% Length of proof is 863.

% Level of proof is 62.

% Maximum clause weight is 27.

% Given clauses 653.

1 x * A = A * x # label(non_clause) # label(goal). [goal].

2 1 * x = x. [assumption].

3 x * 1 = x. [assumption].

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

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

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

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

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

9 (x * y) * (y * z) = y * ((y * x) * z). [copy(8),flip(a)].

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

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

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

13 B * (B * (B * B)) = A. [assumption].

14 A * c1 != c1 * A. [deny(1)].

15 1 \ x = x. [para(4(a,1),2(a,1)),flip(a)].

16 x \ x = 1. [para(3(a,1),5(a,1,2))].

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

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

19 x / (y \ x) = y. [para(4(a,1),6(a,1,1))].

20 (x / y) \ x = y. [para(7(a,1),5(a,1,2))].

22 x * ((x * y) * (x \ z)) = (y * x) * z. [para(4(a,1),9(a,1,2)),flip(a)].

23 (x * y) \ (y * ((y * x) * z)) = y * z. [para(9(a,1),5(a,1,2))].

25 x * ((x * (y / x)) * z) = y * (x * z). [para(7(a,1),9(a,1,1)),flip(a)].

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

30 (x * y) \ (y * (y * x)) = y. [para(10(a,1),5(a,1,2))].

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

32 x * (x * (y / x)) = y * x. [para(7(a,1),10(a,1,1)),flip(a)].

36 (x * (x * y)) * x = x * (x * (y * x)). [para(10(a,1),10(a,1,1))].

37 (x / y) * (y * z) = y * ((y \ x) * z). [para(4(a,1),12(a,1,1,1))].

38 ((x * y) / x) * z = x * (y * (x \ z)). [para(4(a,1),12(a,1,2))].

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

48 B * (B * B) = B \ A. [para(13(a,1),5(a,1,2)),flip(a)].

49 (B \ A) * B = A. [para(13(a,1),10(a,2)),rewrite([10(5),48(5)])].

51 B \ A = A / B. [para(49(a,1),6(a,1,1)),flip(a)].

52 B * (B * B) = A / B. [back_rewrite(48),rewrite([51(8)])].

53 B * (A / B) = A. [para(51(a,1),4(a,1,2))].

56 B * ((B * x) * (A / B)) = (x * B) * A. [para(53(a,1),9(a,1,2)),flip(a)].

57 A * (B * x) = B * (A * x). [para(53(a,1),9(a,2,2,1)),rewrite([7(5)])].

58 (A / B) * A = A * (A / B). [para(53(a,1),10(a,1,1)),rewrite([7(13)]),flip(a)].

59 A * B = B * A. [para(53(a,1),10(a,2,2)),rewrite([7(5)])].

60 A \ (B * A) = B. [para(59(a,1),5(a,1,2))].

71 (B * A) \ (B * (B * A)) = B. [para(59(a,1),30(a,1,1))].

73 (x * y) / x = (x \ y) * x. [para(4(a,1),31(a,1,1,2))].

84 (x * (y * z)) / (x * z) = (x \ y) * x. [back_rewrite(40),rewrite([73(6)])].

86 ((x \ y) * x) * z = x * (y * (x \ z)). [back_rewrite(38),rewrite([73(2)])].

88 x \ (y * x) = x * (y / x). [para(32(a,1),5(a,1,2))].

89 (x * y) / (y * (x / y)) = y. [para(32(a,1),6(a,1,1))].

91 x * ((x * y) * (x * (z / x))) = (y * x) * (z * x). [para(32(a,1),9(a,1,2)),flip(a)].

94 (B * A) * (B / (B * A)) = B. [back_rewrite(71),rewrite([88(9)])].

95 A * (B / A) = B. [back_rewrite(60),rewrite([88(5)])].

96 A \ B = B / A. [para(95(a,1),5(a,1,2))].

97 B / (B / A) = A. [para(95(a,1),6(a,1,1))].

100 (B / A) * B = B * (B / A). [para(95(a,1),10(a,1,1)),rewrite([7(13)]),flip(a)].

101 B * (A * (B \ x)) = A * x. [para(4(a,1),57(a,1,2)),flip(a)].

110 (A \ (A / B)) * A = A / B. [para(58(a,1),6(a,1,1)),rewrite([73(7)])].

116 (x \ 1) * x = 1. [para(3(a,1),73(a,1,1)),rewrite([17(1)]),flip(a)].

