% Proof 1 at 4.05 (+ 0.03) seconds.
% Length of proof is 228.
% Level of proof is 31.
% Maximum clause weight is 25.000.
% Given clauses 464.
1 R(x * y,C,A) = R(x,C,A) * R(y,C,A) #
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(c1 * c2,C,A) != R(c1,C,A) *
R(c2,C,A). [deny(1)].
20 R(c1,C,A) * R(c2,C,A) != R(c1 *
c2,C,A). [copy(19),flip(a)].
21 (C * x) * (y * C) = C * (C * (x * y)). [back_rewrite(15),rewrite([16(9,R)])].
24 x / x = 0. [para(2(a,1),6(a,1,1))].
25 x / 0 = x. [para(3(a,1),6(a,1,1))].
30 0 / x = x'. [para(8(a,1),6(a,1,1))].
32 x'' = x. [para(9(a,1),6(a,1,1)),rewrite([30(3)])].
33 x \ y = x' * y. [para(4(a,1),10(a,1,2)),flip(a)].
34 x / (y * x) = y'. [para(10(a,1),6(a,1,1))].
36 x * (x' * y) = y. [back_rewrite(4),rewrite([33(1)])].
37 (x * (x * y)) / y = x * x. [para(12(a,1),6(a,1,1))].
41 (x * (y * (x * z))) / z = x * (y * x). [para(13(a,1),6(a,1,1))].
42 x * ((y / x) * (x * z)) = (x * y) * z. [para(7(a,1),13(a,1,1,2)),flip(a)].
53 C * (x / C) = x. [para(16(a,2),7(a,1))].
54 C' * (x * C) = x. [para(16(a,1),10(a,1,2))].
56 C * (C * x) = C * (x * C). [para(16(a,1),12(a,2,2)),rewrite([12(4)])].
57 C * (x * x) = x * (x * C). [para(16(a,2),12(a,1))].
60 C * (x * (C * y)) = C * (x * (y * C)).
[para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].
61 (C * (C * x)) * y = C * (x * (C * y)). [para(16(a,2),13(a,1,1,2))].
64 R(0,x,y) = 0. [para(2(a,1),18(a,1,1,1)),rewrite([24(3)]),flip(a)].
67 R(x,y,z) * (y * z) = (x * y) * z. [para(18(a,1),7(a,1,1))].
68 R(x / y,y,z) = (x * z) / (y * z). [para(7(a,1),18(a,1,1,1)),flip(a)].
69 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(7(a,1),18(a,1,2))].
71 (x * y') * y = R(x,y',y).
[para(8(a,1),18(a,1,2)),rewrite([25(5)])].
74 (x * y) * y' = R(x,y,y').
[para(9(a,1),18(a,1,2)),rewrite([25(5)])].
75 R(x',x * y,z) = (y * z) / ((x * y) *
z).
[para(10(a,1),18(a,1,1,1)),flip(a)].
87 (C * (x * y)) / (C * y) = R(x,y,C).
[para(16(a,2),18(a,1,2)),rewrite([16(3,R)])].
90 C * (C * (x * C')) = C * x.
[para(8(a,1),21(a,1,2)),rewrite([3(4)]),flip(a)].
99 (x * C) * (y * C) = C * (C * (x * y)). [para(16(a,1),21(a,1,1))].
100 (C * x) * (C * y) = C * (C * (x * y)). [para(16(a,2),21(a,1,2))].
106 x / C = C' * x. [para(53(a,1),10(a,1,2)),flip(a)].
110 C * (C * ((C' * x) * y)) = x * (y *
C).
[para(53(a,1),21(a,1,1)),rewrite([106(7)]),flip(a)].
112 x' * C = C * x'. [para(16(a,2),33(a,2)),rewrite([33(2)])].
113 (x / y)' = y / x. [para(7(a,1),34(a,1,2)),flip(a)].
115 x / (y * (z * (y * x))) = (y * (z *
y))'. [para(13(a,1),34(a,1,2))].
117 C / (C * x) = x'. [para(16(a,2),34(a,1,2))].
129 C * (x * (C' * x)) = x * x.
[para(54(a,1),13(a,2,2)),rewrite([16(6,R)])].
132 ((x * C') * (y * C)) / y = R(x,C',y *
C). [para(54(a,1),18(a,1,2))].
139 (x * y) / ((z * x) * y) = R(z,x,y)'. [para(18(a,1),113(a,1,1)),flip(a)].
141 (C' * x)' = C / x. [para(106(a,1),113(a,1,1))].
143 R(x',x * y,z) = R(x,y,z)'. [back_rewrite(75),rewrite([139(7)])].
169 (x * y) / (x' * y) = x * x. [para(36(a,1),37(a,1,1,2))].
182 (C * (C * (x * y))) / (C * (C * y)) =
R(x,C,y * C).
[para(56(a,2),18(a,1,2)),rewrite([99(5)])].
189 (C * x)' = (x * C)'.
[para(56(a,1),117(a,1,2)),rewrite([117(6)]),flip(a)].
200 (C * x) * ((x * C)' * y) = y. [para(189(a,1),36(a,1,2,1))].
207 C * ((C' * x) * (C' * x)) = (C' * x) *
x.
[para(7(a,1),57(a,2,2)),rewrite([106(3),106(6),106(11)])].
271 C * (x * C') = R(x,C',C). [para(71(a,1),16(a,2))].
272 (x' * C) * x = R(C,x',x). [para(16(a,1),71(a,1,1))].
275 C * (C * (x * (y * C'))) = (C * x) *
R(y,C',C).
[para(71(a,1),21(a,1,2)),flip(a)].
278 C' * R(x,C',C) = x * C'. [para(71(a,1),54(a,1,2))].
288 C * R(x,C',C) = C * x. [back_rewrite(90),rewrite([271(6)])].
290 R(x,C',C) = x. [para(288(a,1),10(a,1,2)),rewrite([10(5)]),flip(a)].
292 C' * x = x * C'. [back_rewrite(278),rewrite([290(6)])].
293 C * (C * (x * (y * C'))) = (C * x) *
y.
[back_rewrite(275),rewrite([290(14)])].
298 x' * (C' * x) = C'. [para(292(a,2),10(a,1,2))].
304 (C' * (C' * x)) * y = C' * (x * (C' *
y)). [para(292(a,2),13(a,1,1,2))].
314 x * (C' * x') = C'. [para(292(a,2),36(a,1,2))].
315 (x * C')' = C / x. [para(292(a,1),141(a,1,1))].
329 (C * x)' * x = C'. [para(10(a,1),298(a,1,2))].
333 R(C,x',x) = C. [para(298(a,1),21(a,2,2,2)),rewrite([16(8,R),36(8),71(4),9(8),3(6)])].
340 (x' * C) * x = C. [back_rewrite(272),rewrite([333(7)])].
341 R(C,x,x') = C. [para(32(a,1),333(a,1,2))].
351 (C * x)' = C' / x. [para(329(a,1),6(a,1,1)),flip(a)].
374 (x * C)' = C' / x.
[back_rewrite(189),rewrite([351(3)]),flip(a)].
380 (C * x) * ((C' / x) * y) = y. [back_rewrite(200),rewrite([374(5)])].
387 x / C' = C * x. [para(351(a,1),32(a,1,1)),rewrite([113(4)])].
408 (x * C) * x' = C. [para(16(a,1),74(a,1,1)),rewrite([341(7)])].
429 C / x' = x * C. [para(408(a,1),6(a,1,1))].
438 C' / x = C' * x'. [para(408(a,1),34(a,1,2)),rewrite([106(3),374(7)]),flip(a)].
459 (C * x) * ((C' * x') * y) = y. [back_rewrite(380),rewrite([438(5)])].
478 (C * x)' = C' * x'. [back_rewrite(351),rewrite([438(6)])].
485 C / x = x' * C. [para(32(a,1),429(a,1,2))].
503 (x * C')' = x' * C. [back_rewrite(315),rewrite([485(6)])].
511 (C' * x)' = x' * C. [back_rewrite(141),rewrite([485(6)])].
523 (C * x) * x = C * (x * x). [para(129(a,1),21(a,2,2)),rewrite([16(7,R),36(7)])].
541 (C' * x) * x = x * (C' * x).
[para(36(a,1),523(a,1,1)),rewrite([207(13)]),flip(a)].
551 (x * x)' = x' * x'.
[para(8(a,1),169(a,1,1)),rewrite([32(3),30(3)])].
676 (C * x) * y = (x * C) * y. [para(36(a,1),459(a,1,2)),rewrite([511(8),32(5)])].
694 ((x * (y * C)) * z) / ((C * y) * z) = R(x,y
* C,z).
[para(676(a,2),18(a,1,2))].
724 (C' * x) * (C' * x) = C' * (x * (C' *
x)).
[para(541(a,1),169(a,1,1)),rewrite([511(8),340(8),106(6)]),flip(a)].
759 R(x,y,z)' * ((x * y) * z) = y * z. [para(67(a,1),10(a,1,2))].
765 R(x,y,C) * (C * y) = C * (x * y).
[para(16(a,2),67(a,1,2)),rewrite([16(8,R)])].
787 (C' * x) * y = (x * C') * y.
[para(292(a,1),67(a,2,1)),rewrite([67(5)])].
815 (C' * (x * (C' * x))) * y = (C' * x) * ((x
* C') * y). [para(787(a,1),12(a,2,2)),rewrite([724(7)])].
871 (x * y) / (C * y) = R(C' * x,C,y). [para(106(a,1),68(a,1,1)),flip(a)].
899 (x * y) / (C' * y) = R(C * x,C',y). [para(387(a,1),68(a,1,1)),flip(a)].
949 (C * (x * (C' * y))) / y = R(x,C' *
y,C). [para(36(a,1),87(a,1,2))].
962 R(x,C' * C',C) = x.
[para(314(a,1),87(a,1,2)),rewrite([387(11),293(10),292(5,R),10(5)]),flip(a)].
975 C * (x * (C' * C')) = x * C'.
[para(962(a,1),67(a,1,1)),rewrite([16(7,R),36(7),16(11,R)]),flip(a)].
1001 R(R(x,y,C),C * y,C) = R(x,C,y * C).
[para(765(a,1),87(a,1,1,2)),rewrite([182(10)]),flip(a)].
1009 C * (C * ((x * (C' * C')) * y)) = (x * C')
* (y * C).
[para(975(a,1),21(a,1,1)),flip(a)].
1018 R(C,x * (C' * C'),y)' = R(C',x *
C',y).
[para(975(a,1),143(a,1,2)),flip(a)].
1031 x * ((x * y)' * x) = x / y.
[para(8(a,1),41(a,1,1,2)),rewrite([3(2)]),flip(a)].
1032 (x * y) / x' = x * (y * x).
[para(9(a,1),41(a,1,1,2,2)),rewrite([3(2)])].
1119 x' / (x * y) = x' * (y' * x').
[para(10(a,1),1031(a,1,2,1,1)),flip(a)].
1152 (x * (y * x))' = x' * (y' * x').
[para(1032(a,1),113(a,1,1)),rewrite([1119(6)])].
1195 x / (y * (z * (y * x))) = y' * (z' *
y').
[back_rewrite(115),rewrite([1152(7)])].
1235 (x * y) * x' = x * (y / x).
[para(9(a,1),42(a,1,2,2)),rewrite([3(3)]),flip(a)].
1236 (x / y) * (y * z) = y' * ((y * x) *
z).
[para(42(a,1),10(a,1,2)),flip(a)].
1237 (x' * y) * (x * z) = x' * ((y / x') *
z).
[para(10(a,1),42(a,1,2,2)),flip(a)].
1245 C * ((C * x) * y) = x * (C * (C *
y)).
[para(42(a,1),21(a,2,2)),rewrite([106(3),36(5),16(4,R)]),flip(a)].
1248 (x * y) * (x' * z) = x * ((y / x) *
z).
[para(36(a,1),42(a,1,2,2)),flip(a)].
1333 (C * x) * R(y,x,C) = C * (x * y).
[para(87(a,1),1235(a,2,2)),rewrite([100(6),478(9),1248(11),106(7),10(8),1235(5),6(3)]),flip(a)].
1356 C' * ((C * x') * (x * y)) = R(y,x,C).
[para(1333(a,1),10(a,1,2)),rewrite([478(3),1237(8),387(6)])].
1440 x * (C * y) = x * (y * C).
[para(60(a,1),10(a,1,2)),rewrite([10(8)]),flip(a)].
1494 C * (x * C) = x * (C * C).
[para(60(a,2),41(a,1,1)),rewrite([106(8),10(9)]),flip(a)].
1512 R(x,C * y,z) = R(x,y * C,z).
[para(1440(a,1),18(a,1,1,1)),rewrite([694(8)]),flip(a)].
1526 (x * C) * (C * y) = C * (C * (x *
y)).
[para(1440(a,1),676(a,1)),rewrite([21(5)]),flip(a)].
1532 (x * C') * (y * C) = C' * ((C * x) *
y). [para(1440(a,1),787(a,2)),rewrite([1237(6),387(5)]),flip(a)].
1551 C * (C * ((x * (C' * C')) * y)) = C' * ((C
* x) * y).
[back_rewrite(1009),rewrite([1532(17)])].
1553 (C' * ((C * x) * y)) / y = R(x,C',y *
C).
[back_rewrite(132),rewrite([1532(6)])].
1648 C * (C * x) = x * (C * C).
[para(61(a,1),54(a,1,2)),rewrite([10(9)]),flip(a)].
1699 (C * (C * (x * y))) / (y * (C * C)) =
R(x,C,C * y).
[para(1648(a,1),18(a,1,2)),rewrite([1526(5)])].
1701 R(x,C,C * y) = R(x,y,C * C).
[para(1648(a,2),18(a,1,1)),rewrite([1699(10)])].
1702 R(x,C,y * C) = R(x,y,C * C).
[para(1648(a,2),18(a,1,2)),rewrite([1494(5,R),16(4,R),182(10)])].
1720 (x * (C * C)) * y = C * (x * (C *
y)).
[para(1648(a,1),676(a,1,1)),rewrite([16(9,R),61(10)])].
1772 R(x,C * y,C * C) = R(x,C,C * (y *
C)). [para(1440(a,1),1701(a,1,3)),flip(a)].
2226 (x * (C' * C')) * y = C' * (x * (C' *
y)).
[para(975(a,1),759(a,1,2,1)),rewrite([1018(9),67(11),13(7)]),flip(a)].
2266 C' * ((C * x) * y) = C * (x * (C' *
y)).
[back_rewrite(1551),rewrite([2226(9),36(10)]),flip(a)].
2277 R(x,C' * y,C) = R(x,C',y * C).
[back_rewrite(1553),rewrite([2266(6),949(7)])].
2283 C * (x' * (C' * (x * y))) = R(y,x,C).
[back_rewrite(1356),rewrite([2266(8)])].
2325 (C * (x * y)) / (C * (C * y)) = R(C' *
R(x,y,C),C,C * y).
[para(765(a,1),871(a,1,1))].
2436 R(C' * R(C * x,y,C),C,C * y) = x.
[para(1245(a,2),6(a,1,1)),rewrite([2325(10)])].
2438 C' * (x * (C * (C * y))) = (C * x) *
y. [para(1245(a,1),10(a,1,2))].
2476 C * (x * (x * y)) = x * ((C * x) *
y).
[para(129(a,1),1245(a,1,2,1)),rewrite([12(3),13(13),2438(12)])].
2640 (x * (C * C))' = C' * (x' * C').
[para(1720(a,1),34(a,1,2)),rewrite([1195(6)]),flip(a)].
2724 R(x,C',C * (C * y)) = R(x,y,C).
[para(10(a,1),2277(a,1,2)),rewrite([16(8,R)]),flip(a)].
2728 R(x,y * C',C) = R(x,C',y * C). [para(292(a,1),2277(a,1,2))].
2904 C * ((C' * x) * ((x * C') * y)) = (C' * x)
* (x * y).
[para(787(a,1),2476(a,1,2,2)),rewrite([36(18)])].
3125 (C' * (x * (C * y))) / y = R(x,C *
y,C').
[para(292(a,2),69(a,1,1)),rewrite([387(5),387(10)])].
3150 C' * (x * (y * C)) = C * ((C' * x) *
y). [para(110(a,1),10(a,1,2))].
3366 R(C * x,C',C * y) = (x * (C * y)) /
y.
[para(10(a,1),899(a,1,2)),flip(a)].
3392 R(C * R(x,y,C),C',C * y) = (C * (x * y)) /
y.
[para(765(a,1),899(a,1,1)),rewrite([10(8)]),flip(a)].
3399 R(C * x,C',y * C) = (x * (C * y)) /
y.
[para(1440(a,2),899(a,1,1)),rewrite([54(8)]),flip(a)].
3416 R(R(x,C',y * C),y,C) = R(x,C,y).
[para(7(a,1),1001(a,2,3)),rewrite([106(2),2277(5),106(8),36(10)])].
3427 R(R(x,y * C,C),C * (C * y),C) = R(x,C,C *
(y * C)). [para(1440(a,2),1001(a,1,2)),rewrite([16(15,R)])].
3428 R(R(x,C * y,C),y * (C * C),C) = R(x,C,C *
(C * y)).
[para(1648(a,1),1001(a,1,2)),rewrite([16(15,R)])].
3437 R(R(x,C,y * C),C * (C * y),C) =
R(R(x,y,C),C,C * (C * y)).
[para(1001(a,1),1001(a,1,1)),rewrite([16(17,R)])].
3614 C' * ((x * C) * y) = C * (x * (C' *
y)).
[para(16(a,1),1236(a,2,2,1)),rewrite([106(2),1237(6),387(5),2266(6)]),flip(a)].
3630 (C' * x') * (x * y) = x' * ((C' * x) *
y).
[para(292(a,2),1236(a,2,2,1)),rewrite([438(3)])].
3655 R(x,y,C) * ((C * y) * z) = R(x * (y * (C *
z)),y,C).
[para(87(a,1),1236(a,1,1)),rewrite([478(9),100(16),61(17),13(16),1237(18),387(12),
2266(18),2283(18)])].
3756 (x * C) * (C' * y) = C * ((C' * x) *
y).
[para(16(a,1),1248(a,1,1)),rewrite([106(9)])].
3764 (C * x') * (x * y) = x' * ((x * C) *
y).
[para(112(a,1),1248(a,1,1)),rewrite([32(5),485(9),32(8)])].
3775 (C' * x) * (x * y) = x * (x * (C' *
y)).
[para(129(a,1),1248(a,1,1)),rewrite([12(5),106(12),815(14),2904(15)]),flip(a)].
3895 x' * (C' * (x * y)) = C' * R(y,x,C). [para(2283(a,1),10(a,1,2)),flip(a)].
3897 C * (x' * (C' * R(x * y,x,C))) = R(y,x *
x,C).
[para(12(a,1),2283(a,1,2,2,2)),rewrite([551(3),12(10),3895(9)])].
3900 x' * ((x * C) * y) = C * R(y,x,C).
[para(2283(a,1),21(a,2,2)),rewrite([16(9,R),36(9),3764(5)])].
3902 C * (x * (C' * (x' * y))) =
R(y,x',C).
[para(32(a,1),2283(a,1,2,1))].
3916 x' * (C * ((C' * x) * y)) = R(y,C *
x,C).
[para(676(a,1),2283(a,1,2,2,2)),rewrite([478(4),3614(11),1237(12),387(7),3764(11),3756(10),36
(13)])].
3920 R(x,C * y,C) = R(x,C',y * C).
[para(787(a,2),2283(a,1,2,2,2)),rewrite([503(5),3756(12),110(13),16(7,R),3916(8),2728(9)])].
3928 C * (x' * ((C' * x) * y)) =
R(R(y,x,C),C',x * C).
[para(1333(a,1),2283(a,1,2,2,2)),rewrite([478(4),10(11),3630(7),3920(14)])].
3930 C * R(x,C',y * C) = R(C * x,y,C).
[para(1440(a,1),2283(a,1,2,2,2)),rewrite([3150(8),3916(9),3920(5)])].
3932 R(x,y * C,C) = R(x,C',y * C).
[para(1512(a,1),2283(a,2)),rewrite([478(4),2266(11),1237(12),387(7),3764(11),3756(10),3916(11),3920(7),36
(10)]),flip(a)].
3933 C' * R(C * x,y,C) = R(x,y,C).
[para(61(a,1),2283(a,1,2,2,2)),rewrite([478(6),478(6),10(16),304(12),3895(11),36(12),3920(13),16(13,R),27
24(14)])].
3937 R(C * x,C',y * C) = C * R(x,y,C).
[para(100(a,1),2283(a,1,2,2,2)),rewrite([478(4),10(13),1237(9),387(7),3764(8),3900(8),10(8),3920(10)]
),flip(a)].
3945 R(x,y * (C * C),C) = R(x,y,C).
[para(1720(a,1),2283(a,1,2,2,2)),rewrite([2640(6),10(16),13(12),3895(11),3933(10),36(7)]),flip(a)].
3952 R(R(x,y,C),C',y * C) = R(x,C,y * C). [para(1001(a,1),2283(a,2)),rewrite([478(4),1333(12),10(11),3630(7),3928(8)])].
3969 R(R(x,y,C),C,C * (C * y)) = R(R(x,C,y *
C),y,C).
[back_rewrite(3437),rewrite([3920(10),16(10,R),2724(11)]),flip(a)].
3972 R(x,C,C * (C * y)) = R(x,C,y).
[back_rewrite(3428),rewrite([3920(4),3945(11),3416(7)]),flip(a)].
3973 R(x,C,C * (y * C)) = R(x,C,y).
[back_rewrite(3427),rewrite([3932(4),3920(11),16(11,R),2724(12),3416(7)]),flip(a)].
4004 R(R(x,y,C),C,C * y) = x.
[back_rewrite(2436),rewrite([3933(7)])].
4006 (x * (C * y)) / y = C * R(x,y,C). [back_rewrite(3399),rewrite([3937(7)]),flip(a)].
4015 C * (x' * ((C' * x) * y)) = R(y,C,x *
C).
[back_rewrite(3928),rewrite([3952(15)])].
4019 R(R(x,C,y * C),y,C) =
R(R(x,y,C),C,y).
[back_rewrite(3969),rewrite([3972(8)]),flip(a)].
4030 R(x,C * y,C * C) = R(x,C,y).
[back_rewrite(1772),rewrite([3973(12)])].
4042 R(C * x,C',C * y) = C * R(x,y,C).
[back_rewrite(3366),rewrite([4006(11)])].
4052 C * R(R(x,y,C),y,C) = (C * (x * y)) /
y.
[back_rewrite(3392),rewrite([4042(9)])].
4082 R(R(x,C',y * C),C,y) = x. [para(36(a,1),4004(a,1,3)),rewrite([2277(5)])].
4157 R(R(x,y,C),C,y) = x.
[para(4082(a,1),18(a,2)),rewrite([16(7,R),3930(7),871(8),3933(7)])].
4161 R(R(x,C,y * C),y,C) = x.
[back_rewrite(4019),rewrite([4157(10)])].
4234 R(x,C,C' * y) = R(x,C,C * y). [para(36(a,1),3972(a,1,3,2)),flip(a)].
4308 R(x,C',y) = R(x,y,C).
[para(7(a,1),3920(a,2,3)),rewrite([106(3),36(5)]),flip(a)].
4311 R(x,y * y,C) = R(x,C',y * y).
[para(129(a,1),3920(a,1,2)),rewrite([16(11,R),129(11)])].
4318 R(x,y * (z * C),C) = R(x,C',y * (z * C)).
[para(110(a,1),3920(a,1,2)),rewrite([16(15,R),110(15)])].
4338 C * (x' * (C' * R(x * y,x,C))) = R(y,C',x
* x).
[back_rewrite(3897),rewrite([4311(13)])].
4558 C * R(x,y,C) = R(C * x,y,C).
[para(3933(a,1),10(a,1,2)),rewrite([32(3)])].
4564 C' * R(x,y,C) = R(C' * x,y,C). [para(36(a,1),3933(a,1,2,1))].
4582 R(x,C',y * C) = R(x,y,C).
[para(1512(a,1),3933(a,1,2)),rewrite([3932(8),3937(9),4558(6),4564(7),10(5),3920(6)]),flip(a)].
4626 R(R(C * x,y,C),y,C) = (C * (x * y)) /
y. [back_rewrite(4052),rewrite([4558(6),4558(4)])].
4656 C * (x' * R(C' * (x * y),x,C)) = R(y,C',x
* x).
[back_rewrite(4338),rewrite([4564(8)])].
4663 x' * (C' * (x * y)) = R(C' * y,x,C).
[back_rewrite(3895),rewrite([4564(11)])].
4704 R(R(x,y,C),y,C) = R(x,C,y * C). [back_rewrite(3952),rewrite([4582(7)])].
4710 R(x,C,y * C) = R(x,C,y).
[back_rewrite(3416),rewrite([4582(5),4704(4)])].
4721 R(x,C' * y,C) = R(x,y,C).
[back_rewrite(2277),rewrite([4582(10)])].
4733 (C * (x * y)) / y = R(C * x,C,y).
[back_rewrite(4626),rewrite([4704(6),4710(6)]),flip(a)].
4737 R(R(x,C,y),y,C) = x.
[back_rewrite(4161),rewrite([4710(4)])].
4740 C * (x' * ((C' * x) * y)) = R(y,C,x).
[back_rewrite(4015),rewrite([4710(12)])].
4750 R(x,y,C * C) = R(x,C,y).
[back_rewrite(1702),rewrite([4710(4)]),flip(a)].
4760 R(x,C,C * y) = R(x,C,y).
[back_rewrite(4030),rewrite([4750(6)])].
4796 R(x,C,C' * y) = R(x,C,y).
[back_rewrite(4234),rewrite([4760(9)])].
4827 R(R(x,C,y),C',y) = x. [para(4737(a,1),4308(a,2))].
5318 C' * (x * (C * y)) = C * ((C' * x) *
y). [para(36(a,1),2438(a,1,2,2,2)),rewrite([1248(12),106(9)])].
5351 R(x,C * y,C') = R(x,C,y).
[back_rewrite(3125),rewrite([5318(6),4733(7),36(5)]),flip(a)].
5365 R(x,C,y) = R(x,y,C') #
label(flip_matches_hint).
[para(36(a,1),5351(a,1,2)),rewrite([4796(8)]),flip(a)].
5384 R(c1,A,C') * R(c2,C,A) != R(c1 *
c2,C,A).
[para(5365(a,1),20(a,1,1))].
5397 R(R(x,y,C),y,C') = x. [para(5365(a,1),4157(a,1))].
7967 x' * R(C' * y,x,C) = (C' * x') * y.
[para(10(a,1),3775(a,1,2)),rewrite([4663(12)]),flip(a)].
8074 R(x,C',y * y) = R(x,C,y).
[back_rewrite(4656),rewrite([7967(9),3630(7),4740(8)]),flip(a)].
8170 x * (C * ((C' * x') * y)) =
R(y,x',C).
[para(676(a,1),3902(a,1,2)),rewrite([478(8),3756(12),110(13),16(7,R),478(11),4721(14)])].
9941 R(x,y * z,C) = R(x,C',y * z). [para(7(a,1),4318(a,1,2,2)),rewrite([106(7),16(10,R),36(10)])].
13806 R(x * R(y,z',C),z,C) = R(x,z,C) * y.
[para(36(a,1),3655(a,1,2)),rewrite([478(7),8170(11)]),flip(a)].
13857 R(R(x,y',C),y,C) = x.
[para(2(a,1),13806(a,1,1)),rewrite([64(8),2(7)])].
13884 R(x * R(y,C',z'),z,C) = R(x,z,C) *
y.
[para(4308(a,2),13806(a,1,1,2))].
13916 R(R(x,C,y'),C,y) = x.
[para(551(a,1),13857(a,1,1,2)),rewrite([9941(5),8074(6),9941(6),8074(7)])].
13929 R(x,y',C) = R(x,y,C'). [para(13857(a,1),5397(a,1,1)),flip(a)].
14521 R(R(x,C,y),C,y') = x. [para(32(a,1),13916(a,1,1,3))].
14527 R(x,C',y) = R(x,C,y'). [para(13916(a,1),4827(a,1,1))].
14545 R(x * R(y,C,z),z,C) = R(x,z,C) * y.
[back_rewrite(13884),rewrite([14527(4),32(3)])].
16801 R(c1,A,C') * R(c2,C,A) != R(c1 *
c2,A,C'). [para(5365(a,1),5384(a,2))].
21011 R(x,y,C') * R(z,C,y) = R(x *
z,y,C').
[para(14521(a,1),14545(a,1,1,2)),rewrite([13929(4),13929(7)]),flip(a)].
21012 $F.
[resolve(21011,a,16801,a)].
============================== end of proof
==========================
% Proof
1 at 15.69 (+ 0.17) seconds.
% Length
of proof is 380.
% Level
of proof is 51.
%
Maximum clause weight is 1015.000.
% Given
clauses 1121.
1 R(x *
y,A,C) = R(x,A,C) * R(y,A,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
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(c1
* c2,A,C) != R(c1,A,C) * R(c2,A,C).
[deny(1)].
20
R(c1,A,C) * R(c2,A,C) != R(c1 * c2,A,C).
[copy(19),flip(a)].
21 (C *
x) * (y * C) = C * (C * (x * y)).
[back_rewrite(15),rewrite([16(9,R)])].
25 x / 0
= x. [para(3(a,1),6(a,1,1))].
30 0 / x
= x'. [para(8(a,1),6(a,1,1))].
32 x'' =
x.
[para(9(a,1),6(a,1,1)),rewrite([30(3)])].
33 x \ y
= x' * y.
[para(4(a,1),10(a,1,2)),flip(a)].
34 x /
(y * x) = y'.
[para(10(a,1),6(a,1,1))].
36 x *
(x' * y) = y.
[back_rewrite(4),rewrite([33(1)])].
37 (x *
(x * y)) / y = x * x.
[para(12(a,1),6(a,1,1))].
41 (x *
(y * (x * z))) / z = x * (y * x).
[para(13(a,1),6(a,1,1))].
42 x *
((y / x) * (x * z)) = (x * y) * z.
[para(7(a,1),13(a,1,1,2)),flip(a)].
47 (x *
(y * (y * x))) * z = x * (y * (y * (x * z))). [para(12(a,1),13(a,1,1,2)),rewrite([12(7)])].
53 C *
(x / C) = x.
[para(16(a,2),7(a,1))].
54 C' *
(x * C) = x.
[para(16(a,1),10(a,1,2))].
56 C *
(C * x) = C * (x * C).
[para(16(a,1),12(a,2,2)),rewrite([12(4)])].
57 C *
(x * x) = x * (x * C).
[para(16(a,2),12(a,1))].
58 C *
(x * x) = x * (C * x).
[para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].
61 (C *
(C * x)) * y = C * (x * (C * y)).
[para(16(a,2),13(a,1,1,2))].
62 C *
(x * (y * x)) = x * (y * (x * C)).
[para(16(a,2),13(a,1))].
67
R(x,y,z) * (y * z) = (x * y) * z.
[para(18(a,1),7(a,1,1))].
68 R(x /
y,y,z) = (x * z) / (y * z).
[para(7(a,1),18(a,1,1,1)),flip(a)].
71 (x *
y') * y = R(x,y',y).
[para(8(a,1),18(a,1,2)),rewrite([25(5)])].
72
R(x,x',y) = x.
[para(9(a,1),18(a,1,1,1)),rewrite([2(2),34(3),32(2)]),flip(a)].
74 (x *
y) * y' = R(x,y,y').
[para(9(a,1),18(a,1,2)),rewrite([25(5)])].
75
R(x',x * y,z) = (y * z) / ((x * y) * z).
[para(10(a,1),18(a,1,1,1)),flip(a)].
79 ((x *
(y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(12(a,1),18(a,1,2))].
81 (x *
(y * (x * z))) / ((y * x) * z) = R(x,y * x,z). [para(13(a,1),18(a,1,1))].
85 ((C *
x) * y) / (C * y) = R(x,C,y).
[para(16(a,2),18(a,1,1,1))].
87 (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))) / (y * C) = C * x.
[para(21(a,1),6(a,1,1))].
89 C *
(C * (x * (y / C))) = (C * x) * y.
[para(7(a,1),21(a,1,2)),flip(a)].
90 C *
(C * (x * C')) = C * x.
[para(8(a,1),21(a,1,2)),rewrite([3(4)]),flip(a)].
99 (x *
C) * (y * C) = C * (C * (x * y)).
[para(16(a,1),21(a,1,1))].
100 (C *
x) * (C * y) = C * (C * (x * y)).
[para(16(a,2),21(a,1,2))].
106 x /
C = C' * x.
[para(53(a,1),10(a,1,2)),flip(a)].
110 C *
(C * ((C' * x) * y)) = x * (y * C).
[para(53(a,1),21(a,1,1)),rewrite([106(7)]),flip(a)].
111 C *
(C * (x * (C' * y))) = (C * x) * y.
[back_rewrite(89),rewrite([106(4)])].
112 x' *
C = C * x'.
[para(16(a,2),33(a,2)),rewrite([33(2)])].
113 (x /
y)' = y / x.
[para(7(a,1),34(a,1,2)),flip(a)].
117 C /
(C * x) = x'.
[para(16(a,2),34(a,1,2))].
118 (x *
C) / (C * (C * (y * x))) = (C * y)'.
[para(21(a,1),34(a,1,2))].
123
R(x,x' * y,z) = (y * z) / ((x' * y) * z).
[para(36(a,1),18(a,1,1,1)),flip(a)].
125 ((x
* y) * (y' * z)) / z = R(x,y,y' * z).
[para(36(a,1),18(a,1,2))].
129 C *
(x * (C' * x)) = x * x.
[para(54(a,1),13(a,2,2)),rewrite([16(6,R)])].
132 ((x
* C') * (y * C)) / y = R(x,C',y * C).
[para(54(a,1),18(a,1,2))].
135 (x *
y) / ((z * x) * y) = R(z,x,y)'.
[para(18(a,1),113(a,1,1)),flip(a)].
136 (C'
* x)' = C / x.
[para(106(a,1),113(a,1,1))].
137
R(x,x' * y,z) = R(x',y,z)'.
[back_rewrite(123),rewrite([135(8)])].
138
R(x',x * y,z) = R(x,y,z)'.
[back_rewrite(75),rewrite([135(7)])].
154 (x'
* y) / (x * y) = x' * x'.
[para(10(a,1),37(a,1,1,2))].
161 (x *
y) / (x' * y) = x * x.
[para(36(a,1),37(a,1,1,2))].
173 (C *
(C * (x * y))) / (C * (C * y)) = R(x,C,y * C). [para(56(a,2),18(a,1,2)),rewrite([99(5)])].
178 (C *
x)' = (x * C)'. [para(56(a,1),117(a,1,2)),rewrite([117(6)]),flip(a)].
189 (C *
x) * ((x * C)' * y) = y.
[para(178(a,1),36(a,1,2,1))].
201 (C *
(x * x)) * y = x * (C * (x * y)).
[para(58(a,2),13(a,1,1))].
208 C *
(C * (x * (x * y))) = x * (C * (x * (y * C))). [para(58(a,1),21(a,1,1)),rewrite([13(6),12(10)]),flip(a)].
212 x *
(C * (x' * x')) = C * x'.
[para(58(a,2),36(a,1,2))].
213 C *
((C' * x) * (C' * x)) = (C' * x) * x.
[para(36(a,1),58(a,2,2))].
228 C *
(x * C') = R(x,C',C).
[para(71(a,1),16(a,2))].
232 C *
(C * (x * (y * C'))) = (C * x) * R(y,C',C). [para(71(a,1),21(a,1,2)),flip(a)].
235 C' *
R(x,C',C) = x * C'.
[para(71(a,1),54(a,1,2))].
244 C *
R(x,C',C) = C * x.
[back_rewrite(90),rewrite([228(6)])].
246
R(x,C',C) = x.
[para(244(a,1),10(a,1,2)),rewrite([10(5)]),flip(a)].
247 C' *
x = x * C'.
[back_rewrite(235),rewrite([246(6)])].
248 C *
(C * (x * (y * C'))) = (C * x) * y.
[back_rewrite(232),rewrite([246(14)])].
249 C *
(x * C') = x.
[back_rewrite(228),rewrite([246(9)])].
250 (x *
C') / x = C'.
[para(247(a,1),6(a,1,1))].
253 x' *
(C' * x) = C'.
[para(247(a,2),10(a,1,2))].
256 C' *
(x * x) = x * (C' * x).
[para(247(a,2),12(a,2,2)),rewrite([247(4,R)])].
257 (x *
(x * C')) * y = x * (C' * (x * y)).
[para(247(a,1),13(a,1,1,2))].
258 C' *
(x * (C' * y)) = C' * (x * (y * C')).
[para(247(a,1),13(a,2,2,2)),rewrite([13(7)])].
259 (C'
* (C' * x)) * y = C' * (x * (C' * y)).
[para(247(a,2),13(a,1,1,2))].
260 C' *
(x * (y * x)) = x * (y * (x * C')).
[para(247(a,2),13(a,1))].
264 ((C'
* x) * y) / (C' * y) = R(x,C',y).
[para(247(a,2),18(a,1,1,1))].
266 (C'
* (x * y)) / (C' * y) = R(x,y,C').
[para(247(a,2),18(a,1,2)),rewrite([247(4,R)])].
269 x *
(C' * x') = C'.
[para(247(a,2),36(a,1,2))].
270 (x *
C')' = C / x.
[para(247(a,1),136(a,1,1))].
279 (x *
(x * C'))' = C / (x * x). [para(12(a,1),270(a,1,1))].
284 (C *
x)' * x = C'.
[para(10(a,1),253(a,1,2))].
285 (C'
* x) * (x' * ((C' * x) * y)) = C' * (x * (C' * y)).
[para(253(a,1),13(a,1,1,2)),rewrite([247(6,R),259(7)]),flip(a)].
288
R(C,x',x) = C.
[para(253(a,1),21(a,2,2,2)),rewrite([16(8,R),36(8),71(4),9(8),3(6)])].
296
R(C,x,x') = C.
[para(32(a,1),288(a,1,2))].
306 (C *
x)' = C' / x.
[para(284(a,1),6(a,1,1)),flip(a)].
327 (x *
C)' = C' / x.
[back_rewrite(178),rewrite([306(3)]),flip(a)].
329 (x *
C) / (C * (C * (y * x))) = C' / y.
[back_rewrite(118),rewrite([306(11)])].
332 (C *
x) * ((C' / x) * y) = y.
[back_rewrite(189),rewrite([327(5)])].
338 x /
C' = C * x.
[para(306(a,1),32(a,1,1)),rewrite([113(4)])].
359 (x *
C) * x' = C.
[para(16(a,1),74(a,1,1)),rewrite([296(7)])].
378 C /
x' = x * C.
[para(359(a,1),6(a,1,1))].
387 C' /
x = C' * x'.
[para(359(a,1),34(a,1,2)),rewrite([106(3),327(7)]),flip(a)].
405 (C *
x) * ((C' * x') * y) = y.
[back_rewrite(332),rewrite([387(5)])].
408 (x *
C) / (C * (C * (y * x))) = C' * y'.
[back_rewrite(329),rewrite([387(11)])].
409 (x *
C)' = C' * x'.
[back_rewrite(327),rewrite([387(6)])].
423 (C *
x)' = C' * x'.
[back_rewrite(306),rewrite([387(6)])].
429 C /
x = x' * C.
[para(32(a,1),378(a,1,2))].
443 (x *
(x * C'))' = C * (x * x)'. [back_rewrite(279),rewrite([429(8),16(9,R)])].
447 (x *
C')' = x' * C.
[back_rewrite(270),rewrite([429(6)])].
455 (C'
* x)' = x' * C.
[back_rewrite(136),rewrite([429(6)])].
466 (C *
x) * x = C * (x * x).
[para(129(a,1),21(a,2,2)),rewrite([16(7,R),36(7)])].
479 (x *
(C * (x * y))) / (x * y) = R(C * x,x,y).
[para(466(a,1),18(a,1,1,1)),rewrite([201(4)])].
483 (C'
* x) * x = x * (C' * x).
[para(36(a,1),466(a,1,1)),rewrite([213(13)]),flip(a)].
491 C *
((C' * x) * (C' * x)) = x * (C' * x).
[back_rewrite(213),rewrite([483(13)])].
493 (x *
x)' = x' * x'.
[para(8(a,1),161(a,1,1)),rewrite([32(3),30(3)])].
510 (x *
(x * C'))' = C * (x' * x').
[back_rewrite(443),rewrite([493(8)])].
525 R(x
/ y,y,z) = R(y / x,x,z)'.
[para(7(a,1),138(a,1,2)),rewrite([113(2)])].
550 C *
(x * (x * (C * ((C' * x') * y)))) = (C * x) * y. [para(405(a,1),12(a,2,2)),rewrite([100(5),61(11),12(10)])].
556 (C *
x) * y = (x * C) * y.
[para(36(a,1),405(a,1,2)),rewrite([455(8),32(5)])].
589
R(x,y,z)' * ((x * y) * z) = y * z.
[para(67(a,1),10(a,1,2))].
595
R(x,y,C) * (C * y) = C * (x * y).
[para(16(a,2),67(a,1,2)),rewrite([16(8,R)])].
610 (C'
* x) * y = (x * C') * y.
[para(247(a,1),67(a,2,1)),rewrite([67(5)])].
611
R(x,y,C') * (C' * y) = C' * (x * y).
[para(247(a,2),67(a,1,2)),rewrite([247(11,R)])].
631 (C'
* (x * x)) * y = x * (C' * (x * y)).
[para(12(a,1),610(a,2,1)),rewrite([257(10)])].
636 (x *
C') * (y * ((C' * x) * z)) = (x * C') * (y * ((x * C') * z)).
[para(610(a,2),13(a,2,2,2)),rewrite([13(9)]),flip(a)].
646 (x *
C') * x = x * (C' * x).
[para(610(a,1),58(a,2)),rewrite([491(9),36(12)]),flip(a)].
667 (C *
(C * (x * y))) / (C * (y * C)) = R(x,C,y * C). [para(21(a,1),85(a,1,1))].
668 (x *
y) / (C * y) = R(C' * x,C,y).
[para(36(a,1),85(a,1,1,1))].
670 ((C
* x) * (C' * y)) / y = R(x,C,C' * y).
[para(36(a,1),85(a,1,2))].
692 (C *
(x * (C' * y))) / y = R(x,C' * y,C).
[para(36(a,1),87(a,1,2))].
713 x *
((x * y)' * x) = x / y.
[para(8(a,1),41(a,1,1,2)),rewrite([3(2)]),flip(a)].
714 (x *
y) / x' = x * (y * x).
[para(9(a,1),41(a,1,1,2,2)),rewrite([3(2)])].
743 C *
(x * (y * (C' * x))) = x * (y * x).
[para(247(a,2),41(a,1,1,2,2)),rewrite([338(8)])].
794 (x *
y)' * x = x' * (x / y).
[para(713(a,1),10(a,1,2)),flip(a)].
795 x' /
(x * y) = x' * (y' * x').
[para(10(a,1),713(a,1,2,1,1)),flip(a)].
800 x' *
(C * C) = C * (x' * C).
[para(713(a,1),21(a,2,2)),rewrite([423(4),36(6),429(8)])].
826 (x *
(y * x))' = x' * (y' * x').
[para(714(a,1),113(a,1,1)),rewrite([795(6)])].
893 (x *
y) * x' = x * (y / x).
[para(9(a,1),42(a,1,2,2)),rewrite([3(3)]),flip(a)].
894 (x /
y) * (y * z) = y' * ((y * x) * z).
[para(42(a,1),10(a,1,2)),flip(a)].
895 (x'
* y) * (x * z) = x' * ((y / x') * z).
[para(10(a,1),42(a,1,2,2)),flip(a)].
903 C *
((C * x) * y) = x * (C * (C * y)).
[para(42(a,1),21(a,2,2)),rewrite([106(3),36(5),16(4,R)]),flip(a)].
906 (x *
y) * (x' * z) = x * ((y / x) * z).
[para(36(a,1),42(a,1,2,2)),flip(a)].
907 (C'
* x) * (y * C) = C' * ((C * x) * y).
[para(54(a,1),42(a,1,2,2)),rewrite([338(5)]),flip(a)].
944 (C *
((C' * x) * y)) / y = R(x,C,C' * y).
[back_rewrite(670),rewrite([906(6),106(3)])].
980 (C *
x) * R(y,x,C) = C * (x * y).
[para(87(a,1),893(a,2,2)),rewrite([100(6),423(9),906(11),106(7),10(8),893(5),6(3)]),flip(a)].
987 C' *
((C * x') * (x * y)) = R(y,x,C).
[para(980(a,1),10(a,1,2)),rewrite([423(3),895(8),338(6)])].
1025 C *
(C * x) = x * (C * C).
[para(61(a,1),54(a,1,2)),rewrite([10(9)]),flip(a)].
1061 (x
* C) * (C * y) = C * (C * (x * y)).
[para(16(a,2),99(a,1,2))].
1083 x *
(C * y) = x * (y * C).
[para(36(a,1),100(a,1,1)),rewrite([110(11)])].
1100 (x
/ (C * y)) * (y * C) = x.
[para(1083(a,1),7(a,1))].
1101 (x
/ (y * C)) * (C * y) = x.
[para(1083(a,2),7(a,1))].
1110 (C
* x) / (y * (x * C)) = y'.
[para(1083(a,1),34(a,1,2))].
1124 (x
* C') * (C * y) = C' * ((C * x) * y).
[para(1083(a,1),610(a,1)),rewrite([907(6)]),flip(a)].
1125 (x
* C') * (y * C) = C' * ((C * x) * y).
[para(1083(a,1),610(a,2)),rewrite([895(6),338(5)]),flip(a)].
1134 (C'
* ((C * x) * y)) / y = R(x,C',y * C).
[back_rewrite(132),rewrite([1125(6)])].
1156 (x
* C) / (C * (y * x)) = R(y,x,C)'.
[para(16(a,2),135(a,1,2))].
1229 (C
* x) / (y * x) = R(C' * y,C,x)'.
[para(668(a,1),113(a,1,1)),flip(a)].
1306 C'
* (x * (C * (C * y))) = (C * x) * y.
[para(903(a,1),10(a,1,2))].
1437 C'
* (x * (y * C)) = C * ((C' * x) * y).
[para(110(a,1),10(a,1,2))].
1439 C'
* ((C * x) * y) = C * (x * (C' * y)).
[para(13(a,1),110(a,1,2,2)),rewrite([36(10),1125(12)]),flip(a)].
1475
R(x,C' * y,C) = R(x,C',y * C).
[back_rewrite(1134),rewrite([1439(6),692(7)])].
1478 (x
* C') * (C * y) = C * (x * (C' * y)).
[back_rewrite(1124),rewrite([1439(12)])].
1480 C *
(x' * (C' * (x * y))) = R(y,x,C).
[back_rewrite(987),rewrite([1439(8)])].
1488 (C
* (x * (C' * y))) / y = R(x,C',y * C).
[back_rewrite(692),rewrite([1475(12)])].
1504
R(x,C',C * (y * C)) = R(x,y,C).
[para(54(a,1),1475(a,1,2)),rewrite([16(8,R)]),flip(a)].
1505
R(x,y * C',C) = R(x,C',y * C).
[para(247(a,1),1475(a,1,2))].
1538 C'
* (x * (C' * y))' = C * ((C * x) * y)'.
[para(111(a,1),794(a,1,1,1)),rewrite([16(6,R),429(16),423(15),16(18,R),36(18)]),flip(a)].
1651 C'
* ((x * C) * y) = C * (x * (C' * y)).
[para(16(a,1),894(a,2,2,1)),rewrite([106(2),895(6),338(5),1439(6)]),flip(a)].
1653 x'
* ((C * x) * y) = x' * ((x * C) * y).
[para(16(a,2),894(a,2,2,1)),rewrite([429(2),895(5),429(4),32(3)]),flip(a)].
1665 (x
/ y) * (C' * y) = y' * (C' * (y * x)).
[para(247(a,2),894(a,1,2)),rewrite([247(10,R)])].
1666 (C'
* x') * (x * y) = x' * ((C' * x) * y).
[para(247(a,2),894(a,2,2,1)),rewrite([387(3)])].
1685
R(x,y,C) * ((C * y) * z) = R(x * (y * (C * z)),y,C).
[para(87(a,1),894(a,1,1)),rewrite([423(9),100(16),61(17),13(16),895(18),338(12),14
39(18),1480(18)])].
1713 (C'
* x) * (y * (z * C)) = C * (x * ((C' * y) * z)).
[para(110(a,1),894(a,1,2)),rewrite([106(2),100(18),10(19)])].
1715 (C'
* x) * ((C * y) * z) = C * (x * (y * (C' * z))).
[para(111(a,1),894(a,1,2)),rewrite([106(2),100(18),10(19)])].
1716 (x
* (C' * y)) * (C * z) = C' * (((C * x) * y) * z). [para(111(a,1),894(a,2,2,1)),rewrite([106(8),10(9)])].
1733 (x
* C) * (C' * y) = C * ((C' * x) * y).
[para(16(a,1),906(a,1,1)),rewrite([106(9)])].
1748 (C'
* x) * (x' * y) = x * ((C' * x') * y).
[para(247(a,2),906(a,1,1)),rewrite([387(9)])].
1806 x *
((C' * x') * ((C' * x) * y)) = C' * (x * (C' * y)). [back_rewrite(285),rewrite([1748(10)])].
1821 C'
* (x * (C * y)) = C * ((C' * x) * y).
[para(36(a,1),1306(a,1,2,2,2)),rewrite([906(12),106(9)])].
1839 (C
* x) * (y * (C' * z)) = C' * (x * ((C * y) * z)). [para(111(a,1),1306(a,1,2,2)),flip(a)].
1852
R(x,y / x,C) = R(x,y,C).
[para(7(a,1),1480(a,1,2,2,2)),rewrite([113(3),1665(6),1480(8)]),flip(a)].
1853 x'
* (C' * (x * y)) = C' * R(y,x,C).
[para(1480(a,1),10(a,1,2)),flip(a)].
1856 C *
(x' * (C' * R(x * y,x,C))) = R(y,x * x,C).
[para(12(a,1),1480(a,1,2,2,2)),rewrite([493(3),12(10),1853(9)])].
1859 (C
* x') * (x * y) = C * R(y,x,C).
[para(1480(a,1),21(a,2,2)),rewrite([16(9,R),36(9)])].
1861 C *
(x * (C' * (x' * y))) = R(y,x',C).
[para(32(a,1),1480(a,1,2,1))].
1872 C'
* (x' * ((C * x) * y)) = R(y,C * x,C).
[para(556(a,1),1480(a,1,2,2,2)),rewrite([423(4),1651(11),895(12),338(7),1839(11),36(13)])].
1875 x'
* (C * ((C' * x) * y)) = R(y,C',x * C).
[para(610(a,2),1480(a,1,2,2,2)),rewrite([447(5),1733(12),110(13),16(7,R),1505(13)])].
1880 C *
(x' * ((C' * x) * y)) = R(R(y,x,C),C * x,C). [para(980(a,1),1480(a,1,2,2,2)),rewrite([423(4),10(11),1666(7)])].
1881
R(x,C * (C * y),C) = R(x,C',y * C).
[para(61(a,1),1480(a,1,2,2,2)),rewrite([423(6),423(6),10(16),259(12),1821(10),1875(11),36(10)]),fli
p(a)].
1882 x'
* ((x * C) * y) = C * R(y,x,C).
[para(1480(a,1),99(a,2,2)),rewrite([16(9,R),36(9),895(5),429(4),32(3)])].
1884 R(C
* x,C * y,C) = C * R(x,y,C).
[para(100(a,1),1480(a,1,2,2,2)),rewrite([423(4),10(13),895(9),338(7),1859(8),10(8)]),flip(a)].
1889
R(x',C',C * (x * y))' = (x * y) / R(y,x,C). [para(1480(a,1),1156(a,1,2)),rewrite([16(6,R),36(6),1475(11),16(10,R)]),flip(a)].
1905 x'
* ((C * x) * y) = C * R(y,x,C).
[back_rewrite(1653),rewrite([1882(10)])].
1909
R(x,C * y,C) = R(x,y,C).
[back_rewrite(1872),rewrite([1905(7),10(7)]),flip(a)].
1911 C *
R(x,y,C) = R(C * x,y,C).
[back_rewrite(1884),rewrite([1909(6)]),flip(a)].
1912
R(x,C',y * C) = R(x,y,C).
[back_rewrite(1881),rewrite([1909(6),1909(4)]),flip(a)].
1913 C *
(x' * ((C' * x) * y)) = R(R(y,x,C),x,C).
[back_rewrite(1880),rewrite([1909(14)])].
1938 x'
* (C * ((C' * x) * y)) = R(y,x,C).
[back_rewrite(1875),rewrite([1912(13)])].
1942
R(x,y * C',C) = R(x,y,C).
[back_rewrite(1505),rewrite([1912(10)])].
1943 (C
* (x * (C' * y))) / y = R(x,y,C).
[back_rewrite(1488),rewrite([1912(12)])].
1947
R(x,C' * y,C) = R(x,y,C).
[back_rewrite(1475),rewrite([1912(10)])].
1974 x *
(C' * (x' * (y * x'))) = y * (x' * C').
[para(260(a,2),36(a,1,2))].
2006 (C'
* (x * (C' * C'))) * y = C' * ((x * C') * (C' * y)).
[para(260(a,2),610(a,1,1)),rewrite([259(10),247(19,R)]),flip(a)].
2065 (x
* y) / (C' * y) = R(C * x,C',y).
[para(10(a,1),264(a,1,1,1))].
2066
R(x,C',C * y) = R(x,y,C).
[para(10(a,1),264(a,1,2)),rewrite([895(6),338(5),1439(6),1943(7)]),flip(a)].
2081 (x
* y) / R(y,x,C) = R(x,y,C).
[back_rewrite(1889),rewrite([2066(7),138(4),32(4)]),flip(a)].
2086
R(x,y * C,C) = R(x,y,C).
[back_rewrite(1504),rewrite([2066(7)])].
2096
R(x,C * y,C') = R(x,C,C' * y).
[para(10(a,1),266(a,1,2)),rewrite([1821(6),944(7)]),flip(a)].
2100
R(x,y * C,C') = R(x,C,C' * y).
[para(54(a,1),266(a,1,2)),rewrite([1437(6),944(7)]),flip(a)].
2108 (C
* (x * (C' * y))) / (C' * y) = R(C * x,y,C'). [para(556(a,1),266(a,1,1,2)),rewrite([1651(6)])].
2114 R(x
* C,C,C' * y) = (C * (x * y)) / y.
[para(99(a,1),266(a,1,1,2)),rewrite([10(8),54(8),2100(11)]),flip(a)].
2134
R(x,(C * y) * z,C') = R(x,C,y * (C' * z)). [para(111(a,1),2096(a,1,2)),rewrite([10(16)])].
2168
R(R(x,y,C'),y,C) = x.
[para(611(a,1),87(a,1,1,2)),rewrite([36(6),36(6),6(2),1947(8)]),flip(a)].
2193 ((x
* C') * (y * (z * C))) / (C * ((C' * y) * z)) = R(x,C',y * (z * C)). [para(1437(a,1),18(a,1,2))].
2226 C *
((C' * x) * (x * y)) = C * (x * (x * (C' * y))). [para(12(a,1),1439(a,2,2)),rewrite([201(6),1821(7)])].
2228 C *
(x * (C' * (C' * y))) = (C' * x) * y.
[para(1439(a,1),13(a,2)),rewrite([247(7,R),10(7)]),flip(a)].
2229 ((x
* C') * ((C * y) * z)) / (C * (y * (C' * z))) = R(x,C',(C * y) * z). [para(1439(a,1),18(a,1,2))].
2245
((C' * x) * y) * (z * C) = C' * ((x * (y * C)) * z).
[para(110(a,1),1439(a,1,2,1)),rewrite([906(18),106(15),110(19)]),flip(a)].
2253 (C'
* x) * (y * C') = C' * (C' * (x * y)).
[para(260(a,2),1439(a,2,2,2)),rewrite([1839(11),247(9,R),10(9),2228(19)]),flip(a)].
2292 ((C
* x) * y)' = ((x * C) * y)'.
[para(1651(a,1),794(a,1,1,1)),rewrite([423(7),1538(8),247(9,R),10(9),32(7),387(11),36(13)])].
2325 (x
* (y * C)) / y = R(x * C,y,C).
[para(1733(a,1),87(a,1,1,2)),rewrite([110(8),36(8),1947(11)])].
2330 C *
(x * R(y,x,C)) = x * (y * C).
[para(1733(a,1),980(a,2,2)),rewrite([2086(11),13(10),1911(8),36(6),110(13)])].
2349 C'
* (x * (x * (C * y))) = C * (x * (C' * (x * y))). [para(12(a,1),1821(a,1,2)),rewrite([631(13)])].
2387 (x
* C') * (C' * y) = C' * (C' * (x * y)).
[para(260(a,2),1821(a,2,2,1)),rewrite([1716(11),247(9,R),10(9),259(18),36(19)]),flip(a)].
2407 (C'
* (x * (C' * C'))) * y = C' * (C' * (C' * (x * y))). [back_rewrite(2006),rewrite([2387(19)])].
2694 (C'
* R(x,C',C' * y)) * y = C' * (x * y).
[para(67(a,1),2228(a,1,2)),rewrite([2387(8),36(9)]),flip(a)].
2695
R(x,C',y) = R(x,y,C).
[para(2228(a,1),87(a,1,1)),rewrite([36(12),2065(8),36(5),1947(11),1947(8)])].
2712 C *
(x * (C' * (y * (C' * C')))) = C' * (C' * (x * y)). [para(260(a,1),2228(a,1,2,2)),rewrite([2253(19)])].
2718 (C'
* x) * ((y * C) * z) = C * (x * (y * (C' * z))). [para(1651(a,1),2228(a,1,2,2,2)),rewrite([10(10)]),flip(a)].
2720 (C'
* x) * (y * (C * z)) = C * (x * ((C' * y) * z)). [para(1821(a,1),2228(a,1,2,2,2)),rewrite([10(10)]),flip(a)].
2739
R(x,C',x' * y) = R(x',y,C)'.
[para(2695(a,2),137(a,1))].
2832 C'
* ((C' * x) * (C' * y)) = C' * (C' * (C' * (x * y))). [para(259(a,1),610(a,2,1)),rewrite([259(10),2407(20)])].
2859 (C'
* x) * (C' * y) = C' * (C' * (x * y)).
[para(259(a,1),1733(a,1,1)),rewrite([16(6,R),9(6),3(4),259(18),2832(18),36(19)])].
3040 (x
* (C' * C')) * y = C' * (x * (C' * y)).
[para(1748(a,1),13(a,1,1)),rewrite([2859(8),8(6),3(6),1748(17),1806(17)])].
3190 x *
(C' * y) = x * (y * C').
[para(10(a,1),2253(a,1,1)),rewrite([1439(12),10(13)]),flip(a)].
3215 (C'
* x) * (y * x) = x * ((C' * y) * x).
[para(2253(a,1),41(a,1,1,2)),rewrite([338(11),2228(10)])].
3274 ((x
* y) * (C' * z)) / (y * (z * C')) = R(x,y,C' * z). [para(3190(a,1),18(a,1,2))].
3275
R(x,y,C' * z) = R(x,y,z * C').
[para(3190(a,2),18(a,1,1)),rewrite([3274(10)])].
3626
R(R(x,y,C'),C,y) = R(x,y,C).
[para(611(a,1),667(a,1,1,2,2)),rewrite([36(7),16(9,R),36(9),87(6),16(11,R),36(11)]),flip(a)].
3741 x'
* ((C * (x * (y' * x))) * x') = x' / (y * (x' * C')).
[para(1974(a,1),795(a,1,2)),rewrite([455(16),826(13),32(10),32(11),16(13,R)]),
flip(a)].
3948 R(x
* (y * C),y,C) = C * (x * y).
[para(3(a,1),1685(a,1,2)),rewrite([595(5),3(6)]),flip(a)].
3950
R(x,y,C) * y = R(x * y,y,C).
[para(9(a,1),1685(a,2,1,2,2)),rewrite([247(7,R),10(7),3(5)])].
3969 x *
((C * x') * y) = R(C * y,x',C).
[para(36(a,1),1685(a,2,1)),rewrite([72(3)])].
3976 C'
* R(x,y,C) = R(x * C',y,C).
[para(269(a,1),1685(a,1,2)),rewrite([247(5,R),423(11),36(14),269(10)])].
4082 C *
(x' * R(C' * (x * y),x,C)) = R(y,x * x,C). [back_rewrite(1856),rewrite([3976(8),247(6,R)])].
4105 (x
* C') * (y * (z * C)) = C * (x * ((C' * y) * z)). [para(247(a,1),1713(a,1,1))].
4163
R(x,(C' * y) * z,C) = R(x,C',y * (z * C)). [back_rewrite(2193),rewrite([4105(7),87(14)])].
4277 (x
* C') * ((C * y) * z) = C * (x * (y * (C' * z))). [para(247(a,1),1715(a,1,1))].
4341
R(x,y * (C' * z),C) = R(x,C',(C * y) * z). [back_rewrite(2229),rewrite([4277(7),87(14)])].
4376 (C
* x) * (y * (z * C')) = C' * (x * ((C * y) * z)). [para(247(a,1),1839(a,1,2,2))].
4451 ((x
* (y * C)) * z) / (C * (z * C)) = R((C' * x) * y,z,C).
[para(2245(a,1),87(a,1,1,2)),rewrite([36(9),2086(17)])].
5027
R(x,C',C' * y) = R(x,y,C).
[para(3275(a,2),2695(a,1)),rewrite([1942(11)])].
5033
R((x * C') * y,y,C) = C' * (x * y).
[back_rewrite(2694),rewrite([5027(8),3976(5),3950(6)])].
5044
R((C' * x) * y,y,C) = C' * (x * y).
[para(247(a,2),5033(a,1,1,1))].
5060 R(x
* (C' * y),y,C) = (C' * x) * y.
[para(1733(a,1),5033(a,2,2)),rewrite([247(5,R),54(5),1947(9),10(15)])].
5513 x *
(C' * (x' * y)) = R(C' * y,x',C).
[para(47(a,1),1748(a,1)),rewrite([510(9),201(10),1821(11),2226(11),2349(14),36(11),1861(11),510(1
7),10(18),12(14),906(15),250(10)]),flip(a)].
5962 (C
* (x * (y * y))) / (y * (y * C)) = R(x,y * y,C). [para(57(a,1),87(a,1,2))].
6038 C *
(x * (C' * ((x * C') * y))) = x * (C' * (x * y)). [para(249(a,1),13(a,1,1,2)),rewrite([646(4),13(5),1478(15)]),flip(a)].
6364 (C
* (x * (y * x))) * x' = x * R(y * C,x,C).
[para(62(a,2),893(a,1,1)),rewrite([2325(10)])].
6529 x'
/ (y * (x' * C')) = R(y' * C,x,C).
[back_rewrite(3741),rewrite([6364(8),10(8)]),flip(a)].
6545 x *
((x' * C) * y) = R(C * y,x',C).
[para(112(a,1),894(a,2,2,1)),rewrite([429(3),32(2),906(5),429(2),32(7),3969(10)])].
6776
R(x' / y,y,x) = (y * x)'.
[para(8(a,1),68(a,2,1)),rewrite([30(6)])].
6935
R(x' * C,x,y * C') = y / (x * (y * C')).
[para(249(a,1),68(a,2,1)),rewrite([429(2)])].
7614
R(x,C * C,y) = R(x,y,C).
[para(16(a,1),79(a,1,2,2)),rewrite([4451(10),16(5,R),36(5)]),flip(a)].
7626
R(x,C' * C',y) = R(x,C' * y,C').
[para(247(a,1),79(a,1,1,1,2)),rewrite([3040(7),266(14)]),flip(a)].
7689
R(x,C' * C',(y * C) * z) = R(x,C,C' * (y * (C' * z))).
[para(1651(a,1),79(a,1,2,2)),rewrite([3040(10),1651(8),1821(10),10(19),944(15)])
,flip(a)].
7700 ((x
* (C * C)) * (y * (C' * (C' * z)))) / (C * ((C' * y) * z)) = R(x,C',y * (z *
C)).
[para(2228(a,1),79(a,1,2,2)),rewrite([7614(30),43
41(28),906(27),106(24),2066(28),4163(25)])].
7701
R(x,y * y,C) = R(x,C',y * y).
[para(2695(a,2),79(a,2)),rewrite([16(4,R),5962(8)])].
7738 ((x
* (C * C)) * (y * (C' * (z * (C' * C'))))) / (C' * (y * z)) = R(x,y *
z,C).
[para(2712(a,1),79(a,1,2,2)),rewrite([36(24),7614(34),4
341(32),4376(31),247(29,R),10(29),5027(27)])].
7778 (C
* (x * (y * y))) / (y * (y * C)) = R(x,C',y * y). [back_rewrite(5962),rewrite([7701(11)])].
7782 C *
(x' * R(C' * (x * y),x,C)) = R(y,C',x * x). [back_rewrite(4082),rewrite([7701(13)])].
8136
R(R(x,C,C' * y),y,C) = x.
[para(2096(a,1),2168(a,1,1)),rewrite([1909(9)])].
8910 (C
* (x * y)) / y = C * R(x,y,C').
[para(611(a,1),88(a,1,1,2,2)),rewrite([36(7),16(8,R),36(8)])].
8943 R(x
* C,C,C' * y) = C * R(x,y,C').
[back_rewrite(2114),rewrite([8910(11)])].
8944 C *
R(x,C' * y,C') = R(C * x,y,C').
[back_rewrite(2108),rewrite([8910(10)])].
10303 (C
* (C * (x * y))) / (y * (C * C)) = R(x,C,C * y). [para(1025(a,1),18(a,1,2)),rewrite([1061(5)])].
10304
R(x,C,C * y) = R(x,y,C * C).
[para(1025(a,2),18(a,1,1)),rewrite([10303(10)])].
10305
R(x,C,y * C) = R(x,y,C * C).
[para(1025(a,2),18(a,1,2)),rewrite([1025(5,R),173(10)])].
10318 (x
* (C * C)) * y = C * (x * (C * y)).
