062(9),16(11,R),92514(11)])].

92842 R(C',B,x) * R(B * C,x,C) = B. [back_rewrite(62316),rewrite([92828(10)])].

92846 R(B * C,C',x) = R(B * C,B,x). [para(92519(a,2),18(a,2)),rewrite([16(6,R),35225(6),47951(9),16(3)])].

92849 R(B * C,B,x) * x = B * (x * C). [para(92519(a,2),2035(a,1,1)),rewrite([113(6),76117(8),113(11),12145(13),1511(11),33788(13),16(13,R),3

5139(13),33764(13)])].

92852 B * R(C,B,x) = R(B * C,x,C). [para(92519(a,2),3252(a,1)),rewrite([4638(10),76119(11),76119(9),54476(7),24137(14),56065(16),56065(14),9

2356(12)])].

92853 R(B * C,B,B * x) = R(B * C,B,x). [para(92519(a,2),49082(a,1))].

92854 R(B * C,B,x * x) = R(B * C,x',C). [para(92519(a,2),3414(a,1)),rewrite([76119(8),56217(14),92518(12)])].

92865 R(C,B,x * B') = R(C,x,B'). [para(92519(a,2),65305(a,1,2)),rewrite([69820(8)])].

92871 R(B * C,B,x) * B' = R(C,B,x * B). [para(92519(a,2),62238(a,1,1))].

92873 R(B * C,x,C) / R(C,B,x) = B. [para(92519(a,1),71842(a,1,1)),rewrite([92356(7),10(11)])].

92879 x * R(B * C,B,x) = (x * C) * B. [para(92519(a,2),84018(a,2,2)),rewrite([16(7,R),1382(7),46726(9)]),flip(a)].

92885 B * R(C,x,B') = R(B * C,B,x). [back_rewrite(51401),rewrite([92846(12)])].

92892 R(B * C,B,x) / R(B,x,C) = C. [para(19360(a,1),92520(a,1,2)),rewrite([49082(9),76119(7),80388(12),889(12),1828(10),63046(14),55568(11),

79185(10)])].

92893 R(B * C,B,x') / R(B,C,x) = C. [para(21540(a,1),92520(a,1,1)),rewrite([33905(10),56065(12),56065(10),49082(8),33904(14),56065(16),56065

(14),80388(12),889(12),30(10),63046(12)])].

93042 R(C,B,x) = R(C,x,B'). [para(92852(a,1),10(a,1,2)),rewrite([65305(8)]),flip(a)].

93056 R(C,B,x * B) = R(C,B,x). [para(92852(a,1),11880(a,1,1)),rewrite([62276(9),62276(14),749(15),62260(15),92852(14),92842(15),293(7),62238

(8),62276(9),62301(14),62260(10)])].

93078 R(B * C,B,x) * B' = R(C,B,x). [back_rewrite(92871),rewrite([93056(13)])].

93094 R(B * C,x,C) * B' = R(C,B,x). [back_rewrite(62238),rewrite([93056(13)])].

93102 B * R(C * B',B,x) = R(C,B,x). [back_rewrite(25402),rewrite([93056(13)])].

93105 R(C,B,B' * x) = R(C,B,x). [para(93042(a,2),80(a,2)),rewrite([256(4),47803(7),16(5,R),39686(7),53388(7),256(11),93056(11)])].

93108 R(C,B' * x,B') = R(C,B,x). [para(93042(a,1),125(a,2)),rewrite([16(3),246(7),293(4),39686(7),53388(7),93105(6)]),flip(a)].

93110 R(R(C,B,x),x,B) = C. [para(93042(a,1),23049(a,1,1)),rewrite([93108(7)])].

93112 R(C,x',B') = R(C,B,x'). [para(93042(a,2),3201(a,1)),rewrite([74131(6),59762(11)]),flip(a)].

93113 R(C * x,B,C') = R(C,B,x) * x. [para(93042(a,2),2035(a,1,1)),rewrite([256(5),93056(5),256(8),47803(11),16(9,R),39686(11)]),flip(a)].

93118 R(C',B,B' * x) = R(C',B,x). [para(93042(a,2),2235(a,2,1)),rewrite([256(4),47803(7),16(5,R),39686(7),59759(7),256(12),93056(12),62276(1

1)])].

93120 R(C,x * B',B') = R(C,x,B'). [para(93042(a,1),48002(a,2)),rewrite([48002(6),92865(6)]),flip(a)].

93121 R(C,B,B * x) = R(C,x,B'). [para(93042(a,2),48002(a,1)),rewrite([92865(11)])].

93134 R(R(C,x,B'),(B * C) * x,B) = C. [para(93042(a,1),62261(a,1,1))].

93168 R(C,B,x) * B' = R(C * B',B,x). [para(93042(a,2),60795(a,1,1))].

93188 R(C,x * (C' * C'),B') = R(C,B,x). [para(93042(a,1),74184(a,1))].

93234 B * R(C * B',x,B') = R(C,B,x). [back_rewrite(58301),rewrite([93105(15)])].

93236 R(C * x,B,C') / x = R(C,B,x). [back_rewrite(53388),rewrite([93105(13)])].

93242 R(R(C',B,x),x,B) = C'. [back_rewrite(76160),rewrite([93118(10),74225(7)])].

93247 R(C',B,x) * (C * x) = R(x,B,C). [back_rewrite(74398),rewrite([93118(7)])].

93287 B' * R(C,B,x) = R(C * B',x,B'). [para(93110(a,1),60416(a,1,1,2)),rewrite([16(4,R)]),flip(a)].

93447 R(C,B,R(C',B,x) * x) = R(C,B,x). [para(93242(a,1),54117(a,1,1,1)),rewrite([30(3),93105(11),62260(13)])].

93528 R(R(C,B,x),x,C) = R(C,B,x). [para(93105(a,1),4058(a,2,1)),rewrite([16(4),246(8),293(5),39686(8),39692(8),34(14),93236(11),74163(5),34(

11)]),flip(a)].

93541 R(C,x / y,B') = R(C,B,x / y). [para(104(a,1),93112(a,1,2)),rewrite([104(9)])].

93561 R(C,B,R(B',C,x)) = R(C,B,R(B,x,C)). [para(66961(a,1),93121(a,1,3)),rewrite([48002(16),81213(15),93105(16)]),flip(a)].

93661 R(x,R(C,B,x),C') = x. [para(93528(a,1),92303(a,1,1,2)),rewrite([6(8)]),flip(a)].

93718 R(B,x,C) / R(B * C,B,x) = C'. [para(92892(a,1),104(a,1,1)),flip(a)].

93719 C' * R(B * C,B,x) = R(B,x,C). [para(92892(a,1),6610(a,1,1)),rewrite([92892(13),113(6),34(8),93718(17),1511(11,R)]),flip(a)].

93734 R(C * B',C,x) * B = R(C,B,x). [para(93108(a,1),18(a,2)),rewrite([9418(14),54713(15),82(10),259(9),55403(6)])].

94092 C' * R(B,x,C) = R(B * C',C',x). [para(92846(a,1),2051(a,2,2,1)),rewrite([1511(8,R),63(8),49540(6),1511(4),1511(17,R),93719(17)]),flip(

a)].

94096 R(R(C,B',B * x),x,B) = R(C,B,x). [para(92849(a,1),23148(a,1,1,1)),rewrite([16(6,R),34236(7),45892(6),45843(16),92885(14),93078(16)])].

94105 (x * R(C,B,x)) * B = C * (x * B). [para(92879(a,1),16598(a,2,2)),rewrite([92853(7),93078(8),16(12,R),34981(14),10(15)])].

94149 R(C,B,x * x) = R(C,B,x'). [para(18478(a,1),93078(a,2)),rewrite([76119(8),92854(6),93094(9),74162(10)]),flip(a)].

94171 R(C,B,x * (C' * x)) = R(C,B,x'). [back_rewrite(74167),rewrite([94149(11)])].

94255 (B * C) / R(C,B,x) = R(B,x,C'). [para(93094(a,1),51839(a,1,2)),rewrite([92538(16),66961(16),80646(11)])].

94256 R(B,x,C') * R(C,B,x) = B * C. [para(93094(a,1),69200(a,1,2)),rewrite([92538(9),66961(9),80646(4)])].

94425 R(R(C,B,x) * x,B,C) = C * x. [para(93113(a,1),22987(a,1,1)),rewrite([39797(10)])].

94540 R(B,(R(C,B,x) * x)',C * x) = B. [para(94425(a,1),89868(a,1,3))].

94569 R(C,x * (B' * C'),B') = R(C,B,x). [para(24793(a,1),93120(a,1,2)),rewrite([1511(8),141(13),59733(12),93188(20)])].

94573 R(R(C,B,x),B * (x * B'),B) = C. [para(6639(a,1),93134(a,1,2)),rewrite([16(4),35828(5),94569(10),35828(10),36014(13)])].

94623 R(C / x,x,B')' = R(C',B,x) * x. [para(39247(a,1),93247(a,2)),rewrite([74215(7),34(9)]),flip(a)].

94665 C * (R(C',B,x) * x) = R(x,B,C). [back_rewrite(40146),rewrite([94623(7)])].

94788 R(C,R(x,y,z),B') = R(C,B,R(x,y,z)). [para(18(a,1),93541(a,1,2)),rewrite([18(11)])].

94827 R(C * B',C,x) = R(C * B',B,x). [para(93734(a,1),6(a,1,1)),rewrite([293(5),93168(6)]),flip(a)].

94933 R(C * x,B,C') = x * R(C,B,x). [para(94105(a,1),6(a,1,1)),rewrite([293(6),47803(7),16(5,R),39686(7)])].

94939 R(x * R(C,B,x),B,C) = C * x. [para(94105(a,1),100(a,1,1,2)),rewrite([35828(10),11560(12),10(8),85(6),260(5)]),flip(a)].

94944 B * (x * R(C,B,x))' = (B * C') / x. [para(94105(a,1),49513(a,1,2)),rewrite([6741(8),1724(7),51251(8),39762(9),42015(9),293(11),6792(15

),784(13)]),flip(a)].

94965 R(C,x * R(C,B,x),B) = R(C,x,B). [para(94939(a,1),65063(a,1,2)),rewrite([48355(5)]),flip(a)].

95032 R(B,C,R(C,B,x)) = R(B,C,R(B,x,C)). [para(94255(a,1),61281(a,2,3)),rewrite([63373(13),80646(11),56770(11),80502(10),1828(11),293(11),15

11(12),141(17),82382(15),80655(14),80349(15),81648(13)])].

95040 R(B',C,x) * (B * C) = R(C,B,x). [para(94256(a,1),10(a,1,2)),rewrite([80655(5)])].

95184 R(B,(R(C,B,x) * x)',x * C) = B. [para(16(a,1),94540(a,1,3))].

95199 R(R(C,B,R(B,C,x')),R(B,x,C),B) = C. [para(62195(a,1),94573(a,1,2,2)),rewrite([79190(7),30(11),64171(16)])].

95240 R(C * x,B,C') / R(C,B,x) = x. [para(94933(a,2),6(a,1,1))].

95247 (C / x) * R(x,B,C') = R(C,B,x). [para(94933(a,2),185(a,1,2)),rewrite([34(7),74138(13)])].

95255 x * (C' * R(C,B,x)) = R(x,B,C'). [para(94933(a,2),2084(a,2,2)),rewrite([93661(6),39492(16),10(12)])].

95320 R(C,B,x) * x = x * R(C,B,x). [para(94933(a,1),93113(a,1)),flip(a)].

95325 R(B,(x * R(C,B,x))',x * C) = B. [back_rewrite(95184),rewrite([95320(5)])].

96299 R(C,x * (C' * C'),B) = R(C,x,B). [para(74184(a,1),94965(a,1,2,2)),rewrite([24793(11),95255(10),39492(8),65034(10),141(6),48343(5)]),fl

ip(a)].

96316 (B * C) * R(B',x,C') = R(C,B,x). [para(95040(a,1),39687(a,2)),rewrite([80224(7),39691(13)])].

96383 x / R(C,B,x) = R(C',B,x) * x. [para(94665(a,1),95240(a,1,1,1)),rewrite([56055(7),93447(8)])].

96397 C * (x' * R(x,B,C')) = R(C,B,x). [para(4273(a,1),95247(a,1,1)),rewrite([13(13),39692(11),1659(7),74145(14)])].

96401 R(C / x,B,C) * x = R(C,B,x). [para(41509(a,1),95247(a,1,1)),rewrite([56055(12),74158(12)])].

96402 C * (x' * R(x,B,C)) = R(C,B,x'). [para(3043(a,1),95247(a,1,2)),rewrite([6240(6),70(16),39692(14),1698(10),12(10),75553(9),94171(14)])]

.

96745 R(x',R(x,B,C'),C)' = x. [para(96401(a,1),3187(a,1,1,2)),rewrite([74163(5),109(9),65295(10),96397(12),6(8),109(4),65295(5),141(8)]),fli

p(a)].

96766 R(x',R(x,B,C'),C) = x'. [para(96745(a,1),30(a,1,1)),flip(a)].

96771 R(x,R(x',B,C'),C) = x. [para(30(a,1),96766(a,1,1)),rewrite([30(9)])].

96781 R(R(x,B,C),x',C) = R(x,B,C). [para(41403(a,1),96771(a,1,2,1)),rewrite([56055(11)])].

97193 R(x',R(x,B,C),C') = x'. [para(96781(a,1),92303(a,1,1,2)),rewrite([6(9)]),flip(a)].

97197 R(x',R(x,B,C),C) = x'. [para(97193(a,1),56054(a,1,1))].

97243 R(C / x,R(x,B,C),C) = C / x. [para(158(a,1),97197(a,1,1)),rewrite([56316(10),158(11)])].

97328 R(C / x,R(x,B,C),C') = C / x. [para(97243(a,1),56055(a,1,1))].

97443 R(B,C,x * R(x',B,C)) = B. [para(95325(a,1),4058(a,2,1)),rewrite([94944(8),233(9),16(9,R),35803(9),84302(8),92320(5),29766(15),96383(12

),16(15,R),94665(15),96402(13),92873(11),29766(10),96383(7),16(10,R),94665(10),80388(9),91054(9)]),flip(a)].

97461 R(R(B,x,C),B,C) = R(B,x,C). [para(97443(a,1),49556(a,1,1)),rewrite([89858(7),1511(8),33788(15),89858(10)]),flip(a)].

97462 R(B,C,R(B,x,C)) = B. [para(97443(a,1),62988(a,2)),rewrite([89864(9)])].

97482 R(B,C,R(C,B,x)) = B. [back_rewrite(95032),rewrite([97462(12)])].

97497 R(B,C,R(C,B * x,B)) = B. [para(97462(a,1),63166(a,1,1)),rewrite([94092(7),80388(13),784(13),53553(12)])].

97513 R(C,B,R(B,x,C')) = C. [para(97462(a,1),92893(a,1,2)),rewrite([81202(8),293(12),93078(13),93561(8),80646(6)])].

97516 R(C,B,R(B,C,x)) = C. [back_rewrite(68207),rewrite([97513(13)])].

97517 R(C,R(B,x,C),B) = C. [back_rewrite(95199),rewrite([97516(7)])].

97562 R(R(C,B,x),B,C) = R(C,B,x). [para(97482(a,1),80538(a,1,1)),rewrite([93287(7),93234(9)]),flip(a)].

97646 R(C,B,R(B',x,C')) = C. [para(97517(a,1),47659(a,1,1)),rewrite([64488(8),93121(10),94788(9)])].

98079 R(B,C,R(C,x,B)) = B. [para(34(a,1),97497(a,1,3,2))].

98107 R(B,C,R(B * C,B',x)) = B. [para(98079(a,1),62988(a,2)),rewrite([54690(7),16(5)])].

98291 C' * R(C,B,x) = B * R(B',x,C'). [para(97646(a,1),2036(a,1,1,1)),rewrite([16(5),96316(11)])].

98921 R(C,B,x) * (B * C') = R(B,x,C). [para(97562(a,1),40046(a,1,1)),rewrite([98291(14),49(17),82073(16),64171(17)])].

99072 R(C,B,R(B' * C',C,x)) = C. [para(98107(a,1),92507(a,1,2)),rewrite([48717(10),293(14),93094(15)])].

99901 R(C,B,x) / R(C',x,B) = C * C. [para(99072(a,1),2048(a,1,1,1)),rewrite([16(4),35225(13),55387(12),16(9,R),1659(9),94827(7),93102(8),483

46(12),48409(7),99072(18),99072(19)])].

101149 R(B * C',C',x)' = C / R(B,x,C). [para(97461(a,1),97328(a,1,2)),rewrite([2108(11),1511(6,R),94092(6)])].

101150 B * (C / R(B,x,C)) = R(C,B * x,B). [back_rewrite(53553),rewrite([101149(9)])].

101553 C * (C * R(C',B,x)) = R(C,B * x,B). [para(98921(a,1),4326(a,1,2,2)),rewrite([94092(7),749(9),101149(9),101150(7),62276(10),16(12,R)])

,flip(a)].

101777 R(C',x,B) / R(C,B,x) = C' * C'. [para(99901(a,1),104(a,1,1)),rewrite([172(4)]),flip(a)].

101783 R(C,B * x,B) = R(C,x,B). [para(99901(a,1),21297(a,1,2,1)),rewrite([101777(8),210(13),48343(11),16(11,R),12(13),10(12),10(8),62276(7),

99901(15),1382(11,R),16(10,R),101553(11)]),flip(a)].

101794 B * (C / R(B,x,C)) = R(C,x,B). [back_rewrite(101150),rewrite([101783(12)])].

101813 R(R(C,x,B),B,x) = C. [back_rewrite(67447),rewrite([101783(11),96299(9)])].

101849 R(C,B',x * B) = R(C,x,B). [para(101813(a,1),23049(a,1,1)),rewrite([45910(9)]),flip(a)].

101856 R(R(C,B',x),x,B') = C. [para(101813(a,1),54235(a,1)),rewrite([45910(10),82(9),259(8)]),flip(a)].

101944 R(C,B',B * x) = R(C,B',x). [para(101856(a,1),46836(a,1,1))].

101965 R(R(C,B',x),x,B) = R(C,B,x). [back_rewrite(94096),rewrite([101944(6)])].

102078 B * (C / R(B,C,x')) = R(C,x,B). [para(141(a,1),101794(a,1,2,2)),rewrite([79190(7),45910(14),101849(14)])].

102082 R(C,B',x) = R(C,x,B). [para(16667(a,1),101794(a,2)),rewrite([80388(8),784(8),79853(8),102078(8),101944(9)]),flip(a)].

102135 $F. [para(102082(a,2),19(a,1,1,1)),rewrite([101965(8),93110(7)]),xx(a)].

============================== end of proof ==========================

% Proof 1 at 222.06 (+ 6.34) seconds.

% Length of proof is 652.

% Level of proof is 54.

% Maximum clause weight is 37.000.

% Given clauses 4299.

1 L(L(L(C,A,B),A,B),A,B) = C # label(non_clause) # label(goal). [goal].

2 0 * x = x. [assumption].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 C * ((x * y) * C) = (C * x) * (y * C). [assumption].

15 (C * x) * (y * C) = C * ((x * y) * C). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 L(x,y,z) = (z * y)' * (z * (y * x)). [assumption].

18 (x * y)' * (x * (y * z)) = L(z,y,x). [copy(17),flip(a)].

19 L(L(L(C,A,B),A,B),A,B) != C. [deny(1)].

20 (C * x) * (y * C) = C * (C * (x * y)). [back_rewrite(15),rewrite([16(9,R)])].

27 0' = 0. [para(8(a,1),3(a,1)),flip(a)].

29 0 / x = x'. [para(8(a,1),6(a,1,1))].

31 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([29(3)])].

32 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

33 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

35 x * (x' * y) = y. [back_rewrite(4),rewrite([32(1)])].

36 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

40 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

41 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

43 (x * (y * x))' * (x * (y * (x * z))) = z. [para(13(a,1),10(a,1,2))].

45 (x * (y * (x * (x * (y * x))))) * z = x * (y * (x * (x * (y * (x * z))))). [para(13(a,1),12(a,1,1)),rewrite([13(11),13(12)])].

46 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(12(a,1),13(a,1,1,2)),rewrite([12(7)])].

48 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [para(13(a,1),13(a,1,1,2)),rewrite([13(9)])].

52 C * (x / C) = x. [para(16(a,2),7(a,1))].

53 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

54 x' * (C * x) = C. [para(16(a,2),10(a,1,2))].

55 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

56 C * (x * x) = x * (x * C). [para(16(a,2),12(a,1))].

57 C * (x * x) = x * (C * x). [para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].

58 (x * (x * C)) * y = x * (C * (x * y)). [para(16(a,1),13(a,1,1,2))].

59 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

60 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

61 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

62 C * (x * (y * x)) = x * (y * (C * x)). [para(16(a,2),13(a,2,2,2)),rewrite([16(4,R)])].

66 L(x,y,z) / (z * (y * x)) = (z * y)'. [para(18(a,1),6(a,1,1))].

67 x' * ((x / y) * (y * z)) = L(z,y,x / y). [para(7(a,1),18(a,1,1,1))].

68 L(x,y / x,z) = (z * (y / x))' * (z * y). [para(7(a,1),18(a,1,2,2)),flip(a)].

69 L(x,y,z / (y * x)) = ((z / (y * x)) * y)' * z. [para(7(a,1),18(a,1,2)),flip(a)].

71 L(x,x',y) = (y * x')' * y. [para(8(a,1),18(a,1,2,2)),rewrite([3(5)]),flip(a)].

72 L(x,y,(y * x)') = ((y * x)' * y)'. [para(8(a,1),18(a,1,2)),rewrite([3(6)]),flip(a)].

73 L(x,y',y) = x. [para(9(a,1),18(a,1,1,1)),rewrite([27(2),35(4),2(2)]),flip(a)].

74 L(x',x,y) = (y * x)' * y. [para(9(a,1),18(a,1,2,2)),rewrite([3(4)]),flip(a)].

75 (x * y) * L(z,y,x) = x * (y * z). [para(18(a,1),10(a,1,2)),rewrite([31(3)])].

76 x' * (y' * ((y * x) * z)) = L(z,y * x,y'). [para(10(a,1),18(a,1,1,1))].

77 L(x * y,x',z) = (z * x')' * (z * y). [para(10(a,1),18(a,1,2,2)),flip(a)].

78 (x * (x * y))' * (x * (x * (y * z))) = L(z,y,x * x). [para(12(a,1),18(a,1,1,1)),rewrite([12(6)])].

81 (x * (y * (x * z)))' * (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(13(a,1),18(a,1,1,1)),rewrite([13(8)])].

82 (x * (y * (z * y)))' * (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(13(a,1),18(a,1,2,2))].

83 (x * C)' * (C * (x * y)) = L(y,x,C). [para(16(a,1),18(a,1,1,1))].

86 (x * y)' * (x * (C * y)) = L(C,y,x). [para(16(a,2),18(a,1,2,2))].

87 L(x,y,z)' * ((z * y)' * ((z * (y * x)) * u)) = L(u,z * (y * x),(z * y)'). [para(18(a,1),18(a,1,1,1))].

89 ((x * y)' * x)' * L(z,y,x) = L(y * z,x,(x * y)'). [para(18(a,1),18(a,1,2))].

90 (C * (C * (x * y))) / (y * C) = C * x. [para(20(a,1),6(a,1,1))].

91 C * (C * (x * (y / C))) = (C * x) * y. [para(7(a,1),20(a,1,2)),flip(a)].

96 (C * x) * (y * (y * C)) = C * (C * (x * (y * y))). [para(12(a,1),20(a,1,2))].

98 C * (C * ((x * C) * y)) = C * (x * (C * (y * C))). [para(20(a,1),13(a,1))].

99 C * (x * ((C * y) * x)) = x * (C * (C * (y * x))). [para(20(a,1),13(a,2,2)),rewrite([16(6,R)])].

100 (C * x) * (y * (z * (y * C))) = C * (C * (x * (y * (z * y)))). [para(13(a,1),20(a,1,2))].

101 (x * C) * (y * C) = C * (C * (x * y)). [para(16(a,1),20(a,1,1))].

102 (C * x) * (C * y) = C * (C * (x * y)). [para(16(a,2),20(a,1,2))].

104 (x * (C * y))' * (x * (C * (C * (y * z)))) = L(z * C,C * y,x). [para(20(a,1),18(a,1,2,2))].

105 ((C * x) * y)' * (C * (C * (x * y))) = L(C,y,C * x). [para(20(a,1),18(a,1,2))].

107 x' * C = C * x'. [para(16(a,2),32(a,2)),rewrite([32(2)])].

108 (x / y)' = y / x. [para(7(a,1),33(a,1,2)),flip(a)].

110 x / (y * (z * (y * x))) = (y * (z * y))'. [para(13(a,1),33(a,1,2))].

111 x / (x * C) = C'. [para(16(a,1),33(a,1,2))].

112 C / (C * x) = x'. [para(16(a,2),33(a,1,2))].

113 (x * (y * z)) / L(z,y,x) = x * y. [para(18(a,1),33(a,1,2)),rewrite([31(7)])].

118 x / C = C' * x. [para(52(a,1),10(a,1,2)),flip(a)].

122 C * (C * ((C' * x) * y)) = x * (y * C). [para(52(a,1),20(a,1,1)),rewrite([118(7)]),flip(a)].

123 C * (C * (x * (C' * y))) = (C * x) * y. [back_rewrite(91),rewrite([118(4)])].

127 x * (C * x') = C. [para(16(a,2),35(a,1,2))].

128 x' * (y * ((y' * x) * z)) = L(z,y' * x,y). [para(35(a,1),18(a,1,1,1))].

129 L(x' * y,x,z) = (z * x)' * (z * y). [para(35(a,1),18(a,1,2,2)),flip(a)].

133 C * (x * (C' * x)) = x * x. [para(53(a,1),13(a,2,2)),rewrite([16(6,R)])].

136 (x * C')' * (x * y) = L(y * C,C',x). [para(53(a,1),18(a,1,2,2))].

139 C' * (x' * ((C * x) * y)) = L(y,C * x,x'). [para(54(a,1),18(a,1,1,1))].

141 L(x,C,x') = C * (x' * C)'. [para(54(a,1),18(a,1,2)),rewrite([16(6,R)]),flip(a)].

145 x' / x = x' * x'. [para(8(a,1),36(a,1,1,2)),rewrite([3(3)])].

146 x / x' = x * x. [para(9(a,1),36(a,1,1,2)),rewrite([3(2)])].

150 (C * (x * C)) / x = C * C. [para(16(a,1),36(a,1,1,2))].

151 C' * (x * (C * x)) = x * x. [para(16(a,2),36(a,1,1,2)),rewrite([118(5)])].

155 (x * y) / (x' * y) = x * x. [para(35(a,1),36(a,1,1,2))].

158 (x / y) * (y / x) = 0. [para(108(a,1),8(a,1,1))].

159 (x / y) * ((y / x) * z) = z. [para(108(a,1),10(a,1,1))].

161 (x / y) * (C * (y / x)) = C. [para(108(a,1),54(a,1,1))].

164 (C' * x)' = C / x. [para(35(a,1),112(a,1,2)),flip(a)].

176 (x * x)' = x' * x'. [para(146(a,1),108(a,1,1)),rewrite([145(4)])].

185 (C' * x) * (C / x) = 0. [para(118(a,1),158(a,1,1))].

186 (C / x) * (C' * x) = 0. [para(118(a,1),158(a,1,2))].

187 ((x / y) * (z * x)) / y = (x / y) * (z * (x / y)). [para(7(a,1),40(a,1,1,2,2))].

188 x * ((y / (x * z)) * x) = (x * y) / z. [para(7(a,1),40(a,1,1,2)),flip(a)].

190 x * ((x * y)' * x) = x / y. [para(8(a,1),40(a,1,1,2)),rewrite([3(2)]),flip(a)].

191 (x * y) / x' = x * (y * x). [para(9(a,1),40(a,1,1,2,2)),rewrite([3(2)])].

194 (x * (y * (y * (x * z)))) / z = x * (y * (y * x)). [para(12(a,1),40(a,1,1,2)),rewrite([12(7)])].

197 (C * (x * (y * C))) / y = C * (x * C). [para(16(a,1),40(a,1,1,2,2))].

201 (x * L(y,z,x)) / (z * y) = x / z. [para(18(a,1),40(a,1,1,2)),rewrite([190(8)])].

208 (C * C) / x = C * (x' * C). [para(54(a,1),40(a,1,1,2))].

213 (C / x) * (C' * (x * y)) = L(y,x,C'). [para(164(a,1),18(a,1,1))].

216 L(x,C / y,C' * y) = x. [para(164(a,1),73(a,1,2))].

228 (x / y) * ((z / (x / y)) * x) = ((x / y) * z) * y. [para(7(a,1),41(a,1,2,2))].

231 (x / y) * (y * z) = y' * ((y * x) * z). [para(41(a,1),10(a,1,2)),flip(a)].

232 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),41(a,1,2,2)),flip(a)].

237 (x / C') * y = (C * x) * y. [para(41(a,1),16(a,1)),rewrite([118(5),232(9),16(12,R),35(12)]),flip(a)].

239 (C * x) * y = (x * C) * y. [para(16(a,1),41(a,2,1)),rewrite([118(3),232(7),237(7),35(8)])].

243 C * ((C * x) * y) = x * (C * (C * y)). [para(41(a,1),20(a,2,2)),rewrite([118(3),35(5),16(4,R)]),flip(a)].

245 (x * y) * (x' * z) = x * ((y / x) * z). [para(35(a,1),41(a,1,2,2)),flip(a)].

246 (C' * x) * (y * C) = C' * ((C * x) * y). [para(53(a,1),41(a,1,2,2)),rewrite([237(6)]),flip(a)].

247 (x' * y) * (C * x) = x' * (C * (y / x')). [para(54(a,1),41(a,1,2,2)),rewrite([16(5,R)]),flip(a)].

249 (C * x) * (C / x) = C * C. [para(127(a,1),41(a,1,2)),rewrite([118(7),164(9)]),flip(a)].

253 L(x,y * z,y') = L(x,y,z / y). [back_rewrite(67),rewrite([231(4),76(6)])].

256 x' * (y' * ((y * x) * z)) = L(z,y,x / y). [back_rewrite(76),rewrite([253(9)])].

259 x * (C * (C / x)) = C * C. [para(185(a,1),20(a,2,2,2)),rewrite([35(5),16(4,R),3(9)])].

263 (C * (C / x)) * x = C * C. [para(186(a,1),20(a,2,2,2)),rewrite([16(9,R),35(9),3(9)])].

265 C' * ((C / x) * C') = C' / x. [para(186(a,1),40(a,1,1,2)),rewrite([3(4)]),flip(a)].

275 (C * (C * x))' * (C * ((x * C) * y)) = L(y,x * C,C). [para(55(a,2),18(a,1,1,1))].

277 C * (C * ((C * x) * y)) = C * (x * (C * (y * C))). [para(55(a,1),20(a,1,1)),rewrite([13(7)]),flip(a)].

283 (C * x)' = (x * C)'. [para(55(a,1),112(a,1,2)),rewrite([112(6)]),flip(a)].

304 (x * C)' * (C * x) = 0. [para(283(a,1),8(a,1,1))].

305 (C * x)' * (x * C) = 0. [para(283(a,2),8(a,1,1))].

306 (C * x) * (x * C)' = 0. [para(283(a,1),9(a,1,2))].

308 (x * C)' * ((C * x) * y) = y. [para(283(a,1),10(a,1,1))].

309 (C * x)' * ((x * C) * y) = y. [para(283(a,2),10(a,1,1))].

310 (C * (x * x))' = (x * (x * C))'. [para(12(a,1),283(a,2,1))].

311 (C * (x * (y * x)))' = (x * (y * (x * C)))'. [para(13(a,1),283(a,2,1))].

315 (C * x) * ((x * C)' * y) = y. [para(283(a,1),35(a,1,2,1))].

337 C * (C * (x * C)') = C / x. [para(304(a,1),40(a,1,1,2)),rewrite([3(3),16(8,R)]),flip(a)].

344 L(C,x,(C * x)') = ((C * x)' * x)'. [para(305(a,1),18(a,1,2)),rewrite([3(7)]),flip(a)].

351 ((C * x) * y) / (x * C)' = (C * x) * (y * (C * x)). [para(306(a,1),40(a,1,1,2,2)),rewrite([3(4)])].

361 (x * (x * C))' * (x * (C * (x * y))) = y. [para(16(a,1),43(a,1,1,1,2))].

370 (x * ((C * y) * x))' * (x * (C * (C * (y * x)))) = C. [para(20(a,1),43(a,1,2,2))].

434 (C * x) * ((C * x) * y) = C * (x * (x * (C * y))). [para(304(a,1),45(a,1,1,2,2,2,2)),rewrite([3(11),102(10),315(12),60(6),12(5),308(22),

308(18)]),flip(a)].

466 (C * (x * x))' * (x * ((x * C) * y)) = L(y,x * C,x). [para(56(a,2),18(a,1,1,1))].

507 (x * (y * (C * (x * x)))) / (C * x) = x * (y * x). [para(57(a,2),40(a,1,1,2,2))].

509 (C * (x * x))' = (x * (C * x))'. [para(57(a,1),283(a,1,1)),rewrite([16(7,R)]),flip(a)].

609 x * (y * L(z,x,y)) = (x * y) * z. [para(8(a,1),48(a,1,1,2,2)),rewrite([3(2),18(7)]),flip(a)].

728 ((x * C) * y)' * ((C * x) * (y * z)) = L(z,y,C * x). [para(239(a,1),18(a,1,1,1))].

729 (x * (C * y))' * (x * ((y * C) * z)) = L(z,C * y,x). [para(239(a,1),18(a,1,2,2))].

734 (x * C) * (C * x) = C * (x * (x * C)). [para(239(a,1),36(a,2)),rewrite([434(6),194(7)]),flip(a)].

739 (C * (x * (x * C)))' = (C * x)' * (C * x)'. [para(239(a,1),176(a,1,1)),rewrite([734(5)])].

762 L(x,C * y,C) = L(x,y * C,C). [back_rewrite(275),rewrite([729(11)])].

791 (x * (C * (x * C)))' = (C * x)' * (C * x)'. [para(58(a,1),283(a,2,1)),rewrite([739(6)]),flip(a)].

822 (C * x)' * (C * C) = C / x. [para(249(a,1),10(a,1,2))].

830 ((C * x) * (y * (C * C))) / (C / x) = (C * x) * (y * (C * x)). [para(249(a,1),40(a,1,1,2,2))].

842 L(C / x,C,x) = (x * C)' * (C * C). [para(259(a,1),18(a,1,2)),flip(a)].

844 C * (C / x') = x * (C * C). [para(259(a,1),35(a,1,2)),flip(a)].

856 C * (C / x) = C * (x' * C). [para(263(a,1),6(a,1,1)),rewrite([208(4)]),flip(a)].

857 C' * (x' * (C * (x * y))) = L(y,x,C * (x' * C)). [para(263(a,1),18(a,1,1,1)),rewrite([176(4),856(9),13(12),12(13),10(12),856(12)])].

875 C * (x * C) = x * (C * C). [back_rewrite(844),rewrite([856(5),31(3)])].

886 L(C / x,C,x) = C / x. [back_rewrite(842),rewrite([875(11,R),16(10,R),337(11)])].

887 C * (C * (C * x)') = C / x. [back_rewrite(822),rewrite([875(7,R),16(6,R)])].

889 L(x',C,x * C) = x'. [para(33(a,1),886(a,1,1)),rewrite([33(9)])].

895 x * (C * y) = x * (y * C). [para(59(a,1),10(a,1,2)),rewrite([10(8)]),flip(a)].

947 L(x,C,x' * C) = x. [para(31(a,1),889(a,1,1)),rewrite([31(7)])].

949 L(x,C,C * x') = x. [para(107(a,1),889(a,1,3)),rewrite([31(2),31(7)])].

958 L(x * x,C,C * (x' * x')) = x * x. [para(176(a,1),947(a,1,3,1)),rewrite([16(7,R)])].

959 L(C * x,C,C * (x * C)') = C * x. [para(283(a,1),947(a,1,3,1)),rewrite([16(8,R)])].

971 x' * ((x * C) * y) = C * L(y,x,C). [para(18(a,1),60(a,2,2)),rewrite([887(7),231(4)])].

974 C * (C * x) = x * (C * C). [para(60(a,1),53(a,1,2)),rewrite([10(9)]),flip(a)].

1044 C' * x = x * C'. [para(8(a,1),61(a,2,2,2)),rewrite([35(8),3(7)]),flip(a)].

1045 x' * (C * (x * (y * x))) = y * (x * C). [para(61(a,2),10(a,1,2))].

1069 (C * (x * C))' = (x * (C * C))'. [para(61(a,2),112(a,1,2)),rewrite([112(8)])].

1079 (x * C')' = C / x. [para(61(a,2),164(a,1,1)),rewrite([35(8),16(9,R),9(9),3(7)])].

1120 L(x,C / y,y * C') = x. [para(61(a,2),216(a,1,3)),rewrite([16(5,R),9(5),3(3),35(10)])].

1142 C' * (C' * (C / x)) = C' / x. [back_rewrite(265),rewrite([1044(7,R)])].

1144 C * L(x,y,C) = L(x * C,C',y). [back_rewrite(136),rewrite([1079(4),231(4),971(5)])].

1147 x' * ((x * C) * y) = L(y * C,C',x). [back_rewrite(971),rewrite([1144(9)])].

1148 (x * C') / x = C'. [para(1044(a,1),6(a,1,1))].

1151 C * (x * C') = x. [para(1044(a,1),10(a,1,2)),rewrite([31(3)])].

1152 x' * (C' * x) = C'. [para(1044(a,2),10(a,1,2))].

1157 (C' * (C' * x)) * y = C' * (x * (C' * y)). [para(1044(a,2),13(a,1,1,2))].

1163 x * (C' * x') = C'. [para(1044(a,2),35(a,1,2))].

1168 (x * (y * (C' * x))) / C' = x * (y * x). [para(1044(a,2),40(a,1,1,2,2))].

1174 (x / y) * (C' * (y / x)) = C'. [para(1044(a,2),159(a,1,2))].

1181 x / C' = C * x. [para(7(a,1),1151(a,1,2)),flip(a)].

1186 (C * x)' * x = L(C',x,C). [para(1151(a,1),18(a,1,2))].

1200 C * (x * (y * (C' * x))) = x * (y * x). [back_rewrite(1168),rewrite([1181(8)])].

1205 L(C,x,(C * x)') = L(C',x,C)'. [back_rewrite(344),rewrite([1186(9)])].

1211 (C * x)' = C' / x. [para(1181(a,1),108(a,1,1))].

1220 L(C,x,C' / x) = L(C',x,C)'. [back_rewrite(1205),rewrite([1211(4)])].

1224 L(C',x,C) = C'. [back_rewrite(1186),rewrite([1211(3),7(4)]),flip(a)].

1225 (x * (C * C))' = C' / (x * C). [back_rewrite(1069),rewrite([1211(5)]),flip(a)].

1268 (x * (C * (x * C)))' = (C' / x) * (C' / x). [back_rewrite(791),rewrite([1211(9),1211(12)])].

1278 (x * (C * x))' = C' / (x * x). [back_rewrite(509),rewrite([1211(4)]),flip(a)].

1280 (C' / (x * x)) * (x * ((x * C) * y)) = L(y,x * C,x). [back_rewrite(466),rewrite([1211(4)])].

1313 (x * (y * (x * C)))' = C' / (x * (y * x)). [back_rewrite(311),rewrite([1211(5)]),flip(a)].

1314 (x * (x * C))' = C' / (x * x). [back_rewrite(310),rewrite([1211(4)]),flip(a)].

1315 (C' / x) * ((x * C) * y) = y. [back_rewrite(309),rewrite([1211(3)])].

1320 (x * C)' = C' / x. [back_rewrite(283),rewrite([1211(3)]),flip(a)].

1327 L(C,x,C' / x) = C. [back_rewrite(1220),rewrite([1224(9),31(8)])].

1332 L(C * x,C,C * (C' / x)) = C * x. [back_rewrite(959),rewrite([1320(7)])].

1334 L(x,C,x') = C * (C' / x'). [back_rewrite(141),rewrite([1320(8)])].

1338 (C' / x) * (C * (x * y)) = L(y,x,C). [back_rewrite(83),rewrite([1320(3)])].

1339 C' / (x * (C * x)) = (C' / x) * (C' / x). [back_rewrite(1268),rewrite([1313(6)])].

1345 (C' / (x * x)) * (x * (C * (x * y))) = y. [back_rewrite(361),rewrite([1314(4)])].

1350 ((C * x) * y) / (C' / x) = (C * x) * (y * (C * x)). [back_rewrite(351),rewrite([1320(6)])].

1424 (C / x) * ((x * C') * y) = y. [para(1079(a,1),10(a,1,1))].

1483 ((C * x) * y)' = ((x * C) * y)'. [para(239(a,1),66(a,2,1)),rewrite([66(8)])].

1535 L(x,y / x,C) = (C' / (y / x)) * (y * C). [para(16(a,1),68(a,2,2)),rewrite([1211(7)])].

1543 L(x,(y * C) / x,C') = (C / ((y * C) / x)) * y. [para(53(a,1),68(a,2,2)),rewrite([164(13)])].

1565 (C' / (x * C)) * (x * (C * (y * C))) = L(y,C * C,x). [para(150(a,1),68(a,1,2)),rewrite([150(9),1225(9)]),flip(a)].

1637 L(x,C,y / (C * x)) = (C' / (y / (x * C))) * y. [para(16(a,1),69(a,2,1,1,1,2)),rewrite([16(10,R),1211(11)])].

1675 (C' / (C * x)) * (C * (C * (x * y))) = L(y,x,C * C). [para(150(a,1),69(a,1,3)),rewrite([16(8,R),36(11),12(8),1211(9),16(13,R)]),flip(a)

].

1744 L(x,C',x') = C' * (C / x'). [para(1152(a,1),18(a,1,2)),rewrite([1079(5),1044(6,R)]),flip(a)].

1745 (C * x') * x = C. [para(1152(a,1),20(a,2,2,2)),rewrite([16(8,R),35(8),9(9),3(7)])].

1759 C / x = C * x'. [para(1745(a,1),6(a,1,1))].

1761 x * ((C * x') * (x * y)) = (x * C) * y. [para(1745(a,1),13(a,1,1,2)),flip(a)].

1762 C' * ((C * x') * (x * y)) = L(y,x,C * x'). [para(1745(a,1),18(a,1,1,1))].

1765 (C * x) * x' = C. [para(31(a,1),1745(a,1,1,2))].

1768 (C * (x / y)) * (y / x) = C. [para(108(a,1),1745(a,1,1,2))].

1782 L(x,C',x') = x. [back_rewrite(1744),rewrite([1759(9),31(9),10(9)])].

1817 L(x,(y * C) / x,C') = (C * (x / (y * C))) * y. [back_rewrite(1543),rewrite([1759(11),108(11)])].

1840 (C * x') * ((x * C') * y) = y. [back_rewrite(1424),rewrite([1759(2)])].

1848 C' / x = C' * x'. [back_rewrite(1142),rewrite([1759(6),10(8)]),flip(a)].

1851 L(x,C * y',y * C') = x. [back_rewrite(1120),rewrite([1759(2)])].

1853 (x * C')' = C * x'. [back_rewrite(1079),rewrite([1759(6)])].

1862 ((C * x) * (y * (C * C))) / (C * x') = (C * x) * (y * (C * x)). [back_rewrite(830),rewrite([1759(9)])].

1878 C * ((C' * x') * (x * y)) = L(y,x,C'). [back_rewrite(213),rewrite([1759(2),245(8),118(4)])].

1881 (C' * x)' = C * x'. [back_rewrite(164),rewrite([1759(6)])].

1882 L(x,C,x') = x. [back_rewrite(1334),rewrite([1848(8),31(8),35(8)])].

1903 L(x,y,C * (y' * C)) = L(x,y,C * C). [back_rewrite(1675),rewrite([1848(5),1211(5),1848(5),232(13),1181(9),35(8),857(8)])].

1909 L(x,C,y / (C * x)) = (C' * ((x * C) / y)) * y. [back_rewrite(1637),rewrite([1848(11),108(11)])].

1921 C' * (x' * (C' * (x * (C * (y * C))))) = L(y,C * C,x). [back_rewrite(1565),rewrite([1848(5),1320(5),1848(5),1157(13)])].

1924 L(x,y / x,C) = C' * ((C * (x / y)) * y). [back_rewrite(1535),rewrite([1848(7),108(7),246(10)])].

1951 ((C * x) * y) / (C' * x') = (C * x) * (y * (C * x)). [back_rewrite(1350),rewrite([1848(6)])].

1956 (C' * (x' * x')) * (x * (C * (x * y))) = y. [back_rewrite(1345),rewrite([1848(4),176(4)])].

1961 (C' * x') * (C' * x') = C' * (C' * (x' * x')). [back_rewrite(1339),rewrite([1848(6),1278(6),1848(6),176(6),1848(12),1848(16)]),flip(a)]

.

1962 L(x,y,C * y') = L(x,y,C). [back_rewrite(1338),rewrite([1848(3),232(8),1181(6),1762(8)])].

1965 L(C * x,C,x') = C * x. [back_rewrite(1332),rewrite([1848(7),35(9)])].

1967 L(C,x,C' * x') = C. [back_rewrite(1327),rewrite([1848(4)])].

1972 (x * C)' = C' * x'. [back_rewrite(1320),rewrite([1848(6)])].

1976 (C' * x') * ((x * C) * y) = y. [back_rewrite(1315),rewrite([1848(3)])].

1978 (x * (y * (x * C)))' = C' * (x * (y * x))'. [back_rewrite(1313),rewrite([1848(10)])].

1995 (C' * (x' * x')) * (x * ((x * C) * y)) = L(y,x * C,x). [back_rewrite(1280),rewrite([1848(4),176(4)])].

2036 (x * (C * C))' = C' * (C' * x'). [back_rewrite(1225),rewrite([1848(10),1972(10)])].

2042 (C * x)' = C' * x'. [back_rewrite(1211),rewrite([1848(6)])].

2043 C' * (x' * (C * (x * y))) = L(y,x,C * C). [back_rewrite(857),rewrite([1903(14)])].

2056 L(x,x',C) = x. [para(71(a,2),16(a,2)),rewrite([2042(5),31(5),35(5)]),flip(a)].

2096 L(x,x',C * x) = x. [para(1745(a,1),71(a,2,1,1)),rewrite([31(4),31(9),10(9)])].

2099 L(x',x,C) = x'. [para(31(a,1),2056(a,1,2))].

2123 ((C' * x') * x)' = C. [para(16(a,2),72(a,1,3,1)),rewrite([2042(4),1967(6),1972(4)]),flip(a)].

2163 L(x',x,y / x) = y' * (y / x). [para(7(a,1),74(a,2,1,1))].

2171 (C' * x') * x = L(C',C,x). [para(16(a,2),74(a,2,1,1)),rewrite([2042(7)]),flip(a)].

2183 (C' * x) * x' = L(C',C,x'). [para(107(a,1),74(a,2,1,1)),rewrite([2042(9),31(9)]),flip(a)].

2186 x * L(y',y,x) = x / y. [para(74(a,2),40(a,2,2)),rewrite([40(6),190(4)]),flip(a)].

2231 L(C',C,x)' = C. [back_rewrite(2123),rewrite([2171(5)])].

2240 L(C',C,x) = C'. [para(2231(a,1),31(a,1,1)),flip(a)].

2241 (C' * x) * x' = C'. [back_rewrite(2183),rewrite([2240(10)])].

2242 (C' * x') * x = C'. [back_rewrite(2171),rewrite([2240(9)])].

2243 L(x,x',x * C) = x. [para(16(a,1),2096(a,1,3))].

2264 (x * (y * z))' * (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(75(a,1),18(a,1,2,2))].

2269 C * L(x,C * y,y') = y' * ((C * y) * x). [para(54(a,1),75(a,1,1))].

2281 C * L(x,C * (y / z),z / y) = (z / y) * ((C * (y / z)) * x). [para(161(a,1),75(a,1,1))].

2292 x' * (C * (C * x)) = C * C. [para(947(a,1),75(a,1,2)),rewrite([16(5,R),13(6),54(5),247(9),1759(8),31(8)]),flip(a)].

2314 C' * L(x,C' * y,y') = y' * ((C' * y) * x). [para(1152(a,1),75(a,1,1))].

2315 (C * x') * (x * y) = L(y * C,C',x). [para(1745(a,1),75(a,1,1)),rewrite([1962(5),1144(4)]),flip(a)].

2321 L(x',x,y) * L(z,y,(y * x)') = (y * x)' * (y * z). [para(74(a,2),75(a,1,1))].

2324 L(L(x,y,z),z * y,z) = L(x,y,z * z). [back_rewrite(78),rewrite([2264(7)])].

2329 x * L(y * C,C',x) = (x * C) * y. [back_rewrite(1761),rewrite([2315(5)])].

2345 C * (x * ((C' * x') * y)) = L(y,C' * x',x). [para(1163(a,1),18(a,1,1,1)),rewrite([31(3)])].

2443 (C' * x') * (x * y) = L(y * C',C,x). [para(1044(a,1),77(a,1,1)),rewrite([31(6),31(8),1972(8)]),flip(a)].

2488 C * L(x * C',C,y) = L(x,y,C'). [back_rewrite(1878),rewrite([2443(7)])].

2748 L(x,y,z / y) = L(x,y,z). [para(8(a,1),81(a,1,1,1,2)),rewrite([3(2),18(6),10(4),190(5)]),flip(a)].

2750 L(x,y',y * (z * y)) = L(x,z,y). [para(9(a,1),81(a,1,1,1,2,2)),rewrite([3(2),35(5),18(5)]),flip(a)].

2776 x' * (C' * (x * (C * y))) = L(y,C,x * (C' * x)). [para(53(a,1),81(a,1,1,1,2)),rewrite([176(2),12(11),10(10)])].

2853 C' * L(C * x,C,y) = L(x,C,C * (y * C)). [para(59(a,2),81(a,1,1,1)),rewrite([1978(7),2042(7),1972(7),232(18),1181(12),35(11),2443(12),10

44(9,R),10(9)])].

2962 L(x',x,y) = y' * (y / x). [back_rewrite(2163),rewrite([2748(3)])].

2966 x' * (y' * ((y * x) * z)) = L(z,y,x). [back_rewrite(256),rewrite([2748(8)])].

2967 L(x,y * z,y') = L(x,y,z). [back_rewrite(253),rewrite([2748(5)])].

2968 C' * L(x * C,C,y * (C' * y)) = L(x,C * C,y). [back_rewrite(1921),rewrite([2776(12)])].

2999 C * ((C' * x) * (x' * y)) = L(y,x',C' * x). [para(2241(a,1),18(a,1,1,1)),rewrite([31(3)])].

3011 L(x,x',C' * x) = x. [para(2241(a,1),71(a,2,1,1)),rewrite([31(8),35(10)])].

3026 L(x,y,z * y) = L(x,y,z). [para(10(a,1),82(a,1,1,1)),rewrite([10(7),18(5),2967(5)]),flip(a)].

3186 L(x,y,C' * y') = L(x,y,C'). [para(2242(a,1),18(a,1,1,1)),rewrite([31(3),2443(7),2488(7)]),flip(a)].

3189 x * ((C' * (x * y)') * x) = (x * C') / y. [para(2242(a,1),40(a,1,1,2)),flip(a)].

3227 x' * (y' * (C * (y * x))) = L(C,y,x). [para(10(a,1),86(a,1,1,1)),rewrite([2967(11)])].

3230 (x / y) * (C * y) = x * L(C,y,x). [para(86(a,1),13(a,2,2)),rewrite([190(4)])].

3261 C * ((x * (C * y))' * ((C * x) * y)) = L(C,y,C * (C * x)). [para(60(a,1),86(a,1,1,1)),rewrite([2042(6),102(14),232(15),1181(9),102(14),

10(15)])].

3266 (x * (y * C'))' * (x * y) = L(C,y * C',x). [para(1151(a,1),86(a,1,2,2))].

3358 L(x,C,C' * y) = L(x,C,y). [para(54(a,1),87(a,1,2,2,1)),rewrite([1882(3),1972(5),31(5),232(7),1181(6),2966(8),54(6),1972(7),31(7)]),flip

(a)].

3427 L(x,C * C,C' * (C' * y)) = L(x,C,y * (C' * y)). [para(949(a,1),87(a,1,1,1)),rewrite([16(6,R),2042(7),2042(7),31(7),102(13),8(11),3(11),

12(11),232(12),1181(9),35(8),2776(8),102(12),8(10),3(10),16(14,R),2042(15),2042(15),31(15)]),flip(a)].

3484 L(x,C' * y,C) = L(x,C',C * y). [para(1152(a,1),87(a,1,2,2,1)),rewrite([1782(4),1853(6),31(4),245(7),118(4),128(8),1152(10),1853(12),31(

10)])].

3716 L(x,x',x * C') = x. [para(61(a,2),3011(a,1,3)),rewrite([16(4,R),9(4),3(2),16(4,R),9(4),3(2),35(9),16(9,R),9(9),3(7)])].

3722 x * L(y,x,C) = L(x * y,C,x'). [para(16(a,1),89(a,1,1,1,1,1)),rewrite([1972(3),16(6,R),35(6),31(2),2042(8),3358(10)])].

3723 C * L(x,C,y) = L(x * C,y,C'). [para(16(a,1),89(a,2,1)),rewrite([1972(3),2242(5),31(3),1972(9),3186(11)])].

3771 L(x * y,C',C * x') = x * L(y,x,C'). [para(1044(a,1),89(a,1,1,1,1,1)),rewrite([1853(4),1044(6,R),10(6),31(2),1881(11)]),flip(a)].

3772 C' * L(x,C',y) = L(x * C',y,C). [para(1044(a,1),89(a,2,1)),rewrite([1853(4),1745(4),1853(13),1962(13)])].

3878 (C * x) / (x * C) = 0. [para(9(a,1),90(a,2)),rewrite([35(6)])].

3918 (x * C) / (C * x) = 0. [para(3878(a,1),108(a,1,1)),rewrite([27(2)]),flip(a)].

3962 L(x',x',C' * x) = x'. [para(96(a,1),35(a,1)),rewrite([2042(5),2042(9),1961(11),123(14),245(9),118(3),2999(9),2042(9),16(12,R),35(12)])]

.

4049 (x * (C * C)) * y = C * (x * (C * y)). [para(875(a,1),13(a,1,1))].

4054 L(x,y * C,C) = L(x,y,C). [para(875(a,1),18(a,1,1,1)),rewrite([2036(5),232(13),1181(9),35(8),1147(7),3772(8),1044(5,R),53(5)]),flip(a)].

4055 L(x,C,C * (y * y)) = L(x,C * C,y). [para(875(a,2),18(a,1,1,1)),rewrite([2042(5),1972(5),12(11),1157(13),2776(12),2853(11),16(8,R),133(8

)])].

4056 (x * y)' * (x * (C * (y * C))) = L(C * C,y,x). [para(875(a,2),18(a,1,2,2))].

4156 L(x,C * y,C) = L(x,y,C). [back_rewrite(762),rewrite([4054(8)])].

4157 L(x * x,C * C,x') = x * x. [back_rewrite(958),rewrite([4055(8)])].

4291 (x * (y * C)) / (C * y) = x. [para(895(a,1),6(a,1,1))].

4293 (x / (C * y)) * (y * C) = x. [para(895(a,1),7(a,1))].

4300 (C * x) / (y * (x * C)) = y'. [para(895(a,1),33(a,1,2))].

4301 (x * C) / (y * (C * x)) = y'. [para(895(a,2),33(a,1,2))].

4314 (x * C) * (C * y) = C * (C * (x * y)). [para(895(a,1),239(a,1)),rewrite([20(5)]),flip(a)].

4394 L(x,C * y,y') = L(x,y,C). [para(974(a,1),18(a,1,1,1)),rewrite([2036(5),232(13),1181(9),35(8),139(8),4156(8)])].

4403 (x * (x * (C * C))) * y = x * (C * (C * (x * y))). [para(974(a,1),46(a,1,1,2))].

4420 L(x,(C * y) / x,C) = (C' * (x / (C * y))) * (y * (C * C)). [para(974(a,1),68(a,2,2)),rewrite([2042(11),108(11)])].

4467 x' * ((C * x) * y) = L(y * C,C',x). [back_rewrite(2269),rewrite([4394(5),1144(4)]),flip(a)].

4680 L(x,C * C,C' * y) = L(x,y,C). [para(1965(a,1),87(a,1,1,1)),rewrite([2042(3),1972(8),31(8),2292(13),12(11),232(12),1181(9),102(11),10(12

),232(8),1181(6),2315(7),3772(8),1044(5,R),53(5),2292(8),1972(9),31(9)]),flip(a)].

4686 L(x,C,y * (C' * y)) = L(x,C',C * y). [back_rewrite(3427),rewrite([4680(10),3484(5)]),flip(a)].

4692 L(x,C * C,y) = L(x,y,C). [back_rewrite(2968),rewrite([4686(10),3772(10),1044(5,R),53(5),4156(4)]),flip(a)].

4696 L(x,C',C * y) = L(x,y,C). [back_rewrite(4680),rewrite([4692(7),3484(5)])].

4699 L(x * x,x',C) = x * x. [back_rewrite(4157),rewrite([4692(6)])].

4708 L(x,C,C * (y * y)) = L(x,y,C). [back_rewrite(4055),rewrite([4692(9)])].

4720 x * L(y,x,C') = L(x * y,x',C). [back_rewrite(3771),rewrite([4696(7)]),flip(a)].

4880 (C' * (x * ((C * y) * x))') * (x * (C * (C * (C * (y * x))))) = L(C,C * (C * (y * x)),x). [para(99(a,2),86(a,1,1,1)),rewrite([2042(7)])

].

4967 L(x',x,y) / (y / x) = y'. [para(2186(a,1),33(a,1,2))].

5097 (C * x) * (y * (C * C)) = C * (C * (x * (y * C))). [para(1745(a,1),100(a,2,2,2,2,2)),rewrite([20(8),8(6),3(6)])].

5149 (C * (C * (x * (y * C)))) / (C * x') = (C * x) * (y * (C * x)). [back_rewrite(1862),rewrite([5097(7)])].

5151 L(x,y * z,z) = L(x,y,z). [para(33(a,1),2748(a,1,3)),rewrite([2967(3)]),flip(a)].

5156 L(x,y * C,C') = L(x,y * C,y). [para(111(a,1),2748(a,1,3))].

5161 L(x,C',y) = L(x,y,C). [para(1181(a,1),2748(a,1,3)),rewrite([4696(5)]),flip(a)].

5162 L(x,y,y * C') = L(x,y,C'). [para(1148(a,1),2748(a,1,3)),flip(a)].

5165 L(x,C,x) = x. [para(2243(a,1),2748(a,2)),rewrite([191(5),2750(5)])].

5168 L(x,C',x) = x. [para(3716(a,1),2748(a,2)),rewrite([191(6),2750(6)])].

5196 (x * C) * x = x * (C * x). [para(5165(a,1),75(a,1,2))].

5216 L(C' * x,x,C) = C' * x. [para(5168(a,1),89(a,1,2)),rewrite([1853(4),1745(4),1853(10),1962(10)]),flip(a)].

5295 C' * L(x,y,C) = L(C' * x,y,C). [para(5161(a,1),89(a,1,2)),rewrite([1853(4),1745(4),1853(12),1962(12)])].

5296 x * L(y,C',x) = L(x * y,C,x'). [para(5161(a,2),89(a,1,2)),rewrite([2042(3),16(6,R),35(6),31(2),2042(9),3358(11)])].

5310 L(x * (y * C),C,x') = (x * C) * y. [back_rewrite(2329),rewrite([5296(6)])].

5317 L(x,C,C * y) = L(x,y,C * C). [para(102(a,1),18(a,1,2)),rewrite([16(4,R),2042(5),2042(5),232(13),1181(9),35(8),2043(8)]),flip(a)].

5418 L(x,C,C * y) = L(x,C,y). [para(16(a,2),3026(a,1,3))].

5420 L(x,y' * z,y) = L(x,y',z). [para(35(a,1),3026(a,1,3)),rewrite([5151(3)]),flip(a)].

5424 L(x,C * (y / z),z / y) = L(x,y / z,C). [para(161(a,1),3026(a,1,3)),rewrite([4156(5)]),flip(a)].

5438 L(x,y',C * y) = L(x,y',C). [para(1765(a,1),3026(a,1,3)),flip(a)].

5440 L(x,y,L(z',z,y)) = L(x,y,(y * z)'). [para(74(a,2),3026(a,1,3))].

5448 L(x,y',C' * y) = L(x,y',C'). [para(2241(a,1),3026(a,1,3)),flip(a)].

5462 L(x,y / z,C * (z / y)) = L(x,y / z,C). [para(1768(a,1),3026(a,1,3)),flip(a)].

5469 L(x * C,C,x) = x * C. [para(3026(a,1),5165(a,1))].

5471 L(x,y * C',C) = L(x,C',y). [para(3026(a,1),5161(a,1)),flip(a)].

5477 L(x,y,C * C) = L(x,C,y). [back_rewrite(5317),rewrite([5418(4)]),flip(a)].

5480 L(x,C,y * y) = L(x,y,C). [back_rewrite(4708),rewrite([5418(5)])].

5507 (x / y) * ((C * (y / x)) * z) = L(z * C,C',y / x). [back_rewrite(2281),rewrite([5424(6),1144(5)]),flip(a)].

5513 L(x',x',C') = x'. [back_rewrite(3962),rewrite([5448(6)])].

5535 C' * (x' * (C * (x * y))) = L(y,C,x). [back_rewrite(2043),rewrite([5477(12)])].

5599 x' * (C * (x * y)) = L(y * C,C,x). [para(10(a,1),104(a,1,1,1)),rewrite([10(9),2967(12)])].

5653 x' * (C * (C * (x * y))) = L(C * (y * C),C',x). [para(104(a,1),60(a,2,2)),rewrite([2042(7),2042(7),35(10),35(6),4156(14),1144(13),16(11

,R)])].

5754 C' * L(x * C,C,y) = L(x,C,y). [back_rewrite(5535),rewrite([5599(7)])].

5761 x' * L(x * C,C,y) = L(C,y,x). [back_rewrite(3227),rewrite([5599(6)])].

5765 L(C * (x * y),C,y) = x * (y * C). [back_rewrite(1045),rewrite([5599(6),16(3,R)])].

5778 L(x,x,C') = x. [para(31(a,1),5513(a,1,1)),rewrite([31(2),31(5)])].

5784 (C' * x) * x = C' * (x * x). [para(5778(a,1),75(a,1,2))].

5816 ((C * (x * (y * x))) * z)' * (C * (C * (x * (y * (x * z))))) = L(C,z,C * (x * (y * x))). [para(13(a,1),105(a,1,2,2,2))].

5821 L(C,(C' * x') * y,C * x) = y' * (C * L(y,C' * x',x)). [para(35(a,1),105(a,1,1,1)),rewrite([2042(6),2345(10),2042(13)]),flip(a)].

5847 L(C,x,C * (y * (C * C))) = L(C,x,y). [para(61(a,2),105(a,1,1,1,1)),rewrite([60(7),4314(6),2042(8),2042(8),2042(8),4049(18),232(21),1181

(13),35(12),232(15),1181(9),102(14),86(12),10(11),10(7)]),flip(a)].

5855 L(C,x,C * (y * (z * y))) = L(C,x,y * (z * (C * y))). [para(62(a,1),105(a,2,3)),rewrite([13(11),5816(14)])].

5856 ((C * x) * (y * (C * x)))' * (C * (C * (C * (x * (y * x))))) = L(C,y,C * x). [para(62(a,2),105(a,1,2,2,2)),rewrite([5151(23)])].

5872 (x * ((C * y) * z))' * (x * (C * (C * (y * z)))) = L(L(C,z,C * y),(C * y) * z,x). [para(105(a,1),77(a,1,1)),rewrite([31(9),31(13)]),fli

p(a)].

5897 L(C,x,C * (C * ((y * C) * z))) = L(C,x,C * (y * (C * (z * C)))). [para(98(a,1),105(a,2,3)),rewrite([60(8),2042(9),232(21),1181(12),102(

20),3261(19),10(14)])].

5919 L(L(C,x,C * y),C * y,x) = C. [back_rewrite(370),rewrite([5872(12),5151(8)])].

5966 (x * (y * x))' = x' / (x * y). [para(9(a,1),110(a,1,2,2,2)),rewrite([3(3)]),flip(a)].

5972 (x * y) / (z * L(y,x,z)) = x / z. [para(18(a,1),110(a,1,2,2)),rewrite([190(8),108(6)])].

5974 (x' * y) / (x * (z * y)) = x' / (x * z). [para(35(a,1),110(a,1,2,2,2)),rewrite([5966(8)])].

6007 ((x * C) * (y * (C * x)))' = (C' * x') / ((C * x) * y). [para(239(a,1),110(a,2,1)),rewrite([110(8),5966(7),2042(3)]),flip(a)].

6041 (C' * x') / ((C * x) * y) = x' / (C * (C * (x * y))). [para(1765(a,1),110(a,1,2,2,2)),rewrite([20(6),5966(14),2042(10)]),flip(a)].

6101 (x' / (C * (C * (x * y)))) * (C * (C * (C * (x * (y * x))))) = L(C,y,C * x). [back_rewrite(5856),rewrite([5966(7),2042(3),6041(8)])].

6118 (C' * (x' / (x * (C * y)))) * (x * (C * (C * (C * (y * x))))) = L(C,C * (C * (y * x)),x). [back_rewrite(4880),rewrite([5966(7)])].

6198 ((x * C) * (y * (C * x)))' = x' / (C * (C * (x * y))). [back_rewrite(6007),rewrite([6041(15)])].

6248 (x * (y * C)) / L(y,C,x) = x * C. [para(16(a,1),113(a,1,1,2))].

6253 L(x * C,C',y) / L(x,y,C) = C. [para(54(a,1),113(a,2)),rewrite([4467(5),4394(9)])].

6489 C' * (x * (y * C)) = C * ((C' * x) * y). [para(122(a,1),10(a,1,2))].

6532 x * (C * L(y,x,C')) = C * (x * y). [para(75(a,1),122(a,1,2,2)),rewrite([35(7),16(8,R)]),flip(a)].

6533 L(x * (C * ((C' * y) * z)),x',C) = (C' * x) * (y * (z * C)). [para(122(a,1),77(a,2,2)),rewrite([2042(14),31(14)])].

6599 x / (C * y) = x / (y * C). [para(7(a,1),4291(a,1,1))].

6651 (C * x) / y = (x * C) / y. [para(4293(a,1),33(a,1,2)),rewrite([108(7)]),flip(a)].

6718 C' * ((C * x) * y) = C * (x * (C' * y)). [para(123(a,1),10(a,1,2))].

6867 L(x,y / x,C) = C * ((x / y) * (C' * y)). [back_rewrite(1924),rewrite([6718(10)])].

6873 (C' * x) * (y * C) = C * (x * (C' * y)). [back_rewrite(246),rewrite([6718(12)])].

6977 L((C' * x') * y,x * C,C') = x' * (C' * y). [para(53(a,1),129(a,2,1,1)),rewrite([1972(3)])].

6996 (C' * (x' * x')) * (x * y) = L((C' * x') * y,C,x). [para(57(a,2),129(a,2,1,1)),rewrite([2042(3),5151(8),2042(11),176(11)]),flip(a)].

7187 L(x,y * C,y) = L(x,C,y). [back_rewrite(1995),rewrite([6996(11),1976(8)]),flip(a)].

7188 L(L(x,y,C),C,y) = x. [back_rewrite(1956),rewrite([6996(11),232(8),1181(6),2315(7),3772(8),1044(5,R),53(5)])].

7191 L(x,y * C,C') = L(x,C,y). [back_rewrite(5156),rewrite([7187(8)])].

7196 L((C' * x') * y,C,x) = x' * (C' * y). [back_rewrite(6977),rewrite([7191(10)])].

7205 (C' * (x' * x')) * (x * y) = x' * (C' * y). [back_rewrite(6996),rewrite([7196(15)])].

7206 L(C * ((x / y) * (C' * y)),C,y / x) = x. [para(68(a,1),7188(a,1,1)),rewrite([2042(4),108(4),232(7),1181(6),6718(7)])].

7212 L(L(x,C',y),C,y) = x. [para(7188(a,1),2748(a,1)),rewrite([118(2),5420(5)]),flip(a)].

7231 x' * (x' * ((C' * x) * ((C * x) * y))) = L(y,C * x,C' * x). [para(4699(a,1),87(a,1,1,1)),rewrite([176(2),2042(7),31(7),10(10),12(11),10

(15),2042(17),31(17)])].

7260 (C * x) * (x * y) = x * (x * (y * C)). [para(133(a,1),20(a,1,1)),rewrite([12(4),13(11),123(13)]),flip(a)].

7304 L(C,C' * x,C * x) = C. [para(133(a,1),105(a,1,2,2)),rewrite([245(6),118(3),5784(5),35(6),176(2),12(7),5599(6),5469(5),10(4)]),flip(a)].

7307 (x * x) / (C' * x) = C * x. [para(133(a,1),113(a,1,1)),rewrite([5216(6)])].

7384 L(x,y / z,z) = L(x,y,z). [para(7(a,1),5151(a,1,2)),flip(a)].

7385 L(x,y',y * z) = L(x,z,y). [para(10(a,1),5151(a,1,2)),rewrite([3026(2)]),flip(a)].

7391 L(x,y,y' * z) = L(x,z,y'). [para(35(a,1),5151(a,1,2)),rewrite([3026(3)]),flip(a)].

7393 L(x,y',C) = L(x,C,y). [para(54(a,1),5151(a,1,2)),rewrite([5418(4),5438(6)]),flip(a)].

7394 L(x,C,y') = L(x,y,C). [para(127(a,1),5151(a,1,2)),rewrite([5418(5),1962(7)])].

7401 L(x,y / z,C) = L(x,C,z / y). [para(161(a,1),5151(a,1,2)),rewrite([5418(5),5462(8)]),flip(a)].

7405 L(x,C' * y,C') = L(x,y,C'). [para(1044(a,2),5151(a,1,2))].

7406 L(x,C,y * C') = L(x,y,C'). [para(1151(a,1),5151(a,1,2)),rewrite([5162(4)]),flip(a)].

7422 L(x,C' * y,y') = L(x,C',y'). [para(2241(a,1),5151(a,1,2)),flip(a)].

7423 L(x,C' * y',y) = L(x,C',y). [para(2242(a,1),5151(a,1,2)),flip(a)].

7442 L(x,y / z,L(z',z,y)) = L(x,y,(y * z)'). [para(2186(a,1),5151(a,1,2)),rewrite([5440(7)])].

7448 (x' / (C * (C * (x * y)))) * (C * (C * (x * (y * (C * x))))) = L(C,y,C * x). [para(5151(a,1),105(a,2)),rewrite([5966(7),2042(3),6041(8)

])].

7472 L(x,C,y) = L(x,y,C'). [back_rewrite(3358),rewrite([7391(5)]),flip(a)].

7479 L(x,C,x / y) = C * ((x / y) * (C' * y)). [back_rewrite(6867),rewrite([7401(3)])].

7494 L(x,C,x / (C * y)) = (C' * (x / (C * y))) * (y * (C * C)). [back_rewrite(4420),rewrite([7401(5)])].

7654 x' * ((C' * x) * y) = L(y * C',x',C). [back_rewrite(2314),rewrite([7422(7),3772(7)]),flip(a)].

7657 L(C,(C' * x') * y,C * x) = y' * (C * L(y,C',x)). [back_rewrite(5821),rewrite([7423(16)])].

7682 L(x,C * y,C' * y) = L(L(x,C,y),C,y). [back_rewrite(7231),rewrite([7654(10),1044(7,R),6718(7),3722(11),5599(8),16(5,R),35(5),31(5)]),fli

p(a)].

7792 L(x,y',C) = L(x,y,C'). [para(1853(a,1),7393(a,1,2)),rewrite([4156(5),7406(8)])].

7799 C * L(x,y,C') = L(C * x,y,C'). [para(7393(a,2),89(a,1,2)),rewrite([1972(3),2242(5),31(3),7792(4),1972(10),3186(12)])].

7804 L(L(x,C,y),C,y') = x. [para(7393(a,1),7188(a,1,1))].

7818 x' * ((C' * x) * y) = L(y * C',x,C'). [back_rewrite(7654),rewrite([7792(12)])].

7834 L(x * (C * ((C' * y) * z)),x,C') = (C' * x) * (y * (z * C)). [back_rewrite(6533),rewrite([7792(10)])].

7855 x * L(y,x,C') = L(x * y,x,C'). [back_rewrite(4720),rewrite([7792(8)])].

7892 L(x * (C * y),x,C') = C * (x * y). [back_rewrite(6532),rewrite([7799(5),7855(6)])].

7898 (C' * x) * (y * (z * C)) = C * (x * ((C' * y) * z)). [back_rewrite(7834),rewrite([7892(10)]),flip(a)].

7902 L(x,C,x / (C * y)) = C * ((x / (C * y)) * y). [back_rewrite(7494),rewrite([7898(16),16(14,R),35(14)])].

7957 L(x,C',y) = L(x,C,y'). [para(1853(a,1),7394(a,1,3)),rewrite([5418(5),5471(8)]),flip(a)].

7960 L(x,y',C') = L(x,y,C). [para(1972(a,1),7394(a,1,3)),rewrite([7391(6),5151(8)])].

7968 L(L(x,C,y'),C,y) = x. [para(7394(a,2),7188(a,1,1))].

7969 L(L(x,C,y),y,C) = x. [para(7394(a,1),7212(a,1)),rewrite([7957(4),31(3)])].

7992 L(C,(C' * x') * y,C * x) = y' * L(y * C,x,C). [back_rewrite(7657),rewrite([7957(14),3723(15),7960(16)])].

8005 L(x * C,C,y') / L(x,y,C) = C. [back_rewrite(6253),rewrite([7957(5)])].

8014 x' * (C * (C * (x * y))) = L(C * (y * C),C,x'). [back_rewrite(5653),rewrite([7957(14)])].

8024 (x / y) * ((C * (y / x)) * z) = L(z * C,C,x / y). [back_rewrite(5507),rewrite([7957(12),108(11)])].

8078 C * L(x,y,C) = L(x * C,C,y'). [back_rewrite(1144),rewrite([7957(9)])].

8458 L(x,C,y / x) = C' * ((x / y) * (C * y)). [para(5477(a,1),68(a,1)),rewrite([12(8),2042(9),2042(9),108(9),12(14),232(15),1181(12),35(11)]

)].

8526 x' * (C' * (x * y)) = L(C' * y,x,C). [para(5480(a,1),129(a,1)),rewrite([16(8,R),2042(9),176(9),12(13),7205(14)]),flip(a)].

8878 (x * C) / (C' * x) = C * C. [para(16(a,1),155(a,1,1))].

9017 (C * x) / (C * y) = (x * C) / (y * C). [para(6651(a,1),6599(a,2))].

9129 L(C,C' * x,x * C) = C. [para(16(a,1),7304(a,1,3))].

9320 L(x,y / z,C') = L(x,C,y / z). [para(108(a,1),7792(a,1,2)),rewrite([7401(3)]),flip(a)].

9330 L(x,C,(y * C) / x) = (C * (x / (y * C))) * y. [back_rewrite(1817),rewrite([9320(6)])].

9620 (x * C) * (C' * x) = x * x. [para(9129(a,1),113(a,1,2)),rewrite([16(7,R),35(7),5196(3),118(5),151(6)]),flip(a)].

10374 (C * x) * (y * (C * x)) = C * ((C * x) * (y * x)). [para(187(a,1),1181(a,1)),rewrite([1181(3),1181(5),1181(10)])].

10381 L(x * C,C,x / y) / y = C * (x / y). [para(1745(a,1),187(a,2,2)),rewrite([108(4),8024(6),16(9,R)])].

10479 (C * (C * (x * (y * C)))) / (C * x') = C * ((C * x) * (y * x)). [back_rewrite(5149),rewrite([10374(17)])].

10512 ((C * x) * y) / (C' * x') = C * ((C * x) * (y * x)). [back_rewrite(1951),rewrite([10374(14)])].

10588 (x / (y * z)) * y = y' * ((y * x) / z). [para(188(a,1),10(a,1,2)),flip(a)].

10589 (x' * y) / (x * z) = x' * ((y / z) * x'). [para(10(a,1),188(a,1,2,1,2)),flip(a)].