117 (x \ (x \ y)) * x = y / x. [para(4(a,1),73(a,1,1)),flip(a)].

118 ((x / y) \ y) * (x / y) = x / (x / y). [para(7(a,1),73(a,1,1)),flip(a)].

122 x * (x * ((x \ y) * x)) = (x * y) * x. [para(73(a,1),32(a,1,2,2))].

125 (x \ 1) \ 1 = x. [para(116(a,1),5(a,1,2))].

126 x \ 1 = 1 / x. [para(116(a,1),6(a,1,1)),flip(a)].

127 x * (1 / x) = 1. [para(20(a,1),116(a,1,1))].

128 1 / (1 / x) = x. [back_rewrite(125),rewrite([126(2),126(4)])].

130 B * (A * (1 / B)) = A. [para(127(a,1),57(a,1,2)),rewrite([3(3)]),flip(a)].

131 (x \ (1 / x)) * x = 1 / x. [para(127(a,1),73(a,1,1)),flip(a)].

132 A * (1 / B) = A / B. [para(130(a,1),5(a,1,2)),rewrite([51(3)]),flip(a)].

133 A \ (A / B) = 1 / B. [para(132(a,1),5(a,1,2))].

140 (1 / B) * A = A / B. [back_rewrite(110),rewrite([133(5)])].

144 (A / B) / A = 1 / B. [para(140(a,1),6(a,1,1))].

149 (x \ y) * (x / (x \ y)) = (x \ y) \ y. [para(4(a,1),88(a,1,2)),flip(a)].

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

152 (A / B) * (B / (A / B)) = B. [para(53(a,1),88(a,1,2)),rewrite([20(5)]),flip(a)].

153 (x * x) * (x / (x * x)) = x. [para(88(a,1),30(a,1))].

157 (1 / x) * (x / (1 / x)) = x. [para(127(a,1),88(a,1,2)),rewrite([126(4),128(4)]),flip(a)].

163 (B \ (B / A)) * B = B / A. [para(97(a,1),89(a,1,2,2)),rewrite([7(10),73(7)])].

165 ((x * y) * x) / (x * ((x \ y) * x)) = x. [para(73(a,1),89(a,1,2,2))].

167 (B * A) \ B = B / (B * A). [para(94(a,1),5(a,1,2))].

177 (B * (B / A)) * (B / (B * (B / A))) = B. [para(100(a,1),30(a,1,1)),rewrite([88(13)])].

180 B \ (A * x) = A * (B \ x). [para(101(a,1),5(a,1,2))].

191 x \ (x \ y) = (y / x) / x. [para(117(a,1),6(a,1,1)),flip(a)].

196 x \ (1 / x) = (1 / x) / x. [para(131(a,1),6(a,1,1)),flip(a)].

198 (x \ y) / ((y / x) / x) = x. [para(150(a,1),6(a,1,1))].

203 (A / B) \ B = B / (A / B). [para(152(a,1),5(a,1,2))].

204 B / (B / (A / B)) = A / B. [para(152(a,1),6(a,1,1))].

210 (x * x) \ x = x / (x * x). [para(153(a,1),5(a,1,2))].

219 x / (x / (1 / x)) = 1 / x. [para(157(a,1),6(a,1,1))].

226 B \ (B / A) = (B / A) / B. [para(163(a,1),6(a,1,1)),flip(a)].

229 (B / A) / ((B / A) / B) = B. [para(163(a,1),89(a,1,1)),rewrite([226(9),150(12),226(8)])].

230 A * (B \ (A \ x)) = B \ x. [para(4(a,1),180(a,1,2)),flip(a)].

232 A * ((B / A) / B) = 1. [para(95(a,1),180(a,1,2)),rewrite([16(3),226(7)]),flip(a)].

236 (B / A) / B = 1 / A. [para(232(a,1),5(a,1,2)),rewrite([126(3)]),flip(a)].

237 (B / A) / (1 / A) = B. [back_rewrite(229),rewrite([236(8)])].

240 B \ (B / A) = 1 / A. [back_rewrite(226),rewrite([236(10)])].

242 (1 / A) * B = B / A. [para(236(a,1),7(a,1,1))].

243 (1 / A) \ (B / A) = B. [para(236(a,1),20(a,1,1))].