[para(1025(a,1),556(a,1,1)),rewrite([16(9,R),61(10)])].
10435
R(x,y * z,C) = R(x,C',y * z).
[back_rewrite(7738),rewrite([10318(15),2712(13),2228(10),2065(10),36(5)]),flip(a)].
10438
R(x,C',(C' * y) * z) = R(x,C',y * (z * C)).
[back_rewrite(7700),rewrite([10318(12),2228(10),87(14),10435(6)])].
11741
R(x,C',y * x) = R(x,y,C).
[para(6(a,1),1852(a,1,2)),rewrite([10435(5)]),flip(a)].
11782
R(x * y,C',x' * x') = R(x * y,C',x' * y).
[para(154(a,1),1852(a,1,2)),rewrite([10435(6),10435(12)])].
16898 (x
* (C * y)) / y = R(C * x,y,C).
[para(2066(a,1),68(a,1)),rewrite([338(3),10(12)]),flip(a)].
16926
R(C * x,C',x * y) = R(C * x,x,y).
[back_rewrite(479),rewrite([16898(6),10435(5)])].
17370
R(x,C' * x,(x' * C) * y) = R(x,y,C).
[para(256(a,2),125(a,1,1,1)),rewrite([455(8),2718(9),12(8),36(7),1943(7),455(9)]),flip(a)].
18057
R(R(R(x,y,C),y,C),y,C) = x.
[para(6776(a,1),1685(a,1,1)),rewrite([409(3),1715(8),10(7),36(5),387(3),2720(8),1913(8)]),flip(a)].
18212
R(R(x,C,y),y,C) = x.
[para(10(a,1),8136(a,1,1,3)),rewrite([10435(6),2066(7)])].
18984
R(x',x / y,C)' = R(x,(x * y)',C).
[para(794(a,1),11741(a,1,3)),rewrite([2739(6)])].
19637 (C
* (x * C)) / (C * (C * y)) = C' * ((C * x) / y). [para(1100(a,1),408(a,1,2,2,2)),rewrite([16(4,R),113(15)])].
19638 (C
* (C * x)) / (C * (C * y)) = C' * ((x * C) / y). [para(1101(a,1),408(a,1,2,2,2)),rewrite([16(4,R),113(15)])].
19770
R(x,C,y * C) = R(x,y,C').
[back_rewrite(173),rewrite([19638(10),16(5,R),8910(6),10(8)]),flip(a)].
19891
R(x,y,C * C) = R(x,y,C').
[back_rewrite(10305),rewrite([19770(4)]),flip(a)].
20008
R(x,C,C * y) = R(x,y,C').
[back_rewrite(10304),rewrite([19891(8)])].
20165
R(x,C' * y,C') = R(x,C,y).
[para(7(a,1),19770(a,1,3)),rewrite([106(4)]),flip(a)].
20182 C
* R(x,C,y) = R(C * x,y,C').
[back_rewrite(8944),rewrite([20165(7)])].
20184
R(x,C' * C',y) = R(x,C,y).
[back_rewrite(7626),rewrite([20165(12)])].
20212
R(x,C,C' * (y * (C' * z))) = R(x,C,(y * C) * z). [back_rewrite(7689),rewrite([20184(9)]),flip(a)].
20257
R(x,C,C' * (y * (z * C'))) = R(x,C,(C * y) * z). [para(248(a,1),20008(a,1,3)),rewrite([2096(14)]),flip(a)].
21126
R(R(R(x,C',y),y,C),y,C) = x.
[para(2695(a,2),18057(a,1,1,1))].
21130
R(R(x,y,C),y,C) = R(x,y,C').
[para(2168(a,1),18057(a,1,1,1))].
21132
R(R(x,y,C),y / x,C') = x.
[para(1852(a,1),18057(a,1,1,1)),rewrite([21130(8)])].
21133
R(x,C,C' * y) = R(x,y,C').
[para(8136(a,1),18057(a,1,1,1)),rewrite([21130(4)]),flip(a)].
21134
R(x,C,y) = R(x,y,C').
[para(18212(a,1),18057(a,1,1,1)),rewrite([21130(4)]),flip(a)].
21136
R(R(x,C',y),y,C') = x.
[back_rewrite(21126),rewrite([21130(7)])].
21146 C
* (x' * ((C' * x) * y)) = R(y,x,C').
[back_rewrite(1913),rewrite([21130(12)])].
21150
R(x,y * (z * C'),C') = R(x,C,(C * y) * z). [back_rewrite(20257),rewrite([21133(9)])].
21153
R(x,y * (C' * z),C') = R(x,C,(y * C) * z). [back_rewrite(20212),rewrite([21133(9)])].
21190 C
* R(x,y,C') = R(x * C,y,C').
[back_rewrite(8943),rewrite([21133(7)]),flip(a)].
21223
R(x,C * y,C') = R(x,y,C').
[back_rewrite(2096),rewrite([21133(10)])].
21392
R(x,C,y)' = R(x,y,C')'.
[para(21134(a,1),138(a,2,1)),rewrite([138(4)])].
21393
R(x',C,x * y) = R(x,y,C')'.
[para(21134(a,2),138(a,1))].
21396
R(x,C,x' * y) = R(x',y,C')'.
[para(21134(a,2),137(a,1))].
21399
R(x,C,y * C') = R(x,C,y).
[para(21134(a,1),3275(a,1)),rewrite([20165(6)]),flip(a)].
21428
R(x,C,(y * C) * z) = R(x,C,y * (C' * z)).
[para(1439(a,1),21133(a,1,3)),rewrite([20008(8),21153(7),2134(11)])].
21431
R(x,C,(C * y) * z) = R(x,C,y * (C' * z)).
[para(258(a,1),21133(a,1,3)),rewrite([21133(9),21150(7),21153(12),21428(10)])].
21469
R(x,y * z,C') = R(x,C,y * z).
[para(10(a,1),21431(a,2,3,2)),rewrite([100(6),20008(7),21223(6)])].
21500
R(x,y',C') = R(x,C,y').
[para(212(a,1),21431(a,1,3)),rewrite([423(5),36(7),423(10),423(14),3215(16),12(15),743(17),5513(14),5060(14),1
2(11),21133(12),21469(10),21133(9)]),flip(a)].
21591
R(R(x,y,C),C,y * x) = x.
[para(11741(a,1),21136(a,1,1)),rewrite([21469(6)])].
22846
R(C * (x * y),x',C') = x * (y * C).
[para(1110(a,1),21132(a,1,2)),rewrite([10435(7),2066(8),3948(5)])].
23162
R(x,y',C')' = R(x,C,y')'.
[para(21500(a,1),138(a,2,1)),rewrite([21469(6),21393(5)])].
23925
R(x' * C,x,y * C') = R(C' * x,C,y)'.
[para(21399(a,1),525(a,2,1)),rewrite([429(2),106(9)])].
23940 x
/ (y * (x * C')) = R(C' * y,C,x)'.
[back_rewrite(6935),rewrite([23925(7)]),flip(a)].
23959
R(C' * x,C,y')' = R(x' * C,y,C).
[back_rewrite(6529),rewrite([23940(7)])].
24291
R(x,y',C')' = R(x',y,C).
[para(800(a,1),135(a,1,1)),rewrite([1025(11,R),19637(12),1229(8),23959(9),3976(8),247(6,R),54(6),19891(8)]),f
lip(a)].
24361
R(x,C,y')' = R(x',y,C).
[back_rewrite(23162),rewrite([24291(5)]),flip(a)].
24382
R(x',y,C)' = R(x,C,y').
[para(24361(a,1),32(a,1,1))].
24383
R(x,C,y)' = R(x',y',C).
[para(32(a,1),24361(a,1,1,3))].
24484
R(x,(x * y)',C) = R(x,C,y / x).
[back_rewrite(18984),rewrite([24382(5),113(3)]),flip(a)].
24489
R(x,C',x' * y) = R(x,C,y').
[back_rewrite(2739),rewrite([24382(9)])].
24667
R(x,y,C')' = R(x',y',C).
[back_rewrite(21392),rewrite([24383(3)]),flip(a)].
24838
R(x,C,x' * y) = R(x,y',C).
[back_rewrite(21396),rewrite([24667(9),32(6)])].
24852
R(x,C,y / x) = R(x,C,y).
[para(138(a,1),24667(a,1,1)),rewrite([24667(4),24382(5),32(3),32(4),24484(6)]),flip(a)].
24871
R(x,C,y * x) = R(x,C,y).
[para(6(a,1),24852(a,1,3)),flip(a)].
24875
R(x' * y,C,x * y) = R(x' * y,C,x * x).
[para(161(a,1),24852(a,1,3)),flip(a)].
24911
R(R(x,C,y),y / x,C) = x.
[para(24852(a,1),18212(a,1,1))].
24937
R(x,C,(x * y)') = R(x,y,C).
[para(794(a,1),24871(a,1,3)),rewrite([24838(5),113(2),1852(3)]),flip(a)].
25025
R(x,R(y,x,C),C) = R(x,y,C).
[para(21591(a,1),24911(a,1,1)),rewrite([2081(4)])].
25035
R(x,y,C)' = R(x',C,y').
[para(32(a,1),24382(a,1,1,1))].
25607
R(C * x,(x * y)',C') = R(C * x,y,C).
[para(21(a,1),24937(a,1,3,1)),rewrite([423(9),423(9),21133(12),21469(10),21133(9),10435(13),1912(
14)])].
25620
R(x,((C * x) * y)',C') = R(x,y,C).
[para(903(a,2),24937(a,1,3,1)),rewrite([423(7),21133(9),10435(13),2066(14),10435(11),2066(12)])].
25633
R(x,(x * (x * y))',C') = R(x,C',x * (y * C)).
[para(208(a,2),24937(a,1,3,1)),rewrite([423(8),423(8),21133(11),21469(9),21133(8),10435(
13),2066(14),10435(11)])].
25644
R(x,(x * y)',C') = R(x,y,C).
[para(24937(a,1),21134(a,1)),flip(a)].
25655
R(x,C',x * (y * C)) = R(x,C',x * y).
[back_rewrite(25633),rewrite([25644(6),10435(3)]),flip(a)].
25763
R(x,R(y,C,x),C) = R(x,y,C).
[para(18212(a,1),25025(a,1,2)),flip(a)].
25770
R(x / y,R(y,C,x),C) = R(x / y,y,C).
[para(24911(a,1),25025(a,1,2)),flip(a)].
26472
R(x,C',R(C * y,z,C)) = R(x,R(y,z,C),C).
[para(1911(a,1),2066(a,1,3))].
26571
R(x,y,C) * R(y,x,C) = x * y.
[para(2081(a,1),7(a,1,1))].
26805
R(x,((C * y) * z)',C') = R(x,C,((y * C) * z)'). [para(2292(a,1),21500(a,2,3))].
26813
R(x,C,((x * C) * y)') = R(x,y,C).
[back_rewrite(25620),rewrite([26805(7)])].
26971 C
* (x' * R(y,x,C)) = (C * x') * y.
[para(32(a,1),550(a,1,2,2,2,2,1,2)),rewrite([1938(10)])].
26999
R(x,C',y * y) = R(x,y,C').
[back_rewrite(7782),rewrite([26971(10),906(8),106(4),1666(7),21146(8)]),flip(a)].
27056
R(x * y,C',x' * y) = R(x * y,x',C').
[back_rewrite(11782),rewrite([26999(7)]),flip(a)].
27072 (C
* (x * (y * y))) / (y * (y * C)) = R(x,y,C'). [back_rewrite(7778),rewrite([26999(12)])].
27240
R(R(x,y,C'),y,C') = R(x,y,C).
[para(3626(a,1),19770(a,1)),rewrite([10435(4),1912(5),21469(7),19770(6)]),flip(a)].
28831
R(x',C,y') * (x * (y * C)) = R(C * y,x,C).
[para(25025(a,1),589(a,1,1,1)),rewrite([25035(3),16(9,R),2330(9),16(12,R),1911(12)])].
28978
R(x,C,y * y) = R(x,y,C).
[para(21130(a,1),79(a,2)),rewrite([10435(3),26999(4),16(7,R),27072(11),27240(6),21469(6)]),flip(a)].
29017
R(x' * y,C,x * y) = R(x' * y,x,C).
[back_rewrite(24875),rewrite([28978(10)])].
31455
R(x * y,y,C) = x * R(y,C,x).
[para(18212(a,1),26571(a,1,2)),rewrite([25763(4),3950(3)])].
31464 (x
/ y) * R(y,C,x) = R(x,y,C).
[para(24911(a,1),26571(a,1,2)),rewrite([25770(5),3950(4),7(2)]),flip(a)].
32868
R(x,C' * x,y) = R(x,C',x * y).
[para(636(a,1),125(a,1,1)),rewrite([32(6),1478(10),6038(10),81(10),32(9),2066(13),10435(10),10438(11),2
5655(10)])].
32879
R(x,R(y,x',C),C) = R(x,y,C).
[back_rewrite(17370),rewrite([32868(8),6545(7),26472(8)])].
33276 x
* R(x' * y,y,C) = R(y,C,x').
[para(31455(a,2),36(a,1,2))].
33439 x
* R(y,x,C) = R(x * y,C,x').
[para(10(a,1),33276(a,1,2,1)),rewrite([10435(3),11741(4)])].
33459
R(x,y,C) * R(z,y',C') = R(x * z,y,C).
[para(33276(a,1),1685(a,1,2)),rewrite([423(6),21133(8),423(11),5044(15),36(14),36(10)])].
33585 x
* R(y,C,x') = R(x * y,x',C').
[para(161(a,1),31464(a,1,1)),rewrite([29017(6),12(6),33439(5),36(3),10435(9),27056(10)])].
34334
R(x,R(y,C,x'),C) = R(x,y,C).
[para(18212(a,1),32879(a,1,2)),flip(a)].
35651
R(C * x,y',C') = R(C * x,y,C).
[para(34334(a,1),589(a,1,1,1)),rewrite([25035(3),33585(8),16(11,R),21190(11),16(7,R),22846(11),28831(8)
,16(9,R),20182(9)]),flip(a)].
35725
R(C * x,y,C) = R(C * x,x,y).
[back_rewrite(25607),rewrite([35651(7),10435(5),16926(6)]),flip(a)].
36193
R(x,C',x * y) = R(x,y,C).
[para(36(a,1),35725(a,1,1)),rewrite([36(7),32868(6)]),flip(a)].
36319
R(x,C',y) = R(x,C,y').
[para(36(a,1),36193(a,1,3)),rewrite([10435(7),24489(8)])].
36323
R(x,y',C') = R(x,y,C).
[para(903(a,2),36193(a,1,3)),rewrite([36319(8),423(7),21133(9),26805(7),26813(6),10435(8),36319(9),423(8),423(8
),21133(11),21469(9),21133(8)]),flip(a)].
37204
R(x,y,C) * R(z,y,C) = R(x * z,y,C).
[back_rewrite(33459),rewrite([36323(6)])].
37205
$F. [resolve(37204,a,20,a)].
==============================
end of proof ==========================
% Proof
1 at 25494.35 (+ 146.70) seconds.
% Length
of proof is 2171.
% Level
of proof is 140.
%
Maximum clause weight is 1015.000.
% Given
clauses 151083.
1 R(x *
y,A,C) = R(x,A,C) * R(y,A,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(c1
* c2,A,C) != R(c1,A,C) * R(c2,A,C).
[deny(1)].
20
R(c1,A,C) * R(c2,A,C) != R(c1 * c2,A,C).
[copy(19),flip(a)].
23 x / x
= 0. [para(2(a,1),6(a,1,1))].
24 x / 0
= x. [para(3(a,1),6(a,1,1))].
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)].
42 x *
(y * (x * (x * (y * x))')) = 0.
[para(13(a,1),9(a,1))].
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)])].
50 (A *
x) * A = A * (x * A).
[para(2(a,1),15(a,1,2)),rewrite([3(7)])].
51 (A *
((x * y) * A)) / (y * A) = A * x.
[para(15(a,1),6(a,1,1))].
54 A *
((A' * x) * A) = x * A.
[para(9(a,1),15(a,1,1)),rewrite([2(4)]),flip(a)].
58 ((x *
A) * (A * ((y * x) * A))) * z = (x * A) * ((A * y) * ((x * A) * z)). [para(15(a,1),13(a,1,1,2))].
60 (A *
x) * (y * (z * (y * A))) = A * ((x * (y * (z * y))) * A). [para(13(a,1),15(a,1,2))].
61 (x *
C) / x = C.
[para(16(a,1),6(a,1,1))].
63 C *
(x / C) = x.
[para(16(a,2),7(a,1))].
64 C' *
(x * C) = x.
[para(16(a,1),10(a,1,2))].
65 x' *
(C * x) = C.
[para(16(a,2),10(a,1,2))].
66 C *
(C * x) = C * (x * C).
[para(16(a,1),12(a,2,2)),rewrite([12(4)])].
67 C *
(x * x) = x * (x * C).
[para(16(a,2),12(a,1))].
68 C *
(x * x) = x * (C * x).
[para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].
69 (x *
(x * C)) * y = x * (C * (x * y)).
[para(16(a,1),13(a,1,1,2))].
70 C *
(x * (C * y)) = C * (x * (y * C)).
[para(16(a,1),13(a,2,2,2)),rewrite([13(5)])].
71 (C *
(C * x)) * y = C * (x * (C * y)).
[para(16(a,2),13(a,1,1,2))].
72 C *
(x * (y * x)) = x * (y * (x * C)).
[para(16(a,2),13(a,1))].
73 C *
(x * (y * x)) = x * (y * (C * x)).
[para(16(a,2),13(a,2,2,2)),rewrite([16(4,R)])].
74 (A *
x) * (A * C) = A * ((x * C) * A).
[para(16(a,1),15(a,1,2))].
76
R(0,x,y) = 0.
[para(2(a,1),18(a,1,1,1)),rewrite([23(3)]),flip(a)].
77
R(x,0,y) = x.
[para(2(a,1),18(a,1,2)),rewrite([3(2),6(2)]),flip(a)].
78
R(x,y,0) = x.
[para(3(a,1),18(a,1,1)),rewrite([3(3),6(2)]),flip(a)].
79
R(x,y,z) * (y * z) = (x * y) * z.
[para(18(a,1),7(a,1,1))].
80 R(x /
y,y,z) = (x * z) / (y * z).
[para(7(a,1),18(a,1,1,1)),flip(a)].
81 ((x *
(y / z)) * z) / y = R(x,y / z,z).
[para(7(a,1),18(a,1,2))].
82
R(x',x,y) = x'.
[para(8(a,1),18(a,1,1,1)),rewrite([2(2),33(2)]),flip(a)].
83 (x *
y') * y = R(x,y',y).
[para(8(a,1),18(a,1,2)),rewrite([24(5)])].
84
R(x,x',y) = x.
[para(9(a,1),18(a,1,1,1)),rewrite([2(2),33(3),31(2)]),flip(a)].
85
R(x,y,(x * y)') = (y * (x * y)')'.
[para(9(a,1),18(a,1,1)),rewrite([29(5)]),flip(a)].
86 (x *
y) * y' = R(x,y,y').
[para(9(a,1),18(a,1,2)),rewrite([24(5)])].
87
R(x',x * y,z) = (y * z) / ((x * y) * z).
[para(10(a,1),18(a,1,1,1)),flip(a)].
88 ((x *
y') * (y * z)) / z = R(x,y',y * z).
[para(10(a,1),18(a,1,2))].
89 ((x *
(x * y)) * z) / (y * z) = R(x * x,y,z).
[para(12(a,1),18(a,1,1,1))].
90
R(x,x,y) = x.
[para(12(a,1),18(a,1,1)),rewrite([6(4)]),flip(a)].
91 ((x *
(y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(12(a,1),18(a,1,2))].
92 ((x *
(y * (x * z))) * u) / (z * u) = R(x * (y * x),z,u). [para(13(a,1),18(a,1,1,1))].
93 (x *
(y * (x * z))) / ((y * x) * z) = R(x,y * x,z). [para(13(a,1),18(a,1,1))].
94 ((x *
(y * (z * y))) * u) / (y * (z * (y * u))) = R(x,y * (z * y),u). [para(13(a,1),18(a,1,2))].
95 (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)])].
96 (A *
((x * y) * A)) / (x * (y * A)) = R(A,x,y * A). [para(15(a,1),18(a,1,1))].
97 ((x *
(A * y)) * (z * A)) / (A * ((y * z) * A)) = R(x,A * y,z * A). [para(15(a,1),18(a,1,2))].
98 ((x *
C) * y) / (x * y) = R(C,x,y).
[para(16(a,1),18(a,1,1,1))].
101 (C *
(x * y)) / (y * C) = R(x,y,C).
[para(16(a,2),18(a,1,1))].
102 (C *
(x * y)) / (C * y) = R(x,y,C).
[para(16(a,2),18(a,1,2)),rewrite([16(3,R)])].
106 (x *
(y * (x * C))) / (x * (y * x)) = C.
[para(13(a,1),61(a,1,1))].
107 x /
C = C' * x.
[para(63(a,1),10(a,1,2)),flip(a)].
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)].
114 x /
(y * (z * (y * x))) = (y * (z * y))'.
[para(13(a,1),33(a,1,2))].
116 x /
(x * C) = C'.
[para(16(a,1),33(a,1,2))].
117 C /
(C * x) = x'.
[para(16(a,2),33(a,1,2))].
121 A *
(((A' * x) * y) * A) = x * (y * A).
[para(35(a,1),15(a,1,1)),flip(a)].
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)].
125
R(x,y,(x * y)' * z) = z / (y * ((x * y)' * z)). [para(35(a,1),18(a,1,1)),flip(a)].
126 ((x
* y) * (y' * z)) / z = R(x,y,y' * z).
[para(35(a,1),18(a,1,2))].
130 C' *
(x * (y * (x * C))) = x * (y * x).
[para(13(a,1),64(a,1,2))].
131 (x *
y) / ((x * C) * y) = R(C',x * C,y).
[para(64(a,1),18(a,1,1,1))].
132 ((x
* C') * (y * C)) / y = R(x,C',y * C).
[para(64(a,1),18(a,1,2))].
135 C' *
((x * y') * (C * y)) = R(x,y',C * y).
[para(65(a,1),18(a,1,2)),rewrite([107(7)])].
137 (x /
y) * (y / x) = 0.
[para(112(a,1),8(a,1,1))].
138 (x /
y) * ((y / x) * z) = z.
[para(112(a,1),10(a,1,1))].
139 (x *
y) / ((z * x) * y) = R(z,x,y)'.
[para(18(a,1),112(a,1,1)),flip(a)].
141 (C'
* x)' = C / x.
[para(107(a,1),112(a,1,1))].
142
R(x,x' * y,z) = R(x',y,z)'.
[back_rewrite(124),rewrite([139(8)])].
143
R(x',x * y,z) = R(x,y,z)'.
[back_rewrite(87),rewrite([139(7)])].
147 A *
(((C * A') * x) * A) = C * (x * A).
[para(123(a,1),15(a,1,1)),flip(a)].
150 C' *
((x * y) * (C * y')) = R(x,y,C * y').
[para(123(a,1),18(a,1,2)),rewrite([107(7)])].
157 (C'
* x) * (C / x) = 0.
[para(141(a,1),9(a,1,2))].
158 (C /
x) * ((C' * x) * y) = y.
[para(141(a,1),10(a,1,1))].
159 (C'
* x) * ((C / x) * y) = y.
[para(141(a,1),35(a,1,2,1))].
161 ((x
/ y) * x) / y = (x / y) * (x / y).
[para(7(a,1),36(a,1,1,2))].
162 x' /
x = x' * x'.
[para(8(a,1),36(a,1,1,2)),rewrite([3(3)])].
163 x /
x' = x * x.
[para(9(a,1),36(a,1,1,2)),rewrite([3(2)])].
168 (A *
(x * (A * (x * A)))) / A = (A * x) * (A * x). [para(15(a,1),36(a,1,1)),rewrite([13(6)])].
170 C' *
(x * (C * x)) = x * x.
[para(16(a,2),36(a,1,1,2)),rewrite([107(5)])].
175 (x *
x)' = x' * x'.
[para(163(a,1),112(a,1,1)),rewrite([162(4)])].
187 (A *
x)' * (A * (x * A)) = A.
[para(50(a,1),10(a,1,2))].
190 (A *
x) * (A * (y * A)) = A * ((x * (A * y)) * A). [para(50(a,1),15(a,1,2))].
192
R(A,x,A) = A.
[para(50(a,1),18(a,1,1)),rewrite([6(7)]),flip(a)].
193 ((x
* (A * y)) * A) / (A * (y * A)) = R(x,A * y,A). [para(50(a,1),18(a,1,2))].
194 A /
(A * (x * A)) = (A * x)'.
[para(50(a,1),33(a,1,2))].
197
R(C,x,C) = C.
[para(66(a,2),6(a,1,1)),rewrite([101(7)])].
203 (C *
(x * (C * y))) / ((C * x) * y) = R(C,C * x,y). [para(66(a,1),18(a,1,1,1)),rewrite([13(5)])].
210 (C *
x)' = (x * C)'.
[para(66(a,1),117(a,1,2)),rewrite([117(6)]),flip(a)].
214 (C *
x)' * (x * C) = 0.
[para(210(a,2),8(a,1,1))].
215 (C *
x) * (x * C)' = 0. [para(210(a,1),9(a,1,2))].
217 (x *
C)' * ((C * x) * y) = y.
[para(210(a,1),10(a,1,1))].
218 (C *
x)' * ((x * C) * y) = y.
[para(210(a,2),10(a,1,1))].
233 (C *
(C * x))' = (C * (x * C))'.
[para(66(a,1),210(a,1,1)),rewrite([16(9,R)]),flip(a)].
235 C *
(x * ((C * x)' * x)) = x.
[para(214(a,1),13(a,2,2)),rewrite([16(7,R),3(9)])].
248 C *
(x * (C * (y * y))) = C * (x * (y * (y * C))). [para(67(a,1),13(a,2,2,2)),rewrite([13(6)])].
256 (x *
(C * (x * y))) / (x * (x * y)) = R(C,x * x,y). [para(67(a,1),18(a,1,1,1)),rewrite([69(4),12(6)])].
264 x *
(C * (x' * x')) = x' * C.
[para(67(a,2),35(a,1,2))].
266 (x *
(C * (x * x))) / (x * C) = x * x.
[para(67(a,2),36(a,1,1,2))].
274 (C *
(x * x)) * y = x * (C * (x * y)).
[para(68(a,2),13(a,1,1))].
284 (x *
C) * (C * (C * x)) = C * ((x * C) * (x * C)). [para(66(a,2),68(a,2,2)),flip(a)].
285 (C *
(x * x))' = (x * (C * x))'.
[para(68(a,1),210(a,1,1)),rewrite([16(7,R)]),flip(a)].
304 (A'
* x) * A = A' * (x * A).
[para(54(a,1),10(a,1,2)),flip(a)].
307
R(x,A',A) = x. [para(13(a,1),54(a,1,2)),rewrite([8(7),3(5),35(5),83(5)]),flip(a)].
308
R(x,y',y) / y = x * y'.
[para(83(a,1),6(a,1,1))].
311 (x *
(x * y')) * y = R(x * x,y',y).
[para(12(a,1),83(a,1,1))].
312 x *
((y * x') * (x * z)) = (x * R(y,x',x)) * z. [para(83(a,1),13(a,1,1,2)),flip(a)].
313 (x *
(y * (x * z'))) * z = R(x * (y * x),z',z). [para(13(a,1),83(a,1,1))].
314 A *
((x * (y * A')) * A) = (A * x) * y.
[para(83(a,1),15(a,1,2)),rewrite([307(6)]),flip(a)].
316 C *
(x * C') = R(x,C',C).
[para(83(a,1),16(a,2))].
318
(R(x,y',y) * z) / (y * z) = R(x * y',y,z). [para(83(a,1),18(a,1,1,1))].
319 ((x
* (y * z')) * z) / R(y,z',z) = R(x,y * z',z). [para(83(a,1),18(a,1,2))].
321 x /
R(y,x',x) = (y * x')'.
[para(83(a,1),33(a,1,2))].
324 (x *
(C / y)) * (C' * y) = R(x,C / y,C' * y).
[para(141(a,1),83(a,1,1,2)),rewrite([141(11)])].
332
R(x,y,y') / y' = x * y.
[para(86(a,1),6(a,1,1))].
334 (x *
y)' * R(x,y,y') = y'.
[para(86(a,1),10(a,1,2))].
335 (x *
(x * y)) * y' = R(x * x,y,y').
[para(12(a,1),86(a,1,1))].
337 x *
(y * (x * (y * x)')) = R(x,y * x,(y * x)'). [para(86(a,1),13(a,1)),flip(a)].
338 (x *
(y * (x * z))) * z' = R(x * (y * x),z,z'). [para(13(a,1),86(a,1,1))].
340 (x *
C) * x' = R(C,x,x').
[para(16(a,1),86(a,1,1))].
341 (C *
x) * C' = R(x,C,C').
[para(16(a,2),86(a,1,1))].
343 ((x
* (y * z)) * z') / R(y,z,z') = R(x,y * z,z'). [para(86(a,1),18(a,1,2))].
352 C *
(x * (C * (C * x)')) = R(C,C * x,(C * x)'). [para(66(a,1),86(a,1,1)),rewrite([13(8)])].
353 (x *
(C * y)) * (y * C)' = R(x,C * y,(C * y)'). [para(210(a,1),86(a,1,2))].
365 R((A
* x)',A * (x * A),y) = (A * y) / (A * (x * (A * y))). [para(187(a,1),18(a,1,1,1)),rewrite([13(7)]),flip(a)].
372 (C *
x) * y = (x * C) * y.
[para(217(a,1),10(a,1,2)),rewrite([31(4)]),flip(a)].
391 ((C
* x) * (y * (x * C))) * z = (x * C) * (y * ((x * C) * z)). [para(372(a,2),13(a,1,1))].
396 R(C
* x,y,z) = R(x * C,y,z).
[para(372(a,1),18(a,1,1,1)),rewrite([18(6)]),flip(a)].
397 ((x
* (C * y)) * z) / ((y * C) * z) = R(x,C * y,z). [para(372(a,1),18(a,1,2))].
398 ((x
* (y * C)) * z) / ((C * y) * z) = R(x,y * C,z). [para(372(a,2),18(a,1,2))].
400 ((x
* C) * ((C * x) * y)) / y = (C * x) * (C * x). [para(372(a,1),36(a,1,1))].
401 (C *
x) * (C * x) = (x * C) * (x * C).
[para(372(a,2),36(a,1,1,2)),rewrite([400(7)])].
411 R((C
* x)',(x * C) * y,z) = R(x * C,y,z)'.
[para(218(a,1),18(a,1,1,1)),rewrite([139(6)]),flip(a)].
412 ((x
* (C * y)') * ((y * C) * z)) / z = R(x,(C * y)',(y * C) * z). [para(218(a,1),18(a,1,2))].
415 (C *
x)' * R(x,C,C') = C'.
[para(86(a,1),218(a,1,2))].
418 C *
(x * (x * ((C * (x * x))' * (x * x)))) = x * x. [para(12(a,1),235(a,1,2))].
419 C *
(x * (y * (x * ((C * (x * (y * x)))' * (x * (y * x)))))) = x * (y * x). [para(13(a,1),235(a,1,2))].
430
R(x,C / y,C' * y) / (C' * y) = x * (C / y). [para(141(a,1),308(a,1,1,2)),rewrite([141(14)])].
433 x *
(C * y)' = x * (y * C)'.
[para(210(a,1),308(a,2,2)),rewrite([308(9)])].
434
R(x,(C * y)',y * C) / (y * C) = x * (y * C)'. [para(210(a,2),308(a,1,1,2))].
435 x /
A = x * A'.
[para(307(a,1),308(a,1,1))].
437 (A *
x) * (A * x) = A * (x * (A * x)).
[back_rewrite(168),rewrite([435(9),48(10),9(6),3(4)]),flip(a)].
439
R(x,A,A') = x.
[para(435(a,1),6(a,1)),rewrite([86(5)])].
440 (x *
A')' = A / x.
[para(435(a,1),112(a,1,1))].
441 C *
(x * (x * C')) = R(x * x,C',C).
[para(12(a,1),316(a,1,2))].
443 C *
(x * (y * (x * C'))) = R(x * (y * x),C',C). [para(13(a,1),316(a,1,2))].
444
(R(x,C',C) * y) / ((x * C') * y) = R(C,x * C',y). [para(316(a,1),18(a,1,1,1))].
452
R(x,C,C') / (x * C') = R(C,x,C').
[para(341(a,1),18(a,1,1))].
453 ((x
* (C * y)) * C') / R(y,C,C') = R(x,C * y,C'). [para(341(a,1),18(a,1,2))].
454 R(C'
* x,C,C') = x * C'.
[para(35(a,1),341(a,1,1)),flip(a)].
455 ((C
* x) * R(x,C,C')) / C' = (C * x) * (C * x). [para(341(a,1),36(a,1,1,2))].
456 R(C
* x,C,C') = C * x. [para(66(a,1),341(a,1,1)),rewrite([13(7),9(5),3(3)]),flip(a)].
458
R(x,C,C') = x.
[para(35(a,1),456(a,1,1)),rewrite([35(9)])].
460 ((C
* x) * x) / C' = (C * x) * (C * x).
[back_rewrite(455),rewrite([458(6)])].
461 C' *
x = x * C'.
[back_rewrite(454),rewrite([458(7)])].
462 (C'
* (x * (C * y))) / y = R(x,C * y,C').
[back_rewrite(453),rewrite([461(6,R),458(10)])].
463 x /
(x * C') = R(C,x,C').
[back_rewrite(452),rewrite([458(4)])].
466 (C *
x)' * x = C'.
[back_rewrite(415),rewrite([458(7)])].
467 R(x
* (y * x),C',C) = x * (y * x).
[back_rewrite(419),rewrite([466(9),443(7)])].
468 R(x
* x,C',C) = x * x.
[back_rewrite(418),rewrite([466(7),441(6)])].
469 C *
(x * (y * (x * C'))) = x * (y * x).
[back_rewrite(443),rewrite([467(13)])].
470 C *
(x * (x * C')) = x * x.
[back_rewrite(441),rewrite([468(11)])].
471 (x *
C') / x = C'.
[para(461(a,1),6(a,1,1))].
474
R(x,C',C) = x.
[para(461(a,1),10(a,1,2)),rewrite([31(3),316(5)])].
475 x' *
(C' * x) = C'.
[para(461(a,2),10(a,1,2))].
477 C' *
(x * x) = x * (x * C'). [para(461(a,2),12(a,1))].
479 (x *
(x * C')) * y = x * (C' * (x * y)).
[para(461(a,1),13(a,1,1,2))].
481 (C'
* (C' * x)) * y = C' * (x * (C' * y)).
[para(461(a,2),13(a,1,1,2))].
482 C' *
(x * (y * x)) = x * (y * (x * C')).
[para(461(a,2),13(a,1))].
483 C' *
(x * (y * x)) = x * (y * (C' * x)).
[para(461(a,2),13(a,2,2,2)),rewrite([461(5,R)])].
484 (A *
x) * (A * C') = A * ((x * C') * A).
[para(461(a,1),15(a,1,2))].
486 ((x
* C') * y) / (x * y) = R(C',x,y).
[para(461(a,1),18(a,1,1,1))].
489 (C'
* (x * y)) / (y * C') = R(x,y,C').
[para(461(a,2),18(a,1,1))].
490 (C'
* (x * y)) / (C' * y) = R(x,y,C').
[para(461(a,2),18(a,1,2)),rewrite([461(4,R)])].
491
R(C,x,C') = C.
[para(461(a,1),33(a,1,2)),rewrite([463(4),31(7)])].
492 C' /
(C' * x) = x'. [para(461(a,2),33(a,1,2))].
493 x *
(C' * x') = C'.
[para(461(a,2),35(a,1,2))].
494 (x *
C')' = C / x.
[para(461(a,1),141(a,1,1))].
498 (x *
C') * x' = R(C',x,x').
[para(461(a,1),86(a,1,1))].
504 (x *
y) / ((x * C') * y) = R(C,x * C',y).
[back_rewrite(444),rewrite([474(4)])].
507 C *
(x * C') = x.
[back_rewrite(316),rewrite([474(9)])].
508 x /
(x * C') = C.
[back_rewrite(463),rewrite([491(8)])].
509 (C *
x)' = C' / x.
[para(466(a,1),6(a,1,1)),flip(a)].
517
R(x,C' / y,y * C) / (y * C) = x * (y * C)'. [back_rewrite(434),rewrite([509(3)])].
518 x *
(y * C)' = x * (C' / y).
[back_rewrite(433),rewrite([509(3)]),flip(a)].
522 ((x
* (C' / y)) * ((y * C) * z)) / z = R(x,C' / y,(y * C) * z).
[back_rewrite(412),rewrite([509(3),509(12)])].
523 R(C'
/ x,(x * C) * y,z) = R(x * C,y,z)'.
[back_rewrite(411),rewrite([509(3)])].
532 (x *
(C * y)) * (C' / y) = R(x,C * y,C' / y).
[back_rewrite(353),rewrite([518(7),509(12)])].
533 C *
(x * (C * (C' / x))) = R(C,C * x,C' / x).
[back_rewrite(352),rewrite([509(5),509(14)])].
539 (x *
(C * x))' = C' / (x * x).
[back_rewrite(285),rewrite([509(4)]),flip(a)].
547 C' /
(C * x) = C' / (x * C).
[back_rewrite(233),rewrite([509(5),509(10)])].
556 (C'
/ x) * ((x * C) * y) = y.
[back_rewrite(218),rewrite([509(3)])].
559 (x *
C)' = C' / x. [back_rewrite(210),rewrite([509(3)]),flip(a)].
561
R(x,C' / y,y * C) / (y * C) = x * (C' / y). [back_rewrite(517),rewrite([559(12)])].
569 (C *
x) * (C' / x) = 0.
[back_rewrite(215),rewrite([559(5)])].
578 (C'
/ x) * ((C * x) * y) = y.
[back_rewrite(217),rewrite([559(3)])].
590 (x *
(x * C'))' = C / (x * x).
[para(12(a,1),494(a,1,1))].
599 x /
C' = C * x.
[para(509(a,1),31(a,1,1)),rewrite([112(4)])].
600 (C *
x) * (C * x) = C * ((C * x) * x).
[back_rewrite(460),rewrite([599(6)]),flip(a)].
604 (x *
C) * (x * C) = C * ((C * x) * x).
[back_rewrite(401),rewrite([600(5)]),flip(a)].
609 (x *
C) * (C * (C * x)) = C * (C * ((C * x) * x)). [back_rewrite(284),rewrite([604(13)])].
617 C *
((x * y) * (C' * y')) = R(x,y,C' * y').
[para(493(a,1),18(a,1,2)),rewrite([599(9)])].
625 R(x
/ y,y,z) = R(y / x,x,z)'.
[para(7(a,1),143(a,1,2)),rewrite([112(2)])].
628 R((A
* x)',A * ((x * y) * A),z) = R(A * x,y * A,z)'. [para(15(a,1),143(a,1,2))].
629
R(C',x * C,y) = R(C,x,y)'.
[para(16(a,1),143(a,1,2))].
634 R(C
/ x,(C' * x) * y,z) = R(C' * x,y,z)'.
[para(141(a,1),143(a,1,1))].
635 R((A
* x)',A * (x * A),y) = R(A * x,A,y)'.
[para(50(a,1),143(a,1,2))].
643 R(C
* x,y,z)' = R(x * C,y,z)'.
[para(372(a,1),143(a,1,2)),rewrite([509(3),523(7)]),flip(a)].
644
R(C,x * C',y) = R(C',x,y)'.
[para(461(a,1),143(a,1,2)),rewrite([31(3)])].
646 R(C
/ x,(x * C') * y,z) = R(x * C',y,z)'.
[para(494(a,1),143(a,1,1))].
649 (x *
y) / ((x * C) * y) = R(C,x,y)'.
[back_rewrite(131),rewrite([629(10)])].
653 (A *
x) / (A * (y * (A * x))) = R(A * y,A,x)'.
[back_rewrite(365),rewrite([635(8)]),flip(a)].
654 (x *
y) / ((x * C') * y) = R(C',x,y)'.
[back_rewrite(504),rewrite([644(11)])].
676 x *
(y * (y * (x * y))') = y'.
[para(42(a,1),10(a,1,2)),rewrite([3(3)]),flip(a)].
709 x *
(x * (y * x))' = y' * x'.
[para(676(a,1),10(a,1,2)),flip(a)].
750
R(x,y / z,z) * y = (x * (y / z)) * z.
[para(7(a,1),79(a,1,2))].
751
R(x,y,z)' * ((x * y) * z) = y * z.
[para(79(a,1),10(a,1,2))].
752
R(x,y',y * z) * z = (x * y') * (y * z).
[para(10(a,1),79(a,1,2))].
753 R(x,y
* y,z) * (y * (y * z)) = (x * (y * y)) * z. [para(12(a,1),79(a,1,2))].
754 (x *
y) * (R(z,x,y) * ((x * y) * u)) = ((x * y) * ((z * x) * y)) * u. [para(79(a,1),13(a,1,1,2)),flip(a)].
757
R(x,C,y) * (y * C) = (x * C) * y.
[para(16(a,1),79(a,1,2))].
758
R(x,y,C) * (C * y) = C * (x * y).
[para(16(a,2),79(a,1,2)),rewrite([16(8,R)])].
759 (((x
* y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u). [para(79(a,1),18(a,1,1,1))].
760 ((x
* R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u). [para(79(a,1),18(a,1,2))].
761
R(x,y,y' * z) * z = (x * y) * (y' * z).
[para(35(a,1),79(a,1,2))].
768
(R(x,y,z) * ((x * y) * z)) / (y * z) = R(x,y,z) * R(x,y,z). [para(79(a,1),36(a,1,1,2))].
769
R(x,A * y,A) * (A * (y * A)) = (x * (A * y)) * A. [para(50(a,1),79(a,1,2))].
779
R(R(x,y,z),y * z,(y * z)') = ((x * y) * z) * (y * z)'. [para(79(a,1),86(a,1,1)),flip(a)].
780
R(x,y * z,z') * R(y,z,z') = (x * (y * z)) * z'. [para(86(a,1),79(a,1,2))].
783
R(x,C * y,z) * ((y * C) * z) = (x * (C * y)) * z. [para(372(a,1),79(a,1,2))].
786
R(x,C',y) * (y * C') = (x * C') * y.
[para(461(a,1),79(a,1,2))].
787 (C'
* x) * y = (x * C') * y.
[para(461(a,1),79(a,2,1)),rewrite([79(5)])].
788
R(x,y,C') * (C' * y) = C' * (x * y).
[para(461(a,2),79(a,1,2)),rewrite([461(11,R)])].
791
R(x,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u). [para(79(a,1),79(a,1,2))].
796 (C'
* (x * x)) * y = x * (C' * (x * y)).
[para(12(a,1),787(a,2,1)),rewrite([479(10)])].
805 R(C'
* x,y,z) = R(x * C',y,z).
[para(787(a,1),18(a,1,1,1)),rewrite([18(7)]),flip(a)].
806 ((x
* (C' * y)) * z) / ((y * C') * z) = R(x,C' * y,z). [para(787(a,1),18(a,1,2))].
807 ((x
* (y * C')) * z) / ((C' * y) * z) = R(x,y * C',z). [para(787(a,2),18(a,1,2))].
822
R(x,C' * y,z) * ((y * C') * z) = (x * (C' * y)) * z. [para(787(a,1),79(a,1,2))].
825 R((x
/ y) / z,z,y) = x / (z * y).
[para(7(a,1),80(a,2,1))].
826 R(x
/ (y / z),y / z,z) = (x * z) / y.
[para(7(a,1),80(a,2,2))].
829 R(x'
/ y,y,x * z) = z / (y * (x * z)).
[para(10(a,1),80(a,2,1))].
830 R(x
/ y',y',y * z) = (x * (y * z)) / z.
[para(10(a,1),80(a,2,2))].
831 R((x
* x) / y,y,z) = (x * (x * z)) / (y * z).
[para(12(a,1),80(a,2,1))].
832 R(x
/ (y * y),y * y,z) = (x * z) / (y * (y * z)). [para(12(a,1),80(a,2,2))].
838 (x *
y) / (y * C) = R(C' * x,C,y).
[para(16(a,1),80(a,2,2)),rewrite([107(2)]),flip(a)].
839 R(x
/ y,y,C) = (C * x) / (y * C).
[para(16(a,2),80(a,2,1))].
842 R(x
/ y,y,y' * z) = (x * (y' * z)) / z.
[para(35(a,1),80(a,2,2))].
843 R(C'
/ x,x,y * C) = y / (x * (y * C)).
[para(64(a,1),80(a,2,1))].
844 R(C
* x,C',y * C) = (x * (y * C)) / y.
[para(64(a,1),80(a,2,2)),rewrite([599(3)])].
846 R(x
/ y',y',C * y) = C' * (x * (C * y)).
[para(65(a,1),80(a,2,2)),rewrite([107(11)])].
847 (x *
y) / (C * y) = R(C' * x,C,y).
[para(107(a,1),80(a,1,1)),flip(a)].
848 R(x
/ y,y,z)' = (y * z) / (x * z).
[para(80(a,2),112(a,1,1))].
850 R(x
/ y,y,C * y') = C' * (x * (C * y')).
[para(123(a,1),80(a,2,2)),rewrite([107(11)])].
853 R((A
* x) / y,y,A) = (A * (x * A)) / (y * A).
[para(50(a,1),80(a,2,1))].
854 R(x
/ (A * y),A * y,A) = (x * A) / (A * (y * A)). [para(50(a,1),80(a,2,2))].
856 (x *
(C * y)) / (C * (y * C)) = R(C' * x,C,C * y). [para(66(a,1),80(a,2,2)),rewrite([107(2)]),flip(a)].
860 (x *
(y * y)) / (y * (y * C)) = R(C' * x,C,y * y). [para(67(a,1),80(a,2,2)),rewrite([107(2)]),flip(a)].
871 x /
A' = x * A.
[para(80(a,1),307(a,1)),rewrite([8(6),24(4)]),flip(a)].
872 R((x
* y') / z,z,y) = R(x,y',y) / (z * y).
[para(83(a,1),80(a,2,1))].
878 R((C
* x) / y,y,z) = ((x * C) * z) / (y * z).
[para(372(a,1),80(a,2,1))].
880 R((x
* C) / y,y,z) = ((C * x) * z) / (y * z).
[para(372(a,2),80(a,2,1))].
882 (x *
y) / (A * y) = R(x * A',A,y).
[para(435(a,1),80(a,1,1)),flip(a)].
884 (x *
y) / (y * C') = R(C * x,C',y).
[para(461(a,1),80(a,2,2)),rewrite([599(3)]),flip(a)].
889 R(R(x,y,z)
/ u,u,y * z) = ((x * y) * z) / (u * (y * z)). [para(79(a,1),80(a,2,1))].
891
R((C' * x) / y,y,z) = ((x * C') * z) / (y * z). [para(787(a,1),80(a,2,1))].
896 (x *
A)' = A' / x.
[para(871(a,1),112(a,1,1))].
897 (x *
y) / (A' * y) = R(x * A,A',y).
[para(871(a,1),80(a,1,1)),flip(a)].
903 (A'
/ x) * ((x * A) * y) = y.
[para(896(a,1),10(a,1,1))].
906 (x *
A) * ((A' / x) * y) = y.
[para(896(a,1),35(a,1,2,1))].
912 (x *
(A' / y)) * (y * A) = R(x,A' / y,y * A).
[para(896(a,1),83(a,1,1,2)),rewrite([896(10)])].
921 (C *
(x * (C' * y))) / y = R(x,C' * y,C).
[para(7(a,1),101(a,1,2)),rewrite([107(3),107(9)])].
922 (C *
x) / (C * (y * x)) = R(y,x,C)'.
[para(10(a,1),101(a,1,1,2)),rewrite([16(5,R),143(10)])].
923 (C *
(x * (x * y))) / (y * C) = R(x * x,y,C).
[para(12(a,1),101(a,1,1,2))].
924 (C *
(x * (y * y))) / (y * (y * C)) = R(x,y * y,C). [para(12(a,1),101(a,1,2))].
925 (C *
(x * (y * (x * z)))) / (z * C) = R(x * (y * x),z,C). [para(13(a,1),101(a,1,1,2))].
927 (C *
(A * ((x * y) * A))) / (C * (y * A)) = R(A * x,y * A,C).
[para(15(a,1),101(a,1,1,2)),rewrite([16(11,R)])].
928 (C *
(C * x)) / (C * C) = R(x,C,C).
[para(16(a,2),101(a,1,1,2))].
943 (C *
R(x,y,y')) / (y' * C) = R(x * y,y',C).
[para(86(a,1),101(a,1,1,2))].
948 (C *
((x * y) * z)) / (C * (y * z)) = R(R(x,y,z),y * z,C). [para(79(a,1),101(a,1,1,2)),rewrite([16(7,R)])].
956 (C *
(A' * x)) * A = (C * A') * (x * A).
[para(264(a,1),15(a,1,1)),rewrite([16(4,R),274(16),304(18),35(19)]),flip(a)].
975 (x /
y) * x' = x * (x * y)'.
[para(7(a,1),709(a,1,2,1,2)),rewrite([112(5)]),flip(a)].
976 (x *
(y * x))' = x' * (y' * x').
[para(709(a,1),10(a,1,2)),flip(a)].
1008 x *
(C / (x * x)) = C * x'.
[para(461(a,1),709(a,1,2,1,2)),rewrite([590(5),31(7)])].
1010 C *
(C' / (x * C)) = x' * C'.
[para(509(a,1),709(a,1,2))].
1023 C'
/ (x * x) = x' * (C' * x').
[back_rewrite(539),rewrite([976(4)]),flip(a)].
1026 x /
(y * (z * (y * x))) = y' * (z' * y').
[back_rewrite(114),rewrite([976(7)])].
1043 C *
(x * (R(y,C,x) * x)) = x * ((y * C) * x).
[para(757(a,1),13(a,2,2)),rewrite([16(6,R)])].
1046 ((x
* R(y,C,z)) * (z * C)) / ((y * C) * z) = R(x,R(y,C,z),z * C). [para(757(a,1),18(a,1,2))].
1049
R(x,C,y * C') * y = (x * C) * (y * C').
[para(83(a,1),757(a,1,2)),rewrite([474(9)])].
1054 R(x
/ R(y,C,z),R(y,C,z),z * C) = (x * (z * C)) / ((y * C) * z). [para(757(a,1),80(a,2,2))].
1055 (C
* ((x * C) * y)) / (C * (y * C)) = R(R(x,C,y),y * C,C).
[para(757(a,1),101(a,1,1,2)),rewrite([16(9,R)])].
1057 C'
* (C / x) = C * (C' / x).
[para(7(a,1),1010(a,1,2,2)),rewrite([107(7),141(9),461(10,R)]),flip(a)].
1058 C'
/ (x * C) = C' * (x' * C').
[para(1010(a,1),10(a,1,2)),flip(a)].
1068 C'
/ (C * x) = C' * (x' * C').
[back_rewrite(547),rewrite([1058(10)])].
1075 C *
(C * (C' / x)) = C / x.
[para(1057(a,1),10(a,1,2)),rewrite([31(3)])].
1080 C'
/ (C' / x) = C / (C / x).
[para(1057(a,1),141(a,1,1)),rewrite([509(6)])].
1088 (x
/ y) * ((z / (x / y)) * x) = ((x / y) * z) * y. [para(7(a,1),41(a,1,2,2))].
1089 (x'
* y) * x = x' * (y / x').
[para(8(a,1),41(a,1,2,2)),rewrite([3(5)]),flip(a)].
1090 (x
* y) * x' = x * (y / x).
[para(9(a,1),41(a,1,2,2)),rewrite([3(3)]),flip(a)].
1091 (x
/ y) * (y * z) = y' * ((y * x) * z).
[para(41(a,1),10(a,1,2)),flip(a)].
1092 (x'
* y) * (x * z) = x' * ((y / x') * z).
[para(10(a,1),41(a,1,2,2)),flip(a)].
1096 x'
* ((((x * y) * (y / x)) / x') * z) = (y / x) * ((x * y) * z).
[para(41(a,1),13(a,2,2)),rewrite([1091(4),1092(7)])].
1102 (x
* y) * (x' * z) = x * ((y / x) * z).
[para(35(a,1),41(a,1,2,2)),flip(a)].
1103 (C'
* x) * (y * C) = C' * ((C * x) * y).
[para(64(a,1),41(a,1,2,2)),rewrite([599(5)]),flip(a)].
1105 (x
* y) * (C * x') = x * (C * (y / x)).
[para(123(a,1),41(a,1,2,2)),rewrite([16(3,R)]),flip(a)].
1106 (C
* x) * (C / x) = C * C.
[para(123(a,1),41(a,1,2)),rewrite([107(7),141(9)]),flip(a)].
1114 (x
* y') * ((z / (x * y')) * R(x,y',y)) = ((x * y') * z) * y. [para(83(a,1),41(a,1,2,2))].
1121 (x
* y) * (C' * x') = x * (C' * (y / x)).
[para(493(a,1),41(a,1,2,2)),rewrite([461(4,R)]),flip(a)].
1123
R(x,y,z) * ((u / R(x,y,z)) * ((x * y) * z)) = (R(x,y,z) * u) * (y * z). [para(79(a,1),41(a,1,2,2))].
1133 x *
(C' / x) = R(C',x,x').
[back_rewrite(498),rewrite([1090(5)])].
1134 x *
(C / x) = R(C,x,x').
[back_rewrite(340),rewrite([1090(4)])].
1148 (x
* C) * (C / x) = C * C.
[para(16(a,1),1106(a,1,1))].
1156 x *
(C * (C * x')) = C * C.
[para(67(a,1),1106(a,1,1)),rewrite([69(7),1008(5)])].
1166 (x
/ y) * (y / (x / y)) = x * (y / x).
[para(7(a,1),1090(a,1,1)),rewrite([112(2)]),flip(a)].
1172 ((x
* (y / x)) * z) / (x' * z) = R(x * y,x',z). [para(1090(a,1),18(a,1,1,1))].
1173 (x
* (y / x)) / (y * x') = R(x,y,x').
[para(1090(a,1),18(a,1,1))].
1174 ((x
* (y * z)) * y') / (y * (z / y)) = R(x,y * z,y'). [para(1090(a,1),18(a,1,2))].
1175 x'
/ (x * (y / x)) = (x * y)'.
[para(1090(a,1),33(a,1,2))].
1179
R(C,C * x,C' / x) = R(C,x,x').
[para(117(a,1),1090(a,2,2)),rewrite([16(4,R),509(7),532(8),86(11)])].
1184 (x
* (y / x)) * x = R(x * y,x',x).
[para(1090(a,1),83(a,1,1))].
1188 ((x
* C) * y) * (C' / x) = (C * x) * (y / (C * x)). [para(372(a,1),1090(a,1,1)),rewrite([509(6)])].
1196
R(x,y * z,y') * (y * (z / y)) = (x * (y * z)) * y'. [para(1090(a,1),79(a,1,2))].
1201 (x
* y) * R(z / x,x,y) = (x * y) * ((z * y) / (x * y)). [para(80(a,2),1090(a,2,2)),rewrite([1090(6)]),flip(a)].
1203 (C
* (x * (y / x))) / (x' * C) = R(x * y,x',C). [para(1090(a,1),101(a,1,1,2))].
1208 C *
(x * (C * (C' / x))) = R(C,x,x').
[back_rewrite(533),rewrite([1179(15)])].
1214 A *
((C * A') * ((C * x) * A)) = C * (C * (x * A)).
[para(1156(a,1),15(a,1,1)),rewrite([12(6),71(14),956(16)]),flip(a)].
1216 x *
(C * (x' * C)) = C * C.
[para(16(a,1),1156(a,1,2,2))].
1217
R(x,C * (C * x'),y) = R(x',C * y,C)'.
[para(1156(a,1),18(a,1,1,1)),rewrite([12(4),71(10),922(11)]),flip(a)].
1220 x'
* (C * (C * x)) = C * C.
[para(31(a,1),1156(a,1,2,2,2))].
1222 C *
(C * x) = x * (C * C).
[para(1156(a,1),35(a,1,2)),rewrite([31(8)]),flip(a)].
1223 (x
/ y) * (C * (C * (y / x))) = C * C.
[para(112(a,1),1156(a,1,2,2,2))].
1226 C *
(A * C) = A * (C * C).
[para(1156(a,1),50(a,1,1)),rewrite([12(5),16(4),311(14),307(13)])].
1235 (C
* (C * C)) / (C * (C * (C * x'))) = R(x',C * C,C)'. [para(1156(a,1),101(a,1,1,2)),rewrite([16(12,R),1217(20)])].
1242 (x
* (C * C)) / (C * x) = C.
[para(1222(a,1),6(a,1,1))].
1243
R(x,C,C) = x.
[para(1222(a,2),6(a,1,1)),rewrite([928(8)])].
1245 C'
* (x * (C * C)) = C * x.
[para(1222(a,1),10(a,1,2))].
1251 C *
(C * (x * (y * x))) = x * (y * (x * (C * C))). [para(1222(a,2),13(a,1))].
1254 (A
* x) * (A * (C * C)) = A * (C * (x * (A * C))). [para(1222(a,2),15(a,2,2,1)),rewrite([12(7),16(6),1226(7),71(15),16(13)])].
1255 C *
(x * C) = x * (C * C).
[para(16(a,1),1222(a,1,2))].
1258
R(x,C * C,y) = R(x,C * y,C).
[para(1222(a,2),18(a,1,1,1)),rewrite([71(5),12(9),102(10)]),flip(a)].
1259 (C
* (C * (x * y))) / (y * (C * C)) = R(x,y,C * C). [para(1222(a,2),18(a,1,1))].
1260 (C
* (C * (x * y))) / (C * (C * y)) = R(x,y,C * C). [para(1222(a,2),18(a,1,2)),rewrite([1222(5,R)])].
1265 (x
* (C * C)) / x = C * C.
[para(1222(a,1),36(a,1,1))].
1268 C *
(C * (x * (C' * C'))) = R(x,C' * C',C * C). [para(1222(a,2),83(a,1)),rewrite([175(6),175(14)])].
1272 (x
* (C * C)) * y = C * (x * (C * y)).
[para(1222(a,1),372(a,1,1)),rewrite([16(9,R),71(10)])].
1273 (x
* (C * C))' = C' * (x' * C').
[para(1222(a,1),509(a,1,1)),rewrite([1068(10)])].
1280 R(x
/ y,y,C * C) = (C * (C * x)) / (y * (C * C)). [para(1222(a,2),80(a,2,1))].
1281 R(x
/ y,y,C * C) = (x * (C * C)) / (C * (C * y)). [para(1222(a,2),80(a,2,2))].
1283 (x
* (C * C)) / (x * C) = C.
[para(1222(a,1),101(a,1,1)),rewrite([197(10)])].
1284 (C
* (C * (C * x))) / (C * (C * C)) = R(x,C * C,C). [para(1222(a,2),101(a,1,1,2)),rewrite([16(11,R)])].
1285 x *
((C * C) / x) = C * C.
[para(1222(a,1),1106(a,1,1)),rewrite([117(8),1090(6)])].
1294
R(x,C * (x' * C),y) = R(x',C * y,C)'.
[para(1216(a,1),18(a,1,1,1)),rewrite([12(4),13(10),922(11)]),flip(a)].
1301 (C
* (C * C)) / (C * (C * (x' * C))) = R(x',C * C,C)'. [para(1216(a,1),101(a,1,1,2)),rewrite([16(12,R),1294(20)])].
1304 x'
/ (x * y) = x' * (y' * x').
[para(6(a,1),1175(a,1,2,2)),rewrite([976(6)])].
1308 x /
(x' * (y / x')) = (x' * y)'.
[para(31(a,1),1175(a,1,1))].
1329 x'
/ (C * C) = C' * (x' * C').
[para(1222(a,2),1175(a,2,1)),rewrite([1285(6),509(10),1304(10)])].
1345
R((x' * y) / z,z,x) = (x' * (y / x')) / (z * x). [para(1089(a,1),80(a,2,1))].
1354 R(C
* C,x',x) = C * C.
[para(1222(a,2),1089(a,1,1)),rewrite([311(6),1285(12)])].
1375 (x
* (C * (x * C))) * y = C * (x * (x * (C * y))). [para(69(a,1),372(a,2,1)),rewrite([46(6)]),flip(a)].
1378 (x
* C) * (C * ((x * C) * y)) = C * (((C * x) * x) * (C * y)). [para(372(a,2),69(a,1,1,2)),rewrite([16(6,R),609(7),71(8)]),flip(a)].
1406 A *
((C * A') * (x * A)) = x * (A * C).
[para(35(a,1),74(a,1,1)),rewrite([16(10,R),956(12)]),flip(a)].
1410 C *
(A * (A * (C * C))) = A * (C * (A * (C * C))). [para(74(a,1),67(a,1,2)),rewrite([12(7),16(6),1255(7),16(17,R),1255(17),1254(18),125
5(16)])].
1419 C *
(A * (C * C)) = A * (C * (C * C)).
[para(1156(a,1),74(a,1,1)),rewrite([12(7),1255(6),16(16,R),313(18),307(17)])].
1421 (C
* x) * (A * C) = C * (C * (x * A)).
[back_rewrite(1214),rewrite([1406(11)])].
1422 C *
(A * (A * (C * C))) = A * (A * (C * (C * C))). [back_rewrite(1410),rewrite([1419(17)])].
1424 x /
((y * (x / z)) * z) = R(y,x / z,z)'.
[para(7(a,1),139(a,1,1))].
1425 x /
((y * z') * (z * x)) = R(y,z',z * x)'.
[para(10(a,1),139(a,1,1))].
1430 ((x
* y) * z) / (y * (x * (y * z))) = R(y,x * y,z)'. [para(13(a,1),139(a,1,2))].
1435
R(x,y,(x * y)' * z)' = (y * ((x * y)' * z)) / z. [para(35(a,1),139(a,1,2)),flip(a)].
1436 x /
((y * C') * (x * C)) = R(y,C',x * C)'.
[para(64(a,1),139(a,1,1))].
1440 (A
* (x * A)) / ((y * (A * x)) * A) = R(y,A * x,A)'. [para(50(a,1),139(a,1,1))].
1442 ((C
* x) * y) / (C * (x * (C * y))) = R(C,C * x,y)'. [para(66(a,1),139(a,1,2,1)),rewrite([13(8)])].
1457 ((x
* C) * y) / ((z * (C * x)) * y) = R(z,C * x,y)'. [para(372(a,1),139(a,1,1))].
1459 (x
* C') / ((y * C') * x) = R(y,C',x)'.
[para(461(a,1),139(a,1,1))].
1460 (C'
* x) / (C' * (y * x)) = R(y,x,C')'.
[para(461(a,2),139(a,1,1)),rewrite([461(7,R)])].
1472 ((x
* C) * y) / (((z * C) * x) * y) = R(R(z,C,x),x * C,y)'. [para(757(a,1),139(a,1,2,1))].
1483 (C
* (C * x)) / (C * (C * (y * x))) = R(y,x,C * C)'. [para(1222(a,2),139(a,1,1)),rewrite([1222(9,R)])].
1485 (x
* (C * C)) / (C * (C * (y * x))) = R(y,x,C * C)'. [para(1222(a,2),139(a,1,2))].
1487 (x'
* (y / x')) / ((z * (x' * y)) * x) = R(z,x' * y,x)'. [para(1089(a,1),139(a,1,1))].
1496
R(x',C * C,C)' = R(x',C,C * C)'.
[back_rewrite(1301),rewrite([1485(13)]),flip(a)].
1501 (C
* (C * C)) / (C * (C * (C * x'))) = R(x',C,C * C)'. [back_rewrite(1235),rewrite([1496(20)])].
1533 (A
* (A * (C * (C * C)))) * x = C * (A * (C * (A * (C * x)))).
[para(74(a,1),274(a,1,1,2)),rewrite([12(7),16(6),1255(7),1422(9),1378(20
),16(14),50(16),16(15),69(19)])].
1541
R(x,y * x,z)' * (x * (y * (x * z))) = (y * x) * z. [para(13(a,1),751(a,1,2))].
1544
R(x,y,C)' * (C * (x * y)) = y * C.
[para(16(a,2),751(a,1,2))].
1566
R(R(x,y,z)' / u,u,(x * y) * z) = (y * z) / (u * ((x * y) * z)). [para(751(a,1),80(a,2,1))].
1580
R(x' * y,x,z)' * ((x' * (y / x')) * z) = x * z. [para(1089(a,1),751(a,1,2,1))].
1584
R(A,x,A * C)' * (A * ((x * C) * A)) = x * (A * C). [para(74(a,1),751(a,1,2))].
1587
R(C' * (x / y),C,y) = x / (y * C).
[para(7(a,1),838(a,1,1)),flip(a)].
1591
R(C' * x',C,x * y) = y / (C * (x * y)).
[para(10(a,1),838(a,1,1)),rewrite([16(3,R)]),flip(a)].
1593 (x
* (y * (x * z))) / (z * C) = R(C' * (x * (y * x)),C,z). [para(13(a,1),838(a,1,1))].
1600 (x
* C) / (y * x) = R(C' * y,C,x)'.
[para(838(a,1),112(a,1,1)),flip(a)].
1612 ((x
* y) * z) / (C * (y * z)) = R(C' * R(x,y,z),C,y * z). [para(79(a,1),838(a,1,1)),rewrite([16(5,R)])].
1618
R(x,C,C / x) = (C * C) / (C * (C / x)).
[para(1106(a,1),838(a,1,1)),rewrite([16(7,R),10(13)]),flip(a)].
1622 (C
* (C * x)) / (C * (C * C)) = R(C' * x,C,C * C). [para(1222(a,2),838(a,1,1)),rewrite([16(9,R)])].
1629 R(x
* x,C,x) = x * x.
[back_rewrite(266),rewrite([1593(7),170(6)])].
1633
R(x,C * C,C) = R(x,C,C * C).
[back_rewrite(1284),rewrite([1622(12),10(5)]),flip(a)].
1634
R((x / y) * A',A,y) = x / (A * y).
[para(7(a,1),882(a,1,1)),flip(a)].