10691 L(x,C,(C * y) / z) = L(x,C,y / (C * z)). [para(188(a,1),4156(a,1,2)),rewrite([7401(5),16(10,R),4156(12),7401(10)]),flip(a)].

10905 x' / (x * y) = x' * (y' * x'). [back_rewrite(5974),rewrite([10589(5),33(3)]),flip(a)].

11114 (C' * (x' * ((C' * y') * x'))) * (x * (C * (C * (C * (y * x))))) = L(C,C * (C * (y * x)),x). [back_rewrite(6118),rewrite([10905(7),204

2(6)])].

11163 (x * (y * x))' = x' * (y' * x'). [back_rewrite(5966),rewrite([10905(6)])].

11243 (x * y)' * x = x' * (x / y). [para(190(a,1),10(a,1,2)),flip(a)].

11285 (x * C) / (y * C) = C * ((x * C') / y). [para(101(a,1),190(a,1,2,1,1)),rewrite([2042(8),2042(8),6873(13),4314(14),1200(13),3189(8)]),f

lip(a)].

11582 (C * x) / (C * y) = C * ((x * C') / y). [back_rewrite(9017),rewrite([11285(10)])].

11597 C * ((C * x) * (y * x)) = C * (x * ((y * C) * x)). [back_rewrite(10479),rewrite([11582(11),1044(9,R),10(9),191(6)]),flip(a)].

11704 ((C * x) * y) / (C' * x') = C * (x * ((y * C) * x)). [back_rewrite(10512),rewrite([11597(14)])].

11751 (x * C) * (y * (C * x)) = C * (x * ((y * C) * x)). [para(239(a,1),191(a,2)),rewrite([2042(6),11704(8)]),flip(a)].

11801 x' / (C * (C * (x * y))) = C' * (x' * ((C' * y') * x')). [back_rewrite(6198),rewrite([11751(6),2042(7),11163(7),1972(6)]),flip(a)].

11815 C * (x' * L(x,C,y)) = L(C,y,C * x). [back_rewrite(7448),rewrite([11801(7),232(20),1181(13),102(19),13(17),10(15),2443(13),1044(10,R),1

0(10),10(11)])].

11820 C * (x' * L(x,y,C')) = L(C,y,C * x). [back_rewrite(6101),rewrite([11801(7),232(20),1181(13),102(19),13(17),5599(15),16(12,R),5765(14),

7898(13),7818(12),7799(13),1151(10),10(12)])].

12513 L(x,C * y,y' * C') = x. [para(31(a,1),1851(a,1,2,2))].

13255 L(x',x,y) * L(z,y / x,y') = y' * ((y / x) * z). [para(2962(a,2),75(a,1,1))].

13275 L(x,y / z,y') = L(x,y,(y * z)'). [para(2962(a,2),3026(a,1,3)),rewrite([7442(4)]),flip(a)].

13325 (x * y)' * (x * z) = x' * ((x / y) * z). [back_rewrite(13255),rewrite([13275(5),2321(6)])].

13901 x' * ((x / y) * (C * (y * C))) = L(C * C,y,x). [back_rewrite(4056),rewrite([13325(8)])].

13964 L(C,x * C',y) = L(C,x,y). [back_rewrite(3266),rewrite([13325(7),10588(6),1181(6),5599(6),5761(6)]),flip(a)].

14806 (x / y) * ((C' * (y / x)) * x) = (C' * (x / y)) * y. [para(1044(a,2),228(a,2,1)),rewrite([1848(5),108(5)])].

15047 (x / y) * (C * y) = L(x * C,C,y). [para(16(a,2),231(a,1,2)),rewrite([16(8,R),5599(9)])].

15071 (x / y) * (C' * y) = L(C' * x,y,C). [para(1044(a,2),231(a,1,2)),rewrite([1044(10,R),8526(11)])].

15092 L(C * (x * y),C,x) = (C * x) * y. [para(3918(a,1),231(a,1,1)),rewrite([2(5),2042(6),7260(12),4403(13),2443(14),1044(11,R),10(11)]),fli

p(a)].

15094 (x / y) * (C * (y * C)) = L(C * (x * C),C,y'). [para(875(a,2),231(a,1,2)),rewrite([875(12,R),16(11,R),8014(13)])].

15204 L(x,C,y / x) = L(x,C,y). [back_rewrite(8458),rewrite([15047(9),5754(10)])].

15206 L(x * C,C,y) = x * L(C,y,x). [back_rewrite(3230),rewrite([15047(4)])].

15262 L(x,C,x / y) = L(x,C,y'). [back_rewrite(7479),rewrite([15071(9),8078(10),16(8,R),35(8)])].

15263 L(L(x,C,y'),C,y / x) = x. [back_rewrite(7206),rewrite([15071(6),8078(7),16(5,R),35(5)])].

15269 x' * L(C * (x * C),C,y') = L(C * C,y,x). [back_rewrite(13901),rewrite([15094(7)])].

15290 (C * (x / (y * C))) * y = L(x,C,y). [back_rewrite(9330),rewrite([15204(5),3026(4)]),flip(a)].

15298 C * ((x / (C * y)) * y) = L(x,y,C). [back_rewrite(7902),rewrite([15262(5),2042(4),7391(6),7960(4)]),flip(a)].

15333 L(x,C,y * x) = L(x,C,y). [para(6(a,1),15204(a,1,3)),flip(a)].

15347 L(L(x,C,y),C,x / y) = x. [para(15204(a,1),7969(a,1,1)),rewrite([7401(5)])].

15361 L(x,C,y * (x * C)) = L(x,C,y). [para(197(a,1),15204(a,1,3)),rewrite([5418(6),3026(4),5418(9)]),flip(a)].

15367 L(x * (y * C),C,y) = (x * C) * y. [para(4300(a,1),15204(a,1,3)),rewrite([5310(6),5418(10)]),flip(a)].

15392 L(L(x,C,y),C,(y * x)') = x. [para(15333(a,1),7804(a,1,1))].

15405 L(L(x * y,C,y),C,x) = x * y. [para(6(a,1),15347(a,1,3))].

15414 L(x,C,L(x,y,C) / y) = L(x,y,C). [para(7188(a,1),15347(a,1,1))].

15508 (x * C') * (C * y) = C * (x * (C' * y)). [para(1044(a,1),232(a,1,1)),rewrite([1181(11),6718(12)])].

15597 L(x,y * y,C' * y) = L(L(x,C,y),C,y). [para(7307(a,1),7384(a,1,2)),rewrite([7682(6)]),flip(a)].

16421 L(x,y * C,C' * y) = L(x,C,y'). [para(8878(a,1),7384(a,1,2)),rewrite([4692(7),5420(5),7957(3)]),flip(a)].

16673 (C' * x) * (y * (C * (C * z))) = C * (x * (C * (y * (C' * z)))). [para(243(a,1),231(a,1,2)),rewrite([118(2),6718(18),6718(16)])].

16765 L(C,C * (C * (x * y)),y) = L(C,x,C * y). [back_rewrite(11114),rewrite([16673(20),10(16),13(14),5599(12),16(9,R),5765(11),7898(10),7818

(9),7799(10),1151(7),11820(7)]),flip(a)].

16956 L(L(x,C,y),C,y) = L(x,C,y'). [para(9620(a,1),5151(a,1,2)),rewrite([15597(5),16421(10)])].

17456 (x' * C') * ((C * x) * y) = y. [para(12513(a,1),75(a,1,2)),rewrite([15508(7),1152(6),9(4),2(2)]),flip(a)].

17654 L(C,C * x,y) = L(C,x,y). [para(7(a,1),13964(a,1,2)),rewrite([1181(6)]),flip(a)].

17659 L(C,x * C,y) = L(C,x,y). [para(239(a,2),13964(a,1,2)),rewrite([1044(6,R),10(6)]),flip(a)].

17661 L(C,C' * x,y) = L(C,x,y). [para(1044(a,2),13964(a,1,2))].

17684 L(C,x,C * y) = L(C,x,y). [back_rewrite(16765),rewrite([17654(7),17654(5),5151(3)]),flip(a)].

17827 C * (x' * L(x,C,y)) = L(C,y,x). [back_rewrite(11815),rewrite([17684(10)])].

17854 L(C,(C' * x') * y,x) = y' * L(y * C,x,C). [back_rewrite(7992),rewrite([17684(9)])].

17866 L(L(C,x,y),C * y,x) = C. [back_rewrite(5919),rewrite([17684(4)])].

17870 L(C,x,y * (C * (z * C))) = L(C,x,(y * C) * z). [back_rewrite(5897),rewrite([17684(9),17684(7),17684(14)]),flip(a)].

17887 L(C,x,y * (z * (C * y))) = L(C,x,y * (z * y)). [back_rewrite(5855),rewrite([17684(6)]),flip(a)].

17889 L(C,x,y * C) = L(C,x,y). [back_rewrite(5847),rewrite([17887(8),17684(6)])].

17941 L(C,x,y / (C * x)) = L(C,x,y). [para(17654(a,1),2748(a,1)),rewrite([17654(9)])].

17944 L(C,(C' * x) * y,z) = L(C,x * (y * C),z). [para(122(a,1),17654(a,1,2)),rewrite([17654(13)]),flip(a)].

17945 L(C,(C * x) * y,z) = L(C,x * (C' * y),z). [para(123(a,1),17654(a,1,2)),rewrite([17654(13)])].

17971 x' * L(x * C,y,C) = L(C,y',x). [back_rewrite(17854),rewrite([17944(7),5420(6),17889(5)]),flip(a)].

18302 L(C,x,C' * y) = L(C,x,y). [para(35(a,1),17684(a,1,3)),flip(a)].

18304 L(C,x,y * C') = L(C,x,y). [para(1151(a,1),17684(a,1,3)),flip(a)].

18307 L(C,x,(C * y) * z) = L(C,x,y * (C' * z)). [para(123(a,1),17684(a,1,3)),rewrite([17684(13)])].

18310 L(C,x / (C * y),y) = L(C,x,y). [para(17684(a,1),7384(a,1)),rewrite([17684(9)])].

18331 L(L(C,x,y),y,x) = C. [para(35(a,1),17866(a,1,2)),rewrite([18302(5)])].

18362 L(L(C,x,y),y,C * x) = C. [para(17654(a,1),18331(a,1,1))].

18563 L(C,x,(y * C) * z) = L(C,x,y * (C' * z)). [para(277(a,1),17684(a,1,3)),rewrite([17684(9),17870(7),17684(12),18307(10)])].

18627 L(L(C,x,y),y,C * (x / y)) = C. [para(7384(a,1),18362(a,1,1))].

18794 L(L(x,y,C),C,y / (C * x)) = x. [para(2042(a,1),15263(a,1,1,3)),rewrite([7391(6),7960(4),10691(7)])].

18797 L(L(x,y,C),C,y / x) = x. [para(7394(a,1),15263(a,1,1))].

18825 L(L(x,y * x,C),C,y) = x. [para(6(a,1),18797(a,1,3))].

18851 x / L(y * C,C,x') = C' * (x / y). [para(18797(a,1),201(a,1,1,2)),rewrite([7(2),8078(4),118(9)])].

18875 L(x,y * x,C) = L(x,y,C). [para(18825(a,1),7969(a,1,1)),flip(a)].

18983 L(L(x,y,C),C,y * x) = x. [para(18875(a,1),7188(a,1,1))].

19030 L(L(x,C,y'),C,y * x) = x. [para(7394(a,2),18983(a,1,1))].

20551 C' * L(x,C' * (y / z),z / y) = (z / y) * ((C' * (y / z)) * x). [para(1174(a,1),75(a,1,1))].

20554 L(x,C' * (y / z),z / y) = L(x,C,y / z). [para(1174(a,1),3026(a,1,3)),rewrite([7405(7),9320(4)]),flip(a)].

20581 (x / y) * ((C' * (y / x)) * z) = C' * L(z,C,y / x). [back_rewrite(20551),rewrite([20554(8)]),flip(a)].

20590 (C' * (x / y)) * y = C' * L(x,C,y). [back_rewrite(14806),rewrite([20581(7),15204(5)]),flip(a)].

20607 L(x,C,y / (C * x)) = L(x,C,y). [back_rewrite(1909),rewrite([20590(12),5754(12)])].

20694 ((x * C) * y)' * (((C * x) * y) * z) = z. [para(1483(a,1),10(a,1,1))].

25091 L(x * C,C,y) / L(C,y,x) = x. [para(15206(a,2),6(a,1,1))].

25098 L(C * x,C,y) = x * L(C,y,x). [para(16(a,2),15206(a,1,1))].

25195 (C * x') * L(x,C,y) = L(C,y,x). [para(15206(a,2),1840(a,1,2)),rewrite([16(8,R),1151(8),18304(11)])].

25357 L(x * y,C,y) = L(x * y,x,C). [para(15405(a,1),7969(a,1,1)),flip(a)].

26225 L(L(x,y,C),y,C) = L(x,y,C'). [para(176(a,1),16956(a,2,3)),rewrite([5480(3),5480(5),5480(9),7792(7)])].

26230 L(L(x,y,C),C,y') = L(x,C,y). [para(7188(a,1),16956(a,1,1)),flip(a)].

26231 L(L(x,C,y'),y,C) = L(x,C,y). [para(16956(a,1),7394(a,1)),rewrite([31(3)]),flip(a)].

26510 L(C,x * y,L(y,x,C)) = L(C,x,y). [para(66(a,1),17941(a,1,3)),rewrite([2042(5),18302(7),2967(4)]),flip(a)].

26680 L(L(C,x,y),y,x / (C * y)) = C. [para(18310(a,1),18331(a,1,1))].

26749 L(C,x * (y * (C * (x * x))),x) = L(C,x * (y * x),x). [para(507(a,1),18310(a,1,2)),flip(a)].

27732 L(L(x,y,C),C,y / (x * C)) = x. [para(16(a,1),18794(a,1,3,2))].

29095 L(x * y,C,L(y,x,C)) = L(x * y,x,C). [para(66(a,1),20607(a,1,3)),rewrite([2042(5),7391(7),7960(5)]),flip(a)].

29106 L(L(x,C,y),C,((y / (C * x)) * x)') = x. [para(20607(a,1),15392(a,1,1))].

29992 L(L(C,x,y),C,L(C * y,C,x)) = L(L(C,x,y),C,y). [para(25098(a,2),15333(a,1,3))].

30006 L(L(L(C,x,y),C,y'),C,L(C * y,C,x)) = L(C,x,y). [para(25098(a,2),19030(a,1,3))].

30486 C * ((x / (C * y)) * (y * L(C,x,y)))' = ((x / (C * y)) * y)'. [para(26680(a,1),66(a,1,1)),rewrite([1759(9)])].

30487 (x / (C * y)) * (y * L(C,x,y)) = L(x,y,C). [para(26680(a,1),75(a,1,2)),rewrite([16(6,R),15298(6)]),flip(a)].

30494 (x / (C * y)) * y = L(C' * x,y,C). [para(26680(a,1),113(a,1,2)),rewrite([30487(7),118(4),5295(5)]),flip(a)].

30523 L(C' * x,y,C)' = C * L(x,y,C)'. [back_rewrite(30486),rewrite([30487(8),30494(9)]),flip(a)].

30525 L(L(x,C,y),C,L(y,x,C)') = x. [back_rewrite(29106),rewrite([30494(7),30523(9),5418(9)])].

30623 (x / (y * C)) * L(y * C,C,x') = L(x,C,y). [para(27732(a,1),75(a,1,2)),rewrite([16(5,R),15290(6),8078(9)]),flip(a)].

30639 L(L(x,y,C),C,L(y,C,x)) = x. [para(27732(a,1),15361(a,2)),rewrite([16(10,R),8078(10),30623(12)])].

30654 L(L(x,L(y,x,C),C),C,y) = x. [para(7188(a,1),30639(a,1,3))].

30659 L(x,L(y,C,x),C) = L(x,y,C). [para(30639(a,1),7969(a,1,1))].

30663 L(x,C,L(y,C,x)') = L(x,y,C). [para(30639(a,1),7804(a,1,1))].

30758 L(x,L(y,x,C),C) = L(x,y,C). [para(30654(a,1),7969(a,1,1)),flip(a)].

30762 L(L(x,L(y,x,C'),C),C,L(y,x,C)) = x. [para(26225(a,1),30654(a,1,1,2))].

30772 L(x,L(y,x,C'),C) = L(x,y,C). [para(7472(a,1),30659(a,1,2))].

30840 L(L(x,C,y),L(y,x,C),C) = x. [para(30639(a,1),30659(a,1,2)),rewrite([7969(4)]),flip(a)].

30842 L(L(x,y,C),C,L(y,x,C)) = x. [back_rewrite(30762),rewrite([30772(5)])].

30887 L(L(x,y,C),L(y,x,C),C) = L(x,L(y,x,C),C'). [para(30758(a,1),26225(a,1,1))].

30888 L(x,L(y,x,C),C') = L(x,y,C'). [para(26225(a,1),30758(a,2)),rewrite([30758(6),30887(6)])].

30889 L(L(x,y,C),C,L(y,x,C)') = L(x,C,L(y,x,C)). [para(30758(a,1),26230(a,1,1))].

30892 L(L(x,y,C),L(y,x,C),C) = L(x,y,C'). [back_rewrite(30887),rewrite([30888(11)])].

30898 L(x,C,L(y,x,C)) = L(x,C,y). [para(30840(a,1),7188(a,1,1))].

30950 L(L(x,y,C),C,L(y,x,C)') = L(x,C,y). [back_rewrite(30889),rewrite([30898(11)])].

30959 L(L(x,C,y'),C,L(y,x,C)) = x. [para(7394(a,2),30842(a,1,1))].

31701 L(x,C,L(y,x,C')') = L(x,y,C). [para(30842(a,1),30525(a,1,1)),rewrite([30892(7)])].

33796 L(x * C,C,x / y) = L(x * C,y,C). [para(15262(a,1),3723(a,1,2)),rewrite([3723(5),7960(6),9320(10)]),flip(a)].

33878 L(x * C,y,C) / y = C * (x / y). [back_rewrite(10381),rewrite([33796(5)])].

34191 L(C,x * x,y) = L(C,x',y). [para(5480(a,1),5761(a,1,2)),rewrite([17971(6)]),flip(a)].

34392 L(L(C,x',y),y,x * x) = C. [para(34191(a,1),18331(a,1,1))].

35000 L(C,x,L(y,x,C)) = L(C,x,y). [para(5972(a,1),18310(a,1,2)),rewrite([118(3),17661(7),26510(9)])].

35099 L(C,x,L(y,C,x')) = L(C,x,y). [para(7394(a,2),35000(a,1,3))].

35131 (x * C) / L(C,y,x) = L(x,y,C). [para(35000(a,1),25091(a,1,2)),rewrite([16(4,R),8078(4),7968(7)])].

35548 (C * x) / L(C,y,x) = L(x,y,C). [para(16(a,2),35131(a,1,1))].

35556 L(x,L(C,y,z),L(z,y,C)) = L(x,L(C,y,z),z * C). [para(35131(a,1),2748(a,1,3))].

35583 L(L(C,x,L(C,y,x)),L(C,y,x),L(x * C,C,y')) = C. [para(35131(a,1),18627(a,1,3,2)),rewrite([17659(6),8078(10)])].

35661 L(C,x,y) / (C * y) = L(y,x,C)'. [para(35548(a,1),108(a,1,1)),flip(a)].

36243 L(x * C,C,y) / L(x,C,y) = C. [para(26231(a,1),8005(a,1,2)),rewrite([16(5,R),3723(5),7960(6),26230(7)])].

36310 L(x,L(y,C,z),L(y * C,C,z)) = L(x,L(y,C,z),C). [para(36243(a,1),2748(a,1,3)),flip(a)].

36315 L(x * C,C,y)' = C' * L(x,C,y)'. [para(36243(a,1),4967(a,1,2)),rewrite([36310(10),2099(7),118(5)]),flip(a)].

36588 L(C,x,L(y * C,C,z')) = L(C,x,L(y,z,C)). [para(8078(a,1),17684(a,1,3))].

36593 L(x,C,y')' = L(x,y,C)'. [para(8078(a,1),11243(a,1,1,1)),rewrite([36315(6),16(9,R),35(9),1759(10),10(12)])].

36636 L(x,C,y)' = L(x,y,C')'. [para(31(a,1),36593(a,1,1,3)),rewrite([7792(6)])].

36826 L(x,L(y,C,z),C) = L(x,C,L(y,z,C')'). [para(36636(a,1),7394(a,1,3)),flip(a)].

38615 (x / y) * L(y,x,C) = L(x,C,y). [para(30898(a,1),15290(a,2)),rewrite([16(5,R),8078(5),18851(7),35(6)])].

38729 L(x,C,y) / L(y,x,C) = x / y. [para(38615(a,1),6(a,1,1))].

38917 L(x,C,y') / L(y,x,C) = L(x,C,y) / y. [para(16956(a,1),38729(a,1,1)),rewrite([36826(7),31701(9)])].

38958 L(x,C,y) / y = x / L(y,C,x). [para(30959(a,1),38729(a,1,1)),rewrite([36826(7),7960(7),30950(7),38917(9)]),flip(a)].

39284 L(x * y,x,C) / L(y,x,C) = x. [para(18983(a,1),38958(a,2,2)),rewrite([29095(5),6(8)])].

39689 L(x * y,C,y) / L(y,x,C) = x. [para(25357(a,2),39284(a,1,1))].

40020 L(C,x,y * (C' * x')) = L(C,x,y * (x' * C)). [para(15367(a,1),35099(a,1,3)),rewrite([18563(6)])].

40151 L(C,x / y,x) = L(C,y',x). [para(15414(a,1),5761(a,1,2)),rewrite([17971(6),33878(9),17654(8)]),flip(a)].

40170 L(C,x',y * x) = L(C,y,y * x). [para(6(a,1),40151(a,1,2)),flip(a)].

40187 L(C,(x * (C * y))',y) = L(C,x',y). [para(4301(a,1),40151(a,1,2)),rewrite([17889(5),17889(11)]),flip(a)].

41267 L(L(C,x,y),C,y') = L(C,x,y). [para(17827(a,1),15092(a,1,1)),rewrite([25195(11)])].

41274 L(L(C,x,y),C,y) = L(C,x,y). [back_rewrite(30006),rewrite([41267(5),29992(8)])].

41322 L(L(C,x,y),C,x') = L(C,x,y). [para(2967(a,1),41274(a,1,1)),rewrite([2967(9)])].

41328 L(x,L(C,y,x),C) = L(x,C,L(C,y,x)'). [para(41274(a,1),30663(a,1,3,1)),flip(a)].

41345 L(C,x,L(C,y,x)) = C. [para(41274(a,1),17827(a,1,2,2)),rewrite([8(7),3(3)]),flip(a)].

41351 L(C,L(C,x,y),y) = C. [back_rewrite(35583),rewrite([41345(4),36588(9),35556(6),17889(6)])].

41367 L(C,x,L(x,y,C)') = C. [para(41345(a,1),17941(a,2)),rewrite([35661(6)])].

41405 L(x,C,L(C,y,x)') = x. [para(41351(a,1),35131(a,1,2)),rewrite([118(4),53(5),41328(4)]),flip(a)].

41413 L(x,L(C,y,x),C) = x. [back_rewrite(41328),rewrite([41405(9)])].

41421 L(x',L(C,x,y),C) = x'. [para(2967(a,1),41413(a,1,2))].

41469 L(L(x,C * y,z),z,C * y) = x. [para(609(a,1),728(a,1,2)),rewrite([20694(9)]),flip(a)].

41577 L(C,L(x,C,y),x') = C. [para(7969(a,1),41367(a,1,3,1))].

42000 L(C,L(x,y,C),x') = C. [para(7394(a,1),41577(a,1,2))].

42325 L(C,L(x * C,y,C),x') = C. [para(1972(a,1),42000(a,1,3)),rewrite([18302(10)])].

42788 L(L(C,x,y),C,x) = L(C,x,y). [para(41421(a,1),30525(a,1,3,1)),rewrite([41322(5),31(5)])].

47215 C * L(C,x',y) = L(C * C,x,y). [para(42325(a,1),75(a,1,2)),rewrite([17971(6),16(5,R),16(12,R),8078(12),16(10,R),15269(14)])].

47217 C' * L(C * C,x,y) = L(C,x',y). [para(42325(a,1),113(a,1,2)),rewrite([16(7,R),8078(7),16(5,R),15269(9),118(6),17971(13)])].

47436 L(C,x,L(C,x,y)) = C. [para(42788(a,1),17827(a,1,2,2)),rewrite([8(7),3(3)]),flip(a)].

47443 L(C,L(C,x,y),x) = C. [para(47436(a,1),17866(a,1,1)),rewrite([17654(6)])].

47457 L(C,L(C,x',y),x * x) = C. [para(47436(a,1),34392(a,1,1))].

47461 L(C,x / y,L(C,y',x)) = C. [para(40151(a,1),47436(a,1,3))].

47498 L(x,L(C,x,y),C) = x. [para(47443(a,1),35131(a,1,2)),rewrite([118(4),53(5)]),flip(a)].

47509 L(x,C,L(C,x,y)) = x. [para(47498(a,1),7188(a,1,1))].

47558 (L(C,x,y) * (x * C)) / x = C * L(C,x,y). [para(47509(a,1),6248(a,1,2)),rewrite([16(10,R)])].

49812 L(C,x',L(C * C,x,y)) = C. [para(47457(a,1),18362(a,1,1)),rewrite([47215(7),34191(7)])].

49826 L(C,x,L(C,y',x * y)) = C. [para(6(a,1),47461(a,1,2))].

50843 L(C,x,L(C * C,x',y)) = C. [para(31(a,1),49812(a,1,2))].

50851 L(C,x,L(C * C,y,x)) = C. [para(7385(a,1),49812(a,1,3)),rewrite([31(3)])].

50865 L(C,L(C * C,x,y),y) = C. [para(50851(a,1),17866(a,1,1)),rewrite([17654(8)])].

50872 L(L(C * C,x,y),y,C) = L(C * C,x,y). [para(50851(a,1),35131(a,1,2)),rewrite([16(6,R),118(8),10(9)]),flip(a)].

50890 L(x,L(C * C,y,x),C) = x. [para(50865(a,1),35131(a,1,2)),rewrite([118(4),53(5)]),flip(a)].

50910 L(x,L(C * C,x',y),C) = x. [para(5420(a,1),50890(a,1,2))].

50912 L(L(C * C,x,y),C,y) = L(C * C,x,y). [para(50890(a,1),30842(a,1,3)),rewrite([50872(6)])].

50937 L(C,x,L(C,y,x * y')) = C. [para(31(a,1),49826(a,1,3,2))].

50953 L(C,x',y * x) = L(C,x',y). [para(49826(a,1),25091(a,1,2)),rewrite([16(6,R),47215(6),3026(5),50912(6),118(6),47217(7)]),flip(a)].

50971 L(C,x,x * y) = L(C,y',x). [back_rewrite(40170),rewrite([50953(4)]),flip(a)].

51226 L(C * C,x',y) * x = C * (L(C,x,y) * x). [para(50843(a,1),113(a,1,2)),rewrite([118(10),6489(11),47217(9),31(4)]),flip(a)].

51306 C * L(C,x,y) = L(C * C,x',y). [para(50910(a,1),39689(a,1,2)),rewrite([51226(6),5765(7),47558(6)])].

51331 L(C,x,y * x') = L(C,x,y). [para(50937(a,1),25091(a,1,2)),rewrite([16(6,R),51306(6),3026(7),50912(7),118(7),47217(8),31(3)]),flip(a)].

51499 L(C,x * y,x) = L(C,y',x * x). [para(12(a,1),50971(a,1,3)),rewrite([34191(5),7385(5)])].

51500 L(C,(x' * y)',x) = L(C,x,y). [para(35(a,1),50971(a,1,3)),flip(a)].

51532 L(C,((C * x) * y)',x') = L(C,x',y). [para(17456(a,1),50971(a,1,3)),rewrite([13964(6),18304(13)]),flip(a)].

51562 L(L(C,x',y'),y' * x,y * y) = C. [para(50971(a,1),34392(a,1,1))].

51699 L(C,(x * y)',y * y) = L(C,x',y * y). [back_rewrite(26749),rewrite([51499(7),40187(8),51499(8)]),flip(a)].

51876 L(C,x,y * (C' * x')) = L(C,x,y). [para(1972(a,1),51331(a,1,3,2)),rewrite([17659(9),17659(11)])].

51980 L(C,x,y * (x' * C)) = L(C,x,y). [back_rewrite(40020),rewrite([51876(7)]),flip(a)].

54528 L(L(x,y,z),z,y) = x. [para(35(a,1),41469(a,1,1,2)),rewrite([35(6)])].

62874 L(C,x,y * y) = L(C,y,x). [para(61(a,2),51500(a,1,2,1)),rewrite([2042(8),11163(8),31(5),31(6),17661(8),51499(5),51699(6),31(3),51980(9)

])].

63159 L(C,x * y,x) = L(C,x,y'). [back_rewrite(51499),rewrite([62874(7)])].

63480 L(C,x',y') = L(C,x,y). [para(62874(a,1),5420(a,1)),rewrite([176(3),12(5),7391(6),63159(5),176(7),34191(9),31(7)])].

63508 L(C,x,y') = L(C,y,x). [para(62874(a,1),34191(a,1)),rewrite([62874(3),62874(6)]),flip(a)].

63688 L(L(C,x,y),y' * x,y * y) = C. [back_rewrite(51562),rewrite([63480(4)])].

63689 L(C,x',y) = L(C,x,y'). [back_rewrite(51532),rewrite([63480(7),17945(5),63159(6),1881(5),17684(5)]),flip(a)].

64906 L(L(L(C,B,A'),A,B),A,B) != C. [para(63508(a,2),19(a,1,1,1))].

65085 L(L(C,x,y'),x,y) = C. [para(63508(a,2),54528(a,1,1))].

94440 L(L(L(C,x,y),y',x),x,y) = C. [para(63688(a,1),2324(a,2)),rewrite([5420(5),35(7)])].

94454 L(L(C,x,y),y',x) = L(C,y,x). [para(94440(a,1),54528(a,1,1)),flip(a)].

94460 L(L(C,x,y'),y,x) = L(C,y,x'). [para(31(a,1),94454(a,1,2)),rewrite([63689(7)])].

94479 $F. [back_rewrite(64906),rewrite([94460(8),65085(8)]),xx(a)].

============================== end of proof ==========================

% Proof 1 at 130.39 (+ 1.52) seconds.

% Length of proof is 740.

% Level of proof is 44.

% Maximum clause weight is 33.000.

% Given clauses 4190.

1 L(L(L(C,A,B),A,B),A,B) = C # label(non_clause) # label(goal). [goal].

2 0 * x = x. [assumption].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 A * ((x * y) * A) = (A * x) * (y * A). [assumption].

15 (A * x) * (y * A) = A * ((x * y) * A). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 L(x,y,z) = (z * y)' * (z * (y * x)). [assumption].

18 (x * y)' * (x * (y * z)) = L(z,y,x). [copy(17),flip(a)].

19 L(L(L(C,A,B),A,B),A,B) != C. [deny(1)].

23 x / 0 = x. [para(3(a,1),6(a,1,1))].

26 0' = 0. [para(8(a,1),3(a,1)),flip(a)].

28 0 / x = x'. [para(8(a,1),6(a,1,1))].

30 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([28(3)])].

31 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

32 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

34 x * (x' * y) = y. [back_rewrite(4),rewrite([31(1)])].

35 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

37 L(x,y,y) = x. [para(12(a,1),10(a,1,2)),rewrite([18(5)])].

39 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

40 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

42 (x * (y * x))' * (x * (y * (x * z))) = z. [para(13(a,1),10(a,1,2))].

45 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(12(a,1),13(a,1,1,2)),rewrite([12(7)])].

47 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [para(13(a,1),13(a,1,1,2)),rewrite([13(9)])].

49 (A * x) * A = A * (x * A). [para(2(a,1),15(a,1,2)),rewrite([3(7)])].

50 (A * ((x * y) * A)) / (y * A) = A * x. [para(15(a,1),6(a,1,1))].

53 A * ((A' * x) * A) = x * A. [para(9(a,1),15(a,1,1)),rewrite([2(4)]),flip(a)].

54 (A * x)' * (A * ((x * y) * A)) = y * A. [para(15(a,1),10(a,1,2))].

57 ((x * A) * (A * ((y * x) * A))) * z = (x * A) * ((A * y) * ((x * A) * z)). [para(15(a,1),13(a,1,1,2))].

58 A * (((x * A) * y) * A) = A * (x * (A * (y * A))). [para(15(a,1),13(a,1))].

59 (A * x) * (y * (z * (y * A))) = A * ((x * (y * (z * y))) * A). [para(13(a,1),15(a,1,2))].

60 (x * C) / x = C. [para(16(a,1),6(a,1,1))].

62 C * (x / C) = x. [para(16(a,2),7(a,1))].

63 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

64 x' * (C * x) = C. [para(16(a,2),10(a,1,2))].

65 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

66 C * (x * x) = x * (x * C). [para(16(a,2),12(a,1))].

67 C * (x * x) = x * (C * x). [para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].

68 (x * (x * C)) * y = x * (C * (x * y)). [para(16(a,1),13(a,1,1,2))].

69 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

70 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

71 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

72 C * (x * (y * x)) = x * (y * (C * x)). [para(16(a,2),13(a,2,2,2)),rewrite([16(4,R)])].

73 (A * x) * (A * C) = A * ((x * C) * A). [para(16(a,1),15(a,1,2))].

76 L(x,0,y) = x. [para(2(a,1),18(a,1,2,2)),rewrite([3(2),10(3)]),flip(a)].

78 L(x,y,z) / (z * (y * x)) = (z * y)'. [para(18(a,1),6(a,1,1))].

79 x' * ((x / y) * (y * z)) = L(z,y,x / y). [para(7(a,1),18(a,1,1,1))].

80 L(x,y / x,z) = (z * (y / x))' * (z * y). [para(7(a,1),18(a,1,2,2)),flip(a)].

81 L(x,y,z / (y * x)) = ((z / (y * x)) * y)' * z. [para(7(a,1),18(a,1,2)),flip(a)].

83 L(x,x',y) = (y * x')' * y. [para(8(a,1),18(a,1,2,2)),rewrite([3(5)]),flip(a)].

84 L(x,y,(y * x)') = ((y * x)' * y)'. [para(8(a,1),18(a,1,2)),rewrite([3(6)]),flip(a)].

85 L(x,y',y) = x. [para(9(a,1),18(a,1,1,1)),rewrite([26(2),34(4),2(2)]),flip(a)].

86 L(x',x,y) = (y * x)' * y. [para(9(a,1),18(a,1,2,2)),rewrite([3(4)]),flip(a)].

87 (x * y) * L(z,y,x) = x * (y * z). [para(18(a,1),10(a,1,2)),rewrite([30(3)])].

88 x' * (y' * ((y * x) * z)) = L(z,y * x,y'). [para(10(a,1),18(a,1,1,1))].

89 L(x * y,x',z) = (z * x')' * (z * y). [para(10(a,1),18(a,1,2,2)),flip(a)].

92 (x * (y * z)) * ((x * y)' * ((x * (y * z)) * u)) = ((x * (y * z)) * L(z,y,x)) * u. [para(18(a,1),13(a,1,1,2)),flip(a)].

93 (x * (y * (x * z)))' * (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(13(a,1),18(a,1,1,1)),rewrite([13(8)])].

94 (x * (y * (z * y)))' * (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(13(a,1),18(a,1,2,2))].

95 (A * ((x * y) * A))' * ((A * x) * ((y * A) * z)) = L(z,y * A,A * x). [para(15(a,1),18(a,1,1,1))].

96 (x * (A * y))' * (x * (A * ((y * z) * A))) = L(z * A,A * y,x). [para(15(a,1),18(a,1,2,2))].

97 ((A * x) * y)' * (A * ((x * y) * A)) = L(A,y,A * x). [para(15(a,1),18(a,1,2))].

98 (x * C)' * (C * (x * y)) = L(y,x,C). [para(16(a,1),18(a,1,1,1))].

100 (C * x)' * (x * (C * y)) = L(y,C,x). [para(16(a,2),18(a,1,1,1))].

101 (x * y)' * (x * (C * y)) = L(C,y,x). [para(16(a,2),18(a,1,2,2))].

102 L(x,y,z)' * ((z * y)' * ((z * (y * x)) * u)) = L(u,z * (y * x),(z * y)'). [para(18(a,1),18(a,1,1,1))].

103 (x * (y * z)')' * (x * L(u,z,y)) = L(y * (z * u),(y * z)',x). [para(18(a,1),18(a,1,2,2))].

104 ((x * y)' * x)' * L(z,y,x) = L(y * z,x,(x * y)'). [para(18(a,1),18(a,1,2))].

105 x' * C = C * x'. [para(16(a,2),31(a,2)),rewrite([31(2)])].

106 (x / y)' = y / x. [para(7(a,1),32(a,1,2)),flip(a)].

108 x / (y * (z * (y * x))) = (y * (z * y))'. [para(13(a,1),32(a,1,2))].

110 x / (x * C) = C'. [para(16(a,1),32(a,1,2))].

111 C / (C * x) = x'. [para(16(a,2),32(a,1,2))].

112 (x * (y * z)) / L(z,y,x) = x * y. [para(18(a,1),32(a,1,2)),rewrite([30(7)])].

116 x / C = C' * x. [para(62(a,1),10(a,1,2)),flip(a)].

119 (x * C)' * (x * y) = L(C' * y,C,x). [para(62(a,1),18(a,1,2,2)),rewrite([116(7)])].

123 A * (((A' * x) * y) * A) = x * (y * A). [para(34(a,1),15(a,1,1)),flip(a)].

125 x * (C * x') = C. [para(16(a,2),34(a,1,2))].

126 x' * (y * ((y' * x) * z)) = L(z,y' * x,y). [para(34(a,1),18(a,1,1,1))].

127 L(x' * y,x,z) = (z * x)' * (z * y). [para(34(a,1),18(a,1,2,2)),flip(a)].

130 C * (x * (C' * x)) = x * x. [para(63(a,1),13(a,2,2)),rewrite([16(6,R)])].

131 C' * (x * (y * (x * C))) = x * (y * x). [para(13(a,1),63(a,1,2))].

133 (x * C')' * (x * y) = L(y * C,C',x). [para(63(a,1),18(a,1,2,2))].

134 (C' * x)' * x = L(C,x,C'). [para(63(a,1),18(a,1,2))].

135 (C * x) * (x' * ((C * x) * y)) = C * (x * (C * y)). [para(64(a,1),13(a,1,1,2)),rewrite([16(4,R),70(5)]),flip(a)].

137 L(C * x,x',y) = (y * x')' * (y * C). [para(64(a,1),18(a,1,2,2)),flip(a)].

139 L(C,x,C') = C. [para(34(a,1),64(a,1,2)),rewrite([134(5)])].

142 x' / x = x' * x'. [para(8(a,1),35(a,1,1,2)),rewrite([3(3)])].

143 x / x' = x * x. [para(9(a,1),35(a,1,1,2)),rewrite([3(2)])].

144 (x' * y) / (x * y) = x' * x'. [para(10(a,1),35(a,1,1,2))].

148 (A * (x * (A * (x * A)))) / A = (A * x) * (A * x). [para(15(a,1),35(a,1,1)),rewrite([13(6)])].

149 (C * (x * C)) / x = C * C. [para(16(a,1),35(a,1,1,2))].

150 C' * (x * (C * x)) = x * x. [para(16(a,2),35(a,1,1,2)),rewrite([116(5)])].

151 ((x * y)' * L(z,y,x)) / (x * (y * z)) = (x * y)' * (x * y)'. [para(18(a,1),35(a,1,1,2))].

153 (C' * x) / (x * C) = C' * C'. [para(63(a,1),35(a,1,1,2))].

155 (x / y) * (y / x) = 0. [para(106(a,1),8(a,1,1))].

161 (C' * x)' = C / x. [para(34(a,1),111(a,1,2)),flip(a)].

169 A * (((C * A') * x) * A) = C * (x * A). [para(125(a,1),15(a,1,1)),flip(a)].

170 C' * (x * ((C * x') * y)) = L(y,C * x',x). [para(125(a,1),18(a,1,1,1))].

171 L(C * x',x,y) = (y * x)' * (y * C). [para(125(a,1),18(a,1,2,2)),flip(a)].

172 L(x',C,x) = C * (x * C)'. [para(125(a,1),18(a,1,2)),rewrite([16(5,R)]),flip(a)].

174 (x * x)' = x' * x'. [para(143(a,1),106(a,1,1)),rewrite([142(4)])].

178 x' * (C * x') = C * (x' * x'). [para(105(a,1),12(a,2,2)),rewrite([16(5,R)]),flip(a)].

184 (C' * x) * (C / x) = 0. [para(116(a,1),155(a,1,1))].

186 ((x / y) * (z * x)) / y = (x / y) * (z * (x / y)). [para(7(a,1),39(a,1,1,2,2))].

187 x * ((y / (x * z)) * x) = (x * y) / z. [para(7(a,1),39(a,1,1,2)),flip(a)].

188 (x' * y) / x = x' * (y * x'). [para(8(a,1),39(a,1,1,2,2)),rewrite([3(3)])].

189 x * ((x * y)' * x) = x / y. [para(8(a,1),39(a,1,1,2)),rewrite([3(2)]),flip(a)].

190 (x * y) / x' = x * (y * x). [para(9(a,1),39(a,1,1,2,2)),rewrite([3(2)])].

197 (x * (A * ((y * x) * A))) / A = x * ((A * y) * x). [para(15(a,1),39(a,1,1,2))].

198 (C * (x * (y * C))) / y = C * (x * C). [para(16(a,1),39(a,1,1,2,2))].

202 (x * L(y,z,x)) / (z * y) = x / z. [para(18(a,1),39(a,1,1,2)),rewrite([189(8)])].

205 C' * (x * x) = x * (C' * x). [para(63(a,1),39(a,1,1,2)),rewrite([116(3)])].

207 (C * C) / x = C * (x' * C). [para(64(a,1),39(a,1,1,2))].

212 (C / x) * (C' * (x * y)) = L(y,x,C'). [para(161(a,1),18(a,1,1))].

214 (C' * x) * ((C / x) * y) = y. [para(161(a,1),34(a,1,2,1))].

227 (x / y) * ((z / (x / y)) * x) = ((x / y) * z) * y. [para(7(a,1),40(a,1,2,2))].

228 (x' * y) * x = x' * (y / x'). [para(8(a,1),40(a,1,2,2)),rewrite([3(5)]),flip(a)].

229 (x * y) * x' = x * (y / x). [para(9(a,1),40(a,1,2,2)),rewrite([3(3)]),flip(a)].

230 (x / y) * (y * z) = y' * ((y * x) * z). [para(40(a,1),10(a,1,2)),flip(a)].

231 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),40(a,1,2,2)),flip(a)].

235 x' * ((((x * y) * (y / x)) / x') * z) = (y / x) * ((x * y) * z). [para(40(a,1),13(a,2,2)),rewrite([230(4),231(7)])].

237 (x / C') * y = (C * x) * y. [para(40(a,1),16(a,1)),rewrite([116(5),231(9),16(12,R),34(12)]),flip(a)].

239 (C * x) * y = (x * C) * y. [para(16(a,1),40(a,2,1)),rewrite([116(3),231(7),237(7),34(8)])].

241 (x * (y / x))' * ((x * y) * z) = L(x * z,y / x,x). [para(40(a,1),18(a,1,2))].

242 (x * y)' * ((z / (x * y)') * L(u,y,x)) = ((x * y)' * z) * (x * (y * u)). [para(18(a,1),40(a,1,2,2))].

243 (x * y) * (x' * z) = x * ((y / x) * z). [para(34(a,1),40(a,1,2,2)),flip(a)].

245 (x' * y) * (C * x) = x' * (C * (y / x')). [para(64(a,1),40(a,1,2,2)),rewrite([16(5,R)]),flip(a)].

246 (x * y) * (C * x') = x * (C * (y / x)). [para(125(a,1),40(a,1,2,2)),rewrite([16(3,R)]),flip(a)].

247 (C * x) * (C / x) = C * C. [para(125(a,1),40(a,1,2)),rewrite([116(7),161(9)]),flip(a)].

248 (x' * C) * y = (C * x') * y. [para(105(a,1),40(a,2,1)),rewrite([230(7),30(3),10(7)])].

251 x / A' = x * A. [back_rewrite(53),rewrite([228(6),34(8)])].

252 L(x,y * z,y') = L(x,y,z / y). [back_rewrite(79),rewrite([230(4),88(6)])].

255 x' * (y' * ((y * x) * z)) = L(z,y,x / y). [back_rewrite(88),rewrite([252(9)])].

256 (x * A') * A = x. [para(251(a,1),6(a,1))].

257 (x * A) * A' = x. [para(251(a,1),7(a,1,1))].

259 (x * A)' = A' / x. [para(251(a,1),106(a,1,1))].

260 (x * A) * (A' / x) = 0. [para(251(a,1),155(a,1,1))].

264 x / A = x * A'. [para(256(a,1),6(a,1,1))].

267 A * ((x * (y * A')) * A) = (A * x) * y. [para(256(a,1),15(a,1,2)),flip(a)].

268 x' * ((x * A') * (A * y)) = L(y,A,x * A'). [para(256(a,1),18(a,1,1,1))].

269 (x * (y * A'))' * (x * y) = L(A,y * A',x). [para(256(a,1),18(a,1,2,2))].

270 (x * A')' = A / x. [para(256(a,1),32(a,1,2)),flip(a)].

273 (x * (A * ((y * x) * A))) * A' = x * ((A * y) * x). [back_rewrite(197),rewrite([264(8)])].

274 A * ((x * (A * (x * A))) * A') = (A * x) * (A * x). [back_rewrite(148),rewrite([264(9),229(10),264(8)])].

277 (x * (y * (x * A))) * A' = x * (y * x). [para(13(a,1),257(a,1,1))].

278 x' * ((x * A) * (A' * y)) = L(y,A',x * A). [para(257(a,1),18(a,1,1,1))].

281 ((x * A) * (y * x)) * A = (x * A) * (y * (x * A)). [para(257(a,1),39(a,1,1,2,2)),rewrite([251(7)])].

282 (A * x) * (A * x) = A * (x * (A * x)). [back_rewrite(274),rewrite([277(9)]),flip(a)].

284 (x * A') * (A / x) = 0. [para(264(a,1),155(a,1,1))].

302 (A' / x) * ((x * A) * y) = y. [para(259(a,1),10(a,1,1))].

304 (x * (y * (x * A)))' = A' / (x * (y * x)). [para(13(a,1),259(a,1,1))].

305 (A * C)' = C' * A'. [para(16(a,1),259(a,1,1)),rewrite([116(8)])].

306 L(x,A,y * A') = L(x,A,y). [para(259(a,1),18(a,1,1)),rewrite([230(7),268(8)])].

316 L(x,A',y * A) = L(x,A',y). [para(270(a,1),18(a,1,1)),rewrite([230(7),278(8)])].

321 A / C' = A * C. [para(270(a,1),161(a,1)),rewrite([251(8),16(7)])].

325 (A * C) * (C' * A') = 0. [para(321(a,1),155(a,1,1)),rewrite([264(7)])].

346 (x * (x * C))' * (x * (C * (x * y))) = y. [para(16(a,1),42(a,1,1,1,2))].

372 ((x * A) * y) / (A' / x) = (x * A) * (y * (x * A)). [para(260(a,1),39(a,1,1,2,2)),rewrite([3(4)])].

376 ((x * A') * y) / (A / x) = (x * A') * (y * (x * A')). [para(284(a,1),39(a,1,1,2,2)),rewrite([3(5)])].

428 (A * C) * ((C' * A') * x) = x. [para(305(a,1),34(a,1,2,1))].

433 L(A,x,A) = A. [para(49(a,1),10(a,1,2)),rewrite([18(8)])].

434 (A * (A * (x * A))) * y = A * ((A * x) * (A * y)). [para(49(a,1),13(a,1,1,2))].

435 A * ((x * A) * A) = A * (x * (A * A)). [para(49(a,1),13(a,1))].

436 (A * x) * (A * (y * A)) = A * ((x * (A * y)) * A). [para(49(a,1),15(a,1,2))].

441 (A * (x * A))' = A' / (A * x). [para(49(a,1),259(a,1,1))].

447 (A' / (A * (x * y))) * ((A * x) * ((y * A) * z)) = L(z,y * A,A * x). [back_rewrite(95),rewrite([441(6)])].

451 (x * (y * (z * (z * (y * x))))) * u = x * (y * (z * (z * (y * (x * u))))). [para(45(a,1),13(a,1,1,2)),rewrite([45(11)])].

510 L(C,x,C) = C. [para(65(a,2),18(a,1,2)),rewrite([64(8)]),flip(a)].

516 (C * x)' = (x * C)'. [para(65(a,1),111(a,1,2)),rewrite([111(6)]),flip(a)].

529 (C * x) * (x * C)' = 0. [para(516(a,1),9(a,1,2))].

532 (C * x)' * ((x * C) * y) = y. [para(516(a,2),10(a,1,1))].

533 (C * (x * x))' = (x * (x * C))'. [para(12(a,1),516(a,2,1))].

566 C * (x * (y * (z * (y * x)))) = x * (y * (z * (y * (x * C)))). [para(47(a,1),16(a,2))].

567 (x * (C * (y * (x * C)))) * z = x * (C * (y * (C * (x * z)))). [para(16(a,1),47(a,1,1,2,2,2))].

568 C * (x * (y * (x * (C * z)))) = C * (x * (y * (x * (z * C)))). [para(16(a,1),47(a,2,2,2,2,2)),rewrite([47(7)])].

656 (A * (x * A)) / (y * A) = A * (x / y). [para(7(a,1),50(a,1,1,2,1))].

690 (C * (x * x))' * (x * ((x * C) * y)) = L(y,x * C,x). [para(66(a,2),18(a,1,1,1))].

694 x * (C * (x' * x')) = x' * C. [para(66(a,2),34(a,1,2))].

716 (x * (C * x)) / (x * x) = C. [para(67(a,1),6(a,1,1))].

726 L(x,C,x) = L(x,x,C). [para(67(a,1),18(a,1,2)),rewrite([100(7)])].

743 (C * (x * x))' = (x * (C * x))'. [para(67(a,1),516(a,1,1)),rewrite([16(7,R)]),flip(a)].

748 (x * (C * (C * (x * x)))) * y = x * (C * (x * (C * (x * y)))). [para(67(a,2),47(a,1,1,2,2))].

754 L(A,A,C) = A. [para(726(a,1),433(a,1))].

761 L(x * A,x,A) = x * A. [para(12(a,1),54(a,1,2,2)),rewrite([18(9)])].

765 L(x * (y * A),y,A) = (x * y) * A. [para(13(a,1),54(a,1,2,2)),rewrite([18(10)])].

772 L((x * y) * A,A,(A * x)') = (A' / (A * x)') * (y * A). [para(54(a,1),18(a,1,2)),rewrite([259(6)]),flip(a)].

774 L(C * (x * A),C',A) = (x * C) * A. [para(63(a,1),54(a,1,2,2,1)),rewrite([133(10),16(4,R)])].

779 A / x = A * x'. [para(54(a,1),39(a,1,1,2)),rewrite([656(8),32(3),189(10)]),flip(a)].

790 L(x * (y * (x * (z * A))),z,A) = (x * (y * (x * z))) * A. [para(47(a,1),54(a,1,2,2)),rewrite([18(12)])].

800 ((x * A') * y) / (A * x') = (x * A') * (y * (x * A')). [back_rewrite(376),rewrite([779(6)])].

815 (x * A')' = A * x'. [back_rewrite(270),rewrite([779(6)])].

817 (A * x') * x = A. [para(779(a,1),7(a,1,1))].

818 A * (A' / x) = x'. [para(779(a,1),32(a,1)),rewrite([259(4)])].

820 A * (C' * A') = C'. [para(779(a,1),110(a,1)),rewrite([305(5)])].

821 C' * A = A * C'. [para(779(a,1),116(a,1)),flip(a)].

827 C * (A * C') = A. [para(817(a,1),16(a,2))].

831 (A * x) * x' = A. [para(30(a,1),817(a,1,1,2))].

833 (A * (x / y)) * (y / x) = A. [para(106(a,1),817(a,1,1,2))].

835 x * ((A * (x * y)') * x) = (x * A) / y. [para(817(a,1),39(a,1,1,2)),flip(a)].

848 (A * C) / (A * C') = C * C. [para(827(a,1),35(a,1,1,2)),rewrite([16(3)])].

858 (A * x)' = x' * A'. [para(831(a,1),32(a,1,2)),rewrite([264(3)]),flip(a)].

859 x * (A' * x)' = A. [para(34(a,1),831(a,1,1))].

875 L((x * y) * A,A,x') = x * (y * A). [back_rewrite(772),rewrite([858(7),306(9),858(11),32(13),30(8)])].

881 A' / (A * x) = (A' / x) * A'. [back_rewrite(441),rewrite([858(5),259(3)]),flip(a)].

886 ((A' / (x * y)) * A') * ((A * x) * ((y * A) * z)) = L(z,y * A,A * x). [back_rewrite(447),rewrite([881(6)])].

913 A' / x = A' * x'. [para(818(a,1),10(a,1,2)),flip(a)].

920 ((A' * (x * y)') * A') * ((A * x) * ((y * A) * z)) = L(z,y * A,A * x). [back_rewrite(886),rewrite([913(4)])].

923 (A' * x') * A' = A' * (x' * A'). [back_rewrite(881),rewrite([913(5),858(5),913(10)]),flip(a)].

931 ((x * A) * y) / (A' * x') = (x * A) * (y * (x * A)). [back_rewrite(372),rewrite([913(6)])].

940 (x * (y * (x * A)))' = A' * (x * (y * x))'. [back_rewrite(304),rewrite([913(10)])].

942 (A' * x') * ((x * A) * y) = y. [back_rewrite(302),rewrite([913(3)])].

946 (x * A)' = A' * x'. [back_rewrite(259),rewrite([913(6)])].

947 A' * ((x * y)' * (A' * ((A * x) * ((y * A) * z)))) = L(z,y * A,A * x). [back_rewrite(920),rewrite([923(8),13(15)])].

950 (A * x) * (A * C') = A * ((x * C') * A). [para(821(a,1),15(a,1,2))].

958 (A' * x)' = x' * A. [para(859(a,1),10(a,1,2)),flip(a)].

961 x' * ((A * x) * (y * (x * ((x' * A) * z)))) = (x' * (A * ((x * y) * A))) * z. [para(859(a,1),47(a,1,1,2,2,2)),rewrite([958(4),231(7),779

(4),30(4),15(6),958(12),958(15),231(19),779(12),30(12)]),flip(a)].

994 (A * C') * (A * x) = A * (A * (x * C')). [para(184(a,1),57(a,2,2,2)),rewrite([821(4),436(12),264(15),246(17),264(14),257(15),34(11),821(

11),3(15)]),flip(a)].

1012 (A * C) * (A * x) = A * (A * (x * C)). [para(529(a,1),57(a,2,2,2)),rewrite([16(3),436(10),858(14),13(16),820(14),229(10),116(8),34(10),

16(9),3(13)]),flip(a)].

1030 L(x,x * A',A) = x. [para(7(a,1),761(a,1,1)),rewrite([264(2),264(7),256(10)])].

1051 C' * A' = A' * C'. [para(820(a,1),10(a,1,2)),flip(a)].

1053 C * (A' * C') = L(A',C',A). [para(820(a,1),18(a,1,2)),rewrite([858(5),30(3),229(7),116(5),1051(6)])].

1061 (A * C) * ((A' * C') * x) = x. [back_rewrite(428),rewrite([1051(8)])].

1066 A * L(A',C',A) = 0. [back_rewrite(325),rewrite([1051(8),243(9),264(4),229(8),116(6),1051(7),1053(8)])].

1068 ((x * A) * y) * A = x * (A * (y * A)). [para(58(a,1),10(a,1,2)),rewrite([10(10)]),flip(a)].

1086 (x * A) * (y * (x * A)) = x * (A * ((y * x) * A)). [back_rewrite(281),rewrite([1068(6)]),flip(a)].

1092 ((x * A) * y) / (A' * x') = x * (A * ((y * x) * A)). [back_rewrite(931),rewrite([1086(14)])].

1094 (x' * A') * (A * x) = 0. [para(858(a,1),8(a,1,1))].

1095 (A * x) * (x' * A') = 0. [para(858(a,1),9(a,1,2))].

1097 (x' * A') * (A * (x * y)) = L(y,x,A). [para(858(a,1),18(a,1,1))].

1103 (A * x) / (x' * A') = A * (x * (A * x)). [para(858(a,1),143(a,1,2)),rewrite([282(12)])].

1108 (A' * x') * x = A'. [para(913(a,1),7(a,1,1))].

1111 (A' * x') * (x * (A * y)) = L(y,A,x). [para(946(a,1),18(a,1,1))].

1123 (x' * A) * (C * (A' * x)) = C. [para(958(a,1),64(a,1,1))].

1152 A * ((x * (A' * y)) * A) = A * ((x * A') * (y * A)). [para(257(a,1),59(a,2,2,1,2,2)),rewrite([8(10),3(8),243(8),264(3)]),flip(a)].

1168 (A * x) * (A * (A * (A * C))) = A * ((x * (A * (A * C))) * A). [para(66(a,1),59(a,1,2,2)),rewrite([16(15)])].

1189 L(A',C',A) = A'. [para(1066(a,1),10(a,1,2)),rewrite([3(4)]),flip(a)].

1192 C * (A' * C') = A'. [back_rewrite(1053),rewrite([1189(13)])].

1250 (A' * x) * x' = A'. [para(30(a,1),1108(a,1,1,2))].

1254 x * ((A' * (x * y)') * x) = (x * A') / y. [para(1108(a,1),39(a,1,1,2)),flip(a)].

1258 (A' * (x * C)') * (C * x) = A'. [para(516(a,1),1108(a,1,1,2))].

1269 A * (C * ((A' * C') * x)) = L(x,A' * C',C). [para(1192(a,1),18(a,1,1,1)),rewrite([30(3)])].

1318 C * (x * C) = x * (C * C). [para(69(a,2),39(a,1,1)),rewrite([116(8),10(9)]),flip(a)].

1398 C * (C * x) = x * (C * C). [para(70(a,1),63(a,1,2)),rewrite([10(9)]),flip(a)].

1441 ((x * C) * y)' * ((C * x) * (y * z)) = L(z,y,C * x). [para(239(a,1),18(a,1,1,1))].

1447 ((x * C) * ((C * x) * y)) / y = (C * x) * (C * x). [para(239(a,1),35(a,1,1))].

1448 (C * x) * (C * x) = (x * C) * (x * C). [para(239(a,2),35(a,1,1,2)),rewrite([1447(7)])].

1451 ((x * C) * (y * ((C * x) * z))) / z = (C * x) * (y * (C * x)). [para(239(a,1),39(a,1,1))].

1452 (C * x) * (y * (C * x)) = (x * C) * (y * (x * C)). [para(239(a,2),39(a,1,1,2,2)),rewrite([1451(8)])].

1499 A * ((x * (y * ((C * z) * y))) * A) = A * ((x * (y * ((z * C) * y))) * A). [para(239(a,1),59(a,1,2,2)),rewrite([59(9)]),flip(a)].

1518 C * (C * (C * x)') = C / x. [para(247(a,1),10(a,1,2)),rewrite([1318(7,R),16(6,R)])].

1539 C' * x = x * C'. [para(8(a,1),71(a,2,2,2)),rewrite([34(8),3(7)]),flip(a)].

1540 x' * (C * (x * (y * x))) = y * (x * C). [para(71(a,2),10(a,1,2))].

1549 (C * x)' * (x * (y * (x * C))) = L(y * x,x,C). [para(71(a,1),18(a,1,2))].

1557 (x * C) * (x * C) = C * ((x * C) * x). [para(63(a,1),71(a,1,2,2)),rewrite([16(13,R),10(14)]),flip(a)].

1563 (C * (x * C))' = (x * (C * C))'. [para(71(a,2),111(a,1,2)),rewrite([111(8)])].

1573 (x * C')' = C / x. [para(71(a,2),161(a,1,1)),rewrite([34(8),16(9,R),9(9),3(7)])].

1670 (C * x) * (C * x) = C * ((x * C) * x). [back_rewrite(1448),rewrite([1557(10)])].

1673 x' * ((x * C) * y) = L(y * C,C',x). [back_rewrite(133),rewrite([1573(4),230(4)])].

1694 C * (x * C') = x. [para(1539(a,1),10(a,1,2)),rewrite([30(3)])].

1700 (C' * (C' * x)) * y = C' * (x * (C' * y)). [para(1539(a,2),13(a,1,1,2))].

1707 x * (C' * x') = C'. [para(1539(a,2),34(a,1,2))].

1730 C * (x * (x * C')) = x * x. [para(1539(a,1),71(a,1,2,2)),rewrite([63(11)])].

1734 x / C' = C * x. [para(7(a,1),1694(a,1,2)),flip(a)].

1737 x' * (C * ((x * C') * y)) = L(y,x * C',C). [para(1694(a,1),18(a,1,1,1))].

1765 (C * x)' = C' / x. [para(1734(a,1),106(a,1,1))].

1781 (x * (C * C))' = C' / (x * C). [back_rewrite(1563),rewrite([1765(5)]),flip(a)].

1783 x' * ((x * C') * (y * (x * C))) = L(y * x,x,C). [back_rewrite(1549),rewrite([1765(3),230(8)])].

1785 C * (C * (C' / x)) = C / x. [back_rewrite(1518),rewrite([1765(5)])].

1815 (x * (C * x))' = C' / (x * x). [back_rewrite(743),rewrite([1765(4)]),flip(a)].

1817 (C' / (x * x)) * (x * ((x * C) * y)) = L(y,x * C,x). [back_rewrite(690),rewrite([1765(4)])].

1849 (x * (x * C))' = C' / (x * x). [back_rewrite(533),rewrite([1765(4)]),flip(a)].

1850 (C' / x) * ((x * C) * y) = y. [back_rewrite(532),rewrite([1765(3)])].

1852 (x * C)' = C' / x. [back_rewrite(516),rewrite([1765(3)]),flip(a)].

1860 (A' * (C' / x)) * (C * x) = A'. [back_rewrite(1258),rewrite([1852(5)])].

1865 L(x',C,x) = C * (C' / x). [back_rewrite(172),rewrite([1852(7)])].

1869 x' * ((x * C') * y) = L(C' * y,C,x). [back_rewrite(119),rewrite([1852(3),230(5)])].

1870 (C' / x) * (C * (x * y)) = L(y,x,C). [back_rewrite(98),rewrite([1852(3)])].

1875 (C' / (x * x)) * (x * (C * (x * y))) = y. [back_rewrite(346),rewrite([1849(4)])].

1884 L(C' * (x * (y * C)),C,y) = L(x * y,y,C). [back_rewrite(1783),rewrite([1869(9)])].

1939 x * ((A * x') * (C * x)) = C * (x * A). [para(817(a,1),72(a,1,2,2)),flip(a)].

1972 (x * (y * (x * C')))' = C / (x * (y * x)). [para(13(a,1),1573(a,1,1))].

1973 (x * C') * ((C / x) * y) = y. [para(1573(a,1),34(a,1,2,1))].

1995 A * ((C * A') * (x * A)) = x * (A * C). [para(34(a,1),73(a,1,1)),rewrite([16(10,R),1152(13)]),flip(a)].

2051 L(x',x,y) / y = (y * x)'. [para(9(a,1),78(a,1,2,2)),rewrite([3(4)])].

2224 L(x,y / x,A * (x / y)) = A' * ((A * (x / y)) * y). [para(817(a,1),80(a,2,1,1)),rewrite([106(4),106(10)])].

2251 L(x,C / x,C * x) = x. [para(247(a,1),80(a,2,1,1)),rewrite([174(9),16(14,R),12(15),10(14),10(10)])].

2364 L(x,A,y / (A * x)) = (A' * ((A * x) / y)) * y. [para(946(a,1),81(a,2,1)),rewrite([106(11)])].

2464 L(x,x',A') = x. [para(83(a,2),264(a,2)),rewrite([958(5),30(2),264(4),257(5)]),flip(a)].

2488 L(x,x',A' * x) = x. [para(1108(a,1),83(a,2,1,1)),rewrite([30(5),30(8),30(10),34(10)])].

2536 L(x',x,A') = x'. [para(30(a,1),2464(a,1,2))].

2555 L(C * x',x,C') = C / x. [para(125(a,1),84(a,1,3,1)),rewrite([125(10),161(10)])].

2585 L(C',x,C / x) = C'. [para(1539(a,2),84(a,1,3,1)),rewrite([161(6),1573(9),7(8)])].

2656 x / L(y',y,x) = x * y. [para(86(a,2),32(a,1,2)),rewrite([30(6)])].

2657 L(x',x,C) / (C' / x) = C. [para(86(a,2),60(a,1,1)),rewrite([1765(6)])].

2667 x * L(y',y,x) = x / y. [para(86(a,2),39(a,2,2)),rewrite([39(6),189(4)]),flip(a)].

2680 (C' / x) * L(x',x,C) = C * ((C' / x) * (C' / x)). [para(86(a,2),66(a,2,2)),rewrite([1765(4),1765(7),1765(12)]),flip(a)].

2791 (x * C) * L(y,x,C) = C * (x * y). [para(16(a,1),87(a,1,1))].

2800 C * L(x,C * y',y) = y * ((C * y') * x). [para(125(a,1),87(a,1,1))].

2814 A * L(x,y,A * y') = (A * y') * (y * x). [para(817(a,1),87(a,1,1))].

2815 A * L(x,y',A * y) = (A * y) * (y' * x). [para(831(a,1),87(a,1,1))].

2840 x * (C' * y) = x * (y * C'). [para(1539(a,1),87(a,2,2)),rewrite([87(7)])].

2884 L(A,C * A',A * C) = A. [para(264(a,1),2251(a,1,2)),rewrite([16(8)])].

2916 x * L(y * z,y',x) = (x / y') * z. [para(89(a,2),13(a,2,2)),rewrite([189(5)]),flip(a)].

2976 (A * x') * (x * y) = L(A * y,A',x). [para(815(a,1),89(a,2,1)),flip(a)].

3060 A * L(x,y,A * y') = L(A * x,A',y). [back_rewrite(2814),rewrite([2976(11)])].

3093 L(C',C * x,x') = C'. [para(111(a,1),2585(a,1,3))].

3125 x * L(y * C,C',x) = (x * C) * y. [para(63(a,1),92(a,1,1)),rewrite([161(4),63(7),230(4),1673(5),63(11),139(10)])].

3176 (A * (A * (A * C))) * x = A * (A * (A * (x * C))). [para(754(a,1),92(a,2,1,2)),rewrite([66(5),16(8),1852(9),264(9),1539(10),66(15),68(1

6),231(17),251(12),1539(11),2976(16),243(17),264(6),229(7),264(5),125(7),2916(11),251(5),16(4),1012(7),66(13),68(15),66(14)]),flip(a)].

3396 L(x,y,z / y) = L(x,y,z). [para(8(a,1),93(a,1,1,1,2)),rewrite([3(2),18(6),10(4),189(5)]),flip(a)].

3424 x' * (C' * (x * (C * y))) = L(y,C,x * (C' * x)). [para(63(a,1),93(a,1,1,1,2)),rewrite([174(2),12(11),10(10)])].

3425 (C / (x * (y * x))) * (x * (y * (x * z))) = L(z * C,C',x * (y * x)). [para(63(a,1),93(a,1,2,2,2,2)),rewrite([1972(6)])].

3429 C' * (x' * (C * (x * y))) = L(y,x,C * (x' * C)). [para(64(a,1),93(a,1,1,1,2)),rewrite([174(4),12(13),10(12)])].

3435 C' * (x * (C * (x' * y))) = L(y,x',C * (x * C)). [para(125(a,1),93(a,1,1,1,2)),rewrite([174(4),12(13),10(12)])].

3470 (C' / (C * ((x * C) * x))) * (C * ((C * x) * (C * (x * y)))) = L(y,x,C * (C * (C * x))). [para(66(a,1),93(a,1,1,1)),rewrite([16(6,R),67

(7,R),1670(6),1765(8),16(22,R)])].

3478 (x * (y * (x * x)))' * (x * (y * (C * (x * x)))) = L(C,x,x * (y * x)). [para(66(a,2),93(a,1,2,2,2))].

3485 (C' / (C * (x * x))) * (C * (x * (C * (x * y)))) = L(y,x,C * (x * C)). [para(67(a,2),93(a,1,1,1,2)),rewrite([1765(6)])].

3574 x' * (C * (x * (C' * y))) = L(y,C',x * (C * x)). [para(1694(a,1),93(a,1,1,1,2)),rewrite([174(2),12(11),10(10)])].

3671 x' * (y' * ((y * x) * z)) = L(z,y,x). [back_rewrite(255),rewrite([3396(8)])].

3672 L(x,y * z,y') = L(x,y,z). [back_rewrite(252),rewrite([3396(5)])].

3690 L(x,y,z * y) = L(x,y,z). [para(10(a,1),94(a,1,1,1)),rewrite([10(7),18(5),3672(5)]),flip(a)].

3926 x' * ((x * y) * A) = L(y * A,A,x). [para(10(a,1),96(a,1,1,1)),rewrite([10(9),3672(12)])].

4107 L(A,x,A * x') = A. [para(8(a,1),97(a,1,2,2,1)),rewrite([817(4),2(6),10(6)]),flip(a)].

4137 L(A,A,A * x) = A. [para(49(a,1),97(a,1,1,1)),rewrite([858(5),946(3),923(7),435(13),13(14),10(12),10(8),10(6)]),flip(a)].

4153 ((A * (A * x)) * x')' * (A * (A * A)) = L(A,x',A * (A * x)). [para(831(a,1),97(a,1,2,2,1))].

4221 L(A,A,x) = A. [para(34(a,1),4137(a,1,3))].

4223 A' * L(A * A,A,x) = A. [para(4137(a,1),93(a,2)),rewrite([940(7),858(7),946(5),923(9),231(19),251(12),13(11),8(9),3(7),1111(13)])].

4226 (x * A) * A = x * (A * A). [para(4221(a,1),87(a,1,2))].

4256 x' * (y' * (C * (y * x))) = L(C,y,x). [para(10(a,1),101(a,1,1,1)),rewrite([3672(11)])].

4262 L(C,C,x) = C. [para(16(a,2),101(a,1,1,1)),rewrite([1765(3),230(8),1318(8,R),16(7,R),1694(7),64(4)]),flip(a)].

4270 C' * (x' * (C * (C * x))) = L(C,C * x,x'). [para(64(a,1),101(a,1,1,1))].

4281 L(C,x * C,x) = C. [para(66(a,2),101(a,1,1,1)),rewrite([1765(4),1875(10)]),flip(a)].

4286 A' * ((A * x) * (C * x')) = L(C,x',A * x). [para(831(a,1),101(a,1,1,1))].

4306 (C / x) * (C * x) = C * C. [para(101(a,1),70(a,2,2)),rewrite([1765(5),1785(7),510(9)])].

4314 (C' / (x * x)) * (C * (x * (C * x))) = C. [para(71(a,2),101(a,1,2)),rewrite([1849(4),4281(14)])].

4315 (x * (y * C'))' * (x * y) = L(C,y * C',x). [para(1694(a,1),101(a,1,2,2))].

4317 L(C,C * x,x) = C. [para(72(a,2),101(a,1,2)),rewrite([1815(4),4314(10)]),flip(a)].

4334 (x * (y * z))' * (x * (y * (C * z))) = L(L(C,z,y),y * z,x). [para(101(a,1),89(a,1,1)),rewrite([30(5),30(7)]),flip(a)].

4358 L(L(C,x * x,y),y * (x * x),x) = L(C,x,x * (y * x)). [back_rewrite(3478),rewrite([4334(10)])].

4359 C / (x * (C * C)) = C' / x. [para(4262(a,1),78(a,1,1)),rewrite([1852(9)])].

4381 L(C,x,x * C') = C. [para(1694(a,1),4317(a,1,2))].

4449 L(x,C * (y * y),y' * y') = L(x,y,C * (y' * C)). [para(66(a,2),102(a,2,2)),rewrite([37(2),174(4),68(9),12(10),10(9),3429(8),174(11)]),fl

ip(a)].

4478 L(x,A' * C',C) = L(x,C',C * A'). [para(1189(a,1),102(a,1,1,1)),rewrite([30(3),1573(6),264(4),1539(11),34(12),243(9),116(6),1539(7),1269

(10),1539(13),34(14),1573(14),264(12)])].

4656 A * (C * ((A' * C') * x)) = L(x,C',C * A'). [back_rewrite(1269),rewrite([4478(17)])].

4677 (x * C') * (x * C) = C * ((x * C') * x). [para(4381(a,1),87(a,1,2)),rewrite([16(6,R)]),flip(a)].

4833 (A' * x') * (x * y) = L(A' * y,A,x). [para(2488(a,1),103(a,1,2,2)),rewrite([1250(5),30(3),946(3),8(11),3(11),1250(14),30(12)])].

4852 L(A * A,A',x) = A * A. [para(4107(a,1),103(a,1,2,2)),rewrite([817(4),815(4),15(6),8(3),2(4),15(9),8(6),2(7),817(10)]),flip(a)].

4891 L(x,y,A * y') = L(x,y,A). [para(1094(a,1),93(a,1,1,1,2)),rewrite([3(3),1097(11),10(7),256(9)]),flip(a)].

4900 A * L(x,y,A) = L(A * x,A',y). [back_rewrite(3060),rewrite([4891(5)])].

4912 (A * (A * x)) * x' = A * A. [para(1095(a,1),15(a,2,2,1)),rewrite([256(10),2(10)])].

4941 L(A,x',A * (A * x)) = A. [back_rewrite(4153),rewrite([4912(6),174(4),12(11),10(10),10(6)]),flip(a)].

4947 C * L(x,C,y) = L(x * C,y,C'). [para(16(a,1),104(a,2,1)),rewrite([1852(3),7(4),30(3),1852(9),3396(10)])].

4960 A * L(x,A,y) = L(A * x,y,A'). [para(256(a,1),104(a,1,1,1,1,1)),rewrite([10(5),30(3),306(6),256(14),3672(11)])].

4961 A' * L(x,A',y) = L(A' * x,y,A). [para(257(a,1),104(a,1,1,1,1,1)),rewrite([10(4),316(7),257(16),3672(13)])].

4977 x * L(y,x,A) = L(x * y,A,x'). [para(817(a,1),104(a,1,1,1,1,1)),rewrite([10(6),30(2),4891(4),817(11),3672(10)])].

5251 (x * (C * C)) * y = C * (x * (C * y)). [para(1318(a,1),13(a,1,1))].

5261 x * (C * (x' * C)) = C * C. [para(1318(a,2),34(a,1,2))].

5345 ((A * C) * (x * C))' * (A * (C * (x * (A * C)))) = L(A,x * C,A * C). [para(1318(a,1),97(a,1,2,2,1)),rewrite([5251(14),16(12)])].

5347 (C' / (C * (A * x))) * (A * (C * (x * (A * C)))) = L(A,C * C,A * x). [para(1318(a,2),97(a,1,1,1)),rewrite([16(5,R),1765(7),5251(14),16(

12)])].

5361 L(x * y,C * C,C' / (C * x)) = x * L(y,x,C * C). [para(1318(a,2),104(a,1,1,1)),rewrite([12(5),1765(6),16(8,R),1785(9),111(4),30(2),12(13

),1765(14)]),flip(a)].

5381 (x * (y * x))' = x' / (x * y). [para(9(a,1),108(a,1,2,2,2)),rewrite([3(3)]),flip(a)].

5389 (x * y) / (z * L(y,x,z)) = x / z. [para(18(a,1),108(a,1,2,2)),rewrite([189(8),106(6)])].

5390 (x' * y) / (x * (z * y)) = x' / (x * z). [para(34(a,1),108(a,1,2,2,2)),rewrite([5381(8)])].

5396 C' / (C * x) = x' / (C * C). [para(125(a,1),108(a,1,2,2)),rewrite([5381(10)]),flip(a)].

5460 x / (x * (C * (C * x))) = C' / (C * x). [para(72(a,1),108(a,1,2)),rewrite([5381(11)])].

5595 x' * (C * (C * x)) = C * C. [para(1398(a,2),10(a,1,2))].

5600 (C' / (C * x)) * (x * (C * (C * y))) = L(y,C * C,x). [para(1398(a,2),18(a,1,1,1)),rewrite([1765(5),12(9)])].

5603 x * (C * (C * x')) = C * C. [para(1398(a,2),34(a,1,2))].