244 B * ((1 / A) / B) = 1 / A. [para(236(a,1),150(a,1,2,1)),rewrite([240(12)])].

250 B \ (A / B) = (A / B) / B. [para(51(a,1),191(a,1,2))].

253 A \ (1 / B) = (1 / B) / A. [para(133(a,1),191(a,1,2)),rewrite([144(10)])].

256 B \ (1 / A) = (1 / A) / B. [para(236(a,1),191(a,2,1)),rewrite([240(6)])].

257 (1 / A) \ B = B / (1 / A). [para(237(a,1),191(a,2,1)),rewrite([243(10)])].

258 x \ ((y / x) / x) = ((x \ y) / x) / x. [para(191(a,1),191(a,1,2))].

273 B / (B / (1 / A)) = 1 / A. [para(237(a,1),198(a,1,2,1)),rewrite([243(7)])].

281 (B / (A / B)) \ (A / B) = (A / B) / (B / (A / B)). [para(204(a,1),191(a,2,1)),rewrite([20(12)])].

286 (x \ (x / (1 / x))) * x = x / (1 / x). [para(219(a,1),89(a,1,2,2)),rewrite([7(10),73(5)])].

289 A \ (B \ x) = B \ (A \ x). [para(230(a,1),5(a,1,2))].

301 (1 / A) * (B * x) = B * ((1 / A) * x). [para(244(a,1),9(a,2,2,1)),rewrite([7(7)])].

318 (1 / A) / B = (1 / B) / A. [para(126(a,1),289(a,1,2)),rewrite([253(5),126(9),256(10)]),flip(a)].

331 B \ (1 / A) = (1 / B) / A. [back_rewrite(256),rewrite([318(10)])].

332 B * ((1 / B) / A) = 1 / A. [back_rewrite(244),rewrite([318(6)])].

334 ((1 / B) / A) * B = 1 / A. [para(318(a,1),7(a,1,1))].

339 x \ ((y * x) * z) = (x * y) * (x \ z). [para(22(a,1),5(a,1,2))].

361 x * ((x \ y) * (x \ z)) = (y / x) * z. [para(150(a,1),22(a,1,2,1)),rewrite([7(7)])].

375 (x * y) \ (y * z) = y * ((y * x) \ z). [para(4(a,1),23(a,1,2,2))].

381 x * (1 / (x * y)) = (y * x) \ x. [para(127(a,1),23(a,1,2,2)),rewrite([3(3)]),flip(a)].

393 ((x \ y) * x) \ x = x * (1 / y). [para(4(a,1),381(a,1,2,2)),flip(a)].

394 x \ ((y * x) \ x) = 1 / (x * y). [para(381(a,1),5(a,1,2))].

395 ((x * y) \ y) / (1 / (y * x)) = y. [para(381(a,1),6(a,1,1))].

412 (1 / (x * y)) * (x / (1 / (x * y))) = (1 / (x * y)) \ ((y * x) \ x). [para(381(a,1),88(a,1,2)),flip(a)].

417 x * (1 / (x \ y)) = (y / x) \ x. [para(150(a,1),381(a,1,2,2)),rewrite([7(7)])].

421 (x * x) * (1 / x) = x. [para(153(a,1),381(a,1,2,2)),rewrite([7(8),5(6)])].

423 (1 / x) * (1 / x) = (1 / x) / x. [para(157(a,1),381(a,1,2,2)),rewrite([7(11),196(8)])].

424 x \ (x / (1 / x)) = x. [para(157(a,1),381(a,2,1)),rewrite([7(10),7(6)]),flip(a)].

429 B / (1 / A) = B * A. [para(332(a,1),381(a,1,2,2)),rewrite([128(6),334(10),257(8)]),flip(a)].

435 x / (1 / x) = x * x. [back_rewrite(286),rewrite([424(4)]),flip(a)].

442 B / (B * A) = 1 / A. [back_rewrite(273),rewrite([429(6)])].

449 x / (x * x) = 1 / x. [back_rewrite(219),rewrite([435(3)])].

455 (B * A) \ B = 1 / A. [back_rewrite(167),rewrite([442(10)])].

459 (x * x) \ x = 1 / x. [back_rewrite(210),rewrite([449(4)])].

480 x / (x * (1 / y)) = (x \ y) * x. [para(393(a,1),19(a,1,2))].

484 B * (1 / (A / B)) = B / (A / B). [para(250(a,1),393(a,1,1,1)),rewrite([7(7),203(5)]),flip(a)].

488 1 / (x * (y / x)) = x \ (y \ x). [para(7(a,1),394(a,1,2,1)),flip(a)].