1639 (x
* (y * (x * z))) / (A * z) = R(x * (y * (x * A')),A,z).
[para(13(a,1),882(a,1,1)),rewrite([13(11)])].
1641 R(A
* C',C,x)' = R(C * A',A,x).
[para(16(a,1),882(a,1,1)),rewrite([1600(5),461(4)])].
1642 (C
* x) / (A * C) = R(x * A',A,C).
[para(16(a,2),882(a,1,1))].
1647 (A
* x) / (y * x) = R(y * A',A,x)'.
[para(882(a,1),112(a,1,1)),flip(a)].
1660
R((x * y) * A',A,y') = R(x,y,y') / (A * y'). [para(86(a,1),882(a,1,1)),flip(a)].
1663 (x
* C') / (A * x) = R(A' * C',A,x).
[para(461(a,1),882(a,1,1)),rewrite([461(11)])].
1664 (C'
* x) / (A * C') = R(x * A',A,C').
[para(461(a,2),882(a,1,1))].
1666 R(x
* A',A,A' * C') = C * (x * (A' * C')).
[para(493(a,1),882(a,1,2)),rewrite([461(5),599(9),461(17)]),flip(a)].
1667 ((x
* y) * z) / (A * (y * z)) = R(R(x,y,z) * A',A,y * z). [para(79(a,1),882(a,1,1))].
1672 ((x
* C) * y) / (A * (y * C)) = R(R(x,C,y) * A',A,y * C). [para(757(a,1),882(a,1,1))].
1676 R(x
* A',A,C * (C * x')) = (C * C) / (A * (C * (C * x'))). [para(1156(a,1),882(a,1,1)),flip(a)].
1679 (C
* (C * x)) / (A * (C * C)) = R(x * A',A,C * C). [para(1222(a,2),882(a,1,1))].
1702 x *
((x * y)' * x) = x / y.
[para(10(a,1),1304(a,1,2)),rewrite([31(2),31(3),31(5)]),flip(a)].
1707 x /
(x' * y) = x * (y' * x).
[para(31(a,1),1304(a,1,1)),rewrite([31(5),31(6)])].
1708 (x
* y) / x' = x * (y * x).
[para(1304(a,1),112(a,1,1)),rewrite([976(6),31(2),31(2),31(2)]),flip(a)].
1715 (x
* y)' * (y * (x * y)') = (x * y)' / R(x,y,y'). [para(86(a,1),1304(a,1,2)),rewrite([31(9)]),flip(a)].
1731
R(x,y,z) * (((x * y) * z)' * R(x,y,z)) = R(x,y,z) / (y * z).
[para(751(a,1),1304(a,1,2)),rewrite([31(3),31(6),31(10)]),flip(a)].
1735 x *
((x' / y) * x) = (x' * y)'.
[back_rewrite(1308),rewrite([1707(5),112(3)])].
1750 (x'
* y) / x = x' * (y * x').
[para(31(a,1),1708(a,1,2))].
1786 R(x
* (y * x),x',z) = ((x * y) * z) / (x' * z). [para(1708(a,1),80(a,1,1))].
1793 (C
* C) / x' = x * (C * C).
[para(1156(a,1),1708(a,1,1)),rewrite([311(11),1354(10)])].
1800
R(x,y,z)' * (((x * y) * z) * R(x,y,z)') = (y * z) / R(x,y,z). [para(751(a,1),1708(a,1,1)),rewrite([31(4)]),flip(a)].
1817 (C
* C) / x = x' * (C * C).
[para(31(a,1),1793(a,1,2))].
1821 R(x
* A',A,C * (C * x')) = C * (C * (A * (C * (C * x')))').
[back_rewrite(1676),rewrite([1817(21),1222(22,R)])].
1823
R(x,C,C / x) = C / (C / x).
[back_rewrite(1618),rewrite([1817(12),509(9),1222(13,R),1075(13)])].
1841 (A'
* x) * A' = A' * (x * A').
[para(1750(a,1),435(a,1)),flip(a)].
1848
R((x * y)' / x,x,y) = (x * y)' / R(x,y,y'). [para(1750(a,1),80(a,2)),rewrite([1715(10)])].
1863 x /
(C * C) = C' * (x * C').
[para(31(a,1),1329(a,1,1)),rewrite([31(8)])].
1878 (A
* C) / (C * x) = R(x * A',A,C)'.
[para(1642(a,1),112(a,1,1)),flip(a)].
1884 (x
* (C * C)) / (A * C) = R((C * x) * A',A,C). [para(1222(a,1),1642(a,1,1))].
1887 (A'
* (A' * (x * A'))) * y = A' * ((A' * x) * (A' * y)). [para(1841(a,1),13(a,1,1,2))].
1898 (C
* (A' * (x * A'))) / (C * A') = R(A' * x,A',C). [para(1841(a,1),101(a,1,1,2)),rewrite([16(12,R)])].
1903 (A'
* (x * A')) / (C * A') = R(C' * (A' * x),C,A'). [para(1841(a,1),838(a,1,1)),rewrite([16(10,R)])].
1908
((A' * x) * y) * A = A' * (x * (y * A)).
[para(121(a,1),10(a,1,2)),flip(a)].
1913 (x
* (A' * y)) * A = (x * A') * (y * A).
[para(13(a,1),121(a,1,2,1)),rewrite([1089(10),871(10),35(11)])].
1918 ((x
* A) * y) * A = x * (A * (y * A)).
[para(50(a,1),121(a,2,2)),rewrite([1092(7),871(6),1089(9),871(9),35(10)])].
1921 A *
((A' * C') * (x * A)) = x * (A * C').
[para(461(a,1),121(a,2,2)),rewrite([461(7,R),1913(9),461(6)])].
1926 (x
* A) * A = x * (A * A).
[para(1090(a,1),121(a,1,2,1)),rewrite([871(6),1089(8),871(8),35(9),31(7)])].
1927 C *
(A * (C * (x * A))) = A * (C * (x * (A * C))).
[para(1156(a,1),121(a,1,2,1,1)),rewrite([12(5),71(7),16(5),31(13),16(12),1255(13),12
72(16)]),flip(a)].
1929 A *
(C * (A' * (C * (x * A)))) = x * (A * (C * C)).
[para(1222(a,2),121(a,1,2,1)),rewrite([71(10),16(8),1092(9),871(7),16(8,R),12(16),1
6(15),1255(16)])].
1935 (x
* (A * A)) * A' = x * A.
[para(1926(a,1),6(a,1,1)),rewrite([435(6)])].
1938 (A
* (x * (A * A))) * y = A * ((x * A) * (A * y)). [para(1926(a,1),13(a,1,1,2))].
1942
R(x,A,A) = x.
[para(1926(a,1),18(a,1,1)),rewrite([6(8)]),flip(a)].
1946
R(x,A' * A',A * A) = x.
[para(83(a,1),1926(a,2)),rewrite([175(4),1913(8),8(7),3(5),83(5),307(4),175(4)]),flip(a)].
1951 (x
* (A * A))' = A' / (x * A).
[para(1926(a,1),896(a,1,1))].
1963 (x
* (A * (y * A))) * A' = (x * A) * y.
[para(1918(a,1),6(a,1,1)),rewrite([435(7)])].
1965
R(A',x',x) * A = 0.
[para(8(a,1),1918(a,2)),rewrite([976(5),13(9),8(7),3(5),83(5)])].
1966 x *
(A' * x)' = A. [para(9(a,1),1918(a,1,1)),rewrite([2(3),896(5),1735(8)]),flip(a)].
1973 (A
* x) * (y * (A * (z * A))) = A * ((x * ((y * A) * z)) * A). [para(1918(a,1),15(a,1,2))].
1974 ((A
* C) * x) * A = C * (A * (x * A)).
[para(16(a,1),1918(a,1,1,1))].
1996 (x
* (A / x)) * A = x * (A * (x' * A)).
[para(1090(a,1),1918(a,1,1))].
2004 (x
* (A * (y * A))) / (A * C) = R(C' * ((x * A) * y),C,A). [para(1918(a,1),838(a,1,1))].
2008 (x
* (A * (y * A))) * A = ((x * A) * y) * (A * A). [para(1918(a,1),1926(a,1,1))].
2027 (A'
* x)' = x' * A.
[para(1966(a,1),10(a,1,2)),flip(a)].
2028
R(A,x,x') = A.
[para(10(a,1),1966(a,1,2,1)),rewrite([86(4)])].
2050
R(A,x',x) = A.
[para(31(a,1),2028(a,1,3))].
2061 A /
x = A * x'.
[para(2050(a,1),308(a,1,1))].
2068 (x
* (A * x')) * A = x * (A * (x' * A)).
[back_rewrite(1996),rewrite([2061(2)])].
2075 (x
* A')' = A * x'.
[back_rewrite(440),rewrite([2061(6)])].
2076 (A
* x)' = x' * A'.
[back_rewrite(194),rewrite([2061(6),976(6),35(9)]),flip(a)].
2089 R(x
* A',A,C * (C * x')) = C * (x * (A' * C')).
[back_rewrite(1821),rewrite([2076(20),509(18),1304(18),31(16),13(21),461(19),35(22)])].
2104
R(x' * A',A * ((x * y) * A),z) = R(A * x,y * A,z)'. [back_rewrite(628),rewrite([2076(3)])].
2111 A *
(A' / x) = x'.
[para(2061(a,1),33(a,1)),rewrite([896(4)])].
2118 C *
(A * (x * (A * A))) = A * ((C * x) * (A * A)).
[para(15(a,1),1974(a,1,1)),rewrite([13(8),1926(14)]),flip(a)].
2138 ((C
* A') * x) * A = A' * (C * (x * A)).
[para(147(a,1),10(a,1,2)),flip(a)].
2140 A *
(((C * A') * x) * (A * y)) = (C * (x * A)) * y. [para(147(a,1),13(a,1,1)),flip(a)].
2144 A *
((C * ((A' * C') * x)) * A) = C * ((x * C') * A).
[para(787(a,1),147(a,2,2)),rewrite([1102(9),107(6),461(7)])].
2152 (A
* x) * (x' * A') = 0.
[para(9(a,1),314(a,2)),rewrite([2076(4),314(12)])].
2153 (x *
(y * A')) * A = A' * ((A * x) * y).
[para(314(a,1),10(a,1,2)),flip(a)].
2161 (A
* x) * ((x' * A') * y) = y.
[para(35(a,1),314(a,2)),rewrite([2076(4),2153(12),35(13)])].
2162 (A
* x) * (C * (x' * A')) = C.
[para(123(a,1),314(a,2)),rewrite([2076(5),2153(13),35(14)])].
2168 (A
* R(x,y,A')) * y = A * (x * y).
[para(79(a,1),314(a,1,2,1)),rewrite([83(7),307(6)]),flip(a)].
2183 (A
* R(x,y,A')') * (x * y) = A * y.
[para(751(a,1),314(a,1,2,1)),rewrite([83(6),307(5)]),flip(a)].
2197 C'
* ((C * x) * y) = C' * ((x * C) * y).
[para(16(a,1),1091(a,2,2,1)),rewrite([107(2),1092(6),599(5)])].
2198 (x
/ y) * (C * y) = y' * (C * (y * x)).
[para(16(a,2),1091(a,1,2)),rewrite([16(8,R)])].
2206 x *
((x' * C) * y) = x * ((C * x') * y).
[para(111(a,1),1091(a,2,2,1)),rewrite([1091(6),31(2),31(7)])].
2223 (x
* A') * (A * y) = A' * ((A * x) * y).
[para(435(a,1),1091(a,1,1))].
2224 (C
* x) * (y * C') = C * ((C' * x) * y).
[para(461(a,1),1091(a,1,2)),rewrite([599(3),31(9)])].
2226 (x
/ y) * (C' * y) = y' * (C' * (y * x)).
[para(461(a,2),1091(a,1,2)),rewrite([461(10,R)])].
2237 (x
* A) * (A' * y) = A * ((A' * x) * y).
[para(871(a,1),1091(a,1,1)),rewrite([31(9)])].
2238 (C
* (x' * ((x * y) * z))) / (C * (x * z)) = R(y / x,x * z,C).
[para(1091(a,1),101(a,1,1,2)),rewrite([16(9,R)])].
2241 (C
* x) * (C * (C' / y)) = C * ((C' * x) * (C / y)). [para(1057(a,1),1091(a,1,2)),rewrite([599(3),31(11)])].
2247 (C'
* x) * (y * (C * C)) = C' * ((C * x) * (C * y)). [para(1222(a,1),1091(a,1,2)),rewrite([107(2)])].
2249 x'
* (C * (x * (C * y))) = C * (x' * (C * (x * y))).
[para(1222(a,2),1091(a,2,2,1)),rewrite([1817(4),1272(7),71(13)]),flip(a)].
2273 (A
* x') * (x * y) = x' * ((x * A) * y).
[para(2061(a,1),1091(a,1,1))].
2290 (x
* C) * (C' * y) = C * ((C' * x) * y).
[para(16(a,1),1102(a,1,1)),rewrite([107(9)])].
2291 (C
* x) * (x' * y) = x * ((C / x) * y).
[para(16(a,2),1102(a,1,1))].
2293 (x
* ((y / x) * z)) / (y * (x' * z)) = R(x,y,x' * z). [para(1102(a,1),18(a,1,1))].
2312 (x
* C') * (C * y) = C' * ((C * x) * y).
[para(461(a,1),1102(a,1,1)),rewrite([31(6),599(11)])].
2341
R(x,y,x' * z)' * (x * ((y / x) * z)) = y * (x' * z). [para(1102(a,1),751(a,1,2))].
2368 A'
* (C * (A * x)) = A * ((C * A') * x).
[para(7(a,1),1406(a,1,2,2)),rewrite([435(9),2223(14),16(13,R)]),flip(a)].
2369 (C
* A') * (x * A) = A' * (x * (A * C)).
[para(1406(a,1),10(a,1,2)),flip(a)].
2373 A *
((C * A') * (x * (y * (x * A)))) = x * (y * (x * (A * C))).
[para(13(a,1),1406(a,1,2,2)),rewrite([13(17)])].
2375 A *
((C * A') * (A' * (C' * (A * x)))) = R(x,A' * C',A * C). [para(83(a,1),1406(a,2)),rewrite([559(9),435(9),461(10),1913(13),461(12),2
223(13),461(12,R),559(19),435(19),461(20)])].
2377 (x
* C) * (A * C) = C * (C * (x * A)).
[para(372(a,1),1406(a,1,2,2)),rewrite([2369(10),35(11),1421(12)])].
2384 C *
(C * (x * (x * A))) = x * (C * (x * (A * C))).
[para(274(a,1),1406(a,1,2,2)),rewrite([2373(12),1421(14),12(12)]),flip(a)].
2424 ((C
* x) * x) * (C / x) = C * (C * x).
[para(1106(a,1),479(a,2,2,2)),rewrite([461(7,R),10(7),1222(14,R),9(13),3(11),16(10,R)])].
2466 R(A
* x,A * C',C) = (A * C) * (x * C').
[para(484(a,1),101(a,1,1,2)),rewrite([16(15,R),507(15),435(11),1963(12),16(3)]),flip(a)].
2528 C'
* (x * (C * (x * y))) = x * (C' * (x * (C * y))).
[para(796(a,1),1102(a,1)),rewrite([31(5),599(13),274(13)]),flip(a)].
2536 x *
(C * y) = x * (y * C).
[para(10(a,1),1103(a,1,1)),rewrite([71(10),10(11)]),flip(a)].
2548 (x
* C') * (y * C) = C' * ((C * x) * y).
[para(461(a,1),1103(a,1,1))].
2560 (x
* (y * C)) / (C' * ((C * x) * y)) = R(C',x,y * C)'. [para(1103(a,1),139(a,1,2))].
2580 x /
(C' * ((C * y) * x)) = R(y,C',x * C)'.
[back_rewrite(1436),rewrite([2548(6)])].
2582 (C'
* ((C * x) * y)) / y = R(x,C',y * C).
[back_rewrite(132),rewrite([2548(6)])].
2584 (x
* (y * C)) / (C * y) = x.
[para(2536(a,1),6(a,1,1))].
2585 (x
* (C * y)) / (y * C) = x.
[para(2536(a,2),6(a,1,1))].
2586 (x
/ (C * y)) * (y * C) = x.
[para(2536(a,1),7(a,1))].
2587 (x
/ (y * C)) * (C * y) = x.
[para(2536(a,2),7(a,1))].
2594
R(x,C * y,z) = R(x,y * C,z).
[para(2536(a,1),18(a,1,1,1)),rewrite([398(8)]),flip(a)].
2596 ((x
* y) * (C * z)) / (y * (z * C)) = R(x,y,C * z). [para(2536(a,1),18(a,1,2))].
2597
R(x,y,C * z) = R(x,y,z * C).
[para(2536(a,2),18(a,1,1)),rewrite([2596(8)])].
2598 (C
* x) / (y * (x * C)) = y'.
[para(2536(a,1),33(a,1,2))].
2603 (x
* C) * (C * x) = C * ((C * x) * x).
[para(2536(a,2),36(a,2)),rewrite([36(7),604(5)]),flip(a)].
2617 x *
(C * (C * y)) = x * (y * (C * C)).
[para(1222(a,1),2536(a,1,2)),rewrite([16(9,R)]),flip(a)].
2627 (x
* (y * C)) / (A * (C * y)) = R(x * A',A,C * y). [para(2536(a,1),882(a,1,1))].
2632 x *
(((C * y) / x) * z) = x * (((y * C) / x) * z). [para(2536(a,1),1102(a,1,1)),rewrite([1102(6)]),flip(a)].
2635 x /
(C * y) = x / (y * C).
[para(2586(a,1),6(a,1,1)),flip(a)].
2641 (C
* x) / y = (x * C) / y. [para(2586(a,1),33(a,1,2)),rewrite([112(7)]),flip(a)].
2650
R((x / (C * y)) / z,z,y * C) = x / (z * (y * C)). [para(2586(a,1),80(a,2,1))].
2676
R(x,A' * y,A) = R(x,A',y * A).
[para(1913(a,1),18(a,1,1)),rewrite([1089(11),871(11),897(12),83(5),307(4)]),flip(a)].
2680 (x
* (C * (A' * A'))) * A = C * (x * A').
[para(67(a,2),1913(a,1,1,2)),rewrite([16(17,R),83(19),307(18),16(15,R)])].
2703 A'
* (C' * ((A * C) * x)) = A * (C * ((A' * C') * x)).
[para(1103(a,1),1913(a,1,1)),rewrite([2153(10),2312(9),16(7),16(19),2223(20),16(
19,R),2368(20),1102(19),107(16),461(17)])].
2706 (x
* (y * A'))' * (A' * ((A * x) * y)) = A.
[para(2153(a,1),10(a,1,2))].
2707 (x
* (y * (y * A'))) * A = A' * ((A * x) * (y * y)). [para(12(a,1),2153(a,1,1,2))].
2712 (A'
* ((A * x) * y)) / y = R(x,y * A',A).
[para(2153(a,1),18(a,1,1)),rewrite([83(11),307(10)])].
2725 A'
/ (x * (y * A')) = ((A * x) * y)' * A.
[para(2153(a,1),896(a,1,1)),rewrite([2027(7)]),flip(a)].
2744 A'
* ((A * (x / y)) * y) = A' * (y' * ((y * A) * x)). [para(1091(a,1),2153(a,1,1)),rewrite([2153(8),2273(7)]),flip(a)].
2746 A'
* ((A * (x * y)) * x') = A' * ((A * x) * (y / x)). [para(1102(a,1),2153(a,1,1)),rewrite([2153(7)]),flip(a)].
2800 (x
* (x * A')) * (A * y) = A' * ((A * (x * x)) * y). [para(12(a,1),2223(a,1,1))].
2805
R(x,y * A',A) = R(x,A',A * y).
[para(2223(a,1),18(a,1,1)),rewrite([10(11),2712(7)])].
2815 A'
* (C * (C * x)) = C * ((C * A') * x).
[para(1156(a,1),2223(a,2,2,1)),rewrite([71(9),68(8,R),71(12),12(11),2368(10),10(11),12(13)]),f
lip(a)].
2823 A'
* ((A * x) * (x * A')) = x / (A * x').
[para(2223(a,1),1708(a,2)),rewrite([83(5),307(4),2075(4)]),flip(a)].
2835 x *
(C' * y) = x * (y * C').
[para(13(a,1),2224(a,2,2)),rewrite([507(5),35(13)]),flip(a)].
2836 (x
* C) * (y * C') = C * ((C' * x) * y).
[para(16(a,1),2224(a,1,1))].
2838 (C
* ((C' * x) * y)) / (x * (y * C')) = R(C,x,y * C'). [para(2224(a,1),18(a,1,1))].
2843 (C
* ((C' * x) * y)) * (C / y) = R(C * x,y * C',C / y). [para(2224(a,1),86(a,1,1)),rewrite([494(10),494(18)])].
2852 (C
* x) * (C * (C * ((C' * x) * y))) = C * (((C * x) * x) * y).
[para(2224(a,1),69(a,2,2,2)),rewrite([16(6,R),68(7,R),600(6),2224(11),1
0(9)]),flip(a)].
2858 (C
* ((C' * x) * y)) / y = R(x,C,y * C').
[para(2224(a,1),838(a,1,1)),rewrite([16(11,R),507(11),10(12)])].
2869 R(A
* x,A * C',C) = C * ((A * C') * x).
[back_rewrite(2466),rewrite([2836(15),461(13)])].
2870
R(x,C,y * C') * y = C * ((C' * x) * y).
[back_rewrite(1049),rewrite([2836(12)])].
2872 (x
* (C' * y)) / (y * C') = x.
[para(2835(a,2),6(a,1,1))].
2873 (x
/ (C' * y)) * (y * C') = x.
[para(2835(a,1),7(a,1))].
2883 ((x
* y) * (C' * z)) / (y * (z * C')) = R(x,y,C' * z). [para(2835(a,1),18(a,1,2))].
2884
R(x,y,C' * z) = R(x,y,z * C').
[para(2835(a,2),18(a,1,1)),rewrite([2883(10)])].
2885 (C'
* x) / (y * (x * C')) = y'. [para(2835(a,1),33(a,1,2))].
2898 x *
(C' * (C' * y)) = x * (C' * (y * C')).
[para(787(a,1),2835(a,2,2)),rewrite([461(13,R)])].
2951 x *
(C * (C' / x)) = C * R(C',x,x').
[para(86(a,1),2290(a,2,2)),rewrite([1121(7),1057(5)])].
2972 A'
* (C' * (A * (x * C))) = A' * (C * ((A * C') * x)).
[para(2290(a,1),2153(a,1,1)),rewrite([2153(10),2290(9),461(7),461(19,R)]),flip(a
)].
2973 C *
(C * R(C',x,x')) = R(C,x,x').
[back_rewrite(1208),rewrite([2951(7)])].
2978 (x
* C') * (y * (y * C)) = C' * ((C * x) * (y * y)). [para(67(a,1),2312(a,1,2))].
2986 (x
* C') * (y * (C * C)) = C' * ((C * x) * (C * y)). [para(1222(a,1),2312(a,1,2))].
2997 (x
* C) * (y * (y * C')) = C * ((C' * x) * (y * y)). [para(12(a,1),2836(a,1,2))].
3069 A'
* (C' * (A * x)) = A * ((A' * C') * x).
[para(7(a,1),1921(a,1,2,2)),rewrite([435(10),2223(16),461(15,R)]),flip(a)].
3076 (A
* C') * ((C * A') * x) = R(x,C * A',A * C').
[para(83(a,1),1921(a,2)),rewrite([494(11),435(9),2153(13),16(12,R),2368(13),1092(14),87
1(8),461(7),35(15),494(15),435(13)])].
3081 A *
((A' * C') * (A' * (C * (x * A)))) = (C * A') * (x / (C * A')).
[para(1089(a,1),1921(a,2)),rewrite([494(11),435(9),2138(13),494(20)
,435(18),494(24),435(22)])].
3092 A'
* (C * ((A * C') * x)) = A * (C' * ((C * A') * x)). [back_rewrite(2972),rewrite([3069(10),2548(9)]),flip(a)].
3093 (A
* C) * ((A' * C') * x) = R(x,A' * C',A * C). [back_rewrite(2375),rewrite([3069(13),2223(14),35(15)])].
3095 (C
* (x * A)) * A' = A * ((C * A') * x).
[para(9(a,1),2140(a,1,2,2)),rewrite([3(8)]),flip(a)].
3096 ((C
* A') * x) * (A * y) = A' * ((C * (x * A)) * y). [para(2140(a,1),10(a,1,2)),flip(a)].
3101 A *
(C * (A' * (x * (A * C)))) = C * (C * (x * A)).
[para(16(a,2),2140(a,1,2,2)),rewrite([16(9),3096(10),16(9,R),2815(10),2369(9),16(17
,R)])].
3113 C *
((C' * (x * A)) * A') = A * (C' * ((C * A') * x)).
[para(493(a,1),2140(a,1,2,2)),rewrite([461(9,R),461(19),2224(20)]),flip(a)].
3212 (x
* (C' * (y * (x * C')))) * z = x * (C' * (y * (C' * (x * z)))). [para(461(a,1),48(a,1,1,2,2,2))].
3322 C *
(x * ((y / (C * x)) * (x * (C * z)))) = (C * (x * y)) * z.
[para(2586(a,1),48(a,1,1,2,2)),flip(a)].
3372 C *
((x * y') * (C' * y)) = R(x,y',C' * y).
[para(10(a,1),2883(a,1,2)),rewrite([599(9)])].
3385
R(x,C,C' * C') = x.
[para(67(a,1),2883(a,1,2)),rewrite([2836(8),461(7,R),35(8),16(9,R),9(9),3(7),599(6),35(5)]),flip(a)].
3408
R(x,C * C,C' * y) = R(x,y,C).
[para(1222(a,2),2883(a,1,1,1)),rewrite([1102(8),107(5),10(6),12(10),507(9),102(6)]),flip(a)].
3498 (C
* ((C' * x) * (y * x))) * (C / x) = (C * x) * y. [para(1106(a,1),3212(a,2,2,2,2,2)),rewrite([461(9,R),10(9),1102(7),107(3),1222(20,R
),9(19),3(17),64(17)])].
3558 x *
((y / (x * z)) * x) = (x * y) / z.
[para(7(a,1),40(a,1,1,2)),flip(a)].
3563 (x
* A) * (y * x) = x * ((A * y) * x).
[para(15(a,1),40(a,1,1,2)),rewrite([435(8),1963(9)])].
3564 (C
* (x * (y * C))) / y = C * (x * C).
[para(16(a,1),40(a,1,1,2,2))].
3570 (A
* x) * (y * (A * x)) = A * (x * ((y * A) * x)).
[para(50(a,1),40(a,1,1,2,2)),rewrite([1973(8),13(7),435(10),1090(11),435(9),338(10),
439(9)]),flip(a)].
3613 ((x
* y) * (y * z)) / z = (x * y) * (R(x,y,z)' * (x * y)). [para(751(a,1),40(a,1,1,2))].
3660 C *
(x * (x * (C * y))) = x * (C * (C * (x * y))). [para(16(a,1),46(a,1,1,2,2)),rewrite([1375(6)])].
3867 (A
* (x * A)) / (y * A) = A * (x / y).
[para(7(a,1),51(a,1,1,2,1))].
3872 (A
* (A * ((x * y) * (A * A)))) / (y * (A * A)) = A * (A * x).
[para(15(a,1),51(a,1,1,2,1)),rewrite([13(8),1926(13)])].
3904 ((A
* x) * y) * A' = A * (x * (y * A')).
[para(2153(a,1),51(a,1,1,2,1)),rewrite([1089(9),871(9),35(10),882(9),1942(9)])].
3913 A *
(x / (y * (A * x))) = R(y,A * x,A)'.
[back_rewrite(1440),rewrite([3867(10)])].
3914
R((A * x) / y,y,A) = A * (x / y).
[back_rewrite(853),rewrite([3867(12)])].
4010 (x
* y) / (C' * y) = R(C * x,C',y).
[para(599(a,1),80(a,1,1)),flip(a)].
4347 A'
/ x = A' * x'.
[para(2111(a,1),10(a,1,2)),flip(a)].
4394 ((A
* x) * y)' * A = A' * (x * (y * A'))'.
[back_rewrite(2725),rewrite([4347(7)]),flip(a)].
4409 (x
* (A * A))' = A' * (A' * x').
[back_rewrite(1951),rewrite([4347(10),896(10),4347(10)])].
4425 (x
* (A' * y')) * (y * A) = R(x,A' * y',y * A). [back_rewrite(912),rewrite([4347(3),4347(11)])].
4430 (x
* A) * ((A' * x') * y) = y.
[back_rewrite(906),rewrite([4347(5)])].
4433 (A'
* x') * ((x * A) * y) = y.
[back_rewrite(903),rewrite([4347(3)])].
4435 (x
* A)' = A' * x'.
[back_rewrite(896),rewrite([4347(6)])].
4456 (x
* (C * y))' * (C * (x * (y * C))) = C.
[para(70(a,1),65(a,1,2))].
4458 (x
* (C * y))' = (x * (y * C))'.
[para(70(a,1),117(a,1,2)),rewrite([117(7)]),flip(a)].
4521
R(C',x,C / x) = R(C,x,x')'.
[para(157(a,1),18(a,1,1)),rewrite([1134(4),29(5)]),flip(a)].
4627 (A
* C) * (A * x) = A * (A * (x * C)).
[para(569(a,1),58(a,2,2,2)),rewrite([16(3),190(10),435(14),461(15),1102(16),435(11),86(12),439(1
1),461(10,R),10(10),16(9),3(13)]),flip(a)].
4679 x *
(C * (x' * (y * x'))) = y * (x' * C).
[para(72(a,2),35(a,1,2))].
4714 (x
* (y * (x * C))) / (C * (y * x)) = R(x,y * x,C). [para(72(a,1),101(a,1,1)),rewrite([16(7,R)])].
4775 A *
(A * ((C * A') * x)) = C * (A * x).
[para(2223(a,1),72(a,2,2)),rewrite([83(7),307(6),16(11,R),2368(12)]),flip(a)].
4780 C'
* ((C * x) * x) = C * ((x * C') * x).
[para(72(a,2),2312(a,1)),rewrite([507(9),16(15,R),507(15)]),flip(a)].
4846
R(A',x',x) = A'.
[para(1965(a,1),6(a,1,1)),rewrite([435(3),2(4)]),flip(a)].
4871 (A'
* x) * (x' * A) = 0.
[para(2027(a,1),9(a,1,2))].
4873 (A'
* x) * ((x' * A) * y) = y.
[para(2027(a,1),35(a,1,2,1))].
4874 (x'
* A) * (C * (A' * x)) = C.
[para(2027(a,1),65(a,1,1))].
4898
R(x' * A,A' * x,y) = x' * A.
[para(2027(a,1),82(a,1,1)),rewrite([2027(11)])].
4905 (C
* (x * (y * x))) / (y * (C * x)) = x.
[para(73(a,2),6(a,1,1))].
4919 (x
* (C * y)) / (C * (y * (x * y))) = y'.
[para(73(a,2),33(a,1,2))].
4920 x *
(y' * C) = x * (C * y').
[para(73(a,2),35(a,1,2)),rewrite([4679(7)])].
4926 x *
((y * x') * (C * x)) = C * (x * R(y,x',x)). [para(83(a,1),73(a,1,2,2)),flip(a)].
5026
R(x,y' * C,z) = R(x,C * y',z).
[para(4920(a,1),18(a,1,1,1)),rewrite([397(10)]),flip(a)].
5067 (A
* x') * ((x * A') * y) = y.
[para(2075(a,1),10(a,1,1))].
5075 (x
* (A * y')) * (y * A') = R(x,A * y',y * A'). [para(2075(a,1),83(a,1,1,2)),rewrite([2075(12)])].
5094 R(x
* A',A * x',y) = x * A'.
[para(2075(a,1),84(a,1,2))].
5099
R(x,C * A',A * C') = x.
[back_rewrite(3076),rewrite([5067(10)]),flip(a)].
5100 (x'
* A') * ((A * x) * y) = y.
[para(2076(a,1),10(a,1,1))].
5101 (x'
* A') * (C * (A * x)) = C.
[para(2076(a,1),65(a,1,1))].
5133 C *
(x * (C' * C')) = C' * x.
[para(3385(a,1),80(a,1)),rewrite([107(2),35(16),599(12)]),flip(a)].
5134
R(x,C' * C',C * C) = x. [back_rewrite(1268),rewrite([5133(9),35(5)]),flip(a)].
5167 R(A
* C,A',A * x) = (C * (A * x)) / x.
[para(1974(a,1),81(a,1,1)),rewrite([435(4),83(7),307(6),435(10),2805(13)]),flip(a)].
5310
R(A,x,x' * A') = A.
[para(2076(a,1),85(a,1,3)),rewrite([2076(9),35(11),31(9)])].
5363
R(A,x',x * A) = A.
[para(15(a,1),88(a,1,1)),rewrite([8(3),2(4),435(5),12(6),9(5),3(3)]),flip(a)].
5404
R(A' * x,A',A * y) = (A' * (x * y)) / y.
[para(1841(a,1),88(a,1,1,1)),rewrite([13(9),10(7)]),flip(a)].
5442
R(A,x',x * (y * (x * A))) = R(A,y,x * A).
[para(60(a,1),88(a,1,1)),rewrite([10(5),96(9)]),flip(a)].
5457
R(A,A * x',x) = A.
[para(7(a,1),5363(a,1,3)),rewrite([435(3),2075(5)])].
5480
R(A,A * x,x') = A.
[para(31(a,1),5457(a,1,2,2))].
5532 (x
* (C' * (x * y))) / (y * C') = R(x * x,C',y). [para(461(a,1),89(a,1,2)),rewrite([479(5)])].
5533 (x
* (C' * (x * y))) / (C' * y) = R(x * x,C',y). [para(461(a,2),89(a,1,1,1,2)),rewrite([13(5)])].
5611 A'
* ((A * x) * x) = x * x.
[para(2153(a,1),89(a,1,1)),rewrite([8(10),24(8),307(11)])].
5693 R(A
* A,x,x') = A * A.
[para(5480(a,1),79(a,1,1)),rewrite([86(5),2028(4),335(9)]),flip(a)].
5714
R(x,C' * C',C) = x.
[para(64(a,1),91(a,1,2)),rewrite([16(8,R),5133(8),599(6),35(5)]),flip(a)].
5819
R(x,C * C,y * C') = R(x,y,C).
[para(507(a,1),91(a,1,2,2)),rewrite([1272(8),507(6),102(6)]),flip(a)].
6085 R(x
* (x * x),x,y) = x * (x * x).
[para(46(a,1),92(a,1,1)),rewrite([40(6)]),flip(a)].
6142 x /
(C' * C') = C * (x * C).
[para(5714(a,1),80(a,1)),rewrite([16(15,R),35(15),599(11)])].
6150 ((x
* y) / (z * y)) * (R(z / x,x,y) * u) = u.
[para(80(a,2),138(a,1,2,1))].
6222
R(x,A * x,A) = x.
[para(50(a,1),93(a,1,2)),rewrite([6(10)]),flip(a)].
6262
R(x,(C' * y) * x,z) = R(x,(y * C') * x,z). [para(787(a,1),93(a,2,2)),rewrite([93(12)])].
6303
R(x,A' * x,A') = x. [para(1841(a,1),93(a,1,2)),rewrite([6(14)]),flip(a)].
6333 R(C
* x,y * (C * x),z) = R(C * x,y * (x * C),z). [para(2536(a,1),93(a,2,2)),rewrite([93(12)])].
6433
R(A' * x,x,A) = A' * x.
[para(35(a,1),6222(a,1,2))].
6572 C'
* (C' * (C' * (x * (C * (C * C))))) = R(x,C * (C * C),C').
[para(1156(a,1),94(a,1,2)),rewrite([461(9,R),1863(13),461(14,R)])].
6737 R(A
* x,x,A') = A * x.
[para(10(a,1),6303(a,1,2))].
6873 A *
(A * (C * ((A' * C') * x))) = R(A * x,A * C,C'). [para(2836(a,1),95(a,1,1,2)),rewrite([16(12),461(15,R),64(15),435(11),1090(12),435
(10),3095(11),1102(10),107(7),461(8),16(17)])].
6952 (A
* (x * A)) / (y' * ((y * x) * A)) = R(A,x / y,y * A). [para(7(a,1),96(a,1,1,2,1)),rewrite([1091(8)])].
6954
R(A,x,x * A) = A.
[para(12(a,1),96(a,1,1,2)),rewrite([6(9)]),flip(a)].
6958 (A
* ((x * C) * A)) / (C * (x * A)) = R(A,C,x * A). [para(16(a,1),96(a,1,1,2,1))].
6959 (A
* ((C * x) * A)) / (x * (A * C)) = R(A,x,A * C). [para(16(a,2),96(a,1,1,2,1)),rewrite([16(9),16(15)])].
6981 A *
((R(x,y,A) * y) / (x * y)) = R(A,R(x,y,A),y * A). [para(79(a,1),96(a,1,2)),rewrite([3867(11)])].
6996 (A
* (C * (x * (A * C)))) / (x * (A * (C * C))) = R(A,x,A * (C * C)).
[para(1222(a,2),96(a,1,1,2,1)),rewrite([71(7),16(5),12(13),16(12)
,1255(13),12(21),16(20),1255(21)])].
7026
R(A,C' * x,A * C) = R(A,C',(x * C) * A).
[para(2197(a,2),96(a,1,2)),rewrite([64(6),6952(12),107(3),16(7)])].
7044 (A
* (x * A)) / (C * ((x * C') * A)) = R(A,C,(x * C') * A). [para(507(a,1),96(a,1,1,2,1))].
7060
R(A,x * A',x) = A.
[para(7(a,1),6954(a,1,3)),rewrite([435(3)])].
7088
R(A',C',C')' = A.
[para(461(a,1),7060(a,1,2)),rewrite([142(9)])].
7151
R(x,C * (y * A),C) = R(x,C * C,y * A).
[para(1156(a,1),97(a,1,1,1,2)),rewrite([1272(7),71(15),1913(17),2369(17),1421(16),2815(17),2369(
16),3101(18),102(14),1156(14)])].
7168 ((x
* (A * y)) * (A * A)) / (A * (y * (A * A))) = R(x,A * y,A * A). [para(1926(a,1),97(a,1,2,2))].
7220 (A
* (x * A)) / (A * ((C' * x) * A)) = R(C',A,x * A)'. [para(507(a,1),97(a,1,1,1)),rewrite([644(20)])].
7253
R(A',C',C') = A'. [para(7088(a,1),31(a,1,1)),flip(a)].
7254 (A
* ((A' * x) * y)) / y = R(x,A,A' * y).
[para(7088(a,1),88(a,1,1,1,2)),rewrite([7253(9),2237(6),7253(14),31(10),7253(15)])].
7289 C'
* (x * (C * (C / x))) = R(C,x,C * x').
[para(123(a,1),98(a,1,2)),rewrite([1105(6),107(7)])].
7303 (C
* (C * (A * (x * A)))) / (A * ((x * C) * A)) = R(C,A * x,A * C).
[para(74(a,1),98(a,1,2)),rewrite([16(4,R),1421(8),50(6)])].
7326
R(C' * ((A * C) * x),C,A) = R(A * x,A,C).
[para(50(a,1),102(a,1,1,2)),rewrite([16(9),2004(10),16(5)])].
7346 (C
/ x) / R(C,x,x') = x'.
[para(1134(a,1),33(a,1,2))].
7347
R(C,x,C * x') = R(C,x,x').
[para(141(a,1),1134(a,2,3)),rewrite([1707(8),1092(9),599(5),2291(8),16(6,R),7289(8),142(12),4521(10),31(10)]
)].
7350
R(x',R(C,x,x'),y) = R(x,C / x,y)'.
[para(1134(a,1),143(a,1,2))].
7416 R(x
* C,C / x,C) = (C * (C * C)) / (C * (C / x)). [para(1148(a,1),101(a,1,1,2)),rewrite([16(9,R)]),flip(a)].
7422 (C'
/ x) * (((x * C) * y) * (C / x)) = C * (C * (y / (x * C))).
[para(1148(a,1),1091(a,1,2)),rewrite([1222(7,R),559(10)]),flip(a)].
7424 ((x
* C) * x) * (C / x) = C * (x * C).
[para(1148(a,1),479(a,2,2,2)),rewrite([461(7,R),64(7),1222(14,R),9(13),3(11),16(10,R)])].
7556 (C
* (C * (x * y))) / (C * (y * C)) = R(x,y,C * C). [para(1255(a,2),18(a,1,2)),rewrite([1222(5,R)])].
7558 (x
* C) * (x * (C * C)) = C * (C * ((C * x) * x)). [para(1255(a,1),68(a,2,2)),rewrite([604(6)]),flip(a)].
7601
R(x,C',C * (y * C)) = R(x,C',y * (C * C)).
[para(1255(a,1),88(a,2,3)),rewrite([2312(8),2582(11),16(6,R)])].
7627 (A
* (C * (x * (A * C)))) / (A * ((C * x) * A)) = R(C,A * C,x * A).
[para(1255(a,1),97(a,1,1,1)),rewrite([1272(8),1927(8)])].
7629 (C
* (x * (y * C))) / (y * (C * C)) = R(x,y * C,C). [para(1255(a,1),102(a,1,2))].
7634 x /
(C' * (x * C')) = C * C.
[para(7(a,1),1265(a,1,1)),rewrite([1863(4)])].
7638 x /
(x * (C' * C')) = C * C.
[para(83(a,1),1265(a,1,1)),rewrite([175(4),5134(9),175(4)])].
7816 R(A
* x,A,A' * y) = (A * (x * y)) / y.
[para(50(a,1),126(a,1,1,1)),rewrite([1102(8),435(5),86(6),439(5)]),flip(a)].
8035
R(x,A * x,x' * A') = x.
[para(2152(a,1),93(a,1,2)),rewrite([35(6),9(4),3(2),24(2)]),flip(a)].
8113 x *
((C * y) * z) = x * ((y * C) * z).
[para(2584(a,1),1091(a,1,1)),rewrite([509(7),391(14),556(15)])].
8182 x *
(C * (A * (A * C))) = x * (A * (A * (C * C))). [para(74(a,1),8113(a,2,2)),rewrite([16(3),604(7),16(4),50(6),16(5),12(14),16(13),125
5(14)])].
8394 C *
(C * (x / (y * C))) = (C * x) / y.
[para(2587(a,1),40(a,1,1,2)),rewrite([16(9,R)]),flip(a)].
8419 (C'
/ x) * (((x * C) * y) * (C / x)) = (C * y) / x. [back_rewrite(7422),rewrite([8394(17)])].
8551 (x
/ (y * C)) * (((C * y) / x) * z) = z.
[para(2635(a,1),138(a,1,1))].
8565 (C
* (C * x)) / y = (x * (C * C)) / y.
[para(1222(a,1),2641(a,1,1)),rewrite([16(9,R)]),flip(a)].
8633
R(x,A' * x,x' * A) = x. [para(4871(a,1),93(a,1,2)),rewrite([35(6),8(4),3(2),24(2)]),flip(a)].
8670
R(A' * x,A',A * C) = C' * (A' * (x * C)).
[para(1841(a,1),135(a,1,2,1)),rewrite([16(11),13(12),10(10),16(16)]),flip(a)].
8797
R(C' * x,(C / x) * y,z) = R(C / x,y,z)'.
[para(141(a,1),142(a,1,2,1)),rewrite([141(11)])].
8934 (A
* (x * (x * A'))) / (x * A') = A * x.
[para(6737(a,1),18(a,2)),rewrite([3904(6)])].
8935 (A
* x) * (x * A') = A * (x * (x * A')).
[para(6737(a,1),79(a,1,1)),rewrite([3904(12)])].
8948 x /
(A * x') = x * (x * A').
[back_rewrite(2823),rewrite([8935(8),10(9)]),flip(a)].
8967 ((x
* y) * (C * y')) / R(x,y,C * y') = C.
[para(150(a,1),33(a,1,2)),rewrite([31(13)])].
8970 R(A
* x,A,C * A') = C' * (A * (C * x)).
[para(50(a,1),150(a,1,2,1)),rewrite([1105(11),435(8),86(9),439(8)]),flip(a)].
8990 R(A
* x,A * C,A') = C' * (A * (x * C)).
[para(74(a,1),150(a,1,2,1)),rewrite([559(13),435(13),461(14),507(15),1090(11),435(9),86(10),439
(9),559(17),435(17),461(18),507(19)]),flip(a)].
9012 C'
* ((A' * ((A * x) * y)) * (C * A')) = R(x * (y * A'),A,C * A'). [para(2153(a,1),150(a,1,2,1))].
9097
R(x,A' * C',A * C) = x.
[para(871(a,1),158(a,1,1)),rewrite([16(3),461(8),3093(10)])].
9131 (A
* C) * ((A' * C') * x) = x.
[back_rewrite(3093),rewrite([9097(19)])].
9182 (A'
* C') * ((A * C) * x) = x.
[para(871(a,1),159(a,1,2,1)),rewrite([461(5),16(8)])].
9678 (x
* A) * (x * A) = x * (A * (x * A)).
[para(161(a,1),871(a,1)),rewrite([871(3),871(5),871(8),1918(10)])].
10600 (C
* (C * C)) / (C * x) = C * (x' * C).
[para(1220(a,1),40(a,1,1,2))].
10633
R(x * C,C / x,C) = C * x.
[back_rewrite(7416),rewrite([10600(16),112(10),107(9),16(12,R),35(12)])].
10635
R(x',C,C * C)' = x.
[back_rewrite(1501),rewrite([10600(13),509(7),1304(7),31(5),16(9,R),35(9),507(5)]),flip(a)].
10659
R(x',C,C * C) = x'. [para(10635(a,1),31(a,1,1)),flip(a)].
10662
R(x,C,C * C) = x.
[para(31(a,1),10659(a,1,1)),rewrite([31(7)])].
10665
R(x,C * C,C) = x.
[back_rewrite(1633),rewrite([10662(10)])].
10671 x'
* (C * (x * (C * C))) = C * (C * C).
[para(10665(a,1),751(a,1,1,1)),rewrite([16(7,R),16(13,R)])].
10762
((x * (C' * C')) * (y * (C * C))) / y = R(x,C' * C',y * (C * C)).
[para(1245(a,1),91(a,1,2,2)),rewrite([10(16)])].
10918 (x
* y)' * x = x' * (x / y).
[para(1702(a,1),10(a,1,2)),flip(a)].
10934
(x' / y) * x = x' * (x' * y)'.
[para(1702(a,1),1089(a,1,1)),rewrite([10918(9),31(6),1708(9),1735(8)])].
10942 C
* ((C' * x) * A') = R(x * A',A,C).
[para(1642(a,1),1702(a,2)),rewrite([1421(8),509(9),1304(9),4435(7),461(11,R),1092(15),599(14),35(
13),83(9),4846(8),461(7),2224(8)])].
10943 (x
* y)' * (x * z) = x' * ((x / y) * z).
[para(1702(a,1),1091(a,2,2,1)),rewrite([10918(3),1750(4),975(4),10(5)])].
10961
(x' / y) * (x * z) = x' * ((x' * y)' * z).
[para(1702(a,1),1092(a,1,1)),rewrite([10918(10),31(7),1708(10),10934(8),35(11)])].
10972 (C
/ (C / x)) * (C' / x) = C'.
[para(1702(a,1),475(a,1,2)),rewrite([141(4),461(5,R),1057(5),509(6),1080(6)])].
10974 (x
* C') / (y * x) = x / (y * (x * C)).
[para(72(a,2),1702(a,1,2,1,1)),rewrite([509(5),3558(7)])].
10976 x
/ (y * (C * x)) = x / (y * (x * C)).
[para(73(a,2),1702(a,1,2,1,1)),rewrite([509(5),3558(7),10974(5)]),flip(a)].
11017 A
* (C' * ((C * A') * x)) = R(x,A,C).
[back_rewrite(3113),rewrite([10942(10),86(5),439(4)]),flip(a)].
11026 x
/ (A * (x * C)) = R(A' * C',A,x).
[back_rewrite(1663),rewrite([10974(6)])].
11027
R(x,C',y * C)' = R(x,C',y)'.
[back_rewrite(1459),rewrite([10974(8),2548(6),2580(7)])].
11029 A'
* (C * ((A * C') * x)) = R(x,A,C).
[back_rewrite(3092),rewrite([11017(20)])].
11186 (x
* (x * y)') * x = R(x / y,x',x).
[para(10934(a,1),83(a,1,1)),rewrite([31(2),31(2),31(6)])].
11274 (x
/ y) * (((y / x) / x) * z) = y' * ((y / x) * z). [para(7(a,1),10943(a,1,1,1)),rewrite([112(6)]),flip(a)].
11845
R(A',C,A * C) = A'.
[para(871(a,1),1823(a,1,3)),rewrite([16(6),871(12),16(11),33(12)])].
11863 C
* (C * (A * (x * A))) = A * (C * ((C * x) * A)).
[para(1156(a,1),190(a,1,1)),rewrite([12(8),2800(18),1272(17),2368(18),50(20),2138(1
9),35(20)])].
11948 (A
* (C * ((C * x) * A))) / (A * ((x * C) * A)) = R(C,A * x,A * C). [back_rewrite(7303),rewrite([11863(8)])].
11957
R(x,A * A,A') = x.
[para(1935(a,1),18(a,1,1)),rewrite([12(8),9(7),3(5),435(4),86(5),439(4)]),flip(a)].
11985 A'
* ((x * (A * A)) * (C * A')) = C * (A' * (x * A)). [para(1935(a,1),72(a,1,2,2)),rewrite([16(17,R)]),flip(a)].
12025
((x * (A * C')) * A) / (A * (A * C')) = R(x,A * C',A). [para(461(a,1),193(a,1,2,2))].
12026
R(R(x,A,y),A * y,A) = x.
[para(79(a,1),193(a,1,1,1)),rewrite([1918(5),6(10)]),flip(a)].
12030 C'
* (A * ((C * A') * x)) = R(x,A',A * C).
[para(264(a,1),193(a,1,1,1,2)),rewrite([16(4,R),2153(7),16(6,R),2368(7),2153(17),1090(16),4
35(14),123(16),16(12,R),123(13),107(9),264(19),16(14,R),2805(16)])].
12031
R(R(x,C,A),A * C,A) = R(x,C,A * A).
[para(757(a,1),193(a,1,1,1)),rewrite([1926(6),16(10),860(12),64(5)]),flip(a)].
12064
R(x,A * (A * x),A) = x.
[para(46(a,1),193(a,1,1)),rewrite([50(12),6(14)]),flip(a)].
12096
R(A' * x,A * x,A) = A' * x.
[para(35(a,1),12064(a,1,2,2))].
12114
R(R(x,A,A' * y),y,A) = x.
[para(35(a,1),12026(a,1,2))].
12115
R(R(x,A,C * A'),C,A) = x.
[para(123(a,1),12026(a,1,2))].
12199
R(C,A * (A * C),A') = C.
[para(1935(a,1),203(a,1,2)),rewrite([12(9),123(8),1255(5),16(8),1283(9),67(7)]),flip(a)].
12204 x
/ (A' * A') = x * (A * A).
[para(1946(a,1),80(a,1)),rewrite([12(19),10(18),8(14),24(12)])].
12925 C'
* (x * (C * (C * C))) = C * (x * C).
[para(248(a,2),40(a,1,1)),rewrite([1863(12),461(13,R),10(13)])].
13068
R(x,C * (C * C),C') = x.
[back_rewrite(6572),rewrite([12925(13),10(9),64(5)]),flip(a)].
13072 x
/ (C * (C * C)) = C' * (C' * (x * C')).
[para(13068(a,1),80(a,1)),rewrite([461(17,R),10(17),1863(13),461(14,R)])].
13522 x
/ (C * A') = x * (A * C').
[para(5099(a,1),80(a,1)),rewrite([2223(19),461(18,R),64(18),8(14),24(12)])].
13527 A
* ((A' * C') * (A' * (C * (x * A)))) = (C * A') * (x * (A * C')).
[back_rewrite(3081),rewrite([13522(24)])].
13529
R(C' * (A' * x),C,A') = A' * (x * C').
[back_rewrite(1903),rewrite([13522(11),13(11),10(9)]),flip(a)].
13530 C
* ((A' * C') * x) = R(A' * x,A',C).
[back_rewrite(1898),rewrite([13522(13),2224(13),1913(12),461(6),83(11),307(10)])].
13533 A
* (A * R(A' * x,A',C)) = R(A * x,A * C,C'). [back_rewrite(6873),rewrite([13530(10)])].
13536 A'
* (C' * ((A * C) * x)) = A * R(A' * x,A',C). [back_rewrite(2703),rewrite([13530(19)])].
13537 A
* (R(A' * x,A',C) * A) = C * ((x * C') * A). [back_rewrite(2144),rewrite([13530(9)])].
14702 (A
* x) * x = A * (x * x).
[para(5611(a,1),10(a,1,2)),rewrite([31(3)]),flip(a)].
14872 (A
* (x' * x')) * x = R(A * x',x',x).
[para(14702(a,1),83(a,1,1))].
15863 (C
* (x' * C)) / R(C,x,x') = C / x.
[para(141(a,1),7346(a,1,2,3)),rewrite([1707(5),142(12),4521(10),31(10),141(13)])].
15932 (x
* (y * A')) * (A * z) = A' * (((A * x) * y) * z).
[para(312(a,1),2223(a,2,2,1)),rewrite([2223(6),1841(9),3904(8),10(9),307(14)])].
15944 (x
* A) * (y * (x * A)) = x * (A * ((y * x) * A)). [para(60(a,1),312(a,1,2)),rewrite([10(5),2050(9)]),flip(a)].
15948 A'
* ((x * (y * A'))' * A') = ((A * x) * y)'.
[para(312(a,1),2076(a,1,1)),rewrite([307(5),2223(10),2027(11),4394(10),1841(15)]),flip(a
)].
16078 C
* (A * ((x * C) * A)) = A * (C * (C * (x * A))).
[para(313(a,1),1974(a,1)),rewrite([3570(8),16(6,R),307(12),1090(16),435(14),123(16)
]),flip(a)].
16083 (x
* A') * x = x * (A' * x).
[para(313(a,1),1913(a,1)),rewrite([307(8),83(12),307(11)]),flip(a)].
16206
R(A' * x,x,x') = A' * x.
[para(35(a,1),8035(a,1,2)),rewrite([2027(7),86(9),439(8)])].
16263
R(x * C',C,y * C') = (x * (y * C')) / y.
[para(507(a,1),318(a,1,2)),rewrite([474(4)]),flip(a)].
16301 (x
* A') * A' = x * (A' * A').
[para(11957(a,1),318(a,2)),rewrite([175(4),1946(9),12(9),9(8),3(6),435(5),175(10)])].
16365
R(A * x,x,x') = A * x.
[para(10(a,1),8633(a,1,2)),rewrite([2076(5),83(8),307(7)])].
16391
R(A * x',x',x) = A * x'.
[para(31(a,1),16365(a,1,3))].
16412 (A
* x) / x' = A * (x * x). [para(16365(a,1),332(a,1,1)),rewrite([14702(7)])].
16419 (A
* (x' * x')) * x = A * x'.
[back_rewrite(14872),rewrite([16391(11)])].
16428
(C' * (x * (y * C))) / y = R(x,y * C,C').
[para(461(a,2),319(a,1,1)),rewrite([31(5),31(9),458(10),31(10)])].
16472 R(x,A',A')
= x.
[para(6433(a,1),319(a,1,2)),rewrite([12(8),2707(11),1102(10),435(5),16301(9),10(11),12204(12),15932(10),1090(7),435(5)
,2153(9),12(8),10(9),10(5),12(8),2676(10),12(9),8(8),3(6)]),flip(a)].
16494 (x
* (A' * C')) * (A * C) = x.
[para(9097(a,1),18(a,2)),rewrite([2548(19),83(18),307(17),16(14,R),9(14),24(12)])].
16495 x
/ (A' * C') = x * (A * C).
[para(9097(a,1),80(a,1)),rewrite([2548(19),83(18),307(17),16(14,R),9(14),24(12)])].
16628
R(C * A',A * C,C) = C * A'.
[para(871(a,1),10633(a,1,2)),rewrite([16(4,R),16(7)])].
16660 (x
* (A * C)) * (A' * C') = R(x,A * C,A' * C').
[para(871(a,1),324(a,1,1,2)),rewrite([16(3),461(9),871(14),16(13),461(18)])].
16909
R((x * (A' * y)) / y,y,A) = x * A'.
[para(80(a,1),12114(a,1,1)),rewrite([35(9),435(9)])].
16999 (x
* (x * y))' * R(x * x,y,y') = y'.
[para(12(a,1),334(a,1,1,1))].
17540 (C
* (x * (y * C))) * y' = R(C * (x * C),y,y'). [para(16(a,1),338(a,1,1,2,2))].
17759
R(x,A * (y * A),A') = R(x,A,y).
[para(50(a,1),343(a,1,1,1,2)),rewrite([1963(8),439(9),882(6),86(5),439(4),50(6)]),flip(a)].
17776
R(A * x,A * C,C') = C' * ((A * C) * x).
[para(74(a,1),343(a,1,1,1)),rewrite([461(9,R),458(14),435(11),1963(12),461(4),2548(7),16(5)]),
flip(a)].
17790
R(x,C',C') = x.
[para(1629(a,1),343(a,1,2)),rewrite([16(7,R),35(7),461(6,R),6142(12),16(9,R),35(9),507(5),16(7,R),35(7)]),flip(a)].
17820 A
* (A * R(A' * x,A',C)) = C' * ((A * C) * x). [back_rewrite(13533),rewrite([17776(19)])].
18141 (A
* x') / x = A * (x' * x').
[para(31(a,1),16412(a,1,2))].
18581
R(x * C,C * x,y) = C * x.
[para(396(a,1),90(a,1))].
18619 (C
* ((x * C') * x)) * (C / x) = C * x.
[para(18581(a,1),150(a,2)),rewrite([2603(7),509(11),2241(13),4780(9),10(14)])].
18795 x'
* (C' * (x * x)) = x * C'.
[para(477(a,2),10(a,1,2))].
19180 (A
* (C * (x * (A * C)))) / (C * (C * (x * A))) = R(A,C * x,A * C).
[para(74(a,1),397(a,1,1)),rewrite([16(5,R),71(7),16(5),2377(14)])]
.
19511 x
/ (A * C') = x * (C * A').
[para(435(a,1),430(a,1,1,2)),rewrite([461(8),5099(9),461(4),435(8)])].
19516 C'
* ((C * x) * A') = R(x * A',A,C').
[back_rewrite(1664),rewrite([19511(8),1092(8),599(5)])].
19809
((x * C') * A) * (C * A') = R(x,C',A).
[para(1133(a,1),193(a,1,1,1,2)),rewrite([439(6),435(10),461(11),1089(13),871(13),461(12),10(13)
,19511(10),435(15),461(16),35(17)])].
19870
R(A,x,A * x) = A.
[para(437(a,1),18(a,1,1)),rewrite([6(9)]),flip(a)].
19929
R(A',x,x)' = A.
[para(35(a,1),19870(a,1,3)),rewrite([142(5)])].
19945
R(A',x,x) = A'.
[para(19929(a,1),31(a,1,1)),flip(a)].
19948
(A' * x) * x = A' * (x * x).
[para(19945(a,1),79(a,1,1)),flip(a)].
19976
(C' * (x * (A * C))) * A' = R(x,A * C,C'). [para(462(a,1),435(a,1)),rewrite([16(3),16(11)]),flip(a)].
19978
(C' * (x * (C * A'))) * A = R(x,C * A',C'). [para(462(a,1),871(a,1)),flip(a)].
20117 C
* (x * (C * (y * x))) = x * (C * (y * (C * x))). [para(71(a,1),469(a,1,2,2)),rewrite([507(7),71(11)])].
20488 x'
* (C' * (x * (y * x))) = y * (x * C').
[para(482(a,2),10(a,1,2))].
20494 C'
* ((x * C) * x) = C * ((C' * x) * x).
[para(64(a,1),482(a,1,2,2)),rewrite([461(15,R),64(15),2290(12)])].
20538 A
* (A * ((A' * C') * x)) = C' * (A * x).
[para(2223(a,1),482(a,2,2)),rewrite([83(8),307(7),461(13,R),3069(14)]),flip(a)].
20673
R(x,C * C,y) = R(x,y * C,C).
[para(16(a,1),1258(a,2,2))].
20688
R(A,C * C,x * A) = R(A,C * x,A * C).
[para(1258(a,1),96(a,2)),rewrite([12(5),71(7),16(5),12(14),19180(15),7151(14)]),flip(a)].
20902 C'
* ((A * C) * x) = R(A * x,A,C').
[para(50(a,1),489(a,1,1,2)),rewrite([19511(12),1092(12),599(9),1963(11),16(5)])].
20910 C'
* ((C * A') * x) = R(A' * x,A',C').
[para(1841(a,1),489(a,1,1,2)),rewrite([16495(15),1103(13),1913(12),83(11),307(10)])].
20911
R((A * C) * x,A,C') = A * (C * x).
[para(1974(a,1),489(a,1,1,2)),rewrite([10(9),19511(9),1105(9),435(6),86(7),439(6)]),flip(a)].
20945 A
* (A * R(A' * x,A',C)) = R(A * x,A,C').
[back_rewrite(17820),rewrite([20902(18)])].
20947 A'
* R(A * x,A,C') = A * R(A' * x,A',C).
[back_rewrite(13536),rewrite([20902(9)])].
20948
R(R(A * x,A,C'),C,A) = R(A * x,A,C).
[back_rewrite(7326),rewrite([20902(7)])].
20953 A
* R(A' * x,A',C') = R(x,A,C).
[back_rewrite(11017),rewrite([20910(9)])].
21336 (A
* x) * (x' * (A' * x)) = x.
[para(1090(a,1),2161(a,1,2)),rewrite([4347(7),31(7),31(10)])].
21408 C'
* ((x * (A * C)) * A') = R(x,A * C,A').
[para(2162(a,1),397(a,1,2)),rewrite([16(3),461(10),507(11),107(9),16(13),461(19),507(20)])]
.
21589
R(x,A * C',C * A') = x.
[para(4871(a,1),522(a,1,1,2)),rewrite([871(5),461(4),3(7),461(9),19511(10),5075(10),871(14),461(13),16(17,R),4
61(21),2223(22),461(21,R),64(21),8(17),78(15)])].
21593
R(x,y,C * (z * z)) = R(x,y,z * (z * C)).
[para(12(a,1),2597(a,2,3))].
21664
R(x,C' * x,C') = x.
[para(483(a,2),2872(a,1,1)),rewrite([461(13,R),490(14)])].
21669
R(A' * C',(A * C) * x,y) = R(A * C,x,y)'.
[para(435(a,1),523(a,1,1)),rewrite([461(5)])].
21705
R(C * x,x,C') = C * x.
[para(10(a,1),21664(a,1,2))].
21801
R(x * (C * A'),A * C',A) = (x * A) / (A * (A * C')).
[para(2873(a,1),193(a,1,1,1)),rewrite([461(7),461(13),19511(14)]),flip(a)].
22051
R(x,A,(A' * x') * y)' = R(x',A,A' * y).
[para(4430(a,1),139(a,1,2)),rewrite([7254(8)]),flip(a)].
22113 (x
* (C * y)) * (x * (y * C))' = 0.
[para(4458(a,1),9(a,1,2))].
22115 (x
* (y * C))' * ((x * (C * y)) * z) = z.
[para(4458(a,1),10(a,1,1))].
22150
R(x * (C * y),(x * (y * C))',z) = x * (C * y). [para(4458(a,1),84(a,1,2))].
22446 x
/ (A * C) = x * (A' * C').
[para(435(a,1),561(a,1,1,2)),rewrite([461(5),9097(9),435(8),461(9)])].
22457 (x
* (A * (y * A))) * (A' * C') = R(C' * ((x * A) * y),C,A).
[back_rewrite(2004),rewrite([22446(9)])].
22459
R((C * x) * A',A,C) = C * (x * A').
[back_rewrite(1884),rewrite([22446(8),1272(10),507(8)]),flip(a)].
22510
(A' * x) * (x' * (A * A)) = A.
[para(1926(a,1),4873(a,1,2))].
22528
R(x',A,C * (A' * x)) = C / (A * (C * (A' * x))). [para(4874(a,1),18(a,1,1)),flip(a)].
22535
R(x',A,C * (A' * x))' = C' * (A * (C * (A' * x))). [para(4874(a,1),139(a,1,2)),rewrite([107(9)]),flip(a)].
22536 C
* R(x',A,C * (A' * x))' = A * (C * (A' * x)). [para(4874(a,1),751(a,1,2)),rewrite([16(11,R)])].
22731
R(x',A',C * (A * x))' = R(x,A',A * C).
[para(5101(a,1),139(a,1,2)),rewrite([2368(7),107(9),12030(10)]),flip(a)].
22732 C
* R(x,A',A * C) = A * ((C * A') * x).
[para(5101(a,1),751(a,1,2)),rewrite([22731(9),16(8,R),2368(15)])].
23298
R(x,C * C,y * (C' * C')) = R(x,C' * y,C).
[para(7638(a,1),81(a,1,1,1,2)),rewrite([1272(11),5133(9),921(7),7638(12)]),flip(a)].
23577 (x
* A) * x = x * (A * x).
[para(7(a,1),8948(a,2,2)),rewrite([871(3),871(6),4435(6),35(8),1708(4),871(6)]),flip(a)].
23591 (A
* (x' * x')) * (x * (x * A')) = 0.
[para(8948(a,1),137(a,1,2)),rewrite([18141(4)])].
23622 (x
* (A * x)) / x = x * A.
[para(23577(a,1),6(a,1,1))].
23626 (x
* (A * (x * y))) / (x * y) = R(x * A,x,y). [para(23577(a,1),18(a,1,1,1)),rewrite([13(4)])].
23627
R(x,A,x) = x.
[para(23577(a,1),18(a,1,1)),rewrite([6(6)]),flip(a)].
23629 x
/ (x * (A * x)) = A' * x'.
[para(23577(a,1),33(a,1,2)),rewrite([4435(7)])].
23649 (x
* (A * x)) / (A' * x') = x * (A * (x * (x * A))).