5611 (x * (x * (C * C))) * y = x * (C * (C * (x * y))). [para(1398(a,1),45(a,1,1,2))].

5659 (C' / (C * (C * x))) * (C * (x * (C * (C * y)))) = L(y,C,C * (x * C)). [para(1398(a,2),93(a,1,1,1,2)),rewrite([1765(7)])].

5673 L(x,C * (C * y),C' / y) = C' * L(C * x,y,C). [para(1398(a,2),102(a,2,2)),rewrite([4262(3),1852(5),5251(10),1870(11),1852(14)]),flip(a)]

.

5689 L(C,C * x,x') = C. [back_rewrite(4270),rewrite([5595(8),1318(6,R),16(5,R),9(5),3(3)]),flip(a)].

5703 C' * L(C * C,x,C) = C. [para(1765(a,1),5689(a,1,3)),rewrite([5673(9)])].

5966 ((A' * x) * y) * A = A' * (x * (y * A)). [para(123(a,1),10(a,1,2)),flip(a)].

5969 (x * (A' * y)) * A = (x * A') * (y * A). [para(13(a,1),123(a,1,2,1)),rewrite([228(10),251(10),34(11)])].

5982 (x * (A * ((y * x) * A))) * z = (x * A) * (y * ((x * A) * z)). [para(123(a,1),57(a,1,1,2)),rewrite([1086(6),34(14)])].

5990 A * ((A' * C') * (x * A)) = x * (A * C'). [para(1539(a,1),123(a,2,2)),rewrite([1539(7,R),5969(9),1539(6)])].

6006 (C * x) * (A * C) = C * (C * (x * A)). [para(1318(a,2),123(a,1,2,1,1)),rewrite([16(6,R),70(8),5969(10),1995(11),12(12)])].

6008 (x * (y * A)) * A' = A * ((A' * x) * y). [para(123(a,1),112(a,1,1)),rewrite([433(10),264(5)])].

6012 (x * A) * (y * x) = x * ((A * y) * x). [back_rewrite(273),rewrite([5982(9),257(7)])].

6080 L(x,y' * C,y) = L(x,C * y',y). [para(16(a,2),126(a,1,2,2,1)),rewrite([170(8)]),flip(a)].

6087 x / (x' * y) = x * (y' * x). [para(126(a,1),39(a,1,1,2)),rewrite([202(8)])].

6131 L(x,C' * y,C) = L(x,y * C',C). [para(1539(a,1),126(a,1,2,2,1)),rewrite([1737(8)]),flip(a)].

6163 L(L(x,y,z'),z' * y,z) = x. [para(87(a,1),126(a,1,2,2)),rewrite([34(5),10(3)]),flip(a)].

6200 C' * L(C * x,y',C * (y * C)) = L(x,y' * (C * C),y). [para(1318(a,2),126(a,1,2,2,1)),rewrite([174(4),13(11),12(13),3435(12)])].

6202 L(x,y' * (C * C),y) = L(x,C * (y' * C),y). [para(1318(a,2),126(a,2,2)),rewrite([174(4),5251(11),12(13),3435(12),6200(11)])].

6301 x * L(y' * z,y,x) = (x / y) * z. [para(127(a,2),13(a,2,2)),rewrite([189(4)]),flip(a)].

6310 L((C' / x) * y,x * C,C') = x' * (C' * y). [para(63(a,1),127(a,2,1,1)),rewrite([1852(3)])].

6317 x * ((x' * C') * y) = L(C' * y,C,x'). [para(105(a,1),127(a,2,1,1)),rewrite([1765(10),230(13),30(8)]),flip(a)].

6325 x' * ((x * A') * y) = L(A' * y,A,x). [para(256(a,1),127(a,2,1,1)),rewrite([306(8)]),flip(a)].

6353 L((C' / x) * y,C * x,x) = (C' / (x * x)) * (x * y). [para(67(a,2),127(a,2,1,1)),rewrite([1765(3),1765(11)])].

6528 L(C' * (x * A),C,A') = x * (A * C'). [back_rewrite(5990),rewrite([6317(10)])].

6536 L(x',x,y') = y * (y' / x). [para(2667(a,1),34(a,1,2)),flip(a)].

6634 L(C',x,C * (x' * C)) = C'. [para(174(a,1),3093(a,1,3)),rewrite([4449(9)])].

6702 L(x,y * z,z) = L(x,y,z). [para(32(a,1),3396(a,1,3)),rewrite([3672(3)]),flip(a)].

6707 L(x,y * C,C') = L(x,y * C,y). [para(110(a,1),3396(a,1,3))].

6708 L(x,C * y,y') = L(x,C * y,C). [para(111(a,1),3396(a,1,3))].

6710 L(x,y,z * (u * (z * y))) = L(x,y,z * (u * z)). [para(39(a,1),3396(a,1,3)),flip(a)].

6714 L(x,y,C * (y * C)) = L(x,y,C * C). [para(149(a,1),3396(a,1,3)),flip(a)].

6718 L(x,C',C * y) = L(x,C',y). [para(1734(a,1),3396(a,1,3))].

6728 L(x,y * y,y * (C * y)) = L(x,y * y,C). [para(716(a,1),3396(a,1,3)),flip(a)].

6747 (C' / (x * x)) * (x * y) = L((C' / x) * y,C,x). [back_rewrite(6353),rewrite([6702(7)]),flip(a)].

6761 (C' / (C * ((x * C) * x))) * (C * ((C * x) * (C * (x * y)))) = L(y,x,C * (C * C)). [back_rewrite(3470),rewrite([6710(24)])].

6762 (C' / (C * (x * x))) * (C * (x * (C * (x * y)))) = L(y,x,C * C). [back_rewrite(3485),rewrite([6714(18)])].

6763 A * (C * ((A' * C') * x)) = L(x,C',A'). [back_rewrite(4656),rewrite([6718(17)])].

6772 L(L(x,y,C),C,y) = x. [back_rewrite(1875),rewrite([6747(9),1870(7)])].

6773 L(x,y * C,y) = L(x,C,y). [back_rewrite(1817),rewrite([6747(9),1850(7)]),flip(a)].

6781 L(x,y * C,C') = L(x,C,y). [back_rewrite(6707),rewrite([6773(8)])].

6785 L((C' / x) * y,C,x) = x' * (C' * y). [back_rewrite(6310),rewrite([6781(9)])].

6795 (C' / (x * x)) * (x * y) = x' * (C' * y). [back_rewrite(6747),rewrite([6785(12)])].

6826 L(L(x,C' * y,C),C,y) = x. [para(6772(a,1),3396(a,1)),rewrite([116(2)]),flip(a)].

7039 L(x,C,C * y) = L(x,C,y). [para(16(a,2),3690(a,1,3))].

7040 L(x,y' * z,y) = L(x,y',z). [para(34(a,1),3690(a,1,3)),rewrite([6702(3)]),flip(a)].

7045 L(x,y',A * y) = L(x,y',A). [para(831(a,1),3690(a,1,3)),flip(a)].

7067 L(x,C / x,C * C) = x. [para(2251(a,1),3690(a,2)),rewrite([247(7)])].

7073 L(x,y / z,A * (z / y)) = L(x,y / z,A). [para(833(a,1),3690(a,1,3)),flip(a)].

7100 L(x,y * (C' * y),y * y) = L(x,y * (C' * y),C). [para(130(a,1),3690(a,1,3))].

7101 (C' / (C * (C * x))) * (C * (x * (C * (C * y)))) = L(y,C,x). [back_rewrite(5659),rewrite([7039(21),3690(19)])].

7106 L(L(x,C',y),C,y) = x. [back_rewrite(6826),rewrite([7040(5)])].

7119 L(x,C * (y' * C),y) = L(x,y',C * C). [back_rewrite(6202),rewrite([7040(6)]),flip(a)].

7150 L(L(x,y,z'),z',y) = x. [back_rewrite(6163),rewrite([7040(5)])].

7175 L(x,y * C',C) = L(x,C',y). [back_rewrite(6131),rewrite([7040(5)]),flip(a)].

7207 L(x,C * y',y) = L(x,y',C). [back_rewrite(6080),rewrite([7040(4)]),flip(a)].

7218 A' * ((A * x) * (C * x')) = L(C,x',A). [back_rewrite(4286),rewrite([7045(14)])].

7221 (A * x) * (x' * y) = L(A * y,A',x'). [back_rewrite(2815),rewrite([7045(5),4900(5)]),flip(a)].

7247 L(x,y / x,A) = A' * ((A * (x / y)) * y). [back_rewrite(2224),rewrite([7073(5)])].

7283 x * ((C * x') * y) = C * L(y,x',C). [back_rewrite(2800),rewrite([7207(5)]),flip(a)].

7308 C * L(x * A,A',C) = x * (A * C). [back_rewrite(1995),rewrite([7283(9)])].

7319 (C * (C * C)) / x = C * (C * (C / x)). [para(7067(a,1),112(a,1,2)),rewrite([7(6),16(5,R),12(12)])].

7427 L(A * A,A,x) = A * A. [para(4223(a,1),10(a,1,2)),rewrite([30(3)]),flip(a)].

7429 (A * (A * x')) * x = A * A. [para(4223(a,1),81(a,1,3,2)),rewrite([7427(5),264(7),3690(9),4852(6),7427(10),10(9),264(5),815(10),815(8)])

,flip(a)].

7457 (x * (y * (x * A))) * A = x * (y * (x * (A * A))). [para(13(a,1),4226(a,1,1)),rewrite([13(12)])].

7498 L(x,A,y * (A * A)) = L(x,A,y). [para(4226(a,1),3690(a,1,3)),rewrite([3690(10)])].

7515 x' * ((C * x) * y) = L(C * y,x,C). [para(135(a,1),10(a,1,2)),rewrite([1765(3),1870(9)]),flip(a)].

7522 (C * (C' / x)) * ((C * x) * ((C * (C' / x)) * (x * y))) = C * L(y,x,C). [para(18(a,1),135(a,2,2)),rewrite([1765(4),1765(8),106(9),1734(

8),1765(11)])].

7580 (C * (C' / x)) * ((C * x) * ((C * (C' / x)) * y)) = (C / x) * y. [para(127(a,2),135(a,2,2)),rewrite([1765(4),1765(8),106(9),1734(8),176

5(11),6301(21)])].

7593 C * L(x,y,C) = L(x * C,C',y). [back_rewrite(7522),rewrite([7580(16),230(4),1673(5)]),flip(a)].

7601 L(C * (x * A),C',A') = x * (A * C). [back_rewrite(7308),rewrite([7593(8),16(4,R)])].

7606 x * ((C * x') * y) = L(y * C,C',x'). [back_rewrite(7283),rewrite([7593(10)])].

7688 x' * (C * (x * A)) = L(A * C,A',x). [para(257(a,1),137(a,2,1,1)),rewrite([16(3),316(8),16(11,R)]),flip(a)].

7727 L(C',C * C,x) = C'. [para(1707(a,1),137(a,1,1)),rewrite([174(8),30(5),30(6),174(12),30(9),30(10),1781(11),7(14)])].

7826 L(x,C,y) = L(x,y,C'). [para(7727(a,1),102(a,1,1,1)),rewrite([30(3),1781(6),1539(12,R),1318(12,R),16(11,R),9(11),3(9),230(10),1852(4),15

39(9,R),63(9),230(6),1869(7),4947(7),16(5,R),34(5),1539(9,R),1318(9,R),16(8,R),9(8),3(6),1781(10),3396(11),6781(8)]),flip(a)].

7893 C * L(x,y,C') = L(C * x,y,C'). [para(7826(a,1),104(a,1,2)),rewrite([1852(3),7(4),30(3),1852(10),3396(11)])].

7901 L(L(x,y,C),y,C') = x. [para(7826(a,1),6772(a,1))].

7932 (C * x') / (x * C) = x' * x'. [para(16(a,2),144(a,1,1))].

8058 L(x,C,x * (C' * x)) = x. [para(150(a,1),93(a,1,2,2)),rewrite([63(5),174(2),12(6),10(5),10(3)]),flip(a)].

8119 C' * (C' * ((C / x) * (C * (x * y)))) = L(y,x,C * (C * (C / x))). [para(4306(a,1),93(a,1,1,1,2)),rewrite([1849(6),6795(15),16(17,R)])].

8151 L(A,x',A * A) = A. [para(4941(a,1),3690(a,2)),rewrite([4912(8)])].

8172 C' * ((C' / x) * L(x',C,x)) = (C' / x) * (C' / x). [para(125(a,1),151(a,1,2)),rewrite([1852(3),116(9),1852(13),1852(16)])].

8421 (x * A') * A' = x * (A' * A'). [para(8151(a,1),78(a,1,1)),rewrite([12(8),779(9),858(9),5381(7),913(7),858(7),30(5),13(10),34(11),12(11)

,858(12),858(10),30(8)]),flip(a)].

8720 (C' / x) / (C / x) = C' * C'. [para(2667(a,1),153(a,1,1)),rewrite([16(9,R),7893(9),2555(9)])].

8905 L(C * C,x,C) = C * C. [para(5703(a,1),10(a,1,2)),rewrite([30(3)]),flip(a)].

8906 x / (C * C) = C' * (x * C'). [para(5703(a,1),39(a,1,1,2,2)),rewrite([63(5),8905(5)])].

8909 L(x,C * C,C' * (y * C')) = L(x,C,y * (C' * y)). [para(5703(a,1),93(a,1,1,1,2,2)),rewrite([63(5),8905(10),12(9),10(10),3424(8),8905(11)]

),flip(a)].

8921 C' / (C * x) = C' * (x' * C'). [back_rewrite(5396),rewrite([8906(10)])].

8949 C' * L(C * x,C,y) = L(x,C,y). [back_rewrite(7101),rewrite([8921(7),1765(5),1539(8,R),231(17),1734(11),34(10),230(11),1869(12),10(9)])].

8951 L(x,y,C * (y' * C)) = L(x,y,C * C). [back_rewrite(6762),rewrite([8921(6),174(4),1539(8,R),231(16),1734(11),34(10),12(10),10(9),3429(8)]

)].

8952 C' * (((x * C) * x)' * ((C * x) * (C * (x * y)))) = L(y,x,C * (C * C)). [back_rewrite(6761),rewrite([8921(8),1539(9,R),231(19),1734(12)

,34(11)])].

8977 L(x,C,y * (C' * y)) = L(x,C * C,y). [back_rewrite(5600),rewrite([8921(5),13(13),3424(12),8949(11)])].

8983 x / (x * (C * (C * x))) = C' * (x' * C'). [back_rewrite(5460),rewrite([8921(11)])].

8993 L(x * y,C * C,C' * (x' * C')) = x * L(y,x,C * C). [back_rewrite(5361),rewrite([8921(9)])].

8994 C' * ((x' * A') * (C' * (A * (C * (x * (A * C)))))) = L(A,C * C,A * x). [back_rewrite(5347),rewrite([8921(7),858(5),1539(9,R),1700(19)]

)].

9009 L(C',x,C * C) = C'. [back_rewrite(6634),rewrite([8951(8)])].

9012 C' * (x' * (C * (x * y))) = L(y,x,C * C). [back_rewrite(3429),rewrite([8951(14)])].

9020 L(x,C * C,C' * (y * C')) = L(x,C * C,y). [back_rewrite(8909),rewrite([8977(16)])].

9022 L(x,C * C,x) = x. [back_rewrite(8058),rewrite([8977(6)])].

9035 x * L(y,x,C * C) = L(x * y,C * C,x'). [back_rewrite(8993),rewrite([9020(12)]),flip(a)].

9039 C' / (x * C) = C' * (x' * C'). [para(9022(a,1),78(a,1,1)),rewrite([12(4),8983(6),1781(12)]),flip(a)].

9062 (x * (C * C))' = C' * (x' * C'). [back_rewrite(1781),rewrite([9039(10)])].

9142 L(x,C * y,C' * (y' * C')) = L(x,C,y). [para(9009(a,1),102(a,1,1,1)),rewrite([30(3),12(5),1765(6),8921(6),12(15),1694(14),13(12),3671(11

),34(7),12(9),1694(8),12(8),1765(9),8921(9)]),flip(a)].

9198 C * (L(x,A',C) * A) = x * (A * C). [para(87(a,1),169(a,1,2,1)),rewrite([5969(8),7606(9),16(4,R),7601(9)]),flip(a)].

9460 L(C * (C' / x),C * x,C / x) = C' * (C / x). [para(4306(a,1),171(a,2,1,1)),rewrite([1765(4),174(14),16(19,R),12(20),10(19)])].

9516 L(x,y / z,z) = L(x,y,z). [para(7(a,1),6702(a,1,2)),flip(a)].

9517 L(x,y',y * z) = L(x,z,y). [para(10(a,1),6702(a,1,2)),rewrite([3690(2)]),flip(a)].

9518 L(x,y * (y * z),z) = L(x,y * y,z). [para(12(a,1),6702(a,1,2))].

9521 L(x,C * y,C) = L(x,y,C). [para(16(a,2),6702(a,1,2))].

9524 L(x,y,y' * z) = L(x,z,y'). [para(34(a,1),6702(a,1,2)),rewrite([3690(3)]),flip(a)].

9526 L(x,y',C * y) = L(x,C,y). [para(64(a,1),6702(a,1,2)),rewrite([7039(4)]),flip(a)].

9527 L(x,y,C * y') = L(x,C,y'). [para(125(a,1),6702(a,1,2)),rewrite([7039(5)]),flip(a)].

9528 L(x,y * A',A) = L(x,y,A). [para(256(a,1),6702(a,1,2)),flip(a)].

9540 L(x,x,A) = x. [para(1030(a,1),6702(a,2)),rewrite([256(5)])].

9582 L(x,C * (y * C),C * C) = L(x,y,C * C). [para(1318(a,2),6702(a,1,2))].

9604 L(x,C',y * (C * y)) = L(x,y * y,C). [para(150(a,1),6702(a,1,2)),rewrite([6728(5)]),flip(a)].

9611 (x * (y / x))' * ((x * y) * z) = L(x * z,y,x). [back_rewrite(241),rewrite([9516(9)])].

9613 L(x,C',y) = L(x,y,C). [back_rewrite(6718),rewrite([9517(5)]),flip(a)].

9635 L(x,C * y,y') = L(x,y,C). [back_rewrite(6708),rewrite([9521(8)])].

9850 x' * (C * (x * (C' * y))) = L(y,x * x,C). [back_rewrite(3574),rewrite([9604(14)])].

9869 (A * x) * x = A * (x * x). [para(9540(a,1),87(a,1,2))].

9997 (x * C') * L(y,x,C) = x * (C' * y). [para(9613(a,1),87(a,1,2))].

10001 L(x,y * (z * y),C) = L(x,C',y * (z * y)). [para(9613(a,1),93(a,2)),rewrite([1972(6),3425(11),16(5,R),34(5)]),flip(a)].

10007 C' * L(x,y,C) = L(C' * x,y,C). [para(9613(a,1),104(a,1,2)),rewrite([1573(4),7(3),1573(12),3396(11)])].

10025 L(x,y * (C' * y),y * y) = L(x,C',y * (C' * y)). [back_rewrite(7100),rewrite([10001(12)])].

10283 L(x,C,y * (C * C)) = L(x,C,y). [para(71(a,2),7039(a,1,3)),rewrite([7039(8),7039(6),3690(4)]),flip(a)].

10289 L(C * x,C,y) = L(x * C,y,C'). [para(7039(a,1),104(a,1,2)),rewrite([16(4,R),1765(5),8921(5),13(10),10(8),8(4),3(4),30(3),4947(4),16(13,

R),1765(14),8921(14),9142(17)]),flip(a)].

10291 C' * L(x,C,y) = L(C' * x,C,y). [para(7039(a,1),127(a,1)),rewrite([16(9,R),1765(10),8921(10),13(16),3671(15)]),flip(a)].

10294 L(x,C * C,y) = L(x,C,y * y). [para(130(a,1),7039(a,1,3)),rewrite([8977(9)]),flip(a)].

10352 L(L(x,y,z),z,y) = x. [para(30(a,1),7150(a,1,1,3)),rewrite([30(3)])].

10359 L(L(x,y,C'),y,C) = x. [para(7150(a,1),9613(a,1)),flip(a)].

10374 L(x,A,x) = x. [para(9540(a,1),10352(a,1,1))].

10445 (x * A) * x = x * (A * x). [para(10374(a,1),87(a,1,2))].

10589 C * (x * L(y,x,C')) = (C * x) * y. [para(10359(a,1),87(a,1,2)),flip(a)].

11015 (C * x) * (y * (C * x)) = C * ((C * x) * (y * x)). [para(186(a,1),1734(a,1)),rewrite([1734(3),1734(5),1734(10)])].

11122 (x * C) * (y * (x * C)) = C * ((C * x) * (y * x)). [back_rewrite(1452),rewrite([11015(6)]),flip(a)].

11213 (x / (y * z)) * y = y' * ((y * x) / z). [para(187(a,1),10(a,1,2)),flip(a)].

11214 (x' * y) / (x * z) = x' * ((y / z) * x'). [para(10(a,1),187(a,1,2,1,2)),flip(a)].

11591 x' / (x * y) = x' * (y' * x'). [back_rewrite(5390),rewrite([11214(5),32(3)]),flip(a)].

11754 (x * (y * x))' = x' * (y' * x'). [back_rewrite(5381),rewrite([11591(6)])].

11863 (A' * x) * A' = A' * (x * A'). [para(188(a,1),264(a,1)),flip(a)].

11951 (x * y)' * x = x' * (x / y). [para(189(a,1),10(a,1,2)),flip(a)].

11980 C' * (C / x) = C * (C' / x). [para(189(a,1),2251(a,1,3)),rewrite([1765(3),16(5,R),1765(9),16(11,R),111(12),106(9),1734(8),9460(10),176

5(8),16(10,R)])].

12007 C' / (x * (y * (x * C))) = C' * (C' * (x' * (y' * x'))). [para(131(a,1),189(a,1,2,1,1)),rewrite([11754(5),1539(10,R)]),flip(a)].

12419 x / (C' / x) = (x * C) * x. [para(63(a,1),190(a,2,2)),rewrite([1539(5,R),63(5),1852(3)])].

12752 L(A,A' * A',A * C) = A. [para(2884(a,1),9516(a,2)),rewrite([7932(9)])].

12753 L(x,C' / x,C * C) = x. [para(7067(a,1),9516(a,2)),rewrite([8906(6),1539(7,R),11980(7),10(8)])].

13006 L(x,C',y * (C' * y)) = L(x,y * y,C). [para(130(a,1),9521(a,1,2)),rewrite([10001(9)]),flip(a)].

13018 L(x,y * (C' * y),y * y) = L(x,y * y,C). [back_rewrite(10025),rewrite([13006(13)])].

13442 (A * C) * (x * C) = C * (C * (A * x)). [para(73(a,1),198(a,1,1,2)),rewrite([264(10),5982(11),16(3),16(6),229(9),264(7),125(9),16(11,R)

])].

13453 L(A,C * C,A * x) = L(A,x * C,A * C). [back_rewrite(5345),rewrite([13442(6),1765(7),11591(7),858(5),1539(9,R),1700(19),8994(19)])].

13519 x' * L(x * C,C',A) = L(C,x,x * A). [para(10445(a,1),101(a,1,1,1)),rewrite([11754(4),6012(11),13(12),10(10),1673(8)])].

14145 (A * x) / (x * x) = A * x'. [para(9540(a,1),202(a,1,1,2)),rewrite([779(6)])].

14267 (C' * (x * x)) * y = x * (C' * (x * y)). [para(205(a,2),13(a,1,1))].

14370 L(x,y * y,C) = L(x,C',y * y). [para(205(a,1),6702(a,1,2)),rewrite([13018(6)])].

14438 L(x,C',y * (C' * y)) = L(x,C',y * y). [back_rewrite(13006),rewrite([14370(10)])].

14458 x' * (C * (x * (C' * y))) = L(y,C',x * x). [back_rewrite(9850),rewrite([14370(11)])].

14523 L(x,y',C * C) = L(x,C * C,y). [para(207(a,1),9516(a,1,2)),rewrite([7119(6)])].

14544 L(x,C' / x,C / x) = x. [para(12753(a,1),3690(a,2)),rewrite([12(10),1785(10)])].

14750 C' * L(x,y,C') = L(C' * x,C,y). [para(212(a,1),13(a,2,2)),rewrite([1539(7,R),11980(7),10(8),230(5),1869(6)]),flip(a)].

14953 L(x,C' * C',C / x) = x. [para(14544(a,1),9516(a,2)),rewrite([8720(6)])].

15154 (C * x) * x' = x * (C / x). [para(16(a,2),229(a,1,1))].

15214 L(A * x,x,A) = A * x. [para(1094(a,1),229(a,1,1)),rewrite([815(6),30(4),2(4),1103(13),1097(12)]),flip(a)].

15268 L(x,A',x) = x. [para(34(a,1),15214(a,1,1)),rewrite([7040(5),34(8)])].

15397 L(x,x,A') = x. [para(15268(a,1),10352(a,1,1))].

15417 (A' * x) * x = A' * (x * x). [para(15397(a,1),87(a,1,2))].

15422 L(x * A,x,A') = x * A. [para(15397(a,1),9516(a,1)),rewrite([251(3),251(5)]),flip(a)].

15605 (A' * x) * (x * A) = A' * (x * (x * A)). [para(15422(a,1),87(a,1,2))].

15667 L(x,C,A') = L(x,A,C). [para(16(a,1),306(a,1,3)),rewrite([16(5,R),9527(6)])].

15670 L(x,C',A') = L(x,A,C'). [para(1539(a,1),306(a,1,3)),rewrite([9524(7)])].

15678 L(C' * (x * A),A,C) = x * (A * C'). [back_rewrite(6528),rewrite([15667(9)])].

15698 L(C * (x * A),A,C') = x * (A * C). [back_rewrite(7601),rewrite([15670(9)])].

15699 A * (C * ((A' * C') * x)) = L(x,A,C'). [back_rewrite(6763),rewrite([15670(15)])].

15710 L(L(x,A,C),A',C) = x. [para(15667(a,1),10352(a,1,1))].

15794 L(x,A',C) = L(x,C,A). [para(10352(a,1),15710(a,1,1))].

15798 C * (L(x,C,A) * A) = x * (A * C). [back_rewrite(9198),rewrite([15794(5)])].

15800 (C * A') * L(x,C,A) = C * (A' * x). [para(15794(a,1),87(a,1,2))].

15885 A * (L(A' * x,A,y) * A) = L(x * A,A,y). [para(256(a,1),230(a,1,2)),rewrite([11213(5),251(5),3926(5),815(8),15(14),6325(11)]),flip(a)].

15888 (x * A') * (A * y) = A' * ((A * x) * y). [para(264(a,1),230(a,1,1))].

15889 (x / (A * y)) * (A * (y * A)) = (y' * A') * (((A * y) * x) * A). [para(49(a,1),230(a,1,2)),rewrite([858(11)])].

15969 (x * y)' * (x * z) = x' * ((x / y) * z). [para(2667(a,1),230(a,2,2,1)),rewrite([2051(3)])].

15974 (x / (y * A)) * (y * (A * A)) = L(x * A,A,y). [para(4226(a,1),230(a,1,2)),rewrite([946(11),1068(17),4833(18),10(15)])].

16816 L(C,x * C',y) = L(C,x,y). [back_rewrite(4315),rewrite([15969(7),11213(6),1734(6),4256(7)]),flip(a)].

17157 x' * L(x * A,A,y) = L(A,y * A',x). [back_rewrite(269),rewrite([15969(7),11213(6),251(6),3926(6)])].

17292 (x * C') * (C * y) = C' * ((C * x) * y). [para(1539(a,1),231(a,1,1)),rewrite([1734(11)])].

17309 (x' / y) * (x * z) = x' * ((x' * y)' * z). [para(2667(a,1),231(a,1,1)),rewrite([2051(10)])].

17502 L(x,A * C',C * C) = L(x,A * C',A * C). [para(848(a,1),3396(a,1,3))].

17504 C * (C * ((A * C') * x)) = A * (x * C). [para(848(a,1),230(a,1,1)),rewrite([12(9),1573(14),264(12),4677(21),49(20),1539(19),1730(21),1

2(17),15888(18),1012(17),10(18)])].

17570 A * ((A' * (x * x)) * x') = x. [para(1250(a,1),235(a,2,2)),rewrite([30(3),251(7),15605(7),30(10),264(9),11863(10),6008(9),15417(8),34(

9),251(11),257(13)])].

18052 (x * C) * (C' * y) = C * ((C' * x) * y). [para(16(a,1),243(a,1,1)),rewrite([116(9)])].

18053 (C * x) * (x' * y) = x * ((C / x) * y). [para(16(a,2),243(a,1,1))].

18971 (C' / x) * L(x',C,x) = (C' / x) / x. [para(1865(a,2),186(a,2,2)),rewrite([9(7),3(5)]),flip(a)].

19018 (C' / x) * (C' / x) = C' * ((C' / x) / x). [back_rewrite(8172),rewrite([18971(9)]),flip(a)].

19031 (C' / x) * L(x',x,C) = (C' / x) / x. [back_rewrite(2680),rewrite([19018(15),34(16)])].

19690 ((C' / x) / x) * ((C * x) * y) = C' * ((C / x) * y). [para(2657(a,1),243(a,2,2,1)),rewrite([19031(7),106(8),1734(7),17309(14),161(14)]

)].

19694 (x * (y * A')) * A = A' * ((A * x) * y). [para(267(a,1),10(a,1,2)),flip(a)].

19713 ((A * x) * y) * A' = A * (x * (y * A')). [para(267(a,1),112(a,1,1)),rewrite([433(10),264(5)])].

19724 (x * (y * A')) * (A * z) = A' * (((A * x) * y) * z). [para(267(a,1),230(a,2,2,1)),rewrite([19694(6),264(8),11863(9),19713(8),10(9)])].

19725 (A * (x / y)) * y = L(A * x,A',y). [para(230(a,1),267(a,1,2,1)),rewrite([19694(9),2976(8),4961(9),10(6),4900(4)]),flip(a)].

19729 C * (A * (A * x)) = A * ((A * C) * x). [para(245(a,1),267(a,1,2,1)),rewrite([30(4),30(6),264(5),49(10),19694(9),1673(9),3125(9),30(10)

,16(12,R)]),flip(a)].

19783 L(x,y / x,A) = L(x,y,A). [back_rewrite(7247),rewrite([19725(9),4961(11),10(8)])].

19825 L(x,y * x,A) = L(x,y,A). [para(6(a,1),19783(a,1,2)),flip(a)].

19840 L(x,y,A) / (A * y) = (x / y) * A'. [para(19783(a,1),78(a,1,1)),rewrite([7(5),858(9),106(7)])].

19848 (A * x) / L(y,x,A) = A * (x / y). [para(19783(a,1),112(a,1,2)),rewrite([7(3)])].

19869 L(L(x,y,A),A,y / x) = x. [para(19783(a,1),10352(a,1,1))].

20188 L(L(x,y,A),A,y * x) = x. [para(19825(a,1),10352(a,1,1))].

20366 L(L(x,y,A),A,(y * A) / x) = x. [para(6702(a,1),19869(a,1,1))].

20537 L(L(x,y,A),A,(y * A) * x) = x. [para(6702(a,1),20188(a,1,1))].

21688 C' * L(A * C,A',x) = L(A,x,C * C). [para(5261(a,1),97(a,1,1,1,1)),rewrite([12(4),1765(5),11591(5),16(13,R),70(15),5969(17),7606(18),16

(13,R),15670(18),15698(17),6006(13),13(14),10(12),7688(8),16(16,R),5603(18)])].

22263 (A * (A * (A * C'))) * x = A * (A * (A * (x * C'))). [para(1539(a,1),434(a,1,1,2,2)),rewrite([994(17)])].

22406 L(x,A * (A * y'),y) = L(x,A * A,y). [para(7429(a,1),6702(a,1,2)),flip(a)].

22446 A * (L(x * C,C',A) * A) = C * (A * (x * A)). [para(125(a,1),436(a,1,1)),rewrite([15888(14),1673(14)]),flip(a)].

22857 L(x,y * y,y' * (C * y')) = L(x,C,y' * y'). [para(178(a,2),9526(a,1,3)),rewrite([174(4),30(2),30(2)])].

22965 L(x,C',y * y) = L(x,C,y' * y'). [para(130(a,1),9635(a,1,2)),rewrite([11754(6),30(5),22857(7),10001(11),14438(12)]),flip(a)].

22990 x' * (C * (x * (C' * y))) = L(y,C,x' * x'). [back_rewrite(14458),rewrite([22965(12)])].

23673 ((x * C) * x)' = (C' / x) / x. [para(12419(a,1),106(a,1,1))].

23708 L(x,y,C * (C * (C / y))) = L(x,y,C * (C * C)). [back_rewrite(8952),rewrite([23673(6),19690(13),8119(12)])].

23710 C' * (C' * ((C / x) * (C * (x * y)))) = L(y,x,C * (C * C)). [back_rewrite(8119),rewrite([23708(19)])].

23903 C * ((A * C') * x) = L(A * x,A,C). [para(12752(a,1),242(a,1,2,2)),rewrite([243(9),264(4),8421(8),694(9),16(4,R),815(5),243(13),264(8),

8421(12),694(13),16(8,R),815(9),11213(11),1734(11),243(12),264(5),1539(6),17292(11),15888(10),1673(10),4977(10),63(6),30(5),4960(5),15667(6),

243(14),264(9),8421(13),694(14),16(9,R),815(10),12(20),8(19),3(17),229(16),264(14),125(16),16(12,R)]),flip(a)].

23905 L(C * (A * x),C',A) = A * (x * C). [back_rewrite(17504),rewrite([23903(8),7593(7),16(4,R)])].

24081 L(x,A * y',y * y) = L(x,A * y,y * y). [para(14145(a,1),9516(a,1,2))].

24090 L(x,A * C',A * C) = L(x,A * C,C * C). [back_rewrite(17502),rewrite([24081(8)]),flip(a)].

24319 L(A,C' * C',C * A') = A. [para(264(a,1),14953(a,1,3))].

24624 C' * (x * (C * (C / x))) = x * (C / x). [para(34(a,1),15154(a,1,1)),rewrite([161(4),6087(11),231(12),1734(8),18053(11),16(9,R)]),flip(

a)].

24713 L(C,x,y / (x * C')) = L(C,x,y). [para(16816(a,1),3396(a,1)),rewrite([16816(11)])].

26156 (x * (y * (x * (C * C))))' = C' * (C' * (x' * (y' * x'))). [para(566(a,2),111(a,1,2)),rewrite([111(10),1765(7),12007(7)]),flip(a)].

26254 C' * (x * (C * (y * (x * C)))) = x * (C * (y * x)). [para(567(a,1),1539(a,2)),rewrite([1694(15)])].

26285 C' * (A' * ((A * x') * (C * (x * A)))) = L(A,C * C,A * x). [back_rewrite(8994),rewrite([26254(17),15888(13)])].

27590 L((x * y) * A,A,y) = x * (y * A). [para(942(a,1),229(a,1,1)),rewrite([958(5),30(2),1092(15),4833(14),10(11)]),flip(a)].

27609 x / (A' * C') = x * (A * C). [para(1061(a,1),190(a,1,1)),rewrite([1852(4),264(4),1539(5),11122(20),16(10),5966(18),243(19),264(11),243

(18),116(13),1539(14),15699(19),7893(14),15698(14)])].

28745 (x / (y * C')) * (C' * y) = x. [para(2840(a,2),7(a,1))].

28762 (x * C) * (y * C') = C * ((C' * x) * y). [para(2840(a,1),239(a,2)),rewrite([243(6),116(3)]),flip(a)].

28786 x * (C' * (A * C')) = x * (A * (C' * C')). [para(9869(a,1),2840(a,2,2))].

31799 (A' * (x * x)) * x' = A' * x. [para(17570(a,1),10(a,1,2)),flip(a)].

31810 L(A,x * A',y) = L(A,x,y). [para(17570(a,1),97(a,1,1,1,1)),rewrite([31799(9),5966(9),34(10),15969(6),230(5),3926(6),17157(6),31799(13),

34(11)])].

31828 x' * L(x * A,A,y) = L(A,y,x). [back_rewrite(17157),rewrite([31810(11)])].

31833 L(A,x * A,y) = L(A,x,y). [para(7(a,1),31810(a,1,2)),rewrite([251(6)]),flip(a)].

31964 L(A,x,y * (x * A)) = L(A,x,y). [para(31833(a,1),3690(a,1)),rewrite([31833(9)])].

33238 A' * (C * (A * x)) = L(x * C,C,A). [para(765(a,1),7207(a,1)),rewrite([19694(7),16(6,R),256(13),15794(13)])].

33299 (C * (A * x)) * A = A * (C * (x * A)). [para(49(a,1),774(a,1,1,2)),rewrite([23905(10),16(5,R),16(10,R)]),flip(a)].

33300 L((x * C) * A,C,A) = C * (x * A). [para(774(a,1),7106(a,1,1))].

33646 L(x * L(A,y,x),y,A) = x * A. [para(8(a,1),790(a,2,1,2)),rewrite([15969(6),230(5),3926(6),31828(6),3(7)])].

33710 L(C * (C * (x * A')),C',A) = C * (x * (C * A')). [para(245(a,1),800(a,2,2)),rewrite([30(7),15888(7),1673(7),19840(11),1734(5),13(7),30

(14),30(16),264(15),15888(19),1673(19),16(14,R)]),flip(a)].

33723 L(x,A,y * (A * x)) = L(x,A,y). [para(87(a,1),20537(a,1,3)),rewrite([10352(4)])].

34039 L(A * ((C * A') / x),A,C) = C / x. [para(246(a,1),835(a,1,2)),rewrite([264(14),15888(18),1673(18),16(13,R),33710(17),11951(12),815(6),

23903(12),256(16)])].

34323 L(x * A,A,y / x) = L(x * A,A,y). [para(7(a,1),875(a,1,1,1)),rewrite([106(5),230(9),3926(10)])].

34329 L(A * C,A,x) = L(A * C,x,C). [para(64(a,1),875(a,1,1,1)),rewrite([16(3),30(6),7515(11),16(8)])].

34559 L(C' * (A * x),A,C) = (A * C') * x. [para(24319(a,1),92(a,2,1,2)),rewrite([12(11),1539(10),28786(12),15888(12),28762(11),1539(7),1539(

10,R),34(11),10(7),243(12),116(7),1539(8),1539(11,R),34(12),1573(8),251(6),16(5),12(16),1539(15),28786(17),15888(17),28762(16),1539(12),1539(

15,R),34(16),10(12),18052(9),1539(7),23903(9),10007(8),12(19),1539(18),28786(20),15888(20),28762(19),1539(15),1539(18,R),34(19),10(15),1539(1

2)])].

34561 C' * ((A * C) * x) = L(A * x,A,C'). [para(24319(a,1),242(a,1,2,2)),rewrite([243(10),116(5),1539(6),1539(9,R),34(10),1573(6),251(4),16(

3),243(13),116(8),1539(9),1539(12,R),34(13),1573(9),251(7),16(6),11213(9),116(9),243(12),264(4),243(11),116(6),1539(7),231(10),251(9),1539(8)

,1869(10),4977(9),34(6),4960(6),15670(7),243(16),116(11),1539(12),1539(15,R),34(16),1573(12),251(10),16(9),12(21),1539(20),28786(22),15888(22

),28762(21),1539(17),1539(20,R),34(21),10(17),1539(13,R)]),flip(a)].

35332 A' * L(A * x,A,y) = L(x,A,A * y). [para(2(a,1),947(a,1,2,2,2,2,1)),rewrite([3(4),3671(12),2(10)])].

35846 C' * (A * (A * (A * x))) = A * (A * (A * (x * C'))). [para(950(a,1),748(a,1,1,2,2,2)),rewrite([12(14),1539(13),28786(15),19729(16),287

62(15),1539(11),1539(14,R),34(15),1730(12),15(8),1539(5),49(7),1539(6),22263(9),23903(25),9997(24),17292(23),16(14),1012(22),16(20,R),34(20)]

),flip(a)].

36253 L(C * (A * x),A,C') = (A * C) * x. [para(1973(a,1),961(a,1,2)),rewrite([30(3),30(6),16(6),34561(8),7893(8),30(11),264(15),10(17),8(14)

,3(12),16(11)])].

36254 (A * C) * ((A * C') * x) = C * (A * (C' * (A * x))). [para(961(a,1),568(a,1,2)),rewrite([9(8),2(7),14267(8),1539(21),16(24,R),23903(24

),10007(23),34559(23),34561(22),7893(22),36253(22)]),flip(a)].

36478 (x * (A' * C')) * (A * C) = x. [para(27609(a,1),6(a,1))].

36491 (x * C) * (A * C) = C * (C * (x * A)). [para(239(a,1),27609(a,2)),rewrite([27609(8),6006(6)]),flip(a)].

36905 L(x * y,C * C,x') = C * (x * (C' * y)). [para(28745(a,1),566(a,1,2,2,2)),rewrite([63(17),11213(13),1734(13),9012(14),9035(11)]),flip(a

)].

36917 (x * (A * C)) * (A' * C') = x. [para(27609(a,1),28745(a,1,1)),rewrite([1539(9)])].

36918 x * L(y,x,C * C) = C * (x * (C' * y)). [back_rewrite(9035),rewrite([36905(11)])].

39441 x / (C * A') = x * (A * C'). [para(214(a,1),1092(a,1,1)),rewrite([30(5),16(4,R),264(11),1539(16,R),6325(16),15885(17),10007(13),15678(

13)])].

39651 L(x,A,y / (A * x)) = L(x,A,y). [para(7(a,1),33723(a,1,3)),flip(a)].

39696 (A' * ((A * x) / y)) * y = L(x,A,y). [back_rewrite(2364),rewrite([39651(5)]),flip(a)].

39953 L(A * C,C',x) = L(A * C,A,x). [para(34329(a,2),9613(a,2))].

40501 x / (A * C) = x * (A' * C'). [para(36478(a,1),6(a,1,1))].

40502 (x * (A' * C'))' = (A * C) / x. [para(36478(a,1),32(a,1,2)),flip(a)].

41738 (x * (A * C')) * (C * A') = x. [para(39441(a,1),7(a,1,1))].

42317 L(x * C,C,A) = x * L(C,A,x). [para(27609(a,1),1254(a,2)),rewrite([40502(9),39696(8),15888(11),16(10,R),33238(11)]),flip(a)].

42348 x / (A * C') = x * (C * A'). [para(7(a,1),41738(a,1,1)),flip(a)].

42768 L(x * C,C,A) / L(C,A,x) = x. [para(42317(a,2),6(a,1,1))].

43364 C * ((A' * C') * x) = A' * L(x,A,C'). [para(1108(a,1),2791(a,1,1)),rewrite([7175(9),15670(7)]),flip(a)].

43365 L(A,L(x,A,C),A * C) = L(A,C * C,A * x). [para(2791(a,1),97(a,1,1,1)),rewrite([1765(5),7593(11),22446(15),17309(12),161(8),15889(11),16

(10,R),33299(12),15888(13),26285(14)]),flip(a)].

43582 C / L(x * C,y,C') = L(x,C,y)'. [para(4947(a,1),111(a,1,2))].

43676 L(A * x,C,A' * A') = C * (A * (C' * x)). [para(10294(a,1),4960(a,2)),rewrite([36918(7)]),flip(a)].

43744 L(x * L(y,A,x),A,x') = x * y. [para(10352(a,1),4977(a,1,2)),flip(a)].

43913 L(x * A,A,y) = x * L(A,y,x). [para(5389(a,1),20366(a,1,3)),rewrite([33646(5),34323(5)])].

44078 L(C * (x * (A * C)),A,C) = C * (C * (x * A)). [para(10283(a,1),43913(a,2,2)),rewrite([5251(6),16(4),5251(17),4947(15),10589(18),6006(1

5)])].

45270 L(A,C * C,A * x) = L(A,x',C * C). [para(14523(a,2),97(a,2)),rewrite([1318(6,R),16(5,R),1765(7),11591(7),858(5),1539(9,R),5251(17),16(1

5),1700(19),26254(17),15888(13),26285(14),858(11),31810(16)])].

45280 L(x,y',C * C) = L(x,y,C' * C'). [para(14523(a,2),9524(a,1)),rewrite([174(4),12(6),161(7),6087(5),9582(9),174(9)])].

45322 L(x * A,A,C * C) = x * L(A,x,C' * C'). [para(14523(a,2),43913(a,2,2)),rewrite([45280(13)])].

45327 L(A,L(x,A,C),A * C) = L(A,x,C' * C'). [back_rewrite(43365),rewrite([45270(15),45280(14)])].

45329 L(A,x * C,A * C) = L(A,x,C' * C'). [back_rewrite(13453),rewrite([45270(7),45280(6)]),flip(a)].

45614 L(x,A,C) * (A * C) = C * (x * A). [para(10352(a,1),15798(a,1,2,1)),flip(a)].

45650 L(x,A * C,C * C) = L(x,C,A' * A'). [para(950(a,1),1441(a,1,1,1)),rewrite([9(5),2(4),174(4),16(8),36254(14),12(15),22990(14),43676(11),

22990(10),16(14),24090(15)]),flip(a)].

45653 C' * L(A * C,A,x) = L(A,x,C). [para(31964(a,1),1441(a,2)),rewrite([16(4,R),15969(14),1765(5),230(13),7457(13),10(14),17309(12),161(8),

15974(11),16(5)])].

45654 L(x,A * A,A * C) = L(x,C,A). [para(1168(a,1),1441(a,1,1,1)),rewrite([19729(8),16(7,R),1318(7),5611(10),66(8),19729(9),16(8,R),1318(8),

858(12),26156(10),1700(17),1539(15),13(16),16(20),3176(28),1012(29),16(27,R),19729(27),13442(26),451(30),35846(25),1539(22,R),10(22),10(21),1

0(17),10(13),33238(9),10291(8),63(5),16(13),9518(14)]),flip(a)].

45661 L(x,A * C',A * C) = L(x,C,A' * A'). [back_rewrite(24090),rewrite([45650(15)])].

45762 L(x,C,A' * A') = L(x,C,A). [para(45654(a,1),9516(a,2)),rewrite([40501(7),12(9),34(8),45661(8)])].

45786 L(x,C * C,A') = L(x,C,A). [para(45762(a,1),10294(a,2))].

45789 L(x,A,C * C) = L(x,C,A). [para(45786(a,1),9516(a,2)),rewrite([251(6),12(5),16(4),1318(5),3672(8)])].

45796 x * L(A,x,C' * C') = L(x * A,C,A). [back_rewrite(45322),rewrite([45789(7)]),flip(a)].

46145 A * ((C * A') / x) = C / L(x,C,A). [para(125(a,1),19848(a,1,1)),rewrite([9528(7)]),flip(a)].

46183 L(C / L(x,C,A),A,C) = C / x. [back_rewrite(34039),rewrite([46145(7)])].

46196 L(L(x,C,A)',A,C) = x'. [para(10289(a,1),46183(a,1,1,2)),rewrite([43582(8),111(11)])].

46218 L(x,C',A)' = L(x',A,C). [para(7106(a,1),46196(a,1,1,1)),flip(a)].

46220 L(x,C,A)' = L(x',A,C'). [para(46196(a,1),7901(a,1,1)),flip(a)].

46221 L(x,A,C)' = L(x',A,C). [para(10352(a,1),46196(a,1,1,1)),flip(a)].

46374 L(x,C',A) * L(x',A,C) = 0. [para(46218(a,1),9(a,1,2))].

46378 L(x,L(y',A,C),L(y,C',A)) = x. [para(46218(a,1),85(a,1,2))].

46434 L(x',A,C') * L(x,C,A) = 0. [para(46220(a,1),8(a,1,1))].

46658 L(x,C',A) / L(x,A,C) = 0. [para(46374(a,1),2656(a,2)),rewrite([46221(9),30(6),46378(16)])].

46672 x * L(y,C',A) = x * L(y,A,C). [para(46658(a,1),227(a,1,1)),rewrite([46658(9),23(3),2(7),46658(13),2(7)])].

46702 x' * L(x * C,A,C) = L(C,x,x * A). [back_rewrite(13519),rewrite([46672(8)])].

46703 L(A,x,C * (C * C)) = A. [para(1860(a,1),1499(a,1,2,1)),rewrite([8(5),3(3),16(10,R),11591(11),1765(9),1539(12,R),16(19,R),5966(23),70(2

1),16(19),36491(20),231(22),1734(15),34(14),17309(16),161(12),23710(17),34(13)]),flip(a)].

46704 L(A,C * (C * C),x) = A. [para(46703(a,1),10352(a,1,1))].

46716 L(A,C * (C * (C / x)),x) = A. [para(46704(a,1),9516(a,2)),rewrite([7319(7)])].

46749 L(A,C / x,x * (C * C)) = A. [para(4359(a,1),46716(a,1,2,2,2)),rewrite([1785(8)])].

46818 L(A,x,C * (C * (x' * C))) = A. [para(248(a,2),46749(a,1,3)),rewrite([111(6),30(3),1318(8,R),16(7,R)])].

47065 L(x',C,A) * L(x,C,A) = 0. [para(7826(a,2),46434(a,1,1))].

47078 L(x,C,A) * L(x',C,A) = 0. [para(30(a,1),47065(a,1,1,1))].

47092 L(x,L(y',C,A),L(y,C,A)) = x. [para(47065(a,1),6702(a,1,2)),rewrite([76(5)]),flip(a)].

47120 L(x,C,A) / L(x,A,C') = 0. [para(47078(a,1),2656(a,2)),rewrite([46220(8),30(5),47092(15)])].

47150 x * L(y,C,A) = x * L(y,A,C'). [para(47120(a,1),227(a,1,1)),rewrite([47120(9),23(3),2(6),47120(12),2(6)])].

47196 (C * A') * L(x,A,C') = C * (A' * x). [back_rewrite(15800),rewrite([47150(8)])].

47490 x * (C * (x' * A)) = L(A * C,A',x'). [para(831(a,1),1540(a,1,2,2,2)),rewrite([30(2),7221(12)])].

47506 (x * (A * C)) * A' = A * (C * (A' * x)). [para(36917(a,1),1540(a,1,2,2,2)),rewrite([1573(6),251(4),16(3),43364(11),243(11),264(4),4719

6(10),16(18,R),1694(18)]),flip(a)].

47592 L(L(A,x,C * C),C,x') = A. [para(46818(a,1),1441(a,2)),rewrite([16(7,R),70(8),245(7),1765(10),70(20),17309(21),24624(12),9611(17),7688(

8),10291(12),21688(9)])].

47605 L(A,x,C * C) = L(A,x',C). [para(47592(a,1),10352(a,1,1)),flip(a)].

47627 C' * L(A * C,A',x) = L(A,x',C). [back_rewrite(21688),rewrite([47605(14)])].

47628 L(A,x,C' * C') = L(A,x,C). [para(30(a,1),47605(a,2,2)),rewrite([45280(6)])].

47645 L(x * A,C,A) = x * L(A,x,C). [back_rewrite(45796),rewrite([47628(7)]),flip(a)].

47648 L(A,x * C,A * C) = L(A,x,C). [back_rewrite(45329),rewrite([47628(14)])].

47650 L(A,L(x,A,C),A * C) = L(A,x,C). [back_rewrite(45327),rewrite([47628(15)])].

48356 L(A,x,A * C) = L(A,C',x). [para(7(a,1),47648(a,1,2)),rewrite([116(8),7040(11)])].

48369 L(A,C',L(x,A,C)) = L(A,x,C). [back_rewrite(47650),rewrite([48356(8)])].

48857 L(A,L(x,A,C'),C) = L(A,C',x). [para(10359(a,1),48369(a,1,3)),flip(a)].

50060 L(L(A * C,A,x),C',x) = L(A * C,A',x). [para(47645(a,2),1673(a,1,2)),rewrite([33300(8),7688(6),6702(11),16(11,R),7593(11),39953(12)]),f

lip(a)].

50488 L(C,A,C * (x * A)) = L(C,A,x). [para(24713(a,1),7498(a,2)),rewrite([42348(7),19724(11),16(8,R),33299(10),10(11)])].

50517 L(C,A,C * x) = L(C,A,x). [para(7(a,1),50488(a,1,3,2)),rewrite([264(9),306(11)])].

50520 L(C,A,L(x * C,A,C')) = L(C,A,x). [para(50488(a,1),3396(a,2)),rewrite([264(8),6008(9),16(7,R),7606(9),15670(9)])].

50572 L(C,A,L(x * C,y,C')) = L(C,A,L(x,C,y)). [para(4947(a,1),50517(a,1,3))].

50584 L(C,A,L(x,C,A)) = L(C,A,x). [back_rewrite(50520),rewrite([50572(9)])].

50682 L(C,A,L(x,A,C)) = L(C,A,x). [para(10352(a,1),50584(a,1,3)),flip(a)].

50749 (C * (x * A)) / L(C,A,x) = L(x,A,C) * A. [para(50682(a,1),112(a,1,2)),rewrite([45614(7)])].

50764 (x * C) / L(C,A,x) = L(x,A,C). [para(50682(a,1),42768(a,1,2)),rewrite([16(5,R),7593(5),7106(9)])].

50964 L(x,A,C) * A = L(x * A,A,C). [para(3690(a,1),50764(a,1,2)),rewrite([16(4,R),50749(8)])].

51031 L(x,C',A) * A = L(x * A,A,C). [para(9613(a,2),50964(a,1,1))].

53499 L(L(x,C,A),C,A) = L(x,A,C). [para(256(a,1),1884(a,2,1)),rewrite([15888(9),16(8,R),33238(9),47150(8),14750(9),63(5)])].

53503 L(L(A,x',C),C,x) = L(A,x,C). [para(817(a,1),1884(a,2,1)),rewrite([2976(8),47627(9)])].

53589 L(L(A,x,C),x,C) = L(A,x',C). [para(53503(a,1),10352(a,1,1))].

53661 L(A * C,A',x) = L(A * C,A,x'). [para(53589(a,1),7593(a,1,2)),rewrite([7593(6),39953(7),16(11,R),7593(11),39953(12),50060(14)]),flip(a)

].

53674 x * (C * (x' * A)) = L(A * C,A,x). [back_rewrite(47490),rewrite([53661(13),30(12)])].

53678 x' * (C * (x * A)) = L(A * C,A,x'). [back_rewrite(7688),rewrite([53661(12)])].

54266 L(A,x',C) = L(A,C,x). [para(10283(a,1),31828(a,2)),rewrite([9062(5),5251(13),16(11),44078(16),13(14),10(12),53678(8),45653(9)])].

54291 L(A,C',x') = L(A,C,x). [para(54266(a,1),9613(a,2))].

54332 L(A,C,L(x,C,A)) = L(A,C,x). [para(46220(a,1),54266(a,1,2)),rewrite([48857(8),54291(5)]),flip(a)].

54962 (A * x) * (C * x') = L(A * C,A,x). [para(1939(a,1),34(a,1,2)),rewrite([53674(6),30(8)]),flip(a)].

54975 L(C,A,A * x) = L(C,x',A). [back_rewrite(7218),rewrite([54962(8),35332(8)])].

55042 L(L(A,C,x),L(x,C,A),C) = A. [para(54332(a,1),10352(a,1,1))].

55377 L(C,x',A) = L(C,A,x). [para(34(a,1),54975(a,1,3)),rewrite([958(8),6702(9)]),flip(a)].

55386 L(C,A,x') = L(C,x,A). [para(6536(a,2),54975(a,1,3)),rewrite([2536(6),913(8),958(10),30(7),6702(9)])].

55406 L(L(L(C,B',A),A,B),A,B) != C. [para(55377(a,2),19(a,1,1,1))].

55410 L(C,x',A) = L(C,x,A'). [para(958(a,1),55377(a,1,2)),rewrite([6702(6),9524(10)])].

55527 L(L(L(C,B,A'),A,B),A,B) != C. [back_rewrite(55406),rewrite([55410(5)])].

55556 L(C,A,A * x) = L(C,x,A'). [back_rewrite(54975),rewrite([55410(9)])].

55576 L(C,x',A') = L(C,x,A). [para(815(a,1),55386(a,1,3)),rewrite([55556(6),9528(11)])].

55578 L(C,A',x) = L(C,A,x'). [para(958(a,1),55386(a,1,3)),rewrite([3690(6),7040(10)]),flip(a)].

56238 L(L(A,C,x),L(x,A,C),C) = A. [para(53499(a,1),55042(a,1,2)),rewrite([54332(6)])].

56686 C * (L(x,A,C) * L(A,C,x)) = x * (A * C). [para(56238(a,1),87(a,1,2)),rewrite([7593(5),51031(8),27590(7),16(3)]),flip(a)].

56687 A * (C * (A' * x)) = L(x * C,C',A). [para(56238(a,1),112(a,1,2)),rewrite([56686(9),264(6),47506(7),7593(12)])].

62864 L(L(C,x,x * A),x,A') = C. [para(1123(a,1),43744(a,2)),rewrite([3690(13),87(12),56687(8),46672(8),46702(7),946(9),30(9),9524(9)])].

62885 L(C,x,x * A) = L(C,A,x'). [para(62864(a,1),10352(a,1,1)),rewrite([55578(4)]),flip(a)].

62892 x' * L(x * C,A,C) = L(C,A,x'). [back_rewrite(46702),rewrite([62885(11)])].

66317 L(C,A * A,x) = L(C,A,x'). [para(7429(a,1),4256(a,1,2,2,2)),rewrite([858(7),858(5),30(3),8421(7),66(12),19724(13),229(8),264(6),19724(1

2),12(9),16(11,R),19729(11),10(12),1673(8),46672(8),62892(7),22406(11)]),flip(a)].

66443 L(L(C,x,A),x,A) = L(C,x,A'). [para(256(a,1),4358(a,2,3,2)),rewrite([66317(8),815(6),55556(6),55576(5),15888(10),49(9),10(10),6702(7),5

5556(10)])].

67546 L(L(C,x,A'),A,x) = L(C,x,A). [para(66443(a,1),10352(a,1,1))].

67565 $F. [back_rewrite(55527),rewrite([67546(8),10352(7)]),xx(a)].

============================== end of proof ==========================

% Proof 1 at 110.55 (+ 0.86) seconds.

% Length of proof is 738.

% Level of proof is 43.

% Maximum clause weight is 33.000.

% Given clauses 4067.

1 L(L(L(C,A,B),A,B),A,B) = C # label(non_clause) # label(goal). [goal].

2 0 * x = x. [assumption].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 B * ((x * y) * B) = (B * x) * (y * B). [assumption].

15 (B * x) * (y * B) = B * ((x * y) * B). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 L(x,y,z) = (z * y)' * (z * (y * x)). [assumption].

18 (x * y)' * (x * (y * z)) = L(z,y,x). [copy(17),flip(a)].

19 L(L(L(C,A,B),A,B),A,B) != C. [deny(1)].

23 x / 0 = x. [para(3(a,1),6(a,1,1))].

26 0' = 0. [para(8(a,1),3(a,1)),flip(a)].

28 0 / x = x'. [para(8(a,1),6(a,1,1))].

30 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([28(3)])].

31 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

32 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

34 x * (x' * y) = y. [back_rewrite(4),rewrite([31(1)])].

35 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

37 L(x,y,y) = x. [para(12(a,1),10(a,1,2)),rewrite([18(5)])].

39 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

40 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

42 (x * (y * x))' * (x * (y * (x * z))) = z. [para(13(a,1),10(a,1,2))].

45 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(12(a,1),13(a,1,1,2)),rewrite([12(7)])].

47 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [para(13(a,1),13(a,1,1,2)),rewrite([13(9)])].

49 (B * x) * B = B * (x * B). [para(2(a,1),15(a,1,2)),rewrite([3(7)])].

50 (B * ((x * y) * B)) / (y * B) = B * x. [para(15(a,1),6(a,1,1))].

53 B * ((B' * x) * B) = x * B. [para(9(a,1),15(a,1,1)),rewrite([2(4)]),flip(a)].

54 (B * x)' * (B * ((x * y) * B)) = y * B. [para(15(a,1),10(a,1,2))].

57 ((x * B) * (B * ((y * x) * B))) * z = (x * B) * ((B * y) * ((x * B) * z)). [para(15(a,1),13(a,1,1,2))].

58 B * (((x * B) * y) * B) = B * (x * (B * (y * B))). [para(15(a,1),13(a,1))].

59 (B * x) * (y * (z * (y * B))) = B * ((x * (y * (z * y))) * B). [para(13(a,1),15(a,1,2))].

60 (x * C) / x = C. [para(16(a,1),6(a,1,1))].

62 C * (x / C) = x. [para(16(a,2),7(a,1))].

63 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

64 x' * (C * x) = C. [para(16(a,2),10(a,1,2))].

65 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

66 C * (x * x) = x * (x * C). [para(16(a,2),12(a,1))].

67 C * (x * x) = x * (C * x). [para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].

68 (x * (x * C)) * y = x * (C * (x * y)). [para(16(a,1),13(a,1,1,2))].

69 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

70 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

71 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

72 C * (x * (y * x)) = x * (y * (C * x)). [para(16(a,2),13(a,2,2,2)),rewrite([16(4,R)])].

73 (B * x) * (B * C) = B * ((x * C) * B). [para(16(a,1),15(a,1,2))].

76 L(x,0,y) = x. [para(2(a,1),18(a,1,2,2)),rewrite([3(2),10(3)]),flip(a)].

78 L(x,y,z) / (z * (y * x)) = (z * y)'. [para(18(a,1),6(a,1,1))].

79 x' * ((x / y) * (y * z)) = L(z,y,x / y). [para(7(a,1),18(a,1,1,1))].

80 L(x,y / x,z) = (z * (y / x))' * (z * y). [para(7(a,1),18(a,1,2,2)),flip(a)].

81 L(x,y,z / (y * x)) = ((z / (y * x)) * y)' * z. [para(7(a,1),18(a,1,2)),flip(a)].

83 L(x,x',y) = (y * x')' * y. [para(8(a,1),18(a,1,2,2)),rewrite([3(5)]),flip(a)].

84 L(x,y,(y * x)') = ((y * x)' * y)'. [para(8(a,1),18(a,1,2)),rewrite([3(6)]),flip(a)].

85 L(x,y',y) = x. [para(9(a,1),18(a,1,1,1)),rewrite([26(2),34(4),2(2)]),flip(a)].

86 L(x',x,y) = (y * x)' * y. [para(9(a,1),18(a,1,2,2)),rewrite([3(4)]),flip(a)].

87 (x * y) * L(z,y,x) = x * (y * z). [para(18(a,1),10(a,1,2)),rewrite([30(3)])].

88 x' * (y' * ((y * x) * z)) = L(z,y * x,y'). [para(10(a,1),18(a,1,1,1))].

89 L(x * y,x',z) = (z * x')' * (z * y). [para(10(a,1),18(a,1,2,2)),flip(a)].

92 (x * (y * z)) * ((x * y)' * ((x * (y * z)) * u)) = ((x * (y * z)) * L(z,y,x)) * u. [para(18(a,1),13(a,1,1,2)),flip(a)].

93 (x * (y * (x * z)))' * (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(13(a,1),18(a,1,1,1)),rewrite([13(8)])].

94 (x * (y * (z * y)))' * (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(13(a,1),18(a,1,2,2))].

95 (B * ((x * y) * B))' * ((B * x) * ((y * B) * z)) = L(z,y * B,B * x). [para(15(a,1),18(a,1,1,1))].

96 (x * (B * y))' * (x * (B * ((y * z) * B))) = L(z * B,B * y,x). [para(15(a,1),18(a,1,2,2))].

97 ((B * x) * y)' * (B * ((x * y) * B)) = L(B,y,B * x). [para(15(a,1),18(a,1,2))].

98 (x * C)' * (C * (x * y)) = L(y,x,C). [para(16(a,1),18(a,1,1,1))].

100 (C * x)' * (x * (C * y)) = L(y,C,x). [para(16(a,2),18(a,1,1,1))].

101 (x * y)' * (x * (C * y)) = L(C,y,x). [para(16(a,2),18(a,1,2,2))].

102 L(x,y,z)' * ((z * y)' * ((z * (y * x)) * u)) = L(u,z * (y * x),(z * y)'). [para(18(a,1),18(a,1,1,1))].

103 (x * (y * z)')' * (x * L(u,z,y)) = L(y * (z * u),(y * z)',x). [para(18(a,1),18(a,1,2,2))].

104 ((x * y)' * x)' * L(z,y,x) = L(y * z,x,(x * y)'). [para(18(a,1),18(a,1,2))].

105 x' * C = C * x'. [para(16(a,2),31(a,2)),rewrite([31(2)])].

106 (x / y)' = y / x. [para(7(a,1),32(a,1,2)),flip(a)].

108 x / (y * (z * (y * x))) = (y * (z * y))'. [para(13(a,1),32(a,1,2))].

110 x / (x * C) = C'. [para(16(a,1),32(a,1,2))].

111 C / (C * x) = x'. [para(16(a,2),32(a,1,2))].

112 (x * (y * z)) / L(z,y,x) = x * y. [para(18(a,1),32(a,1,2)),rewrite([30(7)])].

116 x / C = C' * x. [para(62(a,1),10(a,1,2)),flip(a)].

119 (x * C)' * (x * y) = L(C' * y,C,x). [para(62(a,1),18(a,1,2,2)),rewrite([116(7)])].

123 B * (((B' * x) * y) * B) = x * (y * B). [para(34(a,1),15(a,1,1)),flip(a)].

125 x * (C * x') = C. [para(16(a,2),34(a,1,2))].

126 x' * (y * ((y' * x) * z)) = L(z,y' * x,y). [para(34(a,1),18(a,1,1,1))].

127 L(x' * y,x,z) = (z * x)' * (z * y). [para(34(a,1),18(a,1,2,2)),flip(a)].

130 C * (x * (C' * x)) = x * x. [para(63(a,1),13(a,2,2)),rewrite([16(6,R)])].

131 C' * (x * (y * (x * C))) = x * (y * x). [para(13(a,1),63(a,1,2))].

133 (x * C')' * (x * y) = L(y * C,C',x). [para(63(a,1),18(a,1,2,2))].

134 (C' * x)' * x = L(C,x,C'). [para(63(a,1),18(a,1,2))].

135 (C * x) * (x' * ((C * x) * y)) = C * (x * (C * y)). [para(64(a,1),13(a,1,1,2)),rewrite([16(4,R),70(5)]),flip(a)].

137 L(C * x,x',y) = (y * x')' * (y * C). [para(64(a,1),18(a,1,2,2)),flip(a)].

139 L(C,x,C') = C. [para(34(a,1),64(a,1,2)),rewrite([134(5)])].

142 x' / x = x' * x'. [para(8(a,1),35(a,1,1,2)),rewrite([3(3)])].

143 x / x' = x * x. [para(9(a,1),35(a,1,1,2)),rewrite([3(2)])].

144 (x' * y) / (x * y) = x' * x'. [para(10(a,1),35(a,1,1,2))].

148 (B * (x * (B * (x * B)))) / B = (B * x) * (B * x). [para(15(a,1),35(a,1,1)),rewrite([13(6)])].

149 (C * (x * C)) / x = C * C. [para(16(a,1),35(a,1,1,2))].

150 C' * (x * (C * x)) = x * x. [para(16(a,2),35(a,1,1,2)),rewrite([116(5)])].

151 ((x * y)' * L(z,y,x)) / (x * (y * z)) = (x * y)' * (x * y)'. [para(18(a,1),35(a,1,1,2))].

153 (C' * x) / (x * C) = C' * C'. [para(63(a,1),35(a,1,1,2))].

155 (x / y) * (y / x) = 0. [para(106(a,1),8(a,1,1))].

161 (C' * x)' = C / x. [para(34(a,1),111(a,1,2)),flip(a)].

169 B * (((C * B') * x) * B) = C * (x * B). [para(125(a,1),15(a,1,1)),flip(a)].

170 C' * (x * ((C * x') * y)) = L(y,C * x',x). [para(125(a,1),18(a,1,1,1))].

171 L(C * x',x,y) = (y * x)' * (y * C). [para(125(a,1),18(a,1,2,2)),flip(a)].

172 L(x',C,x) = C * (x * C)'. [para(125(a,1),18(a,1,2)),rewrite([16(5,R)]),flip(a)].

174 (x * x)' = x' * x'. [para(143(a,1),106(a,1,1)),rewrite([142(4)])].

178 x' * (C * x') = C * (x' * x'). [para(105(a,1),12(a,2,2)),rewrite([16(5,R)]),flip(a)].

184 (C' * x) * (C / x) = 0. [para(116(a,1),155(a,1,1))].

186 ((x / y) * (z * x)) / y = (x / y) * (z * (x / y)). [para(7(a,1),39(a,1,1,2,2))].

187 x * ((y / (x * z)) * x) = (x * y) / z. [para(7(a,1),39(a,1,1,2)),flip(a)].

188 (x' * y) / x = x' * (y * x'). [para(8(a,1),39(a,1,1,2,2)),rewrite([3(3)])].

189 x * ((x * y)' * x) = x / y. [para(8(a,1),39(a,1,1,2)),rewrite([3(2)]),flip(a)].

190 (x * y) / x' = x * (y * x). [para(9(a,1),39(a,1,1,2,2)),rewrite([3(2)])].

197 (x * (B * ((y * x) * B))) / B = x * ((B * y) * x). [para(15(a,1),39(a,1,1,2))].

198 (C * (x * (y * C))) / y = C * (x * C). [para(16(a,1),39(a,1,1,2,2))].

202 (x * L(y,z,x)) / (z * y) = x / z. [para(18(a,1),39(a,1,1,2)),rewrite([189(8)])].

205 C' * (x * x) = x * (C' * x). [para(63(a,1),39(a,1,1,2)),rewrite([116(3)])].

207 (C * C) / x = C * (x' * C). [para(64(a,1),39(a,1,1,2))].

212 (C / x) * (C' * (x * y)) = L(y,x,C'). [para(161(a,1),18(a,1,1))].

214 (C' * x) * ((C / x) * y) = y. [para(161(a,1),34(a,1,2,1))].

227 (x / y) * ((z / (x / y)) * x) = ((x / y) * z) * y. [para(7(a,1),40(a,1,2,2))].

228 (x' * y) * x = x' * (y / x'). [para(8(a,1),40(a,1,2,2)),rewrite([3(5)]),flip(a)].

229 (x * y) * x' = x * (y / x). [para(9(a,1),40(a,1,2,2)),rewrite([3(3)]),flip(a)].

230 (x / y) * (y * z) = y' * ((y * x) * z). [para(40(a,1),10(a,1,2)),flip(a)].

231 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),40(a,1,2,2)),flip(a)].

235 x' * ((((x * y) * (y / x)) / x') * z) = (y / x) * ((x * y) * z). [para(40(a,1),13(a,2,2)),rewrite([230(4),231(7)])].

237 (x / C') * y = (C * x) * y. [para(40(a,1),16(a,1)),rewrite([116(5),231(9),16(12,R),34(12)]),flip(a)].

239 (C * x) * y = (x * C) * y. [para(16(a,1),40(a,2,1)),rewrite([116(3),231(7),237(7),34(8)])].

241 (x * (y / x))' * ((x * y) * z) = L(x * z,y / x,x). [para(40(a,1),18(a,1,2))].

242 (x * y)' * ((z / (x * y)') * L(u,y,x)) = ((x * y)' * z) * (x * (y * u)). [para(18(a,1),40(a,1,2,2))].

243 (x * y) * (x' * z) = x * ((y / x) * z). [para(34(a,1),40(a,1,2,2)),flip(a)].

245 (x' * y) * (C * x) = x' * (C * (y / x')). [para(64(a,1),40(a,1,2,2)),rewrite([16(5,R)]),flip(a)].

246 (x * y) * (C * x') = x * (C * (y / x)). [para(125(a,1),40(a,1,2,2)),rewrite([16(3,R)]),flip(a)].

247 (C * x) * (C / x) = C * C. [para(125(a,1),40(a,1,2)),rewrite([116(7),161(9)]),flip(a)].

248 (x' * C) * y = (C * x') * y. [para(105(a,1),40(a,2,1)),rewrite([230(7),30(3),10(7)])].

251 x / B' = x * B. [back_rewrite(53),rewrite([228(6),34(8)])].

252 L(x,y * z,y') = L(x,y,z / y). [back_rewrite(79),rewrite([230(4),88(6)])].

255 x' * (y' * ((y * x) * z)) = L(z,y,x / y). [back_rewrite(88),rewrite([252(9)])].

256 (x * B') * B = x. [para(251(a,1),6(a,1))].

257 (x * B) * B' = x. [para(251(a,1),7(a,1,1))].

259 (x * B)' = B' / x. [para(251(a,1),106(a,1,1))].

260 (x * B) * (B' / x) = 0. [para(251(a,1),155(a,1,1))].

264 x / B = x * B'. [para(256(a,1),6(a,1,1))].

267 B * ((x * (y * B')) * B) = (B * x) * y. [para(256(a,1),15(a,1,2)),flip(a)].

268 x' * ((x * B') * (B * y)) = L(y,B,x * B'). [para(256(a,1),18(a,1,1,1))].

269 (x * (y * B'))' * (x * y) = L(B,y * B',x). [para(256(a,1),18(a,1,2,2))].

270 (x * B')' = B / x. [para(256(a,1),32(a,1,2)),flip(a)].

273 (x * (B * ((y * x) * B))) * B' = x * ((B * y) * x). [back_rewrite(197),rewrite([264(8)])].

274 B * ((x * (B * (x * B))) * B') = (B * x) * (B * x). [back_rewrite(148),rewrite([264(9),229(10),264(8)])].

277 (x * (y * (x * B))) * B' = x * (y * x). [para(13(a,1),257(a,1,1))].

278 x' * ((x * B) * (B' * y)) = L(y,B',x * B). [para(257(a,1),18(a,1,1,1))].

281 ((x * B) * (y * x)) * B = (x * B) * (y * (x * B)). [para(257(a,1),39(a,1,1,2,2)),rewrite([251(7)])].

282 (B * x) * (B * x) = B * (x * (B * x)). [back_rewrite(274),rewrite([277(9)]),flip(a)].

284 (x * B') * (B / x) = 0. [para(264(a,1),155(a,1,1))].

302 (B' / x) * ((x * B) * y) = y. [para(259(a,1),10(a,1,1))].

304 (x * (y * (x * B)))' = B' / (x * (y * x)). [para(13(a,1),259(a,1,1))].

305 (B * C)' = C' * B'. [para(16(a,1),259(a,1,1)),rewrite([116(8)])].

306 L(x,B,y * B') = L(x,B,y). [para(259(a,1),18(a,1,1)),rewrite([230(7),268(8)])].

316 L(x,B',y * B) = L(x,B',y). [para(270(a,1),18(a,1,1)),rewrite([230(7),278(8)])].

321 B / C' = B * C. [para(270(a,1),161(a,1)),rewrite([251(8),16(7)])].

325 (B * C) * (C' * B') = 0. [para(321(a,1),155(a,1,1)),rewrite([264(7)])].

346 (x * (x * C))' * (x * (C * (x * y))) = y. [para(16(a,1),42(a,1,1,1,2))].

372 ((x * B) * y) / (B' / x) = (x * B) * (y * (x * B)). [para(260(a,1),39(a,1,1,2,2)),rewrite([3(4)])].

376 ((x * B') * y) / (B / x) = (x * B') * (y * (x * B')). [para(284(a,1),39(a,1,1,2,2)),rewrite([3(5)])].

428 (B * C) * ((C' * B') * x) = x. [para(305(a,1),34(a,1,2,1))].

433 L(B,x,B) = B. [para(49(a,1),10(a,1,2)),rewrite([18(8)])].

434 (B * (B * (x * B))) * y = B * ((B * x) * (B * y)). [para(49(a,1),13(a,1,1,2))].

435 B * ((x * B) * B) = B * (x * (B * B)). [para(49(a,1),13(a,1))].

436 (B * x) * (B * (y * B)) = B * ((x * (B * y)) * B). [para(49(a,1),15(a,1,2))].

441 (B * (x * B))' = B' / (B * x). [para(49(a,1),259(a,1,1))].

447 (B' / (B * (x * y))) * ((B * x) * ((y * B) * z)) = L(z,y * B,B * x). [back_rewrite(95),rewrite([441(6)])].

451 (x * (y * (z * (z * (y * x))))) * u = x * (y * (z * (z * (y * (x * u))))). [para(45(a,1),13(a,1,1,2)),rewrite([45(11)])].

510 L(C,x,C) = C. [para(65(a,2),18(a,1,2)),rewrite([64(8)]),flip(a)].

516 (C * x)' = (x * C)'. [para(65(a,1),111(a,1,2)),rewrite([111(6)]),flip(a)].