492 (1 / B) / A = 1 / (B * A). [para(59(a,1),394(a,1,2,1)),rewrite([455(6),331(5)])].

497 1 / (A / B) = B / A. [para(132(a,1),394(a,2,2)),rewrite([140(6),20(6),96(3)]),flip(a)].

498 B \ ((B * (B / A)) \ B) = 1 / (B * (B / A)). [para(100(a,1),394(a,1,2,1))].

501 x \ ((y / x) \ x) = 1 / (x \ y). [para(150(a,1),394(a,2,2)),rewrite([7(3)])].

524 B \ (1 / A) = 1 / (B * A). [back_rewrite(331),rewrite([492(10)])].

538 B / (A / B) = B * (B / A). [back_rewrite(484),rewrite([497(6)]),flip(a)].

545 (B * (B / A)) \ (A / B) = (A / B) / (B * (B / A)). [back_rewrite(281),rewrite([538(5),538(17)])].

550 B / (B * (B / A)) = A / B. [back_rewrite(204),rewrite([538(6)])].

551 (A / B) \ B = B * (B / A). [back_rewrite(203),rewrite([538(10)])].

554 (B * (B / A)) * (A / B) = B. [back_rewrite(177),rewrite([550(12)])].

572 (B * (B / A)) \ B = A / B. [para(538(a,1),20(a,1,1))].

574 1 / (B * (B / A)) = (A / B) / B. [back_rewrite(498),rewrite([572(8),250(5)]),flip(a)].

577 (B * (B / A)) * A = B * B. [para(554(a,1),9(a,2,2)),rewrite([100(5),53(10)])].

578 (B * (B / A)) \ (B * B) = A. [para(577(a,1),5(a,1,2))].

579 (B * B) / A = B * (B / A). [para(577(a,1),6(a,1,1))].

583 (B * B) * A = B * (B * A). [para(577(a,1),10(a,1,1)),rewrite([57(13),95(12),57(10),59(9)])].

591 A \ ((B * B) \ A) = 1 / (B * B). [para(577(a,1),394(a,1,2,1)),rewrite([57(15),95(14)])].

595 A \ (B * (B * A)) = B * B. [para(579(a,1),88(a,2,2)),rewrite([583(6),57(14),95(13)])].

596 (B * (B * A)) / (B * B) = A. [para(579(a,1),89(a,1,2,2)),rewrite([583(5),57(12),95(11)])].

598 B * (B * ((B * B) \ A)) = A. [para(583(a,1),5(a,1,2)),rewrite([375(9),375(8)])].

599 (B * (B * A)) / A = B * B. [para(583(a,1),6(a,1,1))].

612 A \ (B * B) = B * (B / A). [para(595(a,1),191(a,1,2)),rewrite([599(12),579(10)])].

619 (B * B) * (A / (B * B)) = A. [para(596(a,1),150(a,1,2,1)),rewrite([375(18),375(17),598(18)])].

620 (B * B) \ A = A / (B * B). [para(596(a,1),191(a,2,1)),rewrite([375(12),375(11),598(12)])].

623 A \ (A / (B * B)) = 1 / (B * B). [back_rewrite(591),rewrite([620(6)])].

635 (B * B) * (1 / A) = B * (B / A). [para(619(a,1),381(a,1,2,2)),rewrite([7(16),612(12)])].

641 (B * B) \ (A / (B * B)) = (A / (B * B)) / (B * B). [para(620(a,1),191(a,1,2))].

642 (A / (B * B)) / ((A / (B * B)) / (B * B)) = B * B. [para(620(a,1),198(a,1,1))].

659 ((x / y) \ y) / (1 / (y \ x)) = y. [para(150(a,1),395(a,1,2,2)),rewrite([7(3)])].

665 ((1 / x) / x) / (1 / x) = 1 / x. [para(421(a,1),395(a,1,1,1)),rewrite([196(3),37(8),126(6),7(7),3(6)])].

680 (1 / (x \ y)) * ((1 / (x \ y)) * x) = ((y / x) \ x) * (1 / (x \ y)). [para(417(a,1),10(a,1,1)),flip(a)].

681 (x / (x / y)) \ (x / y) = (x / y) * (1 / y). [para(20(a,1),417(a,1,2,2)),flip(a)].

685 (x \ (1 / (x \ y))) * x = ((y / x) \ x) / x. [para(417(a,1),73(a,1,1)),flip(a)].

705 (A / B) / (B * (B / A)) = (A / B) * ((A / B) / B). [para(538(a,1),417(a,2,1)),rewrite([551(9),574(10),545(18)]),flip(a)].