[para(23577(a,1),1708(a,1,1)),rewrite([4435(6),15944(14),12(12)])].
23750
R(A * x,A,A' * C') = C * (A * (x * C')).
[para(50(a,1),617(a,1,2,1)),rewrite([461(10),1102(11),435(6),86(7),439(6),461(15)]),flip(a)].
23757
R(A' * x,A',A * C') = C * (A' * (x * C')).
[para(1841(a,1),617(a,1,2,1)),rewrite([31(12),461(11),13(12),10(10),31(18),461(17)]),flip(a
)].
23759
R((A * C) * x,A,A' * C') = C * R(A * x,A,C).
[para(1974(a,1),617(a,1,2,1)),rewrite([461(12),22457(13),16(6),20902(8),20948(10),461(17)
]),flip(a)].
23921
R(C' * x,C,y) = R(C / x,x,y)'.
[para(107(a,1),625(a,1,1))].
23922 C
* R(x / y,y,z) = C * R(y / x,x,z)'.
[para(625(a,2),111(a,1,1)),rewrite([16(4,R)])].
23940
R(x * (y' * x),x' * y,z) = R(x' * (y * x'),x,z)'. [para(1750(a,1),625(a,2,1,1)),rewrite([1707(3)])].
24003 (x
* A) / (A * (y * A)) = (x / y) * A'.
[para(625(a,1),193(a,2)),rewrite([7(6),3914(12),2076(11),112(9)])].
24058
R(C / (C / x),C' / x,y) = R(C * (C' / x),C',y)'. [para(1080(a,1),625(a,1,1)),rewrite([599(14)])].
24111
R(x / (A * y),A * y,A) = (x / y) * A'.
[back_rewrite(854),rewrite([24003(14)])].
24287 C
* R(A * x,A,C') = (A * C) * x. [para(9131(a,1),12(a,2,2)),rewrite([604(7),16(4),50(6),16(5),46(14),13530(11),20945(12)])].
24290
R(A,C,(A' * C') * x) = x / R(A' * x,A',C). [para(9131(a,1),18(a,1,1)),rewrite([13530(8)]),flip(a)].
24293 C
* (A * (C * (A * R(A' * x,A',C)))) = (A * C) * (C * x).
[para(9131(a,1),69(a,2,2,2)),rewrite([16(8,R),1255(8),7558(9),16(5),50(7),16
(6),8182(9),1422(9),1533(16),13530(12)])].
24294
R(A,C,(A' * C') * x)' = R(A' * x,A',C) / x. [para(9131(a,1),139(a,1,2)),rewrite([13530(8)]),flip(a)].
24295
R(A,C,(A' * C') * x)' * x = R(A' * x,A',C). [para(9131(a,1),751(a,1,2)),rewrite([13530(19)])].
24297 A
* (C * (A * ((A' * C') * x))) = C * ((A * C') * x).
[para(9131(a,1),479(a,2,2,2)),rewrite([461(9,R),64(9),50(5),16(4),69(12),2290(19
),461(17)])].
24307
R(A',C',(A * C) * x) = x / R(A * x,A,C').
[para(9182(a,1),18(a,1,1)),rewrite([20902(7)]),flip(a)].
24311 A'
* (C' * (A' * ((A * C) * x))) = R(A' * x,A',C').
[para(9182(a,1),69(a,2,2,2)),rewrite([16(12,R),507(12),1841(8),461(7),479(13),2312
(21),20910(21)])].
24312 R(A',C',(A
* C) * x)' = R(A * x,A,C') / x.
[para(9182(a,1),139(a,1,2)),rewrite([20902(7)]),flip(a)].
24315 C
* (A * ((A' * C') * x)) = R(x,A',A * C').
[para(9182(a,1),2883(a,1,2)),rewrite([64(12),1913(8),461(7),2223(8),461(7,R),3069(8),599(1
1),64(21),2676(17),461(16)])].
24320 A
* R(x,A',A * C') = C * ((A * C') * x).
[back_rewrite(24297),rewrite([24315(11)])].
24454
R(C / x,C' * (C' * x),y) = R(C' * x,C',y)'. [para(461(a,2),634(a,1,2))].
24474 (C
* x) / (y * x) = R(C' * y,C,x)'.
[para(634(a,1),398(a,2)),rewrite([16(7,R),35(7),7(3),35(7)])].
24549
R(C * (C' / x),C',(C * x) * y)' = R(x,C',y * C).
[para(10972(a,1),126(a,1,1,1)),rewrite([112(6),599(5),2582(7),112(16),599(15),24058(1
6)]),flip(a)].
24707
R(x,C,A') = R(x,A,C).
[para(13522(a,1),18(a,1)),rewrite([2223(10),461(9,R),3069(10),2548(9),20910(9),20953(10)]),flip(a)].
24710 A
* ((A' * C') * x) = R(C' * x,A,C).
[para(13522(a,1),80(a,2)),rewrite([107(2),24707(7),2223(14),461(13,R),3069(14)]),flip(a)].
24719 A
* R(A' * x,A',C) = R(x,A',C).
[para(13522(a,1),102(a,1)),rewrite([15932(10),461(9,R),20902(9),20947(9)])].
24741
R(C' * (A' * x),A,C) = A' * (x * C').
[back_rewrite(13529),rewrite([24707(10)])].
24747 C
* R(C' * x,A,C) = R(x,A',A * C').
[back_rewrite(24315),rewrite([24710(9)])].
24751 A
* R(C' * x,A,C) = C' * (A * x).
[back_rewrite(20538),rewrite([24710(9)])].
24752 (C
* A') * (x * (A * C')) = A' * (x * A).
[back_rewrite(13527),rewrite([24710(15),24741(13),461(9,R),10(9)]),flip(a)].
24756 A'
* (C' * (A * x)) = R(C' * x,A,C).
[back_rewrite(3069),rewrite([24710(16)])].
24758 C
* (A * (C * R(x,A',C))) = (A * C) * (C * x). [back_rewrite(24293),rewrite([24719(12)])].
24759 A'
* R(A * x,A,C') = R(x,A',C).
[back_rewrite(20947),rewrite([24719(18)])].
24760 A
* R(x,A',C) = R(A * x,A,C').
[back_rewrite(20945),rewrite([24719(10)])].
24763
R(x,A',C) = R(x,A,C').
[back_rewrite(24719),rewrite([24760(9),35(5)]),flip(a)].
24764 A
* R(x,A,C') = R(A * x,A,C').
[back_rewrite(24760),rewrite([24763(5)])].
24765 A'
* R(A * x,A,C') = R(x,A,C').
[back_rewrite(24759),rewrite([24763(13)])].
24766 C
* (A * (C * R(x,A,C'))) = (A * C) * (C * x). [back_rewrite(24758),rewrite([24763(7)])].
24769
R(A,C,(A' * C') * x)' * x = R(A' * x,A,C'). [back_rewrite(24295),rewrite([24763(18)])].
24770
R(A,C,(A' * C') * x)' = R(A' * x,A,C') / x. [back_rewrite(24294),rewrite([24763(17)])].
24772
R(A,C,(A' * C') * x) = x / R(A' * x,A,C'). [back_rewrite(24290),rewrite([24763(16)])].
24776 A
* (R(A' * x,A,C') * A) = C * ((x * C') * A). [back_rewrite(13537),rewrite([24763(8)])].
24777 C
* ((A' * C') * x) = R(A' * x,A,C').
[back_rewrite(13530),rewrite([24763(15)])].
24782
R(C / x,x,A') = R(C' * x,A,C)'.
[para(24707(a,1),625(a,2,1)),rewrite([107(7)])].
24784 C
* ((C' * x) * A) = R(x * A,A,C').
[para(24763(a,1),80(a,1)),rewrite([871(3),16(12,R),13522(13),2836(13)]),flip(a)].
24901
R(A',x * A',x) = A'.
[para(16083(a,1),93(a,1,2)),rewrite([6(12)]),flip(a)].
24959
R(A',x,x * A) = A'.
[para(7(a,1),24901(a,1,2)),rewrite([871(5)])].
24981
R(x * C,y,z)' * R(C * x,y,z) = 0.
[para(643(a,1),8(a,1,1))].
24982
R(C * x,y,z)' * R(x * C,y,z) = 0.
[para(643(a,2),8(a,1,1))].
25120
R(A,x,A * (x * A))' = A'.
[para(50(a,1),24959(a,1,3)),rewrite([143(9)])].
25200
R(A,x,A * (x * A)) = A.
[para(25120(a,1),31(a,1,1)),rewrite([31(3)]),flip(a)].
25224 C
* (A * (C' * (A' * x))) = R(x,A,A' * C').
[para(25120(a,1),617(a,1,2,2,2)),rewrite([25200(7),461(8),2237(9),461(8,R),25200(16),25200
(19),461(16)])].
25312
(A' * (x * x)) * x' = A' * x.
[para(16206(a,1),18(a,2)),rewrite([19948(4),9(8),24(8)])].
25351
R(C / x,C * x,y) = R(x * C',C * C,y)'.
[para(1222(a,2),646(a,1,2)),rewrite([507(8)])].
25374 (x
* (A' * C'))' = (A * C) / x.
[para(16494(a,1),33(a,1,2)),flip(a)].
25377
R(x,A',C') = R(x,A,C).
[para(79(a,1),16494(a,1,1)),rewrite([461(6,R),15932(10),16(9,R),11029(10)]),flip(a)].
25389 (A
* x) / R(x,A',A * C') = R(A,R(C' * x,A,C),C).
[para(16494(a,1),93(a,1,1,2)),rewrite([1913(10),461(9),2223(10),461(9,R),24756(10),16
(10,R),24747(10),1913(19),461(18),2223(19),461(18,R),24756(19)])].
25392
R(x * (A' * C'),A * C,A') = C' * (x * A').
[para(16494(a,1),150(a,1,2,1)),rewrite([559(7),435(7),461(8),507(9),559(20),435(20),461(21)
,507(22)]),flip(a)].
25406 A'
* (C' * (A' * ((A * C) * x))) = R(A' * x,A,C). [back_rewrite(24311),rewrite([25377(21)])].
25411 C'
* ((C * A') * x) = R(A' * x,A,C).
[back_rewrite(20910),rewrite([25377(16)])].
25415 C'
* ((C * x) * A) = R(x * A,A,C).
[para(25377(a,1),80(a,1)),rewrite([871(3),16495(14),2548(12)]),flip(a)].
25426
R(x,A * C,A' * C') = x.
[para(16495(a,1),7(a,1,1)),rewrite([16660(10)])].
25466 (x
* (A * C)) * (A' * C') = x.
[back_rewrite(16660),rewrite([25426(19)])].
25475 (A
* (x * A)) / (A * ((C * x) * A)) = R(C,A,x * A)'. [para(15(a,1),649(a,1,2))].
25551 C
/ (A * (C * x)) = C / (A * (x * C)).
[para(123(a,1),653(a,1,1)),rewrite([123(8),8970(14),141(14)]),flip(a)].
25645 x
/ R(C' * x,A,C) = R(C',A,A' * x)'.
[para(9131(a,1),654(a,1,1)),rewrite([461(6,R),64(6),24710(8),629(19),22051(17)])].
25736
R(x,C' * y,C) * y = C * (x * (C' * y)).
[para(16(a,2),750(a,2)),rewrite([107(2),107(9)])].
25747
R(x,y * A,A') * y = (x * (y * A)) * A'.
[para(871(a,1),750(a,1,1,2)),rewrite([871(9)])].
25813
R(x,y * C',C) * y = C * (x * (y * C')).
[para(7634(a,1),750(a,1,1,2)),rewrite([3408(10),7634(13),1272(17),35(15)])].
25843
R(x,A',A * C) = R(x,A,C').
[para(19511(a,1),18(a,1)),rewrite([461(5,R),1092(10),599(7),3095(9),12030(10)])].
25872 A
* ((C * A') * x) = C * R(x,A,C').
[back_rewrite(22732),rewrite([25843(7)]),flip(a)].
25877 C'
* (A' * (x * C)) = R(A' * x,A,C').
[back_rewrite(8670),rewrite([25843(9)]),flip(a)].
25898 A
* (C * R(x,A,C')) = C * (A * x).
[back_rewrite(4775),rewrite([25872(8)])].
25899 (C
* (x * A)) * A' = C * R(x,A,C').
[back_rewrite(3095),rewrite([25872(14)])].
25906 A'
* (C * (A * x)) = C * R(x,A,C').
[back_rewrite(2368),rewrite([25872(14)])].
25908 (A
* C) * (C * x) = C * (C * (A * x)).
[back_rewrite(24766),rewrite([25898(9)]),flip(a)].
26305 A
* (C' * (A' * x)) = R(C' * x,C,A).
[para(22446(a,1),838(a,1)),rewrite([2237(8),461(7,R)])].
26332 C
* R(C' * x,C,A) = R(x,A,A' * C').
[back_rewrite(25224),rewrite([26305(9)])].
26355
R(C,A',C' * (A * A)) = C.
[para(22510(a,1),98(a,1,1)),rewrite([18795(10),508(6)]),flip(a)].
26365
R(C',A',A * (A * C)) = C'.
[para(22510(a,1),486(a,1,1)),rewrite([31(6),67(8),10(9),116(5),31(9),67(11)]),flip(a)].
26432 (C
* (C * (x * y))) / y = C * (C * R(x,y,C)). [para(758(a,1),40(a,1,1,2)),rewrite([16(11,R)])].
26443
R(R(x,y,C),C * y,C') = x.
[para(758(a,1),462(a,1,1,2)),rewrite([10(6),6(2)]),flip(a)].
26446
R(x / y,y,C)' * (C * x) = C * y.
[para(625(a,1),758(a,1,1)),rewrite([7(10)])].
26451
R(R(x,y,C),y * C,C') = x.
[para(16(a,1),26443(a,1,2))].
26452
R(R(x,C' * y,C),y,C') = x.
[para(35(a,1),26443(a,1,2))].
26458
R(R(x,y * C',C),y,C') = x.
[para(2835(a,2),26443(a,1,2)),rewrite([35(10)])].
26483
R(R(x / y,y,C)',C * x,C') = y / x.
[para(625(a,1),26443(a,1,1))].
26516
R(R(x,y,A),y * A,A) = R(x,y,A * A).
[para(1926(a,1),759(a,1,1)),rewrite([1926(9),18(10)]),flip(a)].
26529
R(x,C' * C',y) = R(x,C' * y,C').
[para(17790(a,1),759(a,2,1)),rewrite([461(6,R),13(7),12(13),490(14)]),flip(a)].
26538
R(R(x,y,C),C * C,y) = R(x,y,C * C).
[para(20673(a,2),759(a,2)),rewrite([16(3,R),16(5,R),16(9,R),7556(10)]),flip(a)].
26601 C'
* (A' * ((A * C) * x)) = R(x,A',A * (C * C)). [para(11845(a,1),760(a,1,1,1,2)),rewrite([1255(8),2223(9),1222(8,R),2815(9),2223(8),1
6(13,R),2223(17),16(16,R),1255(16),10(17),1863(13),461(14,R),10(14),11845(17),1255(17)])].
26602
R(x,C,A * C) = R(x,A,C * C).
[para(12199(a,1),760(a,1,1,1,2)),rewrite([1090(10),435(8),1090(9),435(7),123(9),2377(6),46(16),123(14),12
55(11),1679(12),86(5),439(4),12199(14),1090(14),435(12),1090(13),435(11),123(13)]),flip(a)].
26606
R(x * A,A,C') * A' = R(x,C,A * C').
[para(26355(a,1),760(a,1,1,1,2)),rewrite([18795(11),2836(7),24784(7),1102(17),107(11),461(12),1092
(16),871(14),461(13),50(15),461(14),10(16),507(12),435(8),26355(19),18795(19)])].
26609 A'
* R(x,A',A * (C * C)) = R(A' * x,A,C).
[back_rewrite(25406),rewrite([26601(12)])].
27076
R(x,A * C,A) * (A * (A * C)) = (x * (A * C)) * A. [para(16(a,1),769(a,1,2,2))].
27088
R(x * (A * C),A' * C',C) = (C * x) * A.
[para(25466(a,1),101(a,1,1,2)),rewrite([16(9,R),507(9),871(5)]),flip(a)].
27089
R(x,C,A) = R(x,A,C').
[para(757(a,1),25466(a,1,1)),rewrite([2237(10),461(9,R),25877(9),24764(9),35(5)]),flip(a)].
27093 A'
* ((x * (A * C)) * A') = C * (A' * x).
[para(25466(a,1),40(a,1,1,2)),rewrite([599(6)]),flip(a)].
27102
R(x * (A * C),A',A * C') = C * (x * A).
[para(25466(a,1),617(a,1,2,1)),rewrite([494(9),871(7),16(6),64(7),494(21),871(19),16(18),64(19
),2676(15),461(14)]),flip(a)].
27109 C
* R(C' * x,A,C') = R(x,A,A' * C').
[back_rewrite(26332),rewrite([27089(7)])].
27110 A
* (C' * (A' * x)) = R(C' * x,A,C').
[back_rewrite(26305),rewrite([27089(14)])].
27115
R(R(A * x,A,C'),A,C') = R(A * x,A,C).
[back_rewrite(20948),rewrite([27089(9)])].
27117
R(R(x,A,C * A'),A,C') = x.
[back_rewrite(12115),rewrite([27089(9)])].
27118
R(R(x,A,C'),A * C,A) = R(x,C,A * A).
[back_rewrite(12031),rewrite([27089(3)])].
27120
R(x,A,C') * (A * C) = (x * C) * A.
[para(27089(a,1),79(a,1,1)),rewrite([16(7)])].
27127 C'
* (x * (A * C)) = R(x * A,A,C').
[para(25843(a,1),80(a,1)),rewrite([871(3),10(16),107(12)]),flip(a)].
27134
R(x,A * C,C') = R(x,C,A * C').
[back_rewrite(19976),rewrite([27127(7),26606(9)]),flip(a)].
27203
R(x * A,A,C) * A' = R(x,C',A * C).
[para(26365(a,1),760(a,1,1,1,2)),rewrite([10(11),2548(7),25415(7),461(10),2978(16),2223(15),50(14),
16(13),10(15),64(11),435(7),26365(18),10(18)])].
27214
R(x,A * C',C) = R(x,A * C',A).
[para(26452(a,1),12026(a,1,1)),rewrite([461(10)]),flip(a)].
27220
R(R(x,A' * C',C),A,C) = x.
[para(26452(a,1),25377(a,1)),rewrite([461(5)]),flip(a)].
27223
R(A * x,A * C',A) = C * ((A * C') * x).
[back_rewrite(2869),rewrite([27214(8)])].
27321
R(C * x,x * C',C / x) = C * x.
[para(21705(a,1),779(a,1,1)),rewrite([494(9),461(14,R),4780(14),494(18),18619(17)])].
27412
R(x,A * C',A) = R(x,A,C * A').
[para(27117(a,1),12026(a,1,1))].
27413 C'
* (A * (C * x)) = C * ((A * C') * x).
[back_rewrite(27223),rewrite([27412(8),8970(8)])].
27415
R(x,A * C',C) = R(x,A,C * A').
[back_rewrite(27214),rewrite([27412(12)])].
27417
R(x * (C * A'),A,C * A') = (x * A) / (A * (A * C')). [back_rewrite(21801),rewrite([27412(11)])].
27421
((x * (A * C')) * A) / (A * (A * C')) = R(x,A,C * A'). [back_rewrite(12025),rewrite([27412(20)])].
27422
R(x',A,C * (A' * x))' = R(x,A',A * C').
[back_rewrite(22535),rewrite([27413(19),1102(18),435(15),461(16),24710(18),24747(17)])].
27425
R(A * x,A,C * A') = C * ((A * C') * x).
[back_rewrite(8970),rewrite([27413(15)])].
27428 C
* R(x,A',A * C') = A * (C * (A' * x)).
[back_rewrite(22536),rewrite([27422(10)])].
27433 C
* (R(x,A' * C',C) * A) = x * (A * C).
[para(27220(a,1),79(a,1,1)),rewrite([16(15,R)]),flip(a)].
27434
R((x * C) * A,A,C) = x * (A * C).
[para(80(a,1),27220(a,1,1)),rewrite([16(9,R),507(9),871(5),16495(13)])].
27435
R(x,A' * C',C) = R(x,A * C,A).
[para(27220(a,1),12026(a,1,1)),flip(a)].
27441
R(x,A * C,A) = R(x,C,A * C').
[para(27220(a,1),26443(a,1,1)),rewrite([16(3),27134(6),27435(13)]),flip(a)].
27442
R(R(x,C,A * C'),A,C) = x.
[para(27220(a,1),779(a,1,1)),rewrite([559(7),435(7),461(8),25426(9),27435(7),27441(5),2870(8),24784(7),16(8,
R),559(12),435(12),461(13),2224(14),10942(14),26606(9)]),flip(a)].
27443 C
* R(x * A,A,C') = x * (A * C).
[back_rewrite(27433),rewrite([27435(8),27441(6),2870(9),24784(8)])].
27444
R(x * (A * C),C,A * C') = (C * x) * A.
[back_rewrite(27088),rewrite([27435(11),27441(9)])].
27448
R(x,A' * C',C) = R(x,C,A * C').
[back_rewrite(27435),rewrite([27441(12)])].
27449
R(R(x,A,C'),C,A * C') = R(x,C,A * A).
[back_rewrite(27118),rewrite([27441(9)])].
27450
R(x,C,A * C') * (A * (A * C)) = (x * (A * C)) * A. [back_rewrite(27076),rewrite([27441(5)])].
27491 C
* (A * ((C * x) * A)) = A * (C * (C * (x * A))). [para(1974(a,1),783(a,2)),rewrite([783(12),25908(6),71(8),16(6),74(7),16078(8)]),fl
ip(a)].
27502 C
* R(x,A * C,A') = (x * (A * C)) * A'.
[para(2162(a,1),783(a,1,2)),rewrite([16(3),461(9),507(10),16(8,R),16(11),461(18),507(19)])].
27519 x
/ (A * (y * A)) = ((x * A') / y) * A'.
[para(50(a,1),825(a,2,2)),rewrite([435(2),24111(10)]),flip(a)].
27520
R((x * A') / y,y,A) = x / (y * A).
[para(435(a,1),825(a,1,1,1))].
27521
R(C * (x / y),C',y) = x / (y * C').
[para(461(a,1),825(a,2,2)),rewrite([599(4)])].
27524
R((x * A) / y,y,A') = x / (y * A').
[para(871(a,1),825(a,1,1,1))].
27541
R(R(x,C * y,C'),y,C) = x.
[para(2585(a,1),825(a,2)),rewrite([107(5),462(7)])].
27593
R(C' * (x * A),A,C) = x * (A * C').
[para(13522(a,1),825(a,2)),rewrite([871(3),107(4),24707(9)])].
27599
R((C * x) * A,A,C) = x * (A * C).
[para(825(a,1),25377(a,1)),rewrite([16495(6),599(7),871(9)]),flip(a)].
27611 (x
* (A * C')) * A' = R(C' * x,A,C').
[para(825(a,1),27117(a,1,1)),rewrite([123(6),107(2),13522(12),435(14)]),flip(a)].
27612 C'
* (x * (C * A')) = R(x * A',A,C).
[para(825(a,1),27442(a,1,1)),rewrite([507(6),435(2),19511(11),107(13)]),flip(a)].
27613
R(A * C',C,x) * A' = R(C,A,x * A)'.
[back_rewrite(25475),rewrite([27519(11),1090(7),435(5),86(6),439(5),847(5),461(4)])].
27622
R(A * C,C,x) * A' = R(C,A * x,A * C).
[back_rewrite(11948),rewrite([27519(15),1090(11),435(9),25899(10),25898(10),1593(9),1255(7),1245
(8),16(3)])].
27623
((A * (C * (x * C))) / (C * x)) * A' = R(C,A * C,x * A).
[back_rewrite(7627),rewrite([27519(15),1090(11),435(9),17540(10),439(9)])].
27625
R(A * C,C',x) * A' = R(C',A,x * A)'.
[back_rewrite(7220),rewrite([27519(12),1090(7),435(5),86(6),439(5),4010(6),16(3)])].
27643
R(x * A',A,C) * A = R(x,C * A',C').
[back_rewrite(19978),rewrite([27612(8)])].
27644
R(x * (y * A'),A,C * A') = R(x * (y * A'),A,C). [back_rewrite(9012),rewrite([27612(14),1841(9),3904(8),10(9)]),flip(a)].
27649 (x
* A) / (A * (A * C')) = R(x * (C * A'),A,C). [back_rewrite(27417),rewrite([27644(11)]),flip(a)].
27650
R(x,A,C * A') = R(x,A,C).
[back_rewrite(27421),rewrite([27649(14),5075(10),21589(9)]),flip(a)].
27652 C
* ((A * C') * x) = R(A * x,A,C).
[back_rewrite(27425),rewrite([27650(8)]),flip(a)].
27656
R(x,A * C',C) = R(x,A,C).
[back_rewrite(27415),rewrite([27650(12)])].
27658
R(x,A * C',A) = R(x,A,C).
[back_rewrite(27412),rewrite([27650(12)])].
27660
R(R(x,A,C),A,C') = x.
[back_rewrite(27117),rewrite([27650(6)])].
27662 C'
* (A * (C * x)) = R(A * x,A,C).
[back_rewrite(27413),rewrite([27652(14)])].
27664 A
* R(x,A',A * C') = R(A * x,A,C).
[back_rewrite(24320),rewrite([27652(16)])].
27670
R(x,C,A * C') = R(x,A,C').
[para(27442(a,1),27660(a,1,1)),flip(a)].
27671
R(x * (A' * C'),A,C') = (C' * x) * A'.
[para(825(a,1),27660(a,1,1)),rewrite([22446(4),107(12),435(15)])].
27674
R(x,A,C') * (A * (A * C)) = (x * (A * C)) * A. [back_rewrite(27450),rewrite([27670(6)])].
27675
R(R(x,A,C'),A,C') = R(x,C,A * A).
[back_rewrite(27449),rewrite([27670(10)])].
27676
R(x,A' * C',C) = R(x,A,C').
[back_rewrite(27448),rewrite([27670(13)])].
27679
R(x * (A * C),A,C') = (C * x) * A.
[back_rewrite(27444),rewrite([27670(10)])].
27680
R(R(x,A,C'),A,C) = x.
[back_rewrite(27442),rewrite([27670(6)])].
27681
R(x,A * C,A) = R(x,A,C').
[back_rewrite(27441),rewrite([27670(11)])].
27683
R(x * A,A,C') * A' = R(x,A,C').
[back_rewrite(26606),rewrite([27670(15)])].
27684
R(A * x,C,A * A) = R(A * x,A,C).
[back_rewrite(27115),rewrite([27675(10)])].
27685
R(x,A,C') * A = R(x * A,A,C').
[para(27670(a,1),79(a,1,1)),rewrite([507(10),2836(13),24784(13)])].
27691
R(A * (x * A),A,C') * y = A * (R(x,A,C') * (A * y)). [para(27670(a,1),754(a,1,2,1)),rewrite([507(6),507(11),507(15),2836(17),24784(17)
,24764(17)]),flip(a)].
27694 C
* ((x * C') * A) = R(x * A,A,C').
[back_rewrite(24776),rewrite([27685(10),1089(6),871(6),24764(11),35(7)]),flip(a)].
27695 (A
* (x * A)) / R(x * A,A,C') = R(A,C,(x * C') * A). [back_rewrite(7044),rewrite([27694(11)])].
27709 (A
* ((x * C) * A)) / R(A * (x * A),A,C') = C.
[para(27685(a,1),106(a,1,2,2)),rewrite([27120(9),24764(14)])].
27726
R(x,A * C,A') = R(x,C,A * A).
[para(27685(a,1),489(a,1,1,2)),rewrite([19511(14),1092(14),599(11),27443(10),21408(10),27675(14)])].
27745 C
* R(x,A,C') = R(C * x,A,C').
[para(825(a,1),27685(a,1,1)),rewrite([19511(5),2153(7),16(6,R),25906(7),599(9),435(10),83(13),307(12)])
].
27749 C
* R(x,C,A * A) = (x * (A * C)) * A'.
[back_rewrite(27502),rewrite([27726(7)])].
27752
R(x * (A' * C'),C,A * A) = C' * (x * A').
[back_rewrite(25392),rewrite([27726(12)])].
27753 C'
* ((x * (A * C)) * A') = R(x,C,A * A).
[back_rewrite(21408),rewrite([27726(16)])].
27755 C'
* (A * (x * C)) = R(A * x,A,C).
[back_rewrite(8990),rewrite([27726(8),27684(7)]),flip(a)].
27756
R(C * (x * A),A,C') = x * (A * C).
[back_rewrite(27443),rewrite([27745(8)])].
27758
R(x,A,A' * C') = R(x,A,C').
[back_rewrite(27109),rewrite([27745(9),35(5)]),flip(a)].
27764 A'
* (C * (A * x)) = R(C * x,A,C').
[back_rewrite(25906),rewrite([27745(13)])].
27769 (C
* (x * A)) * A' = R(C * x,A,C').
[back_rewrite(25899),rewrite([27745(13)])].
27770
R(A * (C * x),A,C') = C * (A * x).
[back_rewrite(25898),rewrite([27745(7),24764(8)])].
27776 A
* ((C * A') * x) = R(C * x,A,C').
[back_rewrite(25872),rewrite([27745(13)])].
27778
R(C * (A * x),A,C') = (A * C) * x.
[back_rewrite(24287),rewrite([27745(8)])].
27781 C
* R(A * x,A,C) = A * (C * x).
[back_rewrite(23759),rewrite([27758(11),20911(8)]),flip(a)].
27782 C
* (A * (x * C')) = R(A * x,A,C').
[back_rewrite(23750),rewrite([27758(9)]),flip(a)].
27783 C
* (x * (A' * C')) = R(x * A',A,C').
[back_rewrite(1666),rewrite([27758(10)]),flip(a)].
27795
R(x * A',A,C * (C * x')) = R(x * A',A,C'). [back_rewrite(2089),rewrite([27783(18)])].
27908
R(R(A * x',x,C')',A,C) = x * A'.
[para(625(a,1),27680(a,1,1)),rewrite([2061(2),435(12)])].
27909
R(x * (C * A'),A,C) = (C * x) * A'.
[para(825(a,1),27680(a,1,1)),rewrite([19511(5),599(11),435(12)])].
27935
R(R(x,y,C'),C' * y,C) = x.
[para(35(a,1),27541(a,1,1,2))].
27943
R(R(x,y,C'),y * C',C) = x.
[para(2835(a,2),27541(a,1,1,2)),rewrite([35(5)])].
28001 (x
* A) * (C * A') = C * R(x,A,C).
[para(27650(a,1),79(a,1,1)),rewrite([123(9),16(5,R)]),flip(a)].
28004 C
/ (A * (x * C)) = R(A * x,A,C)'.
[para(27650(a,1),653(a,2,1)),rewrite([123(6),123(8)])].
28006 C
* R(x * C',A,C) = R(x,C',A).
[back_rewrite(19809),rewrite([28001(10)])].
28007 C
/ (A * (C * x)) = R(A * x,A,C)'.
[back_rewrite(25551),rewrite([28004(12)])].
28008
R(x',A,C * (A' * x)) = R(x,A,C)'.
[back_rewrite(22528),rewrite([28007(17),35(13)])].
28012
R(x,A',A * C') = R(x,A,C).
[back_rewrite(27422),rewrite([28008(8),31(5)]),flip(a)].
28013 A
* R(x,A,C) = R(A * x,A,C).
[back_rewrite(27664),rewrite([28012(8)])].
28014 A
* (C * (A' * x)) = C * R(x,A,C).
[back_rewrite(27428),rewrite([28012(8)]),flip(a)].
28015
R(x * (A * C),A,C) = C * (x * A).
[back_rewrite(27102),rewrite([28012(11)])].
28016
R(A,R(C' * x,A,C),C) = (A * x) / R(x,A,C). [back_rewrite(25389),rewrite([28012(9)]),flip(a)].
28019 C
* (A' * (x * C')) = R(A' * x,A,C).
[back_rewrite(23757),rewrite([28012(10)]),flip(a)].
28022
R(A * (C' * x),A,C) = C' * (A * x).
[back_rewrite(24751),rewrite([28013(8)])].
28026 C
* R(C * (x * A),A,C) = x * (A * (C * C)).
[back_rewrite(1929),rewrite([28014(11)])].
28028 (C
* ((x * C') * y)) / y = R(R(x,C',y),y * C',C). [para(786(a,1),101(a,1,1,2)),rewrite([16(11,R),507(11)])].
28038
R(x,C',A') = R(x,A,C').
[para(786(a,1),16494(a,1,1)),rewrite([2223(10),16(9,R),27782(9),24765(9)]),flip(a)].
28040 (x
* (C' * C')) * y = C' * (x * (C' * y)).
[para(786(a,1),753(a,2,1)),rewrite([17790(5),753(13),461(13,R),13(14)])].
28043
R(x,C' * C',y * (C * C)) = R(x,C * y,C').
[back_rewrite(10762),rewrite([28040(11),1245(9),462(7)]),flip(a)].
28050 C
* (x * (A * C')) = R(x,A,C) * A.
[para(27656(a,1),79(a,1,1)),rewrite([16(9,R),507(9),16(12,R)]),flip(a)].
28074 x
/ (A * (A * C)) = (C' * (x * A')) * A'.
[para(27681(a,1),825(a,1)),rewrite([435(2),22446(7),27671(13),50(14),16(13)]),flip(a)].
28102
R(x,C,A * A) * (A * C') = C' * R(x * A,A,C'). [para(27685(a,1),788(a,2,2)),rewrite([27675(8),461(9)])].
28159
R(R(x,y,C')',C' * (x * y),C) = x'.
[para(27935(a,1),143(a,2,1)),rewrite([788(11)])].
28250
R(R(x / y,y,C')',x * C',C) = y / x.
[para(625(a,1),27943(a,1,1))].
28314 C'
* R(x,A,C) = R(C' * x,A,C).
[para(28012(a,1),79(a,1,1)),rewrite([10(10),461(6,R),2223(14),461(13,R),24756(14)])].
28315
R(x,A,C) * A = R(x * A,A,C).
[para(28012(a,1),80(a,1)),rewrite([871(3),10(17),599(13),28050(12)]),flip(a)].
28326 C
* (x * (A * C')) = R(x * A,A,C).
[back_rewrite(28050),rewrite([28315(12)])].
28327
R(x,C * A',C') = R(x,A,C).
[back_rewrite(27643),rewrite([28315(8),83(5),307(4)]),flip(a)].
28332
R(A * x,A,C) / R(x,A,C) = A.
[para(28013(a,1),6(a,1,1))].
28334
R(x,A,C) / R(A * x,A,C) = A'.
[para(28013(a,1),33(a,1,2))].
28342
R(A * (C * x),A,C) = R(A * (x * C),A,C).
[para(2536(a,1),28013(a,2,1)),rewrite([28013(7)])].
28465
R(x,C',A * C) = R(x,A,C).
[para(28315(a,1),6(a,1,1)),rewrite([435(7),27203(8)])].
28466
R(x,A,C)' * R(x * A,A,C) = A.
[para(28315(a,1),10(a,1,2))].
28472
R(R(x,A,C),A,C) = R(x,A,C').
[para(28315(a,1),101(a,1,1,2)),rewrite([22446(11),2224(13),28314(9),27593(9),27611(9),27745(9),35(5)]),fl
ip(a)].
28475
R(x,A,C) * (A * A) = R(x * (A * A),A,C).
[para(28315(a,1),1926(a,1,1)),rewrite([28315(7),1926(4)]),flip(a)].
28507 C
* R(x * A,A,C) = (x * C) * A.
[para(28315(a,1),758(a,2,2)),rewrite([28472(6),16(7),27120(8)]),flip(a)].
28518 (x
* (A * C)) * A' = R(C * x,A,C).
[para(28465(a,1),80(a,1)),rewrite([599(3),64(15),435(11)]),flip(a)].
28522
R(x,C,A * A) = R(x,A,C).
[back_rewrite(27753),rewrite([28518(9),28314(8),10(5)]),flip(a)].
28523 C
* R(x,A,C) = R(C * x,A,C).
[back_rewrite(27749),rewrite([28522(6),28518(12)])].
28526 A'
* R(C * x,A,C) = C * (A' * x).
[back_rewrite(27093),rewrite([28518(9)])].
28534
R(x,A,C) * (A * C') = C' * R(x * A,A,C').
[back_rewrite(28102),rewrite([28522(5)])].
28535
R(x * (A' * C'),A,C) = C' * (x * A').
[back_rewrite(27752),rewrite([28522(11)])].
28536
R(x,A * C,A') = R(x,A,C).
[back_rewrite(27726),rewrite([28522(11)])].
28537
R(R(x,A,C'),A,C') = R(x,A,C).
[back_rewrite(27675),rewrite([28522(13)])].
28538
R(C * (x * A),A,C) = (x * C) * A.
[back_rewrite(28507),rewrite([28523(7)])].
28540 C
* ((x * C) * A) = x * (A * (C * C)).
[back_rewrite(28026),rewrite([28538(8)])].
28543 A
* (C * (A' * x)) = R(C * x,A,C).
[back_rewrite(28014),rewrite([28523(12)])].
28544
R(x,C',A) = R(x,A,C).
[back_rewrite(28006),rewrite([28523(8),507(5)]),flip(a)].
28545 (x
* A) * (C * A') = R(C * x,A,C).
[back_rewrite(28001),rewrite([28523(12)])].
28546
R(C * (A * x),A,C) = A * (C * x).
[back_rewrite(27781),rewrite([28523(7)])].
28569 C'
* R(x * A,A,C') = (x * C') * A.
[para(28544(a,1),79(a,1,1)),rewrite([461(7),28534(8)])].
28574
R(C * x,A,C) = R(C' / x,x,A)'.
[para(28544(a,1),625(a,1)),rewrite([599(3)])].
28576
R(x,A,C) * (A * C') = (x * C') * A.
[back_rewrite(28534),rewrite([28569(17)])].
28580
R(x,A,C) * (A * (A * C)) = (x * C) * (A * A). [para(28522(a,1),79(a,1,1)),rewrite([67(8)])].
28587 C
/ R(C * x,A,C) = R(x,A,C)'.
[para(28536(a,1),139(a,2,1)),rewrite([1090(6),435(4),123(6),28518(8)])].
28596
R(x,A,C) * A' = R(x * A',A,C).
[para(28327(a,1),79(a,1,1)),rewrite([461(10,R),10(10),461(14,R),27612(14)])].
28612 (A
* (x * A)) / R(x * A,A,C) = R(A,C',(x * C) * A).
[para(74(a,1),806(a,1,1)),rewrite([16(6,R),35(6),2548(11),25415(11),7026(18)])].
28619
R(x,A * C',A') = R(x,A,C').
[para(21336(a,1),806(a,1,2)),rewrite([461(4),31(8),507(12),27611(8),599(10),27745(9),35(5),461(8),31(11),5
07(15)]),flip(a)].
28622
R(A * (x * C),A,C) / R(C * x,A,C) = A.
[para(2536(a,1),28332(a,1,1,1))].
28651
R(C * x,A,C) / R(x,A,C) = C.
[para(28523(a,1),6(a,1,1))].
28652
R(x,A,C) / R(C * x,A,C) = C'.
[para(28523(a,1),33(a,1,2))].
28687
R(x,R(C * y,A,C),C) = R(x,C * C,R(y,A,C)). [para(28523(a,1),1258(a,2,2)),flip(a)].
28689
R(x,A,C) / R(C' * x,A,C) = C.
[para(28523(a,1),489(a,1,1,2)),rewrite([28314(8),10(5),461(9,R),28314(9),491(17)])].
28707
R(R(C,x,A),x * A,C) = R(C,R(x,A,C),A * C).
[para(28523(a,1),760(a,1,1,1)),rewrite([79(9),16(6,R),16(10,R),948(11)])].
28799
R(x / y,y,C)' = (y * C) / (C * x).
[para(839(a,2),112(a,1,1))].
28958 C'
* R(x,A,C') = R(C' * x,A,C').
[para(21336(a,1),822(a,1,2)),rewrite([461(4),31(7),507(11),28619(7),461(7,R),461(11),31(15),507(19),2
7611(15)])].
29096
(C' * x) / (x' * (C' * (x / y))) = x * y.
[para(10943(a,1),2885(a,1,2)),rewrite([461(8,R),31(13)])].
29170
R(C' / x,x,C * y) = y / (x * (y * C)).
[para(16(a,1),829(a,2,2,2))].
29181
R(x' * A,A',x * y) = y / (A' * (x * y)).
[para(871(a,1),829(a,1,1))].
29263
R(x / y,y,A) = A * ((A' * x) / y).
[para(35(a,1),3914(a,1,1,1))].
29276 (A
* (x * A)) / y = A * (x / (y * A')).
[para(3914(a,1),81(a,2)),rewrite([435(4),435(8),7(10),50(4),435(8)])].
29314
R(A,C',(x * C) * A) = A * (x / R(x,A,C)).
[back_rewrite(28612),rewrite([29276(10),28596(9),86(6),439(5)]),flip(a)].
29315 A
* ((x * C) / R(A * x,A,C')) = C.
[back_rewrite(27709),rewrite([29276(15),27691(14),9(12),3(10),24764(9)])].
29316
R(A,C,(x * C') * A) = A * (x / R(x,A,C')).
[back_rewrite(27695),rewrite([29276(11),27683(10)]),flip(a)].
29324 A
* ((C * x) / R(C * x,A,C)) = R(A,x,A * C). [back_rewrite(6959),rewrite([29276(11),28518(10)])].
29325 A
* ((x * C) / R(C * x,A,C')) = R(A,C,x * A). [back_rewrite(6958),rewrite([29276(11),27769(10)])].
29377
R(C * x,C',y * C) = (x * (C * y)) / y.
[para(16(a,1),830(a,1,3)),rewrite([599(3)])].
29398
R(A * x,x',x * y) = (A * (x * y)) / y.
[para(2061(a,1),830(a,1,1)),rewrite([31(3)])].
29400
R(C * x,C',C * y) = (x * (C * y)) / y.
[para(599(a,1),830(a,1,1))].
29439
R(C * R(x,y,C),C',C * y) = (C * (x * y)) / y. [para(758(a,1),830(a,2,1)),rewrite([599(5)])].
29445
R(R(A * x,x',x * y),y,A) = A * x.
[para(830(a,2),3914(a,1,1)),rewrite([2061(3),31(3),6(10)])].
29509 C
* (x * (x * (A * C'))) = R(x * (x * A),A,C).
[para(831(a,1),28012(a,1)),rewrite([10(13),599(9),871(12),12(11)])].
29549
R(C' * R(x,C,y),C,C * y) = R(C' * x,C * C,y).
[para(838(a,1),832(a,1,1)),rewrite([1243(6),1612(15)]),flip(a)].
29681
R(R(x,C' * y,C'),y * (C' * C'),C) = x.
[para(5133(a,1),27541(a,1,1,2))].
29906 x
/ (C' * (y * x)) = R(C' * y,C',x)'.
[para(481(a,1),843(a,2,2)),rewrite([492(9),141(4),24454(11),11027(9),64(14)]),flip(a)].
29907 x
/ (y * (x * C)) = R(C * y,C',x)'.
[para(843(a,1),625(a,1)),rewrite([599(7),11027(12)])].
29908
R(C * x,C',y * C) = R(C * x,C',y).
[para(843(a,1),625(a,2,1)),rewrite([599(3),29907(11),31(14)])].
29909 x
/ R(A' * x,A,C) = R(A',C',x)'.
[para(16495(a,1),843(a,1,1)),rewrite([64(6),142(9),11027(8),2548(14),25411(14)]),flip(a)].
29910 x
/ R(A * x,A,C') = R(A,C',x)'.
[para(19511(a,1),843(a,1,1)),rewrite([10(7),143(9),11027(7),2548(12),16(10),20902(12)]),flip(a)].
29924
R(C' / x,x,C * y) = R(C * x,C',y)'.
[back_rewrite(29170),rewrite([29907(10)])].
29928
R(A * C,C',x)' = R(A' * C',A,x).
[back_rewrite(11026),rewrite([29907(5),16(3)])].
29930 x
/ (y * (C * x)) = R(C * y,C',x)'.
[back_rewrite(10976),rewrite([29907(8)])].
29933 (x
* (C * y)) / y = R(C * x,C',y).
[back_rewrite(29377),rewrite([29908(7)]),flip(a)].
29935 (x
* (y * C)) / y = R(C * x,C',y).
[back_rewrite(844),rewrite([29908(7)]),flip(a)].
29936
R(A',C',(A * C) * x) = R(A,C',x)'.
[back_rewrite(24307),rewrite([29910(16)])].
29944
R(C * x,C',C * y) = R(C * x,C',y).
[back_rewrite(29400),rewrite([29933(11)])].
29950
R(A * x,A,C') / x = R(A,C',x).
[back_rewrite(24312),rewrite([29936(9),31(6)]),flip(a)].
29957
R(C * R(x,y,C),C',y) = (C * (x * y)) / y.
[back_rewrite(29439),rewrite([29944(9)])].
30179 (x
* (C * C)) / (y * (C * x)) = R(C' * y,C,C * x)'. [para(1222(a,1),848(a,2,1)),rewrite([107(2)]),flip(a)].
30343
R(x * (A * C'),A,C') = C' * (x * A).
[para(13522(a,1),850(a,1,1)),rewrite([2075(15),507(15),2805(11),25843(11),2075(17),507(17)])].
31040
((A' * (x * (A * x))) / x) * A' = A' * x.
[para(12096(a,1),18(a,2)),rewrite([1092(6),871(5),23577(5),1089(8),871(8),13(7),50(12),27519
(13),1841(11),338(10),439(9)])].
31235 A'
* ((A * C) * x) = R(C * x,A,C).
[para(878(a,1),28315(a,1,1)),rewrite([16(4,R),22446(8),13(10),507(8),2153(7),435(11),83(14),307(13)
])].
31246 R(x,A',A
* (C * C)) = R(x,A,C).
[back_rewrite(26601),rewrite([31235(9),28314(8),10(5)]),flip(a)].
31257 A'
* R(x,A,C) = R(A' * x,A,C).
[back_rewrite(26609),rewrite([31246(10)])].
31260
R(A' * (C * x),A,C) = C * (A' * x).
[back_rewrite(28526),rewrite([31257(8)])].
31356
R((x * C) * A,A,C') = C * (x * A).
[para(880(a,1),24763(a,1)),rewrite([16(4,R),16(8,R),13522(9),2224(9),10(6),871(9)]),flip(a)].
31407
R(x,A * x',x * A') = x.
[para(16419(a,1),337(a,1,2,2,2,1)),rewrite([2076(9),31(7),23591(10),3(2),16419(6),16419(9),2076(7),31(5)]),fli
p(a)].
31421
R(x * A,x',x) = x * A.
[para(7(a,1),31407(a,1,3)),rewrite([871(3),871(6),4435(6),35(8),871(7)])].
31432 (x
* (A * x')) * x = x * A.
[para(31421(a,1),18(a,2)),rewrite([1090(4),2061(2),8(7),24(7)])].
31440 (x
* A) / x = x * (A * x').
[para(31421(a,1),308(a,1,1)),rewrite([1090(7),2061(5)])].
31463
((C * x) * (A * (C' / x))) * (C * x) = (x * C) * A. [para(372(a,1),31432(a,2)),rewrite([509(6)])].
31492 C'
* ((x * C) * A) = R(x * A,A,C).
[para(31432(a,1),846(a,2,2)),rewrite([509(6),846(14),31463(13),25415(14)])].
31512
R(C * R(x,C,y),C',y) = x * C.
[para(757(a,1),884(a,1,1)),rewrite([461(8,R),64(8),6(4),29908(11)]),flip(a)].
31514 (x
* (A * A)) * (C * A') = (x * C) * A.
[para(1926(a,1),884(a,1,1)),rewrite([19511(9),28544(17),28538(16)])].
31516
R(C * (x / (C * y)),C',y) = x / y.
[para(2586(a,1),884(a,1,1)),rewrite([461(5,R),64(5),29908(11)]),flip(a)].
31519
R(C * (C' / x),C',(C * x) * y) = R(x,C',y)'.
[para(578(a,1),884(a,1,1)),rewrite([461(6,R),29906(7),10(5)]),flip(a)].
31533 A'
* ((x * C) * A) = C * (A' * (x * A)).
[back_rewrite(11985),rewrite([31514(11)])].
31534
R(x,C',y * C) = R(x,C',y).
[back_rewrite(24549),rewrite([31519(11),31(5)]),flip(a)].
31739
R(x,C',C * y) = R(x,C',y).
[para(16(a,2),31534(a,1,3))].
31757
R(x,C',y * (C * C)) = R(x,C',y).
[back_rewrite(7601),rewrite([31739(7),31534(5)]),flip(a)].
31960
R(R(x,y',z) / y,y,y' * z) = x * y'.
[para(35(a,1),889(a,2,2)),rewrite([6(10)])].
31965
R(x,A',y) * A' = R(x * A',y,A).
[para(889(a,1),12114(a,1,1)),rewrite([35(9),6(5),435(10)]),flip(a)].
32005
R(x,C * A',A * (C * C)) = x.
[para(16628(a,1),760(a,1,1,1,2)),rewrite([16(10,R),1255(10),15932(11),16(6,R),1222(10,R),2815(11),2223(19
),16(18,R),1255(18),10(19),16(16,R),13072(17),461(18,R),10(18),25411(14),27764(9),27680(11),10(5),16628(9),16(9,R),1255(9)]),flip(a)].
32030 A'
* ((A * C') * x) = R(C' * x,A,C').
[para(891(a,1),27685(a,1,1)),rewrite([461(6,R),19511(11),13(11),10(9),2153(8),435(13),83(16),307
(15)])].
32033
(C' * x) * (A * C') = C' * (C' * (x * A)).
[para(891(a,1),32005(a,1)),rewrite([2986(9),16(7),1421(8),10(9),2223(14),1222(13,R),1255(12
),10671(14),13072(10),461(11,R),10(11),13522(16)]),flip(a)].
32255
R(x,A * y,A') = R(x,A,y * A').
[para(7(a,1),17759(a,1,2,2)),rewrite([435(8)])].
32256
R(x,y * A,A') = R(x,A,A' * y).
[para(1089(a,1),17759(a,1,2,2)),rewrite([871(6),35(7)])].
32259
R(x,(A * y) * z,A') = R(x,A,y * (z * A')). [para(2153(a,1),17759(a,1,2,2)),rewrite([35(8)])].
32275 (x
* (y * A)) * A' = A * ((A' * x) * y).
[back_rewrite(25747),rewrite([32256(5),761(6),2237(6)]),flip(a)].
32374
R(x * A',A * A,C) = R(x,A,C') * A'.
[para(2223(a,1),924(a,1,1,2)),rewrite([50(7),10(8),28074(10),32275(9),16(7,R),27776(9),28958(9),10
(5)]),flip(a)].
32383
R(x,A * A,C) = R(x,A,C').
[para(31432(a,1),924(a,1,2,2)),rewrite([507(7),507(8),507(12),16(10),28074(12),19516(12),32275(7),1089(6),87
1(6),35(7),27683(9),507(10),507(11)]),flip(a)].
32384
R(x,A,C') * A' = R(x * A',A,C').
[back_rewrite(32374),rewrite([32383(8)]),flip(a)].
32387 (x
* (A * C)) * A = C * (x * (A * A)).
[para(32383(a,1),79(a,1,1)),rewrite([16(9,R),67(9),27674(10),16(12,R)])].
32414 C
* (C * R(x,y * C,C)) = R(C * (x * C),y,C). [para(16(a,1),925(a,1,1,2,2,2)),rewrite([26432(10)])].
32626
R(R(x,C',y),y,C) = R(x,C,y).
[para(64(a,1),948(a,1,2,2)),rewrite([2548(7),35(8),847(6),10(5),31534(7),64(10)]),flip(a)].
32627
R(R(x,C',y),C' * y,C) = R(x,C,y * C').
[para(461(a,2),948(a,1,1,2,1)),rewrite([35(11),2858(7)]),flip(a)].
32630
R(R(x,C',y),y * C',C) = R(x,C,y * C').
[para(2835(a,1),948(a,1,2)),rewrite([507(11),28028(7),32627(16)])].
32659 (C
* ((x * C') * y)) / y = R(x,C,y * C').
[back_rewrite(28028),rewrite([32630(15)])].
32660 C
* (R(x,C',y) * y) = (x * C) * y.
[para(32626(a,1),79(a,1,1)),rewrite([757(5),16(9,R)]),flip(a)].
32671
R(R(x,C,y),C * y,C') = R(x,C',y).
[para(32626(a,1),26443(a,1,1))].
32681
R(A * (C * x),A,C) = (A * C) * x.
[para(3914(a,1),32626(a,1,1)),rewrite([599(4),599(12),27089(14),27778(15)])].
32697
R(A * (x * C),A,C) = (A * C) * x.
[back_rewrite(28342),rewrite([32681(7)]),flip(a)].
32698
((A * C) * x) / R(C * x,A,C) = A.
[back_rewrite(28622),rewrite([32697(7)])].
32806 (x
* (y * C)) / (x * (C * y)) = 0.
[para(22113(a,1),321(a,2,1)),rewrite([22150(14),27(9)])].
32850 (x
* (y * (C * z))) / (y * (z * C)) = x.
[para(32806(a,1),81(a,1,1,1,2)),rewrite([3(2),32806(15),77(13)])].
33139
R(x,C * (C * A'),C') = R(x,A,C).
[para(25312(a,1),489(a,1,2)),rewrite([1222(8,R),16(14,R),13522(15),32033(15),2707(13),1222(12,R),2815
(13),2223(12),31235(12),28523(11),28314(12),10(9),28314(8),10(5),1222(9,R)]),flip(a)].
33140
R(R(x,C * A',C),A,C) = x.
[para(25312(a,1),26458(a,1,1,2)),rewrite([16(4,R),1222(12,R),33139(15)])].
33156
R(x,C * A',C) = R(x,A,C').
[para(33140(a,1),12026(a,1,1)),rewrite([27681(5)]),flip(a)].
33157
R(R(x,C * C,A'),A,C) = x.
[para(1258(a,2),33140(a,1,1))].
33170
R(x,C * C,A') = R(x,A,C').
[para(33157(a,1),12026(a,1,1)),rewrite([27681(5)]),flip(a)].
33177 (C
* (C * A')) / (x * C) = C / (x * A).
[para(33156(a,1),848(a,1,1)),rewrite([13522(5),30343(9),141(6),16(10,R)]),flip(a)].
33186 x'
* (((x * y) / z) * x') = y / (x * z).
[para(7(a,1),1026(a,1,2,2)),rewrite([112(6)]),flip(a)].
33251 (A
* C) / R(x,A,C) = C / (x * A').
[para(79(a,1),25374(a,1,1)),rewrite([461(6,R),141(7),25377(13)]),flip(a)].
33480
R(x * (C * (x * A)),A,C) = x * (x * (A * C)). [para(12(a,1),27434(a,1,1,1)),rewrite([69(5),12(13)])].
33491
R(x,A,A * C) = R(x,A,C).
[para(50(a,1),1046(a,1,2)),rewrite([27089(4),90(5),16(10),28074(12),28518(11),28538(9),31492(7),28596(8),86(5
),439(4),27089(7),90(8)]),flip(a)].
33502 (x
* C) * (A * A) = (x * A) * (A * C).
[para(33491(a,1),79(a,1,1)),rewrite([28580(9)])].
33624 (x
* (C * (y * C))) / (C * y) = R(C * x,C',y).
[para(1103(a,1),1054(a,2,2)),rewrite([82(6),599(3),82(8),16(8,R),31739(9),31534(7),16(9
,R),12(16),10(17)]),flip(a)].
33627
R(C,A * C,x * A) = R(C',A,x * A)'.
[back_rewrite(27623),rewrite([33624(9),16(3),27625(9)]),flip(a)].
33703
R(A' * x,A,C) / R(x,A,C) = A'.
[para(35(a,1),28334(a,1,2,1))].
33752
R(A * x',x,C) * R(x,A,C) = A.
[para(625(a,1),28466(a,1,1,1)),rewrite([2061(2),31(7),435(7),83(10),307(9)])].
33795 (C
* (A * x)) * A = A * (C * (x * A)).
[para(50(a,1),28538(a,1,1,2)),rewrite([28546(9),16(10,R)]),flip(a)].
33800
((x * C) * A) / R(x * A,A,C) = C.
[para(28538(a,1),28651(a,1,1))].
33813 C /
R(x * C,A,C) = R(x,A,C)'.
[para(16(a,1),28587(a,1,2,1))].
33814
R(C' * x,A,C)' = C / R(x,A,C).
[para(35(a,1),28587(a,1,2,1)),flip(a)].
33841
R(C / x,x,A') = C / R(x,A,C).
[back_rewrite(24782),rewrite([33814(12)])].
33881
R(x,A,C') / R(C * x,A,C') = C'.
[para(28472(a,1),28652(a,1,1)),rewrite([28523(9),28472(12)])].
33976 A'
* R(C * x,A,C') = (C * A') * x.
[para(9131(a,1),1096(a,2,2)),rewrite([435(8),1105(10),435(7),1156(10),871(8),12(7),16(6),1255(7),12
72(14),24777(12),24764(12),35(8),27745(8),435(12)])].
34498 (x
/ (y / x)) / (y * (x / y)) = x / y.
[para(1166(a,1),33(a,1,2)),rewrite([112(7)])].
34595
R((A * C) * x,A,C) = C * (A * x).
[para(1974(a,1),1172(a,1,1)),rewrite([22446(6),1913(10),461(9),2223(10),461(9,R),24756(10),28013(9),
28022(9),35(7),559(6),435(6),461(7),1089(9),871(9),461(8),10(9),599(5),559(12),435(12),461(13),2676(15),461(14),28012(15)]),flip(a)].
34601
R(A' * x,A,x * A) = A' * x.
[para(19948(a,1),1172(a,1,1)),rewrite([871(5),871(7),9678(7),31(11),871(12),27519(13),1841(11),338(10),439
(9),31040(10),31(9),871(10)]),flip(a)].
34624
R(x,A,x') = x.
[para(2061(a,1),1173(a,1,1,2)),rewrite([6(8)]),flip(a)].
34674
R(x,A * x',A) = x.
[para(34624(a,1),12026(a,1,1))].
34740
R(R(x,A * y,A),A,y) = x.
[para(769(a,1),1174(a,1,1,1)),rewrite([86(8),439(7),435(8),86(9),439(8),6(6),32255(11),86(10),439(9)]),flip(a
)].
34765
R(x * A,x',A) = x * A.
[para(4435(a,1),34674(a,1,2,2)),rewrite([35(8)])].
34880
R(R(x,y,A),A,A' * y) = x.
[para(35(a,1),34740(a,1,1,2))].
34964 C
* (A * (A * x)) = A * ((A * C) * x).
[para(1184(a,1),1974(a,2,2,2)),rewrite([435(6),4627(9),16(7,R),50(11),50(10),2153(9),31235(9),2
8013(8),32681(8),307(14)]),flip(a)].
34976
(A' * (x * A)) * (C * A') = (C * A') * x.
[para(13522(a,1),1184(a,1,1,2)),rewrite([24752(10),2075(20),21589(24)])].
34985 (A
* ((A * C) * x)) / (C * x) = R(A * A,x,C).
[para(1184(a,1),927(a,1,1,2,2)),rewrite([307(8),34964(6),435(9),83(12),307(11),435(14),8
3(17),307(16)])].
35079
R(A * (x / y),A,A' * y) = (A * x) / y.
[para(3914(a,1),34880(a,1,1))].
35166 (A
* C) * (x * C) = C * (C * (A * x)).
[para(2536(a,1),32681(a,1,1,2)),rewrite([32681(9),25908(12)])].
35169 C
* ((A * C) * x) = A * (C * (C * x)).
[para(32681(a,1),28523(a,1,2)),rewrite([28546(15)])].
35170 (A
* C) * R(x,A,C) = C * (A * x).
[para(28523(a,1),32681(a,1,1,2)),rewrite([28013(7),32681(7),34595(7)]),flip(a)].
35195
R(A * (x * C),A,C') = C * (A * x).
[para(32697(a,1),28472(a,1,1)),rewrite([34595(7)]),flip(a)].
35199 (x
* (A * y)) * A' = (x * A) * (y * A').
[para(435(a,1),1196(a,1,2,2)),rewrite([32255(5),79(11)]),flip(a)].
35211 (C
* (C * (A * x))) / R(C * (C * x),A,C) = A. [para(2536(a,1),32698(a,1,1)),rewrite([35166(6)])].
35298 A'
* ((C * x) * A) = C * (A' * (x * A)).
[para(27676(a,1),1201(a,1,2)),rewrite([16(7,R),507(7),16495(8),27679(10),16(14,R),507(14),16(
18,R),507(18),871(14),31533(14)])].
35397
R(A * x',x,C) = A * R(x,A,C)'.
[para(33752(a,1),6(a,1,1)),rewrite([2061(5)]),flip(a)].
35406
((C * x) * A) / R(x * A,A,C) = C.
[para(16(a,2),33800(a,1,1,1))].
35551
((C * x) / y) * ((C * y) / x) = C * C.
[para(2635(a,1),1223(a,1,2,2,2)),rewrite([8394(10)])].
35878
R(x,A,A * (x * A)) = x.
[para(10(a,1),34601(a,1,1)),rewrite([50(5),10(11)])].
35903
R(A * x',x,A * x) = A * x'.
[para(35878(a,1),625(a,2,1)),rewrite([2061(2),435(6),83(9),307(8),435(8),2075(10)])].
35937 C
* (C * (x / (C * y))) = (C * x) / y.
[para(1188(a,1),1251(a,1,2,2,2)),rewrite([578(12),1222(20,R),1075(20),8419(17)])].
35997
R(A,C' * x,A * (C * C)) = R(A,C,x * A).
[para(1254(a,1),806(a,1,1)),rewrite([1103(9),25415(9),28523(8),28538(8),2986(15),16(13),1421(1
4),10(15),29276(11),32275(10),16(8,R),27776(10),29325(11)]),flip(a)].
35998
R(A,x * C',A * (C * C)) = R(A,C,x * A).
[para(1254(a,1),807(a,1,1)),rewrite([2548(9),25415(9),28523(8),28538(8),2247(15),16(13),1421(1
4),10(15),29276(11),32275(10),16(8,R),27776(10),29325(11)]),flip(a)].
36016
R(R(x,A,C'),A,C * C) = R(x,A * C,C).
[para(27685(a,1),1259(a,1,1,2,2)),rewrite([27745(9),27756(9),7629(12)]),flip(a)].
36146 (C
* (A * x)) / R(x,A,C) = A * C.
[para(35170(a,1),6(a,1,1))].
36225
R((C * x) / R(x,A,C),R(x,A,C),A) = C.
[para(35406(a,1),826(a,2)),rewrite([435(9),28596(10),86(7),439(6),435(13),28596(14),86(11),439(1
0)])].
36830
R(x,y * C',C)' * (C * (x * (C' * y))) = y. [para(2835(a,2),1544(a,1,2,2)),rewrite([16(18,R),507(18)])].
36897 (C
* (A * x)) / R(A * x,A,C) = R(C,A,R(x,A,C)).
[para(36146(a,1),1634(a,1,1,1)),rewrite([1090(6),435(4),123(6),28013(15)]),flip(a)].
37000 (A
* (x * y)) / y = A * R(x,y,A').
[para(2168(a,1),6(a,1,1))].
37026 C'
* (A * (x * (C * C))) = (A * C) * x.
[para(2168(a,1),1245(a,1,2)),rewrite([33170(17),24764(16),27745(17),27778(17)])].
37144 (A
* (C / R(x,A,C))) * x = A * C.
[para(33841(a,1),2168(a,1,1,2)),rewrite([7(12)])].
37152
R(A * x,x',x * y) = A * R(x,y,A').
[back_rewrite(29398),rewrite([37000(9)])].
37154 A
* R(x,x * A',A') = A * x.
[back_rewrite(8934),rewrite([37000(10)])].
37155
R(A * x,A,A' * y) = A * R(x,y,A').
[back_rewrite(7816),rewrite([37000(11)])].
37167
R(A * R(x,y,A'),y,A) = A * x.
[back_rewrite(29445),rewrite([37152(5)])].
37169 A
* R(x / y,y,A') = (A * x) / y.
[back_rewrite(35079),rewrite([37155(8)])].
37194
R(x * A',A,C)' = A * R(x,A,C)'.
[para(37144(a,1),2584(a,1,1)),rewrite([1878(6),33813(15)])].
37212
R(R(A,C,x),x * C,C) = A.
[para(37144(a,1),1055(a,1,1,2,1)),rewrite([35169(6),32850(11),23627(7),23(5),3(4)]),flip(a)].
37227
R(R(A,C,C' * x),x,C) = A.
[para(7(a,1),37212(a,1,2)),rewrite([107(4)])].
37231
R(R(A,C,x * C'),x,C) = A.
[para(83(a,1),37212(a,1,2)),rewrite([474(10)])].
37253
R(C * (A' * x),A,C) = (C * A') * x.
[para(1345(a,1),28544(a,1)),rewrite([871(5),461(9),19511(10),34976(10),599(11)]),flip(a)].
37276
R(A,C * x,C') = R(A,C,C' * x).
[para(37227(a,1),26443(a,1,1))].
37277
R(A,x * C,C') = R(A,C,C' * x).
[para(37227(a,1),26451(a,1,1))].
37295
R(x,x * A',A') = x. [para(37154(a,1),10(a,1,2)),rewrite([10(5)]),flip(a)].
37301 (A
* ((A * C) * x)) / (x * C) = R(A * A,x,C).
[para(37154(a,1),923(a,1,1,2,2)),rewrite([34964(6),37295(12),37295(18)])].
37302
R(A * x,x',C) = A * R(x',A,C)'.
[para(37154(a,1),943(a,2,1)),rewrite([37295(8),37295(8),2028(4),16(3),37295(9),1647(7),37194(8),37295(
15)]),flip(a)].
37347 (A
* x) / (y * A) = A * ((x * A') / y).
[para(37167(a,1),872(a,2,1)),rewrite([16472(6),1090(5),435(3),3914(8)]),flip(a)].