529 (C * x) * (x * C)' = 0. [para(516(a,1),9(a,1,2))].

532 (C * x)' * ((x * C) * y) = y. [para(516(a,2),10(a,1,1))].

533 (C * (x * x))' = (x * (x * C))'. [para(12(a,1),516(a,2,1))].

566 C * (x * (y * (z * (y * x)))) = x * (y * (z * (y * (x * C)))). [para(47(a,1),16(a,2))].

567 (x * (C * (y * (x * C)))) * z = x * (C * (y * (C * (x * z)))). [para(16(a,1),47(a,1,1,2,2,2))].

568 C * (x * (y * (x * (C * z)))) = C * (x * (y * (x * (z * C)))). [para(16(a,1),47(a,2,2,2,2,2)),rewrite([47(7)])].

656 (B * (x * B)) / (y * B) = B * (x / y). [para(7(a,1),50(a,1,1,2,1))].

690 (C * (x * x))' * (x * ((x * C) * y)) = L(y,x * C,x). [para(66(a,2),18(a,1,1,1))].

694 x * (C * (x' * x')) = x' * C. [para(66(a,2),34(a,1,2))].

716 (x * (C * x)) / (x * x) = C. [para(67(a,1),6(a,1,1))].

726 L(x,C,x) = L(x,x,C). [para(67(a,1),18(a,1,2)),rewrite([100(7)])].

743 (C * (x * x))' = (x * (C * x))'. [para(67(a,1),516(a,1,1)),rewrite([16(7,R)]),flip(a)].

748 (x * (C * (C * (x * x)))) * y = x * (C * (x * (C * (x * y)))). [para(67(a,2),47(a,1,1,2,2))].

754 L(B,B,C) = B. [para(726(a,1),433(a,1))].

761 L(x * B,x,B) = x * B. [para(12(a,1),54(a,1,2,2)),rewrite([18(9)])].

765 L(x * (y * B),y,B) = (x * y) * B. [para(13(a,1),54(a,1,2,2)),rewrite([18(10)])].

772 L((x * y) * B,B,(B * x)') = (B' / (B * x)') * (y * B). [para(54(a,1),18(a,1,2)),rewrite([259(6)]),flip(a)].

774 L(C * (x * B),C',B) = (x * C) * B. [para(63(a,1),54(a,1,2,2,1)),rewrite([133(10),16(4,R)])].

779 B / x = B * x'. [para(54(a,1),39(a,1,1,2)),rewrite([656(8),32(3),189(10)]),flip(a)].

790 L(x * (y * (x * (z * B))),z,B) = (x * (y * (x * z))) * B. [para(47(a,1),54(a,1,2,2)),rewrite([18(12)])].

800 ((x * B') * y) / (B * x') = (x * B') * (y * (x * B')). [back_rewrite(376),rewrite([779(6)])].

815 (x * B')' = B * x'. [back_rewrite(270),rewrite([779(6)])].

817 (B * x') * x = B. [para(779(a,1),7(a,1,1))].

818 B * (B' / x) = x'. [para(779(a,1),32(a,1)),rewrite([259(4)])].

820 B * (C' * B') = C'. [para(779(a,1),110(a,1)),rewrite([305(5)])].

821 C' * B = B * C'. [para(779(a,1),116(a,1)),flip(a)].

827 C * (B * C') = B. [para(817(a,1),16(a,2))].

831 (B * x) * x' = B. [para(30(a,1),817(a,1,1,2))].

833 (B * (x / y)) * (y / x) = B. [para(106(a,1),817(a,1,1,2))].

835 x * ((B * (x * y)') * x) = (x * B) / y. [para(817(a,1),39(a,1,1,2)),flip(a)].

848 (B * C) / (B * C') = C * C. [para(827(a,1),35(a,1,1,2)),rewrite([16(3)])].

858 (B * x)' = x' * B'. [para(831(a,1),32(a,1,2)),rewrite([264(3)]),flip(a)].

859 x * (B' * x)' = B. [para(34(a,1),831(a,1,1))].

875 L((x * y) * B,B,x') = x * (y * B). [back_rewrite(772),rewrite([858(7),306(9),858(11),32(13),30(8)])].

881 B' / (B * x) = (B' / x) * B'. [back_rewrite(441),rewrite([858(5),259(3)]),flip(a)].

886 ((B' / (x * y)) * B') * ((B * x) * ((y * B) * z)) = L(z,y * B,B * x). [back_rewrite(447),rewrite([881(6)])].

913 B' / x = B' * x'. [para(818(a,1),10(a,1,2)),flip(a)].

920 ((B' * (x * y)') * B') * ((B * x) * ((y * B) * z)) = L(z,y * B,B * x). [back_rewrite(886),rewrite([913(4)])].

923 (B' * x') * B' = B' * (x' * B'). [back_rewrite(881),rewrite([913(5),858(5),913(10)]),flip(a)].

931 ((x * B) * y) / (B' * x') = (x * B) * (y * (x * B)). [back_rewrite(372),rewrite([913(6)])].

940 (x * (y * (x * B)))' = B' * (x * (y * x))'. [back_rewrite(304),rewrite([913(10)])].

942 (B' * x') * ((x * B) * y) = y. [back_rewrite(302),rewrite([913(3)])].

946 (x * B)' = B' * x'. [back_rewrite(259),rewrite([913(6)])].

947 B' * ((x * y)' * (B' * ((B * x) * ((y * B) * z)))) = L(z,y * B,B * x). [back_rewrite(920),rewrite([923(8),13(15)])].

950 (B * x) * (B * C') = B * ((x * C') * B). [para(821(a,1),15(a,1,2))].

958 (B' * x)' = x' * B. [para(859(a,1),10(a,1,2)),flip(a)].

961 x' * ((B * x) * (y * (x * ((x' * B) * z)))) = (x' * (B * ((x * y) * B))) * z. [para(859(a,1),47(a,1,1,2,2,2)),rewrite([958(4),231(7),779

(4),30(4),15(6),958(12),958(15),231(19),779(12),30(12)]),flip(a)].

994 (B * C') * (B * x) = B * (B * (x * C')). [para(184(a,1),57(a,2,2,2)),rewrite([821(4),436(12),264(15),246(17),264(14),257(15),34(11),821(

11),3(15)]),flip(a)].

1012 (B * C) * (B * x) = B * (B * (x * C)). [para(529(a,1),57(a,2,2,2)),rewrite([16(3),436(10),858(14),13(16),820(14),229(10),116(8),34(10),

16(9),3(13)]),flip(a)].

1030 L(x,x * B',B) = x. [para(7(a,1),761(a,1,1)),rewrite([264(2),264(7),256(10)])].

1051 C' * B' = B' * C'. [para(820(a,1),10(a,1,2)),flip(a)].

1053 C * (B' * C') = L(B',C',B). [para(820(a,1),18(a,1,2)),rewrite([858(5),30(3),229(7),116(5),1051(6)])].

1061 (B * C) * ((B' * C') * x) = x. [back_rewrite(428),rewrite([1051(8)])].

1066 B * L(B',C',B) = 0. [back_rewrite(325),rewrite([1051(8),243(9),264(4),229(8),116(6),1051(7),1053(8)])].

1068 ((x * B) * y) * B = x * (B * (y * B)). [para(58(a,1),10(a,1,2)),rewrite([10(10)]),flip(a)].

1086 (x * B) * (y * (x * B)) = x * (B * ((y * x) * B)). [back_rewrite(281),rewrite([1068(6)]),flip(a)].

1092 ((x * B) * y) / (B' * x') = x * (B * ((y * x) * B)). [back_rewrite(931),rewrite([1086(14)])].

1094 (x' * B') * (B * x) = 0. [para(858(a,1),8(a,1,1))].

1095 (B * x) * (x' * B') = 0. [para(858(a,1),9(a,1,2))].

1097 (x' * B') * (B * (x * y)) = L(y,x,B). [para(858(a,1),18(a,1,1))].

1103 (B * x) / (x' * B') = B * (x * (B * x)). [para(858(a,1),143(a,1,2)),rewrite([282(12)])].

1108 (B' * x') * x = B'. [para(913(a,1),7(a,1,1))].

1111 (B' * x') * (x * (B * y)) = L(y,B,x). [para(946(a,1),18(a,1,1))].

1123 (x' * B) * (C * (B' * x)) = C. [para(958(a,1),64(a,1,1))].

1152 B * ((x * (B' * y)) * B) = B * ((x * B') * (y * B)). [para(257(a,1),59(a,2,2,1,2,2)),rewrite([8(10),3(8),243(8),264(3)]),flip(a)].

1168 (B * x) * (B * (B * (B * C))) = B * ((x * (B * (B * C))) * B). [para(66(a,1),59(a,1,2,2)),rewrite([16(15)])].

1189 L(B',C',B) = B'. [para(1066(a,1),10(a,1,2)),rewrite([3(4)]),flip(a)].

1192 C * (B' * C') = B'. [back_rewrite(1053),rewrite([1189(13)])].

1250 (B' * x) * x' = B'. [para(30(a,1),1108(a,1,1,2))].

1254 x * ((B' * (x * y)') * x) = (x * B') / y. [para(1108(a,1),39(a,1,1,2)),flip(a)].

1258 (B' * (x * C)') * (C * x) = B'. [para(516(a,1),1108(a,1,1,2))].

1269 B * (C * ((B' * C') * x)) = L(x,B' * C',C). [para(1192(a,1),18(a,1,1,1)),rewrite([30(3)])].

1318 C * (x * C) = x * (C * C). [para(69(a,2),39(a,1,1)),rewrite([116(8),10(9)]),flip(a)].

1398 C * (C * x) = x * (C * C). [para(70(a,1),63(a,1,2)),rewrite([10(9)]),flip(a)].

1441 ((x * C) * y)' * ((C * x) * (y * z)) = L(z,y,C * x). [para(239(a,1),18(a,1,1,1))].

1447 ((x * C) * ((C * x) * y)) / y = (C * x) * (C * x). [para(239(a,1),35(a,1,1))].

1448 (C * x) * (C * x) = (x * C) * (x * C). [para(239(a,2),35(a,1,1,2)),rewrite([1447(7)])].

1451 ((x * C) * (y * ((C * x) * z))) / z = (C * x) * (y * (C * x)). [para(239(a,1),39(a,1,1))].

1452 (C * x) * (y * (C * x)) = (x * C) * (y * (x * C)). [para(239(a,2),39(a,1,1,2,2)),rewrite([1451(8)])].

1499 B * ((x * (y * ((C * z) * y))) * B) = B * ((x * (y * ((z * C) * y))) * B). [para(239(a,1),59(a,1,2,2)),rewrite([59(9)]),flip(a)].

1518 C * (C * (C * x)') = C / x. [para(247(a,1),10(a,1,2)),rewrite([1318(7,R),16(6,R)])].

1539 C' * x = x * C'. [para(8(a,1),71(a,2,2,2)),rewrite([34(8),3(7)]),flip(a)].

1540 x' * (C * (x * (y * x))) = y * (x * C). [para(71(a,2),10(a,1,2))].

1549 (C * x)' * (x * (y * (x * C))) = L(y * x,x,C). [para(71(a,1),18(a,1,2))].

1557 (x * C) * (x * C) = C * ((x * C) * x). [para(63(a,1),71(a,1,2,2)),rewrite([16(13,R),10(14)]),flip(a)].

1563 (C * (x * C))' = (x * (C * C))'. [para(71(a,2),111(a,1,2)),rewrite([111(8)])].

1573 (x * C')' = C / x. [para(71(a,2),161(a,1,1)),rewrite([34(8),16(9,R),9(9),3(7)])].

1670 (C * x) * (C * x) = C * ((x * C) * x). [back_rewrite(1448),rewrite([1557(10)])].

1673 x' * ((x * C) * y) = L(y * C,C',x). [back_rewrite(133),rewrite([1573(4),230(4)])].

1694 C * (x * C') = x. [para(1539(a,1),10(a,1,2)),rewrite([30(3)])].

1700 (C' * (C' * x)) * y = C' * (x * (C' * y)). [para(1539(a,2),13(a,1,1,2))].

1707 x * (C' * x') = C'. [para(1539(a,2),34(a,1,2))].

1730 C * (x * (x * C')) = x * x. [para(1539(a,1),71(a,1,2,2)),rewrite([63(11)])].

1734 x / C' = C * x. [para(7(a,1),1694(a,1,2)),flip(a)].

1737 x' * (C * ((x * C') * y)) = L(y,x * C',C). [para(1694(a,1),18(a,1,1,1))].

1765 (C * x)' = C' / x. [para(1734(a,1),106(a,1,1))].

1781 (x * (C * C))' = C' / (x * C). [back_rewrite(1563),rewrite([1765(5)]),flip(a)].

1783 x' * ((x * C') * (y * (x * C))) = L(y * x,x,C). [back_rewrite(1549),rewrite([1765(3),230(8)])].

1785 C * (C * (C' / x)) = C / x. [back_rewrite(1518),rewrite([1765(5)])].

1815 (x * (C * x))' = C' / (x * x). [back_rewrite(743),rewrite([1765(4)]),flip(a)].

1817 (C' / (x * x)) * (x * ((x * C) * y)) = L(y,x * C,x). [back_rewrite(690),rewrite([1765(4)])].

1849 (x * (x * C))' = C' / (x * x). [back_rewrite(533),rewrite([1765(4)]),flip(a)].

1850 (C' / x) * ((x * C) * y) = y. [back_rewrite(532),rewrite([1765(3)])].

1852 (x * C)' = C' / x. [back_rewrite(516),rewrite([1765(3)]),flip(a)].

1860 (B' * (C' / x)) * (C * x) = B'. [back_rewrite(1258),rewrite([1852(5)])].

1865 L(x',C,x) = C * (C' / x). [back_rewrite(172),rewrite([1852(7)])].

1869 x' * ((x * C') * y) = L(C' * y,C,x). [back_rewrite(119),rewrite([1852(3),230(5)])].

1870 (C' / x) * (C * (x * y)) = L(y,x,C). [back_rewrite(98),rewrite([1852(3)])].

1875 (C' / (x * x)) * (x * (C * (x * y))) = y. [back_rewrite(346),rewrite([1849(4)])].

1884 L(C' * (x * (y * C)),C,y) = L(x * y,y,C). [back_rewrite(1783),rewrite([1869(9)])].

1939 x * ((B * x') * (C * x)) = C * (x * B). [para(817(a,1),72(a,1,2,2)),flip(a)].

1972 (x * (y * (x * C')))' = C / (x * (y * x)). [para(13(a,1),1573(a,1,1))].

1973 (x * C') * ((C / x) * y) = y. [para(1573(a,1),34(a,1,2,1))].

1995 B * ((C * B') * (x * B)) = x * (B * C). [para(34(a,1),73(a,1,1)),rewrite([16(10,R),1152(13)]),flip(a)].

2051 L(x',x,y) / y = (y * x)'. [para(9(a,1),78(a,1,2,2)),rewrite([3(4)])].

2224 L(x,y / x,B * (x / y)) = B' * ((B * (x / y)) * y). [para(817(a,1),80(a,2,1,1)),rewrite([106(4),106(10)])].

2251 L(x,C / x,C * x) = x. [para(247(a,1),80(a,2,1,1)),rewrite([174(9),16(14,R),12(15),10(14),10(10)])].

2364 L(x,B,y / (B * x)) = (B' * ((B * x) / y)) * y. [para(946(a,1),81(a,2,1)),rewrite([106(11)])].

2464 L(x,x',B') = x. [para(83(a,2),264(a,2)),rewrite([958(5),30(2),264(4),257(5)]),flip(a)].

2488 L(x,x',B' * x) = x. [para(1108(a,1),83(a,2,1,1)),rewrite([30(5),30(8),30(10),34(10)])].

2536 L(x',x,B') = x'. [para(30(a,1),2464(a,1,2))].

2555 L(C * x',x,C') = C / x. [para(125(a,1),84(a,1,3,1)),rewrite([125(10),161(10)])].

2585 L(C',x,C / x) = C'. [para(1539(a,2),84(a,1,3,1)),rewrite([161(6),1573(9),7(8)])].

2656 x / L(y',y,x) = x * y. [para(86(a,2),32(a,1,2)),rewrite([30(6)])].

2657 L(x',x,C) / (C' / x) = C. [para(86(a,2),60(a,1,1)),rewrite([1765(6)])].

2667 x * L(y',y,x) = x / y. [para(86(a,2),39(a,2,2)),rewrite([39(6),189(4)]),flip(a)].

2680 (C' / x) * L(x',x,C) = C * ((C' / x) * (C' / x)). [para(86(a,2),66(a,2,2)),rewrite([1765(4),1765(7),1765(12)]),flip(a)].

2791 (x * C) * L(y,x,C) = C * (x * y). [para(16(a,1),87(a,1,1))].

2800 C * L(x,C * y',y) = y * ((C * y') * x). [para(125(a,1),87(a,1,1))].

2814 B * L(x,y,B * y') = (B * y') * (y * x). [para(817(a,1),87(a,1,1))].

2815 B * L(x,y',B * y) = (B * y) * (y' * x). [para(831(a,1),87(a,1,1))].

2840 x * (C' * y) = x * (y * C'). [para(1539(a,1),87(a,2,2)),rewrite([87(7)])].

2884 L(B,C * B',B * C) = B. [para(264(a,1),2251(a,1,2)),rewrite([16(8)])].

2916 x * L(y * z,y',x) = (x / y') * z. [para(89(a,2),13(a,2,2)),rewrite([189(5)]),flip(a)].

2976 (B * x') * (x * y) = L(B * y,B',x). [para(815(a,1),89(a,2,1)),flip(a)].

3060 B * L(x,y,B * y') = L(B * x,B',y). [back_rewrite(2814),rewrite([2976(11)])].

3093 L(C',C * x,x') = C'. [para(111(a,1),2585(a,1,3))].

3125 x * L(y * C,C',x) = (x * C) * y. [para(63(a,1),92(a,1,1)),rewrite([161(4),63(7),230(4),1673(5),63(11),139(10)])].

3176 (B * (B * (B * C))) * x = B * (B * (B * (x * C))). [para(754(a,1),92(a,2,1,2)),rewrite([66(5),16(8),1852(9),264(9),1539(10),66(15),68(1

6),231(17),251(12),1539(11),2976(16),243(17),264(6),229(7),264(5),125(7),2916(11),251(5),16(4),1012(7),66(13),68(15),66(14)]),flip(a)].

3396 L(x,y,z / y) = L(x,y,z). [para(8(a,1),93(a,1,1,1,2)),rewrite([3(2),18(6),10(4),189(5)]),flip(a)].

3424 x' * (C' * (x * (C * y))) = L(y,C,x * (C' * x)). [para(63(a,1),93(a,1,1,1,2)),rewrite([174(2),12(11),10(10)])].

3425 (C / (x * (y * x))) * (x * (y * (x * z))) = L(z * C,C',x * (y * x)). [para(63(a,1),93(a,1,2,2,2,2)),rewrite([1972(6)])].

3429 C' * (x' * (C * (x * y))) = L(y,x,C * (x' * C)). [para(64(a,1),93(a,1,1,1,2)),rewrite([174(4),12(13),10(12)])].

3435 C' * (x * (C * (x' * y))) = L(y,x',C * (x * C)). [para(125(a,1),93(a,1,1,1,2)),rewrite([174(4),12(13),10(12)])].

3470 (C' / (C * ((x * C) * x))) * (C * ((C * x) * (C * (x * y)))) = L(y,x,C * (C * (C * x))). [para(66(a,1),93(a,1,1,1)),rewrite([16(6,R),67

(7,R),1670(6),1765(8),16(22,R)])].

3478 (x * (y * (x * x)))' * (x * (y * (C * (x * x)))) = L(C,x,x * (y * x)). [para(66(a,2),93(a,1,2,2,2))].

3485 (C' / (C * (x * x))) * (C * (x * (C * (x * y)))) = L(y,x,C * (x * C)). [para(67(a,2),93(a,1,1,1,2)),rewrite([1765(6)])].

3574 x' * (C * (x * (C' * y))) = L(y,C',x * (C * x)). [para(1694(a,1),93(a,1,1,1,2)),rewrite([174(2),12(11),10(10)])].

3671 x' * (y' * ((y * x) * z)) = L(z,y,x). [back_rewrite(255),rewrite([3396(8)])].

3672 L(x,y * z,y') = L(x,y,z). [back_rewrite(252),rewrite([3396(5)])].

3690 L(x,y,z * y) = L(x,y,z). [para(10(a,1),94(a,1,1,1)),rewrite([10(7),18(5),3672(5)]),flip(a)].

3926 x' * ((x * y) * B) = L(y * B,B,x). [para(10(a,1),96(a,1,1,1)),rewrite([10(9),3672(12)])].

4107 L(B,x,B * x') = B. [para(8(a,1),97(a,1,2,2,1)),rewrite([817(4),2(6),10(6)]),flip(a)].

4137 L(B,B,B * x) = B. [para(49(a,1),97(a,1,1,1)),rewrite([858(5),946(3),923(7),435(13),13(14),10(12),10(8),10(6)]),flip(a)].

4153 ((B * (B * x)) * x')' * (B * (B * B)) = L(B,x',B * (B * x)). [para(831(a,1),97(a,1,2,2,1))].

4221 L(B,B,x) = B. [para(34(a,1),4137(a,1,3))].

4223 B' * L(B * B,B,x) = B. [para(4137(a,1),93(a,2)),rewrite([940(7),858(7),946(5),923(9),231(19),251(12),13(11),8(9),3(7),1111(13)])].

4226 (x * B) * B = x * (B * B). [para(4221(a,1),87(a,1,2))].

4256 x' * (y' * (C * (y * x))) = L(C,y,x). [para(10(a,1),101(a,1,1,1)),rewrite([3672(11)])].

4262 L(C,C,x) = C. [para(16(a,2),101(a,1,1,1)),rewrite([1765(3),230(8),1318(8,R),16(7,R),1694(7),64(4)]),flip(a)].

4270 C' * (x' * (C * (C * x))) = L(C,C * x,x'). [para(64(a,1),101(a,1,1,1))].

4281 L(C,x * C,x) = C. [para(66(a,2),101(a,1,1,1)),rewrite([1765(4),1875(10)]),flip(a)].

4286 B' * ((B * x) * (C * x')) = L(C,x',B * x). [para(831(a,1),101(a,1,1,1))].

4306 (C / x) * (C * x) = C * C. [para(101(a,1),70(a,2,2)),rewrite([1765(5),1785(7),510(9)])].

4314 (C' / (x * x)) * (C * (x * (C * x))) = C. [para(71(a,2),101(a,1,2)),rewrite([1849(4),4281(14)])].

4315 (x * (y * C'))' * (x * y) = L(C,y * C',x). [para(1694(a,1),101(a,1,2,2))].

4317 L(C,C * x,x) = C. [para(72(a,2),101(a,1,2)),rewrite([1815(4),4314(10)]),flip(a)].

4334 (x * (y * z))' * (x * (y * (C * z))) = L(L(C,z,y),y * z,x). [para(101(a,1),89(a,1,1)),rewrite([30(5),30(7)]),flip(a)].

4358 L(L(C,x * x,y),y * (x * x),x) = L(C,x,x * (y * x)). [back_rewrite(3478),rewrite([4334(10)])].

4359 C / (x * (C * C)) = C' / x. [para(4262(a,1),78(a,1,1)),rewrite([1852(9)])].

4381 L(C,x,x * C') = C. [para(1694(a,1),4317(a,1,2))].

4449 L(x,C * (y * y),y' * y') = L(x,y,C * (y' * C)). [para(66(a,2),102(a,2,2)),rewrite([37(2),174(4),68(9),12(10),10(9),3429(8),174(11)]),fl

ip(a)].

4478 L(x,B' * C',C) = L(x,C',C * B'). [para(1189(a,1),102(a,1,1,1)),rewrite([30(3),1573(6),264(4),1539(11),34(12),243(9),116(6),1539(7),1269

(10),1539(13),34(14),1573(14),264(12)])].

4656 B * (C * ((B' * C') * x)) = L(x,C',C * B'). [back_rewrite(1269),rewrite([4478(17)])].

4677 (x * C') * (x * C) = C * ((x * C') * x). [para(4381(a,1),87(a,1,2)),rewrite([16(6,R)]),flip(a)].

4833 (B' * x') * (x * y) = L(B' * y,B,x). [para(2488(a,1),103(a,1,2,2)),rewrite([1250(5),30(3),946(3),8(11),3(11),1250(14),30(12)])].

4852 L(B * B,B',x) = B * B. [para(4107(a,1),103(a,1,2,2)),rewrite([817(4),815(4),15(6),8(3),2(4),15(9),8(6),2(7),817(10)]),flip(a)].

4891 L(x,y,B * y') = L(x,y,B). [para(1094(a,1),93(a,1,1,1,2)),rewrite([3(3),1097(11),10(7),256(9)]),flip(a)].

4900 B * L(x,y,B) = L(B * x,B',y). [back_rewrite(3060),rewrite([4891(5)])].

4912 (B * (B * x)) * x' = B * B. [para(1095(a,1),15(a,2,2,1)),rewrite([256(10),2(10)])].

4941 L(B,x',B * (B * x)) = B. [back_rewrite(4153),rewrite([4912(6),174(4),12(11),10(10),10(6)]),flip(a)].

4947 C * L(x,C,y) = L(x * C,y,C'). [para(16(a,1),104(a,2,1)),rewrite([1852(3),7(4),30(3),1852(9),3396(10)])].

4960 B * L(x,B,y) = L(B * x,y,B'). [para(256(a,1),104(a,1,1,1,1,1)),rewrite([10(5),30(3),306(6),256(14),3672(11)])].

4961 B' * L(x,B',y) = L(B' * x,y,B). [para(257(a,1),104(a,1,1,1,1,1)),rewrite([10(4),316(7),257(16),3672(13)])].

4977 x * L(y,x,B) = L(x * y,B,x'). [para(817(a,1),104(a,1,1,1,1,1)),rewrite([10(6),30(2),4891(4),817(11),3672(10)])].

5251 (x * (C * C)) * y = C * (x * (C * y)). [para(1318(a,1),13(a,1,1))].

5261 x * (C * (x' * C)) = C * C. [para(1318(a,2),34(a,1,2))].

5345 ((B * C) * (x * C))' * (B * (C * (x * (B * C)))) = L(B,x * C,B * C). [para(1318(a,1),97(a,1,2,2,1)),rewrite([5251(14),16(12)])].

5347 (C' / (C * (B * x))) * (B * (C * (x * (B * C)))) = L(B,C * C,B * x). [para(1318(a,2),97(a,1,1,1)),rewrite([16(5,R),1765(7),5251(14),16(

12)])].

5361 L(x * y,C * C,C' / (C * x)) = x * L(y,x,C * C). [para(1318(a,2),104(a,1,1,1)),rewrite([12(5),1765(6),16(8,R),1785(9),111(4),30(2),12(13

),1765(14)]),flip(a)].

5381 (x * (y * x))' = x' / (x * y). [para(9(a,1),108(a,1,2,2,2)),rewrite([3(3)]),flip(a)].

5389 (x * y) / (z * L(y,x,z)) = x / z. [para(18(a,1),108(a,1,2,2)),rewrite([189(8),106(6)])].

5390 (x' * y) / (x * (z * y)) = x' / (x * z). [para(34(a,1),108(a,1,2,2,2)),rewrite([5381(8)])].

5396 C' / (C * x) = x' / (C * C). [para(125(a,1),108(a,1,2,2)),rewrite([5381(10)]),flip(a)].

5460 x / (x * (C * (C * x))) = C' / (C * x). [para(72(a,1),108(a,1,2)),rewrite([5381(11)])].

5595 x' * (C * (C * x)) = C * C. [para(1398(a,2),10(a,1,2))].

5600 (C' / (C * x)) * (x * (C * (C * y))) = L(y,C * C,x). [para(1398(a,2),18(a,1,1,1)),rewrite([1765(5),12(9)])].

5603 x * (C * (C * x')) = C * C. [para(1398(a,2),34(a,1,2))].

5611 (x * (x * (C * C))) * y = x * (C * (C * (x * y))). [para(1398(a,1),45(a,1,1,2))].

5659 (C' / (C * (C * x))) * (C * (x * (C * (C * y)))) = L(y,C,C * (x * C)). [para(1398(a,2),93(a,1,1,1,2)),rewrite([1765(7)])].

5673 L(x,C * (C * y),C' / y) = C' * L(C * x,y,C). [para(1398(a,2),102(a,2,2)),rewrite([4262(3),1852(5),5251(10),1870(11),1852(14)]),flip(a)]

.

5689 L(C,C * x,x') = C. [back_rewrite(4270),rewrite([5595(8),1318(6,R),16(5,R),9(5),3(3)]),flip(a)].

5703 C' * L(C * C,x,C) = C. [para(1765(a,1),5689(a,1,3)),rewrite([5673(9)])].

5966 ((B' * x) * y) * B = B' * (x * (y * B)). [para(123(a,1),10(a,1,2)),flip(a)].

5969 (x * (B' * y)) * B = (x * B') * (y * B). [para(13(a,1),123(a,1,2,1)),rewrite([228(10),251(10),34(11)])].

5982 (x * (B * ((y * x) * B))) * z = (x * B) * (y * ((x * B) * z)). [para(123(a,1),57(a,1,1,2)),rewrite([1086(6),34(14)])].

5990 B * ((B' * C') * (x * B)) = x * (B * C'). [para(1539(a,1),123(a,2,2)),rewrite([1539(7,R),5969(9),1539(6)])].

6006 (C * x) * (B * C) = C * (C * (x * B)). [para(1318(a,2),123(a,1,2,1,1)),rewrite([16(6,R),70(8),5969(10),1995(11),12(12)])].

6008 (x * (y * B)) * B' = B * ((B' * x) * y). [para(123(a,1),112(a,1,1)),rewrite([433(10),264(5)])].

6012 (x * B) * (y * x) = x * ((B * y) * x). [back_rewrite(273),rewrite([5982(9),257(7)])].

6080 L(x,y' * C,y) = L(x,C * y',y). [para(16(a,2),126(a,1,2,2,1)),rewrite([170(8)]),flip(a)].

6087 x / (x' * y) = x * (y' * x). [para(126(a,1),39(a,1,1,2)),rewrite([202(8)])].

6131 L(x,C' * y,C) = L(x,y * C',C). [para(1539(a,1),126(a,1,2,2,1)),rewrite([1737(8)]),flip(a)].

6163 L(L(x,y,z'),z' * y,z) = x. [para(87(a,1),126(a,1,2,2)),rewrite([34(5),10(3)]),flip(a)].

6200 C' * L(C * x,y',C * (y * C)) = L(x,y' * (C * C),y). [para(1318(a,2),126(a,1,2,2,1)),rewrite([174(4),13(11),12(13),3435(12)])].

6202 L(x,y' * (C * C),y) = L(x,C * (y' * C),y). [para(1318(a,2),126(a,2,2)),rewrite([174(4),5251(11),12(13),3435(12),6200(11)])].

6301 x * L(y' * z,y,x) = (x / y) * z. [para(127(a,2),13(a,2,2)),rewrite([189(4)]),flip(a)].

6310 L((C' / x) * y,x * C,C') = x' * (C' * y). [para(63(a,1),127(a,2,1,1)),rewrite([1852(3)])].

6317 x * ((x' * C') * y) = L(C' * y,C,x'). [para(105(a,1),127(a,2,1,1)),rewrite([1765(10),230(13),30(8)]),flip(a)].

6325 x' * ((x * B') * y) = L(B' * y,B,x). [para(256(a,1),127(a,2,1,1)),rewrite([306(8)]),flip(a)].

6353 L((C' / x) * y,C * x,x) = (C' / (x * x)) * (x * y). [para(67(a,2),127(a,2,1,1)),rewrite([1765(3),1765(11)])].

6528 L(C' * (x * B),C,B') = x * (B * C'). [back_rewrite(5990),rewrite([6317(10)])].

6536 L(x',x,y') = y * (y' / x). [para(2667(a,1),34(a,1,2)),flip(a)].

6634 L(C',x,C * (x' * C)) = C'. [para(174(a,1),3093(a,1,3)),rewrite([4449(9)])].

6702 L(x,y * z,z) = L(x,y,z). [para(32(a,1),3396(a,1,3)),rewrite([3672(3)]),flip(a)].

6707 L(x,y * C,C') = L(x,y * C,y). [para(110(a,1),3396(a,1,3))].

6708 L(x,C * y,y') = L(x,C * y,C). [para(111(a,1),3396(a,1,3))].

6710 L(x,y,z * (u * (z * y))) = L(x,y,z * (u * z)). [para(39(a,1),3396(a,1,3)),flip(a)].

6714 L(x,y,C * (y * C)) = L(x,y,C * C). [para(149(a,1),3396(a,1,3)),flip(a)].

6718 L(x,C',C * y) = L(x,C',y). [para(1734(a,1),3396(a,1,3))].

6728 L(x,y * y,y * (C * y)) = L(x,y * y,C). [para(716(a,1),3396(a,1,3)),flip(a)].

6747 (C' / (x * x)) * (x * y) = L((C' / x) * y,C,x). [back_rewrite(6353),rewrite([6702(7)]),flip(a)].

6761 (C' / (C * ((x * C) * x))) * (C * ((C * x) * (C * (x * y)))) = L(y,x,C * (C * C)). [back_rewrite(3470),rewrite([6710(24)])].

6762 (C' / (C * (x * x))) * (C * (x * (C * (x * y)))) = L(y,x,C * C). [back_rewrite(3485),rewrite([6714(18)])].

6763 B * (C * ((B' * C') * x)) = L(x,C',B'). [back_rewrite(4656),rewrite([6718(17)])].

6772 L(L(x,y,C),C,y) = x. [back_rewrite(1875),rewrite([6747(9),1870(7)])].

6773 L(x,y * C,y) = L(x,C,y). [back_rewrite(1817),rewrite([6747(9),1850(7)]),flip(a)].

6781 L(x,y * C,C') = L(x,C,y). [back_rewrite(6707),rewrite([6773(8)])].

6785 L((C' / x) * y,C,x) = x' * (C' * y). [back_rewrite(6310),rewrite([6781(9)])].

6795 (C' / (x * x)) * (x * y) = x' * (C' * y). [back_rewrite(6747),rewrite([6785(12)])].

6826 L(L(x,C' * y,C),C,y) = x. [para(6772(a,1),3396(a,1)),rewrite([116(2)]),flip(a)].

7039 L(x,C,C * y) = L(x,C,y). [para(16(a,2),3690(a,1,3))].

7040 L(x,y' * z,y) = L(x,y',z). [para(34(a,1),3690(a,1,3)),rewrite([6702(3)]),flip(a)].

7045 L(x,y',B * y) = L(x,y',B). [para(831(a,1),3690(a,1,3)),flip(a)].

7067 L(x,C / x,C * C) = x. [para(2251(a,1),3690(a,2)),rewrite([247(7)])].

7073 L(x,y / z,B * (z / y)) = L(x,y / z,B). [para(833(a,1),3690(a,1,3)),flip(a)].

7100 L(x,y * (C' * y),y * y) = L(x,y * (C' * y),C). [para(130(a,1),3690(a,1,3))].

7101 (C' / (C * (C * x))) * (C * (x * (C * (C * y)))) = L(y,C,x). [back_rewrite(5659),rewrite([7039(21),3690(19)])].

7106 L(L(x,C',y),C,y) = x. [back_rewrite(6826),rewrite([7040(5)])].

7119 L(x,C * (y' * C),y) = L(x,y',C * C). [back_rewrite(6202),rewrite([7040(6)]),flip(a)].

7150 L(L(x,y,z'),z',y) = x. [back_rewrite(6163),rewrite([7040(5)])].

7175 L(x,y * C',C) = L(x,C',y). [back_rewrite(6131),rewrite([7040(5)]),flip(a)].

7207 L(x,C * y',y) = L(x,y',C). [back_rewrite(6080),rewrite([7040(4)]),flip(a)].

7218 B' * ((B * x) * (C * x')) = L(C,x',B). [back_rewrite(4286),rewrite([7045(14)])].

7221 (B * x) * (x' * y) = L(B * y,B',x'). [back_rewrite(2815),rewrite([7045(5),4900(5)]),flip(a)].

7247 L(x,y / x,B) = B' * ((B * (x / y)) * y). [back_rewrite(2224),rewrite([7073(5)])].

7283 x * ((C * x') * y) = C * L(y,x',C). [back_rewrite(2800),rewrite([7207(5)]),flip(a)].

7308 C * L(x * B,B',C) = x * (B * C). [back_rewrite(1995),rewrite([7283(9)])].

7319 (C * (C * C)) / x = C * (C * (C / x)). [para(7067(a,1),112(a,1,2)),rewrite([7(6),16(5,R),12(12)])].

7427 L(B * B,B,x) = B * B. [para(4223(a,1),10(a,1,2)),rewrite([30(3)]),flip(a)].

7429 (B * (B * x')) * x = B * B. [para(4223(a,1),81(a,1,3,2)),rewrite([7427(5),264(7),3690(9),4852(6),7427(10),10(9),264(5),815(10),815(8)])

,flip(a)].

7457 (x * (y * (x * B))) * B = x * (y * (x * (B * B))). [para(13(a,1),4226(a,1,1)),rewrite([13(12)])].

7498 L(x,B,y * (B * B)) = L(x,B,y). [para(4226(a,1),3690(a,1,3)),rewrite([3690(10)])].

7515 x' * ((C * x) * y) = L(C * y,x,C). [para(135(a,1),10(a,1,2)),rewrite([1765(3),1870(9)]),flip(a)].

7522 (C * (C' / x)) * ((C * x) * ((C * (C' / x)) * (x * y))) = C * L(y,x,C). [para(18(a,1),135(a,2,2)),rewrite([1765(4),1765(8),106(9),1734(

8),1765(11)])].

7580 (C * (C' / x)) * ((C * x) * ((C * (C' / x)) * y)) = (C / x) * y. [para(127(a,2),135(a,2,2)),rewrite([1765(4),1765(8),106(9),1734(8),176

5(11),6301(21)])].

7593 C * L(x,y,C) = L(x * C,C',y). [back_rewrite(7522),rewrite([7580(16),230(4),1673(5)]),flip(a)].

7601 L(C * (x * B),C',B') = x * (B * C). [back_rewrite(7308),rewrite([7593(8),16(4,R)])].

7606 x * ((C * x') * y) = L(y * C,C',x'). [back_rewrite(7283),rewrite([7593(10)])].

7688 x' * (C * (x * B)) = L(B * C,B',x). [para(257(a,1),137(a,2,1,1)),rewrite([16(3),316(8),16(11,R)]),flip(a)].

7727 L(C',C * C,x) = C'. [para(1707(a,1),137(a,1,1)),rewrite([174(8),30(5),30(6),174(12),30(9),30(10),1781(11),7(14)])].

7826 L(x,C,y) = L(x,y,C'). [para(7727(a,1),102(a,1,1,1)),rewrite([30(3),1781(6),1539(12,R),1318(12,R),16(11,R),9(11),3(9),230(10),1852(4),15

39(9,R),63(9),230(6),1869(7),4947(7),16(5,R),34(5),1539(9,R),1318(9,R),16(8,R),9(8),3(6),1781(10),3396(11),6781(8)]),flip(a)].

7893 C * L(x,y,C') = L(C * x,y,C'). [para(7826(a,1),104(a,1,2)),rewrite([1852(3),7(4),30(3),1852(10),3396(11)])].

7901 L(L(x,y,C),y,C') = x. [para(7826(a,1),6772(a,1))].

7932 (C * x') / (x * C) = x' * x'. [para(16(a,2),144(a,1,1))].

8058 L(x,C,x * (C' * x)) = x. [para(150(a,1),93(a,1,2,2)),rewrite([63(5),174(2),12(6),10(5),10(3)]),flip(a)].

8119 C' * (C' * ((C / x) * (C * (x * y)))) = L(y,x,C * (C * (C / x))). [para(4306(a,1),93(a,1,1,1,2)),rewrite([1849(6),6795(15),16(17,R)])].

8151 L(B,x',B * B) = B. [para(4941(a,1),3690(a,2)),rewrite([4912(8)])].

8172 C' * ((C' / x) * L(x',C,x)) = (C' / x) * (C' / x). [para(125(a,1),151(a,1,2)),rewrite([1852(3),116(9),1852(13),1852(16)])].

8421 (x * B') * B' = x * (B' * B'). [para(8151(a,1),78(a,1,1)),rewrite([12(8),779(9),858(9),5381(7),913(7),858(7),30(5),13(10),34(11),12(11)

,858(12),858(10),30(8)]),flip(a)].

8720 (C' / x) / (C / x) = C' * C'. [para(2667(a,1),153(a,1,1)),rewrite([16(9,R),7893(9),2555(9)])].

8905 L(C * C,x,C) = C * C. [para(5703(a,1),10(a,1,2)),rewrite([30(3)]),flip(a)].

8906 x / (C * C) = C' * (x * C'). [para(5703(a,1),39(a,1,1,2,2)),rewrite([63(5),8905(5)])].

8909 L(x,C * C,C' * (y * C')) = L(x,C,y * (C' * y)). [para(5703(a,1),93(a,1,1,1,2,2)),rewrite([63(5),8905(10),12(9),10(10),3424(8),8905(11)]

),flip(a)].

8921 C' / (C * x) = C' * (x' * C'). [back_rewrite(5396),rewrite([8906(10)])].

8949 C' * L(C * x,C,y) = L(x,C,y). [back_rewrite(7101),rewrite([8921(7),1765(5),1539(8,R),231(17),1734(11),34(10),230(11),1869(12),10(9)])].

8951 L(x,y,C * (y' * C)) = L(x,y,C * C). [back_rewrite(6762),rewrite([8921(6),174(4),1539(8,R),231(16),1734(11),34(10),12(10),10(9),3429(8)]

)].

8952 C' * (((x * C) * x)' * ((C * x) * (C * (x * y)))) = L(y,x,C * (C * C)). [back_rewrite(6761),rewrite([8921(8),1539(9,R),231(19),1734(12)

,34(11)])].

8977 L(x,C,y * (C' * y)) = L(x,C * C,y). [back_rewrite(5600),rewrite([8921(5),13(13),3424(12),8949(11)])].

8983 x / (x * (C * (C * x))) = C' * (x' * C'). [back_rewrite(5460),rewrite([8921(11)])].

8993 L(x * y,C * C,C' * (x' * C')) = x * L(y,x,C * C). [back_rewrite(5361),rewrite([8921(9)])].

8994 C' * ((x' * B') * (C' * (B * (C * (x * (B * C)))))) = L(B,C * C,B * x). [back_rewrite(5347),rewrite([8921(7),858(5),1539(9,R),1700(19)]

)].

9009 L(C',x,C * C) = C'. [back_rewrite(6634),rewrite([8951(8)])].

9012 C' * (x' * (C * (x * y))) = L(y,x,C * C). [back_rewrite(3429),rewrite([8951(14)])].

9020 L(x,C * C,C' * (y * C')) = L(x,C * C,y). [back_rewrite(8909),rewrite([8977(16)])].

9022 L(x,C * C,x) = x. [back_rewrite(8058),rewrite([8977(6)])].

9035 x * L(y,x,C * C) = L(x * y,C * C,x'). [back_rewrite(8993),rewrite([9020(12)]),flip(a)].

9039 C' / (x * C) = C' * (x' * C'). [para(9022(a,1),78(a,1,1)),rewrite([12(4),8983(6),1781(12)]),flip(a)].

9062 (x * (C * C))' = C' * (x' * C'). [back_rewrite(1781),rewrite([9039(10)])].

9142 L(x,C * y,C' * (y' * C')) = L(x,C,y). [para(9009(a,1),102(a,1,1,1)),rewrite([30(3),12(5),1765(6),8921(6),12(15),1694(14),13(12),3671(11

),34(7),12(9),1694(8),12(8),1765(9),8921(9)]),flip(a)].

9198 C * (L(x,B',C) * B) = x * (B * C). [para(87(a,1),169(a,1,2,1)),rewrite([5969(8),7606(9),16(4,R),7601(9)]),flip(a)].

9460 L(C * (C' / x),C * x,C / x) = C' * (C / x). [para(4306(a,1),171(a,2,1,1)),rewrite([1765(4),174(14),16(19,R),12(20),10(19)])].

9516 L(x,y / z,z) = L(x,y,z). [para(7(a,1),6702(a,1,2)),flip(a)].

9517 L(x,y',y * z) = L(x,z,y). [para(10(a,1),6702(a,1,2)),rewrite([3690(2)]),flip(a)].

9518 L(x,y * (y * z),z) = L(x,y * y,z). [para(12(a,1),6702(a,1,2))].

9521 L(x,C * y,C) = L(x,y,C). [para(16(a,2),6702(a,1,2))].

9524 L(x,y,y' * z) = L(x,z,y'). [para(34(a,1),6702(a,1,2)),rewrite([3690(3)]),flip(a)].

9526 L(x,y',C * y) = L(x,C,y). [para(64(a,1),6702(a,1,2)),rewrite([7039(4)]),flip(a)].

9527 L(x,y,C * y') = L(x,C,y'). [para(125(a,1),6702(a,1,2)),rewrite([7039(5)]),flip(a)].

9528 L(x,y * B',B) = L(x,y,B). [para(256(a,1),6702(a,1,2)),flip(a)].

9540 L(x,x,B) = x. [para(1030(a,1),6702(a,2)),rewrite([256(5)])].

9582 L(x,C * (y * C),C * C) = L(x,y,C * C). [para(1318(a,2),6702(a,1,2))].

9604 L(x,C',y * (C * y)) = L(x,y * y,C). [para(150(a,1),6702(a,1,2)),rewrite([6728(5)]),flip(a)].

9611 (x * (y / x))' * ((x * y) * z) = L(x * z,y,x). [back_rewrite(241),rewrite([9516(9)])].

9613 L(x,C',y) = L(x,y,C). [back_rewrite(6718),rewrite([9517(5)]),flip(a)].

9635 L(x,C * y,y') = L(x,y,C). [back_rewrite(6708),rewrite([9521(8)])].

9850 x' * (C * (x * (C' * y))) = L(y,x * x,C). [back_rewrite(3574),rewrite([9604(14)])].

9869 (B * x) * x = B * (x * x). [para(9540(a,1),87(a,1,2))].

9997 (x * C') * L(y,x,C) = x * (C' * y). [para(9613(a,1),87(a,1,2))].

10001 L(x,y * (z * y),C) = L(x,C',y * (z * y)). [para(9613(a,1),93(a,2)),rewrite([1972(6),3425(11),16(5,R),34(5)]),flip(a)].

10007 C' * L(x,y,C) = L(C' * x,y,C). [para(9613(a,1),104(a,1,2)),rewrite([1573(4),7(3),1573(12),3396(11)])].

10025 L(x,y * (C' * y),y * y) = L(x,C',y * (C' * y)). [back_rewrite(7100),rewrite([10001(12)])].

10283 L(x,C,y * (C * C)) = L(x,C,y). [para(71(a,2),7039(a,1,3)),rewrite([7039(8),7039(6),3690(4)]),flip(a)].

10289 L(C * x,C,y) = L(x * C,y,C'). [para(7039(a,1),104(a,1,2)),rewrite([16(4,R),1765(5),8921(5),13(10),10(8),8(4),3(4),30(3),4947(4),16(13,

R),1765(14),8921(14),9142(17)]),flip(a)].

10291 C' * L(x,C,y) = L(C' * x,C,y). [para(7039(a,1),127(a,1)),rewrite([16(9,R),1765(10),8921(10),13(16),3671(15)]),flip(a)].

10294 L(x,C * C,y) = L(x,C,y * y). [para(130(a,1),7039(a,1,3)),rewrite([8977(9)]),flip(a)].

10352 L(L(x,y,z),z,y) = x. [para(30(a,1),7150(a,1,1,3)),rewrite([30(3)])].

10359 L(L(x,y,C'),y,C) = x. [para(7150(a,1),9613(a,1)),flip(a)].

10374 L(x,B,x) = x. [para(9540(a,1),10352(a,1,1))].

10445 (x * B) * x = x * (B * x). [para(10374(a,1),87(a,1,2))].

10589 C * (x * L(y,x,C')) = (C * x) * y. [para(10359(a,1),87(a,1,2)),flip(a)].

11015 (C * x) * (y * (C * x)) = C * ((C * x) * (y * x)). [para(186(a,1),1734(a,1)),rewrite([1734(3),1734(5),1734(10)])].

11122 (x * C) * (y * (x * C)) = C * ((C * x) * (y * x)). [back_rewrite(1452),rewrite([11015(6)]),flip(a)].

11213 (x / (y * z)) * y = y' * ((y * x) / z). [para(187(a,1),10(a,1,2)),flip(a)].

11214 (x' * y) / (x * z) = x' * ((y / z) * x'). [para(10(a,1),187(a,1,2,1,2)),flip(a)].

11591 x' / (x * y) = x' * (y' * x'). [back_rewrite(5390),rewrite([11214(5),32(3)]),flip(a)].

11754 (x * (y * x))' = x' * (y' * x'). [back_rewrite(5381),rewrite([11591(6)])].

11863 (B' * x) * B' = B' * (x * B'). [para(188(a,1),264(a,1)),flip(a)].

11951 (x * y)' * x = x' * (x / y). [para(189(a,1),10(a,1,2)),flip(a)].

11980 C' * (C / x) = C * (C' / x). [para(189(a,1),2251(a,1,3)),rewrite([1765(3),16(5,R),1765(9),16(11,R),111(12),106(9),1734(8),9460(10),176

5(8),16(10,R)])].

12007 C' / (x * (y * (x * C))) = C' * (C' * (x' * (y' * x'))). [para(131(a,1),189(a,1,2,1,1)),rewrite([11754(5),1539(10,R)]),flip(a)].

12419 x / (C' / x) = (x * C) * x. [para(63(a,1),190(a,2,2)),rewrite([1539(5,R),63(5),1852(3)])].

12752 L(B,B' * B',B * C) = B. [para(2884(a,1),9516(a,2)),rewrite([7932(9)])].

12753 L(x,C' / x,C * C) = x. [para(7067(a,1),9516(a,2)),rewrite([8906(6),1539(7,R),11980(7),10(8)])].

13006 L(x,C',y * (C' * y)) = L(x,y * y,C). [para(130(a,1),9521(a,1,2)),rewrite([10001(9)]),flip(a)].

13018 L(x,y * (C' * y),y * y) = L(x,y * y,C). [back_rewrite(10025),rewrite([13006(13)])].

13442 (B * C) * (x * C) = C * (C * (B * x)). [para(73(a,1),198(a,1,1,2)),rewrite([264(10),5982(11),16(3),16(6),229(9),264(7),125(9),16(11,R)

])].

13453 L(B,C * C,B * x) = L(B,x * C,B * C). [back_rewrite(5345),rewrite([13442(6),1765(7),11591(7),858(5),1539(9,R),1700(19),8994(19)])].

13519 x' * L(x * C,C',B) = L(C,x,x * B). [para(10445(a,1),101(a,1,1,1)),rewrite([11754(4),6012(11),13(12),10(10),1673(8)])].

14145 (B * x) / (x * x) = B * x'. [para(9540(a,1),202(a,1,1,2)),rewrite([779(6)])].

14267 (C' * (x * x)) * y = x * (C' * (x * y)). [para(205(a,2),13(a,1,1))].

14370 L(x,y * y,C) = L(x,C',y * y). [para(205(a,1),6702(a,1,2)),rewrite([13018(6)])].

14438 L(x,C',y * (C' * y)) = L(x,C',y * y). [back_rewrite(13006),rewrite([14370(10)])].

14458 x' * (C * (x * (C' * y))) = L(y,C',x * x). [back_rewrite(9850),rewrite([14370(11)])].

14523 L(x,y',C * C) = L(x,C * C,y). [para(207(a,1),9516(a,1,2)),rewrite([7119(6)])].

14544 L(x,C' / x,C / x) = x. [para(12753(a,1),3690(a,2)),rewrite([12(10),1785(10)])].

14750 C' * L(x,y,C') = L(C' * x,C,y). [para(212(a,1),13(a,2,2)),rewrite([1539(7,R),11980(7),10(8),230(5),1869(6)]),flip(a)].

14953 L(x,C' * C',C / x) = x. [para(14544(a,1),9516(a,2)),rewrite([8720(6)])].

15154 (C * x) * x' = x * (C / x). [para(16(a,2),229(a,1,1))].

15214 L(B * x,x,B) = B * x. [para(1094(a,1),229(a,1,1)),rewrite([815(6),30(4),2(4),1103(13),1097(12)]),flip(a)].

15268 L(x,B',x) = x. [para(34(a,1),15214(a,1,1)),rewrite([7040(5),34(8)])].

15397 L(x,x,B') = x. [para(15268(a,1),10352(a,1,1))].

15417 (B' * x) * x = B' * (x * x). [para(15397(a,1),87(a,1,2))].

15422 L(x * B,x,B') = x * B. [para(15397(a,1),9516(a,1)),rewrite([251(3),251(5)]),flip(a)].

15605 (B' * x) * (x * B) = B' * (x * (x * B)). [para(15422(a,1),87(a,1,2))].

15667 L(x,C,B') = L(x,B,C). [para(16(a,1),306(a,1,3)),rewrite([16(5,R),9527(6)])].

15670 L(x,C',B') = L(x,B,C'). [para(1539(a,1),306(a,1,3)),rewrite([9524(7)])].

15678 L(C' * (x * B),B,C) = x * (B * C'). [back_rewrite(6528),rewrite([15667(9)])].

15698 L(C * (x * B),B,C') = x * (B * C). [back_rewrite(7601),rewrite([15670(9)])].

15699 B * (C * ((B' * C') * x)) = L(x,B,C'). [back_rewrite(6763),rewrite([15670(15)])].

15710 L(L(x,B,C),B',C) = x. [para(15667(a,1),10352(a,1,1))].

15794 L(x,B',C) = L(x,C,B). [para(10352(a,1),15710(a,1,1))].

15798 C * (L(x,C,B) * B) = x * (B * C). [back_rewrite(9198),rewrite([15794(5)])].

15800 (C * B') * L(x,C,B) = C * (B' * x). [para(15794(a,1),87(a,1,2))].

15885 B * (L(B' * x,B,y) * B) = L(x * B,B,y). [para(256(a,1),230(a,1,2)),rewrite([11213(5),251(5),3926(5),815(8),15(14),6325(11)]),flip(a)].

15888 (x * B') * (B * y) = B' * ((B * x) * y). [para(264(a,1),230(a,1,1))].

15889 (x / (B * y)) * (B * (y * B)) = (y' * B') * (((B * y) * x) * B). [para(49(a,1),230(a,1,2)),rewrite([858(11)])].

15969 (x * y)' * (x * z) = x' * ((x / y) * z). [para(2667(a,1),230(a,2,2,1)),rewrite([2051(3)])].

15974 (x / (y * B)) * (y * (B * B)) = L(x * B,B,y). [para(4226(a,1),230(a,1,2)),rewrite([946(11),1068(17),4833(18),10(15)])].

16816 L(C,x * C',y) = L(C,x,y). [back_rewrite(4315),rewrite([15969(7),11213(6),1734(6),4256(7)]),flip(a)].

17157 x' * L(x * B,B,y) = L(B,y * B',x). [back_rewrite(269),rewrite([15969(7),11213(6),251(6),3926(6)])].

17292 (x * C') * (C * y) = C' * ((C * x) * y). [para(1539(a,1),231(a,1,1)),rewrite([1734(11)])].

17309 (x' / y) * (x * z) = x' * ((x' * y)' * z). [para(2667(a,1),231(a,1,1)),rewrite([2051(10)])].

17502 L(x,B * C',C * C) = L(x,B * C',B * C). [para(848(a,1),3396(a,1,3))].

17504 C * (C * ((B * C') * x)) = B * (x * C). [para(848(a,1),230(a,1,1)),rewrite([12(9),1573(14),264(12),4677(21),49(20),1539(19),1730(21),1

2(17),15888(18),1012(17),10(18)])].

17570 B * ((B' * (x * x)) * x') = x. [para(1250(a,1),235(a,2,2)),rewrite([30(3),251(7),15605(7),30(10),264(9),11863(10),6008(9),15417(8),34(

9),251(11),257(13)])].

18052 (x * C) * (C' * y) = C * ((C' * x) * y). [para(16(a,1),243(a,1,1)),rewrite([116(9)])].

18053 (C * x) * (x' * y) = x * ((C / x) * y). [para(16(a,2),243(a,1,1))].

18971 (C' / x) * L(x',C,x) = (C' / x) / x. [para(1865(a,2),186(a,2,2)),rewrite([9(7),3(5)]),flip(a)].

19018 (C' / x) * (C' / x) = C' * ((C' / x) / x). [back_rewrite(8172),rewrite([18971(9)]),flip(a)].

19031 (C' / x) * L(x',x,C) = (C' / x) / x. [back_rewrite(2680),rewrite([19018(15),34(16)])].

19690 ((C' / x) / x) * ((C * x) * y) = C' * ((C / x) * y). [para(2657(a,1),243(a,2,2,1)),rewrite([19031(7),106(8),1734(7),17309(14),161(14)]

)].

19694 (x * (y * B')) * B = B' * ((B * x) * y). [para(267(a,1),10(a,1,2)),flip(a)].

19713 ((B * x) * y) * B' = B * (x * (y * B')). [para(267(a,1),112(a,1,1)),rewrite([433(10),264(5)])].

19724 (x * (y * B')) * (B * z) = B' * (((B * x) * y) * z). [para(267(a,1),230(a,2,2,1)),rewrite([19694(6),264(8),11863(9),19713(8),10(9)])].

19725 (B * (x / y)) * y = L(B * x,B',y). [para(230(a,1),267(a,1,2,1)),rewrite([19694(9),2976(8),4961(9),10(6),4900(4)]),flip(a)].

19729 C * (B * (B * x)) = B * ((B * C) * x). [para(245(a,1),267(a,1,2,1)),rewrite([30(4),30(6),264(5),49(10),19694(9),1673(9),3125(9),30(10)

,16(12,R)]),flip(a)].

19783 L(x,y / x,B) = L(x,y,B). [back_rewrite(7247),rewrite([19725(9),4961(11),10(8)])].

19825 L(x,y * x,B) = L(x,y,B). [para(6(a,1),19783(a,1,2)),flip(a)].

19840 L(x,y,B) / (B * y) = (x / y) * B'. [para(19783(a,1),78(a,1,1)),rewrite([7(5),858(9),106(7)])].

19848 (B * x) / L(y,x,B) = B * (x / y). [para(19783(a,1),112(a,1,2)),rewrite([7(3)])].

19869 L(L(x,y,B),B,y / x) = x. [para(19783(a,1),10352(a,1,1))].

20188 L(L(x,y,B),B,y * x) = x. [para(19825(a,1),10352(a,1,1))].

20366 L(L(x,y,B),B,(y * B) / x) = x. [para(6702(a,1),19869(a,1,1))].

20537 L(L(x,y,B),B,(y * B) * x) = x. [para(6702(a,1),20188(a,1,1))].

21688 C' * L(B * C,B',x) = L(B,x,C * C). [para(5261(a,1),97(a,1,1,1,1)),rewrite([12(4),1765(5),11591(5),16(13,R),70(15),5969(17),7606(18),16

(13,R),15670(18),15698(17),6006(13),13(14),10(12),7688(8),16(16,R),5603(18)])].

22263 (B * (B * (B * C'))) * x = B * (B * (B * (x * C'))). [para(1539(a,1),434(a,1,1,2,2)),rewrite([994(17)])].

22406 L(x,B * (B * y'),y) = L(x,B * B,y). [para(7429(a,1),6702(a,1,2)),flip(a)].

22446 B * (L(x * C,C',B) * B) = C * (B * (x * B)). [para(125(a,1),436(a,1,1)),rewrite([15888(14),1673(14)]),flip(a)].

22857 L(x,y * y,y' * (C * y')) = L(x,C,y' * y'). [para(178(a,2),9526(a,1,3)),rewrite([174(4),30(2),30(2)])].

22965 L(x,C',y * y) = L(x,C,y' * y'). [para(130(a,1),9635(a,1,2)),rewrite([11754(6),30(5),22857(7),10001(11),14438(12)]),flip(a)].

22990 x' * (C * (x * (C' * y))) = L(y,C,x' * x'). [back_rewrite(14458),rewrite([22965(12)])].

23673 ((x * C) * x)' = (C' / x) / x. [para(12419(a,1),106(a,1,1))].

23708 L(x,y,C * (C * (C / y))) = L(x,y,C * (C * C)). [back_rewrite(8952),rewrite([23673(6),19690(13),8119(12)])].

23710 C' * (C' * ((C / x) * (C * (x * y)))) = L(y,x,C * (C * C)). [back_rewrite(8119),rewrite([23708(19)])].

23903 C * ((B * C') * x) = L(B * x,B,C). [para(12752(a,1),242(a,1,2,2)),rewrite([243(9),264(4),8421(8),694(9),16(4,R),815(5),243(13),264(8),

8421(12),694(13),16(8,R),815(9),11213(11),1734(11),243(12),264(5),1539(6),17292(11),15888(10),1673(10),4977(10),63(6),30(5),4960(5),15667(6),

243(14),264(9),8421(13),694(14),16(9,R),815(10),12(20),8(19),3(17),229(16),264(14),125(16),16(12,R)]),flip(a)].

23905 L(C * (B * x),C',B) = B * (x * C). [back_rewrite(17504),rewrite([23903(8),7593(7),16(4,R)])].

24081 L(x,B * y',y * y) = L(x,B * y,y * y). [para(14145(a,1),9516(a,1,2))].

24090 L(x,B * C',B * C) = L(x,B * C,C * C). [back_rewrite(17502),rewrite([24081(8)]),flip(a)].

24319 L(B,C' * C',C * B') = B. [para(264(a,1),14953(a,1,3))].

24624 C' * (x * (C * (C / x))) = x * (C / x). [para(34(a,1),15154(a,1,1)),rewrite([161(4),6087(11),231(12),1734(8),18053(11),16(9,R)]),flip(

a)].

24713 L(C,x,y / (x * C')) = L(C,x,y). [para(16816(a,1),3396(a,1)),rewrite([16816(11)])].

26156 (x * (y * (x * (C * C))))' = C' * (C' * (x' * (y' * x'))). [para(566(a,2),111(a,1,2)),rewrite([111(10),1765(7),12007(7)]),flip(a)].

26254 C' * (x * (C * (y * (x * C)))) = x * (C * (y * x)). [para(567(a,1),1539(a,2)),rewrite([1694(15)])].

26285 C' * (B' * ((B * x') * (C * (x * B)))) = L(B,C * C,B * x). [back_rewrite(8994),rewrite([26254(17),15888(13)])].

27590 L((x * y) * B,B,y) = x * (y * B). [para(942(a,1),229(a,1,1)),rewrite([958(5),30(2),1092(15),4833(14),10(11)]),flip(a)].

27609 x / (B' * C') = x * (B * C). [para(1061(a,1),190(a,1,1)),rewrite([1852(4),264(4),1539(5),11122(20),16(10),5966(18),243(19),264(11),243

(18),116(13),1539(14),15699(19),7893(14),15698(14)])].

28745 (x / (y * C')) * (C' * y) = x. [para(2840(a,2),7(a,1))].

28762 (x * C) * (y * C') = C * ((C' * x) * y). [para(2840(a,1),239(a,2)),rewrite([243(6),116(3)]),flip(a)].

28786 x * (C' * (B * C')) = x * (B * (C' * C')). [para(9869(a,1),2840(a,2,2))].

31799 (B' * (x * x)) * x' = B' * x. [para(17570(a,1),10(a,1,2)),flip(a)].

31810 L(B,x * B',y) = L(B,x,y). [para(17570(a,1),97(a,1,1,1,1)),rewrite([31799(9),5966(9),34(10),15969(6),230(5),3926(6),17157(6),31799(13),

34(11)])].

31828 x' * L(x * B,B,y) = L(B,y,x). [back_rewrite(17157),rewrite([31810(11)])].

31833 L(B,x * B,y) = L(B,x,y). [para(7(a,1),31810(a,1,2)),rewrite([251(6)]),flip(a)].

31964 L(B,x,y * (x * B)) = L(B,x,y). [para(31833(a,1),3690(a,1)),rewrite([31833(9)])].

33238 B' * (C * (B * x)) = L(x * C,C,B). [para(765(a,1),7207(a,1)),rewrite([19694(7),16(6,R),256(13),15794(13)])].

33299 (C * (B * x)) * B = B * (C * (x * B)). [para(49(a,1),774(a,1,1,2)),rewrite([23905(10),16(5,R),16(10,R)]),flip(a)].

33300 L((x * C) * B,C,B) = C * (x * B). [para(774(a,1),7106(a,1,1))].

33646 L(x * L(B,y,x),y,B) = x * B. [para(8(a,1),790(a,2,1,2)),rewrite([15969(6),230(5),3926(6),31828(6),3(7)])].

33710 L(C * (C * (x * B')),C',B) = C * (x * (C * B')). [para(245(a,1),800(a,2,2)),rewrite([30(7),15888(7),1673(7),19840(11),1734(5),13(7),30

(14),30(16),264(15),15888(19),1673(19),16(14,R)]),flip(a)].

33723 L(x,B,y * (B * x)) = L(x,B,y). [para(87(a,1),20537(a,1,3)),rewrite([10352(4)])].

34039 L(B * ((C * B') / x),B,C) = C / x. [para(246(a,1),835(a,1,2)),rewrite([264(14),15888(18),1673(18),16(13,R),33710(17),11951(12),815(6),

23903(12),256(16)])].

34323 L(x * B,B,y / x) = L(x * B,B,y). [para(7(a,1),875(a,1,1,1)),rewrite([106(5),230(9),3926(10)])].

34329 L(B * C,B,x) = L(B * C,x,C). [para(64(a,1),875(a,1,1,1)),rewrite([16(3),30(6),7515(11),16(8)])].

34559 L(C' * (B * x),B,C) = (B * C') * x. [para(24319(a,1),92(a,2,1,2)),rewrite([12(11),1539(10),28786(12),15888(12),28762(11),1539(7),1539(

10,R),34(11),10(7),243(12),116(7),1539(8),1539(11,R),34(12),1573(8),251(6),16(5),12(16),1539(15),28786(17),15888(17),28762(16),1539(12),1539(

15,R),34(16),10(12),18052(9),1539(7),23903(9),10007(8),12(19),1539(18),28786(20),15888(20),28762(19),1539(15),1539(18,R),34(19),10(15),1539(1

2)])].

34561 C' * ((B * C) * x) = L(B * x,B,C'). [para(24319(a,1),242(a,1,2,2)),rewrite([243(10),116(5),1539(6),1539(9,R),34(10),1573(6),251(4),16(

3),243(13),116(8),1539(9),1539(12,R),34(13),1573(9),251(7),16(6),11213(9),116(9),243(12),264(4),243(11),116(6),1539(7),231(10),251(9),1539(8)

,1869(10),4977(9),34(6),4960(6),15670(7),243(16),116(11),1539(12),1539(15,R),34(16),1573(12),251(10),16(9),12(21),1539(20),28786(22),15888(22

),28762(21),1539(17),1539(20,R),34(21),10(17),1539(13,R)]),flip(a)].

35332 B' * L(B * x,B,y) = L(x,B,B * y). [para(2(a,1),947(a,1,2,2,2,2,1)),rewrite([3(4),3671(12),2(10)])].

35846 C' * (B * (B * (B * x))) = B * (B * (B * (x * C'))). [para(950(a,1),748(a,1,1,2,2,2)),rewrite([12(14),1539(13),28786(15),19729(16),287

62(15),1539(11),1539(14,R),34(15),1730(12),15(8),1539(5),49(7),1539(6),22263(9),23903(25),9997(24),17292(23),16(14),1012(22),16(20,R),34(20)]

),flip(a)].

36253 L(C * (B * x),B,C') = (B * C) * x. [para(1973(a,1),961(a,1,2)),rewrite([30(3),30(6),16(6),34561(8),7893(8),30(11),264(15),10(17),8(14)

,3(12),16(11)])].

36254 (B * C) * ((B * C') * x) = C * (B * (C' * (B * x))). [para(961(a,1),568(a,1,2)),rewrite([9(8),2(7),14267(8),1539(21),16(24,R),23903(24

),10007(23),34559(23),34561(22),7893(22),36253(22)]),flip(a)].

36478 (x * (B' * C')) * (B * C) = x. [para(27609(a,1),6(a,1))].

36491 (x * C) * (B * C) = C * (C * (x * B)). [para(239(a,1),27609(a,2)),rewrite([27609(8),6006(6)]),flip(a)].

36905 L(x * y,C * C,x') = C * (x * (C' * y)). [para(28745(a,1),566(a,1,2,2,2)),rewrite([63(17),11213(13),1734(13),9012(14),9035(11)]),flip(a

)].

36917 (x * (B * C)) * (B' * C') = x. [para(27609(a,1),28745(a,1,1)),rewrite([1539(9)])].

36918 x * L(y,x,C * C) = C * (x * (C' * y)). [back_rewrite(9035),rewrite([36905(11)])].

39441 x / (C * B') = x * (B * C'). [para(214(a,1),1092(a,1,1)),rewrite([30(5),16(4,R),264(11),1539(16,R),6325(16),15885(17),10007(13),15678(

13)])].

39651 L(x,B,y / (B * x)) = L(x,B,y). [para(7(a,1),33723(a,1,3)),flip(a)].

39696 (B' * ((B * x) / y)) * y = L(x,B,y). [back_rewrite(2364),rewrite([39651(5)]),flip(a)].

39953 L(B * C,C',x) = L(B * C,B,x). [para(34329(a,2),9613(a,2))].

40501 x / (B * C) = x * (B' * C'). [para(36478(a,1),6(a,1,1))].

40502 (x * (B' * C'))' = (B * C) / x. [para(36478(a,1),32(a,1,2)),flip(a)].

41738 (x * (B * C')) * (C * B') = x. [para(39441(a,1),7(a,1,1))].

42317 L(x * C,C,B) = x * L(C,B,x). [para(27609(a,1),1254(a,2)),rewrite([40502(9),39696(8),15888(11),16(10,R),33238(11)]),flip(a)].

42348 x / (B * C') = x * (C * B'). [para(7(a,1),41738(a,1,1)),flip(a)].

42768 L(x * C,C,B) / L(C,B,x) = x. [para(42317(a,2),6(a,1,1))].

43364 C * ((B' * C') * x) = B' * L(x,B,C'). [para(1108(a,1),2791(a,1,1)),rewrite([7175(9),15670(7)]),flip(a)].

43365 L(B,L(x,B,C),B * C) = L(B,C * C,B * x). [para(2791(a,1),97(a,1,1,1)),rewrite([1765(5),7593(11),22446(15),17309(12),161(8),15889(11),16

(10,R),33299(12),15888(13),26285(14)]),flip(a)].

43582 C / L(x * C,y,C') = L(x,C,y)'. [para(4947(a,1),111(a,1,2))].

43676 L(B * x,C,B' * B') = C * (B * (C' * x)). [para(10294(a,1),4960(a,2)),rewrite([36918(7)]),flip(a)].

43744 L(x * L(y,B,x),B,x') = x * y. [para(10352(a,1),4977(a,1,2)),flip(a)].

43913 L(x * B,B,y) = x * L(B,y,x). [para(5389(a,1),20366(a,1,3)),rewrite([33646(5),34323(5)])].

44078 L(C * (x * (B * C)),B,C) = C * (C * (x * B)). [para(10283(a,1),43913(a,2,2)),rewrite([5251(6),16(4),5251(17),4947(15),10589(18),6006(1

5)])].

45270 L(B,C * C,B * x) = L(B,x',C * C). [para(14523(a,2),97(a,2)),rewrite([1318(6,R),16(5,R),1765(7),11591(7),858(5),1539(9,R),5251(17),16(1

5),1700(19),26254(17),15888(13),26285(14),858(11),31810(16)])].

45280 L(x,y',C * C) = L(x,y,C' * C'). [para(14523(a,2),9524(a,1)),rewrite([174(4),12(6),161(7),6087(5),9582(9),174(9)])].

45322 L(x * B,B,C * C) = x * L(B,x,C' * C'). [para(14523(a,2),43913(a,2,2)),rewrite([45280(13)])].

45327 L(B,L(x,B,C),B * C) = L(B,x,C' * C'). [back_rewrite(43365),rewrite([45270(15),45280(14)])].

45329 L(B,x * C,B * C) = L(B,x,C' * C'). [back_rewrite(13453),rewrite([45270(7),45280(6)]),flip(a)].

45614 L(x,B,C) * (B * C) = C * (x * B). [para(10352(a,1),15798(a,1,2,1)),flip(a)].

45650 L(x,B * C,C * C) = L(x,C,B' * B'). [para(950(a,1),1441(a,1,1,1)),rewrite([9(5),2(4),174(4),16(8),36254(14),12(15),22990(14),43676(11),

22990(10),16(14),24090(15)]),flip(a)].

45653 C' * L(B * C,B,x) = L(B,x,C). [para(31964(a,1),1441(a,2)),rewrite([16(4,R),15969(14),1765(5),230(13),7457(13),10(14),17309(12),161(8),

15974(11),16(5)])].

45654 L(x,B * B,B * C) = L(x,C,B). [para(1168(a,1),1441(a,1,1,1)),rewrite([19729(8),16(7,R),1318(7),5611(10),66(8),19729(9),16(8,R),1318(8),

858(12),26156(10),1700(17),1539(15),13(16),16(20),3176(28),1012(29),16(27,R),19729(27),13442(26),451(30),35846(25),1539(22,R),10(22),10(21),1

0(17),10(13),33238(9),10291(8),63(5),16(13),9518(14)]),flip(a)].

45661 L(x,B * C',B * C) = L(x,C,B' * B'). [back_rewrite(24090),rewrite([45650(15)])].

45762 L(x,C,B' * B') = L(x,C,B). [para(45654(a,1),9516(a,2)),rewrite([40501(7),12(9),34(8),45661(8)])].

45786 L(x,C * C,B') = L(x,C,B). [para(45762(a,1),10294(a,2))].

45789 L(x,B,C * C) = L(x,C,B). [para(45786(a,1),9516(a,2)),rewrite([251(6),12(5),16(4),1318(5),3672(8)])].

45796 x * L(B,x,C' * C') = L(x * B,C,B). [back_rewrite(45322),rewrite([45789(7)]),flip(a)].

46145 B * ((C * B') / x) = C / L(x,C,B). [para(125(a,1),19848(a,1,1)),rewrite([9528(7)]),flip(a)].

46183 L(C / L(x,C,B),B,C) = C / x. [back_rewrite(34039),rewrite([46145(7)])].

46196 L(L(x,C,B)',B,C) = x'. [para(10289(a,1),46183(a,1,1,2)),rewrite([43582(8),111(11)])].

46218 L(x,C',B)' = L(x',B,C). [para(7106(a,1),46196(a,1,1,1)),flip(a)].

46220 L(x,C,B)' = L(x',B,C'). [para(46196(a,1),7901(a,1,1)),flip(a)].

46221 L(x,B,C)' = L(x',B,C). [para(10352(a,1),46196(a,1,1,1)),flip(a)].

46374 L(x,C',B) * L(x',B,C) = 0. [para(46218(a,1),9(a,1,2))].

46378 L(x,L(y',B,C),L(y,C',B)) = x. [para(46218(a,1),85(a,1,2))].

46434 L(x',B,C') * L(x,C,B) = 0. [para(46220(a,1),8(a,1,1))].

46658 L(x,C',B) / L(x,B,C) = 0. [para(46374(a,1),2656(a,2)),rewrite([46221(9),30(6),46378(16)])].

46672 x * L(y,C',B) = x * L(y,B,C). [para(46658(a,1),227(a,1,1)),rewrite([46658(9),23(3),2(7),46658(13),2(7)])].

46702 x' * L(x * C,B,C) = L(C,x,x * B). [back_rewrite(13519),rewrite([46672(8)])].

46703 L(B,x,C * (C * C)) = B. [para(1860(a,1),1499(a,1,2,1)),rewrite([8(5),3(3),16(10,R),11591(11),1765(9),1539(12,R),16(19,R),5966(23),70(2

1),16(19),36491(20),231(22),1734(15),34(14),17309(16),161(12),23710(17),34(13)]),flip(a)].