721 (B * (B / A)) \ (A / B) = (A / B) * ((A / B) / B). [back_rewrite(545),rewrite([705(18)])].

737 (x \ (1 / y)) * x = x / (x * y). [para(19(a,1),480(a,1,2,2)),rewrite([126(4)]),flip(a)].

744 ((x / y) \ y) / y = y / x. [back_rewrite(685),rewrite([737(5),4(2)]),flip(a)].

747 (x \ y) / y = y / (x * y). [para(6(a,1),744(a,1,1,1))].

748 (x / y) \ y = (y / x) * y. [para(744(a,1),7(a,1,1)),flip(a)].

751 (x * (y / x)) / (y * x) = (y / x) / (x * (y / x)). [para(89(a,1),744(a,1,1,1)),rewrite([5(3)]),flip(a)].

763 (A / (B * B)) / A = A / (B * (B * A)). [para(599(a,1),744(a,1,1,1)),rewrite([620(5)])].

765 x / ((x / y) * x) = y / x. [para(744(a,1),744(a,1,1,1)),rewrite([20(2),748(3)]),flip(a)].

779 ((x / y) / x) * (x / y) = (x / y) * (1 / y). [back_rewrite(681),rewrite([748(4)])].

780 (1 / (x \ y)) * ((1 / (x \ y)) * x) = ((x / y) * x) * (1 / (x \ y)). [back_rewrite(680),rewrite([748(10)])].

783 ((x / y) * x) / (1 / (x \ y)) = x. [back_rewrite(659),rewrite([748(2)])].

784 x * ((x / y) / x) = 1 / (x \ y). [back_rewrite(501),rewrite([748(2),88(3)])].

786 x * (1 / (x \ y)) = (x / y) * x. [back_rewrite(417),rewrite([748(6)])].

789 ((x / y) * x) * (y / x) = y / (y / x). [back_rewrite(118),rewrite([748(2)])].

791 (x * y) / (x * (x * y)) = y / (x * y). [para(5(a,1),747(a,1,1)),flip(a)].

792 (x / (y * x)) * x = y \ x. [para(747(a,1),7(a,1,1))].

799 (x / y) / (y * (x / y)) = (x * y) / (y * (x * y)). [para(88(a,1),747(a,1,1)),rewrite([751(4)])].

812 ((A / (B * B)) / (B * B)) / (A / (B * B)) = A / (B * (B * A)). [para(619(a,1),747(a,2,2)),rewrite([641(9),763(22)])].

816 (x / y) * ((y / x) * y) = y. [para(748(a,1),4(a,1,2))].

817 (x / (y * x)) * (y \ x) = (x / y) / y. [para(19(a,1),748(a,1,1)),rewrite([191(2),747(4)]),flip(a)].

818 (x / (x * y)) * x = x * (1 / y). [para(73(a,1),748(a,1,1)),rewrite([393(3)]),flip(a)].

854 (x \ y) / (y / (x * y)) = (x * y) * (y / (x * y)). [para(792(a,1),73(a,1,1)),rewrite([20(7)])].

873 ((x / y) * x) \ (1 / (x \ y)) = 1 / (y / (y / x)). [para(816(a,1),394(a,1,2,1)),rewrite([88(5),784(5),789(11)])].

886 1 / (x \ (y \ x)) = x * (y / x). [para(488(a,1),20(a,1,1)),rewrite([126(4)])].

891 (x * (y / x)) \ (x \ (y \ x)) = (x \ (y \ x)) / (x * (y / x)). [para(488(a,1),191(a,2,1)),rewrite([126(6),488(6)])].

892 (x \ y) \ ((y / x) / x) = 1 / ((x \ y) \ y). [para(191(a,1),488(a,2,2)),rewrite([149(5)]),flip(a)].

900 (x \ (y \ x)) / (x * (y / x)) = (x \ (y \ x)) * (x \ (y \ x)). [para(488(a,1),423(a,1,1)),rewrite([488(6),488(9)]),flip(a)].

908 (x * (y / x)) \ (x \ (y \ x)) = (x \ (y \ x)) * (x \ (y \ x)). [back_rewrite(891),rewrite([900(10)])].

911 1 / ((A / B) / B) = B * (B / A). [para(574(a,1),20(a,1,1)),rewrite([126(7)])].