37353 A
* R(x,A,y * A') = R(A * x,A,y). [para(37167(a,1),34740(a,1,1)),rewrite([32255(10)]),flip(a)].
37460
R(C',(C * x) * x,C / x) = C'.
[para(2424(a,1),486(a,1,2)),rewrite([461(6,R),4780(6),18619(9),33(7)]),flip(a)].
37535
R(C',(x * C) * x,C / x) = C'.
[para(16(a,1),37460(a,1,2,1))].
37562 (C
* x) / (y * (C * (x * C))) = R(C * y,C',x)'.
[para(37535(a,1),889(a,1,1,1)),rewrite([7424(9),29924(8),31534(7),20494(12),2843(15),2
7321(14),7424(14)]),flip(a)].
37972 A'
* (x * (C * C)) = C * ((C * A') * x).
[para(2617(a,2),6433(a,2)),rewrite([6433(13),2815(14)])].
38098
R(x,A',A * (y * A)) = R(x,y,A).
[para(10(a,1),2676(a,1,2)),rewrite([50(8)]),flip(a)].
38114
R(x,y * (z * A'),A) = R(x,A',(A * y) * z). [para(2153(a,1),38098(a,1,3,2)),rewrite([35(10)]),flip(a)].
38163
R(C * x,A,C) / x = R(C,A',A * x).
[para(2805(a,1),98(a,2)),rewrite([16(5,R),2153(7),31235(7),83(10),307(9)])].
38167
R(R(x,y,A'),A',A * y) = x.
[para(2805(a,1),759(a,2)),rewrite([83(6),307(5),83(6),307(5),6(2)]),flip(a)].
38171
R(R(x,A',A * y),A,A' * (y * A')) = x.
[para(2805(a,1),34880(a,1,1))].
38175
R(R(x,A' * y,A'),A',y) = x.
[para(35(a,1),38167(a,1,3))].
38246
R(x,C * A',A') = R(x,A,C).
[para(38175(a,1),26443(a,1,1)),rewrite([28327(7),16(7,R)]),flip(a)].
38362 (x
/ (y * z)) * y = y' * ((y * x) / z).
[para(3558(a,1),10(a,1,2)),flip(a)].
38363
(x' * y) / (x * z) = x' * ((y / z) * x').
[para(10(a,1),3558(a,1,2,1,2)),flip(a)].
38366 (x
* y) / (x' * z) = x * ((y / z) * x).
[para(35(a,1),3558(a,1,2,1,2)),flip(a)].
38380
((x * y) / z) * x' = x * (y / (x * z)).
[para(3558(a,1),1090(a,1,1)),rewrite([38362(7),1750(9),33186(10)])].
38384 x
* (R(C * x,C',y)' * x) = R(C' * x,C,y).
[para(838(a,1),3558(a,2)),rewrite([29907(4)])].
38387 (x
/ (y * z)) * (y * u) = y' * (((y * x) / z) * u). [para(3558(a,1),1091(a,2,2,1)),rewrite([38362(3),1750(5),38380(5),10(5)])].
38392 (C
* x) / (y * C') = C * (C * (x / y)).
[para(507(a,1),3558(a,1,2,1,2)),rewrite([16(4,R)]),flip(a)].
38407
((x' * y) / z) * x = x' * (y / (x' * z)).
[para(3558(a,1),10934(a,2,2,1)),rewrite([38362(6),31(3),1304(6),112(5),38362(6),31(3),10(6),
112(9)])].
38427
R(R(x,C * (y / (C * z)),C),(C * y) / z,C') = x. [para(3558(a,1),26443(a,1,2)),rewrite([16(5,R)])].
38436 (C
* (x * y)) / y = C * (C * R(C' * x,C,y)).
[para(847(a,1),3558(a,1,2,1)),rewrite([16(8,R)]),flip(a)].
38438 C
* (C * R(C' * x,C,C * y)) = R(x * C,C,y).
[para(856(a,1),3558(a,1,2,1)),rewrite([16(10,R),1593(19),10(18)])].
38439
R(C' * x,C,C * y) = R(C' * x,C,y).
[para(856(a,1),3558(a,2)),rewrite([37562(8),38384(8)]),flip(a)].
38446
(A' * (x * y)) / y = A' * R(x,y,A). [para(897(a,1),3558(a,1,2,1)),rewrite([31965(10),86(7),439(6)]),flip(a)].
38447 (C
* (C * x)) / (y * x) = C * (C * R(y,x,C)'). [para(922(a,1),3558(a,1,2,1)),rewrite([16(6,R)]),flip(a)].
38523 C
* (C * R(C' * x,C,y)) = R(x * C,C,y).
[back_rewrite(38438),rewrite([38439(9)])].
38526 (x
* (C * C)) / (y * (C * x)) = R(C' * y,C,x)'. [back_rewrite(30179),rewrite([38439(15)])].
38527
R(C' * R(x,C,y),C,y) = R(C' * x,C * C,y).
[back_rewrite(29549),rewrite([38439(9)])].
38532
R(A' * x,A',A * y) = A' * R(x,y,A).
[back_rewrite(5404),rewrite([38446(13)])].
38546 (C
* (x * y)) / y = R(x * C,C,y).
[back_rewrite(38436),rewrite([38523(13)])].
38549
R(x,C,y * C') = R(x,C,y).
[back_rewrite(32659),rewrite([38546(7),16(5,R),507(5)]),flip(a)].
38553
R(C * R(x,y,C),C',y) = R(x * C,C,y).
[back_rewrite(29957),rewrite([38546(11)])].
38560
R(A * C,A',A * x) = R(A * C,C,x).
[back_rewrite(5167),rewrite([38546(13)])].
38563
R(R(A,C,x),x,C) = A.
[back_rewrite(37231),rewrite([38549(6)])].
38575 (x
* (y * C')) / y = R(x * C',C,y). [back_rewrite(16263),rewrite([38549(8)]),flip(a)].
38579
R(x,C,y) * y = C * ((C' * x) * y).
[back_rewrite(2870),rewrite([38549(5)])].
38618 C
* (R(A,C,x) * x) = A * (x * C).
[para(38563(a,1),79(a,1,1)),rewrite([16(10,R)]),flip(a)].
38626
R(A,C,C' * x) = R(A,C,x).
[para(38563(a,1),26443(a,1,1)),rewrite([37276(6)])].
38627
R(A,C,x) = R(A,x,C').
[para(38563(a,1),26452(a,1,1)),rewrite([38626(10)]),flip(a)].
38632
R(A,x * C,C') = R(A,C,x).
[back_rewrite(37277),rewrite([38626(12)])].
38660
R(A,C,x)' = R(A,x,C')'.
[para(38627(a,1),143(a,2,1)),rewrite([143(6)])].
38666
R(A,C' * x,C') = R(A,C,x).
[para(38627(a,1),2884(a,1)),rewrite([38549(13)])].
38668
R(A * x,A,C) / x = R(A,C,x).
[para(38627(a,1),2883(a,2)),rewrite([2290(7),461(5),27652(7),507(10),38666(13)])].
38669
R(A,C,C * x) = R(A,C,x).
[para(38627(a,2),81(a,2)),rewrite([599(4),461(7,R),27662(7),38668(6),599(8)]),flip(a)].
38672
R(A,C,A' * x) = R(A',x,C')'.
[para(38627(a,2),142(a,1))].
38674
R(A * x,A,C) = R(A,C,x) * x.
[para(38627(a,2),750(a,1,1)),rewrite([599(5),38669(5),599(8),461(11,R),27662(11)]),flip(a)].
38739
R(A,x,C * C) = R(A,C,x).
[para(38669(a,1),18(a,2)),rewrite([25908(6),1260(11)])].
38765
R(A',x,C * C)' = R(A',x,C')'.
[para(38739(a,1),142(a,1)),rewrite([38672(6)]),flip(a)].
38768
R(x,C,C * y) = R(x,C,y).
[para(7(a,1),38549(a,1,3)),rewrite([599(6)]),flip(a)].
38771
R(x,C,y * C) = R(x,C,y).
[para(83(a,1),38549(a,1,3)),rewrite([31(4),458(5),31(6)]),flip(a)].
38772
R(x,C,C' * y) = R(x,C,y).
[para(461(a,2),38549(a,1,3))].
38773
R(x,C,y * (y * C)) = R(x,C,y * y).
[para(69(a,1),38549(a,1,3)),rewrite([507(6)]),flip(a)].
38781
R(x,A,C * C) = R(x,A,C').
[para(26602(a,1),38549(a,2)),rewrite([461(7,R),64(7),27089(3)]),flip(a)].
38830
R(x,A * C,C) = R(x,A,C).
[back_rewrite(36016),rewrite([38781(9),28537(8)]),flip(a)].
38852
R(C / x,x,C * y) = R(C' * x,C,y)'.
[para(38768(a,1),625(a,2,1)),rewrite([107(7)])].
38867
R(C / x,x,y * C) = R(C' * x,C,y)'.
[para(38771(a,1),625(a,2,1)),rewrite([107(7)])].
38878
R((A * C) / x,x,C) = C / (x * A').
[para(38830(a,1),625(a,2,1)),rewrite([22446(10),28535(15),141(13)])].
38913 x
/ R(A * x,A,C) = R(A,C,x)'.
[para(38632(a,1),139(a,2,1)),rewrite([461(5,R),64(5),461(7,R),27755(7)])].
38914
R(A,C,x)' * R(A * x,A,C) = x.
[para(38632(a,1),751(a,1,1,1)),rewrite([461(11,R),27755(11),461(15,R),64(15)])].
38942
R(A,x,C')' * R(A,C,x) = 0.
[para(38660(a,1),8(a,1,1))].
38944
R(A,C,x) * R(A,x,C')' = 0.
[para(38660(a,1),9(a,1,2))].
38946
R(A,x,C')' * (R(A,C,x) * y) = y.
[para(38660(a,1),10(a,1,1))].
38948
R(A,C,x)' * y = R(A,x,C')' * y.
[para(38660(a,1),32(a,2,1)),rewrite([32(4)])].
38965
R(R(A,C,x),R(A,x,C')',y) = R(A,C,x).
[para(38660(a,1),84(a,1,2))].
39138 x
/ (A' * (y * x)) = R(y,x,A)' * A.
[para(1841(a,1),1425(a,1,2,1)),rewrite([13(9),10(7),38532(13),2027(11)])].
39152
R(x' * A,A',x * y) = R(x,y,A)' * A.
[back_rewrite(29181),rewrite([39138(12)])].
39169
R(A,x',C') = R(A,C,x').
[para(4920(a,1),38666(a,1,2)),rewrite([10(7),38771(11)])].
39184
R(A,x / y,C') = R(A,C,x / y).
[para(112(a,1),39169(a,1,2)),rewrite([112(9)])].
39193
R(A,R(A,C,x)',C') = R(A,C,R(A,x,C')').
[para(38660(a,1),39169(a,2,3))].
39205
R(A,C,x * (A * (C * C))) = R(A,x,A * (C * C)).
[para(1251(a,2),38668(a,1,1,1)),rewrite([11863(8),32681(11),15(8),71(7),16(5),6996(15)]
),flip(a)].
39236 C'
* (x * ((A * C) * x)) = x * R(A * x,A,C).
[para(38674(a,2),130(a,2,2)),rewrite([757(8)])].
39251
(R(A,C,x) * x) / R(x,A,C) = A.
[para(38674(a,1),28332(a,1,1))].
39259
R(x,A,C) / (R(A,C,x) * x) = A'.
[para(38674(a,1),28334(a,1,2))].
39311 x
* R(A,C,y) = x * R(A,y,C').
[para(38942(a,1),752(a,1,1,3)),rewrite([31(6),78(6),31(10),38942(18),3(11)])].
39325
R(A,C,x) * y = R(A,x,C') * y.
[para(38944(a,1),752(a,2,1)),rewrite([38965(14),2(11)])].
39351
R(A,R(C' * x,A,C),C)' = R(x,A,C) / (A * x). [para(16494(a,1),1430(a,1,2,2)),rewrite([1913(8),461(7),2223(8),461(7,R),24756(8),16(8,R),
28523(8),35(5),1913(15),461(14),2223(15),461(14,R),24756(15)]),flip(a)].
39387
(R(A,x,C') * x) / R(x,A,C) = A.
[para(38627(a,1),39251(a,1,1,1))].
39485
R(x * C,C,y) * y = C * (x * y). [para(38546(a,1),7(a,1,1))].
39490 x
/ (C * (y * x)) = R(y * C,C,x)'.
[para(38546(a,1),112(a,1,1)),flip(a)].
39494
R(C * R(x,C,y),C,y) = R(x * C,y,C).
[para(757(a,1),38546(a,1,1,2)),rewrite([101(8),16(8,R),38771(12)]),flip(a)].
39499 (C
* (x * (y * C))) / (C * y) = R(x * C,C,y). [para(2536(a,1),38546(a,1,1,2)),rewrite([38768(14)])].
39500 C
* (C * R(x,C,y)) = R(C * (C * x),C,y).
[para(2224(a,1),38546(a,1,1,2)),rewrite([38392(12),38546(9),16(7,R),35(7),16(10,R),38549(15)]
)].
39531
R(C * R(x,C',y),C,y) = C * x.
[para(786(a,1),38546(a,1,1,2)),rewrite([38392(10),6(7),507(6),16(7,R),38549(12)]),flip(a)].
39536
R(C / x,x,x' * y) = R(x' * C,C,y).
[para(38546(a,1),842(a,2))].
39541
R(x,C * C,y) = R(x,y,C).
[para(38546(a,1),1587(a,1,1,2)),rewrite([38527(9),64(5),101(10)])].
39546
R(A * C,C',x) = R(A * C,x,C).
[para(38674(a,2),38546(a,1,1,2)),rewrite([28523(7),28546(7),29933(5),16(3),16(11,R),39494(13)])].
39552
R(C' * x',C,x * y) = R(x * C,C,y)'.
[back_rewrite(1591),rewrite([39490(11)])].
39610
R(x,R(C * y,A,C),C) = R(x,R(y,A,C),C).
[back_rewrite(28687),rewrite([39541(14)])].
39627
R(R(x,y,C),y,C) = R(x,y,C * C).
[back_rewrite(26538),rewrite([39541(6)])].
39645
R(C / x,C * x,y) = R(x * C',y,C)'.
[back_rewrite(25351),rewrite([39541(12)])].
39651
R(x,y * (C' * C'),C) = R(x,C' * y,C).
[back_rewrite(23298),rewrite([39541(10)])].
39658
R(A,C * x,A * C) = R(A,x * A,C).
[back_rewrite(20688),rewrite([39541(7)]),flip(a)].
39664
R(x,y * C,C) = R(x,y,C).
[back_rewrite(20673),rewrite([39541(4)]),flip(a)].
39683
R(x,y * C',C) = R(x,y,C).
[back_rewrite(5819),rewrite([39541(7)])].
39688
R(x,C' * y,C) = R(x,y,C).
[back_rewrite(3408),rewrite([39541(7)])].
39692
R(x,C * y,C) = R(x,y,C).
[back_rewrite(1258),rewrite([39541(4)]),flip(a)].
39711
R(R(x,C' * y,C'),y,C) = x. [back_rewrite(29681),rewrite([39651(14),39688(11)])].
39721 C
* (C * R(x,y,C)) = R(C * (x * C),y,C).
[back_rewrite(32414),rewrite([39664(6)])].
39741
R(x,y,C)' * (C * (x * (C' * y))) = y.
[back_rewrite(36830),rewrite([39683(5)])].
39745
R(R(x / y,y,C')',x,C) = y / x.
[back_rewrite(28250),rewrite([39683(10)])].
39746
R(R(x,y,C'),y,C) = x.
[back_rewrite(27943),rewrite([39683(8)])].
39747
R(R(x,y,C),y,C') = x.
[back_rewrite(26458),rewrite([39683(5)])].
39748
R(x,y,C) * y = C * (x * (y * C')).
[back_rewrite(25813),rewrite([39683(5)])].
39771
R(R(x,y,C')',x * y,C) = x'.
[back_rewrite(28159),rewrite([39688(10)])].
39780
R(x,y,C) * y = C * (x * (C' * y)).
[back_rewrite(25736),rewrite([39688(5)])].
39802
R(R(x,y / (C * z),C),(C * y) / z,C') = x.
[back_rewrite(38427),rewrite([39692(7)])].
39813 (C
* (C * (x * y))) / y = R(C * (x * C),y,C). [back_rewrite(26432),rewrite([39721(12)])].
39839 C
* (R(x,y,C') * y) = x * (y * C).
[para(39746(a,1),79(a,1,1)),rewrite([16(9,R)]),flip(a)].
39840
R(x,C * y,C') = R(x,y,C').
[para(39746(a,1),26443(a,1,1))].
39841
R(x,y * C,C') = R(x,y,C').
[para(39746(a,1),26451(a,1,1))].
39878
R(R(x,C,y),y,C') = R(x,C',y).
[back_rewrite(32671),rewrite([39840(7)])].
39884
R(x,C' * C',y * (C * C)) = R(x,y,C').
[back_rewrite(28043),rewrite([39840(15)])].
39895
R(R(x / y,y,C)',x,C') = y / x.
[back_rewrite(26483),rewrite([39840(9)])].
39916
(C' * (x * (C * y))) / y = R(x,y,C').
[back_rewrite(462),rewrite([39840(12)])].
39922
(C' * (x * (y * C))) / y = R(x,y,C').
[back_rewrite(16428),rewrite([39841(12)])].
39931
R(R(x,y,C)',x * y,C') = x'.
[para(143(a,1),39747(a,1,1))].
39991
R(x,y * C,C * C) = R(x,y,C * C).
[para(39664(a,1),948(a,2,1)),rewrite([16(6,R),16(12,R),1260(14),16(12,R),39692(14),39664(12),39627(10
)])].
40034
R(x,R(A * y,A,C'),C) = R(x,A * (y * C'),C).
[para(2168(a,1),39683(a,1,2)),rewrite([28038(13),24764(13)]),flip(a)].
40094
R(x,C' * y,C') = R(x,y,C').
[para(39711(a,1),39747(a,1,1)),flip(a)].
40099
R(x,C' * C',y) = R(x,y,C').
[back_rewrite(26529),rewrite([40094(12)])].
40102
R(x,y * (C * C),C') = R(x,y,C').
[back_rewrite(39884),rewrite([40099(10)])].
40195
R(x,R(A,C,y) * y,C) = R(x,A * (y * C),C).
[para(38618(a,1),91(a,1,2,2)),rewrite([1272(9),38618(7),102(14),39541(14)]),flip(a)].
40204
R(A * C,x,C)' = R(A' * C',A,x). [para(38618(a,1),829(a,2,2)),rewrite([107(6),39552(13),16(5,R),39494(7),29907(11),16(9),29928(13)])].
40214 A
* (C / (x * A)) = C / R(x,A,C).
[para(38618(a,1),1054(a,2,1)),rewrite([1243(6),27089(4),1243(11),27089(9),1243(14),38867(14),28958(7
),27089(10),28537(11),33814(7),1243(16),37347(15),12(12),33177(15)]),flip(a)].
40219
R(x,R(A,C,y) * y,C') = R(x,A * (y * C),C'). [para(38618(a,1),39840(a,1,2)),flip(a)].
40252
(A' * x) / R(x,A,C) = R(A',x,C').
[para(35(a,1),38913(a,1,2,1)),rewrite([38672(13),31(14)])].
40305
R(A,R(x,y,z),C') = R(A,C,R(x,y,z)).
[para(18(a,1),39184(a,1,2)),rewrite([18(11)])].
40310
R(A,x * y,C') = R(A,C,x * y).
[para(332(a,1),39184(a,1,2)),rewrite([332(11)])].
40318
R(A,C,R(A,C,x)') = R(A,C,R(A,x,C')').
[para(38913(a,1),39184(a,1,2)),rewrite([39193(8),38913(16)]),flip(a)].
40368 A'
* (R(A,C,x) * x) = R(x,A,C).
[para(39259(a,1),7(a,1,1))].
40641
R(R(A,C,x),A,C)' = R(R(A,x,C'),A,C)'.
[para(39311(a,1),28587(a,1,2,1)),rewrite([28587(11)]),flip(a)].
40871 (A
* (x * C)) / R(C * x,A,C) = R(A,R(x,A,C),C).
[para(39387(a,1),839(a,1,1)),rewrite([39839(13),16(15,R),28523(15)]),flip(a)].
40883
R(C * x,C,y) * y = C * (x * y).
[para(16(a,2),39485(a,1,1,1))].
40909
R(C' * x,C,y) * y = x * (C' * y).
[para(481(a,1),39485(a,1,1,1)),rewrite([16(6,R),9(6),3(4),481(14),35(15)])].
40955
R(A * C,x,C) * x = A * (C * x).
[para(38674(a,2),39485(a,2,2)),rewrite([16(5,R),39494(7),28523(13),28546(13)])].
40994
R(A * C,x,C * C) = R(A * C,C,x).
[para(39546(a,1),948(a,2,1)),rewrite([461(7,R),64(7),35(9),38546(5),39688(15),39627(12)]),flip(a)].
41107
R(x',R(x,y,C) * y,C) = R(x,y,C)'.
[para(39747(a,1),39771(a,1,1,1))].
41157
R(x',R(x,y,C') * y,C') = R(x,y,C')'.
[para(39746(a,1),39931(a,1,1,1))].
41235 C
/ ((C * x) * A') = A * R(x,A,C')'.
[para(1424(a,1),40214(a,1,2)),rewrite([435(4),2805(7),25843(7),435(11),27909(16)]),flip(a)].
41254 (C
* (A * (C * C))) / (C * (C * x)) = A * (C / x).
[para(16494(a,1),1483(a,1,2,2,2)),rewrite([1255(6),39991(25),38781(23),27671(22),20
75(19),141(17)])].
41286
R(R(A,C,x),x,A)' * A = x / R(x,A,C).
[para(40368(a,1),829(a,2,2)),rewrite([871(7),39152(13)])].
41290
R(A,R(x,A,C),C) = R(A,x,C).
[para(40368(a,1),922(a,1,2,2)),rewrite([38618(6),28523(9),40871(10),40195(14),143(14),39664(11),31(11)])].
41302
R(R(A,x,C'),R(x,A,C),C) = A. [para(40368(a,1),39771(a,1,2)),rewrite([40219(9),143(9),39841(6),31(6),31(12)])].
41303
R(R(A,x,C),R(x,A,C),C') = A.
[para(40368(a,1),39931(a,1,2)),rewrite([40195(8),143(8),39664(5),31(5),31(12)])].
41305
R(x,A,C) / (A * x) = R(A,x,C)'.
[back_rewrite(39351),rewrite([41290(9),39688(6)]),flip(a)].
41307 (A
* x) / R(x,A,C) = R(A,x,C).
[back_rewrite(28016),rewrite([41290(9),39688(6)]),flip(a)].
41310
R(A,(C * x) * A',C) = R(A,x * A',C).
[para(878(a,1),41290(a,1,2)),rewrite([16(5,R),22446(9),13(11),507(9),39692(8),435(11)]),flip(a)].
41312
R(A,R(x,A,C'),C) = R(A,x,C).
[para(32626(a,1),41290(a,1,2)),rewrite([27089(4),28544(12),41290(13)])].
41314
R(A,(C * x) * A,C) = R(A,x * (A * C),C).
[para(27599(a,1),41290(a,1,2)),flip(a)].
41315
R(A,x * (A * C),C) = R(A,x * A,C).
[para(28015(a,1),41290(a,1,2)),rewrite([39692(7)]),flip(a)].
41316
R(A,A * (C * x),C) = R(A,A * x,C).
[para(28546(a,1),41290(a,1,2)),rewrite([39692(14)])].
41317
R(A,(A * C) * x,C) = R(A,A * x,C).
[para(32681(a,1),41290(a,1,2)),rewrite([41316(14)])].
41321
R(A,(C * x) * A,C) = R(A,x * A,C).
[back_rewrite(41314),rewrite([41315(14)])].
41340
R(R(A,C,R(x,A,C')),x,C) = A.
[para(34740(a,1),41302(a,1,2)),rewrite([27681(6),40305(8)])].
41346
R(R(A,C,x),R(x,A,C),C) = A.
[para(38627(a,2),41302(a,1,1))].
41348
R(A,C,R(x,A,C)) = R(A,x,C').
[para(41302(a,1),39747(a,1,1)),rewrite([40305(7)])].
41391
R(A,x,C) * R(x,A,C) = A * x.
[para(41307(a,1),7(a,1,1))].
41401
R(A,x * A,C) = R(A,x,A * C).
[para(27599(a,1),41307(a,1,2)),rewrite([29276(11),35199(10),28545(10),29324(10),41321(12)]),flip(a)].
41402
R(A,C',x) = R(A,x,C).
[para(34740(a,1),41307(a,1,2)),rewrite([27681(6),24764(6),29950(7),27681(10),41312(11)])].
41405
R(R(A,x,C),R(x,A,C),C * C) = A.
[para(41307(a,1),1280(a,1,1)),rewrite([1222(23,R),28523(22),28523(23),35211(24)])].
41412
R(A,C * x,A * C) = R(A,x,A * C).
[back_rewrite(39658),rewrite([41401(12)])].
41414
R(A,C',x)' = R(A,x,C)'.
[para(41402(a,1),143(a,2,1)),rewrite([143(7)])].
41422
R(A,(C * A') * x,C) = R(A',C',x)'.
[para(41402(a,1),125(a,1)),rewrite([494(6),435(4),494(15),435(13),25411(16),29909(15)])].
41424
R(A * x,A,C') = R(A,x,C) * x.
[para(41402(a,1),752(a,1,1)),rewrite([39692(5),2312(11),16(9),20902(11)]),flip(a)].
41432
R(C * R(A,x,C),C,x) = A * C.
[para(41402(a,1),39531(a,1,1,2)),rewrite([16(10)])].
41435
R(A,C',R(x,A,C)) = R(A,x,C).
[para(41402(a,2),41290(a,1))].
41442
R(A,x,C)' * R(A,C',x) = 0.
[para(41414(a,1),8(a,1,1))].
41444
R(A,C',x) * R(A,x,C)' = 0.
[para(41414(a,1),9(a,1,2))].
41445
R(A,x,C) * R(A,C',x)' = 0.
[para(41414(a,2),9(a,1,2))].
41467
R(R(A,C',x),R(A,x,C)',y) = R(A,C',x).
[para(41414(a,1),84(a,1,2))].
41534
R(A,R(A,x,C)',C') = R(A,C,R(A,C',x)').
[para(41414(a,1),39169(a,1,2))].
41537
R(A' * x,A,C) / x = R(A',C',x).
[para(41414(a,1),1435(a,1)),rewrite([494(6),435(4),41422(8),31(7),494(12),435(10),25411(13)]),flip(a)]
.
41549
R(A,x * (C * A'),C) = R(A,x * A',C).
[para(825(a,1),41312(a,1,2)),rewrite([19511(6),599(12),435(13),41310(16)])].
41565
R(A,C,R(x,A,C')) = R(A,x,C').
[para(41340(a,1),39747(a,1,1)),flip(a)].
41579
R(A,C,(x * C) * A) = R(A,C,x * (A * C)).
[para(27434(a,1),41348(a,1,3)),rewrite([40310(15)]),flip(a)].
41580
R(A,C,(C * x) * A) = R(A,C,x * (A * C)).
[para(27599(a,1),41348(a,1,3)),rewrite([40310(15)]),flip(a)].
41581
R(A,C,x * (A * C)) = R(A,C,x * A).
[para(28015(a,1),41348(a,1,3)),rewrite([38768(7),40310(13)]),flip(a)].
41592
R(A,C,(C * x) * A) = R(A,C,x * A).
[back_rewrite(41580),rewrite([41581(14)])].
41593
R(A,C,(x * C) * A) = R(A,C,x * A).
[back_rewrite(41579),rewrite([41581(14)])].
41595
R(A,x,C)' * (A * x) = R(x,A,C).
[para(41391(a,1),10(a,1,2))].
41617
R(A,x * A',A * C) = R(A,x,C).
[para(7(a,1),41401(a,1,2)),rewrite([435(6)]),flip(a)].
41666 C'
* (x * (A * (C * C))) = (x * C) * A.
[para(41432(a,1),780(a,1,2)),rewrite([474(6),16(3),16(5,R),1255(5),40102(8),27120(8),474(10),1
6(7),16(9,R),1255(9),461(13,R)]),flip(a)].
41670
R(A * C,C,x) = R(A * C,x,C').
[para(41432(a,1),39878(a,1,1)),rewrite([38553(14)]),flip(a)].
41676
R(A,x * A',C) = R(A,C',x * A').
[para(878(a,1),41435(a,1,3)),rewrite([16(7,R),22446(11),13(13),507(11),31739(9),435(12),41310(15)]),fl
ip(a)].
41679
R(A,C',(x * C) * A) = R(A,x,A * C).
[para(28538(a,1),41435(a,1,3)),rewrite([39692(15),41401(13)])].
41682
R(A,A * x,C) = R(A,C',A * x).
[para(34595(a,1),41435(a,1,3)),rewrite([31739(8),41317(13)]),flip(a)].
41685
R(A,x * (C * A'),C) = R(A,C',x * A').
[back_rewrite(41549),rewrite([41676(14)])].
41687 A
* (x / R(x,A,C)) = R(A,x,A * C).
[back_rewrite(29314),rewrite([41679(8)]),flip(a)].
41710 x
* R(A,C',y) = x * R(A,y,C).
[para(41442(a,1),752(a,1,1,3)),rewrite([31(5),78(5),31(10),41442(18),3(11)])].
41727
R(A,x,C) / R(A,C',x) = 0.
[para(41444(a,1),321(a,2,1)),rewrite([41467(15),27(10)])].
41729
R(A,C',x) * y = R(A,x,C) * y.
[para(41444(a,1),752(a,2,1)),rewrite([41467(13),2(11)])].
41746 (C
* R(A,x,C)) / (C * R(A,C',x)) = 0.
[para(41727(a,1),839(a,1,1)),rewrite([76(7),16(12,R)]),flip(a)].
41778 (C
* (A' * x)) * A' = A' * (C * (x * A')).
[para(40883(a,1),1841(a,2,2)),rewrite([24707(8),31257(8),31260(8)])].
41796
R(x * A',A,C')' = A * R(x,A,C')'.
[para(40883(a,1),25374(a,1,1)),rewrite([27783(8),38549(20),24707(17),33251(17),41235(15)])].
41824
R(C' * R(A * C,x,C),C,x) = A.
[para(40955(a,1),838(a,1,1)),rewrite([2585(7)]),flip(a)].
41930
R(A',C',x) = R(A',x,C). [para(35(a,1),41305(a,1,2)),rewrite([41537(7),142(11),31(11)])].
41933
R(A,C,x) * A' = A * R(A,x,C)'.
[para(41305(a,1),3914(a,2,2)),rewrite([28013(5),24111(12),38668(6)])].
41962
R(A' * x,A,C) = R(A',x,C) * x.
[para(41930(a,1),752(a,1,1)),rewrite([39692(6),2312(13),25411(13)]),flip(a)].
41967
R(A' * x,A,C') / x = R(A',x,C * C).
[para(41930(a,1),948(a,2,1)),rewrite([24777(8),35(12),39688(17),39627(14)])].
41968
R(A',x,C * C) = R(A',C,x).
[para(41930(a,2),948(a,2,1)),rewrite([16(6,R),7556(12),39664(15),32626(13)])].
41973
R(A,C,(A' * C') * x)' = R(A',C,x).
[back_rewrite(24770),rewrite([41967(18),41968(16)])].
41974
R(A' * x,A,C') / x = R(A',C,x).
[back_rewrite(41967),rewrite([41968(14)])].
41975
R(A',C,x)' = R(A',x,C')'.
[back_rewrite(38765),rewrite([41968(6)])].
41976
R(A' * x,A,C') = R(A',C,x) * x.
[back_rewrite(24769),rewrite([41973(10)]),flip(a)].
41986
R(A',C,A * x) = R(A,C,x)'.
[para(41968(a,1),143(a,1)),rewrite([38739(11)])].
41990 C
* (A' * (C' * x)) = R(A' * x,A,C).
[para(41968(a,1),1114(a,1,2,2)),rewrite([175(6),175(14),175(24),38549(26),458(23),38362(20),31(11
),6142(18),16(15,R),28040(18),27662(16),28543(11),39627(12),38781(11),33976(11),25411(8),175(12),28040(15),1222(19,R),35(18)]),flip(a)].
41991 x
/ R(A' * x,A,C') = R(A',C,x)'.
[para(41968(a,1),1424(a,2,1)),rewrite([1863(6),1222(13,R),41990(12),28523(11),28019(8),39627(9),38781
(8),1863(15),38772(18),38549(15)])].
41993
R(A,C,(A' * C') * x) = R(A',C,x)'.
[back_rewrite(24772),rewrite([41991(17)])].
41998
R(A',C,x) = R(A',x,C').
[para(35(a,1),41986(a,1,3)),rewrite([38672(10),31(11)])].
42000
R(A',C,R(C' * x,A,C)) = R(A',C,x).
[para(125(a,1),41986(a,2,1)),rewrite([559(8),435(8),461(9),24710(11),559(15),435(15),461(16),24777(
18),41991(18),31(16)])].
42016 (C
* ((C * A') * x)) / (C * (C * x)) = A'.
[para(41998(a,1),948(a,2,1)),rewrite([16(5,R),39692(21),39746(19)])].
42226 A
* (R(A,x,C)' * A) = R(A,C,x).
[para(41595(a,1),40(a,1,1,2)),rewrite([28013(5),38668(6)]),flip(a)].
42231 A'
* (R(A,x,C) * A') = R(A,C,x)'.
[para(41595(a,1),1026(a,1,2,2)),rewrite([28013(5),38913(6),31(11)]),flip(a)].
42233
R(A,C',x)' * (A * x) = R(x,A,C).
[para(41402(a,2),41595(a,1,1,1))].
42240
R(A,x * (C * A'),A * C) = R(A,x,C).
[para(71(a,1),41617(a,1,2)),rewrite([41412(12),39692(17),39692(15)])].
42262
R(A * C,x,C') * x = C * (A * x).
[para(41670(a,1),761(a,1,1)),rewrite([40094(9),16(12,R),1255(12),1272(16),35(14)])].
42326 C'
* R(A * (C * C),x,C) = C * R(A,C',x).
[para(41710(a,2),1245(a,2)),rewrite([1222(9,R),39721(9),1255(7)])].
42384
R(R(A,C',x),A,C)' = R(R(A,x,C),A,C)'.
[para(41710(a,1),28587(a,1,2,1)),rewrite([28587(10)]),flip(a)].
42621
R(A,x,C)' * A = A' * R(A,C,x).
[para(42226(a,1),10(a,1,2)),flip(a)].
42639
R(R(A,x,C)',A,R(A,C,x)) = R(A,x,C)'.
[para(42226(a,1),35878(a,1,3))].
42641 A
* (R(A,C,x)' * A) = R(A,x,C).
[para(42226(a,1),35903(a,1,3)),rewrite([42621(7),2027(8),42621(14),23940(18),41933(8),10(9),42639(9),3
1(5),42621(10),2027(11)]),flip(a)].
42646 A
* (R(A,x,A * C)' * A) = R(A,C,x * A).
[para(41401(a,1),42226(a,1,2,1,1))].
42647
R(A',R(A,C,x),C) = R(A',C',R(A,C,x)).
[para(42226(a,1),41305(a,1,2)),rewrite([42621(6),41537(13),42621(15),142(17),31(17)]),flip(a)].
42648
R(A',R(A,C,x),C') = R(A',C,R(A,C,x)).
[para(42226(a,1),41986(a,1,3)),rewrite([42621(15),38672(16),31(17)]),flip(a)].
42649
R(A,R(A,C,x),C) = R(A,C',R(A,C,x)).
[para(42226(a,1),41682(a,1,2)),rewrite([42621(16),35(17)])].
42678
R(A,C,x)' * A = A' * R(A,x,C).
[para(42641(a,1),10(a,1,2)),flip(a)].
42680
R(A,x,C) * A' = A * R(A,C,x)'.
[para(42641(a,1),1090(a,1,1)),rewrite([42678(13),435(15),1841(16),42231(16)])].
42681
R(A,C,x)' * (A * y) = A' * (R(A,x,C) * y).
[para(42641(a,1),1091(a,2,2,1)),rewrite([42678(6),435(8),1841(9),42680(8),10(9)])].
42695
R(A,x,C) * (C * A') = A * (C * R(A,C,x)'). [para(42641(a,1),1105(a,1,1)),rewrite([42678(16),435(18),1841(19),42680(18),10(19)])].
42701
R(A',R(A,x,C),C) = R(A',C',R(A,x,C)).
[para(42641(a,1),41305(a,1,2)),rewrite([42678(6),41537(13),42678(15),142(17),31(17)]),flip(a)].
42702
R(A',R(A,x,C),C') = R(A',C,R(A,x,C)).
[para(42641(a,1),41986(a,1,3)),rewrite([42678(15),38672(16),31(17)]),flip(a)].
42775
R((A * C) / x,x,C * C) = A * (C / x).
[para(3563(a,1),1281(a,2,1)),rewrite([16(3),16(14,R),1255(14),41254(20)])].
42955
R(A,C',x)' * A = A' * R(A,C,x).
[para(41414(a,1),4898(a,2,1)),rewrite([4898(15),42621(13)])].
43033
R(A',x',C') = R(A',C,x').
[para(5026(a,1),41998(a,2)),rewrite([38771(7),39840(13)]),flip(a)].
43036
R(A',x / y,C') = R(A',C,x / y).
[para(112(a,1),43033(a,1,2)),rewrite([112(11)])].
43049
R(A,x,C') * A' = A * R(A,x,C)'.
[para(39325(a,2),5094(a,2)),rewrite([5094(15),41933(13)])].
43050
R(A,C',x) * A' = A * R(A,C,x)'.
[para(41729(a,1),5094(a,2)),rewrite([5094(15),42680(13)])].
43379 C'
/ (x / (y * C)) = C / ((C * x) / y).
[para(8394(a,1),117(a,1,2)),rewrite([509(11)]),flip(a)].
43383
R(C / x,x,y) = C * (C * R(x * C,C,y)').
[para(80(a,2),8394(a,2)),rewrite([16(5,R),39490(6)]),flip(a)].
43395 C'
* ((x * C) / y) = C * (x / (C * y)).
[para(8394(a,1),10918(a,1,1,1)),rewrite([112(4),16(5,R),117(14),112(11)]),flip(a)].
43405
R(x,(C * y) / z,C') = R(x,y / (z * C),C'). [para(8394(a,1),39840(a,1,2)),rewrite([39840(14)])].
43417
R(R(x,y / (C * z),C),y / (z * C),C') = x.
[back_rewrite(39802),rewrite([43405(11)])].
43641
R(C * A',A,C * x) = R(C * A',A,x).
[para(8565(a,1),882(a,1)),rewrite([38526(9),461(4),1641(7)]),flip(a)].
43700 A
* (R(C * x,A,C) / (x * C)) = R(A,C,x * A).
[para(1584(a,1),40(a,1,1,2)),rewrite([37347(11),35199(8),28545(8),42646(20)])].
44325 A
* R(C * A',A,x) = R(C,A,x * A).
[para(1641(a,1),2075(a,2,2)),rewrite([27613(9),31(7)]),flip(a)].
44367 A
* R(x,A,C')' = R(A * x',A,C').
[para(1156(a,1),1647(a,1,2)),rewrite([1863(11),461(12,R),27662(12),32681(10),20902(8),27795(17),41796
(15)]),flip(a)].
44473
R(A' * C',A,C * x) = R(A' * C',A,x).
[para(10972(a,1),1660(a,1,1,1)),rewrite([461(5),112(10),599(9),112(20),599(19),24058(19),31739(19
),27521(17),33(15),31(11),112(14),599(13),29930(14),16(12),29928(16)])].
44514
R(x,A,x' * A) = x.
[para(34765(a,1),1667(a,2,1,1)),rewrite([1090(4),2061(2),2068(6),27519(12),35199(9),86(8),439(7),1090(4),2061(2),17
08(6),83(4),2050(3),86(5),439(4),86(5),439(4)]),flip(a)].
44534
R(x,A * (x' * A),A) = x.
[para(44514(a,1),12026(a,1,1))].
44582
R(x,A * x',A * A) = x.
[para(44534(a,1),18(a,2)),rewrite([2008(8),1090(4),2061(2),13(15),7168(16)])].
44591
R(x * A,x' * A,A) = x * A.
[para(4435(a,1),44534(a,1,2,2,1)),rewrite([1089(9),871(9),35(10)])].
44631
R(R(C,A * x,A * C),A,x * C) = C.
[para(14702(a,1),1672(a,1,1,1)),rewrite([1272(6),32850(11),27622(9)]),flip(a)].
44704
R(x,A,x' * (A * A)) = x. [para(44591(a,1),1667(a,2,1,1)),rewrite([1102(6),2061(2),50(5),2008(8),1090(4),2061(2),1926(14),7168(16),4458
2(7),86(5),439(4),1926(6)]),flip(a)].
44714
R(A * x,A,x' * A) = A * x.
[para(2076(a,1),44704(a,1,3,1)),rewrite([2223(11),50(10),10(11)])].
44758
R(A * C,A,A * C') = A * C.
[para(16(a,2),44714(a,1,1)),rewrite([16(3),461(8)])].
44775
R(x,A * C,A * (A * C')) = x.
[para(44758(a,1),760(a,1,1,1,2)),rewrite([50(16),16(15),69(21),470(20),27519(17),35199(14),32387(6),1090(
13),435(11),461(12),35(13),461(9,R),10(9),435(6),32275(7),1089(6),871(6),35(7),86(5),439(4),44758(9)]),flip(a)].
44778
R(x,A,C')' = R(x',A,C').
[para(44775(a,1),1472(a,2,1)),rewrite([2997(10),461(5),15(9),461(6),50(8),461(7),29509(10),6085(8),29276(17),
35199(16),1926(8),33502(8),1090(15),435(13),461(14),35(15),461(11,R),27127(11),1926(6),2061(11),44367(12),4409(7),35(10),24764(10),35(6),2708
9(8)]),flip(a)].
44896
R(x,A,C)' = R(x',A,C).
[para(28537(a,1),44778(a,1,1)),rewrite([44778(9),28537(13)])].
44901
R(R(x',A,C'),x * A,C) = x'.
[para(44778(a,1),39771(a,1,1))].
44920
R(R(A,C',x)',A,C) = R(R(A,x,C)',A,C).
[back_rewrite(42384),rewrite([44896(8),44896(15)])].
44936
R(R(A,C,x)',A,C) = R(R(A,x,C')',A,C).
[back_rewrite(40641),rewrite([44896(7),44896(15)])].
44953
R(A * x,x',C) = R(A * x,A,C).
[back_rewrite(37302),rewrite([44896(11),31(8),28013(10)])].
44963
R(A * x',A,C) = R(A * x',x,C).
[back_rewrite(35397),rewrite([44896(10),28013(11)]),flip(a)].
45013
R(x',A,C * (A' * x)) = R(x',A,C).
[back_rewrite(28008),rewrite([44896(12)])].
45404 R(R(x,A,C'),x'
* A,C) = x.
[para(31(a,1),44901(a,1,1,1)),rewrite([31(11)])].
45419
R(R(A,x,C) * x,x',C) = A * x.
[para(41424(a,1),45404(a,1,1)),rewrite([2076(7),83(10),307(9)])].
45473
R(A,C,x) * x = R(A * x,x',C).
[para(44953(a,2),38674(a,1)),flip(a)].
45476
R(A,C,x)' * R(A * x,x',C) = x.
[para(44953(a,2),38914(a,1,2))].
45511 A'
* R(A * x,x',C) = R(x,A,C).
[back_rewrite(40368),rewrite([45473(6)])].
45877
R(A,x,C) * x = R(A * x,x',C').
[para(45419(a,1),39747(a,1,1)),flip(a)].
47155
R(C * R(C / x,x,y)',C',y) = x.
[para(23921(a,1),31512(a,1,1,2)),rewrite([16(14,R),35(14)])].
47562
(A' * R(x,y,A)) * y = A' * (x * y).
[para(1908(a,1),750(a,2)),rewrite([435(5),2805(8),38532(8),435(10),83(13),307(12)])].
47639
R(x,C,R(y * A,A,C)) = R(x,C,(C * y) * A).
[para(25415(a,1),38772(a,1,3))].
48519
R(R(C * x,A,C') / x,x,A) = C.
[para(61(a,1),27520(a,2)),rewrite([16(4,R),32275(7),16(5,R),27776(7)])].
48525
R(R(A,C,x),x,A) = R(A,C,x * A).
[para(38668(a,1),27520(a,2)),rewrite([28596(10),1090(7),435(5),86(6),439(5),38668(6)])].
48533 x
/ R(x,A,C) = A' * R(A,x,A * C).
[back_rewrite(41286),rewrite([48525(5),42678(8),41401(7)]),flip(a)].
48538
R(R(x * C,A,C') / x,x,A) = C.
[para(16(a,1),48519(a,1,1,1,1))].
48569
R(R(C * x,A,C') / x,x,A) = C.
[para(16(a,2),48538(a,1,1,1,1))].
48579
R(R(x * C,A,C') / x,x,A) = C.
[para(16(a,1),48569(a,1,1,1,1))].
48590
R(R(C * x,A,C') / x,x,A) = C.
[para(16(a,2),48579(a,1,1,1,1))].
48605
R(C * x,A,C') / x = R(C,A,A' * x).
[para(48590(a,1),34880(a,1,1)),flip(a)].
48832
R(x,C,R(C' * y,A,C)) = R(x,C,R(y,A,C)).
[para(28314(a,1),38772(a,1,3))].
48833
R(x,R(C' * y,A,C),C) = R(x,R(y,A,C),C).
[para(28314(a,1),39688(a,1,2))].
48837
R(A',C,R(x,A,C)) = R(A',C,x).
[back_rewrite(42000),rewrite([48832(10)])].
48902
R(x,C,(C * y) * A) = R(x,C,y * (A * C')).
[para(28326(a,1),38768(a,1,3)),rewrite([47639(7)])].
48908
R(A,C,x * (A * C')) = R(A,C,x * A).
[back_rewrite(41592),rewrite([48902(7)])].
48983
R(x,C,y * (A * (C * C))) = R(x,C,(y * C) * A). [para(28540(a,1),38768(a,1,3))].
49000
R(A,x,A * (C * C)) = R(A,C,x * A).
[back_rewrite(39205),rewrite([48983(9),41593(7)]),flip(a)].
49001
R(A,C,(x * C') * A) = R(A,C,x * A).
[back_rewrite(35998),rewrite([49000(10)])].
49002
R(A,C,(C' * x) * A) = R(A,C,x * A).
[back_rewrite(35997),rewrite([49000(10)])].
49003 A
* (x / R(x,A,C')) = R(A,C,x * A).
[back_rewrite(29316),rewrite([49001(8)]),flip(a)].
49027
((C * A') * x) / R(C * x,A,C) = R(A',x,C).
[para(28543(a,1),41305(a,1,2)),rewrite([37253(8),39692(19),142(17),31(17)])].
49102
R(C' / x,x,A)' / R(x,A,C) = C.
[para(28574(a,1),28651(a,1,1))].
49258 (x
* A) / (y * A) = A * ((A' * x) / y).
[para(29263(a,1),18(a,2)),rewrite([7(2)])].
49259 A
* R(C * A',C',x) = R(C,x,A).
[para(61(a,1),29263(a,1,1)),rewrite([29935(10)]),flip(a)].
49262
R(x / y,y,A) * A = x / (A' * y).
[para(29263(a,2),50(a,1,1)),rewrite([38407(12),35(14)])].
49264 A
* R(A' * x',x,y) = R(x,y,A)'.
[para(80(a,2),29263(a,2,2)),rewrite([33(2),143(4),4347(7)]),flip(a)].
49268
R(C',x,A)' = R(C,x,A).
[para(508(a,1),29263(a,1,1)),rewrite([644(6),884(13),49259(14)])].
49269
R(C,x,A)' = R(C',x,A).
[para(471(a,1),29263(a,1,1)),rewrite([38575(12),49264(13)]),flip(a)].
49273 A
* R(C * A',x,C) = R(C,C * x,A).
[para(1242(a,1),29263(a,1,1)),rewrite([37972(13),102(16)]),flip(a)].
49293 A
* (R(x,A,C) / x) = R(A,C,x * A).
[para(38668(a,1),29263(a,1,1)),rewrite([48525(5),31257(14),10(11)]),flip(a)].
49316
R(C,C * x,A) = R(C,x,A).
[para(143(a,1),49268(a,1,1)),rewrite([49269(4),49268(5)]),flip(a)].
49363 x
/ R(C' * x,A,C') = R(C,A',A * x).
[para(49268(a,1),1424(a,2)),rewrite([435(4),2153(8),32030(8),435(11),2805(14)])].
49386 A
* R(C * A',x,C) = R(C,x,A).
[back_rewrite(49273),rewrite([49316(13)])].
49396
R(C,A',A * x)' = R(C',A',A * x).
[para(2805(a,1),49269(a,1,1)),rewrite([2805(14)])].
49403
R(C,R(C * x,A,C),A) = R(C,R(x,A,C),A).
[para(28523(a,1),49316(a,1,2))].
49404
R(R(C,x,A),A,A' * (C * x)) = C.
[para(49316(a,1),34880(a,1,1))].
49441 A'
* R(C,x,A) = R(C * A',x,C).
[para(49386(a,1),10(a,1,2))].
49559 (x
* C) / R(A * x,A,C') = C * A'.
[para(29315(a,1),10(a,1,2)),rewrite([16(4,R)]),flip(a)].
50037
R(C',A,x * A)' = R(C,A,x * A).
[para(2118(a,1),1174(a,1,1,1)),rewrite([1090(11),435(9),32275(10),1089(9),871(9),35298(9),28543(10),285
38(8),435(13),32275(14),1089(13),871(13),35(14),27519(11),1090(9),435(7),86(8),439(7),29935(5),16(3),27625(9),32255(17),32275(16),1089(15),87
1(15),35(16)])].
50038
R(C,A * C,x * A) = R(C,A,x * A).
[back_rewrite(33627),rewrite([50037(14)])].
50039
R(A * C,C',x) * A' = R(C,A,x * A).
[back_rewrite(27625),rewrite([50037(16)])].
50159
R(C * A',C',x * A) = R(C * A',x,A).
[para(2138(a,1),18(a,1,1)),rewrite([29933(10)])].
50160 A'
* R(x,A,C') = R(A' * x,A,C').
[para(2138(a,1),3212(a,1)),rewrite([461(12,R),10(12),2153(11),32030(11),27745(11),35(7),83(21),307(20
),16(17,R),9(17),3(15),1102(15),107(12),461(13),24777(15)])].
50197
R(R(A * C,C',x),x,A) = A * C.
[para(29933(a,1),3914(a,1,1)),rewrite([16(3),6(12)])].
50200
R(A * C,C',A * x) = R(A * C,A,x).
[para(29933(a,1),1639(a,1)),rewrite([16(3),9(14),3(12)])].
50204 A
* R(C,x,A') = R(A * C,C',x).
[para(50197(a,1),34880(a,1,1)),rewrite([37155(8)])].
50206
R(R(A * C,x,C),x,A) = A * C.
[para(39546(a,1),50197(a,1,1))].
50216
R(A * C,A * x,C) = R(A * C,A,x).
[para(50206(a,1),34740(a,1,1)),flip(a)].
50221 x'
* ((C * (x * y)) * x') = y / (x * C').
[para(1091(a,1),29935(a,1,1)),rewrite([16(4,R),1750(6),27521(13)])].
50272
R(x * A',A,y)' = A * R(x,y,A')'.
[para(2183(a,1),6(a,1,1)),rewrite([1647(4)])].
50273
R(x,y,A') * A' = R(x * A',A,y).
[para(2183(a,1),33(a,1,2)),rewrite([882(4),2076(12),31(10)]),flip(a)].
50286 (A
* x) / (y * x) = A * R(y,x,A')'.
[back_rewrite(1647),rewrite([50272(10)])].
50414
R(A,C,(C * A') * x) = R(A',C,x)'.
[para(2206(a,1),38668(a,1,1,1)),rewrite([27776(7),39746(9),16(6,R),24474(8),10(7),16(11,R)]),flip(a)
].
50438 R(A',R(x,A,C),C)
= R(A',x,C).
[para(31257(a,1),101(a,1,1,2)),rewrite([28523(8),37253(8),16(10,R),28523(10),49027(11)]),flip(a)].
50453
R(R(A',x,C),R(x,A,C),C') = A'.
[para(50438(a,1),39747(a,1,1))].
50479 (x
/ (C * y)) * y = y' * (C' * (y * x)).
[para(31516(a,1),79(a,1,1)),rewrite([2226(5),461(14,R),10(14)]),flip(a)].
50511
R(x,A,A' * (y * A')) = R(x,y,A').
[para(35(a,1),32255(a,1,2)),rewrite([1841(10)]),flip(a)].
50518
R(R(x,A',A * y),y,A') = x.
[back_rewrite(38171),rewrite([50511(13)])].
50520
R(R(x,A',y),A' * y,A') = x.
[para(35(a,1),50518(a,1,1,3))].
50527
R(x,A,y) * A = R(x * A,y,A').
[para(889(a,1),50518(a,1,1)),rewrite([10(8),6(4),871(10)]),flip(a)].
50534
R(x' * A,x,A') = x' * A.
[para(1848(a,1),50518(a,1,1)),rewrite([10(5),2076(8),143(10),5310(7),871(4),10(11),871(10)])].
50539
R(x * A,x',A') = x * A.
[para(31(a,1),50534(a,1,1,1)),rewrite([31(8)])].
50568
R(x * A,A',A * x') = x * A.
[para(50539(a,1),38167(a,1,1))].
50750
((x * A) * y) * x' = x * (A * (y / x)).
[para(50568(a,1),1123(a,1,1)),rewrite([50568(10),86(10),439(9),38387(10),435(6),2223(11),2746(
11),1102(12),2061(2),1102(11),435(4),5100(10),50568(12),10(13)]),flip(a)].
50825
((x * C) * y) / (R(x,C',y) * y) = C.
[para(32660(a,1),6(a,1,1))].
50840 x
* (R(x,y,C)' * x) = R(x,y,C'). [para(2249(a,1),1460(a,1,2,2)),rewrite([10(8),10(13),38366(9),922(6),39840(14),143(12),39840(10),31(1
0)])].
50964
R(C,A * x,A * C) = R(C,A * x,A).
[para(33795(a,1),18(a,1,1)),rewrite([50(10),27519(11),1090(9),435(7),32275(8),16(6,R),27776(8),24764(
8),27770(8),38546(5),27622(8)])].
50971
R(R(C,A * x,A),A,x * C) = C.
[back_rewrite(44631),rewrite([50964(7)])].
50972
R(A * C,C,x) * A' = R(C,A * x,A).
[back_rewrite(27622),rewrite([50964(15)])].
50976
R(R(C,x,A),A,C * (A' * x)) = C.
[para(35(a,1),50971(a,1,1,2)),rewrite([16(9,R)])].
50981
R(C,A * (x * C),A) = R(C,A * x,A).
[para(50971(a,1),12026(a,1,1))].
51034
R(C,R(x,A,C),A) = R(C,x,A).
[para(50976(a,1),12026(a,1,1)),rewrite([28543(8),49403(8)])].
51037
R(R(C,A',A * x),x * C,A') = C.
[para(1043(a,1),50976(a,1,3)),rewrite([24707(5),28596(7),51034(9),2805(6),50511(16)])].
51041 (x
* (A * C)) / R(x * A,A,C) = R(C,x,A).
[para(51034(a,1),18(a,2)),rewrite([28523(5),50527(7),24707(8),27599(7),50527(9),24707(10)])].
51048
R(C,R(x,A,C'),A) = R(C,x,A).
[para(32626(a,1),51034(a,1,2)),rewrite([27089(4),28544(12),51034(13)])].
51051
R(C,x * (A * C),A) = R(C,x * A,A).
[para(28015(a,1),51034(a,1,2)),rewrite([49316(7)]),flip(a)].
51199
R(x * A,x,x * A) = x * A.
[para(23622(a,1),34498(a,1,2,2)),rewrite([23629(7),23649(8),23626(10),23622(9)])].
51209
R(x,A,x * (x * A)) = x.
[para(51199(a,1),1667(a,2,1,1)),rewrite([23577(3),13(6),6(12),86(5),439(4)]),flip(a)].
51228
R(x,A * (x * (x * A)),A) = x.
[para(51209(a,1),12026(a,1,1))].
51658 A
* R(C',x,A') = R(A * C',C,x).
[para(461(a,1),37000(a,1,1,2)),rewrite([38575(6)]),flip(a)].
51662
R(C,A,x)' = R(C',A,x).
[para(9182(a,1),37000(a,1,1,2)),rewrite([649(7),32259(17),44473(17),37353(16),35(11)])].
51669 A
* R(C * A',x,A') = R(C,A,A' * x).
[para(2206(a,1),37000(a,1,1)),rewrite([27776(7),48605(7),16(11,R)]),flip(a)].
51675
R(A * C',C,x) * A' = R(C',A,x * A).
[back_rewrite(27613),rewrite([51662(15)])].
51676
R(C',A,x) * R(C,A,x) = 0.
[para(51662(a,1),8(a,1,1))].
51677
R(C,A,x) * R(C',A,x) = 0.
[para(51662(a,1),9(a,1,2))].
51679
R(C',A,x)' = R(C,A,x).
[para(51662(a,1),31(a,1,1))].
51764 x
/ R(C' * x,A,C) = R(C,A,A' * x).
[back_rewrite(25645),rewrite([51679(15)])].
51846
R(R(C,A,x),R(C',A,x),y) = R(C,A,x).
[para(51676(a,1),1786(a,1,1,2)),rewrite([3(5),51662(7),51677(16),2(10),51662(12),33(14),51679(13)]
)].
51860
R(C,A,x) * ((A * C') * x) = A * x.
[para(51677(a,1),791(a,2,1)),rewrite([51846(10),461(7),2(13)])].
52081 (x
* A) * R(x,A,C) = x * R(A * x,A,C).
[para(28545(a,1),2528(a,2,2,2)),rewrite([86(10),439(9),3563(7),39236(8),28314(16),10(13)]),flip
(a)].
52085 C
* (x * (x * A)) = x * ((x * C) * A).
[para(2384(a,2),2528(a,1,2)),rewrite([10(10),1255(12),41666(14)])].
52139
((A * x) / y) / R(x / y,y,A') = A.
[para(37169(a,1),6(a,1,1))].
52193
R(C',x,A * C)' = R(C,x,A). [para(31432(a,1),2560(a,1,1,2)),rewrite([16(3),507(14),25415(11),51041(10),507(11)]),flip(a)].
52196
R(C,A,R(x,A,C')) = R(C,A,x * C).
[para(2560(a,1),37169(a,2)),rewrite([16(8),20902(10),49559(10),16(10),20902(12),51669(15),50160(11),1
0(7),51679(14)])].
52202 R(C,x,A
* C) = R(C,x,A).
[para(143(a,1),52193(a,1,1)),rewrite([31(7),49316(10)])].
52204
R(C,x * (A' * C'),A) = R(C,A',A * x).
[para(52193(a,1),1424(a,2)),rewrite([22446(6),1103(13),27783(10),50527(11),83(7),307(6),28038(7)
,28958(7),49363(8),22446(11)]),flip(a)].
52209
R(R(C,x,A),x * A,C) = R(C,x,A).
[back_rewrite(28707),rewrite([52202(15),51034(13)])].
52214
R(R(C,A',A * x),x,C) = R(C,A',A * x).
[para(7(a,1),52209(a,1,2)),rewrite([435(3),2805(6),435(11),2805(14)])].
52317
(R(x,C,y) * y) / ((C' * x) * y) = C.
[para(38579(a,2),6(a,1,1))].
52336
R(A',C,x) * R(x,A,C) = A' * x.
[para(48837(a,1),38579(a,1,1)),rewrite([461(14),24777(19),31257(14),39747(18)])].
52438
R(C / (x * A'),x,C) = A * (C / x).
[para(38878(a,1),39627(a,1,1)),rewrite([42775(15)])].
52531 A
* (R(A',x,C) * x) = R(x,A,C).
[para(39748(a,2),28543(a,1,2)),rewrite([507(12)])].
52532
(R(x,y,C)' * (x * y)) / x = R(y / x,x,C).
[para(39748(a,2),2238(a,1,1)),rewrite([143(4),507(10),39683(12)])].
52635
R(A * C,C,x) * R(C * A',A,x) = C * C.
[para(2627(a,1),35551(a,1,2)),rewrite([1593(9),1255(7),1245(8),16(3),43641(13)])].
52750
R(R(x,y * x,C),y * (C * x),C') = x.
[para(4905(a,1),39895(a,2)),rewrite([4919(8),39692(7),143(5),31(5)])].
52801
R(R(x * C,C,y) / x,x,y * C) = C.
[para(61(a,1),2650(a,2)),rewrite([16(5,R),39499(8)])].
52992 (A
* (x / (y * C))) * ((C * y) / x) = A.
[para(8551(a,1),2706(a,1,1,1)),rewrite([31(3),35(14)])].
53034
R(A,x,A * C) / (x / R(x,A,C)) = A.
[para(41687(a,1),6(a,1,1))].
53035 (x
/ R(x,A,C)) / R(A,x,A * C) = A'.
[para(41687(a,1),33(a,1,2))].
53061 (A
* (x / y)) * y = y' * ((y * A) * x).
[para(2744(a,1),10(a,1,2)),rewrite([31(3),35(10)]),flip(a)].
53084
R(A',x,C')' * A' = A * R(A',x,C).
[para(142(a,1),41933(a,2,2,1)),rewrite([38672(6),31(16)])].
53203
R(C,A * C,x * C') = R(C,A,R(x,A,C)).
[para(2384(a,2),2838(a,1,1,2,1)),rewrite([461(9),35(11),507(7),64(11),16(7),2836(11),461(9),27652
(11),36897(10),64(14),16(10)]),flip(a)].
53205
R(x,A,C) / x = A' * R(A,C,x * A).
[para(42233(a,1),830(a,2,1)),rewrite([871(8),42955(7),38532(11),48525(7)]),flip(a)].
53743
R(A * x',A,C) * x = R(A,x',C' * x).
[para(44963(a,2),39780(a,1,1)),rewrite([3372(16)])].
54034
R(R(A,x,C),x,C' * x') = A.
[para(45877(a,1),617(a,1,2,1)),rewrite([788(12),86(7),2028(6),461(5),507(6)]),flip(a)].
54485
R(C,R(x,A,C),A * C') = R(C,x,A).
[para(49102(a,1),1566(a,1,1)),rewrite([7(8),461(8),7(18),461(18),28576(19),654(17),49268(14)])].
54584
R(x,y,A) * A = R(x * A,A',y).
[para(6(a,1),49262(a,1,1,1)),rewrite([897(9)])].
54870
R(C,A * C,x) = R(C,A,x).
[para(7(a,1),50038(a,1,3)),rewrite([435(9),83(12),307(11)])].
54872
R(C,A,R(x,A,C)) = R(C,A,x * C').
[back_rewrite(53203),rewrite([54870(8)]),flip(a)].
54891
R(A * C,C',x) / R(C,x,A') = A.
[para(50204(a,1),6(a,1,1))].
54892 A'
* R(A * C,C',x) = R(C,x,A').
[para(50204(a,1),10(a,1,2))].
55377
R(x,y,C)' * x = x' * R(x,y,C').
[para(50840(a,1),10(a,1,2)),flip(a)].
55412
R(C,A',x * C) = R(C,A',x).
[para(1887(a,1),50981(a,1,2,2)),rewrite([16(11,R),35(14),38114(11),35(8),35(18),38114(15),9(13),2(11)])].
55419
R(C,A',C' * x) = R(C,A',x).
[para(7(a,1),55412(a,1,3)),rewrite([107(9)]),flip(a)].
55421
R(C,A',C * x) = R(C,A',x).
[para(16(a,2),55412(a,1,3))].
55469
R(R(C,x,A),R(x * A,A,C),A') = C.
[para(482(a,2),51037(a,1,1,3)),rewrite([55419(11),38098(8),16(10,R),28326(10)])].
55471
R(R(C,x,A),C * (x * A),A') = C.
[para(38098(a,1),51037(a,1,1)),rewrite([16(7,R)])].
55493
R(C,x * (A * C'),A) = R(C,x * A,A).
[para(481(a,1),51051(a,1,2)),rewrite([64(9),142(8),49268(7),481(14),461(12),142(16),49268(15)]),fl
ip(a)].
55697 (x
* (A * x')) * (C * x) = (x * C) * A.
[para(52085(a,1),2198(a,2,2)),rewrite([31440(3),10(14)])].
55732
R(C,A,C * (C * x)) = R(C,A,x * C').
[para(28537(a,1),52196(a,1,3)),rewrite([54872(6),16(14,R),27745(14),52196(15),16(12,R)]),flip(a)].
55921
R(R(x * C,C,y) / x,x,y) = C.
[para(7(a,1),52801(a,1,3)),rewrite([107(5),38772(7)])].
55949
R(R(x * C,A,C) / x,x,A * A) = C.
[para(28522(a,1),55921(a,1,1,1))].
55951
R(x * C,A,C) / x = R(C,A',A * x).
[para(55921(a,1),38167(a,1,1)),rewrite([24707(12)]),flip(a)].
55956
R(R(C,A',A * x),x,A * A) = C.
[back_rewrite(55949),rewrite([55951(6)])].
56119 A
* (A * R(A',x,C)) = R(A,C,x * (A * A)).
[para(41962(a,2),3872(a,1,1,2,2,1)),rewrite([28475(12),1092(9),871(7),1926(8),28013(13),35(1
0),28013(9),38668(14)]),flip(a)].
56217
R(A * x,y * A,A) = A * R(x,y,A).
[para(2104(a,1),3913(a,2,1)),rewrite([2223(14),15(13),10(10),10(11),49258(7),38446(7),35(8),31(12)]),
flip(a)].
56380
R(C,x,A * C') = R(C,x,A).
[para(34740(a,1),54485(a,1,2)),rewrite([27681(12),51048(13)])].
56381
R(C,A',A * (C' * x)) = R(C,A',A * x).