46704 L(B,C * (C * C),x) = B. [para(46703(a,1),10352(a,1,1))].

46716 L(B,C * (C * (C / x)),x) = B. [para(46704(a,1),9516(a,2)),rewrite([7319(7)])].

46749 L(B,C / x,x * (C * C)) = B. [para(4359(a,1),46716(a,1,2,2,2)),rewrite([1785(8)])].

46818 L(B,x,C * (C * (x' * C))) = B. [para(248(a,2),46749(a,1,3)),rewrite([111(6),30(3),1318(8,R),16(7,R)])].

47065 L(x',C,B) * L(x,C,B) = 0. [para(7826(a,2),46434(a,1,1))].

47078 L(x,C,B) * L(x',C,B) = 0. [para(30(a,1),47065(a,1,1,1))].

47092 L(x,L(y',C,B),L(y,C,B)) = x. [para(47065(a,1),6702(a,1,2)),rewrite([76(5)]),flip(a)].

47120 L(x,C,B) / L(x,B,C') = 0. [para(47078(a,1),2656(a,2)),rewrite([46220(8),30(5),47092(15)])].

47150 x * L(y,C,B) = x * L(y,B,C'). [para(47120(a,1),227(a,1,1)),rewrite([47120(9),23(3),2(6),47120(12),2(6)])].

47196 (C * B') * L(x,B,C') = C * (B' * x). [back_rewrite(15800),rewrite([47150(8)])].

47490 x * (C * (x' * B)) = L(B * C,B',x'). [para(831(a,1),1540(a,1,2,2,2)),rewrite([30(2),7221(12)])].

47506 (x * (B * C)) * B' = B * (C * (B' * x)). [para(36917(a,1),1540(a,1,2,2,2)),rewrite([1573(6),251(4),16(3),43364(11),243(11),264(4),4719

6(10),16(18,R),1694(18)]),flip(a)].

47592 L(L(B,x,C * C),C,x') = B. [para(46818(a,1),1441(a,2)),rewrite([16(7,R),70(8),245(7),1765(10),70(20),17309(21),24624(12),9611(17),7688(

8),10291(12),21688(9)])].

47605 L(B,x,C * C) = L(B,x',C). [para(47592(a,1),10352(a,1,1)),flip(a)].

47627 C' * L(B * C,B',x) = L(B,x',C). [back_rewrite(21688),rewrite([47605(14)])].

47628 L(B,x,C' * C') = L(B,x,C). [para(30(a,1),47605(a,2,2)),rewrite([45280(6)])].

47645 L(x * B,C,B) = x * L(B,x,C). [back_rewrite(45796),rewrite([47628(7)]),flip(a)].

47648 L(B,x * C,B * C) = L(B,x,C). [back_rewrite(45329),rewrite([47628(14)])].

47650 L(B,L(x,B,C),B * C) = L(B,x,C). [back_rewrite(45327),rewrite([47628(15)])].

48356 L(B,x,B * C) = L(B,C',x). [para(7(a,1),47648(a,1,2)),rewrite([116(8),7040(11)])].

48369 L(B,C',L(x,B,C)) = L(B,x,C). [back_rewrite(47650),rewrite([48356(8)])].

48857 L(B,L(x,B,C'),C) = L(B,C',x). [para(10359(a,1),48369(a,1,3)),flip(a)].

50060 L(L(B * C,B,x),C',x) = L(B * C,B',x). [para(47645(a,2),1673(a,1,2)),rewrite([33300(8),7688(6),6702(11),16(11,R),7593(11),39953(12)]),f

lip(a)].

50488 L(C,B,C * (x * B)) = L(C,B,x). [para(24713(a,1),7498(a,2)),rewrite([42348(7),19724(11),16(8,R),33299(10),10(11)])].

50517 L(C,B,C * x) = L(C,B,x). [para(7(a,1),50488(a,1,3,2)),rewrite([264(9),306(11)])].

50520 L(C,B,L(x * C,B,C')) = L(C,B,x). [para(50488(a,1),3396(a,2)),rewrite([264(8),6008(9),16(7,R),7606(9),15670(9)])].

50572 L(C,B,L(x * C,y,C')) = L(C,B,L(x,C,y)). [para(4947(a,1),50517(a,1,3))].

50584 L(C,B,L(x,C,B)) = L(C,B,x). [back_rewrite(50520),rewrite([50572(9)])].

50682 L(C,B,L(x,B,C)) = L(C,B,x). [para(10352(a,1),50584(a,1,3)),flip(a)].

50749 (C * (x * B)) / L(C,B,x) = L(x,B,C) * B. [para(50682(a,1),112(a,1,2)),rewrite([45614(7)])].

50764 (x * C) / L(C,B,x) = L(x,B,C). [para(50682(a,1),42768(a,1,2)),rewrite([16(5,R),7593(5),7106(9)])].

50964 L(x,B,C) * B = L(x * B,B,C). [para(3690(a,1),50764(a,1,2)),rewrite([16(4,R),50749(8)])].

51031 L(x,C',B) * B = L(x * B,B,C). [para(9613(a,2),50964(a,1,1))].

53499 L(L(x,C,B),C,B) = L(x,B,C). [para(256(a,1),1884(a,2,1)),rewrite([15888(9),16(8,R),33238(9),47150(8),14750(9),63(5)])].

53503 L(L(B,x',C),C,x) = L(B,x,C). [para(817(a,1),1884(a,2,1)),rewrite([2976(8),47627(9)])].

53589 L(L(B,x,C),x,C) = L(B,x',C). [para(53503(a,1),10352(a,1,1))].

53661 L(B * C,B',x) = L(B * C,B,x'). [para(53589(a,1),7593(a,1,2)),rewrite([7593(6),39953(7),16(11,R),7593(11),39953(12),50060(14)]),flip(a)

].

53674 x * (C * (x' * B)) = L(B * C,B,x). [back_rewrite(47490),rewrite([53661(13),30(12)])].

53678 x' * (C * (x * B)) = L(B * C,B,x'). [back_rewrite(7688),rewrite([53661(12)])].

54266 L(B,x',C) = L(B,C,x). [para(10283(a,1),31828(a,2)),rewrite([9062(5),5251(13),16(11),44078(16),13(14),10(12),53678(8),45653(9)])].

54291 L(B,C',x') = L(B,C,x). [para(54266(a,1),9613(a,2))].

54332 L(B,C,L(x,C,B)) = L(B,C,x). [para(46220(a,1),54266(a,1,2)),rewrite([48857(8),54291(5)]),flip(a)].

54962 (B * x) * (C * x') = L(B * C,B,x). [para(1939(a,1),34(a,1,2)),rewrite([53674(6),30(8)]),flip(a)].

54975 L(C,B,B * x) = L(C,x',B). [back_rewrite(7218),rewrite([54962(8),35332(8)])].

55042 L(L(B,C,x),L(x,C,B),C) = B. [para(54332(a,1),10352(a,1,1))].

55377 L(C,x',B) = L(C,B,x). [para(34(a,1),54975(a,1,3)),rewrite([958(8),6702(9)]),flip(a)].

55386 L(C,B,x') = L(C,x,B). [para(6536(a,2),54975(a,1,3)),rewrite([2536(6),913(8),958(10),30(7),6702(9)])].

55409 L(C,x',B) = L(C,x,B'). [para(958(a,1),55377(a,1,2)),rewrite([6702(6),9524(10)])].

55418 L(L(C,x,B'),x,B) = C. [para(55377(a,2),10352(a,1,1)),rewrite([55409(4)])].

55554 L(C,B,B * x) = L(C,x,B'). [back_rewrite(54975),rewrite([55409(9)])].

55575 L(C,x',B') = L(C,x,B). [para(815(a,1),55386(a,1,3)),rewrite([55554(6),9528(11)])].

55577 L(C,B',x) = L(C,B,x'). [para(958(a,1),55386(a,1,3)),rewrite([3690(6),7040(10)]),flip(a)].

56241 L(L(B,C,x),L(x,B,C),C) = B. [para(53499(a,1),55042(a,1,2)),rewrite([54332(6)])].

56657 C * (L(x,B,C) * L(B,C,x)) = x * (B * C). [para(56241(a,1),87(a,1,2)),rewrite([7593(5),51031(8),27590(7),16(3)]),flip(a)].

56658 B * (C * (B' * x)) = L(x * C,C',B). [para(56241(a,1),112(a,1,2)),rewrite([56657(9),264(6),47506(7),7593(12)])].

62879 L(L(C,x,x * B),x,B') = C. [para(1123(a,1),43744(a,2)),rewrite([3690(13),87(12),56658(8),46672(8),46702(7),946(9),30(9),9524(9)])].

62900 L(C,x,x * B) = L(C,B,x'). [para(62879(a,1),10352(a,1,1)),rewrite([55577(4)]),flip(a)].

62907 x' * L(x * C,B,C) = L(C,B,x'). [back_rewrite(46702),rewrite([62900(11)])].

66327 L(C,B * B,x) = L(C,B,x'). [para(7429(a,1),4256(a,1,2,2,2)),rewrite([858(7),858(5),30(3),8421(7),66(12),19724(13),229(8),264(6),19724(1

2),12(9),16(11,R),19729(11),10(12),1673(8),46672(8),62907(7),22406(11)]),flip(a)].

66453 L(L(C,x,B),x,B) = L(C,x,B'). [para(256(a,1),4358(a,2,3,2)),rewrite([66327(8),815(6),55554(6),55575(5),15888(10),49(9),10(10),6702(7),5

5554(10)])].

66462 $F. [back_rewrite(19),rewrite([66453(7),55418(8)]),xx(a)].

============================== end of proof ==========================

% Proof 1 at 78.08 (+ 0.23) seconds.

% Length of proof is 234.

% Level of proof is 25.

% Maximum clause weight is 30.000.

% Given clauses 1573.

1 R(R(R(x,C,A),C,A),C,A) = x # label(non_clause) # label(goal). [goal].

2 0 * x = x. [assumption].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 C * ((x * y) * C) = (C * x) * (y * C). [assumption].

15 (C * x) * (y * C) = C * ((x * y) * C). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 R(x,y,z) = ((x * y) * z) / (y * z). [assumption].

18 ((x * y) * z) / (y * z) = R(x,y,z). [copy(17),flip(a)].

19 R(R(R(c1,C,A),C,A),C,A) != c1. [deny(1)].

20 (C * x) * (y * C) = C * (C * (x * y)). [back_rewrite(15),rewrite([16(9,R)])].

23 x / x = 0. [para(2(a,1),6(a,1,1))].

24 x / 0 = x. [para(3(a,1),6(a,1,1))].

29 0 / x = x'. [para(8(a,1),6(a,1,1))].

31 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([29(3)])].

32 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

33 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

35 x * (x' * y) = y. [back_rewrite(4),rewrite([32(1)])].

36 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

40 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

41 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

45 (x * (y * (x * (x * (y * x))))) * z = x * (y * (x * (x * (y * (x * z))))). [para(13(a,1),12(a,1,1)),rewrite([13(11),13(12)])].

48 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [para(13(a,1),13(a,1,1,2)),rewrite([13(9)])].

52 C * (x / C) = x. [para(16(a,2),7(a,1))].

53 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

54 x' * (C * x) = C. [para(16(a,2),10(a,1,2))].

55 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

59 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

60 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

61 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

64 R(x,0,y) = x. [para(2(a,1),18(a,1,2)),rewrite([3(2),6(2)]),flip(a)].

66 R(x,y,z) * (y * z) = (x * y) * z. [para(18(a,1),7(a,1,1))].

67 R(x / y,y,z) = (x * z) / (y * z). [para(7(a,1),18(a,1,1,1)),flip(a)].

68 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(7(a,1),18(a,1,2))].

70 (x * y') * y = R(x,y',y). [para(8(a,1),18(a,1,2)),rewrite([24(5)])].

75 ((x * y') * (y * z)) / z = R(x,y',y * z). [para(10(a,1),18(a,1,2))].

78 ((x * (y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(12(a,1),18(a,1,2))].

85 (C * (x * y)) / (y * C) = R(x,y,C). [para(16(a,2),18(a,1,1))].

86 (C * (x * y)) / (C * y) = R(x,y,C). [para(16(a,2),18(a,1,2)),rewrite([16(3,R)])].

88 C * (C * (x * (y / C))) = (C * x) * y. [para(7(a,1),20(a,1,2)),flip(a)].

90 (C * x)' * (C * (C * (x * y))) = y * C. [para(20(a,1),10(a,1,2))].

98 (x * C) * (y * C) = C * (C * (x * y)). [para(16(a,1),20(a,1,1))].

99 (C * x) * (C * y) = C * (C * (x * y)). [para(16(a,2),20(a,1,2))].

100 (C * ((x * y) * (C * z))) / ((y * C) * z) = R(C * x,y * C,z). [para(20(a,1),18(a,1,1,1)),rewrite([60(6)])].

102 ((x * (C * y)) * (z * C)) / (C * (C * (y * z))) = R(x,C * y,z * C). [para(20(a,1),18(a,1,2))].

105 (x / y)' = y / x. [para(7(a,1),33(a,1,2)),flip(a)].

109 C / (C * x) = x'. [para(16(a,2),33(a,1,2))].

114 x / C = C' * x. [para(52(a,1),10(a,1,2)),flip(a)].

118 C * (C * ((C' * x) * y)) = x * (y * C). [para(52(a,1),20(a,1,1)),rewrite([114(7)]),flip(a)].

119 C * (C * (x * (C' * y))) = (C * x) * y. [back_rewrite(88),rewrite([114(4)])].

123 x * (C * x') = C. [para(16(a,2),35(a,1,2))].

124 R(x,x' * y,z) = (y * z) / ((x' * y) * z). [para(35(a,1),18(a,1,1,1)),flip(a)].

126 ((x * y) * (y' * z)) / z = R(x,y,y' * z). [para(35(a,1),18(a,1,2))].

133 ((x * C') * (y * C)) / y = R(x,C',y * C). [para(53(a,1),18(a,1,2))].

134 (C * x) * (x' * ((C * x) * y)) = C * (x * (C * y)). [para(54(a,1),13(a,1,1,2)),rewrite([16(4,R),60(5)]),flip(a)].

138 (x / y) * (y / x) = 0. [para(105(a,1),8(a,1,1))].

140 (x * y) / ((z * x) * y) = R(z,x,y)'. [para(18(a,1),105(a,1,1)),flip(a)].

142 (x / y) * (C * (y / x)) = C. [para(105(a,1),54(a,1,1))].

143 R(x,x' * y,z) = R(x',y,z)'. [back_rewrite(124),rewrite([140(8)])].

146 x' / x = x' * x'. [para(8(a,1),36(a,1,1,2)),rewrite([3(3)])].

147 x / x' = x * x. [para(9(a,1),36(a,1,1,2)),rewrite([3(2)])].

151 (C * (x * C)) / x = C * C. [para(16(a,1),36(a,1,1,2))].

155 (x * y) / (x' * y) = x * x. [para(35(a,1),36(a,1,1,2))].

160 (C' * x)' = C / x. [para(35(a,1),109(a,1,2)),flip(a)].

162 (C * x') * (x * ((C * x') * y)) = C * (x' * (C * y)). [para(123(a,1),13(a,1,1,2)),rewrite([16(5,R),60(6)]),flip(a)].

173 (x * x)' = x' * x'. [para(147(a,1),105(a,1,1)),rewrite([146(4)])].

183 (C' * x) * (C / x) = 0. [para(114(a,1),138(a,1,1))].

184 (C / x) * (C' * x) = 0. [para(114(a,1),138(a,1,2))].

192 x * ((y / (x * z)) * x) = (x * y) / z. [para(7(a,1),40(a,1,1,2)),flip(a)].

194 x * ((x * y)' * x) = x / y. [para(8(a,1),40(a,1,1,2)),rewrite([3(2)]),flip(a)].

210 (C * C) / x = C * (x' * C). [para(54(a,1),40(a,1,1,2))].

223 R(C',x,C / x) = (x * (C / x))'. [para(183(a,1),18(a,1,1)),rewrite([29(5)]),flip(a)].

225 x * (C * (C / x)) = C * C. [para(183(a,1),20(a,2,2,2)),rewrite([35(5),16(4,R),3(9)])].

228 (C * (C / x)) * x = C * C. [para(184(a,1),20(a,2,2,2)),rewrite([16(9,R),35(9),3(9)])].

232 (x / y) * ((z / (x / y)) * x) = ((x / y) * z) * y. [para(7(a,1),41(a,1,2,2))].

234 (x * y) * x' = x * (y / x). [para(9(a,1),41(a,1,2,2)),rewrite([3(3)]),flip(a)].

235 (x / y) * (y * z) = y' * ((y * x) * z). [para(41(a,1),10(a,1,2)),flip(a)].

236 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),41(a,1,2,2)),flip(a)].

241 (x / C') * y = (C * x) * y. [para(41(a,1),16(a,1)),rewrite([114(5),236(9),16(12,R),35(12)]),flip(a)].

243 (C * x) * y = (x * C) * y. [para(16(a,1),41(a,2,1)),rewrite([114(3),236(7),241(7),35(8)])].

247 C * ((C * x) * y) = x * (C * (C * y)). [para(41(a,1),20(a,2,2)),rewrite([114(3),35(5),16(4,R)]),flip(a)].

249 (x * y) * (x' * z) = x * ((y / x) * z). [para(35(a,1),41(a,1,2,2)),flip(a)].

250 (C' * x) * (y * C) = C' * ((C * x) * y). [para(53(a,1),41(a,1,2,2)),rewrite([241(6)]),flip(a)].

253 (C * x) * (C / x) = C * C. [para(123(a,1),41(a,1,2)),rewrite([114(7),160(9)]),flip(a)].

270 (C * (C * (x * y))) / (C * (C * y)) = R(x,C,y * C). [para(55(a,2),18(a,1,2)),rewrite([98(5)])].

278 (C * x)' = (x * C)'. [para(55(a,1),109(a,1,2)),rewrite([109(6)]),flip(a)].

285 (C * x)' * (x * C) = 0. [para(278(a,2),8(a,1,1))].

289 (C * x)' * ((x * C) * y) = y. [para(278(a,2),10(a,1,1))].

499 (x * C) * ((x * C) * y) = C * (x * (x * (C * y))). [para(285(a,1),45(a,1,1,2,2,2,2)),rewrite([3(11),98(10),90(11),98(5),60(6),12(5),289(

22),289(18)]),flip(a)].

526 x / (C * (x * C)) = C' * C'. [para(151(a,1),105(a,1,1)),rewrite([173(4)]),flip(a)].

553 (C * (C / x)) / (C * C) = x'. [para(225(a,1),33(a,1,2))].

554 C * (C / x') = x * (C * C). [para(225(a,1),35(a,1,2)),flip(a)].

562 C * (C / x) = C * (x' * C). [para(228(a,1),6(a,1,1)),rewrite([210(4)]),flip(a)].

578 C * (x * C) = x * (C * C). [back_rewrite(554),rewrite([562(5),31(3)])].

579 R(x',C,C) = x'. [back_rewrite(553),rewrite([562(4),85(9)])].

665 R(x,C,C) = x. [para(31(a,1),579(a,1,1)),rewrite([31(5)])].

728 C * (x * ((C * x)' * (y * ((C * x)' * x)))) = x * ((C * x)' * y). [para(285(a,1),48(a,2,2,2,2)),rewrite([16(12,R),3(17)])].

753 (x / y) * (C * ((y / x) * (C * ((x / y) * z)))) = C * ((x / y) * (C * z)). [para(142(a,1),48(a,1,1,2,2)),rewrite([578(5,R),16(4,R),60(6)

]),flip(a)].

882 (C / x) / (C * C) = (C * x)'. [para(253(a,1),33(a,1,2))].

911 x * (C * y) = x * (y * C). [para(59(a,1),10(a,1,2)),rewrite([10(8)]),flip(a)].

1041 (x * (C * C)) * y = C * (x * (C * y)). [para(578(a,1),13(a,1,1))].

1046 (C * (C * (x * y))) / (y * (C * C)) = R(x,C,y * C). [para(578(a,1),18(a,1,2)),rewrite([98(5)])].

1047 R(x,C * C,y) = R(x,C * y,C). [para(578(a,2),18(a,1,1,1)),rewrite([13(5),12(9),86(10)]),flip(a)].

1048 R(x,C,y * C) = R(x,y,C * C). [para(578(a,2),18(a,1,1)),rewrite([16(4,R),1046(10)])].

1049 (C * (C * (x * y))) / (C * (y * C)) = R(x,y,C * C). [para(578(a,2),18(a,1,2)),rewrite([578(5,R),16(4,R)])].

1095 C' * x = x * C'. [para(8(a,1),61(a,2,2,2)),rewrite([35(8),3(7)]),flip(a)].

1120 (x * C')' = C / x. [para(61(a,2),160(a,1,1)),rewrite([35(8),16(9,R),9(9),3(7)])].

1190 C * (x * C') = x. [para(1095(a,1),10(a,1,2)),rewrite([31(3)])].

1191 x' * (C' * x) = C'. [para(1095(a,2),10(a,1,2))].

1211 (x * (y * (C' * x))) / C' = x * (y * x). [para(1095(a,2),40(a,1,1,2,2))].

1224 x / C' = C * x. [para(7(a,1),1190(a,1,2)),flip(a)].

1244 C * (x * (y * (C' * x))) = x * (y * x). [back_rewrite(1211),rewrite([1224(8)])].

1250 (C * x)' = C' / x. [para(1224(a,1),105(a,1,1))].

1272 (C / x) / (C * C) = C' / x. [back_rewrite(882),rewrite([1250(9)])].

1284 C * (x * ((C' / x) * (y * C'))) = x * ((C' / x) * y). [back_rewrite(728),rewrite([1250(4),1250(7),7(8),1250(13)])].

1335 (x * C)' = C' / x. [back_rewrite(278),rewrite([1250(3)]),flip(a)].

1438 (x * C') * ((C / x) * y) = y. [para(1120(a,1),35(a,1,2,1))].

1461 R(x,C,y) * (y * C) = (x * C) * y. [para(16(a,1),66(a,1,2))].

1462 R(x,y,C) * (C * y) = C * (x * y). [para(16(a,2),66(a,1,2)),rewrite([16(8,R)])].

1528 R(C,x',x) = C. [para(1191(a,1),20(a,2,2,2)),rewrite([16(8,R),35(8),70(4),9(8),3(6)])].

1539 R(C,x,x') = C. [para(31(a,1),1528(a,1,2))].

1546 R((x / y) / z,z,y) = x / (z * y). [para(7(a,1),67(a,2,1))].

1559 (x * y) / (y * C) = R(C' * x,C,y). [para(16(a,1),67(a,2,2)),rewrite([114(2)]),flip(a)].

1567 R(C * x,C',y * C) = (x * (y * C)) / y. [para(53(a,1),67(a,2,2)),rewrite([1224(3)])].

1572 (x * y) / (C * y) = R(C' * x,C,y). [para(114(a,1),67(a,1,1)),flip(a)].

1635 (x * y) / (C' * y) = R(C * x,C',y). [para(1224(a,1),67(a,1,1)),flip(a)].

1651 x * (C / x) = C. [para(160(a,1),1539(a,1,3)),rewrite([143(7),223(5),31(5)])].

1659 C / x = x' * C. [para(1651(a,1),10(a,1,2)),flip(a)].

1708 (x * C') * ((x' * C) * y) = y. [back_rewrite(1438),rewrite([1659(5)])].

1717 C' / x = C' * x'. [back_rewrite(1272),rewrite([1659(2),1559(7),665(7)]),flip(a)].

1750 (C' * x)' = x' * C. [back_rewrite(160),rewrite([1659(6)])].

1781 (x * C)' = C' * x'. [back_rewrite(1335),rewrite([1717(6)])].

1814 C * (x * ((C' * x') * (y * C'))) = x * ((C' * x') * y). [back_rewrite(1284),rewrite([1717(4),1717(14)])].

1833 (C * x)' = C' * x'. [back_rewrite(1250),rewrite([1717(6)])].

1843 (C * (x * (C' * y))) / y = R(x,C' * y,C). [para(16(a,2),68(a,1,1)),rewrite([114(3),114(9)])].

1849 (C * (x * (C * y))) / (C * (y * C)) = R(x,C * C,y). [para(151(a,1),68(a,1,1,1,2)),rewrite([1041(5),151(15)])].

1853 (C' * (x * (C * y))) / y = R(x,C * y,C'). [para(1095(a,2),68(a,1,1)),rewrite([1224(5),1224(10)])].

1882 R(x,C',C) = x. [para(70(a,1),16(a,2)),rewrite([1190(5)]),flip(a)].

1885 C * (C * (x * (y * C'))) = (C * x) * y. [para(70(a,1),20(a,1,2)),rewrite([1882(6)]),flip(a)].

2206 R(x,C' * C',C) = x. [para(53(a,1),78(a,1,2)),rewrite([16(8,R),1224(11),1885(10),1095(5,R),10(5)]),flip(a)].

2743 x / (C' * C') = C * (x * C). [para(2206(a,1),67(a,1)),rewrite([16(15,R),35(15),1224(11)])].

2767 (C * (C * (C * (x * y)))) / (C * (y * C)) = R(C * x,y * C,C). [para(20(a,1),85(a,1,1,2)),rewrite([16(11,R)])].

2780 (C * (x * (y * C))) / (C * (C * y)) = R(x,y * C,C). [para(243(a,2),85(a,1,2)),rewrite([16(9,R)])].

2782 R(x,C * C,y) = R(x,y * C,C). [para(59(a,2),85(a,1,1)),rewrite([16(9,R),1849(10)])].

2845 (C * x) / (C * y) = (x * C) / (y * C). [para(67(a,1),86(a,2)),rewrite([7(3)])].

3195 (x * (y * C)) / (C * y) = x. [para(911(a,1),6(a,1,1))].

3196 (x * (C * y)) / (y * C) = x. [para(911(a,2),6(a,1,1))].

3222 (x * C) * (C * y) = C * (C * (x * y)). [para(911(a,1),243(a,1)),rewrite([20(5)]),flip(a)].

4170 (C * (C * (C * (x * (y * C))))) / (C * (C * (C * y))) = R(C * x,C * C,y * C). [para(20(a,1),100(a,1,2)),rewrite([3222(8)])].

4395 R(x,C * y,C * C) = R(x,C,C * (C * y)). [para(16(a,2),102(a,1,2,2,2)),rewrite([578(7,R),16(6,R),270(14),16(5,R)]),flip(a)].

4888 C' * (x * (y * C)) = C * ((C' * x) * y). [para(118(a,1),10(a,1,2))].

4890 (x * C') * (y * C) = C * (x * (C' * y)). [para(13(a,1),118(a,1,2,2)),rewrite([35(10)]),flip(a)].

4985 R(x,C' * y,C) = R(x,C',y * C). [back_rewrite(133),rewrite([4890(6),1843(7)])].

5008 (C * (x * (C' * y))) / y = R(x,C',y * C). [back_rewrite(1843),rewrite([4985(12)])].

5083 C' * ((C * x) * y) = C * (x * (C' * y)). [para(119(a,1),10(a,1,2))].

5169 (C' * x) * (y * C) = C * (x * (C' * y)). [back_rewrite(250),rewrite([5083(12)])].

5405 (C * ((C' * x) * y)) / y = R(x,C,C' * y). [para(16(a,2),126(a,1,1,1)),rewrite([249(6),114(3)])].

5791 C * (x' * (C' * (x * (C * y)))) = x' * ((C * x) * y). [para(134(a,1),10(a,1,2)),rewrite([1833(3),236(10),1224(6),5083(10)])].

6613 (x * C) / (C' * x) = C * C. [para(16(a,1),155(a,1,1))].

6751 C * (x * ((C' * (x * y)') * x)) = (x * C) / (y * C). [para(98(a,1),194(a,1,2,1,1)),rewrite([1833(8),1833(8),5169(13),3222(14),1244(13)]

)].

7025 (x * C) * R(y,x,C) = C * (x * y). [para(85(a,1),234(a,2,2)),rewrite([3222(6),1781(9),249(11),114(7),10(8),234(5),6(3)]),flip(a)].

7179 C * (x' * (C * ((C' * x) * y))) = (C * x') * (x * y). [para(35(a,1),162(a,1,2,2)),rewrite([1833(12),31(12)]),flip(a)].

8365 C' * (C' * (x / (C' * y))) = (C' * x) / y. [para(192(a,1),114(a,2)),rewrite([1095(7,R),114(9)])].

8396 (C' * x) / y = (x * C') / y. [para(1095(a,1),192(a,2,1)),rewrite([1095(9,R),8365(10)])].

8398 x * ((C' * (x * y)') * x) = (C' * x) / y. [para(1095(a,2),192(a,2,1)),rewrite([1717(4)])].

8417 C * (C * ((C' * x) / y)) = x / (C' * y). [para(192(a,1),1750(a,1,1)),rewrite([105(5),1095(11,R),1750(12),105(9),16(10,R),16(12,R)]),fli

p(a)].

8548 (x * C) / (y * C) = C * ((C' * x) / y). [back_rewrite(6751),rewrite([8398(8)]),flip(a)].

8558 (C * x) / (C * y) = C * ((C' * x) / y). [back_rewrite(2845),rewrite([8548(10)])].

8715 R(C * x,C * C,y * C) = C * R(x,C',y). [back_rewrite(4170),rewrite([8558(16),10(11),8558(11),4888(8),8558(11),8417(13),1635(9),35(6)]),f

lip(a)].

8770 R(x,y * C,C) = R(x,C',y). [back_rewrite(2780),rewrite([8558(10),4888(7),8558(10),8417(12),1635(8),35(5)]),flip(a)].

8771 C * R(x,y,C) = R(C * x,C',y). [back_rewrite(2767),rewrite([8558(12),10(9),85(7),8770(10)])].

8799 C * R(C' * x,C,y) = R(x,y,C * C). [back_rewrite(1049),rewrite([8558(10),10(7),1559(5)])].

8803 C * ((C' * (x * y)) / y) = R(x,y,C). [back_rewrite(86),rewrite([8558(6)])].

8824 R(x,C * C,y) = R(x,C',y). [back_rewrite(2782),rewrite([8770(8)])].

8829 R(C * x,C',y * C) = C * R(x,C',y). [back_rewrite(8715),rewrite([8824(8)])].

8908 R(x,C * y,C) = R(x,C',y). [back_rewrite(1047),rewrite([8824(4)]),flip(a)].

8909 (x * (y * C)) / y = C * R(x,C',y). [back_rewrite(1567),rewrite([8829(7)]),flip(a)].

10606 C' * ((x * C) * y) = C * (x * (C' * y)). [para(16(a,1),235(a,2,2,1)),rewrite([114(2),236(6),1224(5),5083(6)]),flip(a)].

10629 C * (x * (C' * (y * (C * z)))) = C * (x * (C * ((C' * y) * z))). [para(59(a,1),235(a,1,2)),rewrite([114(2),236(9),1224(5),5083(9),4888

(7),5083(18)]),flip(a)].

10711 (C * (x * (C' * y))) / (y * C) = C' * x. [para(235(a,1),3196(a,1,1)),rewrite([5083(6),114(11)])].

10717 (x * (C' * y)) * (C * z) = C' * (((C * x) * y) * z). [para(119(a,1),235(a,2,2,1)),rewrite([114(8),10(9)])].

10801 (C * x') * (x * y) = x' * ((C * x) * y). [back_rewrite(5791),rewrite([10629(10),7179(10)])].

10985 (x * C') * (C * y) = C * (x * (C' * y)). [para(1095(a,1),236(a,1,1)),rewrite([1224(11),5083(12)])].

11428 R(x,C',C' * y) = R(x,y,C). [para(6613(a,1),68(a,1,1,1,2)),rewrite([1041(8),35(6),85(6),6613(8),8824(9)]),flip(a)].

12082 R(x,C',C * (C * y)) = R(x,y,C). [para(247(a,2),75(a,1,1)),rewrite([1190(6),8558(6),8803(7)]),flip(a)].

12199 C * (C * (C * (x * ((C' * y) * z)))) = x * (C * (y * (z * C))). [para(118(a,1),247(a,2,2,2)),rewrite([99(10)])].

12749 (C' * x) * (x' * y) = x * ((C' * x') * y). [para(1095(a,2),249(a,1,1)),rewrite([1717(9)])].

15145 C' * (x * (C * y)) = C * ((C' * x) * y). [para(526(a,1),232(a,1,1)),rewrite([526(10),2743(11),13(10),12(11),10(10),526(11),12(12),1071

7(17),9(12),2(10),4888(12)])].

15238 R(x,C * y,C') = R(x,C,C' * y). [back_rewrite(1853),rewrite([15145(6),5405(7)]),flip(a)].

16951 R(x,C' * y,C * C) = R(x,C,y). [para(7(a,1),1048(a,1,3)),rewrite([114(4)]),flip(a)].

16954 R(x,C,C * y) = R(x,y,C * C). [para(16(a,2),1048(a,1,3))].

16961 R(x,C,C * (C * y)) = R(x,C,C * (y * C)). [para(243(a,1),1048(a,1,3)),rewrite([16(5,R),4395(12)]),flip(a)].

20705 (x' * C') * ((x * C) * y) = y. [para(31(a,1),1708(a,1,2,1,1))].

22895 (x * C') / (C' * x) = 0. [para(8396(a,1),23(a,1))].

22995 (x * (C' * y)) / (y * C') = x. [para(22895(a,1),68(a,1,1,1,2)),rewrite([3(2),22895(15),64(13)])].

23549 C * (x' * (C' * (x * (x * (C * y))))) = (x * C) * y. [para(499(a,1),20705(a,1,2)),rewrite([10985(11)])].

26052 R(R(x,C,y),C',y) = x. [para(1461(a,1),85(a,1,1,2)),rewrite([16(9,R),8558(10),10606(7),10711(10),35(5),8770(6)]),flip(a)].

26162 R(R(x,y,C),C',y) = R(x,y,C * C). [para(1462(a,1),85(a,1,1,2)),rewrite([16(9,R),8558(10),10(7),1572(5),8799(7),8908(10)]),flip(a)].

26210 R(R(x,C',y),C,y) = x. [para(3195(a,1),1546(a,2)),rewrite([8909(4),114(7),10(8)])].

26279 R(R(x,C',y * C),y,C') = x. [para(22995(a,1),1546(a,2)),rewrite([1224(7),5008(7)])].

26656 R(x,C,y * C) = R(x,y,C'). [para(26052(a,1),26279(a,1,1)),flip(a)].

26680 R(x,y,C * C) = R(x,y,C'). [back_rewrite(1048),rewrite([26656(4)]),flip(a)].

26692 R(R(x,y,C),C',y) = R(x,y,C'). [back_rewrite(26162),rewrite([26680(9)])].

26710 R(x,C,C * y) = R(x,y,C'). [back_rewrite(16954),rewrite([26680(8)])].

26713 R(x,C' * y,C') = R(x,C,y). [back_rewrite(16951),rewrite([26680(7)])].

26825 R(x,y * C,C') = R(x,C,C' * y). [back_rewrite(16961),rewrite([26710(6),15238(5),26710(11)]),flip(a)].

28765 C' * (x' * ((C * x) * y)) = R(y,x,C). [para(7025(a,1),10(a,1,2)),rewrite([1781(3),236(8),1224(6),10801(7)])].

28792 C * (x' * (C' * (x * y))) = R(y,x,C). [para(7025(a,1),20705(a,1,2)),rewrite([10985(8)])].

28811 R(x * (C * y),x,C) = (x * C) * y. [back_rewrite(23549),rewrite([28792(11)])].

29920 x * R(C * y,C',x) = (C * x) * y. [para(114(a,1),753(a,1,1)),rewrite([1659(6),114(10),3222(14),12199(15),12749(11),236(10),1224(6),1080

1(9),20(8),15145(10),236(9),1224(7),10801(8),28765(9),8771(4),114(9),236(13),1224(12),5083(13),119(14)])].

30934 R(R(x,C',y),C',y * C) = R(x,C,C' * y). [para(8770(a,1),26692(a,1,1)),rewrite([26825(13)])].

30940 R(R(x,y,C'),C,y) = R(x,y,C). [para(26692(a,1),26210(a,1,1))].

30944 R(R(x,C',C * y),y,C) = R(x,C,y). [para(26692(a,1),12082(a,1)),rewrite([15238(7),10(6),8908(8)]),flip(a)].

30979 R(R(x,C,y),C,C' * y) = R(x,C',y * C). [para(26713(a,1),30940(a,1,1)),rewrite([4985(12)])].

31469 R((C * x) * y,x,C) = C * (x * y). [para(7025(a,1),28811(a,2)),rewrite([8771(4),29920(6)])].

32898 C * (x * ((C' * x') * y)) = R(y,x,C). [para(35(a,1),31469(a,1,1)),rewrite([1833(6)]),flip(a)].

32929 x * ((C' * x') * y) = R(y * C',x,C). [back_rewrite(1814),rewrite([32898(11)]),flip(a)].

32939 R(x,C',y) = R(x,y,C). [back_rewrite(32898),rewrite([32929(7),8771(7),1190(5)])].

32967 R(x,C',y * C) = R(x,y,C). [para(32939(a,2),68(a,2)),rewrite([114(2),16(6,R),5008(7),114(9),11428(11)])].

32975 R(x,C',C * y) = R(x,C',y). [para(32939(a,2),8908(a,1))].

32987 R(R(x,y,C),C,y) = x. [para(32939(a,1),26210(a,1,1))].

33029 R(R(x,C,y),C,C' * y) = R(x,y,C). [back_rewrite(30979),rewrite([32967(12)])].

33032 R(R(x,C',y),y,C) = R(x,C,C' * y). [back_rewrite(30934),rewrite([32967(8)])].

33125 R(x,C,C' * y) = R(x,C,y). [back_rewrite(30944),rewrite([32975(5),33032(5)])].

33241 R(R(x,C,y),C,y) = R(x,y,C). [back_rewrite(33029),rewrite([33125(7)])].

33322 $F. [back_rewrite(19),rewrite([33241(7),32987(7)]),xx(a)].

============================== end of proof ==========================

% Proof 1 at 90.28 (+ 0.28) seconds.

% Length of proof is 204.

% Level of proof is 23.

% Maximum clause weight is 27.000.

% Given clauses 1573.

1 R(R(R(x,A,C),A,C),A,C) = x # label(non_clause) # label(goal). [goal].

2 0 * x = x. [assumption].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 C * ((x * y) * C) = (C * x) * (y * C). [assumption].

15 (C * x) * (y * C) = C * ((x * y) * C). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 R(x,y,z) = ((x * y) * z) / (y * z). [assumption].

18 ((x * y) * z) / (y * z) = R(x,y,z). [copy(17),flip(a)].

19 R(R(R(c1,A,C),A,C),A,C) != c1. [deny(1)].

20 (C * x) * (y * C) = C * (C * (x * y)). [back_rewrite(15),rewrite([16(9,R)])].

23 x / x = 0. [para(2(a,1),6(a,1,1))].

24 x / 0 = x. [para(3(a,1),6(a,1,1))].

29 0 / x = x'. [para(8(a,1),6(a,1,1))].

31 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([29(3)])].

32 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

33 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

35 x * (x' * y) = y. [back_rewrite(4),rewrite([32(1)])].

36 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

40 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

41 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

45 (x * (y * (x * (x * (y * x))))) * z = x * (y * (x * (x * (y * (x * z))))). [para(13(a,1),12(a,1,1)),rewrite([13(11),13(12)])].

48 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [para(13(a,1),13(a,1,1,2)),rewrite([13(9)])].

52 C * (x / C) = x. [para(16(a,2),7(a,1))].

53 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

54 x' * (C * x) = C. [para(16(a,2),10(a,1,2))].

55 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

59 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

60 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

61 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

64 R(x,0,y) = x. [para(2(a,1),18(a,1,2)),rewrite([3(2),6(2)]),flip(a)].

66 R(x,y,z) * (y * z) = (x * y) * z. [para(18(a,1),7(a,1,1))].

67 R(x / y,y,z) = (x * z) / (y * z). [para(7(a,1),18(a,1,1,1)),flip(a)].

68 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(7(a,1),18(a,1,2))].

70 (x * y') * y = R(x,y',y). [para(8(a,1),18(a,1,2)),rewrite([24(5)])].

78 ((x * (y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(12(a,1),18(a,1,2))].

85 (C * (x * y)) / (y * C) = R(x,y,C). [para(16(a,2),18(a,1,1))].

86 (C * (x * y)) / (C * y) = R(x,y,C). [para(16(a,2),18(a,1,2)),rewrite([16(3,R)])].

88 C * (C * (x * (y / C))) = (C * x) * y. [para(7(a,1),20(a,1,2)),flip(a)].

90 (C * x)' * (C * (C * (x * y))) = y * C. [para(20(a,1),10(a,1,2))].

98 (x * C) * (y * C) = C * (C * (x * y)). [para(16(a,1),20(a,1,1))].

99 (C * x) * (C * y) = C * (C * (x * y)). [para(16(a,2),20(a,1,2))].

105 (x / y)' = y / x. [para(7(a,1),33(a,1,2)),flip(a)].

109 C / (C * x) = x'. [para(16(a,2),33(a,1,2))].

114 x / C = C' * x. [para(52(a,1),10(a,1,2)),flip(a)].

118 C * (C * ((C' * x) * y)) = x * (y * C). [para(52(a,1),20(a,1,1)),rewrite([114(7)]),flip(a)].

119 C * (C * (x * (C' * y))) = (C * x) * y. [back_rewrite(88),rewrite([114(4)])].

123 x * (C * x') = C. [para(16(a,2),35(a,1,2))].

124 R(x,x' * y,z) = (y * z) / ((x' * y) * z). [para(35(a,1),18(a,1,1,1)),flip(a)].

133 ((x * C') * (y * C)) / y = R(x,C',y * C). [para(53(a,1),18(a,1,2))].

134 (C * x) * (x' * ((C * x) * y)) = C * (x * (C * y)). [para(54(a,1),13(a,1,1,2)),rewrite([16(4,R),60(5)]),flip(a)].

138 (x / y) * (y / x) = 0. [para(105(a,1),8(a,1,1))].

140 (x * y) / ((z * x) * y) = R(z,x,y)'. [para(18(a,1),105(a,1,1)),flip(a)].

142 (x / y) * (C * (y / x)) = C. [para(105(a,1),54(a,1,1))].

143 R(x,x' * y,z) = R(x',y,z)'. [back_rewrite(124),rewrite([140(8)])].

146 x' / x = x' * x'. [para(8(a,1),36(a,1,1,2)),rewrite([3(3)])].

147 x / x' = x * x. [para(9(a,1),36(a,1,1,2)),rewrite([3(2)])].

151 (C * (x * C)) / x = C * C. [para(16(a,1),36(a,1,1,2))].

155 (x * y) / (x' * y) = x * x. [para(35(a,1),36(a,1,1,2))].

160 (C' * x)' = C / x. [para(35(a,1),109(a,1,2)),flip(a)].

162 (C * x') * (x * ((C * x') * y)) = C * (x' * (C * y)). [para(123(a,1),13(a,1,1,2)),rewrite([16(5,R),60(6)]),flip(a)].

173 (x * x)' = x' * x'. [para(147(a,1),105(a,1,1)),rewrite([146(4)])].

183 (C' * x) * (C / x) = 0. [para(114(a,1),138(a,1,1))].

184 (C / x) * (C' * x) = 0. [para(114(a,1),138(a,1,2))].

192 x * ((y / (x * z)) * x) = (x * y) / z. [para(7(a,1),40(a,1,1,2)),flip(a)].

194 x * ((x * y)' * x) = x / y. [para(8(a,1),40(a,1,1,2)),rewrite([3(2)]),flip(a)].

210 (C * C) / x = C * (x' * C). [para(54(a,1),40(a,1,1,2))].

223 R(C',x,C / x) = (x * (C / x))'. [para(183(a,1),18(a,1,1)),rewrite([29(5)]),flip(a)].

225 x * (C * (C / x)) = C * C. [para(183(a,1),20(a,2,2,2)),rewrite([35(5),16(4,R),3(9)])].

228 (C * (C / x)) * x = C * C. [para(184(a,1),20(a,2,2,2)),rewrite([16(9,R),35(9),3(9)])].

232 (x / y) * ((z / (x / y)) * x) = ((x / y) * z) * y. [para(7(a,1),41(a,1,2,2))].

234 (x * y) * x' = x * (y / x). [para(9(a,1),41(a,1,2,2)),rewrite([3(3)]),flip(a)].

235 (x / y) * (y * z) = y' * ((y * x) * z). [para(41(a,1),10(a,1,2)),flip(a)].

236 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),41(a,1,2,2)),flip(a)].

241 (x / C') * y = (C * x) * y. [para(41(a,1),16(a,1)),rewrite([114(5),236(9),16(12,R),35(12)]),flip(a)].

243 (C * x) * y = (x * C) * y. [para(16(a,1),41(a,2,1)),rewrite([114(3),236(7),241(7),35(8)])].

247 C * ((C * x) * y) = x * (C * (C * y)). [para(41(a,1),20(a,2,2)),rewrite([114(3),35(5),16(4,R)]),flip(a)].

249 (x * y) * (x' * z) = x * ((y / x) * z). [para(35(a,1),41(a,1,2,2)),flip(a)].

250 (C' * x) * (y * C) = C' * ((C * x) * y). [para(53(a,1),41(a,1,2,2)),rewrite([241(6)]),flip(a)].

253 (C * x) * (C / x) = C * C. [para(123(a,1),41(a,1,2)),rewrite([114(7),160(9)]),flip(a)].

278 (C * x)' = (x * C)'. [para(55(a,1),109(a,1,2)),rewrite([109(6)]),flip(a)].

285 (C * x)' * (x * C) = 0. [para(278(a,2),8(a,1,1))].

289 (C * x)' * ((x * C) * y) = y. [para(278(a,2),10(a,1,1))].

499 (x * C) * ((x * C) * y) = C * (x * (x * (C * y))). [para(285(a,1),45(a,1,1,2,2,2,2)),rewrite([3(11),98(10),90(11),98(5),60(6),12(5),289(

22),289(18)]),flip(a)].

526 x / (C * (x * C)) = C' * C'. [para(151(a,1),105(a,1,1)),rewrite([173(4)]),flip(a)].

553 (C * (C / x)) / (C * C) = x'. [para(225(a,1),33(a,1,2))].

554 C * (C / x') = x * (C * C). [para(225(a,1),35(a,1,2)),flip(a)].

562 C * (C / x) = C * (x' * C). [para(228(a,1),6(a,1,1)),rewrite([210(4)]),flip(a)].

578 C * (x * C) = x * (C * C). [back_rewrite(554),rewrite([562(5),31(3)])].

579 R(x',C,C) = x'. [back_rewrite(553),rewrite([562(4),85(9)])].

665 R(x,C,C) = x. [para(31(a,1),579(a,1,1)),rewrite([31(5)])].

728 C * (x * ((C * x)' * (y * ((C * x)' * x)))) = x * ((C * x)' * y). [para(285(a,1),48(a,2,2,2,2)),rewrite([16(12,R),3(17)])].

753 (x / y) * (C * ((y / x) * (C * ((x / y) * z)))) = C * ((x / y) * (C * z)). [para(142(a,1),48(a,1,1,2,2)),rewrite([578(5,R),16(4,R),60(6)

]),flip(a)].

882 (C / x) / (C * C) = (C * x)'. [para(253(a,1),33(a,1,2))].

911 x * (C * y) = x * (y * C). [para(59(a,1),10(a,1,2)),rewrite([10(8)]),flip(a)].

1041 (x * (C * C)) * y = C * (x * (C * y)). [para(578(a,1),13(a,1,1))].

1046 (C * (C * (x * y))) / (y * (C * C)) = R(x,C,y * C). [para(578(a,1),18(a,1,2)),rewrite([98(5)])].

1047 R(x,C * C,y) = R(x,C * y,C). [para(578(a,2),18(a,1,1,1)),rewrite([13(5),12(9),86(10)]),flip(a)].

1048 R(x,C,y * C) = R(x,y,C * C). [para(578(a,2),18(a,1,1)),rewrite([16(4,R),1046(10)])].

1049 (C * (C * (x * y))) / (C * (y * C)) = R(x,y,C * C). [para(578(a,2),18(a,1,2)),rewrite([578(5,R),16(4,R)])].

1095 C' * x = x * C'. [para(8(a,1),61(a,2,2,2)),rewrite([35(8),3(7)]),flip(a)].

1120 (x * C')' = C / x. [para(61(a,2),160(a,1,1)),rewrite([35(8),16(9,R),9(9),3(7)])].

1190 C * (x * C') = x. [para(1095(a,1),10(a,1,2)),rewrite([31(3)])].

1191 x' * (C' * x) = C'. [para(1095(a,2),10(a,1,2))].

1211 (x * (y * (C' * x))) / C' = x * (y * x). [para(1095(a,2),40(a,1,1,2,2))].

1224 x / C' = C * x. [para(7(a,1),1190(a,1,2)),flip(a)].

1244 C * (x * (y * (C' * x))) = x * (y * x). [back_rewrite(1211),rewrite([1224(8)])].

1250 (C * x)' = C' / x. [para(1224(a,1),105(a,1,1))].

1272 (C / x) / (C * C) = C' / x. [back_rewrite(882),rewrite([1250(9)])].

1284 C * (x * ((C' / x) * (y * C'))) = x * ((C' / x) * y). [back_rewrite(728),rewrite([1250(4),1250(7),7(8),1250(13)])].

1335 (x * C)' = C' / x. [back_rewrite(278),rewrite([1250(3)]),flip(a)].

1438 (x * C') * ((C / x) * y) = y. [para(1120(a,1),35(a,1,2,1))].

1461 R(x,C,y) * (y * C) = (x * C) * y. [para(16(a,1),66(a,1,2))].

1462 R(x,y,C) * (C * y) = C * (x * y). [para(16(a,2),66(a,1,2)),rewrite([16(8,R)])].

1528 R(C,x',x) = C. [para(1191(a,1),20(a,2,2,2)),rewrite([16(8,R),35(8),70(4),9(8),3(6)])].

1539 R(C,x,x') = C. [para(31(a,1),1528(a,1,2))].

1546 R((x / y) / z,z,y) = x / (z * y). [para(7(a,1),67(a,2,1))].

1559 (x * y) / (y * C) = R(C' * x,C,y). [para(16(a,1),67(a,2,2)),rewrite([114(2)]),flip(a)].

1572 (x * y) / (C * y) = R(C' * x,C,y). [para(114(a,1),67(a,1,1)),flip(a)].

1635 (x * y) / (C' * y) = R(C * x,C',y). [para(1224(a,1),67(a,1,1)),flip(a)].

1651 x * (C / x) = C. [para(160(a,1),1539(a,1,3)),rewrite([143(7),223(5),31(5)])].

1659 C / x = x' * C. [para(1651(a,1),10(a,1,2)),flip(a)].

1708 (x * C') * ((x' * C) * y) = y. [back_rewrite(1438),rewrite([1659(5)])].

1717 C' / x = C' * x'. [back_rewrite(1272),rewrite([1659(2),1559(7),665(7)]),flip(a)].

1750 (C' * x)' = x' * C. [back_rewrite(160),rewrite([1659(6)])].

1781 (x * C)' = C' * x'. [back_rewrite(1335),rewrite([1717(6)])].

1814 C * (x * ((C' * x') * (y * C'))) = x * ((C' * x') * y). [back_rewrite(1284),rewrite([1717(4),1717(14)])].

1833 (C * x)' = C' * x'. [back_rewrite(1250),rewrite([1717(6)])].

1843 (C * (x * (C' * y))) / y = R(x,C' * y,C). [para(16(a,2),68(a,1,1)),rewrite([114(3),114(9)])].

1849 (C * (x * (C * y))) / (C * (y * C)) = R(x,C * C,y). [para(151(a,1),68(a,1,1,1,2)),rewrite([1041(5),151(15)])].

1882 R(x,C',C) = x. [para(70(a,1),16(a,2)),rewrite([1190(5)]),flip(a)].

1885 C * (C * (x * (y * C'))) = (C * x) * y. [para(70(a,1),20(a,1,2)),rewrite([1882(6)]),flip(a)].

2206 R(x,C' * C',C) = x. [para(53(a,1),78(a,1,2)),rewrite([16(8,R),1224(11),1885(10),1095(5,R),10(5)]),flip(a)].

2743 x / (C' * C') = C * (x * C). [para(2206(a,1),67(a,1)),rewrite([16(15,R),35(15),1224(11)])].

2767 (C * (C * (C * (x * y)))) / (C * (y * C)) = R(C * x,y * C,C). [para(20(a,1),85(a,1,1,2)),rewrite([16(11,R)])].

2780 (C * (x * (y * C))) / (C * (C * y)) = R(x,y * C,C). [para(243(a,2),85(a,1,2)),rewrite([16(9,R)])].

2782 R(x,C * C,y) = R(x,y * C,C). [para(59(a,2),85(a,1,1)),rewrite([16(9,R),1849(10)])].

2845 (C * x) / (C * y) = (x * C) / (y * C). [para(67(a,1),86(a,2)),rewrite([7(3)])].

3196 (x * (C * y)) / (y * C) = x. [para(911(a,2),6(a,1,1))].

3222 (x * C) * (C * y) = C * (C * (x * y)). [para(911(a,1),243(a,1)),rewrite([20(5)]),flip(a)].

4888 C' * (x * (y * C)) = C * ((C' * x) * y). [para(118(a,1),10(a,1,2))].

4890 (x * C') * (y * C) = C * (x * (C' * y)). [para(13(a,1),118(a,1,2,2)),rewrite([35(10)]),flip(a)].

4985 R(x,C' * y,C) = R(x,C',y * C). [back_rewrite(133),rewrite([4890(6),1843(7)])].

5008 (C * (x * (C' * y))) / y = R(x,C',y * C). [back_rewrite(1843),rewrite([4985(12)])].

5083 C' * ((C * x) * y) = C * (x * (C' * y)). [para(119(a,1),10(a,1,2))].

5169 (C' * x) * (y * C) = C * (x * (C' * y)). [back_rewrite(250),rewrite([5083(12)])].

5791 C * (x' * (C' * (x * (C * y)))) = x' * ((C * x) * y). [para(134(a,1),10(a,1,2)),rewrite([1833(3),236(10),1224(6),5083(10)])].

6613 (x * C) / (C' * x) = C * C. [para(16(a,1),155(a,1,1))].

6751 C * (x * ((C' * (x * y)') * x)) = (x * C) / (y * C). [para(98(a,1),194(a,1,2,1,1)),rewrite([1833(8),1833(8),5169(13),3222(14),1244(13)]

)].

7025 (x * C) * R(y,x,C) = C * (x * y). [para(85(a,1),234(a,2,2)),rewrite([3222(6),1781(9),249(11),114(7),10(8),234(5),6(3)]),flip(a)].

7179 C * (x' * (C * ((C' * x) * y))) = (C * x') * (x * y). [para(35(a,1),162(a,1,2,2)),rewrite([1833(12),31(12)]),flip(a)].

8365 C' * (C' * (x / (C' * y))) = (C' * x) / y. [para(192(a,1),114(a,2)),rewrite([1095(7,R),114(9)])].

8396 (C' * x) / y = (x * C') / y. [para(1095(a,1),192(a,2,1)),rewrite([1095(9,R),8365(10)])].

8398 x * ((C' * (x * y)') * x) = (C' * x) / y. [para(1095(a,2),192(a,2,1)),rewrite([1717(4)])].

8417 C * (C * ((C' * x) / y)) = x / (C' * y). [para(192(a,1),1750(a,1,1)),rewrite([105(5),1095(11,R),1750(12),105(9),16(10,R),16(12,R)]),fli

p(a)].

8548 (x * C) / (y * C) = C * ((C' * x) / y). [back_rewrite(6751),rewrite([8398(8)]),flip(a)].

8558 (C * x) / (C * y) = C * ((C' * x) / y). [back_rewrite(2845),rewrite([8548(10)])].

8770 R(x,y * C,C) = R(x,C',y). [back_rewrite(2780),rewrite([8558(10),4888(7),8558(10),8417(12),1635(8),35(5)]),flip(a)].

8771 C * R(x,y,C) = R(C * x,C',y). [back_rewrite(2767),rewrite([8558(12),10(9),85(7),8770(10)])].

8799 C * R(C' * x,C,y) = R(x,y,C * C). [back_rewrite(1049),rewrite([8558(10),10(7),1559(5)])].

8824 R(x,C * C,y) = R(x,C',y). [back_rewrite(2782),rewrite([8770(8)])].

8908 R(x,C * y,C) = R(x,C',y). [back_rewrite(1047),rewrite([8824(4)]),flip(a)].

10606 C' * ((x * C) * y) = C * (x * (C' * y)). [para(16(a,1),235(a,2,2,1)),rewrite([114(2),236(6),1224(5),5083(6)]),flip(a)].

10629 C * (x * (C' * (y * (C * z)))) = C * (x * (C * ((C' * y) * z))). [para(59(a,1),235(a,1,2)),rewrite([114(2),236(9),1224(5),5083(9),4888

(7),5083(18)]),flip(a)].

10711 (C * (x * (C' * y))) / (y * C) = C' * x. [para(235(a,1),3196(a,1,1)),rewrite([5083(6),114(11)])].

10717 (x * (C' * y)) * (C * z) = C' * (((C * x) * y) * z). [para(119(a,1),235(a,2,2,1)),rewrite([114(8),10(9)])].

10801 (C * x') * (x * y) = x' * ((C * x) * y). [back_rewrite(5791),rewrite([10629(10),7179(10)])].

10985 (x * C') * (C * y) = C * (x * (C' * y)). [para(1095(a,1),236(a,1,1)),rewrite([1224(11),5083(12)])].

11428 R(x,C',C' * y) = R(x,y,C). [para(6613(a,1),68(a,1,1,1,2)),rewrite([1041(8),35(6),85(6),6613(8),8824(9)]),flip(a)].

12199 C * (C * (C * (x * ((C' * y) * z)))) = x * (C * (y * (z * C))). [para(118(a,1),247(a,2,2,2)),rewrite([99(10)])].

12749 (C' * x) * (x' * y) = x * ((C' * x') * y). [para(1095(a,2),249(a,1,1)),rewrite([1717(9)])].

15145 C' * (x * (C * y)) = C * ((C' * x) * y). [para(526(a,1),232(a,1,1)),rewrite([526(10),2743(11),13(10),12(11),10(10),526(11),12(12),1071

7(17),9(12),2(10),4888(12)])].

20705 (x' * C') * ((x * C) * y) = y. [para(31(a,1),1708(a,1,2,1,1))].

22895 (x * C') / (C' * x) = 0. [para(8396(a,1),23(a,1))].

22995 (x * (C' * y)) / (y * C') = x. [para(22895(a,1),68(a,1,1,1,2)),rewrite([3(2),22895(15),64(13)])].

23549 C * (x' * (C' * (x * (x * (C * y))))) = (x * C) * y. [para(499(a,1),20705(a,1,2)),rewrite([10985(11)])].

26052 R(R(x,C,y),C',y) = x. [para(1461(a,1),85(a,1,1,2)),rewrite([16(9,R),8558(10),10606(7),10711(10),35(5),8770(6)]),flip(a)].

26067 R(R(x,y,C * C),C',y * C) = x. [para(1048(a,1),26052(a,1,1))].

26162 R(R(x,y,C),C',y) = R(x,y,C * C). [para(1462(a,1),85(a,1,1,2)),rewrite([16(9,R),8558(10),10(7),1572(5),8799(7),8908(10)]),flip(a)].

26279 R(R(x,C',y * C),y,C') = x. [para(22995(a,1),1546(a,2)),rewrite([1224(7),5008(7)])].

26656 R(x,C,y * C) = R(x,y,C'). [para(26052(a,1),26279(a,1,1)),flip(a)].

26680 R(x,y,C * C) = R(x,y,C'). [back_rewrite(1048),rewrite([26656(4)]),flip(a)].

26692 R(R(x,y,C),C',y) = R(x,y,C'). [back_rewrite(26162),rewrite([26680(9)])].

26693 R(R(x,y,C'),C',y * C) = x. [back_rewrite(26067),rewrite([26680(4)])].

28765 C' * (x' * ((C * x) * y)) = R(y,x,C). [para(7025(a,1),10(a,1,2)),rewrite([1781(3),236(8),1224(6),10801(7)])].

28792 C * (x' * (C' * (x * y))) = R(y,x,C). [para(7025(a,1),20705(a,1,2)),rewrite([10985(8)])].

28811 R(x * (C * y),x,C) = (x * C) * y. [back_rewrite(23549),rewrite([28792(11)])].

29920 x * R(C * y,C',x) = (C * x) * y. [para(114(a,1),753(a,1,1)),rewrite([1659(6),114(10),3222(14),12199(15),12749(11),236(10),1224(6),1080

1(9),20(8),15145(10),236(9),1224(7),10801(8),28765(9),8771(4),114(9),236(13),1224(12),5083(13),119(14)])].

31469 R((C * x) * y,x,C) = C * (x * y). [para(7025(a,1),28811(a,2)),rewrite([8771(4),29920(6)])].

32898 C * (x * ((C' * x') * y)) = R(y,x,C). [para(35(a,1),31469(a,1,1)),rewrite([1833(6)]),flip(a)].

32929 x * ((C' * x') * y) = R(y * C',x,C). [back_rewrite(1814),rewrite([32898(11)]),flip(a)].

32939 R(x,C',y) = R(x,y,C). [back_rewrite(32898),rewrite([32929(7),8771(7),1190(5)])].

32965 R(R(c1,A,C'),A,C) != c1. [para(32939(a,2),19(a,1,1)),rewrite([26692(8)])].

32970 R(x,C',y * C) = R(x,y,C). [para(32939(a,2),68(a,2)),rewrite([114(2),16(6,R),5008(7),114(9),11428(11)])].

33038 R(R(x,y,C'),y,C) = x. [back_rewrite(26693),rewrite([32970(8)])].

33039 $F. [resolve(33038,a,32965,a)].

============================== end of proof ==========================

% Proof 1 at 52.43 (+ 0.30) seconds.

% Length of proof is 291.

% Level of proof is 37.

% Maximum clause weight is 32.000.

% Given clauses 1973.

1 R(R(R(x,C,A),C,A),C,A) = x # label(non_clause) # label(goal). [goal].

2 0 * x = x. [assumption].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 A * ((x * y) * A) = (A * x) * (y * A). [assumption].

15 (A * x) * (y * A) = A * ((x * y) * A). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 R(x,y,z) = ((x * y) * z) / (y * z). [assumption].

18 ((x * y) * z) / (y * z) = R(x,y,z). [copy(17),flip(a)].

19 R(R(R(c1,C,A),C,A),C,A) != c1. [deny(1)].

23 x / 0 = x. [para(3(a,1),6(a,1,1))].

28 0 / x = x'. [para(8(a,1),6(a,1,1))].

30 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([28(3)])].

31 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

32 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

34 x * (x' * y) = y. [back_rewrite(4),rewrite([31(1)])].

35 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

39 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

40 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

47 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [para(13(a,1),13(a,1,1,2)),rewrite([13(9)])].

49 (A * x) * A = A * (x * A). [para(2(a,1),15(a,1,2)),rewrite([3(7)])].

50 (A * ((x * y) * A)) / (y * A) = A * x. [para(15(a,1),6(a,1,1))].

51 A * ((x * (y / A)) * A) = (A * x) * y. [para(7(a,1),15(a,1,2)),flip(a)].

53 A * ((A' * x) * A) = x * A. [para(9(a,1),15(a,1,1)),rewrite([2(4)]),flip(a)].

54 (A * x)' * (A * ((x * y) * A)) = y * A. [para(15(a,1),10(a,1,2))].

56 (A * x) * (y * (y * A)) = A * ((x * (y * y)) * A). [para(12(a,1),15(a,1,2))].

57 ((x * A) * (A * ((y * x) * A))) * z = (x * A) * ((A * y) * ((x * A) * z)). [para(15(a,1),13(a,1,1,2))].

58 A * (((x * A) * y) * A) = A * (x * (A * (y * A))). [para(15(a,1),13(a,1))].

59 (A * x) * (y * (z * (y * A))) = A * ((x * (y * (z * y))) * A). [para(13(a,1),15(a,1,2))].

62 C * (x / C) = x. [para(16(a,2),7(a,1))].

63 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

65 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

68 (x * (x * C)) * y = x * (C * (x * y)). [para(16(a,1),13(a,1,1,2))].

69 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

70 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

71 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

73 (A * x) * (A * C) = A * ((x * C) * A). [para(16(a,1),15(a,1,2))].

78 R(x,y,z) * (y * z) = (x * y) * z. [para(18(a,1),7(a,1,1))].

79 R(x / y,y,z) = (x * z) / (y * z). [para(7(a,1),18(a,1,1,1)),flip(a)].

80 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(7(a,1),18(a,1,2))].

82 (x * y') * y = R(x,y',y). [para(8(a,1),18(a,1,2)),rewrite([23(5)])].

85 (x * y) * y' = R(x,y,y'). [para(9(a,1),18(a,1,2)),rewrite([23(5)])].

90 ((x * (y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(12(a,1),18(a,1,2))].

95 (A * ((x * y) * A)) / (x * (y * A)) = R(A,x,y * A). [para(15(a,1),18(a,1,1))].

104 (x / y)' = y / x. [para(7(a,1),32(a,1,2)),flip(a)].

106 x / (y * (z * (y * x))) = (y * (z * y))'. [para(13(a,1),32(a,1,2))].

108 x / (x * C) = C'. [para(16(a,1),32(a,1,2))].

109 C / (C * x) = x'. [para(16(a,2),32(a,1,2))].

113 x / C = C' * x. [para(62(a,1),10(a,1,2)),flip(a)].

120 A * (((A' * x) * y) * A) = x * (y * A). [para(34(a,1),15(a,1,1)),flip(a)].

122 x * (C * x') = C. [para(16(a,2),34(a,1,2))].

123 R(x,x' * y,z) = (y * z) / ((x' * y) * z). [para(34(a,1),18(a,1,1,1)),flip(a)].

127 (x * C) * (C' * ((x * C) * y)) = ((x * C) * x) * y. [para(63(a,1),13(a,1,1,2)),flip(a)].

136 (x / y) * (y / x) = 0. [para(104(a,1),8(a,1,1))].

137 (x / y) * ((y / x) * z) = z. [para(104(a,1),10(a,1,1))].

138 (x * y) / ((z * x) * y) = R(z,x,y)'. [para(18(a,1),104(a,1,1)),flip(a)].

141 R(x,x' * y,z) = R(x',y,z)'. [back_rewrite(123),rewrite([138(8)])].

144 x' / x = x' * x'. [para(8(a,1),35(a,1,1,2)),rewrite([3(3)])].

145 x / x' = x * x. [para(9(a,1),35(a,1,1,2)),rewrite([3(2)])].

150 (A * (x * (A * (x * A)))) / A = (A * x) * (A * x). [para(15(a,1),35(a,1,1)),rewrite([13(6)])].

158 (C' * x)' = C / x. [para(34(a,1),109(a,1,2)),flip(a)].

165 C' * ((x * y) * (C * y')) = R(x,y,C * y'). [para(122(a,1),18(a,1,2)),rewrite([113(7)])].

172 (x * x)' = x' * x'. [para(145(a,1),104(a,1,1)),rewrite([144(4)])].

191 ((x / y) * (z * x)) / y = (x / y) * (z * (x / y)). [para(7(a,1),39(a,1,1,2,2))].

192 x * ((y / (x * z)) * x) = (x * y) / z. [para(7(a,1),39(a,1,1,2)),flip(a)].

194 x * ((x * y)' * x) = x / y. [para(8(a,1),39(a,1,1,2)),rewrite([3(2)]),flip(a)].

195 (x * y) / x' = x * (y * x). [para(9(a,1),39(a,1,1,2,2)),rewrite([3(2)])].

201 ((A * x) * (y * (A * ((x * z) * A)))) / (z * A) = (A * x) * (y * (A * x)). [para(15(a,1),39(a,1,1,2,2))].

202 (x * (A * ((y * x) * A))) / A = x * ((A * y) * x). [para(15(a,1),39(a,1,1,2))].

231 (x' * y) * x = x' * (y / x'). [para(8(a,1),40(a,1,2,2)),rewrite([3(5)]),flip(a)].

232 (x * y) * x' = x * (y / x). [para(9(a,1),40(a,1,2,2)),rewrite([3(3)]),flip(a)].

233 (x / y) * (y * z) = y' * ((y * x) * z). [para(40(a,1),10(a,1,2)),flip(a)].

234 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),40(a,1,2,2)),flip(a)].

240 (x / C') * y = (C * x) * y. [para(40(a,1),16(a,1)),rewrite([113(5),234(9),16(12,R),34(12)]),flip(a)].

242 (C * x) * y = (x * C) * y. [para(16(a,1),40(a,2,1)),rewrite([113(3),234(7),240(7),34(8)])].

246 (x * y) * (x' * z) = x * ((y / x) * z). [para(34(a,1),40(a,1,2,2)),flip(a)].

247 (C' * x) * (y * C) = C' * ((C * x) * y). [para(63(a,1),40(a,1,2,2)),rewrite([240(6)]),flip(a)].

249 (x * y) * (C * x') = x * (C * (y / x)). [para(122(a,1),40(a,1,2,2)),rewrite([16(3,R)]),flip(a)].

250 (C * x) * (C / x) = C * C. [para(122(a,1),40(a,1,2)),rewrite([113(7),158(9)]),flip(a)].

256 x / A' = x * A. [back_rewrite(53),rewrite([231(6),34(8)])].

259 R(x,A',A) = x. [para(256(a,1),6(a,1)),rewrite([82(5)])].

260 R(x,A,A') = x. [para(256(a,1),7(a,1,1)),rewrite([85(5)])].

261 (x * A)' = A' / x. [para(256(a,1),104(a,1,1))].

263 (x * A) * (A' / x) = 0. [para(256(a,1),136(a,1,1))].

266 A' / (x / A) = x'. [para(7(a,1),261(a,1,1)),flip(a)].

270 (A * C)' = C' * A'. [para(16(a,1),261(a,1,1)),rewrite([113(8)])].

291 x' * (x / A) = A'. [para(266(a,1),7(a,1,1))].

293 x / A = x * A'. [para(291(a,1),10(a,1,2)),rewrite([30(2)]),flip(a)].

295 ((x * y') * (y * A')) * A = R(x,y',y * A'). [para(291(a,1),18(a,1,2)),rewrite([293(4),256(9),293(11)])].

297 (x * (A * ((y * x) * A))) * A' = x * ((A * y) * x). [back_rewrite(202),rewrite([293(8)])].

298 A * ((x * (A * (x * A))) * A') = (A * x) * (A * x). [back_rewrite(150),rewrite([293(9),232(10),293(8)])].

299 A * ((x * (y * A')) * A) = (A * x) * y. [back_rewrite(51),rewrite([293(3)])].

336 (x * (y * (x * A))) * A' = x * (y * x). [para(293(a,1),39(a,1))].

337 (A * x) * (A * x) = A * (x * (A * x)). [back_rewrite(298),rewrite([336(9)]),flip(a)].

393 (x * (x * A)) * (A' / (x * x)) = 0. [para(12(a,1),263(a,1,1))].

397 (x * (y * A)) * (A' / y) = R(x,y * A,A' / y). [para(263(a,1),18(a,1,2)),rewrite([23(9)])].

467 (A * x) * (A * (y * A)) = A * ((x * (A * y)) * A). [para(49(a,1),15(a,1,2))].

468 (A * (x * (A * y))) / (A * y) = R(A * x,A,y). [para(49(a,1),18(a,1,1,1)),rewrite([13(5)])].

469 R(A,x,A) = A. [para(49(a,1),18(a,1,1)),rewrite([6(7)]),flip(a)].

470 ((x * (A * y)) * A) / (A * (y * A)) = R(x,A * y,A). [para(49(a,1),18(a,1,2))].

471 A / (A * (x * A)) = (A * x)'. [para(49(a,1),32(a,1,2))].

473 (A * (x * A))' = A' / (A * x). [para(49(a,1),261(a,1,1))].

474 A * (x * (A * (A' / (A * x)))) = 0. [para(49(a,1),263(a,1,1)),rewrite([13(10)])].

493 (C * x)' = (x * C)'. [para(65(a,1),109(a,1,2)),rewrite([109(6)]),flip(a)].

523 (x * (y * (z * (y * (x * u))))) / ((y * (z * (y * x))) * u) = R(x,y * (z * (y * x)),u). [para(47(a,1),18(a,1,1))].

540 x * (C * (y * (z * y))) = x * (y * (z * (y * C))). [para(122(a,1),47(a,2,2,2,2,2)),rewrite([249(8),39(5)])].

568 (C * x) * (x * C)' = 0. [para(493(a,1),9(a,1,2))].

619 (A * (x * A)) / (y * A) = A * (x / y). [para(7(a,1),50(a,1,1,2,1))].

620 (A * A) / (x * A) = A * x'. [para(8(a,1),50(a,1,1,2,1)),rewrite([2(4)])].

749 A / x = A * x'. [para(54(a,1),39(a,1,1,2)),rewrite([619(8),32(3),194(10)]),flip(a)].

762 A * (A' / (A * x)) = (A * x)'. [back_rewrite(471),rewrite([749(6),473(6)])].

785 A * (x * (A * x)') = 0. [back_rewrite(474),rewrite([762(8)])].

786 A * (A' / x) = x'. [para(749(a,1),32(a,1)),rewrite([261(4)])].

788 A * (C' * A') = C'. [para(749(a,1),108(a,1)),rewrite([270(5)])].

794 A' / x = A' * x'. [para(786(a,1),10(a,1,2)),flip(a)].

807 (x * (y * A)) * (A' * y') = R(x,y * A,A' * y'). [back_rewrite(397),rewrite([794(6),794(13)])].

809 (x * (x * A)) * (A' * (x' * x')) = 0. [back_rewrite(393),rewrite([794(7),172(7)])].

824 (x * A)' = A' * x'. [back_rewrite(261),rewrite([794(6)])].

858 (x * (A * ((y * (x * x)) * A))) / (x * A) = x * ((A * y) * x). [para(56(a,1),39(a,1,1,2))].

880 x * (A * x)' = A'. [para(785(a,1),10(a,1,2)),rewrite([3(4)]),flip(a)].

882 R(x,A * x,(A * x)') = x. [para(785(a,1),13(a,2,2)),rewrite([85(7),3(8)])].

889 (A * x)' = x' * A'. [para(880(a,1),10(a,1,2)),flip(a)].

893 R(A',x,x') = A'. [para(34(a,1),880(a,1,2,1)),rewrite([85(5)])].

899 R(x,A * x,x' * A') = x. [back_rewrite(882),rewrite([889(5)])].

945 ((x * C) * A) * ((A * C') * (((x * C) * A) * y)) = (((x * C) * A) * (A * (x * A))) * y. [para(63(a,1),57(a,1,1,2,2,1)),flip(a)].

971 (A * C) * (A * x) = A * (A * (x * C)). [para(568(a,1),57(a,2,2,2)),rewrite([16(3),467(10),889(14),13(16),788(14),232(10),113(8),34(10),1

6(9),3(13)]),flip(a)].

987 R(A',x',x) = A'. [para(30(a,1),893(a,1,3))].

1016 (A' * x')' = x * A. [para(794(a,1),104(a,1,1)),rewrite([256(8)])].

1021 ((x * A) * y) * A = x * (A * (y * A)). [para(58(a,1),10(a,1,2)),rewrite([10(10)]),flip(a)].

1071 (A' * x)' = x' * A. [para(30(a,1),1016(a,1,1,2))].

1079 A * ((x * ((y * A') * (z * (y * A')))) * A) = (A * x) * ((y * A') * (z * y)). [para(7(a,1),59(a,1,2,2,2)),rewrite([293(4),293(11),293(1

4)]),flip(a)].

1276 ((x * C) * (y * ((C * x) * z))) / z = (C * x) * (y * (C * x)). [para(242(a,1),39(a,1,1))].

1277 (C * x) * (y * (C * x)) = (x * C) * (y * (x * C)). [para(242(a,2),39(a,1,1,2,2)),rewrite([1276(8)])].

1336 (C * x)' * (C * C) = C / x. [para(250(a,1),10(a,1,2))].

1358 x * (C * y) = x * (y * C). [para(69(a,1),10(a,1,2)),rewrite([10(8)]),flip(a)].

1382 C * (x * C) = x * (C * C). [para(69(a,2),39(a,1,1)),rewrite([113(8),10(9)]),flip(a)].

1419 C * (C * (C * x)') = C / x. [back_rewrite(1336),rewrite([1382(7,R),16(6,R)])].

1511 C' * x = x * C'. [para(8(a,1),71(a,2,2,2)),rewrite([34(8),3(7)]),flip(a)].

1538 (x * C')' = C / x. [para(71(a,2),158(a,1,1)),rewrite([34(8),16(9,R),9(9),3(7)])].

1659 C * (x * C') = x. [para(1511(a,1),10(a,1,2)),rewrite([30(3)])].

1663 (x * (x * C')) * y = x * (C' * (x * y)). [para(1511(a,1),13(a,1,1,2))].