[para(1634(a,1),54485(a,1,2)),rewrite([22446(5),56380(12),52204(9),107(9),2805(15)]),flip(a)].
56602
R(A * C,x,C) / R(C,x,A') = A.
[para(39546(a,1),54891(a,1,1))].
56605
R(C,x,A') / R(A * C,x,C) = A'.
[para(56602(a,1),112(a,1,1)),flip(a)].
57084
R(x,A,C') / (C * x) = R(C',A',A * x).
[para(4425(a,1),1442(a,1,2,2)),rewrite([27783(8),50527(9),83(5),307(4),28038(5),16(13),9097(14),
27783(16),51048(17),2805(13),49396(14)])].
57132 A
* R(C * A',x,A) = R(C,x * A,A).
[para(123(a,1),56217(a,1,1)),flip(a)].
57250 A'
* R(A * C,x,C) = R(C,x,A').
[para(56605(a,1),7(a,1,1))].
57688
R(R(x,A,C) / x,x,A) = A * R(A',x,C).
[para(45473(a,1),16909(a,1,1,1)),rewrite([35(5),2027(4),142(5),44896(5),31(2),38672(12),53084(15)
])].
57821
R(x,(A * C) * y,C) = R(x,A * (y * C'),C).
[para(20902(a,1),39688(a,1,2)),rewrite([40034(8)]),flip(a)].
57822
R(C * R(A,x,C),A,C') = C * R(A,C',x).
[para(3613(a,2),20902(a,1,2)),rewrite([25908(8),39813(9),1255(7),42326(10),42681(15),16(14,R),35
(16)]),flip(a)].
57871 (x
* (C' * y))' * ((x * (y * C')) * z) = z.
[para(2898(a,1),22115(a,1,2,1,2)),rewrite([16(8,R),35(8),35(13)])].
58196 (x
* R(y * C,z,u)) / R(C * y,z,u) = x.
[para(24981(a,1),88(a,1,1,2)),rewrite([31(5),3(6),31(13),24981(19),78(13)])].
58210 (x
/ R(C * y,z,u)) * R(y * C,z,u) = x.
[para(24982(a,1),2341(a,1,1,1,3)),rewrite([78(5),10(17),24982(16),3(10)])].
58542
R(R(A,C,x),x,A') = R(A,C,x * A').
[para(38668(a,1),27524(a,2)),rewrite([50527(10),2153(7),12(6),10(7),24707(6),38668(6)])].
58807
R(C',A',A * R(A,C',x)) = C'.
[para(41710(a,1),33881(a,1,2,1)),rewrite([57822(17),57084(15)])].
58808
R(C,A',A * R(A,C',x)) = C.
[para(58807(a,1),139(a,2,1)),rewrite([10(9),461(9),1092(16),871(11),461(10),32030(16),49363(16),31(13)])].
58818
R(C,A * R(A,C,x)',A) = C.
[para(58808(a,1),2805(a,2)),rewrite([43050(8)])].
58823
R(C,R(A,C',x),A') = C.
[para(58808(a,1),50518(a,1,1))].
58831
R(C,R(A,x,C),A') = C.
[para(41402(a,1),58823(a,1,2))].
58841 (A
* C) * R(A,x,C) = A * (C * R(A,x,C)).
[para(58831(a,1),2168(a,1,1,2))].
58842
R(A * C,R(A,x,C),A) = A * C.
[para(58831(a,1),37167(a,1,1,2))].
58854
R(C,A * R(A,x,C')',A) = C.
[para(38627(a,1),58818(a,1,2,2,1))].
58859
R(A * C,C,R(A,C,x)') = A * C.
[para(58818(a,1),54584(a,1,1)),rewrite([16(3),16(6),38560(15)]),flip(a)].
58963
R(A,C,R(A,x,C) * A) = A.
[para(58842(a,1),1612(a,2,1,2)),rewrite([58841(7),50(9),29276(17),32275(16),16(11,R),27776(16),57822(15),4174
6(13),3(3),64(7)]),flip(a)].
58972
R(A,C',R(A,x,C) * A) = A.
[para(58963(a,1),39878(a,1,1)),rewrite([40310(9),58963(8)]),flip(a)].
58995 A
* R(A,C,R(A,x,C))' = 0.
[para(58972(a,1),1667(a,2,1,1)),rewrite([15(10),29276(21),1090(20),435(18),32275(19),24710(19),28013(18),280
22(18),1460(16),40305(8),9(13),76(20)])].
59012
R(A,C,R(A,x,C)) = A.
[para(58995(a,1),6(a,1,1)),rewrite([29(9),31(8)])].
59028
R(R(A,x,C),A,C) = R(A,x,C).
[para(59012(a,1),45476(a,1,1,1)),rewrite([45511(14)])].
59030
R(C,A,R(A,x,C)) = C.
[para(59012(a,1),52317(a,1,1,1)),rewrite([461(9),654(14),51679(8)])].
59047
R(C,A * R(A,x,C),A) = C. [para(59030(a,1),12026(a,1,1))].
59050
R(C,A,R(A,C',x)) = C.
[para(41402(a,2),59030(a,1,3))].
59082
R(A * C,R(A,C',x),A') = A * C.
[para(59050(a,1),50527(a,1,1)),rewrite([16(3),16(6)]),flip(a)].
59114
R(C,A,C * R(A,x,C)) = C.
[para(59047(a,1),50971(a,1,1)),rewrite([16(7,R)])].
59134 C
* (A * R(A,x,C)) = A * (C * R(A,x,C)).
[para(59114(a,1),751(a,1,1,1)),rewrite([16(5),25908(11),10(12)])].
59141
R(C,A,A' * R(A,x,C)) = C.
[para(59028(a,1),28689(a,1,1)),rewrite([51764(13)])].
59143
R(R(A,x,C)',A,C) = R(A,x,C)'. [para(59028(a,1),44896(a,1,1)),flip(a)].
59145 (A
* C) / R(A,x,C) = A * (C / R(A,x,C)).
[para(59028(a,1),1800(a,1,1,1)),rewrite([16(11,R),59028(17),50221(17),461(7,R),2061(8),141(8)
,59028(16)]),flip(a)].
59146
R(A',C',R(A,x,C)) = A'.
[para(59028(a,1),33703(a,1,2)),rewrite([41537(13)])].
59148
R(A',C,R(A,x,C)) = A'.
[para(59028(a,1),50453(a,1,2)),rewrite([42701(7),59146(8),42702(8)])].
59149
R(R(A,C',x)',A,C) = R(A,x,C)'.
[back_rewrite(44920),rewrite([59143(15)])].
59152
R(A',R(A,x,C),C') = A'. [back_rewrite(42702),rewrite([59148(15)])].
59207
R(C,R(A,x,C),A) = C.
[para(59141(a,1),12026(a,1,1)),rewrite([35(9)])].
59220
R(C,A,A' * (C * R(A,x,C))) = C.
[para(59207(a,1),49404(a,1,1))].
59320
R(C,A',R(A,x,C)) = C.
[para(59146(a,1),50825(a,1,2,1)),rewrite([16(4,R),897(15),83(6),307(5)])].
59324
R(C,A' * R(A,x,C),A') = C.
[para(59320(a,1),50520(a,1,1))].
59396
R(A,C,x * A) = R(A,x,A * C').
[para(461(a,1),5442(a,1,3,2,2)),rewrite([31(4),38772(11),48908(8),461(10)])].
59611
R(C,A,A' * R(A,C,x)') = C. [para(59324(a,1),18(a,2)),rewrite([41778(11),42680(9),27764(11),1841(19),42680(18),10(19),48605(15)])].
59680
R(C,A,A' * R(A',C,x)) = C.
[para(125(a,1),59611(a,1,3,2,1)),rewrite([559(9),435(9),461(10),24777(12),41991(12),31(10)])].
59684
R(R(A,C,x)',A,C) = R(A,C,x)'.
[para(59611(a,1),51860(a,1,1)),rewrite([1102(13),435(6),461(7),24710(13),28523(12),35(9),35(16)])].
59686
R(R(A,x,C')',A,C) = R(A,C,x)'.
[back_rewrite(44936),rewrite([59684(7)]),flip(a)].
59690
R(C,R(A',C,x),A) = C.
[para(59680(a,1),12026(a,1,1)),rewrite([35(10)])].
59767
R(A,R(A,C,x)',C) = R(A,C,R(A,C,x)').
[para(58859(a,1),1612(a,2,1,2)),rewrite([16(5,R),1255(5),1272(10),102(19),39692(9),64(13),38768(1
6)])].
59904
R(A,C,R(A,x,C)') = A.
[para(59143(a,1),28332(a,1,2)),rewrite([38668(14)])].
59910
R(A,R(A,x,C)',C) = A.
[para(59143(a,1),41346(a,1,2)),rewrite([59904(7)])].
59911
R(A,C,R(A,C',x)') = A.
[para(59143(a,1),41303(a,1,2)),rewrite([59910(7),41534(8)])].
59926
R(A,C,R(A',x,C)) = A.
[para(142(a,1),59904(a,1,3,1)),rewrite([31(8)])].
59938
R(A,R(A,C',x)',C) = A.
[para(41402(a,2),59910(a,1,2,1))].
59955
R(C,A,R(A',x,C)) = C.
[para(59926(a,1),52317(a,1,1,1)),rewrite([461(10),654(16),51679(9)])].
59973
R(C,A * R(A',x,C),A) = C.
[para(59955(a,1),12026(a,1,1))].
59984
R(A',C,R(A,C,x))' = A. [para(59911(a,1),48525(a,1,1)),rewrite([192(8),42955(10),38672(10),42648(9)]),flip(a)].
60025
R(A',C,R(A,C,x)) = A'.
[para(59984(a,1),31(a,1,1)),flip(a)].
60031
R(A',R(A,C,x),C') = A'.
[back_rewrite(42648),rewrite([60025(15)])].
60035
R(A',C',R(A,C,x)) = A'.
[para(60025(a,1),39878(a,1,1)),rewrite([60031(8)]),flip(a)].
60038
R(A',R(A,C,x),C) = A'.
[back_rewrite(42647),rewrite([60035(15)])].
60046
R(R(A,C,x),A,C) = R(A,C,x).
[para(60038(a,1),52531(a,1,2,1)),rewrite([35(8)]),flip(a)].
60164
R(R(A',C,x)',A,C) = R(A',C,x)'.
[para(125(a,1),60046(a,1,1)),rewrite([559(5),435(5),461(6),24777(8),41991(8),559(14),435(14),461(15),4
1993(17)])].
60173
R(A,C',R(A,C,x)) = A.
[para(60046(a,1),41307(a,1,2)),rewrite([6(9),42649(7)]),flip(a)].
60174
R(A,C,R(A,C,x)) = A.
[para(60046(a,1),41405(a,1,2)),rewrite([42649(6),60173(7),38739(8)])].
60178 (A
* C) / R(A,C,x) = A * (C / R(A,C,x)).
[para(60046(a,1),1800(a,1,1,1)),rewrite([16(11,R),60046(17),50221(17),461(7,R),2061(8),141(8)
,60046(16)]),flip(a)].
60197
R(C,A,R(A,C,x)) = C.
[para(60174(a,1),52317(a,1,1,1)),rewrite([461(9),654(14),51679(8)])].
60213
R(C,A,R(A,x,C')) = C.
[para(38627(a,1),60197(a,1,3))].
61008
R(R(A,x,A * C'),x * A,C) = A.
[para(59396(a,1),948(a,2,1)),rewrite([15(7),27491(8),6(15),39692(13)]),flip(a)].
61019
R(A,R(A,C,x)',A * C') = A.
[para(42678(a,1),59396(a,1,3)),rewrite([38672(9),59152(8),31(3)]),flip(a)].
61094
R(A,R(A',C,x),A * C') = A.
[para(125(a,1),61019(a,1,2,1)),rewrite([559(6),435(6),461(7),24777(9),41991(9),31(7)])].
61107
R(A,C,R(A',C,x) * A) = A.
[para(61094(a,1),18(a,2)),rewrite([484(11),461(8,R),29276(21),35199(20),461(19),2237(20),461(19,R),27110(20)
,49003(21),49002(12)])].
61113 A
* R(A,R(A',C,x),C)' = 0.
[para(61107(a,1),1667(a,2,1,1)),rewrite([15(10),29276(21),1090(20),435(18),32275(19),16(13,R),27776(19),247
64(19),27770(19),922(16),9(14),76(21)])].
61133
R(A,R(A',C,x),C) = A.
[para(61113(a,1),6(a,1,1)),rewrite([29(10),31(9)])].
61137
R(A,C,R(A,C,x)') = A.
[para(125(a,1),61133(a,1,2)),rewrite([16(6,R),2075(7),27652(8),38913(7),59767(7)])].
61143
R(A,R(A,C,x)',C) = A.
[back_rewrite(59767),rewrite([61137(14)])].
61144
R(A,C,R(A,x,C')') = A.
[back_rewrite(40318),rewrite([61137(7)]),flip(a)].
61146
R(A,R(A,C,x)',C') = A.
[back_rewrite(39193),rewrite([61144(16)])].
61151
R(A,C,R(A',x,C')) = A.
[para(38672(a,1),61137(a,1,3,1)),rewrite([31(9)])].
61160
R(A,R(A,x,C')',C) = A.
[para(38627(a,1),61143(a,1,2,1))].
61176
R(A * A,C',R(A,C,x)') = A * A.
[para(61146(a,1),768(a,1,1,1)),rewrite([461(10,R),461(18,R),5533(19),61146(18),61146(19)])].
61182
R(R(A',x,C'),A,C) = R(A',x,C').
[para(61151(a,1),38914(a,1,1,1)),rewrite([31257(13),10(10)])].
61380
R(C,A',A * R(A,C,x)') = C.
[para(59684(a,1),28651(a,1,2)),rewrite([38163(14)])].
61416
R(C,R(A,C,x)',A * A) = C.
[para(61380(a,1),55956(a,1,1))].
61426
R(C,R(A',C,x),A * A) = C.
[para(125(a,1),61416(a,1,2,1)),rewrite([559(6),435(6),461(7),24777(9),41991(9),31(7)])].
61443
R(C,R(A',C,x) * A,A) = C.
[para(61426(a,1),26516(a,2)),rewrite([59690(7)])].
63777
R(A,C,A * R(A,C,x)') = A. [para(59082(a,1),1612(a,2,1,2)),rewrite([3904(11),43050(9),43050(18),6(19),64(7),43050(10)]),flip(a)].
63780
R(A,C,A * R(A,x,C')') = A.
[para(38627(a,1),63777(a,1,3,2,1))].
63819
R(A * C,A,R(A,x,C')') = A * C.
[para(63780(a,1),31512(a,1,1,2)),rewrite([16(3),50200(13)])].
64600
R(C,A * A,R(A,C,x)') = C.
[para(61176(a,1),50825(a,1,2,1)),rewrite([16(5,R),67(5),69(10),12(18),256(19)])].
64602
R(C,A * A,R(A,x,C')') = C.
[para(38627(a,1),64600(a,1,3,1))].
65186
R(C,A,A * R(A,x,C')') = C.
[para(63819(a,1),1667(a,2,1,1)),rewrite([50(5),16(4),69(11),256(21),64602(10),1090(7),435(5),123(7)]),flip(
a)].
65189
R(C,A,A * R(A,C,x)') = C.
[para(38627(a,2),65186(a,1,3,2,1))].
65193
R(C,A * (A * R(A,C,x)'),A) = C.
[para(65189(a,1),12026(a,1,1))].
65212
R(C,A,(C * R(A,x,C)) * A') = C.
[para(65193(a,1),55471(a,1,1)),rewrite([50(12),50(11),42678(10),35(11),59134(8),32255(11)])].
65998
R((x * C) / R(x,A,C),R(x,A,C),A) = C.
[para(16(a,1),36225(a,1,1,1))].
66036
R(A * A,C',x) = R(A * A,x,C).
[para(37026(a,1),5532(a,1,1,2)),rewrite([461(13,R),1245(13),34985(9),31757(15)]),flip(a)].
66038
R(A * (A * x),A,C) / x = R(A * A,x,C).
[para(66036(a,1),88(a,2)),rewrite([461(6,R),1092(9),599(8),67(7),69(8),27662(9),39692(15)])].
66079
R(A * x,A,y * A) = A * R(x,A,y).
[para(7(a,1),37353(a,1,2,3)),rewrite([871(10)]),flip(a)].
66080 A'
* R(A * x,A,y) = R(x,A,y * A').
[para(37353(a,1),10(a,1,2))].
66291 A
* R(A' * x,A,y) = R(x,A,y * A).
[para(35(a,1),66079(a,1,1)),flip(a)].
66461
R(x,A,C) / (C' * x) = R(C,A',A * x).
[para(10942(a,1),319(a,1,1,1)),rewrite([50527(8),83(5),307(4),24707(4),307(10),2805(16),56381(16)
])].
66719 x
* (((C * x') / y) * x) = C / (x' * y).
[para(123(a,1),38366(a,1,1)),flip(a)].
66727
(C' * (x * y)) * x' = x * (y / (C * x)).
[para(16(a,2),38380(a,2,2,2)),rewrite([107(3)])].
66730 (C
* (x * y)) * x' = x * (y / (C' * x)).
[para(461(a,2),38380(a,2,2,2)),rewrite([599(4)])].
66751 x
/ R(A' * R(x,y,A),y,A') = A.
[para(38446(a,1),52139(a,1,2,1)),rewrite([35(6),6(2)])].
66838 x
/ R(A' * x,A,x * x) = A.
[para(51228(a,1),66751(a,1,2,1,2)),rewrite([32255(11),335(10),439(9)])].
66883
R(A' * x,A,x * x) / x = A'.
[para(66838(a,1),112(a,1,1)),flip(a)].
66891
R(A' * x,A,x * x) = A' * x.
[para(66883(a,1),7(a,1,1)),flip(a)].
66893
R((A' * R(x,y,A)) / x,x,y) = A'.
[para(66883(a,1),825(a,2)),rewrite([66891(9),38446(5)])].
67050
R(A',C,R(A',C,x) * A) = A'.
[para(61443(a,1),66893(a,1,1,1,2)),rewrite([16(4,R),107(6),10(7)])].
67313
R(A',C,A' * R(A,x,C)) = A'.
[para(125(a,1),67050(a,1,3,1)),rewrite([16(8,R),2075(9),27652(10),38913(9),42678(9)])].
67451
R(A',C,A' * R(A,x,A * C)) = A'.
[para(41401(a,1),67313(a,1,3,2))].
70015
R(R(A',C,x),x,A) = R(A',C,x * A).
[para(41974(a,1),27520(a,2)),rewrite([32384(12),32275(8),12(7),35(8),41974(8)])].
70020 A
* (R(A',C,x) * x) = R(x,A,C').
[para(41976(a,2),2168(a,2,2)),rewrite([2168(10),24764(16),35(12)])].
70239
R(A',x * y,C') = R(A',C,x * y).
[para(332(a,1),43036(a,1,2)),rewrite([332(13)])].
70538
R(R(A',x,C')',A,C) = R(A',C,x)'.
[para(41975(a,1),45013(a,2,1)),rewrite([45013(16),60164(8)]),flip(a)].
71360
(A' * R(A,C,x * A)) * x = R(x,A,C).
[para(45473(a,1),47562(a,2,2)),rewrite([48525(7),45511(17)])].
71373
R(A',C,x / R(x,A,C)) = A'.
[para(48533(a,1),43036(a,1,2)),rewrite([70239(13),67451(12)]),flip(a)].
71384
R(A',x / R(x,A,C),C) = A'. [para(71373(a,1),948(a,2,1)),rewrite([16(5,R),42016(20),39692(12)]),flip(a)].
71395
R(x / R(x,A,C),A,C) = x / R(x,A,C).
[para(71384(a,1),52531(a,1,2,1)),rewrite([35(9)]),flip(a)].
71839 x
* R(A,C,x * A) = x * R(A,C,x).
[para(49293(a,1),50750(a,2,2)),rewrite([52081(6),1090(8),38668(6)]),flip(a)].
71841
R(A,C,x * A) = R(A,C,x).
[para(71839(a,1),10(a,1,2)),rewrite([10(6)]),flip(a)].
71843
R(A,C,x * (A * A)) = R(A,C,x).
[para(71839(a,1),4433(a,1,2)),rewrite([71841(11),4433(11),1926(9)]),flip(a)].
71845
R(A,C,x * A') = R(A,C,x).
[para(71839(a,1),5067(a,1,2)),rewrite([5067(14),83(13),307(12)])].
71855
(A' * R(A,C,x)) * x = R(x,A,C).
[back_rewrite(71360),rewrite([71841(7)])].
71897
R(A,x,A * C') = R(A,C,x).
[back_rewrite(59396),rewrite([71841(5)]),flip(a)].
71911
R(x,A,C) / x = A' * R(A,C,x).
[back_rewrite(53205),rewrite([71841(11)])].
71919 A
* (R(x,A,C) / x) = R(A,C,x).
[back_rewrite(49293),rewrite([71841(11)])].
71928 A
* (R(C * x,A,C) / (x * C)) = R(A,C,x).
[back_rewrite(43700),rewrite([71841(15)])].
71941 A
* (A * R(A',x,C)) = R(A,C,x).
[back_rewrite(56119),rewrite([71843(15)])].
71942
R(R(A,C,x),x,A') = R(A,C,x).
[back_rewrite(58542),rewrite([71845(12)])].
71975
R(R(A,C,x),x * A,C) = A.
[back_rewrite(61008),rewrite([71897(6)])].
71997
R(A,C,x * (C * (A' * A'))) = R(A,C,x).
[para(2680(a,1),71841(a,1,3)),rewrite([38768(8),71845(6)]),flip(a)].
72002 A'
* R(A,x,A * C) = A' * R(A,x,C).
[para(71841(a,1),42678(a,1,1,1)),rewrite([42678(6),41401(13)]),flip(a)].
72044 x
/ R(x,A,C) = A' * R(A,x,C).
[back_rewrite(48533),rewrite([72002(12)])].
72061
R(R(A,C,x),x * A',C) = A.
[para(2680(a,1),71975(a,1,2)),rewrite([71997(11),39692(10)])].
72111
R(A',C,x * A) = R(A',C,x).
[para(71897(a,1),1487(a,2,1)),rewrite([494(5),435(3),494(9),435(7),13522(9),24752(10),494(11),435(9),27776(
12),79(16),461(12,R),25415(12),40252(11),70239(7),494(13),435(11),50414(14),31(12)])].
72112
R(R(A',C,x),x,A) = R(A',C,x).
[back_rewrite(70015),rewrite([72111(12)])].
72270
R(R(A,C,x * x),x * (x * A'),C) = A.
[para(12(a,1),72061(a,1,2))].
72421
R(A,x,A * C) = R(A,x,C).
[para(71919(a,1),11186(a,1,1,2,1)),rewrite([50(8),42678(7),35(8),2061(9),112(9),41687(9),307(12)]),flip(a)].
72425
R(A * A,x,C) * A' = R(A,C,A * x).
[para(71919(a,1),38380(a,2)),rewrite([28013(7),66038(8)])].
72466 (x
/ R(x,A,C)) / R(A,x,C) = A'.
[back_rewrite(53035),rewrite([72421(9)])].
72467
R(A,x,C) / (x / R(x,A,C)) = A.
[back_rewrite(53034),rewrite([72421(5)])].
72490
R(A,C',x * A') = R(A,x,C).
[back_rewrite(42240),rewrite([72421(10),41685(8)])].
72523
R(A,x * A,C) = R(A,x,C).
[back_rewrite(41401),rewrite([72421(10)])].
72530
R(A,x * A',C) = R(A,x,C).
[back_rewrite(41676),rewrite([72490(13)])].
72820
R(R(A,C,x),x * C,A') = R(A,C,x).
[para(71942(a,1),2594(a,1)),rewrite([38768(5),38768(8)]),flip(a)].
72908
R(A',C,x * A') = R(A',C,x).
[para(7(a,1),72111(a,1,3)),rewrite([435(9)]),flip(a)].
73281
R(x,R(x,A,C),C) = x.
[para(71855(a,1),4714(a,1,1,2)),rewrite([38771(14),71855(14),28523(11),58196(12),38771(7),71855(7)]),flip(a)].
73283
R(x * C,R(x,A,C),C) = C * x.
[para(73281(a,1),396(a,1)),rewrite([39610(11)]),flip(a)].
73285
R(x * C',R(x,A,C),C) = C' * x.
[para(73281(a,1),805(a,1)),rewrite([48833(14)]),flip(a)].
73290
R(x,R(x,A,C),C') = x.
[para(73281(a,1),39747(a,1,1))].
73298 (x
* C) / R(x,A,C) = R(C,A,A' * x).
[para(73290(a,1),1731(a,1,1)),rewrite([461(7,R),141(8),73290(12),38362(7),35(9),73290(12),461(12,R
),28314(12),51764(13)])].
73299
R(R(C,A,A' * x),R(x,A,C),A) = C.
[back_rewrite(65998),rewrite([73298(6)])].
73345 A'
* R(A,C,x) = A * R(A',x,C).
[para(71911(a,1),27520(a,2)),rewrite([28596(8),86(5),439(4),57688(6),71841(13)]),flip(a)].
73463 A'
* R(A,x,C) = A * R(A',x,C').
[para(71941(a,1),10918(a,1,1,1)),rewrite([42678(6),2061(16),2076(16),55377(17),31(12),10(18)])].
73482 A'
* (R(A,x,C) * A) = R(A',x,C)'.
[para(71941(a,1),16999(a,1,1,1)),rewrite([5693(17),42681(8)])].
73493 x
/ R(x,A,C) = A * R(A',x,C').
[back_rewrite(72044),rewrite([73463(10)])].
73499
R(A,C,x)' * A = A * R(A',x,C').
[back_rewrite(42678),rewrite([73463(12)])].
73553
R(A,R(A',C,x),x * A) = A.
[para(72112(a,1),6981(a,1,2,1,1)),rewrite([23(12),3(3),72112(8)]),flip(a)].
73555
R(A,R(A',C,x),x) = A.
[para(7(a,1),73553(a,1,3)),rewrite([435(6),72908(8)])].
73577 (A
* R(A',C,x)) * x = R(x,A,C').
[para(73555(a,1),79(a,1,1)),rewrite([70020(7)]),flip(a)].
73586
R(A,R(A',C,x),R(x,A,C)) = A.
[para(48837(a,1),73555(a,1,2))].
73653 (A
* R(A',C,x)) * R(x,A,C) = x.
[para(73586(a,1),79(a,1,1)),rewrite([52336(9),35(5)]),flip(a)].
73835 (x
/ R(x,A,C)) * A = R(A',x,C)'.
[para(72466(a,1),1166(a,1,1)),rewrite([72466(13),871(8),73482(8),72467(17)]),flip(a)].
74185 x
/ R(x,A,C) = A * R(A',C,x).
[para(73653(a,1),6(a,1,1))].
74307
R(A,C,x) * (A * R(A',C,x)) = A.
[para(74185(a,1),52992(a,1,2)),rewrite([71928(10),38768(10)])].
74390
R(A,x,C')' * A = A * R(A',C,x). [para(74307(a,1),38946(a,1,2))].
74560 A
* R(A,C,x) = R(A * A,x,C).
[para(72820(a,1),37000(a,2,2)),rewrite([757(7),37301(9)]),flip(a)].
74591
R(A * A,x,C) * R(A,C,x)' = A.
[para(74560(a,1),86(a,1,1)),rewrite([2028(19)])].
74717
R(x,R(x * C,A,C),C) = x. [para(64(a,1),73285(a,2)),rewrite([461(5,R),64(5)])].
74734
R(R(C,A,x),C * (A * x),A) = C.
[para(34595(a,1),73299(a,1,2)),rewrite([31235(9),54872(8),461(7,R),10(7)])].
74745
R(C,A,x * C') = R(C,A,x).
[para(74734(a,1),34880(a,1,1)),rewrite([27764(9),52196(9),16(6,R),55732(7)])].
74749
R(R(C,A,x),C * (C * (A * x)),A) = C.
[para(4926(a,1),74734(a,1,2,2)),rewrite([16(8),2223(9),16(8,R),27764(9),52196(9),16(6,R),55732(7)
,74745(6),307(10)])].
74764
R(C,A,x * C) = R(C,A,x).
[para(83(a,1),74745(a,1,3)),rewrite([31(5),458(6),31(8)]),flip(a)].
75009
R(x,R(x,A,C'),C) = x.
[para(73577(a,1),4714(a,1,1,2)),rewrite([38771(15),73577(15),27745(13),58196(14),38771(7),73577(7)]),flip(a)].
75012
R(R(x,A,C),x,C) = R(x,A,C).
[para(34740(a,1),75009(a,1,2)),rewrite([27658(6),27658(11)])].
75640 C
* (x * R(y,x,C)) = x * (y * C).
[para(20117(a,2),1121(a,1,1)),rewrite([1102(11),107(7),66727(10),102(7),40(13),10(12)])].
75642 C'
* (x * (y * C)) = x * R(y,x,C).
[para(75640(a,1),10(a,1,2))].
75647 x
* (C' * R(y,x,C)) = C' * (x * y).
[para(481(a,1),75640(a,1,2)),rewrite([39688(13),39688(10),35(11),1103(15),35(13)])].
75650 x
* (C * R(A,C,x)) = C * (x * A).
[para(38563(a,1),75640(a,1,2,2)),rewrite([16(9,R)]),flip(a)].
75651 x
* (C * R(y,x,C')) = C * (x * y).
[para(39746(a,1),75640(a,1,2,2)),rewrite([16(8,R)]),flip(a)].
75690 (C
* (x * A)) / (C * R(A,C,x)) = x.
[para(75650(a,1),6(a,1,1))].
75691 x'
* (C * (x * A)) = C * R(A,C,x).
[para(75650(a,1),10(a,1,2))].
75692 (C
* R(A,C,x)) / (C * (x * A)) = x'.
[para(75650(a,1),33(a,1,2))].
75694 (C
* x) * R(A,C,x) = x * (A * C).
[para(75650(a,1),2224(a,2,2)),rewrite([38772(9),461(10,R),10(10),24784(14),27745(14),27756(14)])].
75715
R(R(x,A,C'),R(A,C,x),C) = x.
[para(75690(a,1),39745(a,2)),rewrite([75692(10),39840(8),143(6),44778(5),44778(6),31(2),39692(11)])].
75720
R(x,R(A,C,x),C') = R(x,A,C').
[para(75715(a,1),39747(a,1,1))].
75729 x'
* R(x * A,A,C) = R(A,C,x).
[para(75694(a,1),10(a,1,2)),rewrite([509(3),1091(8),2548(8),25415(8)])].
75731
R(x * A,A,C) = x * R(A,C,x).
[para(35(a,1),75694(a,1,1)),rewrite([38772(6),1103(11),25415(11)]),flip(a)].
75747
R(x * A,A,C) / R(A,C,x) = x.
[para(75731(a,2),6(a,1,1))].
75748 (x
* A') * R(A,C,x) = R(x,A,C).
[para(7(a,1),75731(a,1,1)),rewrite([435(5),435(10),71845(12)]),flip(a)].
75755 (A
* x') * R(x,A,C) = R(A,C,x).
[para(75731(a,2),5067(a,1,2)),rewrite([83(8),307(7),71845(13)])].
75827 (x
* A) / R(A,C,x) = R(x,A,C').
[para(75720(a,1),39916(a,2)),rewrite([75650(8),10(7)])].
75848
R(A * x',A,C') * x = R(A,x,C').
[para(34740(a,1),75755(a,1,2)),rewrite([27681(6),44778(6),24764(7),27681(15),41565(15)])].
75939
R(A * x',x,C')' = x / R(A,C,x).
[para(625(a,1),75827(a,2)),rewrite([435(2),83(5),307(4),435(4),71845(6),2061(6)]),flip(a)].
75947
R(x / R(A,C,x),A,C) = x * A'.
[back_rewrite(27908),rewrite([75939(7)])].
75984
R((x / R(A,C,x)) * A,A,C) = x.
[para(75947(a,1),50527(a,1,1)),rewrite([83(5),307(4),24707(10)]),flip(a)].
75993 (x
/ R(A,C,x)) * A = R(x,A,C').
[para(75984(a,1),12026(a,1,1)),rewrite([27681(5)]),flip(a)].
75996
R(R(C,x / R(A,C,x),A),x,A') = C.
[para(75984(a,1),55469(a,1,2))].
76191 x'
* (C' * (x * (y * C))) = R(y,x,C).
[para(75642(a,2),10(a,1,2))].
76194
R(x,y,C) * R(y,R(x,y,C),C) = x * y.
[para(79(a,1),75642(a,1,2)),rewrite([16(5,R),10(6)]),flip(a)].
76197 x
* R(A * C,x,C) = (x * C) * A.
[para(14702(a,1),75642(a,1,2,2)),rewrite([41666(9)]),flip(a)].
76198 (x
* R(y,x,C)) / y = R(x,y,C').
[para(75642(a,1),489(a,1,1)),rewrite([461(8,R),64(8),39841(9)])].
76200
R(x,y,C') * y = x * R(y,x,C).
[para(75642(a,1),788(a,2)),rewrite([39841(5),64(8)])].
76201
R(x * A,A,C') = x * R(A,x,C).
[para(31432(a,1),75642(a,1,2,2)),rewrite([16(5),27127(7),507(12)])].
76203 (C
* x) * R(A,x,C) = C * (x * A).
[para(1421(a,1),75642(a,1,2)),rewrite([10(9),39692(11)]),flip(a)].
76205 x
/ (y * R(x,y,C)) = R(y,x,C')'.
[para(75642(a,1),1460(a,1,2)),rewrite([64(5),39841(9)])].
76207
R(x,A,C) * R(A,x,C) = x * A.
[para(41290(a,1),75642(a,2,2)),rewrite([79(9),16(6,R),10(7)]),flip(a)].
76219 (x
* A) / R(A,x,C) = R(x,A,C).
[para(76207(a,1),6(a,1,1))].
76229
R(A,x',C' * x) = R(A,x,C).
[para(76207(a,1),6150(a,1,2)),rewrite([50286(6),24707(5),44896(5),28013(6),435(8),83(11),307(10),53743(7),4
35(9),72530(12)])].
76250 (C
* (x * A)) / R(A,x,C) = x * C.
[para(39485(a,1),76219(a,1,1)),rewrite([27089(10),41312(13),39664(9),27089(13),39746(17)])].
76278
R(A,x,C' * x') = R(A,x',C).
[para(31(a,1),76229(a,1,2))].
76294 x'
* ((x * C) * A) = R(A * C,x,C).
[para(76197(a,1),10(a,1,2))].
76361
(R(x,y,C') * y) / R(y,x,C) = x.
[para(76200(a,2),6(a,1,1))].
76363
R(x,y,C) / (R(y,x,C') * x) = y'.
[para(76200(a,2),33(a,1,2))].
76439 x'
* R(x * A,A,C') = R(A,x,C).
[para(76201(a,2),10(a,1,2))].
76443 C'
* R(A * C,x,C) = R(A,x,C).
[para(76201(a,2),556(a,1,2)),rewrite([31356(11),10961(8),141(6),1091(7),76294(8),39664(13)])].
76467
R(R(A,x,C),C,x) = A.
[back_rewrite(41824),rewrite([76443(8)])].
76471 C
* R(A,x,C) = R(A * C,C',x).
[para(76467(a,1),31512(a,1,1,2)),rewrite([16(3),16(11,R)]),flip(a)].
76510
R(C,A,R(C,A,x * A)) = C.
[back_rewrite(65212),rewrite([76471(7),50039(11)])].
76516
R(C,A,R(C,x,A')) = C.
[back_rewrite(59220),rewrite([76471(9),54892(11)])].
76526
R(C,R(A * C,C',x),A) = C.
[para(76516(a,1),12026(a,1,1)),rewrite([50204(7)])].
76544
R(C,A,R(C,A,x)) = C.
[para(7(a,1),76510(a,1,3,3))].
76547
R(C,A * R(C,A,x),A) = C. [para(76544(a,1),12026(a,1,1))].
76618
R(A,C,R(C,A,x))' = A'.
[para(76547(a,1),66893(a,1,1,1,2)),rewrite([16(4,R),107(6),10(7),41986(9)])].
76641
R(A,C,A * R(C,A,x)) = A.
[para(76618(a,1),74591(a,1,2)),rewrite([72425(11)])].
76669
R(A,C,R(A * C,A,x)) = A. [para(37353(a,1),76641(a,1,3))].
76678
R(A,R(A * C,A,x),C) = A.
[para(76669(a,1),948(a,2,1)),rewrite([35169(11),6(21),39692(11)]),flip(a)].
76687
R(A,R(A * C,A,x)',C) = A.
[para(76678(a,1),54034(a,1,1)),rewrite([76278(16)])].
76764 x'
* (C' * (x * (C * y))) = R(y,x,C).
[para(2632(a,1),20488(a,1,2,2)),rewrite([7(7),76191(8),1091(9),461(9,R)]),flip(a)].
76765
R(A * x,A,C') = R(A * x,x,C).
[para(42262(a,1),20488(a,1,2,2,2)),rewrite([76764(10),79(14),461(11,R),20902(11)]),flip(a)].
76770
R(C,R(A * C,x,C),A) = C.
[para(39546(a,1),76526(a,1,2))].
76773
R(C',R(A * C,x,C),A) = C'.
[para(76770(a,1),49269(a,1,1)),flip(a)].
76780
R(A',C,R(A * C,x,C)) = A'.
[para(76770(a,1),66893(a,1,1,1,2)),rewrite([16(4,R),107(6),10(7)])].
76904
R(A,R(C',A,x),C) = A. [para(66079(a,1),76687(a,1,2,1)),rewrite([2076(7),51662(5),72530(10)])].
76907
R(A,C,R(C',A,x)) = A.
[para(76904(a,1),948(a,2,1)),rewrite([16(9,R),16(17,R),1260(19),38739(9),16(14,R),39692(16),76904(14)])].
76919
R(C,A,R(C',A,x)) = C.
[para(76907(a,1),52317(a,1,1,1)),rewrite([461(10),654(16),51679(9)])].
76927
R(C,A,R(C',x,A')) = C.
[para(50511(a,1),76919(a,1,3))].
76944
R(C,R(A * C,C,x),A) = C.
[para(76927(a,1),74749(a,1,1)),rewrite([51658(10),39500(11),507(8),16(4)])].
76968
R(A,C,R(A * C,C,x)) = A. [para(76944(a,1),6981(a,1,2,1,1)),rewrite([23(16),3(3),76944(10),71841(11)]),flip(a)].
76994
R(A,C,R(C,A * x,A)) = A.
[para(76968(a,1),71845(a,2)),rewrite([50972(10)])].
77030
R(A,C,R(C,x,A)) = A.
[para(35(a,1),76994(a,1,3,2))].
77051
R(R(C,x,A),A,C) = R(C,x,A).
[para(77030(a,1),75690(a,1,2,2)),rewrite([54584(6),16(4),16(11),22446(12),2224(14),10942(14),31965(9),1090
(6),435(4),123(6)])].
77615
R(A',C',R(A * C,x,C)) = A'.
[para(76773(a,1),66893(a,1,1,1,2)),rewrite([599(8),507(7)])].
77617
R(A',R(A * C,x,C),C) = A'.
[para(76780(a,1),32626(a,2)),rewrite([77615(10)])].
77975 C
* (A * R(A',x,C')) = R(C,x,A').
[para(77617(a,1),39748(a,1,1)),rewrite([57250(8),461(15,R),76443(15),73463(11)]),flip(a)].
78133 (C
* R(A,C,x)') * A = R(C,x,A').
[para(61143(a,1),76203(a,1,2)),rewrite([73499(15),77975(17)])].
78134 C
* (A * R(A',C,x)) = R(C,x,A').
[para(38948(a,1),76203(a,2,2)),rewrite([61143(13),78133(8),74390(12)]),flip(a)].
78235 C
* R(A,C,x)' = R(C * A',A,x).
[para(61143(a,1),76250(a,1,2)),rewrite([73499(7),77975(9),435(6),50273(7),16(12,R)]),flip(a)].
78236 C
* R(A,x,C')' = R(C * A',A,x).
[para(61160(a,1),76250(a,1,2)),rewrite([74390(8),78134(8),435(6),50273(7),16(13,R)]),flip(a)].
78241
R(A,x,C) * (C * A') = R(C,A,x * A).
[back_rewrite(42695),rewrite([78235(15),44325(16)])].
78354 (x
* y) / R(y,R(x,y,C),C) = R(x,y,C).
[para(39747(a,1),76361(a,1,1,1))].
78356
R(R(x,y,C'),R(y,x,C),C) = x.
[para(76361(a,1),39745(a,2)),rewrite([76363(7),41157(8),31(5)])].
78394
R(R(x,R(y,x,C'),C'),y,C) = x.
[para(39746(a,1),78356(a,1,2))].
78395
R(x,R(y,x,C),C') = R(x,y,C').
[para(78356(a,1),39747(a,1,1))].
78460 C'
/ R(A,x,C) = R(A' * C',A,x).
[para(76443(a,1),492(a,1,2)),rewrite([40204(12)])].
78582
R(A * (C * x),x,C) = C * (A * x).
[para(2536(a,1),76765(a,1,1)),rewrite([35195(8),39692(12)]),flip(a)].
79187
R(A,C,x * x) = R(A,x,C).
[para(21593(a,1),75729(a,2)),rewrite([509(4),1023(4),274(11),33480(14),13(12),10(10),27127(8),76439(8),38773(
9)]),flip(a)].
79199
R(R(A,x,C),x * (x * A'),C) = A.
[back_rewrite(72270),rewrite([79187(4)])].
79534
R(x,R(y,x,C'),C') = R(x,y,C').
[para(78394(a,1),39747(a,1,1)),flip(a)].
79536
R(x,y,C') * R(y,x,C') = x * y.
[para(78394(a,1),76200(a,2,2)),rewrite([79534(6),79534(6),79534(9)])].
79545
R(R(x,y,C),R(y,x,C'),C') = x.
[para(78356(a,1),78395(a,1,2)),rewrite([39747(5)]),flip(a)].
79589 C
* (x / R(x,A,C)) = R(C,x,A').
[para(73493(a,2),78582(a,2,2)),rewrite([78582(16),77975(9)]),flip(a)].
79742
R(R(A,x,C),x * (A * x),C) = A.
[para(7(a,1),79199(a,1,2,2)),rewrite([871(4),72523(5),871(6),23577(6)])].
79747
R(A,C,x * (A * x)) = R(A,x,C).
[para(79742(a,1),39747(a,1,1)),rewrite([40310(7)])].
79752
R(A',C,x * x)' = R(A',x,C)'.
[para(35(a,1),79747(a,1,3,2)),rewrite([19948(6),38672(7),70239(6),142(12)])].
79870
R(x,R(y,x,C'),C) = R(x,y,C).
[para(79545(a,1),948(a,2,1)),rewrite([461(10,R),35(11),461(13,R),35(14),6(10),461(8,R),39688(10)]),flip(a
)].
79877
(R(x,y,C) * y) / R(y,x,C') = x.
[para(79545(a,1),76198(a,2)),rewrite([78356(9)])].
79879 (x
* R(y,x,C')) / y = R(x,y,C).
[para(79545(a,1),76361(a,1,1,1)),rewrite([78356(11)])].
79880
R(R(x,y,C'),R(y,x,C'),C) = x.
[para(39746(a,1),79870(a,2)),rewrite([79534(9)])].
79881
R(x,R(y,x,C),C) = R(x,y,C).
[para(39747(a,1),79870(a,1,2)),flip(a)].
79890 (x
* y) / R(y,x,C) = R(x,y,C).
[back_rewrite(78354),rewrite([79881(5)])].
79891
R(x,y,C) * R(y,x,C) = x * y.
[back_rewrite(76194),rewrite([79881(6)])].
79900
R(x,y,C)' * (x * y) = R(y,x,C).
[para(79881(a,1),39741(a,1,1,1)),rewrite([75647(10),35(9)])].
79908
R(x,y,C) / y = R(x / y,y,C).
[back_rewrite(52532),rewrite([79900(5)])].
79949 x
/ R(y,x / y,C) = R(x / y,y,C).
[para(7(a,1),79890(a,1,1))].
79962
R(x,y,C')' * x = x' * R(x,y,C).
[para(79890(a,1),38362(a,2,2)),rewrite([76205(4)])].
79978
R(x,y / x,C) = R(x,y,C).
[para(79891(a,1),6150(a,1,2)),rewrite([7(7),38362(6),107(6),76191(8)]),flip(a)].
79987
R(x / y,y,C) = x / R(y,x,C).
[back_rewrite(79949),rewrite([79978(3)]),flip(a)].
79988
R(x,y * x,C) = R(x,y,C).
[para(6(a,1),79978(a,1,2)),flip(a)].
79989
R(x * y,x',C) = R(x * y,y,C).
[para(33(a,1),79978(a,1,2))].
80016
R(x,y * (x * C),C) = R(x,y,C).
[para(3564(a,1),79978(a,1,2)),rewrite([39692(6),39664(4),39692(9)]),flip(a)].
80020
R(C,x * A,A) = R(C,x,A).
[para(79978(a,1),49386(a,1,2)),rewrite([49386(8),13522(9),55493(11)]),flip(a)].
80044 x
* R(A,C,x) = R(x * A,x',C).
[para(75731(a,1),79978(a,2)),rewrite([33(6)]),flip(a)].
80058
R(x / y,y,C) * R(y,x,C) = x.
[para(79978(a,1),79891(a,1,2)),rewrite([7(8)])].
80060
R(R(x,y,C),y * (C * x),C') = x.
[back_rewrite(52750),rewrite([79988(3)])].
80071 A
* R(C * A',x,A) = R(C,x,A).
[back_rewrite(57132),rewrite([80020(13)])].
80132 A
* R(C,A,x) = R(A * C,A,x).
[para(74(a,1),79988(a,1,2)),rewrite([50216(11),66079(9),74764(6),50216(12)])].
80142
R(C,A',A * x) = R(C,x,A).
[para(79988(a,1),49386(a,1,2)),rewrite([49386(8),38114(11),16(10,R),55421(11)]),flip(a)].
80144
R(x,R(y,C,x),C) = R(x,y,C).
[para(38579(a,1),79988(a,1,2)),rewrite([39692(8),79988(6),39688(5)]),flip(a)].
80186
R(x,A,C) / (C' * x) = R(C,x,A).
[back_rewrite(66461),rewrite([80142(13)])].
80212
R(x * C,A,C) / x = R(C,x,A).
[back_rewrite(55951),rewrite([80142(12)])].
80220
R(R(C,x,A),x,C) = R(C,x,A).
[back_rewrite(52214),rewrite([80142(6),80142(11)])].
80245
R(C,x * (A * A),A) = R(C,x,A).
[para(1926(a,1),80020(a,1,2)),rewrite([80020(12)])].
80257
R(C * A',x,C) = R(C * A',x,A).
[para(80020(a,1),38446(a,2,2)),rewrite([29933(10),50159(9),49441(12)]),flip(a)].
80260
R(C,x / R(A,C,x),A) = R(C,x,A).
[para(75993(a,1),80020(a,1,2)),rewrite([51048(7)]),flip(a)].
80299
R(R(C,x,A),x,A') = C.
[back_rewrite(75996),rewrite([80260(7)])].
80306
R(R(C,x,A),x * A',A') = C.
[para(2805(a,1),80299(a,1,1)),rewrite([80142(6)])].
80307
R(C,A',x * A) = R(C,A',x).
[para(80299(a,1),38175(a,1,1)),rewrite([2676(10)]),flip(a)].
80667
R(C * x,A,C) = R(C,x,A) * x.
[para(80142(a,1),79(a,1,1)),rewrite([10(8),2223(11),31235(11)]),flip(a)].
80692
R(R(x,y,C),R(y,C',x),C') = x.
[para(80144(a,1),79545(a,1,1)),rewrite([39878(7)])].
80816
R(x / y,y,C) * y = R(x,y,C).
[para(79908(a,1),7(a,1,1))].
80817
R(x / y,y,C)' = y / R(x,y,C).
[para(79908(a,1),112(a,1,1))].
80822 C
* (x' * (C' * (x * y))) = R(y,x,C).
[para(79908(a,1),2587(a,1,1)),rewrite([39664(7),758(8),38362(5),107(5),39664(12)])].
80829
R(x * R(y,x,C),x',C) = x * y.
[para(79908(a,1),1203(a,1,1,2,2)),rewrite([75640(6),16(3,R),38366(8),107(5),10(6),7(2)]),flip(a)].
80832
R(R(x,y,C') / y,y,C) = x / y.
[para(39746(a,1),79908(a,1,1)),flip(a)].
80853 (x
* C) / (C * y) = x / R(y,x,C).
[back_rewrite(28799),rewrite([80817(4)]),flip(a)].
80854 (x
/ R(y,x,C)) * (C * y) = C * x.
[back_rewrite(26446),rewrite([80817(4)])].
80867 (x
/ R(y,x,C)) * y = R(x,y,C).
[para(79987(a,1),39748(a,1,1)),rewrite([1091(10),461(10,R),80822(12)])].
80873
R(x,y,C') / R(y,x,C) = x / y.
[para(79870(a,1),79987(a,2,2)),rewrite([80832(6)]),flip(a)].
80896
R(R(x,y,C'),y * x,C) = x.
[para(39746(a,1),80016(a,2)),rewrite([16(8,R),75651(9),39692(8)])].
80921
R(R(x,y / x,C'),y,C) = x.
[para(7(a,1),80896(a,1,2))].
80932
R(R(x,y,C'),y * (C' * x),C) = x.
[para(481(a,1),80896(a,1,2)),rewrite([40094(9),40094(6),39688(12)])].
80937
R(x,y * x,C') = R(x,y,C').
[para(80896(a,1),39747(a,1,1))].
80946
R(R(x,y,C')',x * (y * x),C) = x'.
[para(80896(a,1),41107(a,1,2,1)),rewrite([80896(14)])].
80949
R(R(x,y,C'),R(y,x,C) * x,C) = x.
[para(78395(a,1),80896(a,1,1))].
80963
R(x,y / x,C') = R(x,y,C').
[para(80921(a,1),39747(a,1,1)),flip(a)].
81005
R(x * C,A,C) = R(C,x,A) * x.
[para(74717(a,1),80058(a,1,2)),rewrite([80212(6),80220(5)]),flip(a)].
81007 (x
/ y) * R(y,x,C) = R(x,y,C').
[para(79870(a,1),80058(a,1,2)),rewrite([80832(6)])].
81019
R(C,A,x * A') = R(C,A,x).
[para(80132(a,1),10(a,1,2)),rewrite([66080(8)])].
81056
R(C,A,x * A) = R(C,A,x).
[para(7(a,1),81019(a,1,3)),rewrite([871(8)]),flip(a)].
81059
R(C,A,A' * x) = R(C,x,A').
[para(1841(a,1),81019(a,1,3)),rewrite([50511(9)]),flip(a)].
81094
R(A,x,C) * (C * A') = R(C,A,x).
[back_rewrite(78241),rewrite([81056(13)])].
81123 A
* R(C * A',A,x) = R(C,A,x).
[back_rewrite(44325),rewrite([81056(13)])].
81139 (x
* C) / R(x,A,C) = R(C,x,A').
[back_rewrite(73298),rewrite([81059(12)])].
81180
R(C',A,x * A) = R(C',A,x).
[para(81056(a,1),139(a,2,1)),rewrite([16(7),15(10),27519(11),1090(7),435(5),86(6),439(5),847(5),461(4),5167
5(9),51662(10)])].
81532
R(R(C,A * (x * (A * A)),A),A,x) = C.
[para(1938(a,1),80306(a,1,2)),rewrite([9(16),3(14),32255(16),86(15),439(14)])].
81668 C
* (A * R(A,x,C')') = R(C,A,x).
[para(58854(a,1),80667(a,2,1)),rewrite([28546(12),78236(8),81123(8)]),flip(a)].
81812
R(x,y,C) * y = R(x * y,y,C).
[para(6(a,1),80816(a,1,1,1))].
81813
R(x * y,y,C) = C * (x * (C' * y)).
[para(838(a,1),80816(a,1,1,1)),rewrite([39664(9),79(10),40909(6),16(6,R),39664(11)]),flip(a)].
81814 C
* R(x,y,C) = R(C * x,y,C).
[para(80816(a,1),71(a,2,2)),rewrite([39692(9),39721(9),16(6,R),35937(7),81812(6),7(4),39692(9)]),flip(a)]
.
81815
R(x * (y * C),y,C) = C * (x * y).
[para(2584(a,1),80816(a,1,1,1)),rewrite([39692(4),758(5),39692(10)]),flip(a)].
81816
R(x * (C * y),y,C) = C * (x * y).
[para(2585(a,1),80816(a,1,1,1)),rewrite([39664(4),79(5),16(3,R),39664(10)]),flip(a)].
81824
R(x,y,C)' * R(C * x,y,C) = C.
[para(80816(a,1),4456(a,1,1,1)),rewrite([39692(4),39692(11),79(12),50479(8),16(12,R),80822(12),81814(7)]
)].
81834
R(C' * (x * (y * C)),y,C) = x * y.
[para(39922(a,1),80816(a,1,1,1)),rewrite([39746(5)]),flip(a)].
81845
R(R(x,y,C'),R(y * x,x,C),C) = x.
[back_rewrite(80949),rewrite([81812(6)])].
81847
R(x * y,y,C) / R(y,x,C') = x.
[back_rewrite(79877),rewrite([81812(3)])].
81862 (x
/ y) * R(y,x,C') = R(x,y,C).
[para(39746(a,1),80867(a,1,1,2)),rewrite([79870(10)])].
81875
R(C,x,A') * R(x,A,C) = C * x.
[para(73283(a,1),80867(a,2)),rewrite([39664(9),75012(7),81139(6)])].
81902
R(x,R(y,C,x),C') = R(x,y,C').
[para(38579(a,1),80937(a,1,2)),rewrite([39840(9),80937(7),40094(6)]),flip(a)].
81985 C
* (A * R(A',x,C)) = R(C,x,A).
[para(59973(a,1),81005(a,2,1)),rewrite([16(8,R),28546(11),81814(7),80257(7),80071(8)]),flip(a)].
82137 C
* R(A,C,x) = R(A * C,C,x).
[para(52438(a,1),81812(a,1,1)),rewrite([53061(5),16(5,R),75691(6),38362(11),871(11),76294(11),39627(12),4
0994(12)])].
82180
R(x,y,C) / R(C * x,y,C) = C'.
[para(81814(a,1),33(a,1,2))].
82181 C
/ R(C * x,y,C) = R(x,y,C)'.
[para(81814(a,1),117(a,1,2))].
82182
R(C * x,y,C)' = C' / R(x,y,C).
[para(81814(a,1),509(a,1,1))].
82213 C
* R(A' * C',A,x) = R(A,x,C)'.
[para(21669(a,1),81814(a,1,2)),rewrite([40204(7),507(16),57821(17),143(18),39683(15)])].
82272
R(C,R(A,C,x),R(C * A',A,x)) = C.
[para(82137(a,1),150(a,1,2,1)),rewrite([78235(13),52635(14),1222(6,R),9(5),3(3),78235(11)]),flip(a)].
82279 C
* R(A,x,C') = R(A * C,C,x).
[para(38627(a,1),82137(a,1,2))].
82287 C
* (A * R(A,x,C)') = R(C,A * x,A).
[para(82137(a,1),22459(a,1,1,1)),rewrite([50972(8),77051(8),41933(12)]),flip(a)].
82453
R(C,x / R(x,A,C),R(x,A,C)) = C.
[para(79589(a,1),81(a,1,1,1)),rewrite([81875(8),6(3)]),flip(a)].
82548 x
* R(y * C,x,C') = C * (x * y).
[para(79879(a,1),2587(a,1,1)),rewrite([39664(4),758(5)]),flip(a)].
82555
R(x * C,y,C)' = C' / R(x,y,C).
[para(79879(a,1),43379(a,1,2)),rewrite([39664(6),82548(13),39813(12),82181(13)]),flip(a)].
82566 x'
* (C * (x * y)) = C * R(y,x,C'). [para(79880(a,1),751(a,1,1,1)),rewrite([79536(8),16(4,R),16(10,R)])].
82571
R(R(x,y,C'),R(y,C',x),C) = x.
[para(39878(a,1),79880(a,1,2)),rewrite([81902(5)])].
82579
(R(x,y,C') / y) * R(y,x,C') = x.
[para(79880(a,1),80867(a,1,1,2)),rewrite([79880(16)])].
82610 A
* R(A,x,C)' = A * R(A',x,C).
[para(79900(a,1),3904(a,2,2)),rewrite([24763(5),44778(6),24764(7),75848(8),43049(7)])].
82612
R(A,x,C)' = R(A',x,C).
[para(59143(a,1),79900(a,2)),rewrite([59910(7),82610(8),10(9)]),flip(a)].
82613
R(A,C',x)' = R(A',x,C).
[para(59938(a,1),79900(a,1,1,1)),rewrite([10(10),59149(13),82612(9)])].
82622
R(A,x,C')' = R(A',x,C').
[para(79900(a,1),15948(a,1,2,1,1)),rewrite([55377(10),31(5),10(10),24763(10),44778(11),24764(12),75848(13)]),
flip(a)].
82625
R(C,A * x,A) = R(C,x,A).
[back_rewrite(82287),rewrite([82612(6),81985(8)]),flip(a)].
82637
R(A,x,C') * A' = A * R(A',x,C).
[back_rewrite(43049),rewrite([82612(12)])].
82643 C
* R(A' * C',A,x) = R(A',x,C).
[back_rewrite(82213),rewrite([82612(13)])].
82747
R(A,x,C) * R(A',x,C) = 0.
[back_rewrite(41445),rewrite([82613(8)])].
82756
R(C,A,x) = R(C,x,A').
[back_rewrite(81668),rewrite([82622(7),77975(9)]),flip(a)].
82760 C
* R(A',x,C') = R(C * A',A,x).
[back_rewrite(78236),rewrite([82622(6)])].
82781
R(A,C,x)' = R(A',x,C'). [back_rewrite(59686),rewrite([82622(5),61182(8)]),flip(a)].
82807
R(R(C,x,A),A,x) = C.
[back_rewrite(81532),rewrite([82625(9),80245(7)])].
82887
R(A * C,C,x) * A' = R(C,x,A).
[back_rewrite(50972),rewrite([82625(13)])].
83018
R(C,A',x) = R(C,x,A). [para(82807(a,1),12114(a,1,1)),rewrite([2676(9),80307(9)]),flip(a)].
83088
R(C,R(A,x,C'),A') = C.
[para(82756(a,1),60213(a,1))].
83301
R(A',x,C')' = R(A,C,x).
[para(83018(a,1),7350(a,1,2)),rewrite([31(3),31(5),1942(5),871(9),16(8),143(9),82781(7)]),flip(a)].
83410
R(A',C,x)' = R(A,C,x).
[back_rewrite(70538),rewrite([83301(6),60046(6)]),flip(a)].
83435
R(A,C,A' * x) = R(A,C,x).
[back_rewrite(38672),rewrite([83301(12)])].
83438
R(A',x,C)' = R(A,x,C).
[back_rewrite(79752),rewrite([83410(6),79187(4)]),flip(a)].
83481 (x
/ R(x,A,C)) * A = R(A,x,C).
[back_rewrite(73835),rewrite([83438(11)])].
83590 C
* R(C',R(A,x,C),R(A',x,C)) = 0.
[para(82612(a,1),2951(a,2,2,3)),rewrite([78460(10),82643(12),82747(8)]),flip(a)].
83591
R(C,R(A,x,C),R(A',x,C)) = C.
[para(82612(a,1),2973(a,1,2,2,3)),rewrite([83590(13),3(3),82612(9)]),flip(a)].
83595 C
/ R(A,x,C) = R(C * A',x,A).
[para(82612(a,1),15863(a,1,1,2,1)),rewrite([16(7,R),81814(7),80257(7),82612(16),83591(17),107(10),10(11)
]),flip(a)].
83644 (A
* C) / R(A,x,C) = R(C,x,A). [back_rewrite(59145),rewrite([83595(13),80071(15)])].
83959 C'
* R(C,x,A) = A * R(A',x,C).
[para(83088(a,1),751(a,1,1,1)),rewrite([82279(8),82887(10),82637(13)])].
84186
R(C,R(A,C,x),R(A',x,C')) = C.
[para(82781(a,1),7347(a,1,3,2)),rewrite([82760(11),82272(11),82781(9)]),flip(a)].
84194 C
/ R(A,C,x) = R(C * A',A,x).
[para(82781(a,1),15863(a,1,1,2,1)),rewrite([16(8,R),82760(8),82781(16),84186(18),107(10),10(11)]),flip(a
)].
84238 (A
* C) / R(A,C,x) = R(C,A,x).
[back_rewrite(60178),rewrite([84194(13),81123(15)])].
84647 A
* (x' * R(x,A,C)) = R(A,C,x).
[para(83435(a,1),75755(a,2)),rewrite([2027(5),13(12),28013(10),35(7)])].
85263
R(C,A,x) / (x / R(x,A,C)) = C.
[para(83481(a,1),8967(a,1,1,1)),rewrite([81094(8),27650(13),71395(10)])].
85374 C
* R(C',A,x) = A * R(A',x,C).
[para(83644(a,1),43395(a,1,2)),rewrite([83959(6),81814(13),16(11),2061(14),82555(14),78460(14),66291(16
),81180(13)]),flip(a)].
86389
(R(C,A,x) * R(x,A,C)) / x = C.
[para(85263(a,1),826(a,1,1)),rewrite([82453(9)]),flip(a)].
86933
R(C,A,x) * R(x,A,C) = C * x.
[para(86389(a,1),7(a,1,1)),flip(a)].
86990
R(C',A,x) * (C * x) = R(x,A,C).
[para(86933(a,1),10(a,1,2)),rewrite([51662(4)])].
87119
R(x * A,x',C) / R(A,C,x) = x.
[para(79989(a,2),75747(a,1,1))].
87122 x'
* R(x * y,y,C) = R(y,x,C'). [para(79989(a,1),75642(a,2,2)),rewrite([16(6,R),82566(7),10(8)]),flip(a)].
87125
R(x,y,C')' * (x * y) = R(y,x,C').
[para(79989(a,1),76200(a,2,2)),rewrite([143(5),87122(11)])].
87127
R(x,y,C') / R(y * x,x,C) = y'.
[para(79989(a,1),76361(a,1,2)),rewrite([143(5),87125(6)])].
87131 x'
* (y' * R(y,x,C)) = R(x,y,C)'.
[para(79989(a,1),80867(a,1,1,2)),rewrite([10961(7),87122(6),79962(6),143(10)])].
87233
R(C * (x * y),y,C') = x * (C * y).
[para(20117(a,2),80060(a,1,2)),rewrite([81816(5),39840(12),80937(10)])].
88312
R(R(x,y,C),y / (C' * x),C') = x.
[para(825(a,1),80692(a,1,2)),rewrite([599(4),39692(5),79978(3)])].
88386 x
* R(y,x,C') = R(x * y,x',C).
[para(39746(a,1),80829(a,1,1,2)),flip(a)].
88421
R(x,y,C') / y = R(x / y,y,C').
[para(80832(a,1),39747(a,1,1)),flip(a)].
88429
R(x / y,y,C') * R(y,x,C') = x.
[back_rewrite(82579),rewrite([88421(4)])].
88441
R(x * C',y,C)' = C / R(x,y,C).
[para(80853(a,1),831(a,1,1)),rewrite([1243(4),39645(5),38447(14),82182(13),1075(15)])].
88454
R(C / x,C * x,y) = C / R(x,y,C). [back_rewrite(39645),rewrite([88441(11)])].
88456 C'
* R(x,y,C) = R(C' * x,y,C).
[para(80854(a,1),8797(a,1,2)),rewrite([1243(5),39541(7),1243(9),88454(10),112(10),107(9)]),flip(a)].
88550 C
* R(x,y,C') = R(C * x,y,C').
[para(6333(a,2),81007(a,2)),rewrite([2598(6),39692(8),81815(6),82566(5),80937(13)])].
88564 x'
* (C * (x * y)) = R(C * y,x,C').
[back_rewrite(82566),rewrite([88550(10)])].
90927
R((x * C) * A,x,C) = C * (x * A).
[para(31432(a,1),81816(a,2,2)),rewrite([55697(7)])].
90944
R(x * y,x',C) / R(y,x,C') = x.
[para(79989(a,2),81847(a,1,1))].
91100 C
/ R(x * C,y,C) = R(x,y,C)'.
[para(16(a,1),82181(a,1,2,1))].
91392
R(R(x,R(C / y,y,x)',C'),y,C) = x.
[para(47155(a,1),82571(a,1,2)),rewrite([39840(9)])].
92675 A
* (x * R(x',A,C)) = R(A,C,x').
[para(31(a,1),84647(a,1,2,1))].
92679
R(x,A,x' * R(x,A,C)) = x.
[para(84647(a,1),2293(a,1,2)),rewrite([2061(2),75755(7),80044(4),87119(9)]),flip(a)].
92681
R(x,R(A,C,x),A) = x.
[para(92679(a,1),12026(a,1,1)),rewrite([84647(7)])].
92698
R(A',x,R(A,C,x)) = A'. [para(92681(a,1),66893(a,1,1,1,2)),rewrite([6(4)])].
92735 x
* (A * R(A',x,C)) = R(x,A,C).
[para(92698(a,1),1541(a,1,1,1)),rewrite([31(3),71845(11),73345(9),35(12),71845(16),75748(14)])].
93484
R(C * x,A,C) = x * R(C,x,A).
[para(86990(a,1),3498(a,1,1,2,2)),rewrite([10(6),117(10),66730(8),80186(7),71(13),85374(11),92735(12),818
14(9)]),flip(a)].
93491 (x
* C') * R(C,x,A) = R(x,A,C).
[para(93484(a,2),787(a,1)),rewrite([35(5),142(12),49268(11)]),flip(a)].
93495
R(C',x,R(C,x,A)) = C'.
[para(93484(a,2),486(a,1,2)),rewrite([93491(7),82180(9)]),flip(a)].
93605
R(C,x,R(C,x,A)) = C.
[para(93495(a,1),1457(a,2,1)),rewrite([49316(7),10(11),49316(11),98(11),31(8)])].