1699 x / C' = C * x. [para(7(a,1),1659(a,1,2)),flip(a)].

1724 (C * x)' = C' / x. [para(1699(a,1),104(a,1,1))].

1730 (C' / x) * ((C * x) * y) = y. [para(1699(a,1),137(a,1,2,1))].

1769 C * (C * (C' / x)) = C / x. [back_rewrite(1419),rewrite([1724(5)])].

1828 (x * C)' = C' / x. [back_rewrite(493),rewrite([1724(3)]),flip(a)].

1934 (x * C') * ((C / x) * y) = y. [para(1538(a,1),34(a,1,2,1))].

2041 R(x,C,y) * (y * C) = (x * C) * y. [para(16(a,1),78(a,1,2))].

2104 R((x / y) / z,z,y) = x / (z * y). [para(7(a,1),79(a,2,1))].

2120 R(x / y,y,C) = (C * x) / (y * C). [para(16(a,2),79(a,2,1))].

2149 R((A * x) / y,y,A) = A * (x / y). [para(49(a,1),79(a,2,1)),rewrite([619(12)])].

2150 R(x / (A * y),A * y,A) = (x * A) / (A * (y * A)). [para(49(a,1),79(a,2,2))].

2249 (C' * (x * (C * y))) / y = R(x,C * y,C'). [para(1511(a,2),80(a,1,1)),rewrite([1699(5),1699(10)])].

2273 (x * y')' * R(x,y',y) = y. [para(82(a,1),10(a,1,2))].

2814 C' * (C' * (x * (C * C))) = R(x,C * C,C'). [para(122(a,1),90(a,1,2)),rewrite([1511(7,R),113(9)])].

3952 (x * (C * y)) / (y * C) = x. [para(1358(a,2),6(a,1,1))].

3953 (x / (C * y)) * (y * C) = x. [para(1358(a,1),7(a,1))].

4120 C' * (x * (C * C)) = x * C. [para(1382(a,1),10(a,1,2))].

4231 R(x,C * C,C') = x. [back_rewrite(2814),rewrite([4120(9),63(5)]),flip(a)].

4256 (x * (y * x))' = x' / (x * y). [para(9(a,1),106(a,1,2,2,2)),rewrite([3(3)]),flip(a)].

4419 x / (C * C) = C' * (x * C'). [para(4231(a,1),79(a,1)),rewrite([1511(13,R),1382(13,R),16(12,R),9(12),3(10),113(9)])].

4610 (x * (A' * y)) * A = (x * A') * (y * A). [para(13(a,1),120(a,1,2,1)),rewrite([231(10),256(10),34(11)])].

5089 ((x * C) * x) * ((C' / x) * y) = (x * C) * (C' * y). [para(34(a,1),127(a,1,2,2)),rewrite([1828(12)]),flip(a)].

6174 x' / (x * y) = x' * (y' * x'). [para(10(a,1),194(a,1,2,1,1)),flip(a)].

6182 x / (C * x') = x * (C' * x). [para(122(a,1),194(a,1,2,1,1)),flip(a)].

6208 (A * x) / (A * C) = A * (C' * (x * A')). [para(73(a,1),194(a,1,2,1,1)),rewrite([4256(9),6174(9),1828(7),13(14),10(12),7(8),246(8),293(3

),1511(7,R)]),flip(a)].

6502 x / (C' / x) = (x * C) * x. [para(63(a,1),195(a,2,2)),rewrite([1511(5,R),63(5),1828(3)])].

6518 x / (C / x) = (x * C') * x. [para(1659(a,1),195(a,2,2)),rewrite([16(5,R),1659(5),1538(4)])].

6745 R(x,A,A)' = x'. [para(824(a,1),620(a,2,2)),rewrite([138(8),34(10)])].

6792 R(x,A,A) = x. [para(6745(a,1),30(a,1,1)),rewrite([30(2)]),flip(a)].

6793 (x * A) * A = x * (A * A). [para(6792(a,1),78(a,1,1)),flip(a)].

6823 (x * (A * A)) * A' = x * A. [para(6793(a,1),6(a,1,1)),rewrite([293(6)])].

6830 (A * x) * (y * (A * A)) = A * ((x * (y * A)) * A). [para(6793(a,1),15(a,1,2))].

6831 A * ((x * (A * A)) * A) = A * (x * (A * (A * A))). [para(6793(a,1),15(a,2,2,1)),rewrite([13(8)]),flip(a)].

6875 (x * (A * A)) * A = (x * A) * (A * A). [para(6793(a,1),6793(a,1,1))].

6893 A * ((x * A) * (A * A)) = A * (x * (A * (A * A))). [back_rewrite(6831),rewrite([6875(7)])].

7049 R(A' * x,x,x') = A' * x. [para(34(a,1),899(a,1,2)),rewrite([1071(7),85(9),260(8)])].

7806 ((x * C') * x) * ((C / x) * y) = (x * C') * (C * y). [para(1934(a,1),68(a,2,2,2)),rewrite([16(8,R),1659(8)])].

8897 (C * x) * (y * (C * x)) = C * ((C * x) * (y * x)). [para(191(a,1),1699(a,1)),rewrite([1699(3),1699(5),1699(10)])].

9118 (x * C) * (y * (x * C)) = C * ((C * x) * (y * x)). [back_rewrite(1277),rewrite([8897(6)]),flip(a)].

9200 (x / (y * z)) * y = y' * ((y * x) / z). [para(192(a,1),10(a,1,2)),flip(a)].

9204 (A * x) * ((y / (A * ((x * z) * A))) * (A * x)) = ((A * x) * y) / (z * A). [para(15(a,1),192(a,1,2,1,2))].

9339 (C * x) / (C * (C' / y)) = C * (C * (x / (C / y))). [para(1769(a,1),192(a,1,2,1,2)),rewrite([16(6,R)]),flip(a)].

9954 (A * x) * (y * (A * x)) = A * (x * ((y * A) * x)). [para(9(a,1),201(a,1,1,2,2,2,1)),rewrite([2(6),6830(7),619(11),195(6)]),flip(a)].

9956 (A * x) * x = A * (x * x). [para(10(a,1),201(a,1,1,2)),rewrite([15(6),619(9),35(4),10(10)]),flip(a)].

10077 ((A * C) * (x * (A * ((C / y) * A)))) / ((C * (C' / y)) * A) = C * (A * ((C * x) * A)). [para(1769(a,1),201(a,1,1,2,2,2,1)),rewrite([9

118(27),16(23),15(26)])].

10114 A * (x * ((A' * ((A * y) / ((x * z) * A))) * x)) = ((A * x) * y) / (z * A). [back_rewrite(9204),rewrite([9954(12),9200(9)])].

10225 R(A,x,A * (A * A)) = A. [para(9956(a,1),95(a,1,2,2)),rewrite([6875(7),6893(8),6(15),12(7)]),flip(a)].

10333 R(A',x,A * (A * A))' = A. [para(10225(a,1),141(a,1)),flip(a)].

11955 (x * A') * (A * y) = A' * ((A * x) * y). [para(293(a,1),233(a,1,1))].

11964 (A * x') * (x * y) = x' * ((x * A) * y). [para(749(a,1),233(a,1,1))].

12145 (x * C) * (C' * y) = C * ((C' * x) * y). [para(6502(a,1),233(a,1,1)),rewrite([5089(8),104(10),1699(9),7(12),246(12),113(9)])].

12146 (x * C') * (C * y) = C' * ((C * x) * y). [para(6518(a,1),233(a,1,1)),rewrite([7806(8),104(9),113(8),7(12),234(12),1699(11)])].

12312 R(A',x,A * (A * A)) = A'. [para(10333(a,1),30(a,1,1)),flip(a)].

12316 C' * (A' * (C * (A * x))) = R(x,A',A * C). [para(10333(a,1),165(a,1,2,2,2)),rewrite([12312(10),16(8),11955(9),16(8,R),12312(18),12312(

21),30(16),16(15)])].

13836 (x * C') * (y * C) = C' * ((C * x) * y). [para(71(a,2),247(a,1,1)),rewrite([34(8),16(13,R),9(13),3(11)])].

16312 (C' * ((C * x) * A')) * A = R(x,C',C * A'). [para(16(a,1),295(a,1,1,2)),rewrite([16(7,R),12146(8)])].

16328 A' * (C' * (A * (x * C))) = R(x,C,A' * C'). [para(1511(a,1),295(a,1,1,2)),rewrite([30(3),4610(10),1511(9),11955(10),1511(9,R),30(13),1

511(16)])].

16405 (x * (A * (y * A))) * A' = x * ((A * (y / x)) * x). [para(7(a,1),297(a,1,1,2,2,1))].

16598 (x * (y * A')) * A = A' * ((A * x) * y). [para(299(a,1),10(a,1,2)),flip(a)].

16636 (A * (x / y)) * y = y' * ((y * A) * x). [para(233(a,1),299(a,1,2,1)),rewrite([16598(9),11964(8),34(10)]),flip(a)].

16657 A' * (C' * ((A * C) * x)) = R(x,C',C * A'). [back_rewrite(16312),rewrite([16598(10),12146(9),16(7)])].

16673 (x * (A * (y * A))) * A' = (x * A) * y. [back_rewrite(16405),rewrite([16636(12),34(14)])].

17618 R(A,x,A * x) = A. [para(337(a,1),18(a,1,1)),rewrite([6(9)]),flip(a)].

17677 R(A',x,x)' = A. [para(34(a,1),17618(a,1,3)),rewrite([141(5)])].

17686 R(A',x,x) = A'. [para(17677(a,1),30(a,1,1)),flip(a)].

17687 (A' * x) * x = A' * (x * x). [para(17686(a,1),78(a,1,1)),flip(a)].

21527 x * (C' * (x * ((C * x') * y))) = (C' / x') * (R(C,x',x) * y). [para(6182(a,1),233(a,1,1)),rewrite([13(9),1724(13),82(17)])].

21843 R(A' * x',x',x) = A' * x'. [para(30(a,1),7049(a,1,3))].

22986 (A * ((x * C) * (A * A))) / (A * (A * C)) = R(A * x,A * C,A). [para(73(a,1),470(a,1,1,1)),rewrite([13(8),16(12)])].

22987 R(R(x,A,y),A * y,A) = x. [para(78(a,1),470(a,1,1,1)),rewrite([1021(5),6(10)]),flip(a)].

23049 R(R(x,A,A' * y),y,A) = x. [para(34(a,1),22987(a,1,2))].

23050 R(R(x,A,C * A'),C,A) = x. [para(122(a,1),22987(a,1,2))].

23765 R(x,x * A,A' * x') = x. [para(17687(a,1),2273(a,1,1,1)),rewrite([1071(7),172(4),30(2),30(2),12(3),21843(9),807(8)])].

24502 x * (C' * y) = x * (y * C'). [para(8(a,1),540(a,2,2,2,2)),rewrite([34(8),3(8)]),flip(a)].

25344 (A * x) / (y * A) = A * ((x * A') / y). [para(7(a,1),619(a,1,1,2)),rewrite([293(8)])].

25346 (x * A) / (A * (y * A)) = (x / y) * A'. [para(619(a,1),104(a,1,1)),rewrite([889(4),104(2)]),flip(a)].

25390 ((A * x) * y) / (z * A) = A * ((x * (y * A')) / z). [back_rewrite(10114),rewrite([25344(9),10(11),9200(7),34(9)]),flip(a)].

25428 R(x / (A * y),A * y,A) = (x / y) * A'. [back_rewrite(2150),rewrite([25346(14)])].

25430 C * (A * ((C * x) * A)) = A * (C * (C * (x * A))). [back_rewrite(10077),rewrite([25390(19),16673(12),9339(14),6(11)]),flip(a)].

25535 (x * C) * (y * C') = C * ((C' * x) * y). [para(24502(a,1),242(a,2)),rewrite([246(6),113(3)]),flip(a)].

26799 R(A * R(x,C,A),A,C) = A * x. [para(2041(a,1),468(a,1,1,2)),rewrite([6208(10),85(10),260(9),63(6)]),flip(a)].

26804 R(A * x,A * C,A) = A * R(x,C,A). [para(26799(a,1),22987(a,1,1))].

26806 (A * ((x * C) * (A * A))) / (A * (A * C)) = A * R(x,C,A). [back_rewrite(22986),rewrite([26804(21)])].

26864 R(R(x,C * y,C'),y,C) = x. [para(3952(a,1),2104(a,2)),rewrite([113(5),2249(7)])].

27013 R(x,A * C,C') = R(x,A * C,A). [para(26864(a,1),22987(a,1,1)),rewrite([16(8)]),flip(a)].

27522 (C * x) / (A * C) = R(x * A',A,C). [para(293(a,1),2120(a,1,1)),flip(a)].

29284 R(x',A' * x,x') = x'. [para(809(a,1),523(a,1,1,2,2)),rewrite([3(5),807(14),23765(13),85(9),893(8),256(7),82(6),259(5),807(12),23765(11

)]),flip(a)].

29288 R(x,A' * x',x) = x. [para(30(a,1),29284(a,1,1)),rewrite([30(6),30(7)])].

29312 (x * (A' * x')) * x = x * A'. [para(29288(a,1),78(a,1,1)),rewrite([82(5),987(4)]),flip(a)].

29976 C * (C * (A * (C' * (x * C')))) = R(A * x,A,C). [para(3953(a,1),858(a,1,1,2,2,1)),rewrite([16(9),27522(10),232(7),293(5),85(6),260(5),

4419(11),16(16,R)]),flip(a)].

29977 C * (C * (A * (C' * x))) = A * ((x * A) * (C * A')). [para(247(a,1),858(a,1,1,2,2,1)),rewrite([16(8,R),10(9),25430(8),16(11),6208(12),

70(12),10(13),16(17,R)]),flip(a)].

29983 A * (((x * C') * A) * (C * A')) = R(A * x,A,C). [back_rewrite(29976),rewrite([29977(12)])].

31306 A * (A * (C * (A' * x))) = (A * C) * x. [para(34(a,1),971(a,1,2)),rewrite([16(11,R)]),flip(a)].

32157 C' * ((A * C) * (x * C)) = C * (A * x). [para(1730(a,1),1079(a,1,2,1)),rewrite([16598(8),16(7,R),34(9),256(10),1511(9),1663(18),21527(

18),256(9),1511(8),259(13),12146(13),16(9)]),flip(a)].

32245 x / (A * (A * C)) = (C' * (x * A')) * A'. [para(2104(a,1),27013(a,2)),rewrite([293(2),27013(13),25428(12),113(5),49(14),16(13)]),flip(

a)].

32247 C' * ((A * C) * x) = A * R(x,C,A). [back_rewrite(26806),rewrite([32245(14),232(13),293(11),6823(12),16673(12),1511(4),13836(7),16(5)])

].

32248 A * R(x * C,C,A) = C * (A * x). [back_rewrite(32157),rewrite([32247(9)])].

32253 R(x,C',C * A') = R(x,C,A). [back_rewrite(16657),rewrite([32247(9),10(8)]),flip(a)].

32259 A' * (C * (A * x)) = R(C * x,C,A). [para(32253(a,1),79(a,1)),rewrite([1699(3),10(17),256(13),16598(12),16(11,R)]),flip(a)].

32272 C' * R(C * x,C,A) = R(x,A',A * C). [back_rewrite(12316),rewrite([32259(9)])].

32704 C * (A * R(x,C,A)) = (A * C) * x. [para(29312(a,1),945(a,1,1,1)),rewrite([82(6),259(5),1659(12),16(9,R),82(11),259(10),12146(8),16(6),

32247(8),1659(14),16(11,R),82(13),259(12),1659(16),8(13),3(11),16(10)])].

33725 C * (A * (C' * x)) = A * R(x,C,A). [para(7(a,1),32248(a,1,2,1)),rewrite([113(9)]),flip(a)].

33764 R(C * (A * x),A,C) = A * (x * C). [para(32248(a,1),26799(a,1,1))].

33780 A * ((x * A) * (C * A')) = (A * C) * x. [back_rewrite(29977),rewrite([33725(8),32704(7)]),flip(a)].

33788 C * ((A * C') * x) = R(A * x,A,C). [back_rewrite(29983),rewrite([33780(12),25535(7),1511(5)])].

34236 A * (C * (A' * x)) = R(C * x,A,C). [para(34(a,1),33764(a,1,1,2)),rewrite([16(11,R)]),flip(a)].

34252 A * R(C * x,A,C) = (A * C) * x. [back_rewrite(31306),rewrite([34236(8)])].

34415 A' * ((A * C) * x) = R(C * x,A,C). [para(34252(a,1),10(a,1,2))].

34420 A * R(x,A,C) = R(A * x,A,C). [para(34(a,1),34252(a,1,2,1)),rewrite([12145(12),1511(10),33788(12)])].

34431 R(A * (C * x),A,C) = (A * C) * x. [para(242(a,2),34252(a,2)),rewrite([34420(7),16(10)])].

34496 R(A * x,A,C) / R(x,A,C) = A. [para(34420(a,1),6(a,1,1))].

34497 A' * R(A * x,A,C) = R(x,A,C). [para(34420(a,1),10(a,1,2))].

34581 (A * x) / R(R(x,C,A),A,C) = A. [para(26799(a,1),34496(a,1,1))].

34603 A * (x / R(R(x,C,A),A,C)) = A. [para(34581(a,1),2149(a,1,1)),rewrite([469(9)]),flip(a)].

34613 x / R(R(x,C,A),A,C) = 0. [para(34603(a,1),10(a,1,2)),rewrite([8(4)]),flip(a)].

34635 R(R(x,C,A),A,C) = x. [para(34613(a,1),7(a,1,1)),rewrite([2(8)])].

34640 C * (R(x,C,A) * A) = x * (A * C). [para(34635(a,1),78(a,1,1)),rewrite([16(11,R)]),flip(a)].

34641 R(x,A * C,A) = R(x,C,A). [para(34635(a,1),22987(a,1,1))].

34642 R(x,A,C * A') = R(x,A,C). [para(23049(a,1),34635(a,1,1)),rewrite([16(8,R)]),flip(a)].

34650 R(x,A * C,C') = R(x,C,A). [back_rewrite(27013),rewrite([34641(11)])].

34651 A * R(x,C,A) = R(A * x,C,A). [back_rewrite(26804),rewrite([34641(7)]),flip(a)].

34653 R(R(x,A,C),C,A) = x. [back_rewrite(23050),rewrite([34642(6)])].

34684 C * R(A * x,C,A) = (A * C) * x. [back_rewrite(32704),rewrite([34651(6)])].

34702 (x * A) * (C * A') = C * R(x,A,C). [para(34642(a,1),78(a,1,1)),rewrite([122(9),16(5,R)]),flip(a)].

34704 C' * (A * (x * C)) = R(A * x,A,C). [para(34642(a,1),468(a,2)),rewrite([122(7),122(10),113(6)])].

34708 A * (C * R(x,A,C)) = (A * C) * x. [back_rewrite(33780),rewrite([34702(8)])].

34714 R(x,C,A' * C') = R(x,A,C). [back_rewrite(16328),rewrite([34704(9),34497(8)]),flip(a)].

34790 A' * (C' * (A * x)) = R(C' * x,A,C). [para(34714(a,1),79(a,1)),rewrite([113(2),1659(19),256(15),4610(14),1511(13),11955(14),1511(13,R)

]),flip(a)].

34841 R(R(C * x,A,C),A,C) = A * ((C * A') * x). [para(246(a,1),34431(a,2)),rewrite([34236(7),293(12)])].

34967 C' * R(C * x,A,C) = C * R(C' * x,A,C). [para(2104(a,1),34640(a,1,2,1)),rewrite([16(4),9200(7),113(7),34790(9),293(10),113(13),247(18),

16598(17),34415(17)]),flip(a)].

35019 A * ((C * A') * x) = C * R(x,C,A). [para(34(a,1),34684(a,1,2,1)),rewrite([246(12),293(9)]),flip(a)].

35060 R(R(C * x,A,C),A,C) = C * R(x,C,A). [back_rewrite(34841),rewrite([35019(15)])].

35139 C * R(x,A,C) = R(C * x,A,C). [para(34708(a,1),10(a,1,2)),rewrite([34415(7)]),flip(a)].

35208 C' * R(C * x,A,C) = R(x,A,C). [back_rewrite(34967),rewrite([35139(16),34(13)])].

35330 R(C * R(x,C,A),A,C) = C * x. [para(26864(a,1),35139(a,1,2)),rewrite([16(6),34650(9)]),flip(a)].

35393 C * R(x,C,A) = R(C * x,C,A). [para(35330(a,1),22987(a,1,1)),rewrite([34641(7)]),flip(a)].

35402 R(R(C * x,A,C),A,C) = R(C * x,C,A). [back_rewrite(35060),rewrite([35393(13)])].

35418 R(x,A',A * C) = R(x,C,A). [para(35393(a,1),10(a,1,2)),rewrite([32272(8)])].

35494 C' * R(C * x,C,A) = R(x,C,A). [back_rewrite(32272),rewrite([35418(14)])].

36055 R(R(x,A,C),A,C) = R(x,C,A). [para(35139(a,1),35208(a,1,2,1)),rewrite([35402(10),35494(8)]),flip(a)].

36062 R(R(x,C,A),C,A) = R(x,A,C). [para(36055(a,1),22987(a,1,1)),rewrite([34641(8)])].

36067 $F. [back_rewrite(19),rewrite([36062(7),34653(7)]),xx(a)].

============================== end of proof ==========================

% Proof 1 at 47.68 (+ 0.23) seconds.

% Length of proof is 288.

% Level of proof is 36.

% Maximum clause weight is 32.000.

% Given clauses 1972.

1 R(R(R(x,A,C),A,C),A,C) = x # label(non_clause) # label(goal). [goal].

2 0 * x = x. [assumption].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 A * ((x * y) * A) = (A * x) * (y * A). [assumption].

15 (A * x) * (y * A) = A * ((x * y) * A). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 R(x,y,z) = ((x * y) * z) / (y * z). [assumption].

18 ((x * y) * z) / (y * z) = R(x,y,z). [copy(17),flip(a)].

19 R(R(R(c1,A,C),A,C),A,C) != c1. [deny(1)].

23 x / 0 = x. [para(3(a,1),6(a,1,1))].

28 0 / x = x'. [para(8(a,1),6(a,1,1))].

30 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([28(3)])].

31 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

32 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

34 x * (x' * y) = y. [back_rewrite(4),rewrite([31(1)])].

35 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

39 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

40 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

47 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [para(13(a,1),13(a,1,1,2)),rewrite([13(9)])].

49 (A * x) * A = A * (x * A). [para(2(a,1),15(a,1,2)),rewrite([3(7)])].

50 (A * ((x * y) * A)) / (y * A) = A * x. [para(15(a,1),6(a,1,1))].

51 A * ((x * (y / A)) * A) = (A * x) * y. [para(7(a,1),15(a,1,2)),flip(a)].

53 A * ((A' * x) * A) = x * A. [para(9(a,1),15(a,1,1)),rewrite([2(4)]),flip(a)].

54 (A * x)' * (A * ((x * y) * A)) = y * A. [para(15(a,1),10(a,1,2))].

56 (A * x) * (y * (y * A)) = A * ((x * (y * y)) * A). [para(12(a,1),15(a,1,2))].

57 ((x * A) * (A * ((y * x) * A))) * z = (x * A) * ((A * y) * ((x * A) * z)). [para(15(a,1),13(a,1,1,2))].

58 A * (((x * A) * y) * A) = A * (x * (A * (y * A))). [para(15(a,1),13(a,1))].

59 (A * x) * (y * (z * (y * A))) = A * ((x * (y * (z * y))) * A). [para(13(a,1),15(a,1,2))].

62 C * (x / C) = x. [para(16(a,2),7(a,1))].

63 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

65 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

68 (x * (x * C)) * y = x * (C * (x * y)). [para(16(a,1),13(a,1,1,2))].

69 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

70 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

71 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

73 (A * x) * (A * C) = A * ((x * C) * A). [para(16(a,1),15(a,1,2))].

78 R(x,y,z) * (y * z) = (x * y) * z. [para(18(a,1),7(a,1,1))].

79 R(x / y,y,z) = (x * z) / (y * z). [para(7(a,1),18(a,1,1,1)),flip(a)].

80 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(7(a,1),18(a,1,2))].

82 (x * y') * y = R(x,y',y). [para(8(a,1),18(a,1,2)),rewrite([23(5)])].

85 (x * y) * y' = R(x,y,y'). [para(9(a,1),18(a,1,2)),rewrite([23(5)])].

90 ((x * (y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(12(a,1),18(a,1,2))].

95 (A * ((x * y) * A)) / (x * (y * A)) = R(A,x,y * A). [para(15(a,1),18(a,1,1))].

104 (x / y)' = y / x. [para(7(a,1),32(a,1,2)),flip(a)].

106 x / (y * (z * (y * x))) = (y * (z * y))'. [para(13(a,1),32(a,1,2))].

108 x / (x * C) = C'. [para(16(a,1),32(a,1,2))].

109 C / (C * x) = x'. [para(16(a,2),32(a,1,2))].

113 x / C = C' * x. [para(62(a,1),10(a,1,2)),flip(a)].

120 A * (((A' * x) * y) * A) = x * (y * A). [para(34(a,1),15(a,1,1)),flip(a)].

122 x * (C * x') = C. [para(16(a,2),34(a,1,2))].

123 R(x,x' * y,z) = (y * z) / ((x' * y) * z). [para(34(a,1),18(a,1,1,1)),flip(a)].

127 (x * C) * (C' * ((x * C) * y)) = ((x * C) * x) * y. [para(63(a,1),13(a,1,1,2)),flip(a)].

136 (x / y) * (y / x) = 0. [para(104(a,1),8(a,1,1))].

137 (x / y) * ((y / x) * z) = z. [para(104(a,1),10(a,1,1))].

138 (x * y) / ((z * x) * y) = R(z,x,y)'. [para(18(a,1),104(a,1,1)),flip(a)].

141 R(x,x' * y,z) = R(x',y,z)'. [back_rewrite(123),rewrite([138(8)])].

144 x' / x = x' * x'. [para(8(a,1),35(a,1,1,2)),rewrite([3(3)])].

145 x / x' = x * x. [para(9(a,1),35(a,1,1,2)),rewrite([3(2)])].

150 (A * (x * (A * (x * A)))) / A = (A * x) * (A * x). [para(15(a,1),35(a,1,1)),rewrite([13(6)])].

158 (C' * x)' = C / x. [para(34(a,1),109(a,1,2)),flip(a)].

165 C' * ((x * y) * (C * y')) = R(x,y,C * y'). [para(122(a,1),18(a,1,2)),rewrite([113(7)])].

172 (x * x)' = x' * x'. [para(145(a,1),104(a,1,1)),rewrite([144(4)])].

191 ((x / y) * (z * x)) / y = (x / y) * (z * (x / y)). [para(7(a,1),39(a,1,1,2,2))].

192 x * ((y / (x * z)) * x) = (x * y) / z. [para(7(a,1),39(a,1,1,2)),flip(a)].

194 x * ((x * y)' * x) = x / y. [para(8(a,1),39(a,1,1,2)),rewrite([3(2)]),flip(a)].

195 (x * y) / x' = x * (y * x). [para(9(a,1),39(a,1,1,2,2)),rewrite([3(2)])].

201 ((A * x) * (y * (A * ((x * z) * A)))) / (z * A) = (A * x) * (y * (A * x)). [para(15(a,1),39(a,1,1,2,2))].

202 (x * (A * ((y * x) * A))) / A = x * ((A * y) * x). [para(15(a,1),39(a,1,1,2))].

231 (x' * y) * x = x' * (y / x'). [para(8(a,1),40(a,1,2,2)),rewrite([3(5)]),flip(a)].

232 (x * y) * x' = x * (y / x). [para(9(a,1),40(a,1,2,2)),rewrite([3(3)]),flip(a)].

233 (x / y) * (y * z) = y' * ((y * x) * z). [para(40(a,1),10(a,1,2)),flip(a)].

234 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),40(a,1,2,2)),flip(a)].

240 (x / C') * y = (C * x) * y. [para(40(a,1),16(a,1)),rewrite([113(5),234(9),16(12,R),34(12)]),flip(a)].

242 (C * x) * y = (x * C) * y. [para(16(a,1),40(a,2,1)),rewrite([113(3),234(7),240(7),34(8)])].

246 (x * y) * (x' * z) = x * ((y / x) * z). [para(34(a,1),40(a,1,2,2)),flip(a)].

247 (C' * x) * (y * C) = C' * ((C * x) * y). [para(63(a,1),40(a,1,2,2)),rewrite([240(6)]),flip(a)].

249 (x * y) * (C * x') = x * (C * (y / x)). [para(122(a,1),40(a,1,2,2)),rewrite([16(3,R)]),flip(a)].

250 (C * x) * (C / x) = C * C. [para(122(a,1),40(a,1,2)),rewrite([113(7),158(9)]),flip(a)].

256 x / A' = x * A. [back_rewrite(53),rewrite([231(6),34(8)])].

259 R(x,A',A) = x. [para(256(a,1),6(a,1)),rewrite([82(5)])].

260 R(x,A,A') = x. [para(256(a,1),7(a,1,1)),rewrite([85(5)])].

261 (x * A)' = A' / x. [para(256(a,1),104(a,1,1))].

263 (x * A) * (A' / x) = 0. [para(256(a,1),136(a,1,1))].

266 A' / (x / A) = x'. [para(7(a,1),261(a,1,1)),flip(a)].

270 (A * C)' = C' * A'. [para(16(a,1),261(a,1,1)),rewrite([113(8)])].

291 x' * (x / A) = A'. [para(266(a,1),7(a,1,1))].

293 x / A = x * A'. [para(291(a,1),10(a,1,2)),rewrite([30(2)]),flip(a)].

295 ((x * y') * (y * A')) * A = R(x,y',y * A'). [para(291(a,1),18(a,1,2)),rewrite([293(4),256(9),293(11)])].

297 (x * (A * ((y * x) * A))) * A' = x * ((A * y) * x). [back_rewrite(202),rewrite([293(8)])].

298 A * ((x * (A * (x * A))) * A') = (A * x) * (A * x). [back_rewrite(150),rewrite([293(9),232(10),293(8)])].

299 A * ((x * (y * A')) * A) = (A * x) * y. [back_rewrite(51),rewrite([293(3)])].

336 (x * (y * (x * A))) * A' = x * (y * x). [para(293(a,1),39(a,1))].

337 (A * x) * (A * x) = A * (x * (A * x)). [back_rewrite(298),rewrite([336(9)]),flip(a)].

393 (x * (x * A)) * (A' / (x * x)) = 0. [para(12(a,1),263(a,1,1))].

397 (x * (y * A)) * (A' / y) = R(x,y * A,A' / y). [para(263(a,1),18(a,1,2)),rewrite([23(9)])].

467 (A * x) * (A * (y * A)) = A * ((x * (A * y)) * A). [para(49(a,1),15(a,1,2))].

468 (A * (x * (A * y))) / (A * y) = R(A * x,A,y). [para(49(a,1),18(a,1,1,1)),rewrite([13(5)])].

469 R(A,x,A) = A. [para(49(a,1),18(a,1,1)),rewrite([6(7)]),flip(a)].

470 ((x * (A * y)) * A) / (A * (y * A)) = R(x,A * y,A). [para(49(a,1),18(a,1,2))].

471 A / (A * (x * A)) = (A * x)'. [para(49(a,1),32(a,1,2))].

473 (A * (x * A))' = A' / (A * x). [para(49(a,1),261(a,1,1))].

474 A * (x * (A * (A' / (A * x)))) = 0. [para(49(a,1),263(a,1,1)),rewrite([13(10)])].

493 (C * x)' = (x * C)'. [para(65(a,1),109(a,1,2)),rewrite([109(6)]),flip(a)].

523 (x * (y * (z * (y * (x * u))))) / ((y * (z * (y * x))) * u) = R(x,y * (z * (y * x)),u). [para(47(a,1),18(a,1,1))].

540 x * (C * (y * (z * y))) = x * (y * (z * (y * C))). [para(122(a,1),47(a,2,2,2,2,2)),rewrite([249(8),39(5)])].

568 (C * x) * (x * C)' = 0. [para(493(a,1),9(a,1,2))].

619 (A * (x * A)) / (y * A) = A * (x / y). [para(7(a,1),50(a,1,1,2,1))].

620 (A * A) / (x * A) = A * x'. [para(8(a,1),50(a,1,1,2,1)),rewrite([2(4)])].

749 A / x = A * x'. [para(54(a,1),39(a,1,1,2)),rewrite([619(8),32(3),194(10)]),flip(a)].

762 A * (A' / (A * x)) = (A * x)'. [back_rewrite(471),rewrite([749(6),473(6)])].

785 A * (x * (A * x)') = 0. [back_rewrite(474),rewrite([762(8)])].

786 A * (A' / x) = x'. [para(749(a,1),32(a,1)),rewrite([261(4)])].

788 A * (C' * A') = C'. [para(749(a,1),108(a,1)),rewrite([270(5)])].

794 A' / x = A' * x'. [para(786(a,1),10(a,1,2)),flip(a)].

807 (x * (y * A)) * (A' * y') = R(x,y * A,A' * y'). [back_rewrite(397),rewrite([794(6),794(13)])].

809 (x * (x * A)) * (A' * (x' * x')) = 0. [back_rewrite(393),rewrite([794(7),172(7)])].

824 (x * A)' = A' * x'. [back_rewrite(261),rewrite([794(6)])].

858 (x * (A * ((y * (x * x)) * A))) / (x * A) = x * ((A * y) * x). [para(56(a,1),39(a,1,1,2))].

880 x * (A * x)' = A'. [para(785(a,1),10(a,1,2)),rewrite([3(4)]),flip(a)].

882 R(x,A * x,(A * x)') = x. [para(785(a,1),13(a,2,2)),rewrite([85(7),3(8)])].

889 (A * x)' = x' * A'. [para(880(a,1),10(a,1,2)),flip(a)].

893 R(A',x,x') = A'. [para(34(a,1),880(a,1,2,1)),rewrite([85(5)])].

899 R(x,A * x,x' * A') = x. [back_rewrite(882),rewrite([889(5)])].

945 ((x * C) * A) * ((A * C') * (((x * C) * A) * y)) = (((x * C) * A) * (A * (x * A))) * y. [para(63(a,1),57(a,1,1,2,2,1)),flip(a)].

971 (A * C) * (A * x) = A * (A * (x * C)). [para(568(a,1),57(a,2,2,2)),rewrite([16(3),467(10),889(14),13(16),788(14),232(10),113(8),34(10),1

6(9),3(13)]),flip(a)].

987 R(A',x',x) = A'. [para(30(a,1),893(a,1,3))].

1016 (A' * x')' = x * A. [para(794(a,1),104(a,1,1)),rewrite([256(8)])].

1021 ((x * A) * y) * A = x * (A * (y * A)). [para(58(a,1),10(a,1,2)),rewrite([10(10)]),flip(a)].

1071 (A' * x)' = x' * A. [para(30(a,1),1016(a,1,1,2))].

1079 A * ((x * ((y * A') * (z * (y * A')))) * A) = (A * x) * ((y * A') * (z * y)). [para(7(a,1),59(a,1,2,2,2)),rewrite([293(4),293(11),293(1

4)]),flip(a)].

1276 ((x * C) * (y * ((C * x) * z))) / z = (C * x) * (y * (C * x)). [para(242(a,1),39(a,1,1))].

1277 (C * x) * (y * (C * x)) = (x * C) * (y * (x * C)). [para(242(a,2),39(a,1,1,2,2)),rewrite([1276(8)])].

1336 (C * x)' * (C * C) = C / x. [para(250(a,1),10(a,1,2))].

1358 x * (C * y) = x * (y * C). [para(69(a,1),10(a,1,2)),rewrite([10(8)]),flip(a)].

1382 C * (x * C) = x * (C * C). [para(69(a,2),39(a,1,1)),rewrite([113(8),10(9)]),flip(a)].

1419 C * (C * (C * x)') = C / x. [back_rewrite(1336),rewrite([1382(7,R),16(6,R)])].

1511 C' * x = x * C'. [para(8(a,1),71(a,2,2,2)),rewrite([34(8),3(7)]),flip(a)].

1538 (x * C')' = C / x. [para(71(a,2),158(a,1,1)),rewrite([34(8),16(9,R),9(9),3(7)])].

1659 C * (x * C') = x. [para(1511(a,1),10(a,1,2)),rewrite([30(3)])].

1663 (x * (x * C')) * y = x * (C' * (x * y)). [para(1511(a,1),13(a,1,1,2))].

1699 x / C' = C * x. [para(7(a,1),1659(a,1,2)),flip(a)].

1724 (C * x)' = C' / x. [para(1699(a,1),104(a,1,1))].

1730 (C' / x) * ((C * x) * y) = y. [para(1699(a,1),137(a,1,2,1))].

1769 C * (C * (C' / x)) = C / x. [back_rewrite(1419),rewrite([1724(5)])].

1828 (x * C)' = C' / x. [back_rewrite(493),rewrite([1724(3)]),flip(a)].

1934 (x * C') * ((C / x) * y) = y. [para(1538(a,1),34(a,1,2,1))].

2041 R(x,C,y) * (y * C) = (x * C) * y. [para(16(a,1),78(a,1,2))].

2104 R((x / y) / z,z,y) = x / (z * y). [para(7(a,1),79(a,2,1))].

2120 R(x / y,y,C) = (C * x) / (y * C). [para(16(a,2),79(a,2,1))].

2149 R((A * x) / y,y,A) = A * (x / y). [para(49(a,1),79(a,2,1)),rewrite([619(12)])].

2150 R(x / (A * y),A * y,A) = (x * A) / (A * (y * A)). [para(49(a,1),79(a,2,2))].

2249 (C' * (x * (C * y))) / y = R(x,C * y,C'). [para(1511(a,2),80(a,1,1)),rewrite([1699(5),1699(10)])].

2273 (x * y')' * R(x,y',y) = y. [para(82(a,1),10(a,1,2))].

2814 C' * (C' * (x * (C * C))) = R(x,C * C,C'). [para(122(a,1),90(a,1,2)),rewrite([1511(7,R),113(9)])].

3952 (x * (C * y)) / (y * C) = x. [para(1358(a,2),6(a,1,1))].

3953 (x / (C * y)) * (y * C) = x. [para(1358(a,1),7(a,1))].

4120 C' * (x * (C * C)) = x * C. [para(1382(a,1),10(a,1,2))].

4231 R(x,C * C,C') = x. [back_rewrite(2814),rewrite([4120(9),63(5)]),flip(a)].

4256 (x * (y * x))' = x' / (x * y). [para(9(a,1),106(a,1,2,2,2)),rewrite([3(3)]),flip(a)].

4419 x / (C * C) = C' * (x * C'). [para(4231(a,1),79(a,1)),rewrite([1511(13,R),1382(13,R),16(12,R),9(12),3(10),113(9)])].

4610 (x * (A' * y)) * A = (x * A') * (y * A). [para(13(a,1),120(a,1,2,1)),rewrite([231(10),256(10),34(11)])].

5089 ((x * C) * x) * ((C' / x) * y) = (x * C) * (C' * y). [para(34(a,1),127(a,1,2,2)),rewrite([1828(12)]),flip(a)].

6174 x' / (x * y) = x' * (y' * x'). [para(10(a,1),194(a,1,2,1,1)),flip(a)].

6182 x / (C * x') = x * (C' * x). [para(122(a,1),194(a,1,2,1,1)),flip(a)].

6208 (A * x) / (A * C) = A * (C' * (x * A')). [para(73(a,1),194(a,1,2,1,1)),rewrite([4256(9),6174(9),1828(7),13(14),10(12),7(8),246(8),293(3

),1511(7,R)]),flip(a)].

6502 x / (C' / x) = (x * C) * x. [para(63(a,1),195(a,2,2)),rewrite([1511(5,R),63(5),1828(3)])].

6518 x / (C / x) = (x * C') * x. [para(1659(a,1),195(a,2,2)),rewrite([16(5,R),1659(5),1538(4)])].

6745 R(x,A,A)' = x'. [para(824(a,1),620(a,2,2)),rewrite([138(8),34(10)])].

6792 R(x,A,A) = x. [para(6745(a,1),30(a,1,1)),rewrite([30(2)]),flip(a)].

6793 (x * A) * A = x * (A * A). [para(6792(a,1),78(a,1,1)),flip(a)].

6823 (x * (A * A)) * A' = x * A. [para(6793(a,1),6(a,1,1)),rewrite([293(6)])].

6830 (A * x) * (y * (A * A)) = A * ((x * (y * A)) * A). [para(6793(a,1),15(a,1,2))].

6831 A * ((x * (A * A)) * A) = A * (x * (A * (A * A))). [para(6793(a,1),15(a,2,2,1)),rewrite([13(8)]),flip(a)].

6875 (x * (A * A)) * A = (x * A) * (A * A). [para(6793(a,1),6793(a,1,1))].

6893 A * ((x * A) * (A * A)) = A * (x * (A * (A * A))). [back_rewrite(6831),rewrite([6875(7)])].

7049 R(A' * x,x,x') = A' * x. [para(34(a,1),899(a,1,2)),rewrite([1071(7),85(9),260(8)])].

7806 ((x * C') * x) * ((C / x) * y) = (x * C') * (C * y). [para(1934(a,1),68(a,2,2,2)),rewrite([16(8,R),1659(8)])].

8897 (C * x) * (y * (C * x)) = C * ((C * x) * (y * x)). [para(191(a,1),1699(a,1)),rewrite([1699(3),1699(5),1699(10)])].

9118 (x * C) * (y * (x * C)) = C * ((C * x) * (y * x)). [back_rewrite(1277),rewrite([8897(6)]),flip(a)].

9200 (x / (y * z)) * y = y' * ((y * x) / z). [para(192(a,1),10(a,1,2)),flip(a)].

9204 (A * x) * ((y / (A * ((x * z) * A))) * (A * x)) = ((A * x) * y) / (z * A). [para(15(a,1),192(a,1,2,1,2))].

9339 (C * x) / (C * (C' / y)) = C * (C * (x / (C / y))). [para(1769(a,1),192(a,1,2,1,2)),rewrite([16(6,R)]),flip(a)].

9954 (A * x) * (y * (A * x)) = A * (x * ((y * A) * x)). [para(9(a,1),201(a,1,1,2,2,2,1)),rewrite([2(6),6830(7),619(11),195(6)]),flip(a)].

9956 (A * x) * x = A * (x * x). [para(10(a,1),201(a,1,1,2)),rewrite([15(6),619(9),35(4),10(10)]),flip(a)].

10077 ((A * C) * (x * (A * ((C / y) * A)))) / ((C * (C' / y)) * A) = C * (A * ((C * x) * A)). [para(1769(a,1),201(a,1,1,2,2,2,1)),rewrite([9

118(27),16(23),15(26)])].

10114 A * (x * ((A' * ((A * y) / ((x * z) * A))) * x)) = ((A * x) * y) / (z * A). [back_rewrite(9204),rewrite([9954(12),9200(9)])].

10225 R(A,x,A * (A * A)) = A. [para(9956(a,1),95(a,1,2,2)),rewrite([6875(7),6893(8),6(15),12(7)]),flip(a)].

10333 R(A',x,A * (A * A))' = A. [para(10225(a,1),141(a,1)),flip(a)].

11955 (x * A') * (A * y) = A' * ((A * x) * y). [para(293(a,1),233(a,1,1))].

11964 (A * x') * (x * y) = x' * ((x * A) * y). [para(749(a,1),233(a,1,1))].

12145 (x * C) * (C' * y) = C * ((C' * x) * y). [para(6502(a,1),233(a,1,1)),rewrite([5089(8),104(10),1699(9),7(12),246(12),113(9)])].

12146 (x * C') * (C * y) = C' * ((C * x) * y). [para(6518(a,1),233(a,1,1)),rewrite([7806(8),104(9),113(8),7(12),234(12),1699(11)])].

12312 R(A',x,A * (A * A)) = A'. [para(10333(a,1),30(a,1,1)),flip(a)].

12316 C' * (A' * (C * (A * x))) = R(x,A',A * C). [para(10333(a,1),165(a,1,2,2,2)),rewrite([12312(10),16(8),11955(9),16(8,R),12312(18),12312(

21),30(16),16(15)])].

13836 (x * C') * (y * C) = C' * ((C * x) * y). [para(71(a,2),247(a,1,1)),rewrite([34(8),16(13,R),9(13),3(11)])].

16312 (C' * ((C * x) * A')) * A = R(x,C',C * A'). [para(16(a,1),295(a,1,1,2)),rewrite([16(7,R),12146(8)])].

16328 A' * (C' * (A * (x * C))) = R(x,C,A' * C'). [para(1511(a,1),295(a,1,1,2)),rewrite([30(3),4610(10),1511(9),11955(10),1511(9,R),30(13),1

511(16)])].

16405 (x * (A * (y * A))) * A' = x * ((A * (y / x)) * x). [para(7(a,1),297(a,1,1,2,2,1))].

16598 (x * (y * A')) * A = A' * ((A * x) * y). [para(299(a,1),10(a,1,2)),flip(a)].

16636 (A * (x / y)) * y = y' * ((y * A) * x). [para(233(a,1),299(a,1,2,1)),rewrite([16598(9),11964(8),34(10)]),flip(a)].

16657 A' * (C' * ((A * C) * x)) = R(x,C',C * A'). [back_rewrite(16312),rewrite([16598(10),12146(9),16(7)])].

16673 (x * (A * (y * A))) * A' = (x * A) * y. [back_rewrite(16405),rewrite([16636(12),34(14)])].

17618 R(A,x,A * x) = A. [para(337(a,1),18(a,1,1)),rewrite([6(9)]),flip(a)].

17677 R(A',x,x)' = A. [para(34(a,1),17618(a,1,3)),rewrite([141(5)])].

17686 R(A',x,x) = A'. [para(17677(a,1),30(a,1,1)),flip(a)].

17687 (A' * x) * x = A' * (x * x). [para(17686(a,1),78(a,1,1)),flip(a)].

21527 x * (C' * (x * ((C * x') * y))) = (C' / x') * (R(C,x',x) * y). [para(6182(a,1),233(a,1,1)),rewrite([13(9),1724(13),82(17)])].

21843 R(A' * x',x',x) = A' * x'. [para(30(a,1),7049(a,1,3))].

22986 (A * ((x * C) * (A * A))) / (A * (A * C)) = R(A * x,A * C,A). [para(73(a,1),470(a,1,1,1)),rewrite([13(8),16(12)])].

22987 R(R(x,A,y),A * y,A) = x. [para(78(a,1),470(a,1,1,1)),rewrite([1021(5),6(10)]),flip(a)].

23049 R(R(x,A,A' * y),y,A) = x. [para(34(a,1),22987(a,1,2))].

23765 R(x,x * A,A' * x') = x. [para(17687(a,1),2273(a,1,1,1)),rewrite([1071(7),172(4),30(2),30(2),12(3),21843(9),807(8)])].

24502 x * (C' * y) = x * (y * C'). [para(8(a,1),540(a,2,2,2,2)),rewrite([34(8),3(8)]),flip(a)].

25344 (A * x) / (y * A) = A * ((x * A') / y). [para(7(a,1),619(a,1,1,2)),rewrite([293(8)])].

25346 (x * A) / (A * (y * A)) = (x / y) * A'. [para(619(a,1),104(a,1,1)),rewrite([889(4),104(2)]),flip(a)].

25390 ((A * x) * y) / (z * A) = A * ((x * (y * A')) / z). [back_rewrite(10114),rewrite([25344(9),10(11),9200(7),34(9)]),flip(a)].

25428 R(x / (A * y),A * y,A) = (x / y) * A'. [back_rewrite(2150),rewrite([25346(14)])].

25430 C * (A * ((C * x) * A)) = A * (C * (C * (x * A))). [back_rewrite(10077),rewrite([25390(19),16673(12),9339(14),6(11)]),flip(a)].

25535 (x * C) * (y * C') = C * ((C' * x) * y). [para(24502(a,1),242(a,2)),rewrite([246(6),113(3)]),flip(a)].

26799 R(A * R(x,C,A),A,C) = A * x. [para(2041(a,1),468(a,1,1,2)),rewrite([6208(10),85(10),260(9),63(6)]),flip(a)].

26804 R(A * x,A * C,A) = A * R(x,C,A). [para(26799(a,1),22987(a,1,1))].

26806 (A * ((x * C) * (A * A))) / (A * (A * C)) = A * R(x,C,A). [back_rewrite(22986),rewrite([26804(21)])].

26864 R(R(x,C * y,C'),y,C) = x. [para(3952(a,1),2104(a,2)),rewrite([113(5),2249(7)])].

27013 R(x,A * C,C') = R(x,A * C,A). [para(26864(a,1),22987(a,1,1)),rewrite([16(8)]),flip(a)].

27522 (C * x) / (A * C) = R(x * A',A,C). [para(293(a,1),2120(a,1,1)),flip(a)].

29284 R(x',A' * x,x') = x'. [para(809(a,1),523(a,1,1,2,2)),rewrite([3(5),807(14),23765(13),85(9),893(8),256(7),82(6),259(5),807(12),23765(11

)]),flip(a)].

29288 R(x,A' * x',x) = x. [para(30(a,1),29284(a,1,1)),rewrite([30(6),30(7)])].

29312 (x * (A' * x')) * x = x * A'. [para(29288(a,1),78(a,1,1)),rewrite([82(5),987(4)]),flip(a)].

29976 C * (C * (A * (C' * (x * C')))) = R(A * x,A,C). [para(3953(a,1),858(a,1,1,2,2,1)),rewrite([16(9),27522(10),232(7),293(5),85(6),260(5),

4419(11),16(16,R)]),flip(a)].

29977 C * (C * (A * (C' * x))) = A * ((x * A) * (C * A')). [para(247(a,1),858(a,1,1,2,2,1)),rewrite([16(8,R),10(9),25430(8),16(11),6208(12),

70(12),10(13),16(17,R)]),flip(a)].

29983 A * (((x * C') * A) * (C * A')) = R(A * x,A,C). [back_rewrite(29976),rewrite([29977(12)])].

31306 A * (A * (C * (A' * x))) = (A * C) * x. [para(34(a,1),971(a,1,2)),rewrite([16(11,R)]),flip(a)].

32157 C' * ((A * C) * (x * C)) = C * (A * x). [para(1730(a,1),1079(a,1,2,1)),rewrite([16598(8),16(7,R),34(9),256(10),1511(9),1663(18),21527(

18),256(9),1511(8),259(13),12146(13),16(9)]),flip(a)].

32245 x / (A * (A * C)) = (C' * (x * A')) * A'. [para(2104(a,1),27013(a,2)),rewrite([293(2),27013(13),25428(12),113(5),49(14),16(13)]),flip(

a)].

32247 C' * ((A * C) * x) = A * R(x,C,A). [back_rewrite(26806),rewrite([32245(14),232(13),293(11),6823(12),16673(12),1511(4),13836(7),16(5)])

].

32248 A * R(x * C,C,A) = C * (A * x). [back_rewrite(32157),rewrite([32247(9)])].

32253 R(x,C',C * A') = R(x,C,A). [back_rewrite(16657),rewrite([32247(9),10(8)]),flip(a)].

32259 A' * (C * (A * x)) = R(C * x,C,A). [para(32253(a,1),79(a,1)),rewrite([1699(3),10(17),256(13),16598(12),16(11,R)]),flip(a)].

32272 C' * R(C * x,C,A) = R(x,A',A * C). [back_rewrite(12316),rewrite([32259(9)])].

32704 C * (A * R(x,C,A)) = (A * C) * x. [para(29312(a,1),945(a,1,1,1)),rewrite([82(6),259(5),1659(12),16(9,R),82(11),259(10),12146(8),16(6),

32247(8),1659(14),16(11,R),82(13),259(12),1659(16),8(13),3(11),16(10)])].

33725 C * (A * (C' * x)) = A * R(x,C,A). [para(7(a,1),32248(a,1,2,1)),rewrite([113(9)]),flip(a)].

33764 R(C * (A * x),A,C) = A * (x * C). [para(32248(a,1),26799(a,1,1))].

33780 A * ((x * A) * (C * A')) = (A * C) * x. [back_rewrite(29977),rewrite([33725(8),32704(7)]),flip(a)].

33788 C * ((A * C') * x) = R(A * x,A,C). [back_rewrite(29983),rewrite([33780(12),25535(7),1511(5)])].

34236 A * (C * (A' * x)) = R(C * x,A,C). [para(34(a,1),33764(a,1,1,2)),rewrite([16(11,R)]),flip(a)].

34252 A * R(C * x,A,C) = (A * C) * x. [back_rewrite(31306),rewrite([34236(8)])].

34415 A' * ((A * C) * x) = R(C * x,A,C). [para(34252(a,1),10(a,1,2))].

34420 A * R(x,A,C) = R(A * x,A,C). [para(34(a,1),34252(a,1,2,1)),rewrite([12145(12),1511(10),33788(12)])].

34431 R(A * (C * x),A,C) = (A * C) * x. [para(242(a,2),34252(a,2)),rewrite([34420(7),16(10)])].

34496 R(A * x,A,C) / R(x,A,C) = A. [para(34420(a,1),6(a,1,1))].

34497 A' * R(A * x,A,C) = R(x,A,C). [para(34420(a,1),10(a,1,2))].

34581 (A * x) / R(R(x,C,A),A,C) = A. [para(26799(a,1),34496(a,1,1))].

34603 A * (x / R(R(x,C,A),A,C)) = A. [para(34581(a,1),2149(a,1,1)),rewrite([469(9)]),flip(a)].

34613 x / R(R(x,C,A),A,C) = 0. [para(34603(a,1),10(a,1,2)),rewrite([8(4)]),flip(a)].

34635 R(R(x,C,A),A,C) = x. [para(34613(a,1),7(a,1,1)),rewrite([2(8)])].

34640 C * (R(x,C,A) * A) = x * (A * C). [para(34635(a,1),78(a,1,1)),rewrite([16(11,R)]),flip(a)].

34641 R(x,A * C,A) = R(x,C,A). [para(34635(a,1),22987(a,1,1))].

34642 R(x,A,C * A') = R(x,A,C). [para(23049(a,1),34635(a,1,1)),rewrite([16(8,R)]),flip(a)].

34650 R(x,A * C,C') = R(x,C,A). [back_rewrite(27013),rewrite([34641(11)])].

34651 A * R(x,C,A) = R(A * x,C,A). [back_rewrite(26804),rewrite([34641(7)]),flip(a)].

34684 C * R(A * x,C,A) = (A * C) * x. [back_rewrite(32704),rewrite([34651(6)])].

34702 (x * A) * (C * A') = C * R(x,A,C). [para(34642(a,1),78(a,1,1)),rewrite([122(9),16(5,R)]),flip(a)].

34704 C' * (A * (x * C)) = R(A * x,A,C). [para(34642(a,1),468(a,2)),rewrite([122(7),122(10),113(6)])].

34708 A * (C * R(x,A,C)) = (A * C) * x. [back_rewrite(33780),rewrite([34702(8)])].

34714 R(x,C,A' * C') = R(x,A,C). [back_rewrite(16328),rewrite([34704(9),34497(8)]),flip(a)].

34790 A' * (C' * (A * x)) = R(C' * x,A,C). [para(34714(a,1),79(a,1)),rewrite([113(2),1659(19),256(15),4610(14),1511(13),11955(14),1511(13,R)

]),flip(a)].

34841 R(R(C * x,A,C),A,C) = A * ((C * A') * x). [para(246(a,1),34431(a,2)),rewrite([34236(7),293(12)])].

34967 C' * R(C * x,A,C) = C * R(C' * x,A,C). [para(2104(a,1),34640(a,1,2,1)),rewrite([16(4),9200(7),113(7),34790(9),293(10),113(13),247(18),

16598(17),34415(17)]),flip(a)].

35019 A * ((C * A') * x) = C * R(x,C,A). [para(34(a,1),34684(a,1,2,1)),rewrite([246(12),293(9)]),flip(a)].

35060 R(R(C * x,A,C),A,C) = C * R(x,C,A). [back_rewrite(34841),rewrite([35019(15)])].

35139 C * R(x,A,C) = R(C * x,A,C). [para(34708(a,1),10(a,1,2)),rewrite([34415(7)]),flip(a)].

35208 C' * R(C * x,A,C) = R(x,A,C). [back_rewrite(34967),rewrite([35139(16),34(13)])].

35330 R(C * R(x,C,A),A,C) = C * x. [para(26864(a,1),35139(a,1,2)),rewrite([16(6),34650(9)]),flip(a)].

35393 C * R(x,C,A) = R(C * x,C,A). [para(35330(a,1),22987(a,1,1)),rewrite([34641(7)]),flip(a)].

35402 R(R(C * x,A,C),A,C) = R(C * x,C,A). [back_rewrite(35060),rewrite([35393(13)])].

35418 R(x,A',A * C) = R(x,C,A). [para(35393(a,1),10(a,1,2)),rewrite([32272(8)])].

35494 C' * R(C * x,C,A) = R(x,C,A). [back_rewrite(32272),rewrite([35418(14)])].

36055 R(R(x,A,C),A,C) = R(x,C,A). [para(35139(a,1),35208(a,1,2,1)),rewrite([35402(10),35494(8)]),flip(a)].

36057 $F. [back_rewrite(19),rewrite([36055(7),34635(7)]),xx(a)].

============================== end of proof ==========================

% Proof 1 at 3.04 (+ 0.02) seconds.

% Length of proof is 253.

% Level of proof is 23.

% Maximum clause weight is 30.000.

% Given clauses 467.

1 L(L(L(x,C,A),C,A),C,A) = x # label(non_clause) # label(goal). [goal].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 C * ((x * y) * C) = (C * x) * (y * C). [assumption].

15 (C * x) * (y * C) = C * ((x * y) * C). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 L(x,y,z) = (z * y)' * (z * (y * x)). [assumption].

18 (x * y)' * (x * (y * z)) = L(z,y,x). [copy(17),flip(a)].

19 L(L(L(c1,C,A),C,A),C,A) != c1. [deny(1)].

20 (C * x) * (y * C) = C * (C * (x * y)). [back_rewrite(15),rewrite([16(9,R)])].

29 0 / x = x'. [para(8(a,1),6(a,1,1))].

31 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([29(3)])].

32 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

33 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

35 x * (x' * y) = y. [back_rewrite(4),rewrite([32(1)])].

36 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

40 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

41 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

43 (x * (y * x))' * (x * (y * (x * z))) = z. [para(13(a,1),10(a,1,2))].

45 (x * (y * (x * (x * (y * x))))) * z = x * (y * (x * (x * (y * (x * z))))). [para(13(a,1),12(a,1,1)),rewrite([13(11),13(12)])].

52 C * (x / C) = x. [para(16(a,2),7(a,1))].

53 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

54 x' * (C * x) = C. [para(16(a,2),10(a,1,2))].

55 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

57 C * (x * x) = x * (C * x). [para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].

58 (x * (x * C)) * y = x * (C * (x * y)). [para(16(a,1),13(a,1,1,2))].

59 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

60 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

61 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

67 x' * ((x / y) * (y * z)) = L(z,y,x / y). [para(7(a,1),18(a,1,1,1))].

68 L(x,y / x,z) = (z * (y / x))' * (z * y). [para(7(a,1),18(a,1,2,2)),flip(a)].

71 L(x,x',y) = (y * x')' * y. [para(8(a,1),18(a,1,2,2)),rewrite([3(5)]),flip(a)].

72 L(x,y,(y * x)') = ((y * x)' * y)'. [para(8(a,1),18(a,1,2)),rewrite([3(6)]),flip(a)].

74 L(x',x,y) = (y * x)' * y. [para(9(a,1),18(a,1,2,2)),rewrite([3(4)]),flip(a)].

75 (x * y) * L(z,y,x) = x * (y * z). [para(18(a,1),10(a,1,2)),rewrite([31(3)])].

76 x' * (y' * ((y * x) * z)) = L(z,y * x,y'). [para(10(a,1),18(a,1,1,1))].

77 L(x * y,x',z) = (z * x')' * (z * y). [para(10(a,1),18(a,1,2,2)),flip(a)].

81 (x * (y * (x * z)))' * (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(13(a,1),18(a,1,1,1)),rewrite([13(8)])].

82 (x * (y * (z * y)))' * (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(13(a,1),18(a,1,2,2))].

83 (x * C)' * (C * (x * y)) = L(y,x,C). [para(16(a,1),18(a,1,1,1))].

87 L(x,y,z)' * ((z * y)' * ((z * (y * x)) * u)) = L(u,z * (y * x),(z * y)'). [para(18(a,1),18(a,1,1,1))].

89 ((x * y)' * x)' * L(z,y,x) = L(y * z,x,(x * y)'). [para(18(a,1),18(a,1,2))].

91 C * (C * (x * (y / C))) = (C * x) * y. [para(7(a,1),20(a,1,2)),flip(a)].

96 (C * x) * (y * (y * C)) = C * (C * (x * (y * y))). [para(12(a,1),20(a,1,2))].

102 (C * x) * (C * y) = C * (C * (x * y)). [para(16(a,2),20(a,1,2))].

104 (x * (C * y))' * (x * (C * (C * (y * z)))) = L(z * C,C * y,x). [para(20(a,1),18(a,1,2,2))].

105 ((C * x) * y)' * (C * (C * (x * y))) = L(C,y,C * x). [para(20(a,1),18(a,1,2))].

107 x' * C = C * x'. [para(16(a,2),32(a,2)),rewrite([32(2)])].

108 (x / y)' = y / x. [para(7(a,1),33(a,1,2)),flip(a)].

112 C / (C * x) = x'. [para(16(a,2),33(a,1,2))].

113 (x * (y * z)) / L(z,y,x) = x * y. [para(18(a,1),33(a,1,2)),rewrite([31(7)])].

118 x / C = C' * x. [para(52(a,1),10(a,1,2)),flip(a)].

123 C * (C * (x * (C' * y))) = (C * x) * y. [back_rewrite(91),rewrite([118(4)])].

127 x * (C * x') = C. [para(16(a,2),35(a,1,2))].

128 x' * (y * ((y' * x) * z)) = L(z,y' * x,y). [para(35(a,1),18(a,1,1,1))].

129 L(x' * y,x,z) = (z * x)' * (z * y). [para(35(a,1),18(a,1,2,2)),flip(a)].

133 C * (x * (C' * x)) = x * x. [para(53(a,1),13(a,2,2)),rewrite([16(6,R)])].

136 (x * C')' * (x * y) = L(y * C,C',x). [para(53(a,1),18(a,1,2,2))].

141 L(x,C,x') = C * (x' * C)'. [para(54(a,1),18(a,1,2)),rewrite([16(6,R)]),flip(a)].

145 x' / x = x' * x'. [para(8(a,1),36(a,1,1,2)),rewrite([3(3)])].

146 x / x' = x * x. [para(9(a,1),36(a,1,1,2)),rewrite([3(2)])].

150 (C * (x * C)) / x = C * C. [para(16(a,1),36(a,1,1,2))].

151 C' * (x * (C * x)) = x * x. [para(16(a,2),36(a,1,1,2)),rewrite([118(5)])].

155 (x * y) / (x' * y) = x * x. [para(35(a,1),36(a,1,1,2))].

158 (x / y) * (y / x) = 0. [para(108(a,1),8(a,1,1))].

164 (C' * x)' = C / x. [para(35(a,1),112(a,1,2)),flip(a)].

176 (x * x)' = x' * x'. [para(146(a,1),108(a,1,1)),rewrite([145(4)])].

185 (C' * x) * (C / x) = 0. [para(118(a,1),158(a,1,1))].

186 (C / x) * (C' * x) = 0. [para(118(a,1),158(a,1,2))].

190 x * ((x * y)' * x) = x / y. [para(8(a,1),40(a,1,1,2)),rewrite([3(2)]),flip(a)].

191 (x * y) / x' = x * (y * x). [para(9(a,1),40(a,1,1,2,2)),rewrite([3(2)])].

194 (x * (y * (y * (x * z)))) / z = x * (y * (y * x)). [para(12(a,1),40(a,1,1,2)),rewrite([12(7)])].

208 (C * C) / x = C * (x' * C). [para(54(a,1),40(a,1,1,2))].

231 (x / y) * (y * z) = y' * ((y * x) * z). [para(41(a,1),10(a,1,2)),flip(a)].

232 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),41(a,1,2,2)),flip(a)].

237 (x / C') * y = (C * x) * y. [para(41(a,1),16(a,1)),rewrite([118(5),232(9),16(12,R),35(12)]),flip(a)].

239 (C * x) * y = (x * C) * y. [para(16(a,1),41(a,2,1)),rewrite([118(3),232(7),237(7),35(8)])].

245 (x * y) * (x' * z) = x * ((y / x) * z). [para(35(a,1),41(a,1,2,2)),flip(a)].

247 (x' * y) * (C * x) = x' * (C * (y / x')). [para(54(a,1),41(a,1,2,2)),rewrite([16(5,R)]),flip(a)].

249 (C * x) * (C / x) = C * C. [para(127(a,1),41(a,1,2)),rewrite([118(7),164(9)]),flip(a)].

253 L(x,y * z,y') = L(x,y,z / y). [back_rewrite(67),rewrite([231(4),76(6)])].

256 x' * (y' * ((y * x) * z)) = L(z,y,x / y). [back_rewrite(76),rewrite([253(9)])].

259 x * (C * (C / x)) = C * C. [para(185(a,1),20(a,2,2,2)),rewrite([35(5),16(4,R),3(9)])].

263 (C * (C / x)) * x = C * C. [para(186(a,1),20(a,2,2,2)),rewrite([16(9,R),35(9),3(9)])].

265 C' * ((C / x) * C') = C' / x. [para(186(a,1),40(a,1,1,2)),rewrite([3(4)]),flip(a)].

275 (C * (C * x))' * (C * ((x * C) * y)) = L(y,x * C,C). [para(55(a,2),18(a,1,1,1))].

283 (C * x)' = (x * C)'. [para(55(a,1),112(a,1,2)),rewrite([112(6)]),flip(a)].

304 (x * C)' * (C * x) = 0. [para(283(a,1),8(a,1,1))].

305 (C * x)' * (x * C) = 0. [para(283(a,2),8(a,1,1))].

308 (x * C)' * ((C * x) * y) = y. [para(283(a,1),10(a,1,1))].

310 (C * (x * x))' = (x * (x * C))'. [para(12(a,1),283(a,2,1))].

311 (C * (x * (y * x)))' = (x * (y * (x * C)))'. [para(13(a,1),283(a,2,1))].

315 (C * x) * ((x * C)' * y) = y. [para(283(a,1),35(a,1,2,1))].

337 C * (C * (x * C)') = C / x. [para(304(a,1),40(a,1,1,2)),rewrite([3(3),16(8,R)]),flip(a)].

344 L(C,x,(C * x)') = ((C * x)' * x)'. [para(305(a,1),18(a,1,2)),rewrite([3(7)]),flip(a)].

361 (x * (x * C))' * (x * (C * (x * y))) = y. [para(16(a,1),43(a,1,1,1,2))].

434 (C * x) * ((C * x) * y) = C * (x * (x * (C * y))). [para(304(a,1),45(a,1,1,2,2,2,2)),rewrite([3(11),102(10),315(12),60(6),12(5),308(22),

308(18)]),flip(a)].

509 (C * (x * x))' = (x * (C * x))'. [para(57(a,1),283(a,1,1)),rewrite([16(7,R)]),flip(a)].

729 (x * (C * y))' * (x * ((y * C) * z)) = L(z,C * y,x). [para(239(a,1),18(a,1,2,2))].

734 (x * C) * (C * x) = C * (x * (x * C)). [para(239(a,1),36(a,2)),rewrite([434(6),194(7)]),flip(a)].

739 (C * (x * (x * C)))' = (C * x)' * (C * x)'. [para(239(a,1),176(a,1,1)),rewrite([734(5)])].

762 L(x,C * y,C) = L(x,y * C,C). [back_rewrite(275),rewrite([729(11)])].

791 (x * (C * (x * C)))' = (C * x)' * (C * x)'. [para(58(a,1),283(a,2,1)),rewrite([739(6)]),flip(a)].

822 (C * x)' * (C * C) = C / x. [para(249(a,1),10(a,1,2))].

842 L(C / x,C,x) = (x * C)' * (C * C). [para(259(a,1),18(a,1,2)),flip(a)].

844 C * (C / x') = x * (C * C). [para(259(a,1),35(a,1,2)),flip(a)].

856 C * (C / x) = C * (x' * C). [para(263(a,1),6(a,1,1)),rewrite([208(4)]),flip(a)].

875 C * (x * C) = x * (C * C). [back_rewrite(844),rewrite([856(5),31(3)])].

886 L(C / x,C,x) = C / x. [back_rewrite(842),rewrite([875(11,R),16(10,R),337(11)])].

887 C * (C * (C * x)') = C / x. [back_rewrite(822),rewrite([875(7,R),16(6,R)])].

889 L(x',C,x * C) = x'. [para(33(a,1),886(a,1,1)),rewrite([33(9)])].

947 L(x,C,x' * C) = x. [para(31(a,1),889(a,1,1)),rewrite([31(7)])].

949 L(x,C,C * x') = x. [para(107(a,1),889(a,1,3)),rewrite([31(2),31(7)])].

958 L(x * x,C,C * (x' * x')) = x * x. [para(176(a,1),947(a,1,3,1)),rewrite([16(7,R)])].

959 L(C * x,C,C * (x * C)') = C * x. [para(283(a,1),947(a,1,3,1)),rewrite([16(8,R)])].

971 x' * ((x * C) * y) = C * L(y,x,C). [para(18(a,1),60(a,2,2)),rewrite([887(7),231(4)])].

1044 C' * x = x * C'. [para(8(a,1),61(a,2,2,2)),rewrite([35(8),3(7)]),flip(a)].

1069 (C * (x * C))' = (x * (C * C))'. [para(61(a,2),112(a,1,2)),rewrite([112(8)])].

1079 (x * C')' = C / x. [para(61(a,2),164(a,1,1)),rewrite([35(8),16(9,R),9(9),3(7)])].

1142 C' * (C' * (C / x)) = C' / x. [back_rewrite(265),rewrite([1044(7,R)])].

1144 C * L(x,y,C) = L(x * C,C',y). [back_rewrite(136),rewrite([1079(4),231(4),971(5)])].

1147 x' * ((x * C) * y) = L(y * C,C',x). [back_rewrite(971),rewrite([1144(9)])].

1148 (x * C') / x = C'. [para(1044(a,1),6(a,1,1))].

1151 C * (x * C') = x. [para(1044(a,1),10(a,1,2)),rewrite([31(3)])].

1152 x' * (C' * x) = C'. [para(1044(a,2),10(a,1,2))].

1157 (C' * (C' * x)) * y = C' * (x * (C' * y)). [para(1044(a,2),13(a,1,1,2))].

1181 x / C' = C * x. [para(7(a,1),1151(a,1,2)),flip(a)].

1186 (C * x)' * x = L(C',x,C). [para(1151(a,1),18(a,1,2))].

1205 L(C,x,(C * x)') = L(C',x,C)'. [back_rewrite(344),rewrite([1186(9)])].

1211 (C * x)' = C' / x. [para(1181(a,1),108(a,1,1))].

1220 L(C,x,C' / x) = L(C',x,C)'. [back_rewrite(1205),rewrite([1211(4)])].

1224 L(C',x,C) = C'. [back_rewrite(1186),rewrite([1211(3),7(4)]),flip(a)].

1225 (x * (C * C))' = C' / (x * C). [back_rewrite(1069),rewrite([1211(5)]),flip(a)].

1268 (x * (C * (x * C)))' = (C' / x) * (C' / x). [back_rewrite(791),rewrite([1211(9),1211(12)])].

1278 (x * (C * x))' = C' / (x * x). [back_rewrite(509),rewrite([1211(4)]),flip(a)].

1313 (x * (y * (x * C)))' = C' / (x * (y * x)). [back_rewrite(311),rewrite([1211(5)]),flip(a)].

1314 (x * (x * C))' = C' / (x * x). [back_rewrite(310),rewrite([1211(4)]),flip(a)].

1320 (x * C)' = C' / x. [back_rewrite(283),rewrite([1211(3)]),flip(a)].

1327 L(C,x,C' / x) = C. [back_rewrite(1220),rewrite([1224(9),31(8)])].

1332 L(C * x,C,C * (C' / x)) = C * x. [back_rewrite(959),rewrite([1320(7)])].

1334 L(x,C,x') = C * (C' / x'). [back_rewrite(141),rewrite([1320(8)])].

1338 (C' / x) * (C * (x * y)) = L(y,x,C). [back_rewrite(83),rewrite([1320(3)])].

1339 C' / (x * (C * x)) = (C' / x) * (C' / x). [back_rewrite(1268),rewrite([1313(6)])].

1345 (C' / (x * x)) * (x * (C * (x * y))) = y. [back_rewrite(361),rewrite([1314(4)])].

1565 (C' / (x * C)) * (x * (C * (y * C))) = L(y,C * C,x). [para(150(a,1),68(a,1,2)),rewrite([150(9),1225(9)]),flip(a)].

1744 L(x,C',x') = C' * (C / x'). [para(1152(a,1),18(a,1,2)),rewrite([1079(5),1044(6,R)]),flip(a)].

1745 (C * x') * x = C. [para(1152(a,1),20(a,2,2,2)),rewrite([16(8,R),35(8),9(9),3(7)])].

1759 C / x = C * x'. [para(1745(a,1),6(a,1,1))].

1762 C' * ((C * x') * (x * y)) = L(y,x,C * x'). [para(1745(a,1),18(a,1,1,1))].

1765 (C * x) * x' = C. [para(31(a,1),1745(a,1,1,2))].

1782 L(x,C',x') = x. [back_rewrite(1744),rewrite([1759(9),31(9),10(9)])].

1848 C' / x = C' * x'. [back_rewrite(1142),rewrite([1759(6),10(8)]),flip(a)].

1853 (x * C')' = C * x'. [back_rewrite(1079),rewrite([1759(6)])].

1882 L(x,C,x') = x. [back_rewrite(1334),rewrite([1848(8),31(8),35(8)])].

1921 C' * (x' * (C' * (x * (C * (y * C))))) = L(y,C * C,x). [back_rewrite(1565),rewrite([1848(5),1320(5),1848(5),1157(13)])].

1956 (C' * (x' * x')) * (x * (C * (x * y))) = y. [back_rewrite(1345),rewrite([1848(4),176(4)])].

1961 (C' * x') * (C' * x') = C' * (C' * (x' * x')). [back_rewrite(1339),rewrite([1848(6),1278(6),1848(6),176(6),1848(12),1848(16)]),flip(a)]

.

1962 L(x,y,C * y') = L(x,y,C). [back_rewrite(1338),rewrite([1848(3),232(8),1181(6),1762(8)])].

1965 L(C * x,C,x') = C * x. [back_rewrite(1332),rewrite([1848(7),35(9)])].

1967 L(C,x,C' * x') = C. [back_rewrite(1327),rewrite([1848(4)])].

1972 (x * C)' = C' * x'. [back_rewrite(1320),rewrite([1848(6)])].

1978 (x * (y * (x * C)))' = C' * (x * (y * x))'. [back_rewrite(1313),rewrite([1848(10)])].

2036 (x * (C * C))' = C' * (C' * x'). [back_rewrite(1225),rewrite([1848(10),1972(10)])].

2042 (C * x)' = C' * x'. [back_rewrite(1211),rewrite([1848(6)])].

2096 L(x,x',C * x) = x. [para(1745(a,1),71(a,2,1,1)),rewrite([31(4),31(9),10(9)])].

2123 ((C' * x') * x)' = C. [para(16(a,2),72(a,1,3,1)),rewrite([2042(4),1967(6),1972(4)]),flip(a)].

2171 (C' * x') * x = L(C',C,x). [para(16(a,2),74(a,2,1,1)),rewrite([2042(7)]),flip(a)].

2183 (C' * x) * x' = L(C',C,x'). [para(107(a,1),74(a,2,1,1)),rewrite([2042(9),31(9)]),flip(a)].

2231 L(C',C,x)' = C. [back_rewrite(2123),rewrite([2171(5)])].

2240 L(C',C,x) = C'. [para(2231(a,1),31(a,1,1)),flip(a)].

2241 (C' * x) * x' = C'. [back_rewrite(2183),rewrite([2240(10)])].

2243 L(x,x',x * C) = x. [para(16(a,1),2096(a,1,3))].

2292 x' * (C * (C * x)) = C * C. [para(947(a,1),75(a,1,2)),rewrite([16(5,R),13(6),54(5),247(9),1759(8),31(8)]),flip(a)].