96097
R(x * A,A,C') = R(x * A,x,C).
[para(7(a,1),90927(a,1,1,1)),rewrite([107(4),39688(7),107(7),24784(11)]),flip(a)].
97894
R(x * A,x',C') = R(x * A,x,C).
[para(96097(a,1),80963(a,2)),rewrite([33(6)])].
97904 x'
* R(x * A,x,C) = R(A,x,C).
[para(96097(a,1),81862(a,1,2)),rewrite([33(4),79988(11)])].
99410
R(R(x,y / (C' * x),C'),y,C) = x.
[para(7(a,1),80932(a,1,2))].
99939 (x
/ y) * R(y * C,x,C') = C * x.
[para(839(a,2),88429(a,1,1,1)),rewrite([39841(8),39747(6),39840(8)])].
103613 x
* R(A,C,x') = R(x * A,x,C).
[para(97894(a,1),81007(a,2)),rewrite([1708(4),143(8),44896(7),13(8),92675(7)])].
103615
R(A,C,x') = R(A,x,C).
[para(103613(a,1),10(a,1,2)),rewrite([97904(6)]),flip(a)].
103933
R(C,A,x') = R(C,x,A).
[para(103615(a,2),83644(a,1,2)),rewrite([84238(8)])].
105890
R(C,x,R(C,A,x')) = C.
[para(103933(a,2),93605(a,1,3))].
106759
R(x' * C,C,R(C,A,x)) = C * x'.
[para(105890(a,1),31960(a,1,1,1)),rewrite([31(7),39536(8)])].
110321
R(C * (x * y),x,C) = x * (C * y).
[para(3660(a,2),50479(a,2,2,2)),rewrite([50479(9),76764(11),10(15),10(11)])].
110330 x
* (C * (x' * y)) = R(C * y,x,C).
[para(35(a,1),110321(a,1,1,2)),flip(a)].
110335
R(R(x,y,C),x / y,C) = x.
[para(2226(a,1),110321(a,1,1,2)),rewrite([80822(8),35(11),7(7)])].
110344
R(x * y,x,C)' * (x * (C * y)) = C.
[para(110321(a,1),81824(a,1,2))].
110349
R(R(x * y,y,C),x,C) = x * y.
[para(81813(a,2),110321(a,1,1)),rewrite([35(10)])].
110381
R(x,x / y,C') = R(x,y,C).
[para(110335(a,1),39747(a,1,1))].
110393
R(R(x,y,C),C / y,C) = x.
[para(6262(a,1),110335(a,1,1)),rewrite([79988(6),39683(5),33(7),141(6)])].
110406
R(x,x / y,C) = R(x,y,C').
[para(78356(a,1),110335(a,1,1)),rewrite([80873(6)])].
110422
R(x,y',C) = R(x,y,C').
[para(81845(a,1),110335(a,1,1)),rewrite([87127(7)])].
110458
R(x * y,x,C') / R(y,x,C') = x.
[back_rewrite(90944),rewrite([110422(4)])].
110459 x
* R(y,x,C') = R(x * y,x,C').
[back_rewrite(88386),rewrite([110422(8)])].
110508
R(x,y',C') = R(x,y,C).
[para(110393(a,1),43417(a,1,1)),rewrite([33(4),39692(8)])].
110524
R(R(x,R(C / y,y,x),C),y,C) = x.
[back_rewrite(91392),rewrite([110508(7)])].
110593
R(R(x,y,C),(C' * x) / y,C) = x.
[para(88312(a,1),110422(a,2)),rewrite([112(7)])].
110637
(x' / y) * R(y,x,C) = R(x',y,C).
[para(110508(a,1),81862(a,1,2))].
110711
R(R(x,y,C),R(x / y,x,C),C) = x.
[para(110381(a,1),78356(a,1,1))].
110816
R(R(x,y / z,C),z / y,C) = x.
[para(138(a,1),110349(a,1,1,1)),rewrite([79988(4),138(10)])].
111001
R(x,R(C / y,y,x),C) = R(x,y,C').
[para(110524(a,1),39747(a,1,1)),flip(a)].
111062
R(R(x',x / y,C)',x * y,C) = x.
[para(29096(a,1),110593(a,1,2)),rewrite([142(8),39688(7)])].
112751
R(C / x',x',R(C,A,x)) = C / x'. [para(106759(a,1),43383(a,2,2,2,1)),rewrite([509(14),1075(16)])].
115961 x
* ((x' / y) * R(C * y,x,C)) = C.
[para(110637(a,1),110344(a,1,1,1,1)),rewrite([110335(7),31(2),81814(6)])].
116229
R(x,y,C') / R(C * x,y,C') = C'.
[para(111001(a,1),82180(a,1,2)),rewrite([38852(5),110422(8),81902(8),40094(6)])].
118263 x
* ((x' / y) * R(y * C,x,C)) = C.
[para(16(a,1),115961(a,1,2,2,1))].
119327 x
* ((x' / (C' * y)) * R(y,x,C)) = C.
[para(7(a,1),118263(a,1,2,2,1)),rewrite([107(3)])].
119338
(x' / y) * R(C * y,x,C) = x' * C.
[para(118263(a,1),10961(a,2,2)),rewrite([31(6),110422(12),99939(13),110330(7)])].
122469
R(R(x * C,y / x,C'),y,C) = x * C.
[para(76191(a,1),99410(a,1,1,2,2)),rewrite([10(7),1243(5),10(15)])].
122782
R(x * y,x,C') = C * (x * (C' * y)).
[para(2852(a,1),57871(a,1,2)),rewrite([35(5),507(7),479(7),88564(9),35(6),13(13),35(14)])].
123276
R(R(x,x * y,C)',x / y,C) = x'.
[para(10918(a,1),80946(a,1,2,2)),rewrite([110508(5),35(8)])].
123289
R(x,x * y,C)' = R(x',y / x,C).
[para(123276(a,1),110816(a,1,1)),flip(a)].
123308
R(x',y / x,C)' = R(x,x * y,C).
[para(123289(a,1),31(a,1,1))].
125218
x' * R(x,y,C) = y * R(y,x,C)'.
[para(87131(a,1),10(a,1,2)),rewrite([31(2)]),flip(a)].
125221 x
* (y * R(y,x,C)') = R(x,y,C).
[para(125218(a,1),10(a,1,2)),rewrite([31(2)])].
128392 C
/ R(x,y,C) = R(C / x,y,C).
[para(76191(a,1),66719(a,2,2)),rewrite([38366(10),1304(6),559(5),16(10,R),71(12),13(11),65(9),16(7,R),11
0330(10),1075(7)]),flip(a)].
128418
R(x,y,C)' = R(x',y,C).
[back_rewrite(91100),rewrite([128392(6),33(4)]),flip(a)].
128463 x
* (y * R(y',x,C)) = R(x,y,C).
[back_rewrite(125221),rewrite([128418(3)])].
128466
x' * R(x,y,C) = y * R(y',x,C).
[back_rewrite(125218),rewrite([128418(7)])].
128467
R(x,x * y,C) = R(x,y,C).
[back_rewrite(123308),rewrite([128418(5),31(2),79978(3)]),flip(a)].
128472
R(R(x,y,C'),x * y,C) = x.
[back_rewrite(111062),rewrite([128418(5),31(2),110406(3)])].
128579
R(C / (x * (y * C)),y,C) = (x * y)'.
[para(81834(a,1),128418(a,1,1)),rewrite([141(9)]),flip(a)].
128664
R(C * x,x * y,C) = R(C * x,y,C).
[para(128467(a,1),81814(a,1,2)),rewrite([81814(4)]),flip(a)].
128726
R(x,x * y,C') = R(x,y,C').
[para(128472(a,1),39747(a,1,1))].
129169 x
* (y' * R(y,x,C)) = R(x,y,C').
[para(31(a,1),128463(a,1,2,2,1)),rewrite([110422(8)])].
129173
R(x,y,x' * R(x,y,C)) = x.
[para(128463(a,1),2293(a,1,2)),rewrite([31(3),81007(4),110459(4),110422(7),110458(8),31(3)]),flip(a)].
129196
R(x,y,x * R(x',y,C))' = x'.
[para(129173(a,1),143(a,1)),rewrite([31(3),143(5),128418(4)]),flip(a)].
129478
R(x,y,x * R(x',y,C)) = x.
[para(129196(a,1),31(a,1,1)),rewrite([31(2)]),flip(a)].
129479
R(x',y,x' * R(x,y,C)) = x'.
[para(31(a,1),129478(a,1,3,2,1))].
129794 x
* (x * R(x',y,C)) = R(x,y,C').
[para(128466(a,2),12(a,2,2)),rewrite([12(5),129169(10)])].
129795 x
* (y' * R(y,x,C')) = R(x,y,C).
[para(128466(a,2),35(a,1,2)),rewrite([110422(4),31(8)])].
129833
R(x',y,y * R(y',x,C)) = x'.
[para(128466(a,1),129479(a,1,3))].
129927
R(x,y,y * R(y',x,C')) = x.
[para(31(a,1),129833(a,1,1)),rewrite([110422(4),31(8)])].
129930 x
* (x * R(x',y,C')) = R(x,y,C).
[para(129927(a,1),1580(a,1,1,1)),rewrite([128726(13),1092(13),10943(15),31(2),11274(12),81862(8),110
422(4),129795(6),128726(8)]),flip(a)].
130038
R(x,(C / x) * y,C) = R(x,y,C).
[para(159(a,1),128664(a,1,2)),rewrite([35(5),35(7)]),flip(a)].
130047
R(x,y / (C / x),C) = R(x,y,C).
[para(1088(a,1),130038(a,1,2)),rewrite([79988(6),130038(5),16(7,R),39692(9)]),flip(a)].
130066
R(x,(C / x) / y,C') = R(x,y,C).
[para(130047(a,1),110508(a,2)),rewrite([112(4)])].
130465
R(x,(C / x') / y,C) = R(x,y,C').
[para(130066(a,1),129930(a,1,2,2)),rewrite([129794(5)]),flip(a)].
130919
R(x',(C / x) / y,C) = R(x',y,C').
[para(31(a,1),130465(a,1,2,1,2))].
133677 C
* R(C' * x',C,R(C,A,x)) = x'.
[para(112751(a,1),23922(a,2,2,1)),rewrite([107(4),112(16),107(15),35(17)])].
136379
C' * R(x * C,y,C') = R(x,y,C').
[para(116229(a,1),58210(a,1,1))].
137676 C
/ ((x' / (C' * y)) * R(y,x,C)) = x.
[para(119327(a,1),6(a,1,1))].
137698
R(C * x,y,C) / (y' * C) = x / y'.
[para(119338(a,1),33(a,1,2)),rewrite([112(11)])].
144306
R(x',R(y,x,C),C') = R(x',y,C').
[para(79534(a,1),130919(a,2)),rewrite([110508(7),130919(8)])].
146685
R(C' * x',C,R(C,A,x)) = C' * x'.
[para(133677(a,1),10(a,1,2)),flip(a)].
146722
R(C * (x * (C' * y')),y,C) = x * y'.
[para(133677(a,1),87233(a,2,2)),rewrite([146685(10),146685(16),40094(14),110508(11)])].
150234 C
/ ((x' / R(y,x,C')) * (y * C)) = x.
[para(122469(a,1),137676(a,1,2,2)),rewrite([136379(11),80963(6)])].
156029
R(R(x / y,y,C),R(y,x,C),C') = x / y.
[para(110711(a,1),144306(a,1,2)),rewrite([128418(4),112(2),39747(6),128418(5),112(3)]),flip(a)].
161714
((x' / R(y,x,C')) * y)' = R(x,y,C).
[para(150234(a,1),128579(a,1,1)),flip(a)].
163294
R(R(x * y',x,C'),y,C) = x * y'.
[para(122782(a,2),146722(a,1,1))].
168683
(x' / R(y,x,C')) * y = R(x',y,C).
[para(161714(a,1),31(a,1,1)),rewrite([128418(3)]),flip(a)].
170110
R(x,y,C') * y' = R(x * y',y,C').
[para(81812(a,1),163294(a,2)),rewrite([110422(3),110422(8),163294(13),110422(10)])].
172821
R(x' / y,y,C) = x' / R(y,x,C').
[para(168683(a,1),6(a,1,1)),rewrite([79908(4)])].
174822
R(x,y,C') / y' = R(x / y',y,C').
[para(172821(a,1),143(a,2,1)),rewrite([112(3),7(5),110422(5),112(11)]),flip(a)].
177225
x' * (C' * (x * y)) = R(C' * y,x,C).
[para(156029(a,1),751(a,1,1,1)),rewrite([112(2),80058(7),1091(5),461(5,R),461(11,R),88456(11)])]
.
190573
R(x / y',y,C') = (C * x) / (y' * C).
[para(174822(a,1),137698(a,2)),rewrite([88550(5),39746(7)]),flip(a)].
203996 x
* (C' * (x' * (C * y))) = R(y,x,C').
[para(190573(a,2),38362(a,1,1)),rewrite([170110(7),7(4),31(5),107(9)]),flip(a)].
216275 C
* (x * (C' * (x' * y))) = R(y,x,C').
[para(1273(a,1),203996(a,1,2,2,1)),rewrite([13(16),10(14),1272(13),35(11),40102(15)])].
229772
R(x * R(y,z,C),z,C') = R(x,z,C') * y.
[para(216275(a,1),3322(a,2,1)),rewrite([38363(9),1750(6),461(10,R),481(15),13(14),177225(12),10
(9),216275(11)])].
229789
R(x,A,C) * R(y,A,C) = R(x * y,A,C) # label(non_clause) # label(goal).
[para(38175(a,1),229772(a,1,1,2)),rewrite([110508(6),110508(9),
16(11,R),38246(14)]),flip(a)].
229790
$F. [resolve(229789,a,20,a)].
==============================
end of proof ==========================
% Proof
1 at 2.40 (+ 0.05) seconds.
% Length
of proof is 213.
% Level
of proof is 35.
%
Maximum clause weight is 27.000.
% Given
clauses 327.
1 R(x *
y,C,A) = R(x,C,A) * R(y,C,A) # 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(x *
y,A,C) = R(x,A,C) * R(y,A,C).
[assumption].
20
R(x,A,C) * R(y,A,C) = R(x * y,A,C) # label(non_clause) # label(goal). [copy(19),flip(a)].
21 R(c1
* c2,C,A) != R(c1,C,A) * R(c2,C,A).
[deny(1)].
22
R(c1,C,A) * R(c2,C,A) != R(c1 * c2,C,A).
[copy(21),flip(a)].
26 x / 0
= x. [para(3(a,1),6(a,1,1))].
31 0 / x
= x'. [para(8(a,1),6(a,1,1))].
33 x'' =
x.
[para(9(a,1),6(a,1,1)),rewrite([31(3)])].
34 x \ y
= x' * y.
[para(4(a,1),10(a,1,2)),flip(a)].
35 x /
(y * x) = y'.
[para(10(a,1),6(a,1,1))].
37 x *
(x' * y) = y. [back_rewrite(4),rewrite([34(1)])].
42 (x *
(y * (x * z))) / z = x * (y * x).
[para(13(a,1),6(a,1,1))].
43 x *
((y / x) * (x * z)) = (x * y) * z.
[para(7(a,1),13(a,1,1,2)),flip(a)].
44 x *
(y * (x * (x * (y * x))')) = 0.
[para(13(a,1),9(a,1))].
52 (A *
x) * A = A * (x * A).
[para(2(a,1),15(a,1,2)),rewrite([3(7)])].
53 (A *
((x * y) * A)) / (y * A) = A * x.
[para(15(a,1),6(a,1,1))].
56 A *
((A' * x) * A) = x * A.
[para(9(a,1),15(a,1,1)),rewrite([2(4)]),flip(a)].
65 C *
(x / C) = x.
[para(16(a,2),7(a,1))].
66 C' *
(x * C) = x.
[para(16(a,1),10(a,1,2))].
67 x' *
(C * x) = C.
[para(16(a,2),10(a,1,2))].
68 C *
(C * x) = C * (x * C).
[para(16(a,1),12(a,2,2)),rewrite([12(4)])].
71 (x *
(x * C)) * y = x * (C * (x * y)).
[para(16(a,1),13(a,1,1,2))].
73 (C *
(C * x)) * y = C * (x * (C * y)).
[para(16(a,2),13(a,1,1,2))].
74 C *
(x * (y * x)) = x * (y * (x * C)).
[para(16(a,2),13(a,1))].
76 (A *
x) * (A * C) = A * ((x * C) * A).
[para(16(a,1),15(a,1,2))].
81
R(x,y,z) * (y * z) = (x * y) * z.
[para(18(a,1),7(a,1,1))].
82 R(x /
y,y,z) = (x * z) / (y * z).
[para(7(a,1),18(a,1,1,1)),flip(a)].
85 (x *
y') * y = R(x,y',y).
[para(8(a,1),18(a,1,2)),rewrite([26(5)])].
88 (x *
y) * y' = R(x,y,y').
[para(9(a,1),18(a,1,2)),rewrite([26(5)])].
89
R(x',x * y,z) = (y * z) / ((x * y) * z).
[para(10(a,1),18(a,1,1,1)),flip(a)].
92
R(x,x,y) = x.
[para(12(a,1),18(a,1,1)),rewrite([6(4)]),flip(a)].
103 (C *
(x * y)) / (y * C) = R(x,y,C).
[para(16(a,2),18(a,1,1))].
113 A *
R(x,A,C) = R(A * x,A,C).
[para(92(a,1),20(a,1,1))].
114
R(x,A,C) * A = R(x * A,A,C).
[para(92(a,1),20(a,1,2))].
118 x /
C = C' * x.
[para(65(a,1),10(a,1,2)),flip(a)].
123 (x /
y)' = y / x.
[para(7(a,1),35(a,1,2)),flip(a)].
127 x /
(x * C) = C'.
[para(16(a,1),35(a,1,2))].
128 C /
(C * x) = x'.
[para(16(a,2),35(a,1,2))].
133 A *
(((A' * x) * y) * A) = x * (y * A).
[para(37(a,1),15(a,1,1)),flip(a)].
135 x *
(C * x') = C.
[para(16(a,2),37(a,1,2))].
141 C *
(x * (C' * x)) = x * x.
[para(66(a,1),13(a,2,2)),rewrite([16(6,R)])].
142 C' *
(x * (y * (x * C))) = x * (y * x).
[para(13(a,1),66(a,1,2))].
150 (x /
y) * ((y / x) * z) = z.
[para(123(a,1),10(a,1,1))].
151 (x *
y) / ((z * x) * y) = R(z,x,y)'.
[para(18(a,1),123(a,1,1)),flip(a)].
153 (C'
* x)' = C / x.
[para(118(a,1),123(a,1,1))].
155
R(x',x * y,z) = R(x,y,z)'. [back_rewrite(89),rewrite([151(7)])].
223
R(C,x,C) = C.
[para(68(a,2),6(a,1,1)),rewrite([103(7)])].
238 (C *
x)' = (x * C)'.
[para(68(a,1),128(a,1,2)),rewrite([128(6)]),flip(a)].
244 (C *
x)' * (x * C) = 0.
[para(238(a,2),8(a,1,1))].
247 (x *
C)' * ((C * x) * y) = y.
[para(238(a,1),10(a,1,1))].
248 (C *
x)' * ((x * C) * y) = y.
[para(238(a,2),10(a,1,1))].
263 (C *
(C * x))' = (C * (x * C))'.
[para(68(a,1),238(a,1,1)),rewrite([16(9,R)]),flip(a)].
272 C *
(x * ((C * x)' * x)) = x.
[para(244(a,1),13(a,2,2)),rewrite([16(7,R),3(9)])].
353 (A'
* x) * A = A' * (x * A).
[para(56(a,1),10(a,1,2)),flip(a)].
356
R(x,A',A) = x.
[para(13(a,1),56(a,1,2)),rewrite([8(7),3(5),37(5),85(5)]),flip(a)].
361
R(x,y',y) / y = x * y'.
[para(85(a,1),6(a,1,1))].
369 C *
(x * C') = R(x,C',C).
[para(85(a,1),16(a,2))].
392 (C *
x) * C' = R(x,C,C').
[para(16(a,2),88(a,1,1))].
435 (x *
(C' * x))' = C / (x * x).
[para(141(a,1),128(a,1,2)),flip(a)].
492 (C *
x) * y = (x * C) * y.
[para(248(a,1),10(a,1,2)),rewrite([33(4)])].
503 (C *
x)' * R(x,C,C') = C'.
[para(88(a,1),248(a,1,2))].
538 x *
((C * x)' * x) = C' * x.
[para(272(a,1),10(a,1,2)),flip(a)].
556 x /
A = x * A'.
[para(356(a,1),361(a,1,1))].
561
R(x,A,A') = x.
[para(556(a,1),6(a,1)),rewrite([88(5)])].
562 (x *
A')' = A / x.
[para(556(a,1),123(a,1,1))].
612 A' *
R(A * x,A,C) = R(x,A,C).
[para(113(a,1),10(a,1,2))].
622 R(x
* A,A,C) * A' = R(x,A,C).
[para(114(a,1),6(a,1,1)),rewrite([556(7)])].
630 R(x
/ y,y,z) = R(y / x,x,z)'.
[para(7(a,1),155(a,1,2)),rewrite([123(2)])].
635
R(x',C * x,y) = R(x,C,y)'.
[para(16(a,2),155(a,1,2))].
712 (C *
x)' * x = x' * (C' * x).
[para(538(a,1),10(a,1,2)),flip(a)].
720 (C *
x) * ((C * (x * C))' * (C * x)) = x.
[para(68(a,1),538(a,1,2,1,1)),rewrite([10(16)])].
729 C' *
A' = A' * C'. [para(562(a,1),538(a,1,2,1)),rewrite([118(5),88(9),561(8)]),flip(a)].
734 C' *
A = A * C'.
[para(729(a,1),15(a,2,2,1)),rewrite([8(8),3(6),353(12),37(13)]),flip(a)].
759 (A *
x) * (A * C') = A * ((x * C') * A).
[para(734(a,1),15(a,1,2))].
779 x *
(y * (y * (x * y))') = y'.
[para(44(a,1),10(a,1,2)),rewrite([3(3)]),flip(a)].
806 x *
(x * (y * x))' = y' * x'.
[para(779(a,1),10(a,1,2)),flip(a)].
861
R(x,y,C) * (C * y) = C * (x * y).
[para(16(a,2),81(a,1,2)),rewrite([16(8,R)])].
940 R(C
/ x,x,y) = (y * C) / (x * y).
[para(16(a,1),82(a,2,1))].
996 x /
A' = x * A.
[para(82(a,1),356(a,1)),rewrite([8(6),26(4)]),flip(a)].
1019 (x
* y) / (A * y) = R(x * A',A,y).
[para(556(a,1),82(a,1,1)),flip(a)].
1112
R(C',x,C) = C'.
[para(37(a,1),103(a,1,1)),rewrite([127(3)]),flip(a)].
1113 (C
* C) / (C * (C * x)) = R(x,C,C)'.
[para(67(a,1),103(a,1,1,2)),rewrite([16(7,R),635(13)])].
1138 C'
* R(x,A,C) = R(C' * x,A,C).
[para(1112(a,1),20(a,1,1))].
1165 R(C
* A',A,C) = C * A'.
[para(135(a,1),612(a,1,2,1)),rewrite([223(6),16(4,R)]),flip(a)].
1175
R(x,A,C) * A' = R(x * A',A,C).
[para(7(a,1),622(a,1,1,1)),rewrite([556(8)])].
1236 (x
/ y) * x' = x * (x * y)'.
[para(7(a,1),806(a,1,2,1,2)),rewrite([123(5)]),flip(a)].
1237 (x
* (y * x))' = x' * (y' * x').
[para(806(a,1),10(a,1,2)),flip(a)].
1287
R(x,C,C') = x.
[back_rewrite(720),rewrite([1237(7),13(12),10(10),8(6),3(6),392(5)])].
1291 C /
(x * x) = x' * (C * x').
[back_rewrite(435),rewrite([1237(5),33(4)]),flip(a)].
1293 (C
* (C * x))' = C' * (x' * C').
[back_rewrite(263),rewrite([1237(10)])].
1307 x'
* (C' * x) = C'.
[back_rewrite(503),rewrite([1287(7),712(4)])].
1340 C'
* x = x * C'.
[para(1307(a,1),10(a,1,2)),rewrite([33(2)]),flip(a)].
1368
R(x,C',C) = x.
[para(1340(a,1),10(a,1,2)),rewrite([33(3),369(5)])].
1379 (C'
* (x * y)) / (C' * y) = R(x,y,C').
[para(1340(a,2),18(a,1,2)),rewrite([1340(4,R)])].
1381 (x
* C')' = C / x.
[para(1340(a,1),153(a,1,1))].
1398 (C'
* x) * y = (x * C') * y.
[para(1340(a,1),81(a,2,1)),rewrite([81(5)])].
1399
R(x,y,C') * (C' * y) = C' * (x * y).
[para(1340(a,2),81(a,1,2)),rewrite([1340(11,R)])].
1419 C *
(x * C') = x.
[back_rewrite(369),rewrite([1368(9)])].
1424 x /
C' = x * C.
[para(1368(a,1),82(a,1)),rewrite([16(9,R),9(9),26(7)])].
1432 (x
* C)' = C' / x.
[para(1424(a,1),123(a,1,1))].
1436 (C'
/ x) * ((x * C) * y) = y.
[para(1424(a,1),150(a,1,2,1))].
1497 (C'
/ x) * ((C * x) * y) = y.
[back_rewrite(247),rewrite([1432(3)])].
1500 (C
* x)' = C' / x.
[back_rewrite(238),rewrite([1432(6)])].
1546 C'
/ (C * x) = C' * (x' * C').
[back_rewrite(1293),rewrite([1500(5)])].
1802
R(x,C' * y,C) * y = C * (x * (C' * y)).
[para(37(a,1),861(a,1,2))].
1827 (C
* A') * R(x,A,C) = R((C * A') * x,A,C).
[para(940(a,1),20(a,1,1)),rewrite([1019(7),1165(7),556(11)])].
1844 (x
* C) / (y * x) = R(C' * y,C,x)'.
[para(940(a,1),630(a,1)),rewrite([118(6)])].
1853
R(C' * x,C,C)' * (C * x) = C * C.
[para(940(a,1),861(a,1,1)),rewrite([1844(6),7(14)])].
1883 x *
((x * y)' * x) = x / y.
[para(8(a,1),42(a,1,1,2)),rewrite([3(2)]),flip(a)].
1884 (x
* y) / x' = x * (y * x). [para(9(a,1),42(a,1,1,2,2)),rewrite([3(2)])].
1898 (C
* C) / x = C * (x' * C).
[para(67(a,1),42(a,1,1,2))].
1964
R(x,C,C)' = x'.
[back_rewrite(1113),rewrite([1898(8),1500(6),1546(6),16(10,R),37(10),1419(6)]),flip(a)].
1968 (C
/ x) * (C * x) = C * C. [back_rewrite(1853),rewrite([1964(7),153(4)])].
1996 (x
* y)' * x = x' * (x / y).
[para(1883(a,1),10(a,1,2)),flip(a)].
1997 x'
/ (x * y) = x' * (y' * x').
[para(10(a,1),1883(a,1,2,1,1)),flip(a)].
2004 x /
(x' * y) = x * (y' * x).
[para(37(a,1),1883(a,1,2,1,1)),flip(a)].
2028 (x
* y) * x' = x * (y / x).
[para(1883(a,1),1236(a,2,2,1)),rewrite([1996(3),2004(4),123(2),7(2),123(5)])].
2039 (x
* C) * (C / x) = C * C.
[para(1883(a,1),1968(a,1,2)),rewrite([1500(4),16(6,R),128(7),123(4),1424(3)])].
2046 x *
(C * (C * x')) = C * C.
[para(12(a,1),2039(a,1,1)),rewrite([1291(6),71(9),37(7)])].
2111 ((x
* C) * y) / (C' / x) = (C * x) * (y * (C * x)). [para(492(a,1),1884(a,1,1)),rewrite([1500(6)])].
2145 x /
(C * C) = C' * (x * C').
[para(1898(a,1),123(a,1,1)),rewrite([1237(6),33(4)]),flip(a)].
2168 (x'
* y) * x = x' * (y / x').
[para(33(a,1),2028(a,1,2))].
2201 x *
(C * y) = x * (y * C).
[para(1436(a,1),2028(a,1,1)),rewrite([123(4),1424(3),2111(13),1497(13)]),flip(a)].
2218 (x
/ (y * C)) * (C * y) = x.
[para(2201(a,2),7(a,1))].
2255 (C'
* x) * (C * y) = (x * C') * (y * C).
[para(2201(a,1),1398(a,2))].
2433 A *
((C * (A' * (C * x))) * A) = C * (C * (x * A)). [para(2046(a,1),15(a,1,1)),rewrite([12(6),73(14)]),flip(a)].
2556 C'
* (x * C') = x * (C' * C').
[para(2046(a,1),2004(a,1,2)),rewrite([2145(4),33(10),1500(11),1997(11),13(14),1307(13)])].
2649 (A
* x) * (A' * (y * A)) = A * ((x * (A' * y)) * A). [para(2168(a,1),15(a,1,2)),rewrite([996(7)])].
2689 (x
/ y) * (y * z) = y' * ((y * x) * z).
[para(43(a,1),10(a,1,2)),flip(a)].
2690 (x'
* y) * (x * z) = x' * ((y / x') * z).
[para(10(a,1),43(a,1,2,2)),flip(a)].
2701 (x
* y) * (x' * z) = x * ((y / x) * z).
[para(37(a,1),43(a,1,2,2)),flip(a)].
2702 (C'
* x) * (y * C) = C' * ((x * C) * y).
[para(66(a,1),43(a,1,2,2)),rewrite([1424(5)]),flip(a)].
2790 (x
* C') * (y * C) = C' * ((x * C) * y).
[back_rewrite(2255),rewrite([2690(6),1424(5)]),flip(a)].
2796 A *
((x * (A' * y)) * A) = A * ((x * A') * (y * A)). [back_rewrite(2649),rewrite([2701(8),556(3)]),flip(a)].
2819 A *
((C * A') * ((C * x) * A)) = C * (C * (x * A)). [back_rewrite(2433),rewrite([2796(11)])].
2845 (A
* (x * A)) / (y * A) = A * (x / y).
[para(7(a,1),53(a,1,1,2,1))].
3647 A *
((C * A') * (x * A)) = x * (A * C).
[para(37(a,1),76(a,1,1)),rewrite([16(10,R),2796(13)]),flip(a)].
3661 ((A
* x) * (y * (A * ((x * C) * A)))) / (A * C) = (A * x) * (y * (A * x)). [para(76(a,1),42(a,1,1,2,2))].
3671 (C
* x) * (A * C) = C * (C * (x * A)).
[back_rewrite(2819),rewrite([3647(11)])].
4139
R((x / y) * A',A,y) = x / (A * y).
[para(7(a,1),1019(a,1,1)),flip(a)].
4146 (C
* x) / (A * C) = R(x * A',A,C).
[para(16(a,2),1019(a,1,1))].
4659 C *
(x * (C' * C')) = x * C'.
[para(2556(a,1),10(a,1,2)),rewrite([33(3)])].
4664 (x
* (C' * C')) * y = C' * (x * (C' * y)).
[para(2556(a,1),13(a,1,1))].
4747 (A
* C) * (C' * (x * (A * C'))) = A * ((x * C') * A). [para(4659(a,1),15(a,2,2,1)),rewrite([4664(11),1340(9)])].
5100 (A
* (x * A)) / y = A * (x / (y * A')).
[para(7(a,1),2845(a,1,2)),rewrite([556(8)])].
5346 C *
(C * ((C' * x) * A)) = x * (A * C).
[para(37(a,1),3671(a,1,1)),flip(a)].
5384 C'
* ((x * C) * A) = C * (x * (A * C')).
[para(4659(a,1),3671(a,1,1)),rewrite([2790(7),4664(17),1340(15),37(18)])].
5399 (x
/ (A * C)) * A = R(C' * x,A,C).
[para(4139(a,1),114(a,1,1)),rewrite([118(8),85(14),356(13)])].
5591 (x
* (A' * y)) * A = (x * A') * (y * A).
[para(13(a,1),133(a,1,2,1)),rewrite([2168(10),996(10),37(11)])].
5594 ((x
* A) * y) * A = x * (A * (y * A)).
[para(52(a,1),133(a,2,2)),rewrite([2690(7),996(6),2168(9),996(9),37(10)])].
5601 A *
((A' * C') * (x * A)) = x * (A * C').
[para(1340(a,1),133(a,2,2)),rewrite([1340(7,R),5591(9),1340(6)])].
5610 R(A
* (C * ((A' * C') * x)),A,C) = x.
[para(2218(a,1),133(a,2)),rewrite([16(10,R),5591(12),5399(11),1827(12),2701(9),118(6),1340(7),113
(13)])].
5687 (x
* (A * (y * A))) * A' = (x * A) * y.
[para(5594(a,1),6(a,1,1)),rewrite([556(7)])].
5695 (A
* x) * (y * (A * (z * A))) = A * ((x * ((y * A) * z)) * A). [para(5594(a,1),15(a,1,2))].
5752 (A
* x) * (y * (A * x)) = A * (x * ((y * A) * x)). [back_rewrite(3661),rewrite([5695(10),5100(14),2028(13),556(11),135(13),118(9),142(1
0)]),flip(a)].
6086 (x
* A) * (A' * y) = A * ((A' * x) * y).
[para(996(a,1),2689(a,1,1)),rewrite([33(9)])].
6091 (x
* C) * (y * C') = C * ((C' * x) * y).
[para(1340(a,1),2689(a,1,2)),rewrite([1424(3),33(9)])].
6092 (x
* C) * (C' * y) = C * ((x * C') * y).
[para(1340(a,1),2689(a,2,2,1)),rewrite([1424(3),33(9)])].
6214 C *
(A * (C' * (C' * (x * A)))) = A * ((x * C') * A). [back_rewrite(4747),rewrite([6092(12),5752(11),1340(9,R)])].
6270 (C
* x) * (y * C') = C * ((C' * x) * y).
[para(1340(a,1),2701(a,1,2)),rewrite([118(9)])].
6926 C'
* (x * (A * C)) = C * ((C' * x) * A).
[para(5346(a,1),10(a,1,2))].
7038 R(x
* (A * (C * ((A' * C') * y))),A,C) = R(x,A,C) * y. [para(5610(a,1),20(a,1,2)),flip(a)].
7039 R(A
* (C * x),A,C) = (A * C) * x.
[para(37(a,1),5610(a,1,1,2,2)),rewrite([1381(13),996(11),16(10)])].
7054 C *
((A * C') * x) = R(A * x,A,C).
[para(37(a,1),7039(a,1,1,2)),rewrite([6092(12)]),flip(a)].
7088 C *
(A * ((A' * C') * x)) = R(x,A,C).
[para(37(a,1),7054(a,2,1)),rewrite([2701(9),556(6),1340(7)])].
7117 C *
(A * ((x * C') * A)) = R(A * (x * A),A,C).
[para(74(a,2),7054(a,1,2)),rewrite([5752(12),1340(10,R),6214(13),16(16,R),1419(16)])].
7160 (x
* (y * A)) * A' = A * ((A' * x) * y).
[para(2168(a,1),5687(a,1,1,2,2)),rewrite([996(6),37(7),6086(12)])].
7199 A *
((A' * C') * x) = R(C' * x,A,C).
[para(7088(a,1),10(a,1,2)),rewrite([1138(6)]),flip(a)].
7235
R(C' * (x * A),A,C) = x * (A * C').
[back_rewrite(5601),rewrite([7199(10)])].
7244 R(C
* (x * (A * C')),A,C) = C * ((C' * x) * A). [para(492(a,1),7235(a,1,1,2)),rewrite([5384(7),6270(17)])].
7338 R(A
* x,A * C',C) = R(A * x,A,C).
[para(759(a,1),103(a,1,1,2)),rewrite([7117(9),16(13,R),1419(13),556(9),1175(10),2028(7),556(5),88(6),
561(5)]),flip(a)].
7363
R(x,A * C',C) = R(x,A,C).
[para(37(a,1),7338(a,1,1)),rewrite([37(11)])].
7465
R(R(x,A,C),A,C') = x.
[para(114(a,1),1379(a,1,1,2)),rewrite([1138(8),7235(8),1340(9),6(10)]),flip(a)].
7547
R(x,y * C,C') * y = C' * (x * (y * C)).
[para(66(a,1),1399(a,1,2))].
8787 (C
* ((C' * x) * y)) / y = R(x,C,y * C').
[para(6091(a,1),18(a,1,1)),rewrite([1419(11)])].
8998 A *
(C * ((A' * C') * x)) = R(x,A * C,C').
[para(6926(a,1),1379(a,1,1)),rewrite([66(13),556(9),7160(10),16(5,R),2701(9),118(6),1340(7)]
)].
9011 R(x
* R(y,A * C,C'),A,C) = R(x,A,C) * y.
[back_rewrite(7038),rewrite([8998(10)])].
10072
R(R(x * A,A,C),A,C) = C * ((C' * x) * A).
[para(1802(a,1),114(a,2,1)),rewrite([1340(4),7363(6),114(8),114(5),1340(13),7244(18)])].
10076 C
* (x * (A * C')) = R(x * A,A,C).
[para(1802(a,1),996(a,2)),rewrite([1340(4),7363(6),996(6),114(5),1340(10)]),flip(a)].
10218 C'
* ((x * C) * A) = R(x * A,A,C).
[back_rewrite(5384),rewrite([10076(14)])].
11276
R(R(x,y * C,C'),y,C) = x.
[para(7547(a,1),103(a,1,1,2)),rewrite([37(8),6(6)]),flip(a)].
11317
R(x,A * C,C') = R(x,A,C').
[para(11276(a,1),7465(a,1,1)),flip(a)].
11329
R(x * R(y,A,C'),A,C) = R(x,A,C) * y.
[back_rewrite(9011),rewrite([11317(6)])].
11427 C
* ((C' * x) * A) = R(x,A,C') * A.
[para(11317(a,1),81(a,1,1)),rewrite([1340(10,R),66(10),1340(13,R),6926(13)]),flip(a)].
11437
R(R(x * A,A,C),A,C) = R(x,A,C') * A.
[back_rewrite(10072),rewrite([11427(15)])].
11499 C
* (R(x,A,C') * A) = x * (A * C).
[back_rewrite(5346),rewrite([11427(8)])].
11539
R(R(x,A,C) * y,A,C') = x * R(y,A,C').
[para(11329(a,1),7465(a,1,1))].
11601
R(R(x,A,C),A,C) = R(x,C,A).
[para(8787(a,1),4146(a,1)),rewrite([1340(7,R),66(7),2702(10),10218(10),1175(11),88(8),561(7)]),flip(a)].
11625
R(x,A,C') * A = R(x * A,C,A).
[back_rewrite(11437),rewrite([11601(8)]),flip(a)].
11638 C
* R(x * A,C,A) = x * (A * C).
[back_rewrite(11499),rewrite([11625(7)])].
11763
R(x,C,A) * A = R(x * A,C,A).
[para(11601(a,1),114(a,1,1)),rewrite([114(10),11601(13)])].
11776
R(R(x,C,A),A,C) = R(R(x,A,C),C,A).
[para(11601(a,1),11601(a,1,1))].
11804
R(R(x,A,C),C,A) = x.
[para(11763(a,1),103(a,1,1,2)),rewrite([11638(7),6(8),11776(6)]),flip(a)].
11899
R(x,C,A) = R(x,A,C').
[para(11276(a,1),11804(a,1,1)),rewrite([11317(9)])].
12084
R(c1,A,C') * R(c2,A,C') != R(c1 * c2,A,C'). [back_rewrite(22),rewrite([11899(4),11899(9),11899(17)])].
12319
R(x,A,C') * R(y,A,C') = R(x * y,A,C').
[para(11276(a,1),11539(a,1,1,1)),rewrite([11317(11)]),flip(a)].
12320
$F. [resolve(12319,a,12084,a)].
==============================
end of proof ==========================
% Proof
1 at 0.16 (+ 0.00) seconds.
% Length
of proof is 143.
% Level
of proof is 22.
%
Maximum clause weight is 25.000.
% Given
clauses 101.
1 L(x *
y,C,A) = L(x,C,A) * L(y,C,A) # 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(c1
* c2,C,A) != L(c1,C,A) * L(c2,C,A).
[deny(1)].
20
L(c1,C,A) * L(c2,C,A) != L(c1 * c2,C,A).
[copy(19),flip(a)].
21 (C *
x) * (y * C) = C * (C * (x * y)).
[back_rewrite(15),rewrite([16(9,R)])].
30 0 / x
= x'. [para(8(a,1),6(a,1,1))].
32 x'' =
x.
[para(9(a,1),6(a,1,1)),rewrite([30(3)])].
33 x \ y
= x' * y.
[para(4(a,1),10(a,1,2)),flip(a)].
34 x /
(y * x) = y'.
[para(10(a,1),6(a,1,1))].
36 x *
(x' * y) = y.
[back_rewrite(4),rewrite([33(1)])].
41 (x *
(y * (x * z))) / z = x * (y * x).
[para(13(a,1),6(a,1,1))].
42 x *
((y / x) * (x * z)) = (x * y) * z.
[para(7(a,1),13(a,1,1,2)),flip(a)].
44 (x *
(y * x))' * (x * (y * (x * z))) = z.
[para(13(a,1),10(a,1,2))].
49 (x *
(y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))).
[para(13(a,1),13(a,1,1,2)),rewrite([13(9)])].
53 C *
(x / C) = x.
[para(16(a,2),7(a,1))].
54 C' *
(x * C) = x. [para(16(a,1),10(a,1,2))].
55 x' *
(C * x) = C.
[para(16(a,2),10(a,1,2))].
56 C *
(C * x) = C * (x * C).
[para(16(a,1),12(a,2,2)),rewrite([12(4)])].
58 C *
(x * x) = x * (C * x).
[para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].
68 x' *
((x / y) * (y * z)) = L(z,y,x / y).
[para(7(a,1),18(a,1,1,1))].
75
L(x',x,y) = (y * x)' * y.
[para(9(a,1),18(a,1,2,2)),rewrite([3(4)]),flip(a)].
76 (x *
y) * L(z,y,x) = x * (y * z).
[para(18(a,1),10(a,1,2)),rewrite([32(3)])].
77 x' *
(y' * ((y * x) * z)) = L(z,y * x,y').
[para(10(a,1),18(a,1,1,1))].
84 (x *
C)' * (C * (x * y)) = L(y,x,C).
[para(16(a,1),18(a,1,1,1))].
109 x /
C = C' * x.
[para(53(a,1),10(a,1,2)),flip(a)].
112 (x *
C)' * (x * y) = L(C' * y,C,x).
[para(53(a,1),18(a,1,2,2)),rewrite([109(7)])].
116 (x /
y)' = y / x. [para(7(a,1),34(a,1,2)),flip(a)].
120 C /
(C * x) = x'.
[para(16(a,2),34(a,1,2))].
135 (x *
C')' * (x * y) = L(y * C,C',x).
[para(54(a,1),18(a,1,2,2))].
146 (C'
* x)' = C / x.
[para(109(a,1),116(a,1,1))].
168 (C *
x)' = (x * C)'.
[para(56(a,1),120(a,1,2)),rewrite([120(6)]),flip(a)].
196 (C *
(x * x))' * (x * ((C * x) * y)) = L(y,C * x,x). [para(58(a,2),18(a,1,1,1))].
207 (C *
(x * x))' = (x * (C * x))'.
[para(58(a,1),168(a,1,1)),rewrite([16(7,R)]),flip(a)].
210
L(x',x,y) / y = (y * x)'.
[para(75(a,2),6(a,1,1))].
221 (C *
x)' * x = L(C',C,x).
[para(16(a,2),75(a,2,1,1)),flip(a)].
228 x /
L(y',y,x) = x * y.
[para(75(a,2),34(a,1,2)),rewrite([32(6)])].
235
L(x',x,C') = (C / x) * C'.
[para(146(a,1),75(a,2,1))].
279 (C *
(x * C))' * (C * x) = L(C',C,C * x).
[para(56(a,1),221(a,1,1,1))].
336 (x *
(y * z))' * (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(76(a,1),18(a,1,2,2))].
341 C *
L(x,C * y,y') = y' * ((C * y) * x).
[para(55(a,1),76(a,1,1))].
347
L(x',x,y) * L(z,y,(y * x)') = (y * x)' * (y * z). [para(75(a,2),76(a,1,1))].
357
L(L(x,y,z),z * y,y) = x.
[back_rewrite(44),rewrite([336(7)])].
367
L(L(x,y * C,C'),y,y * C) = x.
[para(54(a,1),357(a,1,2))].
380
L(x,y * (z * y),z * y) = L(x,y,z).
[para(357(a,1),357(a,1,1))].
385
L(L(x,C * y,C'),y,y * C) = x.
[para(16(a,2),367(a,1,1,2))].
395 x *
((x * y)' * x) = x / y.
[para(8(a,1),41(a,1,1,2)),rewrite([3(2)]),flip(a)].
396 (x *
y) / x' = x * (y * x).
[para(9(a,1),41(a,1,1,2,2)),rewrite([3(2)])].
420 x *
L(y',y,x) = x / y.
[para(75(a,2),41(a,2,2)),rewrite([41(6),395(4)]),flip(a)].
432
L(x',x,y) = y' * (y / x).
[para(420(a,1),10(a,1,2)),flip(a)].
464 x' /
(x * y) = x' * (y' * x').
[para(10(a,1),395(a,1,2,1,1)),flip(a)].
514 x' *
((C * x) * x') = C / x.
[para(55(a,1),396(a,1,1)),rewrite([32(3)]),flip(a)].
515 (x *
(y * x))' = x' * (y' * x').
[para(396(a,1),116(a,1,1)),rewrite([464(6)])].
530 C' *
(C' * (C / x)) = C' / x.
[para(235(a,2),396(a,2,2)),rewrite([32(8),109(7),420(15)])].
546
L(C',C,C * x) = C'.
[back_rewrite(279),rewrite([515(5),13(10),10(8),8(4),3(4)]),flip(a)].
550 (C *
(x * x))' = x' * (C' * x').
[back_rewrite(207),rewrite([515(8)])].
558
L(x,C * y,C') = L(x,C * y,y).
[back_rewrite(196),rewrite([550(4),13(11),10(9),77(8)])].
576
L(C',C,x) = C'.
[para(36(a,1),546(a,1,3))].
599 x /
C' = x * C. [para(576(a,1),228(a,1,2))].
600 (x *
C)' = C' / x.
[para(576(a,1),210(a,1,1)),flip(a)].
603 C' *
x = x * C'.
[para(576(a,1),420(a,1,2)),rewrite([109(5)]),flip(a)].
627 (C'
/ x) * (x * y) = L(C' * y,C,x).
[back_rewrite(112),rewrite([600(3)])].
628 (C'
/ x) * (C * (x * y)) = L(y,x,C).
[back_rewrite(84),rewrite([600(3)])].
707 (C'
* (C' * x)) * y = C' * (x * (C' * y)).
[para(603(a,2),13(a,1,1,2))].
714 x *
(C' * x') = C'.
[para(603(a,2),36(a,1,2))].
715 (x *
C')' = C / x.
[para(603(a,1),146(a,1,1))].
724 (C /
x) * (x * y) = L(y * C,C',x).
[back_rewrite(135),rewrite([715(4)])].
740 (C *
x) * x' = C.
[para(714(a,1),21(a,2,2,2)),rewrite([16(8,R),36(8),9(9),3(7)])].
742 (C'
* x) * (C' * (C / x)) = C'.
[para(146(a,1),714(a,1,2,2))].
751 C /
x = x' * C. [back_rewrite(514),rewrite([740(5)]),flip(a)].
753 (C'
* x) * x' = C'.
[back_rewrite(742),rewrite([751(7),54(9)])].
763 (x'
* C) * (x * y) = L(y * C,C',x).
[back_rewrite(724),rewrite([751(2)])].
778 C' /
x = C' * x'.
[back_rewrite(530),rewrite([751(6),54(8)]),flip(a)].
853 (C'
* x') * (C * (x * y)) = L(y,x,C).
[back_rewrite(628),rewrite([778(3)])].
854 (C'
* x') * (x * y) = L(C' * y,C,x).
[back_rewrite(627),rewrite([778(3)])].
892 C *
L(x,y',C * y) = (C * y) * (y' * x).
[para(740(a,1),76(a,1,1))].
900 (C'
* x') * x = C'.
[para(32(a,1),753(a,1,2))].
907 C' *
L(x,y,C' * y') = L(C' * x,C,y).
[para(900(a,1),76(a,1,1)),rewrite([854(14)])].
922
L(x',x,y) * L(z,y / x,y') = y' * ((y / x) * z). [para(432(a,2),76(a,1,1))].
944 (x'
* y) * x = x' * (y / x'). [para(8(a,1),42(a,1,2,2)),rewrite([3(5)]),flip(a)].
945 (x *
y) * x' = x * (y / x).
[para(9(a,1),42(a,1,2,2)),rewrite([3(3)]),flip(a)].
946 (x /
y) * (y * z) = y' * ((y * x) * z).
[para(42(a,1),10(a,1,2)),flip(a)].
947 (x'
* y) * (x * z) = x' * ((y / x') * z).
[para(10(a,1),42(a,1,2,2)),flip(a)].
961 (x *
y) * (x' * z) = x * ((y / x) * z).
[para(36(a,1),42(a,1,2,2)),flip(a)].
992
L(x,y * z,y') = L(x,y,z / y).
[back_rewrite(68),rewrite([946(4),77(6)])].
994
L(x,y,y' * C) = L(x,y,C).
[back_rewrite(853),rewrite([947(8),599(6),947(7),751(6),32(5),77(8),992(4),751(2)])].
996 x' *
((x * C) * y) = L(y * C,C',x).
[back_rewrite(763),rewrite([947(5),751(4),32(3)])].
1009
L(x,C * y,y) = L(x,C,C' * y).
[back_rewrite(558),rewrite([992(5),109(3)]),flip(a)].
1010
L(L(x,C,C' * y),y,y * C) = x.
[back_rewrite(385),rewrite([992(5),109(3)])].
1015 x'
* (y' * ((y * x) * z)) = L(z,y,x / y).
[back_rewrite(77),rewrite([992(9)])].
1026
L(x,y / z,z) = L(x,z',z * y).
[para(945(a,1),18(a,1,1,1)),rewrite([961(7),18(7)])].
1036 L(L(x,y',y
* z),y,(z / y) / y) = x.
[para(945(a,1),357(a,1,2)),rewrite([992(7)])].
1044
L(x,y,C * y') = L(x,y,C).
[para(16(a,2),994(a,1,3))].
1046
L(x,y',y * C) = L(x,y',C).
[para(32(a,1),994(a,1,3,1))].
1048 C *
L(x,y,C) = L(x * C,C',y).
[para(994(a,1),76(a,1,2)),rewrite([944(4),751(4),32(3),10(4),947(9),751(8),32(7),996(9)])].
1054
L(x,y',C * y) = L(x,y',C).
[para(32(a,1),1044(a,1,3,2))].
1058 (C
* x) * (x' * y) = L(y * C,C',x').
[back_rewrite(892),rewrite([1054(5),1048(5)]),flip(a)].
1088
L(x,y / z,z / (y / z)) = L(x,y,z / y).
[para(7(a,1),992(a,1,2)),rewrite([116(2)]),flip(a)].
1091
L(x,y',y * (z * y)) = L(x,z,y).
[para(10(a,1),992(a,1,2)),rewrite([32(2),396(5)]),flip(a)].
1095
L(x,C * y,y') = L(x,y,C).
[para(16(a,2),992(a,1,2)),rewrite([751(6),994(8)])].
1103
L(x,y / z,y') = L(x,y,(y * z)').
[para(210(a,1),992(a,2,3)),rewrite([420(3)])].
1120 x'
* ((C * x) * y) = L(y * C,C',x).
[back_rewrite(341),rewrite([1095(5),1048(4)]),flip(a)].
1128 (x
* y)' * (x * z) = x' * ((x / y) * z).
[back_rewrite(922),rewrite([1103(5),347(6)])].
1159
L(x,y,z / y) = L(x,y,z).
[back_rewrite(18),rewrite([1128(5),946(4),1015(6)])].
1172
L(x,y',y * z) = L(x,z,y).
[back_rewrite(1088),rewrite([1159(4),1026(2),1159(5)])].
1173
L(L(x,y,z),z,y) = x.
[back_rewrite(1036),rewrite([1172(3),1159(4),1159(3)])].
1188
L(x,y * z,z) = L(x,y,z).
[back_rewrite(1091),rewrite([1172(4)])].
1190
L(x,y',C) = L(x,C,y).
[back_rewrite(1046),rewrite([1172(4)]),flip(a)].
1194
L(x,C,C' * y) = L(x,C,y).
[back_rewrite(1009),rewrite([1188(3)]),flip(a)].
1198
L(x,y,z * y) = L(x,y,z).
[back_rewrite(380),rewrite([1188(4)])].
1209
L(L(x,C,y),y,y * C) = x.
[back_rewrite(1010),rewrite([1194(5)])].
1223
L(x,C,y') = L(x,y,C).
[para(32(a,1),1190(a,1,2)),flip(a)].
1235
L(x,C',y * C) = L(x,C',y).
[para(599(a,1),1159(a,1,3))].
1236
L(x,y,C' * y') = L(x,y,C').
[para(778(a,1),1159(a,1,3))].
1241 C'
* L(x,y,C') = L(C' * x,C,y).
[back_rewrite(907),rewrite([1236(7)])].
1248
L(x,y,y' * z) = L(x,z,y').
[para(36(a,1),1188(a,1,2)),rewrite([1198(3)]),flip(a)].
1249
L(x,y,y * C) = L(x,C',y).
[para(54(a,1),1188(a,1,2)),rewrite([1235(8)])].
1262
L(x,C,y) = L(x,y,C').
[back_rewrite(1194),rewrite([1248(5)]),flip(a)].
1263
L(L(x,C,y),C',y) = x.
[back_rewrite(1209),rewrite([1249(5)])].
1272
L(c1,C,A) * L(c2,A,C') != L(c1 * c2,C,A).
[para(1262(a,1),20(a,1,2))].
1283
L(x,y',C) = L(x,y,C').
[para(1262(a,1),1190(a,2))].
1290
L(x,C',y) = L(x,y,C).
[para(1173(a,1),1263(a,1,1))].
1295
L(x,C',y) = L(x,C,y').
[para(1290(a,2),1223(a,2)),flip(a)].
1308 x'
* ((C * x) * y) = L(y * C,C,x').
[back_rewrite(1120),rewrite([1295(10)])].
1314 (C
* x) * (x' * y) = L(y * C,C,x).
[back_rewrite(1058),rewrite([1295(11),32(10)])].
1553 C'
* L(x,C,y) = L(C' * x,C,y).
[para(1262(a,2),1241(a,1,2))].
1771 L(C
* (x * L(y * C,C,z')),C,z) = L(C * (x * C),C,z) * y.
[para(55(a,1),49(a,1,1,2,2,2)),rewrite([1314(7),16(4,R),1308(15),1314(18),16(1
5,R)]),flip(a)].
1869 L(x
* L(y,C,z'),C,z) = L(x,C,z) * y.
[para(707(a,1),1771(a,1,1,2)),rewrite([1553(11),54(8),36(9),16(15,R),36(15),36(11)])].
1889
L(x,C,y) * L(z,y,C') = L(x * z,C,y).
[para(1173(a,1),1869(a,1,1,2)),rewrite([1283(8)]),flip(a)].
1890
$F. [resolve(1889,a,1272,a)].
==============================
end of proof ==========================
% Proof
1 at 1.66 (+ 0.01) seconds.
% Length
of proof is 223.
% Level
of proof is 33.
%
Maximum clause weight is 27.000.
% Given
clauses 288.
1 L(x *
y,A,C) = L(x,A,C) * L(y,A,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
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(c1
* c2,A,C) != L(c1,A,C) * L(c2,A,C).
[deny(1)].
20
L(c1,A,C) * L(c2,A,C) != L(c1 * c2,A,C).
[copy(19),flip(a)].
21 (C *
x) * (y * C) = C * (C * (x * y)).
[back_rewrite(15),rewrite([16(9,R)])].
30 0 / x
= x'. [para(8(a,1),6(a,1,1))].
32 x'' =
x.
[para(9(a,1),6(a,1,1)),rewrite([30(3)])].
33 x \ y
= x' * y.
[para(4(a,1),10(a,1,2)),flip(a)].
34 x /
(y * x) = y'.
[para(10(a,1),6(a,1,1))].
36 x *
(x' * y) = y.
[back_rewrite(4),rewrite([33(1)])].
37 (x *
(x * y)) / y = x * x.
[para(12(a,1),6(a,1,1))].
41 (x *
(y * (x * z))) / z = x * (y * x).
[para(13(a,1),6(a,1,1))].
42 x *
((y / x) * (x * z)) = (x * y) * z.
[para(7(a,1),13(a,1,1,2)),flip(a)].
44 (x *
(y * x))' * (x * (y * (x * z))) = z.
[para(13(a,1),10(a,1,2))].
49 (x *
(y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))).
[para(13(a,1),13(a,1,1,2)),rewrite([13(9)])].
53 C *
(x / C) = x.
[para(16(a,2),7(a,1))].
54 C' *
(x * C) = x.
[para(16(a,1),10(a,1,2))].
55 x' *
(C * x) = C. [para(16(a,2),10(a,1,2))].
56 C *
(C * x) = C * (x * C).
[para(16(a,1),12(a,2,2)),rewrite([12(4)])].
57 C *
(x * x) = x * (x * C).
[para(16(a,2),12(a,1))].
58 C *
(x * x) = x * (C * x).
[para(16(a,2),12(a,2,2)),rewrite([16(3,R)])].
61 (C *
(C * x)) * y = C * (x * (C * y)).
[para(16(a,2),13(a,1,1,2))].
68 x' *
((x / y) * (y * z)) = L(z,y,x / y).
[para(7(a,1),18(a,1,1,1))].
75
L(x',x,y) = (y * x)' * y.
[para(9(a,1),18(a,1,2,2)),rewrite([3(4)]),flip(a)].
76 (x *
y) * L(z,y,x) = x * (y * z).
[para(18(a,1),10(a,1,2)),rewrite([32(3)])].
77 x' *
(y' * ((y * x) * z)) = L(z,y * x,y').
[para(10(a,1),18(a,1,1,1))].
84 (x *
C)' * (C * (x * y)) = L(y,x,C).
[para(16(a,1),18(a,1,1,1))].
109 x /
C = C' * x.
[para(53(a,1),10(a,1,2)),flip(a)].
112 (x *
C)' * (x * y) = L(C' * y,C,x).
[para(53(a,1),18(a,1,2,2)),rewrite([109(7)])].
113 C *
(C * ((C' * x) * y)) = x * (y * C).
[para(53(a,1),21(a,1,1)),rewrite([109(7)]),flip(a)].
115 x' *
C = C * x'.
[para(16(a,2),33(a,2)),rewrite([33(2)])].
116 (x /
y)' = y / x. [para(7(a,1),34(a,1,2)),flip(a)].
120 C /
(C * x) = x'.
[para(16(a,2),34(a,1,2))].
126 x *
(C * x') = C.
[para(16(a,2),36(a,1,2))].
132 C *
(x * (C' * x)) = x * x.
[para(54(a,1),13(a,2,2)),rewrite([16(6,R)])].
134 x' *
(C' * ((x * C) * y)) = L(y,x * C,C').
[para(54(a,1),18(a,1,1,1))].
143 (x /
y) * (y / x) = 0.
[para(116(a,1),8(a,1,1))].
147 (C'
* x)' = C / x.
[para(109(a,1),116(a,1,1))].
162 (C /
x) * (C' * x) = 0.
[para(109(a,1),143(a,1,2))].
173 x' /
x = x' * x'.
[para(8(a,1),37(a,1,1,2)),rewrite([3(3)])].
174 x /
x' = x * x.
[para(9(a,1),37(a,1,1,2)),rewrite([3(2)])].
189 (x *
x)' = x' * x'.
[para(174(a,1),116(a,1,1)),rewrite([173(4)])].
215 (C *
x)' = (x * C)'.
[para(56(a,1),120(a,1,2)),rewrite([120(6)]),flip(a)].
233 (C *
(x * x))' * (x * ((x * C) * y)) = L(y,x * C,x). [para(57(a,2),18(a,1,1,1))].
247 (C *
(x * x)) * y = x * (C * (x * y)).
[para(58(a,2),13(a,1,1))].
251 (C *
(x * x))' * (x * ((C * x) * y)) = L(y,C * x,x). [para(58(a,2),18(a,1,1,1))].
259 x *
(C * x) = x * (x * C).
[para(58(a,1),57(a,1))].
282
L(x',x,y) / y = (y * x)'.
[para(75(a,2),6(a,1,1))].
291
L(x',x,C) = C * (C * x)'.
[para(75(a,2),16(a,2)),flip(a)].
293 (C *
x)' * x = L(C',C,x).
[para(16(a,2),75(a,2,1,1)),flip(a)].
300 x /
L(y',y,x) = x * y.
[para(75(a,2),34(a,1,2)),rewrite([32(6)])].
302 C' *
L(x',x,C) = (C * x)'.
[para(75(a,2),54(a,1,2))].
317 L((x
* C)',x * C,x) = (C * (x * x))' * x.
[para(57(a,2),75(a,2,1,1))].
335 x' *
(x' * (C * (x * (C' * (x * y))))) = L(y,x * (C' * x),C).
[para(132(a,1),18(a,1,1,1)),rewrite([189(2),13(9),12(11)])].
378 (C *
(x * x))' = (x * (C * x))'.
[para(259(a,2),282(a,2,1)),rewrite([317(6),6(6)])].
437 x *
(C * y) = x * (y * C).
[para(16(a,1),76(a,2,2)),rewrite([76(5)])].
440 (x *
(y * z))' * (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(76(a,1),18(a,1,2,2))].
445 C *
L(x,C * y,y') = y' * ((C * y) * x).
[para(55(a,1),76(a,1,1))].
446 C *
L(x,C * y',y) = y * ((C * y') * x).
[para(126(a,1),76(a,1,1))].
457
L(x',x,y) * L(z,y,(y * x)') = (y * x)' * (y * z). [para(75(a,2),76(a,1,1))].
466
L(L(x,y,z),z * y,y) = x.
[back_rewrite(44),rewrite([440(7)])].
481 L(C
* x,y,z) = L(x * C,y,z).
[para(437(a,1),18(a,1,2,2)),rewrite([18(7)]),flip(a)].
482 (x *
(C * y))' * (x * ((y * C) * z)) = L(z,y * C,x). [para(437(a,2),18(a,1,1,1))].
667 (x'
* y) / x = x' * (y * x').
[para(8(a,1),41(a,1,1,2,2)),rewrite([3(3)])].
668 x *
((x * y)' * x) = x / y.
[para(8(a,1),41(a,1,1,2)),rewrite([3(2)]),flip(a)].
669 (x *
y) / x' = x * (y * x).
[para(9(a,1),41(a,1,1,2,2)),rewrite([3(2)])].
688 C' *
((C / x) * C') = C' / x.
[para(162(a,1),41(a,1,1,2)),rewrite([3(4)]),flip(a)].
702 x *
L(y',y,x) = x / y.
[para(75(a,2),41(a,2,2)),rewrite([41(6),668(4)]),flip(a)].
716
L(x',x,y) = y' * (y / x).
[para(702(a,1),10(a,1,2)),flip(a)].
770 x' /
(x * y) = x' * (y' * x').
[para(10(a,1),668(a,1,2,1,1)),flip(a)].
878 x' *
((C * x) * x') = C / x.
[para(55(a,1),669(a,1,1)),rewrite([32(3)]),flip(a)].
879 (x *
(y * x))' = x' * (y' * x').
[para(669(a,1),116(a,1,1)),rewrite([770(6)])].
905 (C *
(x * x))' = x' * (C' * x').
[back_rewrite(378),rewrite([879(8)])].
915
L(x,C * y,C') = L(x,C * y,y).
[back_rewrite(251),rewrite([905(4),13(11),10(9),77(8)])].
916
L(x,y * C,C') = L(x,y * C,y).
[back_rewrite(233),rewrite([905(4),13(11),10(9),134(8)])].
968 x' *
((x / y) * x') = (x * y)'.
[para(716(a,1),282(a,1,1)),rewrite([667(4)])].
971
L(x',x,y) * L(z,y / x,y') = y' * ((y / x) * z). [para(716(a,2),76(a,1,1))].
983 (C *
x)' = C' / x.
[back_rewrite(688),rewrite([968(8)])].
1041 C'
* L(x',x,C) = C' / x.
[back_rewrite(302),rewrite([983(9)])].
1044
L(C',C,x) = C'.
[back_rewrite(293),rewrite([983(3),7(4)]),flip(a)].
1045
L(x',x,C) = C * (C' / x).
[back_rewrite(291),rewrite([983(7)])].
1048 (x
* C)' = C' / x.
[back_rewrite(215),rewrite([983(3)]),flip(a)].
1076 (C'
/ x) * (x * y) = L(C' * y,C,x). [back_rewrite(112),rewrite([1048(3)])].
1077 (C'
/ x) * (C * (x * y)) = L(y,x,C).
[back_rewrite(84),rewrite([1048(3)])].
1085 x /
C' = x * C.
[para(1044(a,1),300(a,1,2))].
1087 C'
* x = x * C'.
[para(1044(a,1),702(a,1,2)),rewrite([109(5)]),flip(a)].
1098 (C
* x) * ((C' / x) * y) = y.
[para(983(a,1),36(a,1,2,1))].
1119 (C'
* (C' * x)) * y = C' * (x * (C' * y)).
[para(1087(a,2),13(a,1,1,2))].
1126 x *
(C' * x') = C'.
[para(1087(a,2),36(a,1,2))].
1181 (C
* x) * x' = C.
[para(1126(a,1),21(a,2,2,2)),rewrite([16(8,R),36(8),9(9),3(7)])].
1183 (C'
* x) * (C' * (C / x)) = C'.
[para(147(a,1),1126(a,1,2,2))].
1191 C /
x = x' * C.
[back_rewrite(878),rewrite([1181(5)]),flip(a)].