2314 C' * L(x,C' * y,y') = y' * ((C' * y) * x). [para(1152(a,1),75(a,1,1))].

2315 (C * x') * (x * y) = L(y * C,C',x). [para(1745(a,1),75(a,1,1)),rewrite([1962(5),1144(4)]),flip(a)].

2443 (C' * x') * (x * y) = L(y * C',C,x). [para(1044(a,1),77(a,1,1)),rewrite([31(6),31(8),1972(8)]),flip(a)].

2748 L(x,y,z / y) = L(x,y,z). [para(8(a,1),81(a,1,1,1,2)),rewrite([3(2),18(6),10(4),190(5)]),flip(a)].

2750 L(x,y',y * (z * y)) = L(x,z,y). [para(9(a,1),81(a,1,1,1,2,2)),rewrite([3(2),35(5),18(5)]),flip(a)].

2776 x' * (C' * (x * (C * y))) = L(y,C,x * (C' * x)). [para(53(a,1),81(a,1,1,1,2)),rewrite([176(2),12(11),10(10)])].

2853 C' * L(C * x,C,y) = L(x,C,C * (y * C)). [para(59(a,2),81(a,1,1,1)),rewrite([1978(7),2042(7),1972(7),232(18),1181(12),35(11),2443(12),10

44(9,R),10(9)])].

2966 x' * (y' * ((y * x) * z)) = L(z,y,x). [back_rewrite(256),rewrite([2748(8)])].

2967 L(x,y * z,y') = L(x,y,z). [back_rewrite(253),rewrite([2748(5)])].

2968 C' * L(x * C,C,y * (C' * y)) = L(x,C * C,y). [back_rewrite(1921),rewrite([2776(12)])].

2999 C * ((C' * x) * (x' * y)) = L(y,x',C' * x). [para(2241(a,1),18(a,1,1,1)),rewrite([31(3)])].

3011 L(x,x',C' * x) = x. [para(2241(a,1),71(a,2,1,1)),rewrite([31(8),35(10)])].

3026 L(x,y,z * y) = L(x,y,z). [para(10(a,1),82(a,1,1,1)),rewrite([10(7),18(5),2967(5)]),flip(a)].

3358 L(x,C,C' * y) = L(x,C,y). [para(54(a,1),87(a,1,2,2,1)),rewrite([1882(3),1972(5),31(5),232(7),1181(6),2966(8),54(6),1972(7),31(7)]),flip

(a)].

3427 L(x,C * C,C' * (C' * y)) = L(x,C,y * (C' * y)). [para(949(a,1),87(a,1,1,1)),rewrite([16(6,R),2042(7),2042(7),31(7),102(13),8(11),3(11),

12(11),232(12),1181(9),35(8),2776(8),102(12),8(10),3(10),16(14,R),2042(15),2042(15),31(15)]),flip(a)].

3484 L(x,C' * y,C) = L(x,C',C * y). [para(1152(a,1),87(a,1,2,2,1)),rewrite([1782(4),1853(6),31(4),245(7),118(4),128(8),1152(10),1853(12),31(

10)])].

3716 L(x,x',x * C') = x. [para(61(a,2),3011(a,1,3)),rewrite([16(4,R),9(4),3(2),16(4,R),9(4),3(2),35(9),16(9,R),9(9),3(7)])].

3722 x * L(y,x,C) = L(x * y,C,x'). [para(16(a,1),89(a,1,1,1,1,1)),rewrite([1972(3),16(6,R),35(6),31(2),2042(8),3358(10)])].

3772 C' * L(x,C',y) = L(x * C',y,C). [para(1044(a,1),89(a,2,1)),rewrite([1853(4),1745(4),1853(13),1962(13)])].

3962 L(x',x',C' * x) = x'. [para(96(a,1),35(a,1)),rewrite([2042(5),2042(9),1961(11),123(14),245(9),118(3),2999(9),2042(9),16(12,R),35(12)])]

.

4054 L(x,y * C,C) = L(x,y,C). [para(875(a,1),18(a,1,1,1)),rewrite([2036(5),232(13),1181(9),35(8),1147(7),3772(8),1044(5,R),53(5)]),flip(a)].

4055 L(x,C,C * (y * y)) = L(x,C * C,y). [para(875(a,2),18(a,1,1,1)),rewrite([2042(5),1972(5),12(11),1157(13),2776(12),2853(11),16(8,R),133(8

)])].

4156 L(x,C * y,C) = L(x,y,C). [back_rewrite(762),rewrite([4054(8)])].

4157 L(x * x,C * C,x') = x * x. [back_rewrite(958),rewrite([4055(8)])].

4680 L(x,C * C,C' * y) = L(x,y,C). [para(1965(a,1),87(a,1,1,1)),rewrite([2042(3),1972(8),31(8),2292(13),12(11),232(12),1181(9),102(11),10(12

),232(8),1181(6),2315(7),3772(8),1044(5,R),53(5),2292(8),1972(9),31(9)]),flip(a)].

4686 L(x,C,y * (C' * y)) = L(x,C',C * y). [back_rewrite(3427),rewrite([4680(10),3484(5)]),flip(a)].

4692 L(x,C * C,y) = L(x,y,C). [back_rewrite(2968),rewrite([4686(10),3772(10),1044(5,R),53(5),4156(4)]),flip(a)].

4696 L(x,C',C * y) = L(x,y,C). [back_rewrite(4680),rewrite([4692(7),3484(5)])].

4699 L(x * x,x',C) = x * x. [back_rewrite(4157),rewrite([4692(6)])].

5151 L(x,y * z,z) = L(x,y,z). [para(33(a,1),2748(a,1,3)),rewrite([2967(3)]),flip(a)].

5161 L(x,C',y) = L(x,y,C). [para(1181(a,1),2748(a,1,3)),rewrite([4696(5)]),flip(a)].

5162 L(x,y,y * C') = L(x,y,C'). [para(1148(a,1),2748(a,1,3)),flip(a)].

5165 L(x,C,x) = x. [para(2243(a,1),2748(a,2)),rewrite([191(5),2750(5)])].

5168 L(x,C',x) = x. [para(3716(a,1),2748(a,2)),rewrite([191(6),2750(6)])].

5196 (x * C) * x = x * (C * x). [para(5165(a,1),75(a,1,2))].

5216 L(C' * x,x,C) = C' * x. [para(5168(a,1),89(a,1,2)),rewrite([1853(4),1745(4),1853(10),1962(10)]),flip(a)].

5418 L(x,C,C * y) = L(x,C,y). [para(16(a,2),3026(a,1,3))].

5420 L(x,y' * z,y) = L(x,y',z). [para(35(a,1),3026(a,1,3)),rewrite([5151(3)]),flip(a)].

5438 L(x,y',C * y) = L(x,y',C). [para(1765(a,1),3026(a,1,3)),flip(a)].

5448 L(x,y',C' * y) = L(x,y',C'). [para(2241(a,1),3026(a,1,3)),flip(a)].

5469 L(x * C,C,x) = x * C. [para(3026(a,1),5165(a,1))].

5471 L(x,y * C',C) = L(x,C',y). [para(3026(a,1),5161(a,1)),flip(a)].

5513 L(x',x',C') = x'. [back_rewrite(3962),rewrite([5448(6)])].

5599 x' * (C * (x * y)) = L(y * C,C,x). [para(10(a,1),104(a,1,1,1)),rewrite([10(9),2967(12)])].

5778 L(x,x,C') = x. [para(31(a,1),5513(a,1,1)),rewrite([31(2),31(5)])].

5784 (C' * x) * x = C' * (x * x). [para(5778(a,1),75(a,1,2))].

6718 C' * ((C * x) * y) = C * (x * (C' * y)). [para(123(a,1),10(a,1,2))].

6996 (C' * (x' * x')) * (x * y) = L((C' * x') * y,C,x). [para(57(a,2),129(a,2,1,1)),rewrite([2042(3),5151(8),2042(11),176(11)]),flip(a)].

7188 L(L(x,y,C),C,y) = x. [back_rewrite(1956),rewrite([6996(11),232(8),1181(6),2315(7),3772(8),1044(5,R),53(5)])].

7231 x' * (x' * ((C' * x) * ((C * x) * y))) = L(y,C * x,C' * x). [para(4699(a,1),87(a,1,1,1)),rewrite([176(2),2042(7),31(7),10(10),12(11),10

(15),2042(17),31(17)])].

7304 L(C,C' * x,C * x) = C. [para(133(a,1),105(a,1,2,2)),rewrite([245(6),118(3),5784(5),35(6),176(2),12(7),5599(6),5469(5),10(4)]),flip(a)].

7307 (x * x) / (C' * x) = C * x. [para(133(a,1),113(a,1,1)),rewrite([5216(6)])].

7384 L(x,y / z,z) = L(x,y,z). [para(7(a,1),5151(a,1,2)),flip(a)].

7393 L(x,y',C) = L(x,C,y). [para(54(a,1),5151(a,1,2)),rewrite([5418(4),5438(6)]),flip(a)].

7394 L(x,C,y') = L(x,y,C). [para(127(a,1),5151(a,1,2)),rewrite([5418(5),1962(7)])].

7406 L(x,C,y * C') = L(x,y,C'). [para(1151(a,1),5151(a,1,2)),rewrite([5162(4)]),flip(a)].

7422 L(x,C' * y,y') = L(x,C',y'). [para(2241(a,1),5151(a,1,2)),flip(a)].

7654 x' * ((C' * x) * y) = L(y * C',x',C). [back_rewrite(2314),rewrite([7422(7),3772(7)]),flip(a)].

7682 L(x,C * y,C' * y) = L(L(x,C,y),C,y). [back_rewrite(7231),rewrite([7654(10),1044(7,R),6718(7),3722(11),5599(8),16(5,R),35(5),31(5)]),fli

p(a)].

7787 L(L(L(c1,A',C),C,A),C,A) != c1. [para(7393(a,2),19(a,1,1,1))].

7795 L(x,y',C) = L(x,y,C'). [para(1853(a,1),7393(a,1,2)),rewrite([4156(5),7406(8)])].

7807 L(L(x,C,y),C,y') = x. [para(7393(a,1),7188(a,1,1))].

7815 L(L(L(c1,A,C'),C,A),C,A) != c1. [back_rewrite(7787),rewrite([7795(5)])].

7963 L(x,C',y) = L(x,C,y'). [para(1853(a,1),7394(a,1,3)),rewrite([5418(5),5471(8)]),flip(a)].

8213 L(L(x,y,C'),C,y') = x. [para(1853(a,1),7807(a,1,3)),rewrite([7406(5),5418(8)])].

8888 (x * C) / (C' * x) = C * C. [para(16(a,1),155(a,1,1))].

9139 L(C,C' * x,x * C) = C. [para(16(a,1),7304(a,1,3))].

9630 (x * C) * (C' * x) = x * x. [para(9139(a,1),113(a,1,2)),rewrite([16(7,R),35(7),5196(3),118(5),151(6)]),flip(a)].

15607 L(x,y * y,C' * y) = L(L(x,C,y),C,y). [para(7307(a,1),7384(a,1,2)),rewrite([7682(6)]),flip(a)].

16431 L(x,y * C,C' * y) = L(x,C,y'). [para(8888(a,1),7384(a,1,2)),rewrite([4692(7),5420(5),7963(3)]),flip(a)].

16966 L(L(x,C,y),C,y) = L(x,C,y'). [para(9630(a,1),5151(a,1,2)),rewrite([15607(5),16431(10)])].

16991 $F. [back_rewrite(7815),rewrite([16966(11),8213(9)]),xx(a)].

============================== end of proof ==========================

% Proof 1 at 3.17 (+ 0.03) seconds.

% Length of proof is 249.

% Level of proof is 23.

% Maximum clause weight is 30.000.

% Given clauses 474.

1 L(L(L(x,A,C),A,C),A,C) = x # label(non_clause) # label(goal). [goal].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 C * ((x * y) * C) = (C * x) * (y * C). [assumption].

15 (C * x) * (y * C) = C * ((x * y) * C). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 L(x,y,z) = (z * y)' * (z * (y * x)). [assumption].

18 (x * y)' * (x * (y * z)) = L(z,y,x). [copy(17),flip(a)].

19 L(L(L(c1,A,C),A,C),A,C) != c1. [deny(1)].

20 (C * x) * (y * C) = C * (C * (x * y)). [back_rewrite(15),rewrite([16(9,R)])].

29 0 / x = x'. [para(8(a,1),6(a,1,1))].

31 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([29(3)])].

32 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

33 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

35 x * (x' * y) = y. [back_rewrite(4),rewrite([32(1)])].

36 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

40 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

41 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

43 (x * (y * x))' * (x * (y * (x * z))) = z. [para(13(a,1),10(a,1,2))].

45 (x * (y * (x * (x * (y * x))))) * z = x * (y * (x * (x * (y * (x * z))))). [para(13(a,1),12(a,1,1)),rewrite([13(11),13(12)])].

52 C * (x / C) = x. [para(16(a,2),7(a,1))].

53 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

54 x' * (C * x) = C. [para(16(a,2),10(a,1,2))].

55 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

57 C * (x * x) = x * (C * x). [para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].

58 (x * (x * C)) * y = x * (C * (x * y)). [para(16(a,1),13(a,1,1,2))].

59 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

60 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

61 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

67 x' * ((x / y) * (y * z)) = L(z,y,x / y). [para(7(a,1),18(a,1,1,1))].

68 L(x,y / x,z) = (z * (y / x))' * (z * y). [para(7(a,1),18(a,1,2,2)),flip(a)].

71 L(x,x',y) = (y * x')' * y. [para(8(a,1),18(a,1,2,2)),rewrite([3(5)]),flip(a)].

72 L(x,y,(y * x)') = ((y * x)' * y)'. [para(8(a,1),18(a,1,2)),rewrite([3(6)]),flip(a)].

74 L(x',x,y) = (y * x)' * y. [para(9(a,1),18(a,1,2,2)),rewrite([3(4)]),flip(a)].

75 (x * y) * L(z,y,x) = x * (y * z). [para(18(a,1),10(a,1,2)),rewrite([31(3)])].

76 x' * (y' * ((y * x) * z)) = L(z,y * x,y'). [para(10(a,1),18(a,1,1,1))].

77 L(x * y,x',z) = (z * x')' * (z * y). [para(10(a,1),18(a,1,2,2)),flip(a)].

81 (x * (y * (x * z)))' * (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(13(a,1),18(a,1,1,1)),rewrite([13(8)])].

82 (x * (y * (z * y)))' * (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(13(a,1),18(a,1,2,2))].

83 (x * C)' * (C * (x * y)) = L(y,x,C). [para(16(a,1),18(a,1,1,1))].

87 L(x,y,z)' * ((z * y)' * ((z * (y * x)) * u)) = L(u,z * (y * x),(z * y)'). [para(18(a,1),18(a,1,1,1))].

89 ((x * y)' * x)' * L(z,y,x) = L(y * z,x,(x * y)'). [para(18(a,1),18(a,1,2))].

91 C * (C * (x * (y / C))) = (C * x) * y. [para(7(a,1),20(a,1,2)),flip(a)].

96 (C * x) * (y * (y * C)) = C * (C * (x * (y * y))). [para(12(a,1),20(a,1,2))].

102 (C * x) * (C * y) = C * (C * (x * y)). [para(16(a,2),20(a,1,2))].

104 (x * (C * y))' * (x * (C * (C * (y * z)))) = L(z * C,C * y,x). [para(20(a,1),18(a,1,2,2))].

105 ((C * x) * y)' * (C * (C * (x * y))) = L(C,y,C * x). [para(20(a,1),18(a,1,2))].

107 x' * C = C * x'. [para(16(a,2),32(a,2)),rewrite([32(2)])].

108 (x / y)' = y / x. [para(7(a,1),33(a,1,2)),flip(a)].

112 C / (C * x) = x'. [para(16(a,2),33(a,1,2))].

113 (x * (y * z)) / L(z,y,x) = x * y. [para(18(a,1),33(a,1,2)),rewrite([31(7)])].

118 x / C = C' * x. [para(52(a,1),10(a,1,2)),flip(a)].

123 C * (C * (x * (C' * y))) = (C * x) * y. [back_rewrite(91),rewrite([118(4)])].

127 x * (C * x') = C. [para(16(a,2),35(a,1,2))].

128 x' * (y * ((y' * x) * z)) = L(z,y' * x,y). [para(35(a,1),18(a,1,1,1))].

129 L(x' * y,x,z) = (z * x)' * (z * y). [para(35(a,1),18(a,1,2,2)),flip(a)].

133 C * (x * (C' * x)) = x * x. [para(53(a,1),13(a,2,2)),rewrite([16(6,R)])].

136 (x * C')' * (x * y) = L(y * C,C',x). [para(53(a,1),18(a,1,2,2))].

141 L(x,C,x') = C * (x' * C)'. [para(54(a,1),18(a,1,2)),rewrite([16(6,R)]),flip(a)].

145 x' / x = x' * x'. [para(8(a,1),36(a,1,1,2)),rewrite([3(3)])].

146 x / x' = x * x. [para(9(a,1),36(a,1,1,2)),rewrite([3(2)])].

150 (C * (x * C)) / x = C * C. [para(16(a,1),36(a,1,1,2))].

151 C' * (x * (C * x)) = x * x. [para(16(a,2),36(a,1,1,2)),rewrite([118(5)])].

155 (x * y) / (x' * y) = x * x. [para(35(a,1),36(a,1,1,2))].

158 (x / y) * (y / x) = 0. [para(108(a,1),8(a,1,1))].

164 (C' * x)' = C / x. [para(35(a,1),112(a,1,2)),flip(a)].

176 (x * x)' = x' * x'. [para(146(a,1),108(a,1,1)),rewrite([145(4)])].

185 (C' * x) * (C / x) = 0. [para(118(a,1),158(a,1,1))].

186 (C / x) * (C' * x) = 0. [para(118(a,1),158(a,1,2))].

190 x * ((x * y)' * x) = x / y. [para(8(a,1),40(a,1,1,2)),rewrite([3(2)]),flip(a)].

191 (x * y) / x' = x * (y * x). [para(9(a,1),40(a,1,1,2,2)),rewrite([3(2)])].

194 (x * (y * (y * (x * z)))) / z = x * (y * (y * x)). [para(12(a,1),40(a,1,1,2)),rewrite([12(7)])].

208 (C * C) / x = C * (x' * C). [para(54(a,1),40(a,1,1,2))].

231 (x / y) * (y * z) = y' * ((y * x) * z). [para(41(a,1),10(a,1,2)),flip(a)].

232 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),41(a,1,2,2)),flip(a)].

237 (x / C') * y = (C * x) * y. [para(41(a,1),16(a,1)),rewrite([118(5),232(9),16(12,R),35(12)]),flip(a)].

239 (C * x) * y = (x * C) * y. [para(16(a,1),41(a,2,1)),rewrite([118(3),232(7),237(7),35(8)])].

245 (x * y) * (x' * z) = x * ((y / x) * z). [para(35(a,1),41(a,1,2,2)),flip(a)].

247 (x' * y) * (C * x) = x' * (C * (y / x')). [para(54(a,1),41(a,1,2,2)),rewrite([16(5,R)]),flip(a)].

249 (C * x) * (C / x) = C * C. [para(127(a,1),41(a,1,2)),rewrite([118(7),164(9)]),flip(a)].

253 L(x,y * z,y') = L(x,y,z / y). [back_rewrite(67),rewrite([231(4),76(6)])].

256 x' * (y' * ((y * x) * z)) = L(z,y,x / y). [back_rewrite(76),rewrite([253(9)])].

259 x * (C * (C / x)) = C * C. [para(185(a,1),20(a,2,2,2)),rewrite([35(5),16(4,R),3(9)])].

263 (C * (C / x)) * x = C * C. [para(186(a,1),20(a,2,2,2)),rewrite([16(9,R),35(9),3(9)])].

265 C' * ((C / x) * C') = C' / x. [para(186(a,1),40(a,1,1,2)),rewrite([3(4)]),flip(a)].

275 (C * (C * x))' * (C * ((x * C) * y)) = L(y,x * C,C). [para(55(a,2),18(a,1,1,1))].

283 (C * x)' = (x * C)'. [para(55(a,1),112(a,1,2)),rewrite([112(6)]),flip(a)].

304 (x * C)' * (C * x) = 0. [para(283(a,1),8(a,1,1))].

305 (C * x)' * (x * C) = 0. [para(283(a,2),8(a,1,1))].

308 (x * C)' * ((C * x) * y) = y. [para(283(a,1),10(a,1,1))].

310 (C * (x * x))' = (x * (x * C))'. [para(12(a,1),283(a,2,1))].

311 (C * (x * (y * x)))' = (x * (y * (x * C)))'. [para(13(a,1),283(a,2,1))].

315 (C * x) * ((x * C)' * y) = y. [para(283(a,1),35(a,1,2,1))].

337 C * (C * (x * C)') = C / x. [para(304(a,1),40(a,1,1,2)),rewrite([3(3),16(8,R)]),flip(a)].

344 L(C,x,(C * x)') = ((C * x)' * x)'. [para(305(a,1),18(a,1,2)),rewrite([3(7)]),flip(a)].

361 (x * (x * C))' * (x * (C * (x * y))) = y. [para(16(a,1),43(a,1,1,1,2))].

434 (C * x) * ((C * x) * y) = C * (x * (x * (C * y))). [para(304(a,1),45(a,1,1,2,2,2,2)),rewrite([3(11),102(10),315(12),60(6),12(5),308(22),

308(18)]),flip(a)].

509 (C * (x * x))' = (x * (C * x))'. [para(57(a,1),283(a,1,1)),rewrite([16(7,R)]),flip(a)].

729 (x * (C * y))' * (x * ((y * C) * z)) = L(z,C * y,x). [para(239(a,1),18(a,1,2,2))].

734 (x * C) * (C * x) = C * (x * (x * C)). [para(239(a,1),36(a,2)),rewrite([434(6),194(7)]),flip(a)].

739 (C * (x * (x * C)))' = (C * x)' * (C * x)'. [para(239(a,1),176(a,1,1)),rewrite([734(5)])].

762 L(x,C * y,C) = L(x,y * C,C). [back_rewrite(275),rewrite([729(11)])].

791 (x * (C * (x * C)))' = (C * x)' * (C * x)'. [para(58(a,1),283(a,2,1)),rewrite([739(6)]),flip(a)].

822 (C * x)' * (C * C) = C / x. [para(249(a,1),10(a,1,2))].

842 L(C / x,C,x) = (x * C)' * (C * C). [para(259(a,1),18(a,1,2)),flip(a)].

844 C * (C / x') = x * (C * C). [para(259(a,1),35(a,1,2)),flip(a)].

856 C * (C / x) = C * (x' * C). [para(263(a,1),6(a,1,1)),rewrite([208(4)]),flip(a)].

875 C * (x * C) = x * (C * C). [back_rewrite(844),rewrite([856(5),31(3)])].

886 L(C / x,C,x) = C / x. [back_rewrite(842),rewrite([875(11,R),16(10,R),337(11)])].

887 C * (C * (C * x)') = C / x. [back_rewrite(822),rewrite([875(7,R),16(6,R)])].

889 L(x',C,x * C) = x'. [para(33(a,1),886(a,1,1)),rewrite([33(9)])].

947 L(x,C,x' * C) = x. [para(31(a,1),889(a,1,1)),rewrite([31(7)])].

949 L(x,C,C * x') = x. [para(107(a,1),889(a,1,3)),rewrite([31(2),31(7)])].

958 L(x * x,C,C * (x' * x')) = x * x. [para(176(a,1),947(a,1,3,1)),rewrite([16(7,R)])].

959 L(C * x,C,C * (x * C)') = C * x. [para(283(a,1),947(a,1,3,1)),rewrite([16(8,R)])].

971 x' * ((x * C) * y) = C * L(y,x,C). [para(18(a,1),60(a,2,2)),rewrite([887(7),231(4)])].

1044 C' * x = x * C'. [para(8(a,1),61(a,2,2,2)),rewrite([35(8),3(7)]),flip(a)].

1069 (C * (x * C))' = (x * (C * C))'. [para(61(a,2),112(a,1,2)),rewrite([112(8)])].

1079 (x * C')' = C / x. [para(61(a,2),164(a,1,1)),rewrite([35(8),16(9,R),9(9),3(7)])].

1142 C' * (C' * (C / x)) = C' / x. [back_rewrite(265),rewrite([1044(7,R)])].

1144 C * L(x,y,C) = L(x * C,C',y). [back_rewrite(136),rewrite([1079(4),231(4),971(5)])].

1147 x' * ((x * C) * y) = L(y * C,C',x). [back_rewrite(971),rewrite([1144(9)])].

1151 C * (x * C') = x. [para(1044(a,1),10(a,1,2)),rewrite([31(3)])].

1152 x' * (C' * x) = C'. [para(1044(a,2),10(a,1,2))].

1157 (C' * (C' * x)) * y = C' * (x * (C' * y)). [para(1044(a,2),13(a,1,1,2))].

1181 x / C' = C * x. [para(7(a,1),1151(a,1,2)),flip(a)].

1186 (C * x)' * x = L(C',x,C). [para(1151(a,1),18(a,1,2))].

1205 L(C,x,(C * x)') = L(C',x,C)'. [back_rewrite(344),rewrite([1186(9)])].

1211 (C * x)' = C' / x. [para(1181(a,1),108(a,1,1))].

1220 L(C,x,C' / x) = L(C',x,C)'. [back_rewrite(1205),rewrite([1211(4)])].

1224 L(C',x,C) = C'. [back_rewrite(1186),rewrite([1211(3),7(4)]),flip(a)].

1225 (x * (C * C))' = C' / (x * C). [back_rewrite(1069),rewrite([1211(5)]),flip(a)].

1268 (x * (C * (x * C)))' = (C' / x) * (C' / x). [back_rewrite(791),rewrite([1211(9),1211(12)])].

1278 (x * (C * x))' = C' / (x * x). [back_rewrite(509),rewrite([1211(4)]),flip(a)].

1313 (x * (y * (x * C)))' = C' / (x * (y * x)). [back_rewrite(311),rewrite([1211(5)]),flip(a)].

1314 (x * (x * C))' = C' / (x * x). [back_rewrite(310),rewrite([1211(4)]),flip(a)].

1320 (x * C)' = C' / x. [back_rewrite(283),rewrite([1211(3)]),flip(a)].

1327 L(C,x,C' / x) = C. [back_rewrite(1220),rewrite([1224(9),31(8)])].

1332 L(C * x,C,C * (C' / x)) = C * x. [back_rewrite(959),rewrite([1320(7)])].

1334 L(x,C,x') = C * (C' / x'). [back_rewrite(141),rewrite([1320(8)])].

1338 (C' / x) * (C * (x * y)) = L(y,x,C). [back_rewrite(83),rewrite([1320(3)])].

1339 C' / (x * (C * x)) = (C' / x) * (C' / x). [back_rewrite(1268),rewrite([1313(6)])].

1345 (C' / (x * x)) * (x * (C * (x * y))) = y. [back_rewrite(361),rewrite([1314(4)])].

1565 (C' / (x * C)) * (x * (C * (y * C))) = L(y,C * C,x). [para(150(a,1),68(a,1,2)),rewrite([150(9),1225(9)]),flip(a)].

1744 L(x,C',x') = C' * (C / x'). [para(1152(a,1),18(a,1,2)),rewrite([1079(5),1044(6,R)]),flip(a)].

1745 (C * x') * x = C. [para(1152(a,1),20(a,2,2,2)),rewrite([16(8,R),35(8),9(9),3(7)])].

1759 C / x = C * x'. [para(1745(a,1),6(a,1,1))].

1762 C' * ((C * x') * (x * y)) = L(y,x,C * x'). [para(1745(a,1),18(a,1,1,1))].

1765 (C * x) * x' = C. [para(31(a,1),1745(a,1,1,2))].

1782 L(x,C',x') = x. [back_rewrite(1744),rewrite([1759(9),31(9),10(9)])].

1848 C' / x = C' * x'. [back_rewrite(1142),rewrite([1759(6),10(8)]),flip(a)].

1853 (x * C')' = C * x'. [back_rewrite(1079),rewrite([1759(6)])].

1882 L(x,C,x') = x. [back_rewrite(1334),rewrite([1848(8),31(8),35(8)])].

1921 C' * (x' * (C' * (x * (C * (y * C))))) = L(y,C * C,x). [back_rewrite(1565),rewrite([1848(5),1320(5),1848(5),1157(13)])].

1956 (C' * (x' * x')) * (x * (C * (x * y))) = y. [back_rewrite(1345),rewrite([1848(4),176(4)])].

1961 (C' * x') * (C' * x') = C' * (C' * (x' * x')). [back_rewrite(1339),rewrite([1848(6),1278(6),1848(6),176(6),1848(12),1848(16)]),flip(a)]

.

1962 L(x,y,C * y') = L(x,y,C). [back_rewrite(1338),rewrite([1848(3),232(8),1181(6),1762(8)])].

1965 L(C * x,C,x') = C * x. [back_rewrite(1332),rewrite([1848(7),35(9)])].

1967 L(C,x,C' * x') = C. [back_rewrite(1327),rewrite([1848(4)])].

1972 (x * C)' = C' * x'. [back_rewrite(1320),rewrite([1848(6)])].

1978 (x * (y * (x * C)))' = C' * (x * (y * x))'. [back_rewrite(1313),rewrite([1848(10)])].

2036 (x * (C * C))' = C' * (C' * x'). [back_rewrite(1225),rewrite([1848(10),1972(10)])].

2042 (C * x)' = C' * x'. [back_rewrite(1211),rewrite([1848(6)])].

2096 L(x,x',C * x) = x. [para(1745(a,1),71(a,2,1,1)),rewrite([31(4),31(9),10(9)])].

2123 ((C' * x') * x)' = C. [para(16(a,2),72(a,1,3,1)),rewrite([2042(4),1967(6),1972(4)]),flip(a)].

2171 (C' * x') * x = L(C',C,x). [para(16(a,2),74(a,2,1,1)),rewrite([2042(7)]),flip(a)].

2183 (C' * x) * x' = L(C',C,x'). [para(107(a,1),74(a,2,1,1)),rewrite([2042(9),31(9)]),flip(a)].

2231 L(C',C,x)' = C. [back_rewrite(2123),rewrite([2171(5)])].

2240 L(C',C,x) = C'. [para(2231(a,1),31(a,1,1)),flip(a)].

2241 (C' * x) * x' = C'. [back_rewrite(2183),rewrite([2240(10)])].

2243 L(x,x',x * C) = x. [para(16(a,1),2096(a,1,3))].

2292 x' * (C * (C * x)) = C * C. [para(947(a,1),75(a,1,2)),rewrite([16(5,R),13(6),54(5),247(9),1759(8),31(8)]),flip(a)].

2314 C' * L(x,C' * y,y') = y' * ((C' * y) * x). [para(1152(a,1),75(a,1,1))].

2315 (C * x') * (x * y) = L(y * C,C',x). [para(1745(a,1),75(a,1,1)),rewrite([1962(5),1144(4)]),flip(a)].

2443 (C' * x') * (x * y) = L(y * C',C,x). [para(1044(a,1),77(a,1,1)),rewrite([31(6),31(8),1972(8)]),flip(a)].

2748 L(x,y,z / y) = L(x,y,z). [para(8(a,1),81(a,1,1,1,2)),rewrite([3(2),18(6),10(4),190(5)]),flip(a)].

2750 L(x,y',y * (z * y)) = L(x,z,y). [para(9(a,1),81(a,1,1,1,2,2)),rewrite([3(2),35(5),18(5)]),flip(a)].

2776 x' * (C' * (x * (C * y))) = L(y,C,x * (C' * x)). [para(53(a,1),81(a,1,1,1,2)),rewrite([176(2),12(11),10(10)])].

2853 C' * L(C * x,C,y) = L(x,C,C * (y * C)). [para(59(a,2),81(a,1,1,1)),rewrite([1978(7),2042(7),1972(7),232(18),1181(12),35(11),2443(12),10

44(9,R),10(9)])].

2966 x' * (y' * ((y * x) * z)) = L(z,y,x). [back_rewrite(256),rewrite([2748(8)])].

2967 L(x,y * z,y') = L(x,y,z). [back_rewrite(253),rewrite([2748(5)])].

2968 C' * L(x * C,C,y * (C' * y)) = L(x,C * C,y). [back_rewrite(1921),rewrite([2776(12)])].

2999 C * ((C' * x) * (x' * y)) = L(y,x',C' * x). [para(2241(a,1),18(a,1,1,1)),rewrite([31(3)])].

3011 L(x,x',C' * x) = x. [para(2241(a,1),71(a,2,1,1)),rewrite([31(8),35(10)])].

3026 L(x,y,z * y) = L(x,y,z). [para(10(a,1),82(a,1,1,1)),rewrite([10(7),18(5),2967(5)]),flip(a)].

3358 L(x,C,C' * y) = L(x,C,y). [para(54(a,1),87(a,1,2,2,1)),rewrite([1882(3),1972(5),31(5),232(7),1181(6),2966(8),54(6),1972(7),31(7)]),flip

(a)].

3427 L(x,C * C,C' * (C' * y)) = L(x,C,y * (C' * y)). [para(949(a,1),87(a,1,1,1)),rewrite([16(6,R),2042(7),2042(7),31(7),102(13),8(11),3(11),

12(11),232(12),1181(9),35(8),2776(8),102(12),8(10),3(10),16(14,R),2042(15),2042(15),31(15)]),flip(a)].

3484 L(x,C' * y,C) = L(x,C',C * y). [para(1152(a,1),87(a,1,2,2,1)),rewrite([1782(4),1853(6),31(4),245(7),118(4),128(8),1152(10),1853(12),31(

10)])].

3716 L(x,x',x * C') = x. [para(61(a,2),3011(a,1,3)),rewrite([16(4,R),9(4),3(2),16(4,R),9(4),3(2),35(9),16(9,R),9(9),3(7)])].

3722 x * L(y,x,C) = L(x * y,C,x'). [para(16(a,1),89(a,1,1,1,1,1)),rewrite([1972(3),16(6,R),35(6),31(2),2042(8),3358(10)])].

3772 C' * L(x,C',y) = L(x * C',y,C). [para(1044(a,1),89(a,2,1)),rewrite([1853(4),1745(4),1853(13),1962(13)])].

3962 L(x',x',C' * x) = x'. [para(96(a,1),35(a,1)),rewrite([2042(5),2042(9),1961(11),123(14),245(9),118(3),2999(9),2042(9),16(12,R),35(12)])]

.

4054 L(x,y * C,C) = L(x,y,C). [para(875(a,1),18(a,1,1,1)),rewrite([2036(5),232(13),1181(9),35(8),1147(7),3772(8),1044(5,R),53(5)]),flip(a)].

4055 L(x,C,C * (y * y)) = L(x,C * C,y). [para(875(a,2),18(a,1,1,1)),rewrite([2042(5),1972(5),12(11),1157(13),2776(12),2853(11),16(8,R),133(8

)])].

4156 L(x,C * y,C) = L(x,y,C). [back_rewrite(762),rewrite([4054(8)])].

4157 L(x * x,C * C,x') = x * x. [back_rewrite(958),rewrite([4055(8)])].

4680 L(x,C * C,C' * y) = L(x,y,C). [para(1965(a,1),87(a,1,1,1)),rewrite([2042(3),1972(8),31(8),2292(13),12(11),232(12),1181(9),102(11),10(12

),232(8),1181(6),2315(7),3772(8),1044(5,R),53(5),2292(8),1972(9),31(9)]),flip(a)].

4686 L(x,C,y * (C' * y)) = L(x,C',C * y). [back_rewrite(3427),rewrite([4680(10),3484(5)]),flip(a)].

4692 L(x,C * C,y) = L(x,y,C). [back_rewrite(2968),rewrite([4686(10),3772(10),1044(5,R),53(5),4156(4)]),flip(a)].

4696 L(x,C',C * y) = L(x,y,C). [back_rewrite(4680),rewrite([4692(7),3484(5)])].

4699 L(x * x,x',C) = x * x. [back_rewrite(4157),rewrite([4692(6)])].

5151 L(x,y * z,z) = L(x,y,z). [para(33(a,1),2748(a,1,3)),rewrite([2967(3)]),flip(a)].

5161 L(x,C',y) = L(x,y,C). [para(1181(a,1),2748(a,1,3)),rewrite([4696(5)]),flip(a)].

5165 L(x,C,x) = x. [para(2243(a,1),2748(a,2)),rewrite([191(5),2750(5)])].

5168 L(x,C',x) = x. [para(3716(a,1),2748(a,2)),rewrite([191(6),2750(6)])].

5196 (x * C) * x = x * (C * x). [para(5165(a,1),75(a,1,2))].

5216 L(C' * x,x,C) = C' * x. [para(5168(a,1),89(a,1,2)),rewrite([1853(4),1745(4),1853(10),1962(10)]),flip(a)].

5278 L(L(L(c1,C',A),A,C),A,C) != c1. [para(5161(a,2),19(a,1,1,1))].

5387 L(L(L(c1,C',A),C',A),A,C) != c1. [para(5161(a,2),5278(a,1,1))].

5425 L(x,C,C * y) = L(x,C,y). [para(16(a,2),3026(a,1,3))].

5427 L(x,y' * z,y) = L(x,y',z). [para(35(a,1),3026(a,1,3)),rewrite([5151(3)]),flip(a)].

5445 L(x,y',C * y) = L(x,y',C). [para(1765(a,1),3026(a,1,3)),flip(a)].

5455 L(x,y',C' * y) = L(x,y',C'). [para(2241(a,1),3026(a,1,3)),flip(a)].

5476 L(x * C,C,x) = x * C. [para(3026(a,1),5165(a,1))].

5478 L(x,y * C',C) = L(x,C',y). [para(3026(a,1),5161(a,1)),flip(a)].

5520 L(x',x',C') = x'. [back_rewrite(3962),rewrite([5455(6)])].

5606 x' * (C * (x * y)) = L(y * C,C,x). [para(10(a,1),104(a,1,1,1)),rewrite([10(9),2967(12)])].

5785 L(x,x,C') = x. [para(31(a,1),5520(a,1,1)),rewrite([31(2),31(5)])].

5791 (C' * x) * x = C' * (x * x). [para(5785(a,1),75(a,1,2))].

6725 C' * ((C * x) * y) = C * (x * (C' * y)). [para(123(a,1),10(a,1,2))].

7003 (C' * (x' * x')) * (x * y) = L((C' * x') * y,C,x). [para(57(a,2),129(a,2,1,1)),rewrite([2042(3),5151(8),2042(11),176(11)]),flip(a)].

7195 L(L(x,y,C),C,y) = x. [back_rewrite(1956),rewrite([7003(11),232(8),1181(6),2315(7),3772(8),1044(5,R),53(5)])].

7238 x' * (x' * ((C' * x) * ((C * x) * y))) = L(y,C * x,C' * x). [para(4699(a,1),87(a,1,1,1)),rewrite([176(2),2042(7),31(7),10(10),12(11),10

(15),2042(17),31(17)])].

7311 L(C,C' * x,C * x) = C. [para(133(a,1),105(a,1,2,2)),rewrite([245(6),118(3),5791(5),35(6),176(2),12(7),5606(6),5476(5),10(4)]),flip(a)].

7314 (x * x) / (C' * x) = C * x. [para(133(a,1),113(a,1,1)),rewrite([5216(6)])].

7391 L(x,y / z,z) = L(x,y,z). [para(7(a,1),5151(a,1,2)),flip(a)].

7400 L(x,y',C) = L(x,C,y). [para(54(a,1),5151(a,1,2)),rewrite([5425(4),5445(6)]),flip(a)].

7401 L(x,C,y') = L(x,y,C). [para(127(a,1),5151(a,1,2)),rewrite([5425(5),1962(7)])].

7429 L(x,C' * y,y') = L(x,C',y'). [para(2241(a,1),5151(a,1,2)),flip(a)].

7661 x' * ((C' * x) * y) = L(y * C',x',C). [back_rewrite(2314),rewrite([7429(7),3772(7)]),flip(a)].

7689 L(x,C * y,C' * y) = L(L(x,C,y),C,y). [back_rewrite(7238),rewrite([7661(10),1044(7,R),6725(7),3722(11),5606(8),16(5,R),35(5),31(5)]),fli

p(a)].

7811 L(L(x,C,y),C,y') = x. [para(7400(a,1),7195(a,1,1))].

7967 L(x,C',y) = L(x,C,y'). [para(1853(a,1),7401(a,1,3)),rewrite([5425(5),5478(8)]),flip(a)].

7977 L(L(L(c1,C,A'),C,A'),C,A') != c1. [para(7401(a,2),5387(a,1)),rewrite([7967(5),7967(9)])].

8892 (x * C) / (C' * x) = C * C. [para(16(a,1),155(a,1,1))].

9143 L(C,C' * x,x * C) = C. [para(16(a,1),7311(a,1,3))].

9634 (x * C) * (C' * x) = x * x. [para(9143(a,1),113(a,1,2)),rewrite([16(7,R),35(7),5196(3),118(5),151(6)]),flip(a)].

15611 L(x,y * y,C' * y) = L(L(x,C,y),C,y). [para(7314(a,1),7391(a,1,2)),rewrite([7689(6)]),flip(a)].

16435 L(x,y * C,C' * y) = L(x,C,y'). [para(8892(a,1),7391(a,1,2)),rewrite([4692(7),5427(5),7967(3)]),flip(a)].

16970 L(L(x,C,y),C,y) = L(x,C,y'). [para(9634(a,1),5151(a,1,2)),rewrite([15611(5),16435(10)])].

16995 $F. [back_rewrite(7977),rewrite([16970(9),31(5),7811(8)]),xx(a)].

============================== end of proof ==========================

% Proof 1 at 40.38 (+ 0.22) seconds.

% Length of proof is 418.

% Level of proof is 25.

% Maximum clause weight is 31.000.

% Given clauses 2045.

1 L(L(L(x,C,A),C,A),C,A) = x # label(non_clause) # label(goal). [goal].

2 0 * x = x. [assumption].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 A * ((x * y) * A) = (A * x) * (y * A). [assumption].

15 (A * x) * (y * A) = A * ((x * y) * A). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 L(x,y,z) = (z * y)' * (z * (y * x)). [assumption].

18 (x * y)' * (x * (y * z)) = L(z,y,x). [copy(17),flip(a)].

19 L(L(L(c1,C,A),C,A),C,A) != c1. [deny(1)].

28 0 / x = x'. [para(8(a,1),6(a,1,1))].

30 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([28(3)])].

31 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

32 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

34 x * (x' * y) = y. [back_rewrite(4),rewrite([31(1)])].

35 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

39 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

40 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

45 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(12(a,1),13(a,1,1,2)),rewrite([12(7)])].

47 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [para(13(a,1),13(a,1,1,2)),rewrite([13(9)])].

49 (A * x) * A = A * (x * A). [para(2(a,1),15(a,1,2)),rewrite([3(7)])].

50 (A * ((x * y) * A)) / (y * A) = A * x. [para(15(a,1),6(a,1,1))].

53 A * ((A' * x) * A) = x * A. [para(9(a,1),15(a,1,1)),rewrite([2(4)]),flip(a)].

54 (A * x)' * (A * ((x * y) * A)) = y * A. [para(15(a,1),10(a,1,2))].

57 ((x * A) * (A * ((y * x) * A))) * z = (x * A) * ((A * y) * ((x * A) * z)). [para(15(a,1),13(a,1,1,2))].

58 A * (((x * A) * y) * A) = A * (x * (A * (y * A))). [para(15(a,1),13(a,1))].

59 (A * x) * (y * (z * (y * A))) = A * ((x * (y * (z * y))) * A). [para(13(a,1),15(a,1,2))].

62 C * (x / C) = x. [para(16(a,2),7(a,1))].

63 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

64 x' * (C * x) = C. [para(16(a,2),10(a,1,2))].

65 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

66 C * (x * x) = x * (x * C). [para(16(a,2),12(a,1))].

67 C * (x * x) = x * (C * x). [para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].

68 (x * (x * C)) * y = x * (C * (x * y)). [para(16(a,1),13(a,1,1,2))].

69 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

70 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

71 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

73 (A * x) * (A * C) = A * ((x * C) * A). [para(16(a,1),15(a,1,2))].

78 L(x,y,z) / (z * (y * x)) = (z * y)'. [para(18(a,1),6(a,1,1))].

79 x' * ((x / y) * (y * z)) = L(z,y,x / y). [para(7(a,1),18(a,1,1,1))].

80 L(x,y / x,z) = (z * (y / x))' * (z * y). [para(7(a,1),18(a,1,2,2)),flip(a)].

84 L(x,y,(y * x)') = ((y * x)' * y)'. [para(8(a,1),18(a,1,2)),rewrite([3(6)]),flip(a)].

86 L(x',x,y) = (y * x)' * y. [para(9(a,1),18(a,1,2,2)),rewrite([3(4)]),flip(a)].

87 (x * y) * L(z,y,x) = x * (y * z). [para(18(a,1),10(a,1,2)),rewrite([30(3)])].

88 x' * (y' * ((y * x) * z)) = L(z,y * x,y'). [para(10(a,1),18(a,1,1,1))].

89 L(x * y,x',z) = (z * x')' * (z * y). [para(10(a,1),18(a,1,2,2)),flip(a)].

92 (x * (y * z)) * ((x * y)' * ((x * (y * z)) * u)) = ((x * (y * z)) * L(z,y,x)) * u. [para(18(a,1),13(a,1,1,2)),flip(a)].

93 (x * (y * (x * z)))' * (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(13(a,1),18(a,1,1,1)),rewrite([13(8)])].

94 (x * (y * (z * y)))' * (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(13(a,1),18(a,1,2,2))].

97 ((A * x) * y)' * (A * ((x * y) * A)) = L(A,y,A * x). [para(15(a,1),18(a,1,2))].

98 (x * C)' * (C * (x * y)) = L(y,x,C). [para(16(a,1),18(a,1,1,1))].

100 (C * x)' * (x * (C * y)) = L(y,C,x). [para(16(a,2),18(a,1,1,1))].

101 (x * y)' * (x * (C * y)) = L(C,y,x). [para(16(a,2),18(a,1,2,2))].

102 L(x,y,z)' * ((z * y)' * ((z * (y * x)) * u)) = L(u,z * (y * x),(z * y)'). [para(18(a,1),18(a,1,1,1))].

104 ((x * y)' * x)' * L(z,y,x) = L(y * z,x,(x * y)'). [para(18(a,1),18(a,1,2))].

105 x' * C = C * x'. [para(16(a,2),31(a,2)),rewrite([31(2)])].

106 (x / y)' = y / x. [para(7(a,1),32(a,1,2)),flip(a)].

108 x / (y * (z * (y * x))) = (y * (z * y))'. [para(13(a,1),32(a,1,2))].

110 x / (x * C) = C'. [para(16(a,1),32(a,1,2))].

111 C / (C * x) = x'. [para(16(a,2),32(a,1,2))].

116 x / C = C' * x. [para(62(a,1),10(a,1,2)),flip(a)].

119 (x * C)' * (x * y) = L(C' * y,C,x). [para(62(a,1),18(a,1,2,2)),rewrite([116(7)])].

123 A * (((A' * x) * y) * A) = x * (y * A). [para(34(a,1),15(a,1,1)),flip(a)].

125 x * (C * x') = C. [para(16(a,2),34(a,1,2))].

126 x' * (y * ((y' * x) * z)) = L(z,y' * x,y). [para(34(a,1),18(a,1,1,1))].

127 L(x' * y,x,z) = (z * x)' * (z * y). [para(34(a,1),18(a,1,2,2)),flip(a)].

130 C * (x * (C' * x)) = x * x. [para(63(a,1),13(a,2,2)),rewrite([16(6,R)])].

131 C' * (x * (y * (x * C))) = x * (y * x). [para(13(a,1),63(a,1,2))].

133 (x * C')' * (x * y) = L(y * C,C',x). [para(63(a,1),18(a,1,2,2))].

134 (C' * x)' * x = L(C,x,C'). [para(63(a,1),18(a,1,2))].

135 (C * x) * (x' * ((C * x) * y)) = C * (x * (C * y)). [para(64(a,1),13(a,1,1,2)),rewrite([16(4,R),70(5)]),flip(a)].

137 L(C * x,x',y) = (y * x')' * (y * C). [para(64(a,1),18(a,1,2,2)),flip(a)].

139 L(C,x,C') = C. [para(34(a,1),64(a,1,2)),rewrite([134(5)])].

142 x' / x = x' * x'. [para(8(a,1),35(a,1,1,2)),rewrite([3(3)])].

143 x / x' = x * x. [para(9(a,1),35(a,1,1,2)),rewrite([3(2)])].

144 (x' * y) / (x * y) = x' * x'. [para(10(a,1),35(a,1,1,2))].

149 (C * (x * C)) / x = C * C. [para(16(a,1),35(a,1,1,2))].

150 C' * (x * (C * x)) = x * x. [para(16(a,2),35(a,1,1,2)),rewrite([116(5)])].

153 (C' * x) / (x * C) = C' * C'. [para(63(a,1),35(a,1,1,2))].

155 (x / y) * (y / x) = 0. [para(106(a,1),8(a,1,1))].

161 (C' * x)' = C / x. [para(34(a,1),111(a,1,2)),flip(a)].

170 C' * (x * ((C * x') * y)) = L(y,C * x',x). [para(125(a,1),18(a,1,1,1))].

171 L(C * x',x,y) = (y * x)' * (y * C). [para(125(a,1),18(a,1,2,2)),flip(a)].

174 (x * x)' = x' * x'. [para(143(a,1),106(a,1,1)),rewrite([142(4)])].

178 x' * (C * x') = C * (x' * x'). [para(105(a,1),12(a,2,2)),rewrite([16(5,R)]),flip(a)].

184 (C' * x) * (C / x) = 0. [para(116(a,1),155(a,1,1))].

186 ((x / y) * (z * x)) / y = (x / y) * (z * (x / y)). [para(7(a,1),39(a,1,1,2,2))].

187 x * ((y / (x * z)) * x) = (x * y) / z. [para(7(a,1),39(a,1,1,2)),flip(a)].

189 x * ((x * y)' * x) = x / y. [para(8(a,1),39(a,1,1,2)),rewrite([3(2)]),flip(a)].

190 (x * y) / x' = x * (y * x). [para(9(a,1),39(a,1,1,2,2)),rewrite([3(2)])].

198 (C * (x * (y * C))) / y = C * (x * C). [para(16(a,1),39(a,1,1,2,2))].

202 (x * L(y,z,x)) / (z * y) = x / z. [para(18(a,1),39(a,1,1,2)),rewrite([189(8)])].

205 C' * (x * x) = x * (C' * x). [para(63(a,1),39(a,1,1,2)),rewrite([116(3)])].

207 (C * C) / x = C * (x' * C). [para(64(a,1),39(a,1,1,2))].

228 (x' * y) * x = x' * (y / x'). [para(8(a,1),40(a,1,2,2)),rewrite([3(5)]),flip(a)].

229 (x * y) * x' = x * (y / x). [para(9(a,1),40(a,1,2,2)),rewrite([3(3)]),flip(a)].

230 (x / y) * (y * z) = y' * ((y * x) * z). [para(40(a,1),10(a,1,2)),flip(a)].

231 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),40(a,1,2,2)),flip(a)].

237 (x / C') * y = (C * x) * y. [para(40(a,1),16(a,1)),rewrite([116(5),231(9),16(12,R),34(12)]),flip(a)].

239 (C * x) * y = (x * C) * y. [para(16(a,1),40(a,2,1)),rewrite([116(3),231(7),237(7),34(8)])].

242 (x * y)' * ((z / (x * y)') * L(u,y,x)) = ((x * y)' * z) * (x * (y * u)). [para(18(a,1),40(a,1,2,2))].

243 (x * y) * (x' * z) = x * ((y / x) * z). [para(34(a,1),40(a,1,2,2)),flip(a)].

245 (x' * y) * (C * x) = x' * (C * (y / x')). [para(64(a,1),40(a,1,2,2)),rewrite([16(5,R)]),flip(a)].

246 (x * y) * (C * x') = x * (C * (y / x)). [para(125(a,1),40(a,1,2,2)),rewrite([16(3,R)]),flip(a)].

247 (C * x) * (C / x) = C * C. [para(125(a,1),40(a,1,2)),rewrite([116(7),161(9)]),flip(a)].

251 x / A' = x * A. [back_rewrite(53),rewrite([228(6),34(8)])].

252 L(x,y * z,y') = L(x,y,z / y). [back_rewrite(79),rewrite([230(4),88(6)])].

255 x' * (y' * ((y * x) * z)) = L(z,y,x / y). [back_rewrite(88),rewrite([252(9)])].

256 (x * A') * A = x. [para(251(a,1),6(a,1))].

257 (x * A) * A' = x. [para(251(a,1),7(a,1,1))].

259 (x * A)' = A' / x. [para(251(a,1),106(a,1,1))].

264 x / A = x * A'. [para(256(a,1),6(a,1,1))].

267 A * ((x * (y * A')) * A) = (A * x) * y. [para(256(a,1),15(a,1,2)),flip(a)].

268 x' * ((x * A') * (A * y)) = L(y,A,x * A'). [para(256(a,1),18(a,1,1,1))].

270 (x * A')' = A / x. [para(256(a,1),32(a,1,2)),flip(a)].

281 ((x * A) * (y * x)) * A = (x * A) * (y * (x * A)). [para(257(a,1),39(a,1,1,2,2)),rewrite([251(7)])].

305 (A * C)' = C' * A'. [para(16(a,1),259(a,1,1)),rewrite([116(8)])].

306 L(x,A,y * A') = L(x,A,y). [para(259(a,1),18(a,1,1)),rewrite([230(7),268(8)])].

321 A / C' = A * C. [para(270(a,1),161(a,1)),rewrite([251(8),16(7)])].

325 (A * C) * (C' * A') = 0. [para(321(a,1),155(a,1,1)),rewrite([264(7)])].

428 (A * C) * ((C' * A') * x) = x. [para(305(a,1),34(a,1,2,1))].

433 L(A,x,A) = A. [para(49(a,1),10(a,1,2)),rewrite([18(8)])].

434 (A * (A * (x * A))) * y = A * ((A * x) * (A * y)). [para(49(a,1),13(a,1,1,2))].

435 A * ((x * A) * A) = A * (x * (A * A)). [para(49(a,1),13(a,1))].

436 (A * x) * (A * (y * A)) = A * ((x * (A * y)) * A). [para(49(a,1),15(a,1,2))].

441 (A * (x * A))' = A' / (A * x). [para(49(a,1),259(a,1,1))].

451 (x * (y * (z * (z * (y * x))))) * u = x * (y * (z * (z * (y * (x * u))))). [para(45(a,1),13(a,1,1,2)),rewrite([45(11)])].

458 C * (x * (y * (y * x))) = x * (y * (y * (x * C))). [para(45(a,1),16(a,2))].

510 L(C,x,C) = C. [para(65(a,2),18(a,1,2)),rewrite([64(8)]),flip(a)].

516 (C * x)' = (x * C)'. [para(65(a,1),111(a,1,2)),rewrite([111(6)]),flip(a)].

529 (C * x) * (x * C)' = 0. [para(516(a,1),9(a,1,2))].

532 (C * x)' * ((x * C) * y) = y. [para(516(a,2),10(a,1,1))].

533 (C * (x * x))' = (x * (x * C))'. [para(12(a,1),516(a,2,1))].

566 C * (x * (y * (z * (y * x)))) = x * (y * (z * (y * (x * C)))). [para(47(a,1),16(a,2))].

568 C * (x * (y * (x * (C * z)))) = C * (x * (y * (x * (z * C)))). [para(16(a,1),47(a,2,2,2,2,2)),rewrite([47(7)])].

656 (A * (x * A)) / (y * A) = A * (x / y). [para(7(a,1),50(a,1,1,2,1))].

690 (C * (x * x))' * (x * ((x * C) * y)) = L(y,x * C,x). [para(66(a,2),18(a,1,1,1))].

694 x * (C * (x' * x')) = x' * C. [para(66(a,2),34(a,1,2))].

716 (x * (C * x)) / (x * x) = C. [para(67(a,1),6(a,1,1))].

726 L(x,C,x) = L(x,x,C). [para(67(a,1),18(a,1,2)),rewrite([100(7)])].

748 (x * (C * (C * (x * x)))) * y = x * (C * (x * (C * (x * y)))). [para(67(a,2),47(a,1,1,2,2))].

754 L(A,A,C) = A. [para(726(a,1),433(a,1))].

761 L(x * A,x,A) = x * A. [para(12(a,1),54(a,1,2,2)),rewrite([18(9)])].

765 L(x * (y * A),y,A) = (x * y) * A. [para(13(a,1),54(a,1,2,2)),rewrite([18(10)])].

779 A / x = A * x'. [para(54(a,1),39(a,1,1,2)),rewrite([656(8),32(3),189(10)]),flip(a)].

815 (x * A')' = A * x'. [back_rewrite(270),rewrite([779(6)])].

817 (A * x') * x = A. [para(779(a,1),7(a,1,1))].

818 A * (A' / x) = x'. [para(779(a,1),32(a,1)),rewrite([259(4)])].

820 A * (C' * A') = C'. [para(779(a,1),110(a,1)),rewrite([305(5)])].

821 C' * A = A * C'. [para(779(a,1),116(a,1)),flip(a)].

827 C * (A * C') = A. [para(817(a,1),16(a,2))].

831 (A * x) * x' = A. [para(30(a,1),817(a,1,1,2))].

848 (A * C) / (A * C') = C * C. [para(827(a,1),35(a,1,1,2)),rewrite([16(3)])].

858 (A * x)' = x' * A'. [para(831(a,1),32(a,1,2)),rewrite([264(3)]),flip(a)].

859 x * (A' * x)' = A. [para(34(a,1),831(a,1,1))].

881 A' / (A * x) = (A' / x) * A'. [back_rewrite(441),rewrite([858(5),259(3)]),flip(a)].

913 A' / x = A' * x'. [para(818(a,1),10(a,1,2)),flip(a)].

923 (A' * x') * A' = A' * (x' * A'). [back_rewrite(881),rewrite([913(5),858(5),913(10)]),flip(a)].

946 (x * A)' = A' * x'. [back_rewrite(259),rewrite([913(6)])].

950 (A * x) * (A * C') = A * ((x * C') * A). [para(821(a,1),15(a,1,2))].

958 (A' * x)' = x' * A. [para(859(a,1),10(a,1,2)),flip(a)].

961 x' * ((A * x) * (y * (x * ((x' * A) * z)))) = (x' * (A * ((x * y) * A))) * z. [para(859(a,1),47(a,1,1,2,2,2)),rewrite([958(4),231(7),779

(4),30(4),15(6),958(12),958(15),231(19),779(12),30(12)]),flip(a)].

994 (A * C') * (A * x) = A * (A * (x * C')). [para(184(a,1),57(a,2,2,2)),rewrite([821(4),436(12),264(15),246(17),264(14),257(15),34(11),821(

11),3(15)]),flip(a)].

1012 (A * C) * (A * x) = A * (A * (x * C)). [para(529(a,1),57(a,2,2,2)),rewrite([16(3),436(10),858(14),13(16),820(14),229(10),116(8),34(10),

16(9),3(13)]),flip(a)].

1030 L(x,x * A',A) = x. [para(7(a,1),761(a,1,1)),rewrite([264(2),264(7),256(10)])].

1051 C' * A' = A' * C'. [para(820(a,1),10(a,1,2)),flip(a)].

1053 C * (A' * C') = L(A',C',A). [para(820(a,1),18(a,1,2)),rewrite([858(5),30(3),229(7),116(5),1051(6)])].

1061 (A * C) * ((A' * C') * x) = x. [back_rewrite(428),rewrite([1051(8)])].

1066 A * L(A',C',A) = 0. [back_rewrite(325),rewrite([1051(8),243(9),264(4),229(8),116(6),1051(7),1053(8)])].

1068 ((x * A) * y) * A = x * (A * (y * A)). [para(58(a,1),10(a,1,2)),rewrite([10(10)]),flip(a)].

1086 (x * A) * (y * (x * A)) = x * (A * ((y * x) * A)). [back_rewrite(281),rewrite([1068(6)]),flip(a)].

1094 (x' * A') * (A * x) = 0. [para(858(a,1),8(a,1,1))].

1095 (A * x) * (x' * A') = 0. [para(858(a,1),9(a,1,2))].

1097 (x' * A') * (A * (x * y)) = L(y,x,A). [para(858(a,1),18(a,1,1))].

1152 A * ((x * (A' * y)) * A) = A * ((x * A') * (y * A)). [para(257(a,1),59(a,2,2,1,2,2)),rewrite([8(10),3(8),243(8),264(3)]),flip(a)].

1168 (A * x) * (A * (A * (A * C))) = A * ((x * (A * (A * C))) * A). [para(66(a,1),59(a,1,2,2)),rewrite([16(15)])].

1189 L(A',C',A) = A'. [para(1066(a,1),10(a,1,2)),rewrite([3(4)]),flip(a)].

1192 C * (A' * C') = A'. [back_rewrite(1053),rewrite([1189(13)])].

1269 A * (C * ((A' * C') * x)) = L(x,A' * C',C). [para(1192(a,1),18(a,1,1,1)),rewrite([30(3)])].

1318 C * (x * C) = x * (C * C). [para(69(a,2),39(a,1,1)),rewrite([116(8),10(9)]),flip(a)].

1398 C * (C * x) = x * (C * C). [para(70(a,1),63(a,1,2)),rewrite([10(9)]),flip(a)].

1441 ((x * C) * y)' * ((C * x) * (y * z)) = L(z,y,C * x). [para(239(a,1),18(a,1,1,1))].

1451 ((x * C) * (y * ((C * x) * z))) / z = (C * x) * (y * (C * x)). [para(239(a,1),39(a,1,1))].

1452 (C * x) * (y * (C * x)) = (x * C) * (y * (x * C)). [para(239(a,2),39(a,1,1,2,2)),rewrite([1451(8)])].

1518 C * (C * (C * x)') = C / x. [para(247(a,1),10(a,1,2)),rewrite([1318(7,R),16(6,R)])].

1539 C' * x = x * C'. [para(8(a,1),71(a,2,2,2)),rewrite([34(8),3(7)]),flip(a)].

1563 (C * (x * C))' = (x * (C * C))'. [para(71(a,2),111(a,1,2)),rewrite([111(8)])].

1573 (x * C')' = C / x. [para(71(a,2),161(a,1,1)),rewrite([34(8),16(9,R),9(9),3(7)])].

1673 x' * ((x * C) * y) = L(y * C,C',x). [back_rewrite(133),rewrite([1573(4),230(4)])].

1694 C * (x * C') = x. [para(1539(a,1),10(a,1,2)),rewrite([30(3)])].

1700 (C' * (C' * x)) * y = C' * (x * (C' * y)). [para(1539(a,2),13(a,1,1,2))].

1707 x * (C' * x') = C'. [para(1539(a,2),34(a,1,2))].

1730 C * (x * (x * C')) = x * x. [para(1539(a,1),71(a,1,2,2)),rewrite([63(11)])].

1734 x / C' = C * x. [para(7(a,1),1694(a,1,2)),flip(a)].

1765 (C * x)' = C' / x. [para(1734(a,1),106(a,1,1))].

1781 (x * (C * C))' = C' / (x * C). [back_rewrite(1563),rewrite([1765(5)]),flip(a)].

1785 C * (C * (C' / x)) = C / x. [back_rewrite(1518),rewrite([1765(5)])].

1817 (C' / (x * x)) * (x * ((x * C) * y)) = L(y,x * C,x). [back_rewrite(690),rewrite([1765(4)])].

1849 (x * (x * C))' = C' / (x * x). [back_rewrite(533),rewrite([1765(4)]),flip(a)].

1850 (C' / x) * ((x * C) * y) = y. [back_rewrite(532),rewrite([1765(3)])].

1852 (x * C)' = C' / x. [back_rewrite(516),rewrite([1765(3)]),flip(a)].

1869 x' * ((x * C') * y) = L(C' * y,C,x). [back_rewrite(119),rewrite([1852(3),230(5)])].

1870 (C' / x) * (C * (x * y)) = L(y,x,C). [back_rewrite(98),rewrite([1852(3)])].

1972 (x * (y * (x * C')))' = C / (x * (y * x)). [para(13(a,1),1573(a,1,1))].

1973 (x * C') * ((C / x) * y) = y. [para(1573(a,1),34(a,1,2,1))].

1995 A * ((C * A') * (x * A)) = x * (A * C). [para(34(a,1),73(a,1,1)),rewrite([16(10,R),1152(13)]),flip(a)].

2251 L(x,C / x,C * x) = x. [para(247(a,1),80(a,2,1,1)),rewrite([174(9),16(14,R),12(15),10(14),10(10)])].

2555 L(C * x',x,C') = C / x. [para(125(a,1),84(a,1,3,1)),rewrite([125(10),161(10)])].

2564 L(x,A,x') = x. [para(817(a,1),84(a,1,3,1)),rewrite([252(6),264(4),306(6),817(7),10(9),30(5)])].

2602 L(A * x,A,x') = A * x. [para(858(a,1),2564(a,1,3)),rewrite([306(8)])].

2667 x * L(y',y,x) = x / y. [para(86(a,2),39(a,2,2)),rewrite([39(6),189(4)]),flip(a)].

2800 C * L(x,C * y',y) = y * ((C * y') * x). [para(125(a,1),87(a,1,1))].

2840 x * (C' * y) = x * (y * C'). [para(1539(a,1),87(a,2,2)),rewrite([87(7)])].

2884 L(A,C * A',A * C) = A. [para(264(a,1),2251(a,1,2)),rewrite([16(8)])].

2916 x * L(y * z,y',x) = (x / y') * z. [para(89(a,2),13(a,2,2)),rewrite([189(5)]),flip(a)].

2976 (A * x') * (x * y) = L(A * y,A',x). [para(815(a,1),89(a,2,1)),flip(a)].

3125 x * L(y * C,C',x) = (x * C) * y. [para(63(a,1),92(a,1,1)),rewrite([161(4),63(7),230(4),1673(5),63(11),139(10)])].

3176 (A * (A * (A * C))) * x = A * (A * (A * (x * C))). [para(754(a,1),92(a,2,1,2)),rewrite([66(5),16(8),1852(9),264(9),1539(10),66(15),68(1

6),231(17),251(12),1539(11),2976(16),243(17),264(6),229(7),264(5),125(7),2916(11),251(5),16(4),1012(7),66(13),68(15),66(14)]),flip(a)].

3396 L(x,y,z / y) = L(x,y,z). [para(8(a,1),93(a,1,1,1,2)),rewrite([3(2),18(6),10(4),189(5)]),flip(a)].

3424 x' * (C' * (x * (C * y))) = L(y,C,x * (C' * x)). [para(63(a,1),93(a,1,1,1,2)),rewrite([174(2),12(11),10(10)])].

3425 (C / (x * (y * x))) * (x * (y * (x * z))) = L(z * C,C',x * (y * x)). [para(63(a,1),93(a,1,2,2,2,2)),rewrite([1972(6)])].

3429 C' * (x' * (C * (x * y))) = L(y,x,C * (x' * C)). [para(64(a,1),93(a,1,1,1,2)),rewrite([174(4),12(13),10(12)])].

3435 C' * (x * (C * (x' * y))) = L(y,x',C * (x * C)). [para(125(a,1),93(a,1,1,1,2)),rewrite([174(4),12(13),10(12)])].

3485 (C' / (C * (x * x))) * (C * (x * (C * (x * y)))) = L(y,x,C * (x * C)). [para(67(a,2),93(a,1,1,1,2)),rewrite([1765(6)])].

3574 x' * (C * (x * (C' * y))) = L(y,C',x * (C * x)). [para(1694(a,1),93(a,1,1,1,2)),rewrite([174(2),12(11),10(10)])].

3671 x' * (y' * ((y * x) * z)) = L(z,y,x). [back_rewrite(255),rewrite([3396(8)])].

3672 L(x,y * z,y') = L(x,y,z). [back_rewrite(252),rewrite([3396(5)])].

3690 L(x,y,z * y) = L(x,y,z). [para(10(a,1),94(a,1,1,1)),rewrite([10(7),18(5),3672(5)]),flip(a)].

4137 L(A,A,A * x) = A. [para(49(a,1),97(a,1,1,1)),rewrite([858(5),946(3),923(7),435(13),13(14),10(12),10(8),10(6)]),flip(a)].

4153 ((A * (A * x)) * x')' * (A * (A * A)) = L(A,x',A * (A * x)). [para(831(a,1),97(a,1,2,2,1))].

4221 L(A,A,x) = A. [para(34(a,1),4137(a,1,3))].

4226 (x * A) * A = x * (A * A). [para(4221(a,1),87(a,1,2))].

4262 L(C,C,x) = C. [para(16(a,2),101(a,1,1,1)),rewrite([1765(3),230(8),1318(8,R),16(7,R),1694(7),64(4)]),flip(a)].

4270 C' * (x' * (C * (C * x))) = L(C,C * x,x'). [para(64(a,1),101(a,1,1,1))].

4306 (C / x) * (C * x) = C * C. [para(101(a,1),70(a,2,2)),rewrite([1765(5),1785(7),510(9)])].

4478 L(x,A' * C',C) = L(x,C',C * A'). [para(1189(a,1),102(a,1,1,1)),rewrite([30(3),1573(6),264(4),1539(11),34(12),243(9),116(6),1539(7),1269

(10),1539(13),34(14),1573(14),264(12)])].

4656 A * (C * ((A' * C') * x)) = L(x,C',C * A'). [back_rewrite(1269),rewrite([4478(17)])].

4891 L(x,y,A * y') = L(x,y,A). [para(1094(a,1),93(a,1,1,1,2)),rewrite([3(3),1097(11),10(7),256(9)]),flip(a)].

4912 (A * (A * x)) * x' = A * A. [para(1095(a,1),15(a,2,2,1)),rewrite([256(10),2(10)])].

4941 L(A,x',A * (A * x)) = A. [back_rewrite(4153),rewrite([4912(6),174(4),12(11),10(10),10(6)]),flip(a)].

4947 C * L(x,C,y) = L(x * C,y,C'). [para(16(a,1),104(a,2,1)),rewrite([1852(3),7(4),30(3),1852(9),3396(10)])].

4960 A * L(x,A,y) = L(A * x,y,A'). [para(256(a,1),104(a,1,1,1,1,1)),rewrite([10(5),30(3),306(6),256(14),3672(11)])].

4977 x * L(y,x,A) = L(x * y,A,x'). [para(817(a,1),104(a,1,1,1,1,1)),rewrite([10(6),30(2),4891(4),817(11),3672(10)])].

5251 (x * (C * C)) * y = C * (x * (C * y)). [para(1318(a,1),13(a,1,1))].

5361 L(x * y,C * C,C' / (C * x)) = x * L(y,x,C * C). [para(1318(a,2),104(a,1,1,1)),rewrite([12(5),1765(6),16(8,R),1785(9),111(4),30(2),12(13

),1765(14)]),flip(a)].

5381 (x * (y * x))' = x' / (x * y). [para(9(a,1),108(a,1,2,2,2)),rewrite([3(3)]),flip(a)].

5390 (x' * y) / (x * (z * y)) = x' / (x * z). [para(34(a,1),108(a,1,2,2,2)),rewrite([5381(8)])].

5396 C' / (C * x) = x' / (C * C). [para(125(a,1),108(a,1,2,2)),rewrite([5381(10)]),flip(a)].

5595 x' * (C * (C * x)) = C * C. [para(1398(a,2),10(a,1,2))].

5600 (C' / (C * x)) * (x * (C * (C * y))) = L(y,C * C,x). [para(1398(a,2),18(a,1,1,1)),rewrite([1765(5),12(9)])].

5611 (x * (x * (C * C))) * y = x * (C * (C * (x * y))). [para(1398(a,1),45(a,1,1,2))].

5659 (C' / (C * (C * x))) * (C * (x * (C * (C * y)))) = L(y,C,C * (x * C)). [para(1398(a,2),93(a,1,1,1,2)),rewrite([1765(7)])].

5673 L(x,C * (C * y),C' / y) = C' * L(C * x,y,C). [para(1398(a,2),102(a,2,2)),rewrite([4262(3),1852(5),5251(10),1870(11),1852(14)]),flip(a)]

.

5689 L(C,C * x,x') = C. [back_rewrite(4270),rewrite([5595(8),1318(6,R),16(5,R),9(5),3(3)]),flip(a)].

5703 C' * L(C * C,x,C) = C. [para(1765(a,1),5689(a,1,3)),rewrite([5673(9)])].

5966 ((A' * x) * y) * A = A' * (x * (y * A)). [para(123(a,1),10(a,1,2)),flip(a)].

5982 (x * (A * ((y * x) * A))) * z = (x * A) * (y * ((x * A) * z)). [para(123(a,1),57(a,1,1,2)),rewrite([1086(6),34(14)])].

6066 L(C',A,A * C) = C'. [para(1707(a,1),2602(a,1,1)),rewrite([1539(8),1573(9),251(7),16(6),1539(13),34(14)])].

6074 C * ((C' / (A * A)) * (A * (A * x))) = L(x,A * A,C'). [para(6066(a,1),102(a,1,1,1)),rewrite([30(3),49(6),16(5),1849(7),950(15),9(12),2(

11),12(11),950(21),9(18),2(17),49(21),16(20),1849(22),3396(23)])].

6080 L(x,y' * C,y) = L(x,C * y',y). [para(16(a,2),126(a,1,2,2,1)),rewrite([170(8)]),flip(a)].

6087 x / (x' * y) = x * (y' * x). [para(126(a,1),39(a,1,1,2)),rewrite([202(8)])].

6163 L(L(x,y,z'),z' * y,z) = x. [para(87(a,1),126(a,1,2,2)),rewrite([34(5),10(3)]),flip(a)].

6200 C' * L(C * x,y',C * (y * C)) = L(x,y' * (C * C),y). [para(1318(a,2),126(a,1,2,2,1)),rewrite([174(4),13(11),12(13),3435(12)])].

6202 L(x,y' * (C * C),y) = L(x,C * (y' * C),y). [para(1318(a,2),126(a,2,2)),rewrite([174(4),5251(11),12(13),3435(12),6200(11)])].

6301 x * L(y' * z,y,x) = (x / y) * z. [para(127(a,2),13(a,2,2)),rewrite([189(4)]),flip(a)].

6353 L((C' / x) * y,C * x,x) = (C' / (x * x)) * (x * y). [para(67(a,2),127(a,2,1,1)),rewrite([1765(3),1765(11)])].

6702 L(x,y * z,z) = L(x,y,z). [para(32(a,1),3396(a,1,3)),rewrite([3672(3)]),flip(a)].

6706 L(x,y,z * (z * y)) = L(x,y,z * z). [para(35(a,1),3396(a,1,3)),flip(a)].

6707 L(x,y * C,C') = L(x,y * C,y). [para(110(a,1),3396(a,1,3))].

6708 L(x,C * y,y') = L(x,C * y,C). [para(111(a,1),3396(a,1,3))].

6714 L(x,y,C * (y * C)) = L(x,y,C * C). [para(149(a,1),3396(a,1,3)),flip(a)].

6718 L(x,C',C * y) = L(x,C',y). [para(1734(a,1),3396(a,1,3))].

6728 L(x,y * y,y * (C * y)) = L(x,y * y,C). [para(716(a,1),3396(a,1,3)),flip(a)].

6747 (C' / (x * x)) * (x * y) = L((C' / x) * y,C,x). [back_rewrite(6353),rewrite([6702(7)]),flip(a)].

6762 (C' / (C * (x * x))) * (C * (x * (C * (x * y)))) = L(y,x,C * C). [back_rewrite(3485),rewrite([6714(18)])].

6763 A * (C * ((A' * C') * x)) = L(x,C',A'). [back_rewrite(4656),rewrite([6718(17)])].

6767 L(L(x,A,C'),A,C') = L(x,A * A,C'). [back_rewrite(6074),rewrite([6747(12),264(5),1539(6),231(9),251(8),1539(7),1869(9),4977(11),4977(8),

34(5)])].

6773 L(x,y * C,y) = L(x,C,y). [back_rewrite(1817),rewrite([6747(9),1850(7)]),flip(a)].

6781 L(x,y * C,C') = L(x,C,y). [back_rewrite(6707),rewrite([6773(8)])].

7039 L(x,C,C * y) = L(x,C,y). [para(16(a,2),3690(a,1,3))].

7040 L(x,y' * z,y) = L(x,y',z). [para(34(a,1),3690(a,1,3)),rewrite([6702(3)]),flip(a)].

7067 L(x,C / x,C * C) = x. [para(2251(a,1),3690(a,2)),rewrite([247(7)])].

7100 L(x,y * (C' * y),y * y) = L(x,y * (C' * y),C). [para(130(a,1),3690(a,1,3))].

7101 (C' / (C * (C * x))) * (C * (x * (C * (C * y)))) = L(y,C,x). [back_rewrite(5659),rewrite([7039(21),3690(19)])].