1192 (C'
* x) * x' = C'.
[back_rewrite(1183),rewrite([1191(7),54(9)])].
1263 (C'
* x)' = x' * C.
[back_rewrite(147),rewrite([1191(6)])].
1264 C *
(C' / x) = x'.
[back_rewrite(120),rewrite([1191(4),983(3),16(5,R)])].
1271
L(x',x,C) = x'.
[back_rewrite(1045),rewrite([1264(8)])].
1278 C'
/ x = C' * x'.
[back_rewrite(1041),rewrite([1271(5)]),flip(a)].
1295 (C
* x) * ((C' * x') * y) = y.
[back_rewrite(1098),rewrite([1278(5)])].
1301 (C'
* x') * (C * (x * y)) = L(y,x,C).
[back_rewrite(1077),rewrite([1278(3)])].
1302 (C'
* x') * (x * y) = L(C' * y,C,x).
[back_rewrite(1076),rewrite([1278(3)])].
1317 (x
* C)' = C' * x'.
[back_rewrite(1048),rewrite([1278(6)])].
1334 (C
* x)' = C' * x'.
[back_rewrite(983),rewrite([1278(6)])].
1340 (C
* x') * x = C.
[para(32(a,1),1181(a,1,2))].
1345 C *
L(x,y',C * y) = (C * y) * (y' * x).
[para(1181(a,1),76(a,1,1))].
1354 C *
L(x,y,C * y') = (C * y') * (y * x).
[para(1340(a,1),76(a,1,1))].
1362 (C'
* x') * x = C'.
[para(32(a,1),1192(a,1,2))].
1381
L(x,y,C' * y') = C * L(C' * x,C,y).
[para(1362(a,1),18(a,1,1,1)),rewrite([32(3),1302(7)]),flip(a)].
1386 C'
* L(x,y,C' * y') = L(C' * x,C,y).
[para(1362(a,1),76(a,1,1)),rewrite([1302(14)])].
1517 (C
* x') * ((C' * x) * y) = y.
[para(32(a,1),1295(a,1,2,1,2))].
1518 (C
* x) * y = (x * C) * y.
[para(36(a,1),1295(a,1,2)),rewrite([1263(8),32(5)])].
1543
L(x,C * y,z) = L(x,y * C,z).
[para(1518(a,1),18(a,1,2,2)),rewrite([482(9)]),flip(a)].
1554 (x
* C) * (C * y) = C * (C * (x * y)).
[para(1518(a,1),437(a,1)),rewrite([21(10)])].
1590 (C
* x') * (C' * (x * y)) = L(y,x,C').
[para(76(a,1),1517(a,1,2))].
1704
L(x,C * (C * y),C * y) = L(x,C * (y * C),C').
[para(1518(a,1),916(a,1,2)),rewrite([16(4,R),16(11,R)]),flip(a)].
1711 (x
* y) * x' = x * (y / x).
[para(9(a,1),42(a,1,2,2)),rewrite([3(3)]),flip(a)].
1712 (x
/ y) * (y * z) = y' * ((y * x) * z).
[para(42(a,1),10(a,1,2)),flip(a)].
1713 (x'
* y) * (x * z) = x' * ((y / x') * z).
[para(10(a,1),42(a,1,2,2)),flip(a)].
1723 C *
((C * x) * y) = x * (C * (C * y)).
[para(42(a,1),21(a,2,2)),rewrite([109(3),36(5),16(4,R)]),flip(a)].
1726 (x
* y) * (x' * z) = x * ((y / x) * z).
[para(36(a,1),42(a,1,2,2)),flip(a)].
1730 C'
* ((x * C) * (C' * y)) = (C' * x) * y.
[para(42(a,1),109(a,2)),rewrite([1085(3),109(8)])].
1760 (C'
* x) * y = (x * C') * y.
[para(1087(a,1),42(a,2,1)),rewrite([1085(5),1730(9)])].
1795
L(x,y * z,y') = L(x,y,z / y).
[back_rewrite(68),rewrite([1712(4),77(6)])].
1796
L(x,y,y' * C) = L(x,y,C).
[back_rewrite(1301),rewrite([1713(8),1085(6),1713(7),1191(6),32(5),77(8),1795(4),1191(2)])].
1800 C *
L(C' * x,C,y) = L(x,y,C').
[back_rewrite(1590),rewrite([1726(8),109(4),1302(7)])].
1808
L(x,C * (C * y),C * y) = L(x,C,y).
[back_rewrite(1704),rewrite([1795(14),109(12),54(13)])].
1813
L(x,C * y,y) = L(x,C,C' * y).
[back_rewrite(915),rewrite([1795(5),109(3)]),flip(a)].
1815 x'
* (y' * ((y * x) * z)) = L(z,y,x / y).
[back_rewrite(77),rewrite([1795(9)])].
1816
L(x,y,C' * y') = L(x,y,C').
[back_rewrite(1381),rewrite([1800(12)])].
1819 C'
* L(x,y,C') = L(C' * x,C,y).
[back_rewrite(1386),rewrite([1816(7)])].
1825
L(x,y / z,z) = L(x,z',z * y).
[para(1711(a,1),18(a,1,1,1)),rewrite([1726(7),18(7)])].
1894 (x
* C') * (y * C) = C' * ((x * C) * y).
[para(1760(a,1),437(a,2)),rewrite([1713(6),1085(5)]),flip(a)].
1941
L(x,y / z,z / (y / z)) = L(x,y,z / y).
[para(7(a,1),1795(a,1,2)),rewrite([116(2)]),flip(a)].
1944
L(x,y',y * (z * y)) = L(x,z,y).
[para(10(a,1),1795(a,1,2)),rewrite([32(2),669(5)]),flip(a)].
1947
L(x,y * C,C') = L(x,C,C' * y).
[para(16(a,1),1795(a,1,2)),rewrite([109(8)])].
1948
L(x,C * y,y') = L(x,y,C).
[para(16(a,2),1795(a,1,2)),rewrite([1191(6),1796(8)])].
1955 L(x,C
* y',y) = L(x,y',y * C).
[para(115(a,1),1795(a,1,2)),rewrite([32(5),1191(8),32(7)])].
1963
L(x,y / z,y') = L(x,y,(y * z)').
[para(282(a,1),1795(a,2,3)),rewrite([702(3)])].
1999 x'
* (C' * ((x * C) * y)) = L(y,C,C' * x).
[back_rewrite(134),rewrite([1947(13)])].
2002 x'
* ((C * x) * y) = C * L(y,x,C).
[back_rewrite(445),rewrite([1948(5)]),flip(a)].
2009 C *
L(x,y',y * C) = y * ((C * y') * x).
[back_rewrite(446),rewrite([1955(5)])].
2013 (x
* y)' * (x * z) = x' * ((x / y) * z).
[back_rewrite(971),rewrite([1963(5),457(6)])].
2072
L(x,y,z / y) = L(x,y,z).
[back_rewrite(18),rewrite([2013(5),1712(4),1815(6)])].
2103
L(x,y',y * z) = L(x,z,y).
[back_rewrite(1941),rewrite([2072(4),1825(2),2072(5)])].
2106
L(x,y * z,y') = L(x,y,z).
[back_rewrite(1795),rewrite([2072(5)])].
2119 x *
((C * x') * y) = C * L(y,C,x).
[back_rewrite(2009),rewrite([2103(5)]),flip(a)].
2123
L(x,y * z,z) = L(x,y,z).
[back_rewrite(1944),rewrite([2103(4)])].
2133
L(x,C,C' * y) = L(x,C,y).
[back_rewrite(1813),rewrite([2123(3)]),flip(a)].
2134
L(x,C,C * y) = L(x,C,y).
[back_rewrite(1808),rewrite([2123(7)])].
2137
L(L(x,y,z),z,y) = x.
[back_rewrite(466),rewrite([2123(3)])].
2139 x'
* (C' * ((x * C) * y)) = L(y,C,x).
[back_rewrite(1999),rewrite([2133(13)])].
2156 x *
(y * L(z,x,y)) = (x * y) * z.
[para(2137(a,1),76(a,1,2)),flip(a)].
2164
L(x,y,z * y) = L(x,y,z).
[para(6(a,1),2072(a,1,3)),flip(a)].
2185
L(x,C * y,C) = L(x,y,C).
[para(16(a,2),2123(a,1,2))].
2187
L(x,y,y' * z) = L(x,z,y').
[para(36(a,1),2123(a,1,2)),rewrite([2164(3)]),flip(a)].
2189
L(x,y',C * y) = L(x,C,y).
[para(55(a,1),2123(a,1,2)),rewrite([2134(4)]),flip(a)].
2190
L(x,y,C * y') = L(x,C,y').
[para(126(a,1),2123(a,1,2)),rewrite([2134(5)]),flip(a)].
2206
L(x,C,y') = L(x,y,C).
[para(1181(a,1),2123(a,1,2)),rewrite([1948(7)])].
2211
L(x,C,y) = L(x,y,C').
[back_rewrite(2133),rewrite([2187(5)]),flip(a)].
2212 (C
* x) * (x' * y) = C * L(y,C,x).
[back_rewrite(1345),rewrite([2189(5)]),flip(a)].
2213 (C
* x') * (x * y) = C * L(y,C,x').
[back_rewrite(1354),rewrite([2190(5)]),flip(a)].
2227
L(x,y',C) = L(x,C,y).
[para(32(a,1),2206(a,1,3)),flip(a)].
2228
L(x,y / z,C) = L(x,C,z / y).
[para(116(a,1),2206(a,1,3)),flip(a)].
2229
L(x,y * y,C) = L(x,C,y' * y').
[para(189(a,1),2206(a,1,3)),flip(a)].
2232 L(C
* x,y,C) = L(x * C,C,y').
[para(2206(a,1),481(a,1))].
2236
L(x,y',C') = L(x,y,C).
[para(2206(a,2),1543(a,1)),rewrite([1334(4),2187(6),2123(8)])].
2241
L(L(x,C,y'),C,y) = x.
[para(2206(a,2),2137(a,1,1))].
2242
L(L(x,C,y),C,y') = x.
[para(2206(a,2),2137(a,1))].
2260
L(L(x,C,y),C',y) = x.
[para(2211(a,2),2137(a,1,1))].
2271
L(x,y',C) = L(x,y,C').
[para(2227(a,2),2072(a,2)),rewrite([109(3),2187(5)]),flip(a)].
2280
L(L(x,C,y * y),C,y' * y') = x.
[para(189(a,1),2242(a,1,3))].
2294
L(x,C',y) = L(x,C,y').
[para(2241(a,1),2260(a,1,1))].
2356
L(x,y * (C' * y),C) = L(x,C,y' * y').
[para(132(a,1),2185(a,1,2)),rewrite([2229(3)]),flip(a)].
2361 x'
* (x' * (C * (x * (C' * (x * y))))) = L(y,C,x' * x'). [back_rewrite(335),rewrite([2356(17)])].
2416
L(x,y * z,C) = L(x,C,(y * z)').
[para(300(a,1),2228(a,1,2)),rewrite([282(7)])].
2417
L(x,y * z,C') = L(x,C,y * z).
[para(300(a,1),2228(a,2,3)),rewrite([282(3),2271(4)])].
3443 C'
* (x * (C * (C * y))) = (C * x) * y.
[para(1723(a,1),10(a,1,2))].
3579 C *
L(x,C,y) = L(C * x,y,C').
[para(10(a,1),1800(a,1,2,1))].
3619 (C
* x') * (x * y) = L(C * y,x,C).
[back_rewrite(2213),rewrite([3579(10),2236(11)])].
3620 (C
* x) * (x' * y) = L(C * y,x,C').
[back_rewrite(2212),rewrite([3579(9)])].
3624 x *
((C * x') * y) = L(C * y,x,C').
[back_rewrite(2119),rewrite([3579(9)])].
3688 C *
L(x,y,C) = L(C * x,y,C).
[para(13(a,1),2002(a,1,2)),rewrite([1317(3),1713(10),1085(6),1713(9),1191(6),32(5),1554(8),3443(10),3619(5
),2123(9)]),flip(a)].
3690 C *
L(x,y,C') = L(C * x,y,C').
[para(32(a,1),2002(a,1,1)),rewrite([3624(5),2271(9)]),flip(a)].
3695 L(C
* x,C,y' * y') = y' * (C * (y * x)).
[para(189(a,1),2002(a,1,1)),rewrite([247(7),12(8),10(7),2416(9),189(9),3579(12),2417(13)]),fli
p(a)].
3738 x'
* ((C * x) * y) = L(C * y,x,C).
[back_rewrite(2002),rewrite([3688(9)])].
3747 C'
* L(C * x,y,C) = L(x,y,C).
[para(3688(a,1),10(a,1,2))].
3803 C'
* L(C * x,C,y') = L(x,y,C).
[para(2206(a,2),3747(a,1,2))].
4131 L(C
* (C * x),y,C') * z = C * (L(x,y,C') * (C * z)). [para(3690(a,1),61(a,1,1,2)),rewrite([3690(7)])].
4173 C'
* (x' * (C * (x * y))) = L(y,C,x' * x').
[para(189(a,1),3803(a,1,2,3)),rewrite([3695(9),2416(11),189(11)])].
4208 C'
* ((x * C) * y) = C * (x * (C' * y)).
[para(13(a,1),113(a,1,2,2)),rewrite([36(10),1894(12)]),flip(a)].
4218 x *
L(C * y,x,C') = C * (x * y).
[para(76(a,1),113(a,1,2,2)),rewrite([36(7),16(8,R),3690(8)]),flip(a)].
4258 x'
* (C * (x * (C' * y))) = L(y,C,x).
[back_rewrite(2139),rewrite([4208(7)])].
4275 x'
* L(x * y,C,x) = L(y,C,x' * x').
[back_rewrite(2361),rewrite([4258(10)])].
4279 x'
* (C * (x * y)) = L(C * y,x,C').
[para(4218(a,1),10(a,1,2))].
4344
L(x,C,y' * y') = L(x,C,y).
[back_rewrite(4173),rewrite([4279(7),1819(8),10(5)]),flip(a)].
4367 x'
* L(x * y,C,x) = L(y,C,x).
[back_rewrite(4275),rewrite([4344(10)])].
4385
L(L(x,C,y * y),C,y) = x.
[back_rewrite(2280),rewrite([4344(8)])].
4394
L(x,C,y * y) = L(x,y,C).
[para(4385(a,1),2137(a,1,1)),flip(a)].
5770 C'
* L(x,C,y) = L(C' * x,C,y).
[para(1302(a,1),2156(a,2)),rewrite([2294(8),32(7),4367(7)])].
11104
L(C * (x * L(C * y,z,C)),z,C') = L(C * (x * C),z,C') * y.
[para(55(a,1),49(a,1,1,2,2,2)),rewrite([3620(7),3738(16),3620(18)]),flip(a)]
.
11368
L(C * (x * C),y,C') * z = C * (L(x,y,C') * (C * z)).
[para(16(a,2),11104(a,2,1,1,2)),rewrite([11104(10),4131(16)])].
11385
L(C * (x * L(C * y,z,C)),C,z) = L(C * (x * C),C,z) * y.
[para(11104(a,1),1543(a,1)),rewrite([2106(9),2416(14),1334(14),2187(16),2236(1
4),2417(19),2164(18)]),flip(a)].
11388
L(C * (x * C),C,y) * z = C * (L(x,y,C') * (C * z)). [para(11104(a,1),2211(a,2)),rewrite([11385(9),11368(15)])].
11391
L(C * (x * L(y * C,C,z')),z,C') = C * (L(x,z,C') * (C * y)).
[para(2232(a,1),11104(a,1,1,2,2)),rewrite([11368(19)])].
11412 C
* (L(C' * x,y,C') * (C * z)) = L(C * x,C,y) * z. [para(7(a,1),11388(a,1,1,1,2)),rewrite([109(8)]),flip(a)].
11454
L(C * (x * L(y * C,C,z')),C,z) = C * (L(x,z,C') * (C * y)). [para(11391(a,1),2211(a,2))].
11483
L(x * L(y,C,z'),C,z) = L(x,C,z) * y.
[para(1119(a,1),11454(a,1,1,2)),rewrite([5770(11),54(8),36(9),11412(20),36(11)])].
11508
L(x,C,y) * L(z,C,y) = L(x * z,C,y).
[para(2241(a,1),11483(a,1,1,2)),rewrite([32(8)]),flip(a)].
11618
L(x,y,C) * L(z,y,C) = L(x * z,y,C) # label(non_clause) # label(goal).
[para(4394(a,1),11508(a,1,1)),rewrite([4394(5),4394(9)])].
11619
$F. [resolve(11618,a,20,a)].
==============================
end of proof ==========================
% Proof
1 at 1.45 (+ 0.02) seconds.
% Length
of proof is 247.
% Level
of proof is 36.
%
Maximum clause weight is 28.000.
% Given
clauses 389.
1 L(x *
y,A,C) = L(x,A,C) * L(y,A,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(c1
* c2,A,C) != L(c1,A,C) * L(c2,A,C).
[deny(1)].
20
L(c1,A,C) * L(c2,A,C) != L(c1 * c2,A,C).
[copy(19),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)])].
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))].
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)])].
50 (A *
x) * A = A * (x * A).
[para(2(a,1),15(a,1,2)),rewrite([3(7)])].
54 A *
((A' * x) * A) = x * A.
[para(9(a,1),15(a,1,1)),rewrite([2(4)]),flip(a)].
63 C *
(x / C) = x.
[para(16(a,2),7(a,1))].
64 C' *
(x * C) = x.
[para(16(a,1),10(a,1,2))].
65 x' *
(C * x) = C.
[para(16(a,2),10(a,1,2))].
66 C *
(C * x) = C * (x * C).
[para(16(a,1),12(a,2,2)),rewrite([12(4)])].
67 C *
(x * x) = x * (x * C). [para(16(a,2),12(a,1))].
69 (x *
(x * C)) * y = x * (C * (x * y)).
[para(16(a,1),13(a,1,1,2))].
87
L(x',x,y) = (y * x)' * y.
[para(9(a,1),18(a,1,2,2)),rewrite([3(4)]),flip(a)].
88 (x *
y) * L(z,y,x) = x * (y * z).
[para(18(a,1),10(a,1,2)),rewrite([31(3)])].
89 x' *
(y' * ((y * x) * z)) = L(z,y * x,y').
[para(10(a,1),18(a,1,1,1))].
91 (x *
(x * y))' * (x * (x * (y * z))) = L(z,y,x * x). [para(12(a,1),18(a,1,1,1)),rewrite([12(6)])].
109 x /
C = C' * x.
[para(63(a,1),10(a,1,2)),flip(a)].
112 (x *
C)' * (x * y) = L(C' * y,C,x).
[para(63(a,1),18(a,1,2,2)),rewrite([109(7)])].
113 x' *
C = C * x'.
[para(16(a,2),32(a,2)),rewrite([32(2)])].
114 (x /
y)' = y / x.
[para(7(a,1),33(a,1,2)),flip(a)].
119 C /
(C * x) = x'.
[para(16(a,2),33(a,1,2))].
120 (x *
(y * z)) / L(z,y,x) = x * y.
[para(18(a,1),33(a,1,2)),rewrite([31(7)])].
126 x *
(C * x') = C.
[para(16(a,2),35(a,1,2))].
133 x' *
(C' * ((x * C) * y)) = L(y,x * C,C').
[para(64(a,1),18(a,1,1,1))].
134 (x *
C')' * (x * y) = L(y * C,C',x).
[para(64(a,1),18(a,1,2,2))].
137 C' *
(x' * ((C * x) * y)) = L(y,C * x,x').
[para(65(a,1),18(a,1,1,1))].
146 (C'
* x)' = C / x.
[para(109(a,1),114(a,1,1))].
153
L(x',C,x) = C * (x * C)'.
[para(126(a,1),18(a,1,2)),rewrite([16(5,R)]),flip(a)].
197
L(A,x,A) = A. [para(50(a,1),10(a,1,2)),rewrite([18(8)])].
203 A /
(A * (x * A)) = (A * x)'.
[para(50(a,1),33(a,1,2))].
219 (C *
x)' = (x * C)'.
[para(66(a,1),119(a,1,2)),rewrite([119(6)]),flip(a)].
226 (x *
C)' * ((C * x) * y) = y.
[para(219(a,1),10(a,1,1))].
313 (x *
A') * A = x. [para(13(a,1),54(a,1,2)),rewrite([8(7),3(5),35(5)]),flip(a)].
315 x /
A = x * A'.
[para(313(a,1),6(a,1,1))].
316 x /
A' = x * A.
[para(7(a,1),313(a,1,1)),flip(a)].
321 A *
((x * (y * A')) * A) = (A * x) * y.
[para(313(a,1),15(a,1,2)),flip(a)].
323 (x *
(y * A'))' * (x * y) = L(A,y * A',x).
[para(313(a,1),18(a,1,2,2))].
332 (x *
A)' = A' / x.
[para(316(a,1),114(a,1,1))].
358 (A *
C)' = C' * A'.
[para(16(a,1),332(a,1,1)),rewrite([109(8)])].
369
L(x',x,y) / y = (y * x)'.
[para(87(a,2),6(a,1,1))].
381
L(x',x,C) = C * (C * x)'.
[para(87(a,2),16(a,2)),flip(a)].
382
L(x',x,C) = C * (x * C)'.
[para(16(a,1),87(a,2,1,1)),rewrite([16(8,R)])].
383 (C *
x)' * x = L(C',C,x).
[para(16(a,2),87(a,2,1,1)),flip(a)].
388 x /
L(y',y,x) = x * y. [para(87(a,2),33(a,1,2)),rewrite([31(6)])].
487 L((x
* C)',C,C * x) = C * (C * (C * x))'.
[para(219(a,1),153(a,1,1)),rewrite([16(12,R)])].
492 L(x
* C,(x * C)',C) = C * L(x',C,x)'.
[para(153(a,2),87(a,2,1,1)),rewrite([31(4),16(13,R)])].
517 A /
(A * (A * C)) = C' * A'.
[para(16(a,1),203(a,1,2,2)),rewrite([358(11)])].
521 (C *
x) * y = (x * C) * y.
[para(226(a,1),10(a,1,2)),rewrite([31(4)]),flip(a)].
567 L((C
* x)',C,C * x) = C * (C * (x * C))'.
[para(521(a,1),153(a,2,2,1)),rewrite([16(12,R)])].
612 L((C
* x)',x * C,C) = C * (C * (x * C))'.
[para(219(a,2),381(a,1,1))].
631
L(x',C,x) = L(x',x,C).
[para(382(a,2),388(a,2)),rewrite([31(5),492(8),119(8),31(5)])].
637 C *
(C * (C * x))' = C * (C * (x * C))'.
[para(219(a,1),631(a,1,1)),rewrite([487(7),631(14,R),567(14)])].
650 (x *
C)' * x = L(C',C,x).
[para(16(a,1),383(a,1,1,1))].
676 (x *
L(C',C,x)) * y = x * L(C' * y,C,x).
[para(650(a,1),13(a,1,1,2)),rewrite([112(11)])].
678
L(C',C,x)' * L(C' * y,C,x) = L(y,x,(x * C)'). [para(650(a,1),18(a,1,1,1)),rewrite([112(10)])].
785 x *
(C * y) = x * (y * C).
[para(16(a,1),88(a,2,2)),rewrite([88(5)])].
788 (x *
(y * z))' * (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(88(a,1),18(a,1,2,2))].
791 x *
L(y,x * C,C') = C' * ((x * C) * y).
[para(64(a,1),88(a,1,1))].
792 C *
L(x,C * y,y') = y' * ((C * y) * x).
[para(65(a,1),88(a,1,1))].
793 C *
L(x,C * y',y) = y * ((C * y') * x).
[para(126(a,1),88(a,1,1))].
807
L(x',x,y) * L(z,y,(y * x)') = (y * x)' * (y * z). [para(87(a,2),88(a,1,1))].
826
L(L(x,y,z),z * y,z) = L(x,y,z * z).
[back_rewrite(91),rewrite([788(7)])].
827
L(L(x,y,z),z * y,y) = x.
[back_rewrite(43),rewrite([788(7)])].
853
L(L(x,y,z / y),z,y) = x.
[para(7(a,1),827(a,1,2))].
867
L(A,A * x,x) = A.
[para(197(a,1),827(a,1,1))].
910 L(x'
* (x / y),x,y) = y'.
[para(87(a,1),853(a,1,1)),rewrite([7(2)])].
912 L(C
* x',x,C) = C / x.
[para(153(a,1),853(a,1,1)),rewrite([109(3),16(6,R),35(6),109(7),146(9)])].
917
L(x,y * z,z) = L(x,y,z / y).
[para(853(a,1),827(a,1,1))].
918
L(x,y / z,z / (y / z)) = L(x,y,z).
[para(853(a,1),853(a,1,1)),flip(a)].
930
L(x',x,C * C) = x'.
[para(381(a,2),912(a,1,1)),rewrite([826(7),119(9)])].
934 (C *
x) * (C / x) = C * C.
[para(912(a,1),88(a,1,2)),rewrite([126(10)])].
945 (C *
(C * x))' = x' / (C * C). [para(930(a,1),369(a,1,1)),rewrite([12(9)]),flip(a)].
954 C *
(C * (x * C))' = C * (x' / (C * C)).
[back_rewrite(637),rewrite([945(6)]),flip(a)].
959 L((C
* x)',x * C,C) = C * (x' / (C * C)).
[back_rewrite(612),rewrite([954(14)])].
976 (C *
L(x',x,C)) * (C * x) = C * C.
[para(388(a,1),934(a,1,2))].
1021 (x
* y) * x' = x * (y / x).
[para(910(a,1),88(a,1,2)),rewrite([35(7)])].
1044 (x
/ y) * (y / (x / y)) = x * (y / x).
[para(7(a,1),1021(a,1,1)),rewrite([114(2)]),flip(a)].
1051 (C
* x) * x' = x * (C / x).
[para(16(a,2),1021(a,1,1))].
1055 (x'
* y) * x = x' * (y / x').
[para(31(a,1),1021(a,1,2))].
1056 x'
/ (x * (y / x)) = (x * y)'.
[para(1021(a,1),33(a,1,2))].
1082
L(C',C,x) = C'.
[para(1021(a,1),226(a,1,2)),rewrite([109(6),35(8),650(4)])].
1093 (x
* (y / x)) * L(z,x',x * y) = (x * y) * (x' * z). [para(1021(a,1),88(a,1,1))].
1103
L(x,y,(y * C)') = C * L(C' * x,C,y).
[back_rewrite(678),rewrite([1082(4),31(3)]),flip(a)].
1105 x *
L(C' * y,C,x) = (x * C') * y.
[back_rewrite(676),rewrite([1082(4)]),flip(a)].
1122 x /
C' = x * C.
[para(1082(a,1),388(a,1,2))].
1123 (x
* C)' = C' / x.
[para(1082(a,1),369(a,1,1)),flip(a)].
1126
L(x,y,C' / y) = C * L(C' * x,C,y).
[back_rewrite(1103),rewrite([1123(3)])].
1221 (C
* x)' = C' / x.
[back_rewrite(219),rewrite([1123(6)])].
1225 (C'
/ x) * (x * y) = L(C' * y,C,x).
[back_rewrite(112),rewrite([1123(3)])].
1303
L(C' / x,x * C,C) = C * (x' / (C * C)).
[back_rewrite(959),rewrite([1221(3)])].
1306 C'
/ (C * x) = x' / (C * C).
[back_rewrite(945),rewrite([1221(5)])].
1345 C *
(x * C') = x.
[para(1122(a,1),6(a,1)),rewrite([16(5,R)])].
1351 C'
* x = x * C'.
[para(1345(a,1),10(a,1,2))].
1358 (x
* C')' = C / x.
[para(1345(a,1),119(a,1,2)),flip(a)].
1366 A /
(A * (A * C)) = A' * C'.
[back_rewrite(517),rewrite([1351(12)])].
1372 (C
/ x) * (x * y) = L(y * C,C',x).
[back_rewrite(134),rewrite([1358(4)])].
1485
L(x,y',(y * z) / y') = L(x,z,y * z).
[para(10(a,1),917(a,1,2)),flip(a)].
1490
L(x,C * y,C) = L(x,y,C / y).
[para(16(a,2),917(a,1,2))].
1494
L(x,y,(y' * z) / y) = L(x,z,y' * z).
[para(35(a,1),917(a,1,2)),flip(a)].
1497
L(x,C * y,y) = L(x,C,C' * y).
[para(109(a,1),917(a,2,3))].
1512
L(x,A * y,y) = L(x,A,y * A').
[para(315(a,1),917(a,2,3))].
1515
L((x * y)',x,y / x) = (y * (x * y))' * y.
[para(917(a,1),87(a,1))].
1528
L((x * y)',x,y / x) / y = (y * (x * y))'.
[para(917(a,1),369(a,1,1))].
1529
L(x,y * L(z',z,y),L(z',z,y)) = L(x,y,(y * z)'). [para(369(a,1),917(a,2,3))].
1539
L(L(x,y,z),z,y / z) = x.
[para(917(a,1),827(a,1))].
1541
L(A,A,x * A') = A.
[para(917(a,1),867(a,1)),rewrite([315(4)])].
1563
L(A,A,x) = A.
[para(7(a,1),1541(a,1,3))].
1565 (x
* A) * A = x * (A * A).
[para(1563(a,1),88(a,1,2))].
1608
L(x,y * (A * A),A) = L(x,y * A,y').
[para(1565(a,1),917(a,1,2)),rewrite([33(12)])].
1622 (x
* (y * x))' = x' / (x * y).
[para(6(a,1),1056(a,1,2,2)),flip(a)].
1655
L((x * y)',x,y / x) / y = y' / (y * x).
[back_rewrite(1528),rewrite([1622(8)])].
1656
L((x * y)',x,y / x) = (y' / (y * x)) * y.
[back_rewrite(1515),rewrite([1622(7)])].
1669 C'
/ (C * x') = x / (C * C).
[para(31(a,1),1306(a,2,1))].
1677
L(L(x,C * y,y' / (C * C)),C',C * y) = x.
[para(1306(a,1),853(a,1,1,3))].
1686
L(x,C * y,y' / (C * C)) = L(x,y,C').
[para(1306(a,1),917(a,2,3)),rewrite([1351(5,R),10(5)]),flip(a)].
1688
L(L(x,C',C * y),y,C') = x.
[para(1306(a,1),1539(a,1,3)),rewrite([1686(13)])].
1691
L(L(x,y,C'),C',C * y) = x.
[back_rewrite(1677),rewrite([1686(8)])].
1712 C *
L(x,C * y,C) = L(x * C,C',y).
[para(1490(a,2),88(a,1,2)),rewrite([7(3),1372(10)])].
1728 (x'
/ (x * y)) * (x * ((y * x) * z)) = L(z,y * x,x). [para(1622(a,1),18(a,1,1))].
1730 (x
* y) / x' = x * (y * x).
[para(1622(a,1),31(a,1,1)),rewrite([114(4)])].
1784
L(x,y',y * (z * y)) = L(x,z,y * z).
[back_rewrite(1485),rewrite([1730(4)])].
1801 (C
* x) / x' = x * (C * x).
[para(16(a,2),1730(a,1,1))].
1803 (x'
* y) / x = x' * (y * x').
[para(31(a,1),1730(a,1,2))].
1845
L(x,y,z' * y) = L(x,z,z' * (y * z')).
[back_rewrite(1494),rewrite([1803(3)]),flip(a)].
2182 x *
((y / (x * z)) * x) = (x * y) / z.
[para(7(a,1),40(a,1,1,2)),flip(a)].
2183 x *
((x * y)' * x) = x / y.
[para(8(a,1),40(a,1,1,2)),rewrite([3(2)]),flip(a)].
2194 (x
* L(y,z,x)) / (z * y) = x / z.
[para(18(a,1),40(a,1,1,2)),rewrite([2183(8)])].
2214 x *
L(y',y,x) = x / y.
[para(87(a,2),40(a,2,2)),rewrite([40(6),2183(4)]),flip(a)].
2254
L(x,y / z,L(z',z,y)) = L(x,y,(y * z)').
[back_rewrite(1529),rewrite([2214(3)])].
2256 (C
/ x) * (C * x) = C * C.
[back_rewrite(976),rewrite([2214(5)])].
2265 L(x',x,y)
= y' * (y / x).
[para(2214(a,1),10(a,1,2)),flip(a)].
2325 (x'
/ y) * x = x' * (x' * y)'.
[para(2214(a,1),1055(a,1,1)),rewrite([369(9)])].
2336
L((x * y)',x,y / x) = y' * x'.
[back_rewrite(1656),rewrite([2325(8),10(8)])].
2343 x'
/ (x * y) = x' * (y' * x').
[back_rewrite(1655),rewrite([2336(4),1803(4)]),flip(a)].
2399
L(x,y * z,y') = L(x,y * z,z).
[back_rewrite(1728),rewrite([2343(3),13(9),10(7),89(6)])].
2410 x /
(C * C) = C' * (x * C').
[back_rewrite(1669),rewrite([2343(6),31(4)]),flip(a)].
2450
L(C' / x,x * C,C) = x' * C'.
[back_rewrite(1303),rewrite([2410(13),35(16)])].
2524 x'
* (C * (x * C)) = C * C.
[para(33(a,1),2256(a,1,1))].
2691
L(x',x,y) * L(z,y / x,y') = y' * ((y / x) * z). [para(2265(a,2),88(a,1,1))].
2799 C *
(x * C) = x * (C * C).
[para(2524(a,1),10(a,1,2)),rewrite([31(2)]),flip(a)].
2835 C *
(C * x) = x * (C * C).
[para(16(a,2),2799(a,1,2))].
2847 (x
* (C * C))' = C' * (x' * C').
[para(2799(a,1),369(a,2,1)),rewrite([1123(3),2450(7),109(6)]),flip(a)].
2879
L(x,C * y,y') = L(x,C * y,C).
[para(2835(a,1),18(a,1,1,1)),rewrite([2847(5),13(13),10(11),137(8)])].
3312 (x
/ y) * (y * z) = x * L(z,y,x).
[para(2194(a,1),7(a,1,1))].
3402
L(x,y,z / y) = L(x,y,z).
[para(7(a,1),2399(a,1,2)),rewrite([114(2),7(4)])].
3403
L(x,y,z * y) = L(x,y,z).
[para(10(a,1),2399(a,1,2)),rewrite([31(2),10(4)]),flip(a)].
3407
L(x,C * y,y) = L(x,y * C,C').
[para(16(a,1),2399(a,1,2)),flip(a)].
3416
L(x,y' * C,C) = L(x,C * y',y).
[para(113(a,1),2399(a,1,2)),rewrite([31(5)]),flip(a)].
3465
L(x,y * z,y') = L(x,y,z).
[para(2399(a,2),917(a,1)),rewrite([3402(5)])].
3467
L(L(x,y,z),z,y) = x.
[para(2399(a,2),1539(a,1,1)),rewrite([3465(3),6(3)])].
3476
L(x,y / z,y') = L(x,y,(y * z)').
[para(2214(a,1),2399(a,1,2)),rewrite([2214(6),2254(7)])].
3526
L(x,C * y,C) = L(x,y,C).
[back_rewrite(1490),rewrite([3402(7)])].
3530 C *
L(C' * x,C,y) = L(x,y,C').
[back_rewrite(1126),rewrite([3402(4)]),flip(a)].
3531
L(x,y / z,z) = L(x,y,z).
[back_rewrite(918),rewrite([3402(4)])].
3532
L(x,y * z,z) = L(x,y,z).
[back_rewrite(917),rewrite([3402(4)])].
3541
L(x,y,y' * (z * y')) = L(x,z,y').
[back_rewrite(1845),rewrite([3403(3)]),flip(a)].
3542
L(x,y',y * (z * y)) = L(x,z,y).
[back_rewrite(1784),rewrite([3403(6)])].
3594
L(x,y * (A * A),A) = L(x,y,A).
[back_rewrite(1608),rewrite([3465(10)])].
3598 x'
* (y' * ((y * x) * z)) = L(z,y,x).
[back_rewrite(89),rewrite([3465(9)])].
3603 (x
* y)' * (x * z) = x' * ((x / y) * z).
[back_rewrite(2691),rewrite([3476(5),807(6)])].
3623
L(x,C * y',y) = L(x,y',C).
[back_rewrite(3416),rewrite([3532(5)]),flip(a)].
3650
L(x,C * y,y') = L(x,y,C).
[back_rewrite(2879),rewrite([3526(8)])].
3652 C *
L(x,y,C) = L(x * C,C',y).
[back_rewrite(1712),rewrite([3526(5)])].
3679
L(x,y * C,C') = L(x,C,y).
[back_rewrite(3407),rewrite([3532(3)]),flip(a)].
3694
L(x,A,y * A') = L(x,A,y).
[back_rewrite(1512),rewrite([3532(3)]),flip(a)].
3697
L(x,C,C' * y) = L(x,C,y).
[back_rewrite(1497),rewrite([3532(3)]),flip(a)].
3752 x'
* ((x / (y * A')) * y) = L(A,y * A',x).
[back_rewrite(323),rewrite([3603(7)])].
3772 x *
((C * x') * y) = L(y * C,C',x').
[back_rewrite(793),rewrite([3623(5),3652(5)]),flip(a)].
3784 x'
* ((C * x) * y) = L(y * C,C',x).
[back_rewrite(792),rewrite([3650(5),3652(4)]),flip(a)].
3811 C'
* ((x * C) * y) = x * L(y,C,x).
[back_rewrite(791),rewrite([3679(5)]),flip(a)].
3812 x'
* (C' * ((x * C) * y)) = L(y,C,x).
[back_rewrite(133),rewrite([3679(13)])].
3855
L(x,y',y * z) = L(x,z,y).
[para(1730(a,1),3402(a,1,3)),rewrite([3542(4)]),flip(a)].
3856
L(x,y',C * y) = L(x,C,y).
[para(1801(a,1),3402(a,1,3)),rewrite([3855(5),3532(3)]),flip(a)].
3857
L(x,y,y' * z) = L(x,z,y').
[para(1803(a,1),3402(a,1,3)),rewrite([3541(5)]),flip(a)].
3884
L(L(x,y,C'),y,C) = x.
[back_rewrite(1691),rewrite([3855(8)])].
3885
L(L(x,y,C),y,C') = x. [back_rewrite(1688),rewrite([3855(5)])].
3887 (x
* (y / x)) * L(z,y,x) = (x * y) * (x' * z). [back_rewrite(1093),rewrite([3855(5)])].
3890
L(x,C,y) = L(x,y,C').
[back_rewrite(3697),rewrite([3857(5)]),flip(a)].
3900
L(x,C',y) = L(x,y,C).
[para(3467(a,1),3884(a,1,1)),flip(a)].
3931
L(c1,A,C) * L(c2,C',A) != L(c1 * c2,A,C).
[para(3900(a,2),20(a,1,2))].
4061 (x
* y) * (x' * z) = x * ((y / x) * z).
[para(3531(a,1),88(a,1,2)),rewrite([3887(4)])].
4085 (x
* (y / x)) * L(z,y,x) = x * ((y / x) * z). [back_rewrite(3887),rewrite([4061(8)])].
4149
L(x,C',A') = L(x,A,C').
[para(1351(a,1),3694(a,1,3)),rewrite([3857(7)])].
4218 (C
* x) * (x' * y) = x * ((C / x) * y).
[para(3856(a,1),88(a,1,2)),rewrite([1051(4),4085(6)]),flip(a)].
4259
L(x,A * (A * C),A) = L(x,C,A).
[para(16(a,1),3594(a,1,2)),rewrite([16(5,R),67(5)])].
4323 (x'
* y) * (x * z) = x' * ((y / x') * z).
[para(3857(a,1),88(a,1,2)),rewrite([1055(3),4085(7)]),flip(a)].
4391 x *
L(y' * z,y,x) = (x / y) * z.
[para(35(a,1),3312(a,1,2)),flip(a)].
4518 C'
* L(x,C,y) = L(C' * x,C,y).
[para(3890(a,2),3312(a,2,2)),rewrite([1225(5)]),flip(a)].
4542 A'
* ((A * C') * (C * (A * x))) = A * L(x,C,A). [para(4259(a,1),3312(a,2,2)),rewrite([1366(7),69(11),4323(12),316(7),1351(6)])].
4545 (C'
* x) * y = (x * C') * y.
[back_rewrite(1105),rewrite([4391(6),109(2)])].
4584 (C'
* x) * (y * C) = (x * C') * (C * y).
[para(4545(a,1),785(a,1)),flip(a)].
4867 (C'
* x) * (y * C) = C' * ((x * C) * y).
[para(64(a,1),41(a,1,2,2)),rewrite([1122(5)]),flip(a)].
4900 (C
* x) * (y * C') = C * ((C' * x) * y).
[para(1345(a,1),41(a,1,2,2)),rewrite([109(3)]),flip(a)].
5005 (x
* C') * (C * y) = C' * ((x * C) * y).
[back_rewrite(4584),rewrite([4867(6)]),flip(a)].
5006 A *
L(x,C,A) = L(A * x,C,A).
[back_rewrite(4542),rewrite([5005(11),3812(12)]),flip(a)].
5010 L(A
* x,C,A) / L(x,C,A) = A.
[para(5006(a,1),6(a,1,1))].
5015
L(x,C,A) / L(A * x,C,A) = A'.
[para(5006(a,1),33(a,1,2))].
5017 L(A
* x,C,A) * A = A * (L(x,C,A) * A).
[para(5006(a,1),50(a,1,1))].
5030 A *
L(x,A,C') = L(A * x,C,A).
[para(3890(a,1),5006(a,1,2))].
5070 A *
(L(x,C,A) * A) = A * (L(x,A,C') * A).
[para(5030(a,1),50(a,1,1)),rewrite([5017(7)])].
5085 L(A
* x,C,A) * A = A * (L(x,A,C') * A).
[back_rewrite(5017),rewrite([5070(14)])].
5822
L(x,C,A) * A = L(x,A,C') * A.
[para(5010(a,1),1044(a,2,2)),rewrite([5015(9),5015(16),316(10),5085(9),10(11)]),flip(a)].
5839 (x
* (L(y,A,C') * A)) / L(A,L(y,C,A),x) = x * L(y,C,A). [para(5822(a,1),120(a,1,1,2))].
5854 (x
/ (y * z)) * y = y' * ((y * x) / z).
[para(2182(a,1),10(a,1,2)),flip(a)].
5988
L(A,x * A',y) = L(A,x,y).
[back_rewrite(3752),rewrite([5854(6),316(6),3598(7)]),flip(a)].
6039
L(A,x * A,y) = L(A,x,y).
[para(7(a,1),5988(a,1,2)),rewrite([316(6)]),flip(a)].
6087
L(A,L(x,C,A),y) = L(A,L(x,A,C'),y).
[para(5822(a,1),6039(a,1,2)),rewrite([6039(8)]),flip(a)].
6095 x *
L(y,C,A) = x * L(y,A,C').
[back_rewrite(5839),rewrite([6087(12),120(14)]),flip(a)].
6143 (x
* L(y,A,C')) * L(z,L(y,C,A),x) = x * (L(y,C,A) * z). [para(6095(a,1),88(a,1,1))].
6173
L(x,L(y,C,A),z) = L(x,L(y,A,C'),z).
[para(6095(a,1),3855(a,1,3)),rewrite([3855(7)]),flip(a)].
6188 x *
(L(y,C,A) * z) = x * (L(y,A,C') * z).
[back_rewrite(6143),rewrite([6173(9),88(11)]),flip(a)].
6633 C *
L(x,C,y) = L(C * x,y,C').
[para(10(a,1),3530(a,1,2,1))].
6898 C'
* ((A * C) * x) = L(A * x,C,A).
[para(3811(a,2),6095(a,1)),rewrite([5030(13)])].
7173 (A
* x) * x' = A.
[para(35(a,1),321(a,1,2,1)),rewrite([8(5),3(3)]),flip(a)].
7423
L(x,y',A * y) = L(x,y',A).
[para(7173(a,1),3403(a,1,3)),flip(a)].
10546
L(C * x,y,C') * (z * C') = C * (L(C' * x,C,y) * z). [para(6633(a,1),4900(a,1,1)),rewrite([4518(15)])].
12012
L(x,C,A) * y = L(x,A,C') * y.
[para(6188(a,1),2(a,1)),rewrite([2(7)]),flip(a)].
12931 x
* ((C / x) * (y * L(z * C,C',x))) = (x * ((C / x) * (y * C))) * z.
[para(65(a,1),48(a,1,1,2,2,2)),rewrite([4218(7),3784(15),4218(18)
]),flip(a)].
13165 (x
* ((C / x) * (y * C))) * (z * C') = x * ((C / x) * (y * L(z,C',x))). [para(4545(a,2),12931(a,1,2,2,2,1)),rewrite([16(7,R),35(7)]),f
lip(a)].
13196
L(x * L(y,C',A),C,A) = L(x,A,C') * y.
[para(13165(a,2),6898(a,1,2)),rewrite([33(10),4061(11),315(6),3772(11),16(6,R),4149(11),10546(14
),64(8),12012(7),10(10),33(11),7423(14),35(15)]),flip(a)].
13210 L(L(x,A,C')
* y,A,C) = x * L(y,C',A).
[para(13196(a,1),3467(a,1,1))].
13235
L(x,A,C) * L(y,C',A) = L(x * y,A,C).
[para(3885(a,1),13210(a,1,1,1)),flip(a)].
13236
$F. [resolve(13235,a,3931,a)].
==============================
end of proof ==========================
% Proof
1 at 0.21 (+ 0.00) seconds.
% Length
of proof is 189.
% Level
of proof is 29.
%
Maximum clause weight is 28.000.
% Given
clauses 148.
1 L(x *
y,C,A) = L(x,C,A) * L(y,C,A) # 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(c1
* c2,C,A) != L(c1,C,A) * L(c2,C,A).
[deny(1)].
20
L(c1,C,A) * L(c2,C,A) != L(c1 * c2,C,A).
[copy(19),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)])].
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))].
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)])].
50 (A *
x) * A = A * (x * A).
[para(2(a,1),15(a,1,2)),rewrite([3(7)])].
51 (A *
((x * y) * A)) / (y * A) = A * x.
[para(15(a,1),6(a,1,1))].
54 A *
((A' * x) * A) = x * A.
[para(9(a,1),15(a,1,1)),rewrite([2(4)]),flip(a)].
63 C *
(x / C) = x.
[para(16(a,2),7(a,1))].
64 C' *
(x * C) = x.
[para(16(a,1),10(a,1,2))].
65 x' *
(C * x) = C.
[para(16(a,2),10(a,1,2))].
67 C *
(x * x) = x * (x * C).
[para(16(a,2),12(a,1))].
69 (x *
(x * C)) * y = x * (C * (x * y)).
[para(16(a,1),13(a,1,1,2))].
71 (C *
(C * x)) * y = C * (x * (C * y)).
[para(16(a,2),13(a,1,1,2))].
87
L(x',x,y) = (y * x)' * y.
[para(9(a,1),18(a,1,2,2)),rewrite([3(4)]),flip(a)].
88 (x *
y) * L(z,y,x) = x * (y * z).
[para(18(a,1),10(a,1,2)),rewrite([31(3)])].
89 x' *
(y' * ((y * x) * z)) = L(z,y * x,y').
[para(10(a,1),18(a,1,1,1))].
107 x /
C = C' * x.
[para(63(a,1),10(a,1,2)),flip(a)].
110 (x *
C)' * (x * y) = L(C' * y,C,x).
[para(63(a,1),18(a,1,2,2)),rewrite([107(7)])].
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)].
117 C /
(C * x) = x'.
[para(16(a,2),33(a,1,2))].
118 (x *
(y * z)) / L(z,y,x) = x * y.
[para(18(a,1),33(a,1,2)),rewrite([31(7)])].
124 x *
(C * x') = C.
[para(16(a,2),35(a,1,2))].
132 (x *
C')' * (x * y) = L(y * C,C',x).
[para(64(a,1),18(a,1,2,2))].
168
L(A,x,A) = A.
[para(50(a,1),10(a,1,2)),rewrite([18(8)])].
174 A /
(A * (x * A)) = (A * x)'.
[para(50(a,1),33(a,1,2))].
233 (x *
A') * A = x.
[para(13(a,1),54(a,1,2)),rewrite([8(7),3(5),35(5)]),flip(a)].
235 x /
A = x * A'.
[para(233(a,1),6(a,1,1))].
236 x /
A' = x * A.
[para(7(a,1),233(a,1,1)),flip(a)].
243 (x *
(y * A'))' * (x * y) = L(A,y * A',x).
[para(233(a,1),18(a,1,2,2))].
245 (x *
A) * A' = x.
[para(235(a,1),6(a,1))].
249 (x *
A)' = A' / x.
[para(236(a,1),112(a,1,1))].
264 (A *
C)' = C' * A'. [para(16(a,1),249(a,1,1)),rewrite([107(8)])].
274 (C'
* A') * (A * (C * x)) = L(x,C,A).
[para(264(a,1),18(a,1,1))].
277
L(x',x,y) / y = (y * x)'.
[para(87(a,2),6(a,1,1))].
291 (C *
x)' * x = L(C',C,x).
[para(16(a,2),87(a,2,1,1)),flip(a)].
295 x /
L(y',y,x) = x * y.
[para(87(a,2),33(a,1,2)),rewrite([31(6)])].
345 A /
(A * (A * C)) = C' * A'.
[para(16(a,1),174(a,1,2,2)),rewrite([264(11)])].
361 x *
((C * x)' * (x * y)) = (x * L(C',C,x)) * y. [para(291(a,1),13(a,1,1,2)),flip(a)].
363 (x *
C)' * x = L(C',C,x).
[para(16(a,1),291(a,1,1,1))].
374 (x *
L(C',C,x)) * y = x * L(C' * y,C,x).
[para(363(a,1),13(a,1,1,2)),rewrite([110(11)])].
376
L(C',C,x)' * L(C' * y,C,x) = L(y,x,(x * C)'). [para(363(a,1),18(a,1,1,1)),rewrite([110(10)])].
379 x *
((C * x)' * (x * y)) = x * L(C' * y,C,x).
[back_rewrite(361),rewrite([374(12)])].
396 x *
(C * y) = x * (y * C).
[para(16(a,1),88(a,2,2)),rewrite([88(5)])].
399 (x *
(y * z))' * (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(88(a,1),18(a,1,2,2))].
403 C *
L(x,C * y,y') = y' * ((C * y) * x).
[para(65(a,1),88(a,1,1))].
404 C *
L(x,C * y',y) = y * ((C * y') * x).
[para(124(a,1),88(a,1,1))].
415
L(x',x,y) * L(z,y,(y * x)') = (y * x)' * (y * z). [para(87(a,2),88(a,1,1))].
422
L(L(x,y,z),z * y,y) = x.
[back_rewrite(43),rewrite([399(7)])].
452
L(L(x,y,z / y),z,y) = x.
[para(7(a,1),422(a,1,2))].
465
L(A,A * x,x) = A.
[para(168(a,1),422(a,1,1))].
480 L(x'
* (x / y),x,y) = y'.
[para(87(a,1),452(a,1,1)),rewrite([7(2)])].
484
L(x,y * z,z) = L(x,y,z / y).
[para(452(a,1),422(a,1,1))].
485
L(x,y / z,z / (y / z)) = L(x,y,z).
[para(452(a,1),452(a,1,1)),flip(a)].
503 (x *
y) * x' = x * (y / x).
[para(480(a,1),88(a,1,2)),rewrite([35(7)])].
507 (x /
y) * (y / (x / y)) = x * (y / x).
[para(7(a,1),503(a,1,1)),rewrite([112(2)]),flip(a)].
516 (C *
x) * x' = x * (C / x).
[para(16(a,2),503(a,1,1))].
520 (x'
* y) * x = x' * (y / x').
[para(31(a,1),503(a,1,2))].
521 x' /
(x * (y / x)) = (x * y)'.
[para(503(a,1),33(a,1,2))].
548 (x *
(y / x)) * L(z,x',x * y) = (x * y) * (x' * z). [para(503(a,1),88(a,1,1))].
563 (x *
(C / x)) * L(y,x',C * x) = (C * x) * (x' * y). [para(516(a,1),88(a,1,1))].
566 (x *
(y * x))' = x' / (x * y).
[para(6(a,1),521(a,1,2,2)),flip(a)].
569 (C *
x)' = C' / x.
[para(16(a,1),521(a,1,2)),rewrite([107(4),16(7,R),35(7)]),flip(a)].
570 (x *
C)' = C' / x.
[para(16(a,1),521(a,2,1)),rewrite([107(5),35(7)]),flip(a)].
610 x *
L(C' * y,C,x) = (x * C') * y.
[back_rewrite(379),rewrite([569(3),41(6)]),flip(a)].
627
L(C',C,x) = C'. [back_rewrite(291),rewrite([569(3),7(4)]),flip(a)].
642
L(x,y,C' / y) = C * L(C' * x,C,y).
[back_rewrite(376),rewrite([627(4),31(3),570(10)]),flip(a)].
668 x /
C' = x * C.
[para(627(a,1),295(a,1,2))].
669 C *
(x * C') = x.
[para(668(a,1),6(a,1)),rewrite([16(5,R)])].
673 C' *
x = x * C'.
[para(669(a,1),10(a,1,2))].
682 (x *
C')' = C / x.
[para(669(a,1),117(a,1,2)),flip(a)].
706 A /
(A * (A * C)) = A' * C'.
[back_rewrite(345),rewrite([673(12)])].
713 (A'
* C') * (A * (C * x)) = L(x,C,A).
[back_rewrite(274),rewrite([673(5)])].
719 (C /
x) * (x * y) = L(y * C,C',x).
[back_rewrite(132),rewrite([682(4)])].
765 (x'
/ (x * y)) * (x * ((y * x) * z)) = L(z,y * x,x). [para(566(a,1),18(a,1,1))].
907 (x'
* (y / x')) * L(z,x,x' * y) = (x' * y) * (x * z). [para(520(a,1),88(a,1,1))].
917 x *
((y / (x * z)) * x) = (x * y) / z.
[para(7(a,1),40(a,1,1,2)),flip(a)].
918 x *
((x * y)' * x) = x / y.
[para(8(a,1),40(a,1,1,2)),rewrite([3(2)]),flip(a)].
929 (x *
L(y,z,x)) / (z * y) = x / z.
[para(18(a,1),40(a,1,1,2)),rewrite([918(8)])].
946 x *
L(y',y,x) = x / y.
[para(87(a,2),40(a,2,2)),rewrite([40(6),918(4)]),flip(a)].
962
L(x',x,y) = y' * (y / x).
[para(946(a,1),10(a,1,2)),flip(a)].
1004 x'
/ (x * y) = x' * (y' * x').
[para(10(a,1),918(a,1,2,1,1)),flip(a)].
1081
L(x,y * z,y') = L(x,y * z,z).
[back_rewrite(765),rewrite([1004(3),13(9),10(7),89(6)])].
1129
L(x',x,y) * L(z,y / x,y') = y' * ((y / x) * z). [para(962(a,2),88(a,1,1))].
1179 (x
/ y) * (y * z) = x * L(z,y,x).
[para(929(a,1),7(a,1,1))].
1197 (A
* A) / (x * A) = A / x. [para(168(a,1),929(a,1,1,2))].
1220 (A
* A) / x = A / (x * A').
[para(7(a,1),1197(a,1,2)),rewrite([235(7)])].
1233
L(x,y,z / y) = L(x,y,z).
[para(7(a,1),1081(a,1,2)),rewrite([112(2),7(4)])].
1234
L(x,y,z * y) = L(x,y,z).
[para(10(a,1),1081(a,1,2)),rewrite([31(2),10(4)]),flip(a)].
1238
L(x,C * y,y) = L(x,y * C,C').
[para(16(a,1),1081(a,1,2)),flip(a)].
1240
L(x,C * y,y') = L(x,y * C,C).
[para(16(a,2),1081(a,1,2))].
1245
L(x,C,C * y) = L(x,C,y).
[para(65(a,1),1081(a,1,2)),rewrite([31(3),65(6)]),flip(a)].
1247
L(x,y' * C,C) = L(x,C * y',y).
[para(111(a,1),1081(a,1,2)),rewrite([31(5)]),flip(a)].
1282
L(x,y / z,L(z',z,y)) = L(x,y / z,y').
[para(946(a,1),1081(a,1,2)),rewrite([946(6)]),flip(a)].
1287 C *
L(C' * x,C,y) = L(x,y,C').
[back_rewrite(642),rewrite([1233(4)]),flip(a)].
1288
L(x,y / z,z) = L(x,y,z).
[back_rewrite(485),rewrite([1233(4)])].
1289
L(x,y * z,z) = L(x,y,z).
[back_rewrite(484),rewrite([1233(4)])].
1290
L(L(x,y,z),z,y) = x.
[back_rewrite(452),rewrite([1233(2)])].
1324
L(x,C * y',y) = L(x,y',C).
[back_rewrite(1247),rewrite([1289(5)]),flip(a)].
1327
L(x,C * y,y') = L(x,y,C).
[back_rewrite(1240),rewrite([1289(8)])].
1328
L(x,y * C,C') = L(x,C,y).
[back_rewrite(1238),rewrite([1289(3)]),flip(a)].
1330
L(x,y * z,y') = L(x,y,z).
[back_rewrite(1081),rewrite([1289(5)])].
1337
L(A,A,x) = A.
[back_rewrite(465),rewrite([1289(4)])].
1351 x *
((C * x') * y) = C * L(y,x',C).
[back_rewrite(404),rewrite([1324(5)]),flip(a)].
1359 x'
* ((C * x) * y) = C * L(y,x,C).
[back_rewrite(403),rewrite([1327(5)]),flip(a)].
1376 x'
* (y' * ((y * x) * z)) = L(z,y,x).
[back_rewrite(89),rewrite([1330(9)])].
1382 (x
* A) * A = x * (A * A).
[para(1337(a,1),88(a,1,2))].
1386
L(x,A,y * A') = L(x,A,y).
[para(235(a,1),1233(a,1,3))].
1389
L(x,y,L(z',z,y)) = L(x,y,(y * z)').
[para(277(a,1),1233(a,1,3)),flip(a)].
1437
L(x,y',y * z) = L(x,z,y).
[para(33(a,1),1288(a,1,2)),rewrite([1234(5)])].
1439
L(x,y',C * y) = L(x,C,y).
[para(117(a,1),1288(a,1,2)),rewrite([1245(8)])].
1447 (x
* (y / x)) * L(z,y,x) = x * ((y / x) * z). [para(1288(a,1),88(a,1,2))].
1448
L(x,C,y) = L(x,y,C').
[para(668(a,1),1288(a,1,2)),rewrite([1328(5)])].
1457 (x
* y) * (x' * z) = x * ((y / x) * z).
[back_rewrite(548),rewrite([1437(5),1447(4)]),flip(a)].
1458 (C
* x) * (x' * y) = x * ((C / x) * y).
[back_rewrite(563),rewrite([1439(7),1447(6)]),flip(a)].
1495
L(c1,A,C') * L(c2,C,A) != L(c1 * c2,C,A).
[para(1448(a,1),20(a,1,1))].
1515
L(x,y,y' * z) = L(x,z,y').
[para(35(a,1),1289(a,1,2)),rewrite([1234(3)]),flip(a)].
1518
L(x,y / z,y') = L(x,y,(y * z)').
[para(946(a,1),1289(a,1,2)),rewrite([1282(4),1389(6)])].
1524 (x'
* y) * (x * z) = x' * ((y / x') * z).
[back_rewrite(907),rewrite([1515(7),1447(7)]),flip(a)].
1526 (x
* y)' * (x * z) = x' * ((x / y) * z).
[back_rewrite(1129),rewrite([1518(5),415(6)])].
1530 A'
* ((A * C') * (C * x)) = L(x,C,A).
[back_rewrite(713),rewrite([1524(10),236(7),673(6)])].
1554 x'
* ((x / (y * A')) * y) = L(A,y * A',x).
[back_rewrite(243),rewrite([1526(7)])].
1583
L(x,y * (A * A),A) = L(x,y,A).
[para(1382(a,1),1289(a,1,2)),rewrite([1289(10)])].
1600
L(x,C',A') = L(x,A,C').
[para(673(a,1),1386(a,1,3)),rewrite([1515(7)])].
1682
L(x,A * (A * C),A) = L(x,C,A).
[para(16(a,1),1583(a,1,2)),rewrite([16(5,R),67(5)])].
1722 C *
L(x,y,C) = L(x * C,C',y). [para(1179(a,2),16(a,1)),rewrite([719(4),16(9,R)]),flip(a)].
1728 x *
L(y' * z,y,x) = (x / y) * z.
[para(35(a,1),1179(a,1,2)),flip(a)].
1806 A *
L(x,C,A) = L(A * x,C,A).
[para(1682(a,1),1179(a,2,2)),rewrite([706(7),69(11),1524(12),236(7),673(6),1530(12)]),flip(a)].
1809 x'
* ((C * x) * y) = L(y * C,C',x).
[back_rewrite(1359),rewrite([1722(9)])].
1810 x *
((C * x') * y) = L(y * C,C',x'). [back_rewrite(1351),rewrite([1722(10)])].
1811 (C'
* x) * y = (x * C') * y.
[back_rewrite(610),rewrite([1728(6),107(2)])].
1815 L(A
* x,C,A) / L(x,C,A) = A.
[para(1806(a,1),6(a,1,1))].
1821
L(x,C,A) / L(A * x,C,A) = A'.
[para(1806(a,1),33(a,1,2))].
1822 L(A
* x,C,A) * A = A * (L(x,C,A) * A).
[para(1806(a,1),50(a,1,1))].
1840 (A
* C') * (C * x) = L(A * x,C,A).
[para(1806(a,1),1179(a,2)),rewrite([107(3),673(4)])].
1864 (C'
* x) * (y * C) = (x * C') * (C * y).
[para(1811(a,1),396(a,1)),flip(a)].
1901 L(A
* x,C,A) / L(x,A,C') = A.
[para(1448(a,1),1815(a,1,2))].
1932
L(x,A,C') / L(A * x,C,A) = A'.
[para(1448(a,1),1821(a,1,1))].
1965 (C'
* x) * (y * C) = C' * ((x * C) * y).
[para(64(a,1),41(a,1,2,2)),rewrite([668(5)]),flip(a)].
2060 (x
* C') * (C * y) = C' * ((x * C) * y).
[back_rewrite(1864),rewrite([1965(6)]),flip(a)].
2062 C'
* ((A * C) * x) = L(A * x,C,A).
[back_rewrite(1840),rewrite([2060(7)])].
2067 A /
x = A * x'.
[para(8(a,1),51(a,1,1,2,1)),rewrite([2(4),1220(6),245(6)])].
2134 (A
* x') * x = A.
[para(2067(a,1),7(a,1,1))].
2152 (A
* x) * x' = A.
[para(31(a,1),2134(a,1,1,2))].
2180
L(x,y',A * y) = L(x,y',A).
[para(2152(a,1),1234(a,1,3)),flip(a)].
2284
L(x,C,A) * A = L(x,A,C') * A.
[para(1901(a,1),507(a,2,2)),rewrite([1932(10),1932(17),236(10),1822(9),10(10)])].
2297 (x
* (L(y,A,C') * A)) / L(A,L(y,C,A),x) = x * L(y,C,A). [para(2284(a,1),118(a,1,1,2))].
2316 (x
/ (y * z)) * y = y' * ((y * x) / z).
[para(917(a,1),10(a,1,2)),flip(a)].
2387
L(A,x * A',y) = L(A,x,y).
[back_rewrite(1554),rewrite([2316(6),236(6),1376(7)]),flip(a)].
2406
L(A,x * A,y) = L(A,x,y).
[para(7(a,1),2387(a,1,2)),rewrite([236(6)]),flip(a)].
2440
L(A,L(x,C,A),y) = L(A,L(x,A,C'),y).
[para(2284(a,1),2406(a,1,2)),rewrite([2406(8)]),flip(a)].
2442 x *
L(y,C,A) = x * L(y,A,C'). [back_rewrite(2297),rewrite([2440(12),118(14)]),flip(a)].
2465
L(c1,A,C') * L(c2,A,C') != L(c1 * c2,C,A). [back_rewrite(1495),rewrite([2442(10)])].
2476 (x
* L(y,A,C')) * L(z,L(y,C,A),x) = x * (L(y,C,A) * z). [para(2442(a,1),88(a,1,1))].
2489
L(x,L(y,C,A),z) = L(x,L(y,A,C'),z).
[para(2442(a,1),1437(a,1,3)),rewrite([1437(7)]),flip(a)].
2498 x *
(L(y,C,A) * z) = x * (L(y,A,C') * z).
[back_rewrite(2476),rewrite([2489(9),88(11)]),flip(a)].
2527 C *
L(x,C,y) = L(C * x,y,C').
[para(10(a,1),1287(a,1,2,1))].
2576 C *
L(x,y,C') = L(C * x,y,C').
[para(1448(a,1),2527(a,1,2))].
2581 L(C
* (C * x),y,C') * z = C * (L(x,C,y) * (C * z)). [para(2527(a,1),71(a,1,1,2)),rewrite([2576(7)])].
3147 L(C
* (x * C),y,C') * z = C * (L(x,C,y) * (C * z)). [para(16(a,1),2581(a,1,1,1,2))].
3210 x *
((C / x) * (y * L(z * C,C',x))) = (x * ((C / x) * (y * C))) * z.
[para(65(a,1),48(a,1,1,2,2,2)),rewrite([1458(7),1809(15),1458(18)]
),flip(a)].
3399 (x
* ((C / x) * (y * C))) * (z * C') = x * ((C / x) * (y * L(z,C',x))). [para(1811(a,2),3210(a,1,2,2,2,1)),rewrite([16(7,R),35(7)]),fli
p(a)].
3530 L(x
* L(y,C',A),C,A) = L(x,A,C') * y.
[para(3399(a,2),2062(a,1,2)),rewrite([33(10),1457(11),235(6),1810(11),16(6,R),1600(11),3147(14),6
69(11),2498(8),10(10),33(11),2180(14),35(15)]),flip(a)].
3589
L(x,A,C') * L(y,A,C') = L(x * y,C,A).
[para(1290(a,1),3530(a,1,1,2)),flip(a)].
3590
$F. [resolve(3589,a,2465,a)].
==============================
end of proof ==========================