7119 L(x,C * (y' * C),y) = L(x,y',C * C). [back_rewrite(6202),rewrite([7040(6)]),flip(a)].

7150 L(L(x,y,z'),z',y) = x. [back_rewrite(6163),rewrite([7040(5)])].

7207 L(x,C * y',y) = L(x,y',C). [back_rewrite(6080),rewrite([7040(4)]),flip(a)].

7283 x * ((C * x') * y) = C * L(y,x',C). [back_rewrite(2800),rewrite([7207(5)]),flip(a)].

7308 C * L(x * A,A',C) = x * (A * C). [back_rewrite(1995),rewrite([7283(9)])].

7522 (C * (C' / x)) * ((C * x) * ((C * (C' / x)) * (x * y))) = C * L(y,x,C). [para(18(a,1),135(a,2,2)),rewrite([1765(4),1765(8),106(9),1734(

8),1765(11)])].

7580 (C * (C' / x)) * ((C * x) * ((C * (C' / x)) * y)) = (C / x) * y. [para(127(a,2),135(a,2,2)),rewrite([1765(4),1765(8),106(9),1734(8),176

5(11),6301(21)])].

7593 C * L(x,y,C) = L(x * C,C',y). [back_rewrite(7522),rewrite([7580(16),230(4),1673(5)]),flip(a)].

7601 L(C * (x * A),C',A') = x * (A * C). [back_rewrite(7308),rewrite([7593(8),16(4,R)])].

7727 L(C',C * C,x) = C'. [para(1707(a,1),137(a,1,1)),rewrite([174(8),30(5),30(6),174(12),30(9),30(10),1781(11),7(14)])].

7826 L(x,C,y) = L(x,y,C'). [para(7727(a,1),102(a,1,1,1)),rewrite([30(3),1781(6),1539(12,R),1318(12,R),16(11,R),9(11),3(9),230(10),1852(4),15

39(9,R),63(9),230(6),1869(7),4947(7),16(5,R),34(5),1539(9,R),1318(9,R),16(8,R),9(8),3(6),1781(10),3396(11),6781(8)]),flip(a)].

7873 L(L(L(c1,C,A),A,C'),C,A) != c1. [para(7826(a,1),19(a,1,1))].

7896 C * L(x,y,C') = L(C * x,y,C'). [para(7826(a,1),104(a,1,2)),rewrite([1852(3),7(4),30(3),1852(10),3396(11)])].

7935 (C * x') / (x * C) = x' * x'. [para(16(a,2),144(a,1,1))].

8098 L(L(c1,C,A),A * A,C') != c1. [para(7826(a,1),7873(a,1)),rewrite([6767(12)])].

8100 L(L(c1,C,A),C,A * A) != c1. [para(7826(a,2),8098(a,1))].

8163 L(A,x',A * A) = A. [para(4941(a,1),3690(a,2)),rewrite([4912(8)])].

8433 (x * A') * A' = x * (A' * A'). [para(8163(a,1),78(a,1,1)),rewrite([12(8),779(9),858(9),5381(7),913(7),858(7),30(5),13(10),34(11),12(11)

,858(12),858(10),30(8)]),flip(a)].

8732 (C' / x) / (C / x) = C' * C'. [para(2667(a,1),153(a,1,1)),rewrite([16(9,R),7896(9),2555(9)])].

8917 L(C * C,x,C) = C * C. [para(5703(a,1),10(a,1,2)),rewrite([30(3)]),flip(a)].

8918 x / (C * C) = C' * (x * C'). [para(5703(a,1),39(a,1,1,2,2)),rewrite([63(5),8917(5)])].

8921 L(x,C * C,C' * (y * C')) = L(x,C,y * (C' * y)). [para(5703(a,1),93(a,1,1,1,2,2)),rewrite([63(5),8917(10),12(9),10(10),3424(8),8917(11)]

),flip(a)].

8933 C' / (C * x) = C' * (x' * C'). [back_rewrite(5396),rewrite([8918(10)])].

8961 C' * L(C * x,C,y) = L(x,C,y). [back_rewrite(7101),rewrite([8933(7),1765(5),1539(8,R),231(17),1734(11),34(10),230(11),1869(12),10(9)])].

8963 L(x,y,C * (y' * C)) = L(x,y,C * C). [back_rewrite(6762),rewrite([8933(6),174(4),1539(8,R),231(16),1734(11),34(10),12(10),10(9),3429(8)]

)].

8989 L(x,C,y * (C' * y)) = L(x,C * C,y). [back_rewrite(5600),rewrite([8933(5),13(13),3424(12),8961(11)])].

9005 L(x * y,C * C,C' * (x' * C')) = x * L(y,x,C * C). [back_rewrite(5361),rewrite([8933(9)])].

9024 C' * (x' * (C * (x * y))) = L(y,x,C * C). [back_rewrite(3429),rewrite([8963(14)])].

9032 L(x,C * C,C' * (y * C')) = L(x,C * C,y). [back_rewrite(8921),rewrite([8989(16)])].

9047 x * L(y,x,C * C) = L(x * y,C * C,x'). [back_rewrite(9005),rewrite([9032(12)]),flip(a)].

9472 L(C * (C' / x),C * x,C / x) = C' * (C / x). [para(4306(a,1),171(a,2,1,1)),rewrite([1765(4),174(14),16(19,R),12(20),10(19)])].

9528 L(x,y / z,z) = L(x,y,z). [para(7(a,1),6702(a,1,2)),flip(a)].

9529 L(x,y',y * z) = L(x,z,y). [para(10(a,1),6702(a,1,2)),rewrite([3690(2)]),flip(a)].

9530 L(x,y * (y * z),z) = L(x,y * y,z). [para(12(a,1),6702(a,1,2))].

9533 L(x,C * y,C) = L(x,y,C). [para(16(a,2),6702(a,1,2))].

9536 L(x,y,y' * z) = L(x,z,y'). [para(34(a,1),6702(a,1,2)),rewrite([3690(3)]),flip(a)].

9538 L(x,y',C * y) = L(x,C,y). [para(64(a,1),6702(a,1,2)),rewrite([7039(4)]),flip(a)].

9539 L(x,y,C * y') = L(x,C,y'). [para(125(a,1),6702(a,1,2)),rewrite([7039(5)]),flip(a)].

9552 L(x,x,A) = x. [para(1030(a,1),6702(a,2)),rewrite([256(5)])].

9594 L(x,C * (y * C),C * C) = L(x,y,C * C). [para(1318(a,2),6702(a,1,2))].

9609 L(x,y * (A * A),A) = L(x,y,A). [para(4226(a,1),6702(a,1,2)),rewrite([6702(10)])].

9616 L(x,C',y * (C * y)) = L(x,y * y,C). [para(150(a,1),6702(a,1,2)),rewrite([6728(5)]),flip(a)].

9625 L(x,C',y) = L(x,y,C). [back_rewrite(6718),rewrite([9529(5)]),flip(a)].

9647 L(x,C * y,y') = L(x,y,C). [back_rewrite(6708),rewrite([9533(8)])].

9862 x' * (C * (x * (C' * y))) = L(y,x * x,C). [back_rewrite(3574),rewrite([9616(14)])].

9881 (A * x) * x = A * (x * x). [para(9552(a,1),87(a,1,2))].

10009 (x * C') * L(y,x,C) = x * (C' * y). [para(9625(a,1),87(a,1,2))].

10013 L(x,y * (z * y),C) = L(x,C',y * (z * y)). [para(9625(a,1),93(a,2)),rewrite([1972(6),3425(11),16(5,R),34(5)]),flip(a)].

10019 C' * L(x,y,C) = L(C' * x,y,C). [para(9625(a,1),104(a,1,2)),rewrite([1573(4),7(3),1573(12),3396(11)])].

10037 L(x,y * (C' * y),y * y) = L(x,C',y * (C' * y)). [back_rewrite(7100),rewrite([10013(12)])].

10303 C' * L(x,C,y) = L(C' * x,C,y). [para(7039(a,1),127(a,1)),rewrite([16(9,R),1765(10),8933(10),13(16),3671(15)]),flip(a)].

10306 L(x,C * C,y) = L(x,C,y * y). [para(130(a,1),7039(a,1,3)),rewrite([8989(9)]),flip(a)].

10364 L(L(x,y,z),z,y) = x. [para(30(a,1),7150(a,1,1,3)),rewrite([30(3)])].

11027 (C * x) * (y * (C * x)) = C * ((C * x) * (y * x)). [para(186(a,1),1734(a,1)),rewrite([1734(3),1734(5),1734(10)])].

11134 (x * C) * (y * (x * C)) = C * ((C * x) * (y * x)). [back_rewrite(1452),rewrite([11027(6)]),flip(a)].

11225 (x / (y * z)) * y = y' * ((y * x) / z). [para(187(a,1),10(a,1,2)),flip(a)].

11226 (x' * y) / (x * z) = x' * ((y / z) * x'). [para(10(a,1),187(a,1,2,1,2)),flip(a)].

11603 x' / (x * y) = x' * (y' * x'). [back_rewrite(5390),rewrite([11226(5),32(3)]),flip(a)].

11766 (x * (y * x))' = x' * (y' * x'). [back_rewrite(5381),rewrite([11603(6)])].

11992 C' * (C / x) = C * (C' / x). [para(189(a,1),2251(a,1,3)),rewrite([1765(3),16(5,R),1765(9),16(11,R),111(12),106(9),1734(8),9472(10),176

5(8),16(10,R)])].

12019 C' / (x * (y * (x * C))) = C' * (C' * (x' * (y' * x'))). [para(131(a,1),189(a,1,2,1,1)),rewrite([11766(5),1539(10,R)]),flip(a)].

12764 L(A,A' * A',A * C) = A. [para(2884(a,1),9528(a,2)),rewrite([7935(9)])].

12765 L(x,C' / x,C * C) = x. [para(7067(a,1),9528(a,2)),rewrite([8918(6),1539(7,R),11992(7),10(8)])].

13018 L(x,C',y * (C' * y)) = L(x,y * y,C). [para(130(a,1),9533(a,1,2)),rewrite([10013(9)]),flip(a)].

13030 L(x,y * (C' * y),y * y) = L(x,y * y,C). [back_rewrite(10037),rewrite([13018(13)])].

13454 (A * C) * (x * C) = C * (C * (A * x)). [para(73(a,1),198(a,1,1,2)),rewrite([264(10),5982(11),16(3),16(6),229(9),264(7),125(9),16(11,R)

])].

14157 (A * x) / (x * x) = A * x'. [para(9552(a,1),202(a,1,1,2)),rewrite([779(6)])].

14279 (C' * (x * x)) * y = x * (C' * (x * y)). [para(205(a,2),13(a,1,1))].

14382 L(x,y * y,C) = L(x,C',y * y). [para(205(a,1),6702(a,1,2)),rewrite([13030(6)])].

14450 L(x,C',y * (C' * y)) = L(x,C',y * y). [back_rewrite(13018),rewrite([14382(10)])].

14470 x' * (C * (x * (C' * y))) = L(y,C',x * x). [back_rewrite(9862),rewrite([14382(11)])].

14535 L(x,y',C * C) = L(x,C * C,y). [para(207(a,1),9528(a,1,2)),rewrite([7119(6)])].

14556 L(x,C' / x,C / x) = x. [para(12765(a,1),3690(a,2)),rewrite([12(10),1785(10)])].

14965 L(x,C' * C',C / x) = x. [para(14556(a,1),9528(a,2)),rewrite([8732(6)])].

15679 L(x,C,A') = L(x,A,C). [para(16(a,1),306(a,1,3)),rewrite([16(5,R),9539(6)])].

15682 L(x,C',A') = L(x,A,C'). [para(1539(a,1),306(a,1,3)),rewrite([9536(7)])].

15710 L(C * (x * A),A,C') = x * (A * C). [back_rewrite(7601),rewrite([15682(9)])].

15711 A * (C * ((A' * C') * x)) = L(x,A,C'). [back_rewrite(6763),rewrite([15682(15)])].

15722 L(L(x,A,C),A',C) = x. [para(15679(a,1),10364(a,1,1))].

15806 L(x,A',C) = L(x,C,A). [para(10364(a,1),15722(a,1,1))].

15900 (x * A') * (A * y) = A' * ((A * x) * y). [para(264(a,1),230(a,1,1))].

17304 (x * C') * (C * y) = C' * ((C * x) * y). [para(1539(a,1),231(a,1,1)),rewrite([1734(11)])].

17514 L(x,A * C',C * C) = L(x,A * C',A * C). [para(848(a,1),3396(a,1,3))].

18064 (x * C) * (C' * y) = C * ((C' * x) * y). [para(16(a,1),243(a,1,1)),rewrite([116(9)])].

19706 (x * (y * A')) * A = A' * ((A * x) * y). [para(267(a,1),10(a,1,2)),flip(a)].

19741 C * (A * (A * x)) = A * ((A * C) * x). [para(245(a,1),267(a,1,2,1)),rewrite([30(4),30(6),264(5),49(10),19706(9),1673(9),3125(9),30(10)

,16(12,R)]),flip(a)].

22275 (A * (A * (A * C'))) * x = A * (A * (A * (x * C'))). [para(1539(a,1),434(a,1,1,2,2)),rewrite([994(17)])].

22869 L(x,y * y,y' * (C * y')) = L(x,C,y' * y'). [para(178(a,2),9538(a,1,3)),rewrite([174(4),30(2),30(2)])].

22977 L(x,C',y * y) = L(x,C,y' * y'). [para(130(a,1),9647(a,1,2)),rewrite([11766(6),30(5),22869(7),10013(11),14450(12)]),flip(a)].

23002 x' * (C * (x * (C' * y))) = L(y,C,x' * x'). [back_rewrite(14470),rewrite([22977(12)])].

23108 L(x,C,y * (y * (C * C))) = L(x,C,y * y). [para(458(a,2),7039(a,1,3)),rewrite([7039(9),7039(7),6706(5)]),flip(a)].

23915 C * ((A * C') * x) = L(A * x,A,C). [para(12764(a,1),242(a,1,2,2)),rewrite([243(9),264(4),8433(8),694(9),16(4,R),815(5),243(13),264(8),

8433(12),694(13),16(8,R),815(9),11225(11),1734(11),243(12),264(5),1539(6),17304(11),15900(10),1673(10),4977(10),63(6),30(5),4960(5),15679(6),

243(14),264(9),8433(13),694(14),16(9,R),815(10),12(20),8(19),3(17),229(16),264(14),125(16),16(12,R)]),flip(a)].

24093 L(x,A * y',y * y) = L(x,A * y,y * y). [para(14157(a,1),9528(a,1,2))].

24102 L(x,A * C',A * C) = L(x,A * C,C * C). [back_rewrite(17514),rewrite([24093(8)]),flip(a)].

24331 L(A,C' * C',C * A') = A. [para(264(a,1),14965(a,1,3))].

26168 (x * (y * (x * (C * C))))' = C' * (C' * (x' * (y' * x'))). [para(566(a,2),111(a,1,2)),rewrite([111(10),1765(7),12019(7)]),flip(a)].

27621 x / (A' * C') = x * (A * C). [para(1061(a,1),190(a,1,1)),rewrite([1852(4),264(4),1539(5),11134(20),16(10),5966(18),243(19),264(11),243

(18),116(13),1539(14),15711(19),7896(14),15710(14)])].

28757 (x / (y * C')) * (C' * y) = x. [para(2840(a,2),7(a,1))].

28774 (x * C) * (y * C') = C * ((C' * x) * y). [para(2840(a,1),239(a,2)),rewrite([243(6),116(3)]),flip(a)].

28798 x * (C' * (A * C')) = x * (A * (C' * C')). [para(9881(a,1),2840(a,2,2))].

30154 L(L(c1,C,A),C * C,A) != c1. [para(10306(a,2),8100(a,1))].

30158 L(L(x,y,C * C),C,y * y) = x. [para(10306(a,1),10364(a,1))].

30190 L(x,A * (A * (C * C)),A) = L(x,C,A * A). [para(10306(a,1),9609(a,2)),rewrite([12(7),66(6),19741(7),16(6,R),1318(6)])].

33236 A' * (C * (A * x)) = L(x * C,C,A). [para(765(a,1),7207(a,1)),rewrite([19706(7),16(6,R),256(13),15806(13)])].

34559 L(C' * (A * x),A,C) = (A * C') * x. [para(24331(a,1),92(a,2,1,2)),rewrite([12(11),1539(10),28798(12),15900(12),28774(11),1539(7),1539(

10,R),34(11),10(7),243(12),116(7),1539(8),1539(11,R),34(12),1573(8),251(6),16(5),12(16),1539(15),28798(17),15900(17),28774(16),1539(12),1539(

15,R),34(16),10(12),18064(9),1539(7),23915(9),10019(8),12(19),1539(18),28798(20),15900(20),28774(19),1539(15),1539(18,R),34(19),10(15),1539(1

2)])].

34561 C' * ((A * C) * x) = L(A * x,A,C'). [para(24331(a,1),242(a,1,2,2)),rewrite([243(10),116(5),1539(6),1539(9,R),34(10),1573(6),251(4),16(

3),243(13),116(8),1539(9),1539(12,R),34(13),1573(9),251(7),16(6),11225(9),116(9),243(12),264(4),243(11),116(6),1539(7),231(10),251(9),1539(8)

,1869(10),4977(9),34(6),4960(6),15682(7),243(16),116(11),1539(12),1539(15,R),34(16),1573(12),251(10),16(9),12(21),1539(20),28798(22),15900(22

),28774(21),1539(17),1539(20,R),34(21),10(17),1539(13,R)]),flip(a)].

35846 C' * (A * (A * (A * x))) = A * (A * (A * (x * C'))). [para(950(a,1),748(a,1,1,2,2,2)),rewrite([12(14),1539(13),28798(15),19741(16),287

74(15),1539(11),1539(14,R),34(15),1730(12),15(8),1539(5),49(7),1539(6),22275(9),23915(25),10009(24),17304(23),16(14),1012(22),16(20,R),34(20)

]),flip(a)].

36253 L(C * (A * x),A,C') = (A * C) * x. [para(1973(a,1),961(a,1,2)),rewrite([30(3),30(6),16(6),34561(8),7896(8),30(11),264(15),10(17),8(14)

,3(12),16(11)])].

36254 (A * C) * ((A * C') * x) = C * (A * (C' * (A * x))). [para(961(a,1),568(a,1,2)),rewrite([9(8),2(7),14279(8),1539(21),16(24,R),23915(24

),10019(23),34559(23),34561(22),7896(22),36253(22)]),flip(a)].

36477 (x * (A' * C')) * (A * C) = x. [para(27621(a,1),6(a,1))].

36906 L(x * y,C * C,x') = C * (x * (C' * y)). [para(28757(a,1),566(a,1,2,2,2)),rewrite([63(17),11225(13),1734(13),9024(14),9047(11)]),flip(a

)].

36919 x * L(y,x,C * C) = C * (x * (C' * y)). [back_rewrite(9047),rewrite([36906(11)])].

37108 L(L(x,A * C,C * C),C,A * A) = x. [para(73(a,1),30158(a,1,3)),rewrite([12(14),16(13),1318(14),23108(16)])].

40501 x / (A * C) = x * (A' * C'). [para(36477(a,1),6(a,1,1))].

43646 L(A * x,C,A' * A') = C * (A * (C' * x)). [para(10306(a,1),4960(a,2)),rewrite([36919(7)]),flip(a)].

45238 L(x,y',C * C) = L(x,y,C' * C'). [para(14535(a,2),9536(a,1)),rewrite([174(4),12(6),161(7),6087(5),9594(9),174(9)])].

45239 L(x,C,A * A) = L(x,A,C' * C'). [para(14535(a,2),9609(a,2)),rewrite([12(7),66(6),19741(7),16(6,R),1318(6),30190(9),45238(11)])].

45242 L(L(c1,C,A),A,C' * C') != c1. [para(14535(a,2),30154(a,1)),rewrite([45238(10)])].

45318 L(L(x,A * C,C * C),A,C' * C') = x. [back_rewrite(37108),rewrite([45239(12)])].

45646 L(x,A * C,C * C) = L(x,C,A' * A'). [para(950(a,1),1441(a,1,1,1)),rewrite([9(5),2(4),174(4),16(8),36254(14),12(15),23002(14),43646(11),

23002(10),16(14),24102(15)]),flip(a)].

45650 L(x,A * A,A * C) = L(x,C,A). [para(1168(a,1),1441(a,1,1,1)),rewrite([19741(8),16(7,R),1318(7),5611(10),66(8),19741(9),16(8,R),1318(8),

858(12),26168(10),1700(17),1539(15),13(16),16(20),3176(28),1012(29),16(27,R),19741(27),13454(26),451(30),35846(25),1539(22,R),10(22),10(21),1

0(17),10(13),33236(9),10303(8),63(5),16(13),9530(14)]),flip(a)].

45656 L(L(x,C,A' * A'),A,C' * C') = x. [back_rewrite(45318),rewrite([45646(7)])].

45657 L(x,A * C',A * C) = L(x,C,A' * A'). [back_rewrite(24102),rewrite([45646(15)])].

45758 L(x,C,A' * A') = L(x,C,A). [para(45650(a,1),9528(a,2)),rewrite([40501(7),12(9),34(8),45657(8)])].

45763 L(L(x,C,A),A,C' * C') = x. [back_rewrite(45656),rewrite([45758(7)])].

45764 $F. [resolve(45763,a,45242,a)].

============================== end of proof ==========================

% Proof 1 at 77.44 (+ 0.45) seconds.

% Length of proof is 403.

% Level of proof is 29.

% Maximum clause weight is 31.000.

% Given clauses 2593.

1 L(L(L(x,A,C),A,C),A,C) = x # label(non_clause) # label(goal). [goal].

2 0 * x = x. [assumption].

3 x * 0 = x. [assumption].

4 x * (x \ y) = y. [assumption].

6 (x * y) / y = x. [assumption].

7 (x / y) * y = x. [assumption].

8 x' * x = 0. [assumption].

9 x * x' = 0. [assumption].

10 x' * (x * y) = y. [assumption].

11 x * (x * y) = (x * x) * y. [assumption].

12 (x * x) * y = x * (x * y). [copy(11),flip(a)].

13 (x * (y * x)) * z = x * (y * (x * z)). [assumption].

14 A * ((x * y) * A) = (A * x) * (y * A). [assumption].

15 (A * x) * (y * A) = A * ((x * y) * A). [copy(14),flip(a)].

16 C * x = x * C. [assumption].

17 L(x,y,z) = (z * y)' * (z * (y * x)). [assumption].

18 (x * y)' * (x * (y * z)) = L(z,y,x). [copy(17),flip(a)].

19 L(L(L(c1,A,C),A,C),A,C) != c1. [deny(1)].

28 0 / x = x'. [para(8(a,1),6(a,1,1))].

30 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([28(3)])].

31 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].

32 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].

34 x * (x' * y) = y. [back_rewrite(4),rewrite([31(1)])].

35 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].

39 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].

40 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].

42 (x * (y * x))' * (x * (y * (x * z))) = z. [para(13(a,1),10(a,1,2))].

45 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(12(a,1),13(a,1,1,2)),rewrite([12(7)])].

47 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [para(13(a,1),13(a,1,1,2)),rewrite([13(9)])].

49 (A * x) * A = A * (x * A). [para(2(a,1),15(a,1,2)),rewrite([3(7)])].

50 (A * ((x * y) * A)) / (y * A) = A * x. [para(15(a,1),6(a,1,1))].

53 A * ((A' * x) * A) = x * A. [para(9(a,1),15(a,1,1)),rewrite([2(4)]),flip(a)].

54 (A * x)' * (A * ((x * y) * A)) = y * A. [para(15(a,1),10(a,1,2))].

57 ((x * A) * (A * ((y * x) * A))) * z = (x * A) * ((A * y) * ((x * A) * z)). [para(15(a,1),13(a,1,1,2))].

58 A * (((x * A) * y) * A) = A * (x * (A * (y * A))). [para(15(a,1),13(a,1))].

59 (A * x) * (y * (z * (y * A))) = A * ((x * (y * (z * y))) * A). [para(13(a,1),15(a,1,2))].

62 C * (x / C) = x. [para(16(a,2),7(a,1))].

63 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].

64 x' * (C * x) = C. [para(16(a,2),10(a,1,2))].

65 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].

66 C * (x * x) = x * (x * C). [para(16(a,2),12(a,1))].

67 C * (x * x) = x * (C * x). [para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].

68 (x * (x * C)) * y = x * (C * (x * y)). [para(16(a,1),13(a,1,1,2))].

69 C * (x * (C * y)) = C * (x * (y * C)). [para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].

70 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].

71 C * (x * (y * x)) = x * (y * (x * C)). [para(16(a,2),13(a,1))].

73 (A * x) * (A * C) = A * ((x * C) * A). [para(16(a,1),15(a,1,2))].

78 L(x,y,z) / (z * (y * x)) = (z * y)'. [para(18(a,1),6(a,1,1))].

79 x' * ((x / y) * (y * z)) = L(z,y,x / y). [para(7(a,1),18(a,1,1,1))].

80 L(x,y / x,z) = (z * (y / x))' * (z * y). [para(7(a,1),18(a,1,2,2)),flip(a)].

84 L(x,y,(y * x)') = ((y * x)' * y)'. [para(8(a,1),18(a,1,2)),rewrite([3(6)]),flip(a)].

86 L(x',x,y) = (y * x)' * y. [para(9(a,1),18(a,1,2,2)),rewrite([3(4)]),flip(a)].

87 (x * y) * L(z,y,x) = x * (y * z). [para(18(a,1),10(a,1,2)),rewrite([30(3)])].

88 x' * (y' * ((y * x) * z)) = L(z,y * x,y'). [para(10(a,1),18(a,1,1,1))].

89 L(x * y,x',z) = (z * x')' * (z * y). [para(10(a,1),18(a,1,2,2)),flip(a)].

92 (x * (y * z)) * ((x * y)' * ((x * (y * z)) * u)) = ((x * (y * z)) * L(z,y,x)) * u. [para(18(a,1),13(a,1,1,2)),flip(a)].

93 (x * (y * (x * z)))' * (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(13(a,1),18(a,1,1,1)),rewrite([13(8)])].

94 (x * (y * (z * y)))' * (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(13(a,1),18(a,1,2,2))].

97 ((A * x) * y)' * (A * ((x * y) * A)) = L(A,y,A * x). [para(15(a,1),18(a,1,2))].

98 (x * C)' * (C * (x * y)) = L(y,x,C). [para(16(a,1),18(a,1,1,1))].

100 (C * x)' * (x * (C * y)) = L(y,C,x). [para(16(a,2),18(a,1,1,1))].

101 (x * y)' * (x * (C * y)) = L(C,y,x). [para(16(a,2),18(a,1,2,2))].

102 L(x,y,z)' * ((z * y)' * ((z * (y * x)) * u)) = L(u,z * (y * x),(z * y)'). [para(18(a,1),18(a,1,1,1))].

104 ((x * y)' * x)' * L(z,y,x) = L(y * z,x,(x * y)'). [para(18(a,1),18(a,1,2))].

105 x' * C = C * x'. [para(16(a,2),31(a,2)),rewrite([31(2)])].

106 (x / y)' = y / x. [para(7(a,1),32(a,1,2)),flip(a)].

108 x / (y * (z * (y * x))) = (y * (z * y))'. [para(13(a,1),32(a,1,2))].

110 x / (x * C) = C'. [para(16(a,1),32(a,1,2))].

111 C / (C * x) = x'. [para(16(a,2),32(a,1,2))].

116 x / C = C' * x. [para(62(a,1),10(a,1,2)),flip(a)].

119 (x * C)' * (x * y) = L(C' * y,C,x). [para(62(a,1),18(a,1,2,2)),rewrite([116(7)])].

123 A * (((A' * x) * y) * A) = x * (y * A). [para(34(a,1),15(a,1,1)),flip(a)].

125 x * (C * x') = C. [para(16(a,2),34(a,1,2))].

126 x' * (y * ((y' * x) * z)) = L(z,y' * x,y). [para(34(a,1),18(a,1,1,1))].

127 L(x' * y,x,z) = (z * x)' * (z * y). [para(34(a,1),18(a,1,2,2)),flip(a)].

130 C * (x * (C' * x)) = x * x. [para(63(a,1),13(a,2,2)),rewrite([16(6,R)])].

131 C' * (x * (y * (x * C))) = x * (y * x). [para(13(a,1),63(a,1,2))].

133 (x * C')' * (x * y) = L(y * C,C',x). [para(63(a,1),18(a,1,2,2))].

134 (C' * x)' * x = L(C,x,C'). [para(63(a,1),18(a,1,2))].

135 (C * x) * (x' * ((C * x) * y)) = C * (x * (C * y)). [para(64(a,1),13(a,1,1,2)),rewrite([16(4,R),70(5)]),flip(a)].

137 L(C * x,x',y) = (y * x')' * (y * C). [para(64(a,1),18(a,1,2,2)),flip(a)].

139 L(C,x,C') = C. [para(34(a,1),64(a,1,2)),rewrite([134(5)])].

142 x' / x = x' * x'. [para(8(a,1),35(a,1,1,2)),rewrite([3(3)])].

143 x / x' = x * x. [para(9(a,1),35(a,1,1,2)),rewrite([3(2)])].

144 (x' * y) / (x * y) = x' * x'. [para(10(a,1),35(a,1,1,2))].

149 (C * (x * C)) / x = C * C. [para(16(a,1),35(a,1,1,2))].

150 C' * (x * (C * x)) = x * x. [para(16(a,2),35(a,1,1,2)),rewrite([116(5)])].

153 (C' * x) / (x * C) = C' * C'. [para(63(a,1),35(a,1,1,2))].

155 (x / y) * (y / x) = 0. [para(106(a,1),8(a,1,1))].

161 (C' * x)' = C / x. [para(34(a,1),111(a,1,2)),flip(a)].

170 C' * (x * ((C * x') * y)) = L(y,C * x',x). [para(125(a,1),18(a,1,1,1))].

171 L(C * x',x,y) = (y * x)' * (y * C). [para(125(a,1),18(a,1,2,2)),flip(a)].

174 (x * x)' = x' * x'. [para(143(a,1),106(a,1,1)),rewrite([142(4)])].

178 x' * (C * x') = C * (x' * x'). [para(105(a,1),12(a,2,2)),rewrite([16(5,R)]),flip(a)].

184 (C' * x) * (C / x) = 0. [para(116(a,1),155(a,1,1))].

186 ((x / y) * (z * x)) / y = (x / y) * (z * (x / y)). [para(7(a,1),39(a,1,1,2,2))].

187 x * ((y / (x * z)) * x) = (x * y) / z. [para(7(a,1),39(a,1,1,2)),flip(a)].

189 x * ((x * y)' * x) = x / y. [para(8(a,1),39(a,1,1,2)),rewrite([3(2)]),flip(a)].

190 (x * y) / x' = x * (y * x). [para(9(a,1),39(a,1,1,2,2)),rewrite([3(2)])].

198 (C * (x * (y * C))) / y = C * (x * C). [para(16(a,1),39(a,1,1,2,2))].

202 (x * L(y,z,x)) / (z * y) = x / z. [para(18(a,1),39(a,1,1,2)),rewrite([189(8)])].

205 C' * (x * x) = x * (C' * x). [para(63(a,1),39(a,1,1,2)),rewrite([116(3)])].

228 (x' * y) * x = x' * (y / x'). [para(8(a,1),40(a,1,2,2)),rewrite([3(5)]),flip(a)].

229 (x * y) * x' = x * (y / x). [para(9(a,1),40(a,1,2,2)),rewrite([3(3)]),flip(a)].

230 (x / y) * (y * z) = y' * ((y * x) * z). [para(40(a,1),10(a,1,2)),flip(a)].

231 (x' * y) * (x * z) = x' * ((y / x') * z). [para(10(a,1),40(a,1,2,2)),flip(a)].

237 (x / C') * y = (C * x) * y. [para(40(a,1),16(a,1)),rewrite([116(5),231(9),16(12,R),34(12)]),flip(a)].

239 (C * x) * y = (x * C) * y. [para(16(a,1),40(a,2,1)),rewrite([116(3),231(7),237(7),34(8)])].

242 (x * y)' * ((z / (x * y)') * L(u,y,x)) = ((x * y)' * z) * (x * (y * u)). [para(18(a,1),40(a,1,2,2))].

243 (x * y) * (x' * z) = x * ((y / x) * z). [para(34(a,1),40(a,1,2,2)),flip(a)].

245 (x' * y) * (C * x) = x' * (C * (y / x')). [para(64(a,1),40(a,1,2,2)),rewrite([16(5,R)]),flip(a)].

246 (x * y) * (C * x') = x * (C * (y / x)). [para(125(a,1),40(a,1,2,2)),rewrite([16(3,R)]),flip(a)].

247 (C * x) * (C / x) = C * C. [para(125(a,1),40(a,1,2)),rewrite([116(7),161(9)]),flip(a)].

251 x / A' = x * A. [back_rewrite(53),rewrite([228(6),34(8)])].

252 L(x,y * z,y') = L(x,y,z / y). [back_rewrite(79),rewrite([230(4),88(6)])].

255 x' * (y' * ((y * x) * z)) = L(z,y,x / y). [back_rewrite(88),rewrite([252(9)])].

256 (x * A') * A = x. [para(251(a,1),6(a,1))].

257 (x * A) * A' = x. [para(251(a,1),7(a,1,1))].

259 (x * A)' = A' / x. [para(251(a,1),106(a,1,1))].

264 x / A = x * A'. [para(256(a,1),6(a,1,1))].

267 A * ((x * (y * A')) * A) = (A * x) * y. [para(256(a,1),15(a,1,2)),flip(a)].

268 x' * ((x * A') * (A * y)) = L(y,A,x * A'). [para(256(a,1),18(a,1,1,1))].

270 (x * A')' = A / x. [para(256(a,1),32(a,1,2)),flip(a)].

281 ((x * A) * (y * x)) * A = (x * A) * (y * (x * A)). [para(257(a,1),39(a,1,1,2,2)),rewrite([251(7)])].

305 (A * C)' = C' * A'. [para(16(a,1),259(a,1,1)),rewrite([116(8)])].

306 L(x,A,y * A') = L(x,A,y). [para(259(a,1),18(a,1,1)),rewrite([230(7),268(8)])].

321 A / C' = A * C. [para(270(a,1),161(a,1)),rewrite([251(8),16(7)])].

325 (A * C) * (C' * A') = 0. [para(321(a,1),155(a,1,1)),rewrite([264(7)])].

346 (x * (x * C))' * (x * (C * (x * y))) = y. [para(16(a,1),42(a,1,1,1,2))].

428 (A * C) * ((C' * A') * x) = x. [para(305(a,1),34(a,1,2,1))].

433 L(A,x,A) = A. [para(49(a,1),10(a,1,2)),rewrite([18(8)])].

434 (A * (A * (x * A))) * y = A * ((A * x) * (A * y)). [para(49(a,1),13(a,1,1,2))].

436 (A * x) * (A * (y * A)) = A * ((x * (A * y)) * A). [para(49(a,1),15(a,1,2))].

451 (x * (y * (z * (z * (y * x))))) * u = x * (y * (z * (z * (y * (x * u))))). [para(45(a,1),13(a,1,1,2)),rewrite([45(11)])].

510 L(C,x,C) = C. [para(65(a,2),18(a,1,2)),rewrite([64(8)]),flip(a)].

516 (C * x)' = (x * C)'. [para(65(a,1),111(a,1,2)),rewrite([111(6)]),flip(a)].

529 (C * x) * (x * C)' = 0. [para(516(a,1),9(a,1,2))].

532 (C * x)' * ((x * C) * y) = y. [para(516(a,2),10(a,1,1))].

533 (C * (x * x))' = (x * (x * C))'. [para(12(a,1),516(a,2,1))].

566 C * (x * (y * (z * (y * x)))) = x * (y * (z * (y * (x * C)))). [para(47(a,1),16(a,2))].

568 C * (x * (y * (x * (C * z)))) = C * (x * (y * (x * (z * C)))). [para(16(a,1),47(a,2,2,2,2,2)),rewrite([47(7)])].

656 (A * (x * A)) / (y * A) = A * (x / y). [para(7(a,1),50(a,1,1,2,1))].

690 (C * (x * x))' * (x * ((x * C) * y)) = L(y,x * C,x). [para(66(a,2),18(a,1,1,1))].

694 x * (C * (x' * x')) = x' * C. [para(66(a,2),34(a,1,2))].

716 (x * (C * x)) / (x * x) = C. [para(67(a,1),6(a,1,1))].

726 L(x,C,x) = L(x,x,C). [para(67(a,1),18(a,1,2)),rewrite([100(7)])].

748 (x * (C * (C * (x * x)))) * y = x * (C * (x * (C * (x * y)))). [para(67(a,2),47(a,1,1,2,2))].

754 L(A,A,C) = A. [para(726(a,1),433(a,1))].

761 L(x * A,x,A) = x * A. [para(12(a,1),54(a,1,2,2)),rewrite([18(9)])].

765 L(x * (y * A),y,A) = (x * y) * A. [para(13(a,1),54(a,1,2,2)),rewrite([18(10)])].

779 A / x = A * x'. [para(54(a,1),39(a,1,1,2)),rewrite([656(8),32(3),189(10)]),flip(a)].

815 (x * A')' = A * x'. [back_rewrite(270),rewrite([779(6)])].

817 (A * x') * x = A. [para(779(a,1),7(a,1,1))].

818 A * (A' / x) = x'. [para(779(a,1),32(a,1)),rewrite([259(4)])].

820 A * (C' * A') = C'. [para(779(a,1),110(a,1)),rewrite([305(5)])].

821 C' * A = A * C'. [para(779(a,1),116(a,1)),flip(a)].

827 C * (A * C') = A. [para(817(a,1),16(a,2))].

831 (A * x) * x' = A. [para(30(a,1),817(a,1,1,2))].

848 (A * C) / (A * C') = C * C. [para(827(a,1),35(a,1,1,2)),rewrite([16(3)])].

858 (A * x)' = x' * A'. [para(831(a,1),32(a,1,2)),rewrite([264(3)]),flip(a)].

859 x * (A' * x)' = A. [para(34(a,1),831(a,1,1))].

913 A' / x = A' * x'. [para(818(a,1),10(a,1,2)),flip(a)].

950 (A * x) * (A * C') = A * ((x * C') * A). [para(821(a,1),15(a,1,2))].

958 (A' * x)' = x' * A. [para(859(a,1),10(a,1,2)),flip(a)].

961 x' * ((A * x) * (y * (x * ((x' * A) * z)))) = (x' * (A * ((x * y) * A))) * z. [para(859(a,1),47(a,1,1,2,2,2)),rewrite([958(4),231(7),779

(4),30(4),15(6),958(12),958(15),231(19),779(12),30(12)]),flip(a)].

994 (A * C') * (A * x) = A * (A * (x * C')). [para(184(a,1),57(a,2,2,2)),rewrite([821(4),436(12),264(15),246(17),264(14),257(15),34(11),821(

11),3(15)]),flip(a)].

1012 (A * C) * (A * x) = A * (A * (x * C)). [para(529(a,1),57(a,2,2,2)),rewrite([16(3),436(10),858(14),13(16),820(14),229(10),116(8),34(10),

16(9),3(13)]),flip(a)].

1030 L(x,x * A',A) = x. [para(7(a,1),761(a,1,1)),rewrite([264(2),264(7),256(10)])].

1051 C' * A' = A' * C'. [para(820(a,1),10(a,1,2)),flip(a)].

1053 C * (A' * C') = L(A',C',A). [para(820(a,1),18(a,1,2)),rewrite([858(5),30(3),229(7),116(5),1051(6)])].

1061 (A * C) * ((A' * C') * x) = x. [back_rewrite(428),rewrite([1051(8)])].

1066 A * L(A',C',A) = 0. [back_rewrite(325),rewrite([1051(8),243(9),264(4),229(8),116(6),1051(7),1053(8)])].

1068 ((x * A) * y) * A = x * (A * (y * A)). [para(58(a,1),10(a,1,2)),rewrite([10(10)]),flip(a)].

1086 (x * A) * (y * (x * A)) = x * (A * ((y * x) * A)). [back_rewrite(281),rewrite([1068(6)]),flip(a)].

1094 (x' * A') * (A * x) = 0. [para(858(a,1),8(a,1,1))].

1095 (A * x) * (x' * A') = 0. [para(858(a,1),9(a,1,2))].

1097 (x' * A') * (A * (x * y)) = L(y,x,A). [para(858(a,1),18(a,1,1))].

1152 A * ((x * (A' * y)) * A) = A * ((x * A') * (y * A)). [para(257(a,1),59(a,2,2,1,2,2)),rewrite([8(10),3(8),243(8),264(3)]),flip(a)].

1168 (A * x) * (A * (A * (A * C))) = A * ((x * (A * (A * C))) * A). [para(66(a,1),59(a,1,2,2)),rewrite([16(15)])].

1189 L(A',C',A) = A'. [para(1066(a,1),10(a,1,2)),rewrite([3(4)]),flip(a)].

1192 C * (A' * C') = A'. [back_rewrite(1053),rewrite([1189(13)])].

1269 A * (C * ((A' * C') * x)) = L(x,A' * C',C). [para(1192(a,1),18(a,1,1,1)),rewrite([30(3)])].

1318 C * (x * C) = x * (C * C). [para(69(a,2),39(a,1,1)),rewrite([116(8),10(9)]),flip(a)].

1398 C * (C * x) = x * (C * C). [para(70(a,1),63(a,1,2)),rewrite([10(9)]),flip(a)].

1441 ((x * C) * y)' * ((C * x) * (y * z)) = L(z,y,C * x). [para(239(a,1),18(a,1,1,1))].

1451 ((x * C) * (y * ((C * x) * z))) / z = (C * x) * (y * (C * x)). [para(239(a,1),39(a,1,1))].

1452 (C * x) * (y * (C * x)) = (x * C) * (y * (x * C)). [para(239(a,2),39(a,1,1,2,2)),rewrite([1451(8)])].

1518 C * (C * (C * x)') = C / x. [para(247(a,1),10(a,1,2)),rewrite([1318(7,R),16(6,R)])].

1521 C' * (C' * ((C * x) * ((C / x) * y))) = L(y,C / x,C * x). [para(247(a,1),18(a,1,1,1)),rewrite([174(4),12(12)])].

1539 C' * x = x * C'. [para(8(a,1),71(a,2,2,2)),rewrite([34(8),3(7)]),flip(a)].

1540 x' * (C * (x * (y * x))) = y * (x * C). [para(71(a,2),10(a,1,2))].

1549 (C * x)' * (x * (y * (x * C))) = L(y * x,x,C). [para(71(a,1),18(a,1,2))].

1563 (C * (x * C))' = (x * (C * C))'. [para(71(a,2),111(a,1,2)),rewrite([111(8)])].

1573 (x * C')' = C / x. [para(71(a,2),161(a,1,1)),rewrite([34(8),16(9,R),9(9),3(7)])].

1673 x' * ((x * C) * y) = L(y * C,C',x). [back_rewrite(133),rewrite([1573(4),230(4)])].

1694 C * (x * C') = x. [para(1539(a,1),10(a,1,2)),rewrite([30(3)])].

1700 (C' * (C' * x)) * y = C' * (x * (C' * y)). [para(1539(a,2),13(a,1,1,2))].

1707 x * (C' * x') = C'. [para(1539(a,2),34(a,1,2))].

1730 C * (x * (x * C')) = x * x. [para(1539(a,1),71(a,1,2,2)),rewrite([63(11)])].

1734 x / C' = C * x. [para(7(a,1),1694(a,1,2)),flip(a)].

1765 (C * x)' = C' / x. [para(1734(a,1),106(a,1,1))].

1781 (x * (C * C))' = C' / (x * C). [back_rewrite(1563),rewrite([1765(5)]),flip(a)].

1783 x' * ((x * C') * (y * (x * C))) = L(y * x,x,C). [back_rewrite(1549),rewrite([1765(3),230(8)])].

1785 C * (C * (C' / x)) = C / x. [back_rewrite(1518),rewrite([1765(5)])].

1817 (C' / (x * x)) * (x * ((x * C) * y)) = L(y,x * C,x). [back_rewrite(690),rewrite([1765(4)])].

1849 (x * (x * C))' = C' / (x * x). [back_rewrite(533),rewrite([1765(4)]),flip(a)].

1850 (C' / x) * ((x * C) * y) = y. [back_rewrite(532),rewrite([1765(3)])].

1852 (x * C)' = C' / x. [back_rewrite(516),rewrite([1765(3)]),flip(a)].

1869 x' * ((x * C') * y) = L(C' * y,C,x). [back_rewrite(119),rewrite([1852(3),230(5)])].

1870 (C' / x) * (C * (x * y)) = L(y,x,C). [back_rewrite(98),rewrite([1852(3)])].

1875 (C' / (x * x)) * (x * (C * (x * y))) = y. [back_rewrite(346),rewrite([1849(4)])].

1884 L(C' * (x * (y * C)),C,y) = L(x * y,y,C). [back_rewrite(1783),rewrite([1869(9)])].

1972 (x * (y * (x * C')))' = C / (x * (y * x)). [para(13(a,1),1573(a,1,1))].

1973 (x * C') * ((C / x) * y) = y. [para(1573(a,1),34(a,1,2,1))].

1995 A * ((C * A') * (x * A)) = x * (A * C). [para(34(a,1),73(a,1,1)),rewrite([16(10,R),1152(13)]),flip(a)].

2251 L(x,C / x,C * x) = x. [para(247(a,1),80(a,2,1,1)),rewrite([174(9),16(14,R),12(15),10(14),10(10)])].

2555 L(C * x',x,C') = C / x. [para(125(a,1),84(a,1,3,1)),rewrite([125(10),161(10)])].

2667 x * L(y',y,x) = x / y. [para(86(a,2),39(a,2,2)),rewrite([39(6),189(4)]),flip(a)].

2800 C * L(x,C * y',y) = y * ((C * y') * x). [para(125(a,1),87(a,1,1))].

2840 x * (C' * y) = x * (y * C'). [para(1539(a,1),87(a,2,2)),rewrite([87(7)])].

2884 L(A,C * A',A * C) = A. [para(264(a,1),2251(a,1,2)),rewrite([16(8)])].

2916 x * L(y * z,y',x) = (x / y') * z. [para(89(a,2),13(a,2,2)),rewrite([189(5)]),flip(a)].

2976 (A * x') * (x * y) = L(A * y,A',x). [para(815(a,1),89(a,2,1)),flip(a)].

3125 x * L(y * C,C',x) = (x * C) * y. [para(63(a,1),92(a,1,1)),rewrite([161(4),63(7),230(4),1673(5),63(11),139(10)])].

3176 (A * (A * (A * C))) * x = A * (A * (A * (x * C))). [para(754(a,1),92(a,2,1,2)),rewrite([66(5),16(8),1852(9),264(9),1539(10),66(15),68(1

6),231(17),251(12),1539(11),2976(16),243(17),264(6),229(7),264(5),125(7),2916(11),251(5),16(4),1012(7),66(13),68(15),66(14)]),flip(a)].

3396 L(x,y,z / y) = L(x,y,z). [para(8(a,1),93(a,1,1,1,2)),rewrite([3(2),18(6),10(4),189(5)]),flip(a)].

3424 x' * (C' * (x * (C * y))) = L(y,C,x * (C' * x)). [para(63(a,1),93(a,1,1,1,2)),rewrite([174(2),12(11),10(10)])].

3425 (C / (x * (y * x))) * (x * (y * (x * z))) = L(z * C,C',x * (y * x)). [para(63(a,1),93(a,1,2,2,2,2)),rewrite([1972(6)])].

3429 C' * (x' * (C * (x * y))) = L(y,x,C * (x' * C)). [para(64(a,1),93(a,1,1,1,2)),rewrite([174(4),12(13),10(12)])].

3485 (C' / (C * (x * x))) * (C * (x * (C * (x * y)))) = L(y,x,C * (x * C)). [para(67(a,2),93(a,1,1,1,2)),rewrite([1765(6)])].

3574 x' * (C * (x * (C' * y))) = L(y,C',x * (C * x)). [para(1694(a,1),93(a,1,1,1,2)),rewrite([174(2),12(11),10(10)])].

3671 x' * (y' * ((y * x) * z)) = L(z,y,x). [back_rewrite(255),rewrite([3396(8)])].

3672 L(x,y * z,y') = L(x,y,z). [back_rewrite(252),rewrite([3396(5)])].

3690 L(x,y,z * y) = L(x,y,z). [para(10(a,1),94(a,1,1,1)),rewrite([10(7),18(5),3672(5)]),flip(a)].

4153 ((A * (A * x)) * x')' * (A * (A * A)) = L(A,x',A * (A * x)). [para(831(a,1),97(a,1,2,2,1))].

4262 L(C,C,x) = C. [para(16(a,2),101(a,1,1,1)),rewrite([1765(3),230(8),1318(8,R),16(7,R),1694(7),64(4)]),flip(a)].

4270 C' * (x' * (C * (C * x))) = L(C,C * x,x'). [para(64(a,1),101(a,1,1,1))].

4306 (C / x) * (C * x) = C * C. [para(101(a,1),70(a,2,2)),rewrite([1765(5),1785(7),510(9)])].

4478 L(x,A' * C',C) = L(x,C',C * A'). [para(1189(a,1),102(a,1,1,1)),rewrite([30(3),1573(6),264(4),1539(11),34(12),243(9),116(6),1539(7),1269

(10),1539(13),34(14),1573(14),264(12)])].

4656 A * (C * ((A' * C') * x)) = L(x,C',C * A'). [back_rewrite(1269),rewrite([4478(17)])].

4891 L(x,y,A * y') = L(x,y,A). [para(1094(a,1),93(a,1,1,1,2)),rewrite([3(3),1097(11),10(7),256(9)]),flip(a)].

4912 (A * (A * x)) * x' = A * A. [para(1095(a,1),15(a,2,2,1)),rewrite([256(10),2(10)])].

4941 L(A,x',A * (A * x)) = A. [back_rewrite(4153),rewrite([4912(6),174(4),12(11),10(10),10(6)]),flip(a)].

4947 C * L(x,C,y) = L(x * C,y,C'). [para(16(a,1),104(a,2,1)),rewrite([1852(3),7(4),30(3),1852(9),3396(10)])].

4960 A * L(x,A,y) = L(A * x,y,A'). [para(256(a,1),104(a,1,1,1,1,1)),rewrite([10(5),30(3),306(6),256(14),3672(11)])].

4977 x * L(y,x,A) = L(x * y,A,x'). [para(817(a,1),104(a,1,1,1,1,1)),rewrite([10(6),30(2),4891(4),817(11),3672(10)])].

5251 (x * (C * C)) * y = C * (x * (C * y)). [para(1318(a,1),13(a,1,1))].

5361 L(x * y,C * C,C' / (C * x)) = x * L(y,x,C * C). [para(1318(a,2),104(a,1,1,1)),rewrite([12(5),1765(6),16(8,R),1785(9),111(4),30(2),12(13

),1765(14)]),flip(a)].

5381 (x * (y * x))' = x' / (x * y). [para(9(a,1),108(a,1,2,2,2)),rewrite([3(3)]),flip(a)].

5390 (x' * y) / (x * (z * y)) = x' / (x * z). [para(34(a,1),108(a,1,2,2,2)),rewrite([5381(8)])].

5396 C' / (C * x) = x' / (C * C). [para(125(a,1),108(a,1,2,2)),rewrite([5381(10)]),flip(a)].

5595 x' * (C * (C * x)) = C * C. [para(1398(a,2),10(a,1,2))].

5600 (C' / (C * x)) * (x * (C * (C * y))) = L(y,C * C,x). [para(1398(a,2),18(a,1,1,1)),rewrite([1765(5),12(9)])].

5611 (x * (x * (C * C))) * y = x * (C * (C * (x * y))). [para(1398(a,1),45(a,1,1,2))].

5659 (C' / (C * (C * x))) * (C * (x * (C * (C * y)))) = L(y,C,C * (x * C)). [para(1398(a,2),93(a,1,1,1,2)),rewrite([1765(7)])].

5673 L(x,C * (C * y),C' / y) = C' * L(C * x,y,C). [para(1398(a,2),102(a,2,2)),rewrite([4262(3),1852(5),5251(10),1870(11),1852(14)]),flip(a)]

.

5689 L(C,C * x,x') = C. [back_rewrite(4270),rewrite([5595(8),1318(6,R),16(5,R),9(5),3(3)]),flip(a)].

5703 C' * L(C * C,x,C) = C. [para(1765(a,1),5689(a,1,3)),rewrite([5673(9)])].

5966 ((A' * x) * y) * A = A' * (x * (y * A)). [para(123(a,1),10(a,1,2)),flip(a)].

5982 (x * (A * ((y * x) * A))) * z = (x * A) * (y * ((x * A) * z)). [para(123(a,1),57(a,1,1,2)),rewrite([1086(6),34(14)])].

6080 L(x,y' * C,y) = L(x,C * y',y). [para(16(a,2),126(a,1,2,2,1)),rewrite([170(8)]),flip(a)].

6163 L(L(x,y,z'),z' * y,z) = x. [para(87(a,1),126(a,1,2,2)),rewrite([34(5),10(3)]),flip(a)].

6301 x * L(y' * z,y,x) = (x / y) * z. [para(127(a,2),13(a,2,2)),rewrite([189(4)]),flip(a)].

6353 L((C' / x) * y,C * x,x) = (C' / (x * x)) * (x * y). [para(67(a,2),127(a,2,1,1)),rewrite([1765(3),1765(11)])].

6702 L(x,y * z,z) = L(x,y,z). [para(32(a,1),3396(a,1,3)),rewrite([3672(3)]),flip(a)].

6707 L(x,y * C,C') = L(x,y * C,y). [para(110(a,1),3396(a,1,3))].

6708 L(x,C * y,y') = L(x,C * y,C). [para(111(a,1),3396(a,1,3))].

6714 L(x,y,C * (y * C)) = L(x,y,C * C). [para(149(a,1),3396(a,1,3)),flip(a)].

6718 L(x,C',C * y) = L(x,C',y). [para(1734(a,1),3396(a,1,3))].

6728 L(x,y * y,y * (C * y)) = L(x,y * y,C). [para(716(a,1),3396(a,1,3)),flip(a)].

6747 (C' / (x * x)) * (x * y) = L((C' / x) * y,C,x). [back_rewrite(6353),rewrite([6702(7)]),flip(a)].

6762 (C' / (C * (x * x))) * (C * (x * (C * (x * y)))) = L(y,x,C * C). [back_rewrite(3485),rewrite([6714(18)])].

6763 A * (C * ((A' * C') * x)) = L(x,C',A'). [back_rewrite(4656),rewrite([6718(17)])].

6772 L(L(x,y,C),C,y) = x. [back_rewrite(1875),rewrite([6747(9),1870(7)])].

6773 L(x,y * C,y) = L(x,C,y). [back_rewrite(1817),rewrite([6747(9),1850(7)]),flip(a)].

6781 L(x,y * C,C') = L(x,C,y). [back_rewrite(6707),rewrite([6773(8)])].

6826 L(L(x,C' * y,C),C,y) = x. [para(6772(a,1),3396(a,1)),rewrite([116(2)]),flip(a)].

7039 L(x,C,C * y) = L(x,C,y). [para(16(a,2),3690(a,1,3))].

7040 L(x,y' * z,y) = L(x,y',z). [para(34(a,1),3690(a,1,3)),rewrite([6702(3)]),flip(a)].

7067 L(x,C / x,C * C) = x. [para(2251(a,1),3690(a,2)),rewrite([247(7)])].

7086 L(x,C * C,C * (C * y)) = L(x,C * C,y). [para(1398(a,2),3690(a,1,3))].

7100 L(x,y * (C' * y),y * y) = L(x,y * (C' * y),C). [para(130(a,1),3690(a,1,3))].

7101 (C' / (C * (C * x))) * (C * (x * (C * (C * y)))) = L(y,C,x). [back_rewrite(5659),rewrite([7039(21),3690(19)])].

7106 L(L(x,C',y),C,y) = x. [back_rewrite(6826),rewrite([7040(5)])].

7150 L(L(x,y,z'),z',y) = x. [back_rewrite(6163),rewrite([7040(5)])].

7207 L(x,C * y',y) = L(x,y',C). [back_rewrite(6080),rewrite([7040(4)]),flip(a)].

7283 x * ((C * x') * y) = C * L(y,x',C). [back_rewrite(2800),rewrite([7207(5)]),flip(a)].

7308 C * L(x * A,A',C) = x * (A * C). [back_rewrite(1995),rewrite([7283(9)])].

7522 (C * (C' / x)) * ((C * x) * ((C * (C' / x)) * (x * y))) = C * L(y,x,C). [para(18(a,1),135(a,2,2)),rewrite([1765(4),1765(8),106(9),1734(

8),1765(11)])].

7580 (C * (C' / x)) * ((C * x) * ((C * (C' / x)) * y)) = (C / x) * y. [para(127(a,2),135(a,2,2)),rewrite([1765(4),1765(8),106(9),1734(8),176

5(11),6301(21)])].

7593 C * L(x,y,C) = L(x * C,C',y). [back_rewrite(7522),rewrite([7580(16),230(4),1673(5)]),flip(a)].

7601 L(C * (x * A),C',A') = x * (A * C). [back_rewrite(7308),rewrite([7593(8),16(4,R)])].

7727 L(C',C * C,x) = C'. [para(1707(a,1),137(a,1,1)),rewrite([174(8),30(5),30(6),174(12),30(9),30(10),1781(11),7(14)])].

7826 L(x,C,y) = L(x,y,C'). [para(7727(a,1),102(a,1,1,1)),rewrite([30(3),1781(6),1539(12,R),1318(12,R),16(11,R),9(11),3(9),230(10),1852(4),15

39(9,R),63(9),230(6),1869(7),4947(7),16(5,R),34(5),1539(9,R),1318(9,R),16(8,R),9(8),3(6),1781(10),3396(11),6781(8)]),flip(a)].

7893 C * L(x,y,C') = L(C * x,y,C'). [para(7826(a,1),104(a,1,2)),rewrite([1852(3),7(4),30(3),1852(10),3396(11)])].

7932 (C * x') / (x * C) = x' * x'. [para(16(a,2),144(a,1,1))].

8151 L(A,x',A * A) = A. [para(4941(a,1),3690(a,2)),rewrite([4912(8)])].

8421 (x * A') * A' = x * (A' * A'). [para(8151(a,1),78(a,1,1)),rewrite([12(8),779(9),858(9),5381(7),913(7),858(7),30(5),13(10),34(11),12(11)

,858(12),858(10),30(8)]),flip(a)].

8720 (C' / x) / (C / x) = C' * C'. [para(2667(a,1),153(a,1,1)),rewrite([16(9,R),7893(9),2555(9)])].

8905 L(C * C,x,C) = C * C. [para(5703(a,1),10(a,1,2)),rewrite([30(3)]),flip(a)].

8906 x / (C * C) = C' * (x * C'). [para(5703(a,1),39(a,1,1,2,2)),rewrite([63(5),8905(5)])].

8909 L(x,C * C,C' * (y * C')) = L(x,C,y * (C' * y)). [para(5703(a,1),93(a,1,1,1,2,2)),rewrite([63(5),8905(10),12(9),10(10),3424(8),8905(11)]

),flip(a)].

8921 C' / (C * x) = C' * (x' * C'). [back_rewrite(5396),rewrite([8906(10)])].

8949 C' * L(C * x,C,y) = L(x,C,y). [back_rewrite(7101),rewrite([8921(7),1765(5),1539(8,R),231(17),1734(11),34(10),230(11),1869(12),10(9)])].

8951 L(x,y,C * (y' * C)) = L(x,y,C * C). [back_rewrite(6762),rewrite([8921(6),174(4),1539(8,R),231(16),1734(11),34(10),12(10),10(9),3429(8)]

)].

8977 L(x,C,y * (C' * y)) = L(x,C * C,y). [back_rewrite(5600),rewrite([8921(5),13(13),3424(12),8949(11)])].

8993 L(x * y,C * C,C' * (x' * C')) = x * L(y,x,C * C). [back_rewrite(5361),rewrite([8921(9)])].

9012 C' * (x' * (C * (x * y))) = L(y,x,C * C). [back_rewrite(3429),rewrite([8951(14)])].

9020 L(x,C * C,C' * (y * C')) = L(x,C * C,y). [back_rewrite(8909),rewrite([8977(16)])].

9035 x * L(y,x,C * C) = L(x * y,C * C,x'). [back_rewrite(8993),rewrite([9020(12)]),flip(a)].

9460 L(C * (C' / x),C * x,C / x) = C' * (C / x). [para(4306(a,1),171(a,2,1,1)),rewrite([1765(4),174(14),16(19,R),12(20),10(19)])].

9516 L(x,y / z,z) = L(x,y,z). [para(7(a,1),6702(a,1,2)),flip(a)].

9517 L(x,y',y * z) = L(x,z,y). [para(10(a,1),6702(a,1,2)),rewrite([3690(2)]),flip(a)].

9518 L(x,y * (y * z),z) = L(x,y * y,z). [para(12(a,1),6702(a,1,2))].

9521 L(x,C * y,C) = L(x,y,C). [para(16(a,2),6702(a,1,2))].

9524 L(x,y,y' * z) = L(x,z,y'). [para(34(a,1),6702(a,1,2)),rewrite([3690(3)]),flip(a)].

9526 L(x,y',C * y) = L(x,C,y). [para(64(a,1),6702(a,1,2)),rewrite([7039(4)]),flip(a)].

9527 L(x,y,C * y') = L(x,C,y'). [para(125(a,1),6702(a,1,2)),rewrite([7039(5)]),flip(a)].

9540 L(x,x,A) = x. [para(1030(a,1),6702(a,2)),rewrite([256(5)])].

9604 L(x,C',y * (C * y)) = L(x,y * y,C). [para(150(a,1),6702(a,1,2)),rewrite([6728(5)]),flip(a)].

9613 L(x,C',y) = L(x,y,C). [back_rewrite(6718),rewrite([9517(5)]),flip(a)].

9635 L(x,C * y,y') = L(x,y,C). [back_rewrite(6708),rewrite([9521(8)])].

9850 x' * (C * (x * (C' * y))) = L(y,x * x,C). [back_rewrite(3574),rewrite([9604(14)])].

9869 (A * x) * x = A * (x * x). [para(9540(a,1),87(a,1,2))].

9990 L(L(L(c1,C',A),A,C),A,C) != c1. [para(9613(a,2),19(a,1,1,1))].

10000 (x * C') * L(y,x,C) = x * (C' * y). [para(9613(a,1),87(a,1,2))].

10004 L(x,y * (z * y),C) = L(x,C',y * (z * y)). [para(9613(a,1),93(a,2)),rewrite([1972(6),3425(11),16(5,R),34(5)]),flip(a)].

10010 C' * L(x,y,C) = L(C' * x,y,C). [para(9613(a,1),104(a,1,2)),rewrite([1573(4),7(3),1573(12),3396(11)])].

10026 L(x,y * (C' * y),y * y) = L(x,C',y * (C' * y)). [back_rewrite(7100),rewrite([10004(12)])].

10107 L(L(L(c1,C',A),A,C),C',A) != c1. [para(9613(a,2),9990(a,1))].

10262 C' * L(x,C,y) = L(C' * x,C,y). [para(7039(a,1),127(a,1)),rewrite([16(9,R),1765(10),8921(10),13(16),3671(15)]),flip(a)].

10265 L(x,C * C,y) = L(x,C,y * y). [para(130(a,1),7039(a,1,3)),rewrite([8977(9)]),flip(a)].

10323 L(L(x,y,z),z,y) = x. [para(30(a,1),7150(a,1,1,3)),rewrite([30(3)])].

10327 L(L(x,C,y),C',y) = x. [para(7826(a,2),7150(a,1,1))].

10988 (C * x) * (y * (C * x)) = C * ((C * x) * (y * x)). [para(186(a,1),1734(a,1)),rewrite([1734(3),1734(5),1734(10)])].

11094 (x * C) * (y * (x * C)) = C * ((C * x) * (y * x)). [back_rewrite(1452),rewrite([10988(6)]),flip(a)].

11185 (x / (y * z)) * y = y' * ((y * x) / z). [para(187(a,1),10(a,1,2)),flip(a)].

11186 (x' * y) / (x * z) = x' * ((y / z) * x'). [para(10(a,1),187(a,1,2,1,2)),flip(a)].

11561 x' / (x * y) = x' * (y' * x'). [back_rewrite(5390),rewrite([11186(5),32(3)]),flip(a)].

11722 (x * (y * x))' = x' * (y' * x'). [back_rewrite(5381),rewrite([11561(6)])].

11948 C' * (C / x) = C * (C' / x). [para(189(a,1),2251(a,1,3)),rewrite([1765(3),16(5,R),1765(9),16(11,R),111(12),106(9),1734(8),9460(10),176

5(8),16(10,R)])].

11975 C' / (x * (y * (x * C))) = C' * (C' * (x' * (y' * x'))). [para(131(a,1),189(a,1,2,1,1)),rewrite([11722(5),1539(10,R)]),flip(a)].

12719 L(A,A' * A',A * C) = A. [para(2884(a,1),9516(a,2)),rewrite([7932(9)])].

12720 L(x,C' / x,C * C) = x. [para(7067(a,1),9516(a,2)),rewrite([8906(6),1539(7,R),11948(7),10(8)])].

12973 L(x,C',y * (C' * y)) = L(x,y * y,C). [para(130(a,1),9521(a,1,2)),rewrite([10004(9)]),flip(a)].

12983 L(x,y * (C' * y),y * y) = L(x,y * y,C). [back_rewrite(10026),rewrite([12973(13)])].

13406 (A * C) * (x * C) = C * (C * (A * x)). [para(73(a,1),198(a,1,1,2)),rewrite([264(10),5982(11),16(3),16(6),229(9),264(7),125(9),16(11,R)

])].

14109 (A * x) / (x * x) = A * x'. [para(9540(a,1),202(a,1,1,2)),rewrite([779(6)])].

14231 (C' * (x * x)) * y = x * (C' * (x * y)). [para(205(a,2),13(a,1,1))].

14334 L(x,y * y,C) = L(x,C',y * y). [para(205(a,1),6702(a,1,2)),rewrite([12983(6)])].

14398 L(x,C',y * (C' * y)) = L(x,C',y * y). [back_rewrite(12973),rewrite([14334(10)])].

14415 x' * (C * (x * (C' * y))) = L(y,C',x * x). [back_rewrite(9850),rewrite([14334(11)])].

14501 L(x,C' / x,C / x) = x. [para(12720(a,1),3690(a,2)),rewrite([12(10),1785(10)])].

14910 L(x,C' * C',C / x) = x. [para(14501(a,1),9516(a,2)),rewrite([8720(6)])].

15625 L(x,C,A') = L(x,A,C). [para(16(a,1),306(a,1,3)),rewrite([16(5,R),9527(6)])].

15628 L(x,C',A') = L(x,A,C'). [para(1539(a,1),306(a,1,3)),rewrite([9524(7)])].

15656 L(C * (x * A),A,C') = x * (A * C). [back_rewrite(7601),rewrite([15628(9)])].

15657 A * (C * ((A' * C') * x)) = L(x,A,C'). [back_rewrite(6763),rewrite([15628(15)])].

15668 L(L(x,A,C),A',C) = x. [para(15625(a,1),10323(a,1,1))].

15752 L(x,A',C) = L(x,C,A). [para(10323(a,1),15668(a,1,1))].

15846 (x * A') * (A * y) = A' * ((A * x) * y). [para(264(a,1),230(a,1,1))].

17248 (x * C') * (C * y) = C' * ((C * x) * y). [para(1539(a,1),231(a,1,1)),rewrite([1734(11)])].

17460 L(x,A * C',C * C) = L(x,A * C',A * C). [para(848(a,1),3396(a,1,3))].

18012 (x * C) * (C' * y) = C * ((C' * x) * y). [para(16(a,1),243(a,1,1)),rewrite([116(9)])].

19661 (x * (y * A')) * A = A' * ((A * x) * y). [para(267(a,1),10(a,1,2)),flip(a)].

19696 C * (A * (A * x)) = A * ((A * C) * x). [para(245(a,1),267(a,1,2,1)),rewrite([30(4),30(6),264(5),49(10),19661(9),1673(9),3125(9),30(10)

,16(12,R)]),flip(a)].

21705 L(x,y',C * (C * y)) = L(x,C * C,y). [para(5595(a,1),6702(a,1,2)),rewrite([7086(8)]),flip(a)].

22230 (A * (A * (A * C'))) * x = A * (A * (A * (x * C'))). [para(1539(a,1),434(a,1,1,2,2)),rewrite([994(17)])].

22824 L(x,y * y,y' * (C * y')) = L(x,C,y' * y'). [para(178(a,2),9526(a,1,3)),rewrite([174(4),30(2),30(2)])].

22932 L(x,C',y * y) = L(x,C,y' * y'). [para(130(a,1),9635(a,1,2)),rewrite([11722(6),30(5),22824(7),10004(11),14398(12)]),flip(a)].

22957 x' * (C * (x * (C' * y))) = L(y,C,x' * x'). [back_rewrite(14415),rewrite([22932(12)])].

23869 C * ((A * C') * x) = L(A * x,A,C). [para(12719(a,1),242(a,1,2,2)),rewrite([243(9),264(4),8421(8),694(9),16(4,R),815(5),243(13),264(8),

8421(12),694(13),16(8,R),815(9),11185(11),1734(11),243(12),264(5),1539(6),17248(11),15846(10),1673(10),4977(10),63(6),30(5),4960(5),15625(6),

243(14),264(9),8421(13),694(14),16(9,R),815(10),12(20),8(19),3(17),229(16),264(14),125(16),16(12,R)]),flip(a)].

24047 L(x,A * y',y * y) = L(x,A * y,y * y). [para(14109(a,1),9516(a,1,2))].

24056 L(x,A * C',A * C) = L(x,A * C,C * C). [back_rewrite(17460),rewrite([24047(8)]),flip(a)].

24285 L(A,C' * C',C * A') = A. [para(264(a,1),14910(a,1,3))].

26122 (x * (y * (x * (C * C))))' = C' * (C' * (x' * (y' * x'))). [para(566(a,2),111(a,1,2)),rewrite([111(10),1765(7),11975(7)]),flip(a)].

27575 x / (A' * C') = x * (A * C). [para(1061(a,1),190(a,1,1)),rewrite([1852(4),264(4),1539(5),11094(20),16(10),5966(18),243(19),264(11),243

(18),116(13),1539(14),15657(19),7893(14),15656(14)])].

28711 (x / (y * C')) * (C' * y) = x. [para(2840(a,2),7(a,1))].

28728 (x * C) * (y * C') = C * ((C' * x) * y). [para(2840(a,1),239(a,2)),rewrite([243(6),116(3)]),flip(a)].

28752 x * (C' * (A * C')) = x * (A * (C' * C')). [para(9869(a,1),2840(a,2,2))].

33207 A' * (C * (A * x)) = L(x * C,C,A). [para(765(a,1),7207(a,1)),rewrite([19661(7),16(6,R),256(13),15752(13)])].

34515 L(C' * (A * x),A,C) = (A * C') * x. [para(24285(a,1),92(a,2,1,2)),rewrite([12(11),1539(10),28752(12),15846(12),28728(11),1539(7),1539(

10,R),34(11),10(7),243(12),116(7),1539(8),1539(11,R),34(12),1573(8),251(6),16(5),12(16),1539(15),28752(17),15846(17),28728(16),1539(12),1539(

15,R),34(16),10(12),18012(9),1539(7),23869(9),10010(8),12(19),1539(18),28752(20),15846(20),28728(19),1539(15),1539(18,R),34(19),10(15),1539(1

2)])].

34517 C' * ((A * C) * x) = L(A * x,A,C'). [para(24285(a,1),242(a,1,2,2)),rewrite([243(10),116(5),1539(6),1539(9,R),34(10),1573(6),251(4),16(

3),243(13),116(8),1539(9),1539(12,R),34(13),1573(9),251(7),16(6),11185(9),116(9),243(12),264(4),243(11),116(6),1539(7),231(10),251(9),1539(8)

,1869(10),4977(9),34(6),4960(6),15628(7),243(16),116(11),1539(12),1539(15,R),34(16),1573(12),251(10),16(9),12(21),1539(20),28752(22),15846(22

),28728(21),1539(17),1539(20,R),34(21),10(17),1539(13,R)]),flip(a)].

35808 C' * (A * (A * (A * x))) = A * (A * (A * (x * C'))). [para(950(a,1),748(a,1,1,2,2,2)),rewrite([12(14),1539(13),28752(15),19696(16),287

28(15),1539(11),1539(14,R),34(15),1730(12),15(8),1539(5),49(7),1539(6),22230(9),23869(25),10000(24),17248(23),16(14),1012(22),16(20,R),34(20)

]),flip(a)].

36218 L(C * (A * x),A,C') = (A * C) * x. [para(1973(a,1),961(a,1,2)),rewrite([30(3),30(6),16(6),34517(8),7893(8),30(11),264(15),10(17),8(14)

,3(12),16(11)])].

36219 (A * C) * ((A * C') * x) = C * (A * (C' * (A * x))). [para(961(a,1),568(a,1,2)),rewrite([9(8),2(7),14231(8),1539(21),16(24,R),23869(24

),10010(23),34515(23),34517(22),7893(22),36218(22)]),flip(a)].

36443 (x * (A' * C')) * (A * C) = x. [para(27575(a,1),6(a,1))].

36872 L(x * y,C * C,x') = C * (x * (C' * y)). [para(28711(a,1),566(a,1,2,2,2)),rewrite([63(17),11185(13),1734(13),9012(14),9035(11)]),flip(a

)].

36885 x * L(y,x,C * C) = C * (x * (C' * y)). [back_rewrite(9035),rewrite([36872(11)])].

40475 x / (A * C) = x * (A' * C'). [para(36443(a,1),6(a,1,1))].

43620 L(A * x,C,A' * A') = C * (A * (C' * x)). [para(10265(a,1),4960(a,2)),rewrite([36885(7)]),flip(a)].

45624 L(x,A * C,C * C) = L(x,C,A' * A'). [para(950(a,1),1441(a,1,1,1)),rewrite([9(5),2(4),174(4),16(8),36219(14),12(15),22957(14),43620(11),

22957(10),16(14),24056(15)]),flip(a)].

45628 L(x,A * A,A * C) = L(x,C,A). [para(1168(a,1),1441(a,1,1,1)),rewrite([19696(8),16(7,R),1318(7),5611(10),66(8),19696(9),16(8,R),1318(8),

858(12),26122(10),1700(17),1539(15),13(16),16(20),3176(28),1012(29),16(27,R),19696(27),13406(26),451(30),35808(25),1539(22,R),10(22),10(21),1

0(17),10(13),33207(9),10262(8),63(5),16(13),9518(14)]),flip(a)].

45635 L(x,A * C',A * C) = L(x,C,A' * A'). [back_rewrite(24056),rewrite([45624(15)])].

45738 L(x,C,A' * A') = L(x,C,A). [para(45628(a,1),9516(a,2)),rewrite([40475(7),12(9),34(8),45635(8)])].

45762 L(x,C * C,A') = L(x,C,A). [para(45738(a,1),10265(a,2))].

45765 L(x,A,C * C) = L(x,C,A). [para(45762(a,1),9516(a,2)),rewrite([251(6),12(5),16(4),1318(5),3672(8)])].

45787 L(L(x,C,A),C * C,A) = x. [para(45765(a,1),10323(a,1,1))].

45796 L(x,C * C,A) = L(x,C',A). [para(7106(a,1),45787(a,1,1))].

47220 C' * (x * (C * (x' * y))) = L(y,C * C,x). [para(111(a,1),1521(a,1,2,2,2,1)),rewrite([70(11),10(12),111(12),21705(14)])].

47482 (x * A) * (C * A') = A * (C * (A' * x)). [para(257(a,1),1540(a,1,2,2,2)),rewrite([30(3),16(13,R)]),flip(a)].

53456 L(L(x,C',A),A,C) = L(x,C,A). [para(257(a,1),1884(a,2,1)),rewrite([16(8,R),47482(9),47220(10),45796(5),15625(8),15752(11)])].

53483 $F. [back_rewrite(10107),rewrite([53456(8),10327(8)]),xx(a)].

============================== end of proof ==========================