928 (B * B) * (((B * B) * x) * (1 / A)) = (x * (B * B)) * (B * (B / A)). [para(635(a,1),9(a,1,2)),flip(a)].

937 (A / B) / B = A / (B * B). [para(635(a,1),394(a,2,2)),rewrite([301(10),242(9),578(12),620(5),574(12)]),flip(a)].

955 1 / (A / (B * B)) = B * (B / A). [back_rewrite(911),rewrite([937(6)])].

960 (B * (B / A)) \ (A / B) = (A / B) * (A / (B * B)). [back_rewrite(721),rewrite([937(17)])].

966 1 / (B * (B / A)) = A / (B * B). [back_rewrite(574),rewrite([937(12)])].

977 (A / (B * B)) \ (A / B) = B. [para(937(a,1),20(a,1,1))].

981 (A / (B * B)) * (A / B) = (A / B) * (A / (B * B)). [para(937(a,1),748(a,2,1)),rewrite([538(5),960(9)]),flip(a)].

991 (x \ (1 / y)) \ (x / (x * y)) = x. [para(737(a,1),5(a,1,2))].

992 (x / (x * y)) / x = x \ (1 / y). [para(737(a,1),6(a,1,1))].

993 (x / (x * y)) * (x * z) = x * ((1 / y) * z). [para(737(a,1),9(a,1,1)),rewrite([4(8)])].

1009 x / (x * (y * (z / y))) = (x \ (y \ (z \ y))) * x. [para(488(a,1),737(a,1,1,2)),flip(a)].

1031 x \ (1 / (x \ y)) = (x / y) / x. [para(784(a,1),5(a,1,2))].

1032 (1 / (x \ y)) / ((x / y) / x) = x. [para(784(a,1),6(a,1,1))].

1033 (x * y) * (x / (x * y)) = 1 / ((x * y) \ y). [para(6(a,1),784(a,1,2,1))].

1042 1 / (x * ((x * y) \ (y / x))) = (y * x) * (x / (y * x)). [para(89(a,1),784(a,1,2,1)),rewrite([375(9)]),flip(a)].

1050 (x \ y) * ((y / (x * y)) / (x \ y)) = 1 / ((x \ y) \ y). [para(747(a,1),784(a,1,2,1))].

1052 (1 / x) / x = 1 / (x * x). [para(665(a,1),784(a,1,2)),rewrite([423(5),748(7),18(6)])].

1073 (1 / x) * (1 / x) = 1 / (x * x). [back_rewrite(423),rewrite([1052(8)])].

1075 x \ (1 / x) = 1 / (x * x). [back_rewrite(196),rewrite([1052(6)])].

1076 (1 / (x * x)) * x = 1 / x. [para(1052(a,1),7(a,1,1))].

1083 1 / ((x * (y / x)) * (x * (y / x))) = (x \ (y \ x)) * (x \ (y \ x)). [para(488(a,1),1052(a,1,1)),rewrite([900(5)]),flip(a)].

1179 A / (B * (B * A)) = 1 / (B * B). [para(612(a,1),1031(a,1,2,2)),rewrite([966(8),623(7),763(12)]),flip(a)].

1190 ((A / (B * B)) / (B * B)) / (A / (B * B)) = 1 / (B * B). [back_rewrite(812),rewrite([1179(22)])].

1208 x \ (y * (x * z)) = (x * (y / x)) * z. [para(25(a,1),5(a,1,2))].

1214 x * ((y / x) * y) = y * (x * (y / x)). [para(10(a,1),25(a,1,2)),rewrite([7(3)])].

1220 x * (y * ((z / (y * (x / y))) / (y * (x / y)))) = y * ((y * (x / y)) \ z). [para(150(a,1),25(a,1,2)),flip(a)].

1262 (x * (y * x)) * x = x * (y * (x * x)). [para(32(a,1),36(a,1,1,2)),rewrite([25(7)])].

1378 (B \ ((B * x) * (A / B))) * B = ((x * B) * A) / B. [para(56(a,1),73(a,1,1)),flip(a)].

1394 x * (y * (1 / x)) = (x \ y) * x. [para(86(a,1),3(a,1)),rewrite([126(2)])].

1396 (x * (y * (x \ z))) / z = (x \ y) * x. [para(86(a,1),6(a,1,1))].

1421 (x / ((y / x) * y)) * y = (x / y) * x. [para(1076(a,1),86(a,2,2)),rewrite([737(7),361(4),786(8)])].

1429 x * ((x \ y) / x) = y * (1 / x). [para(1394(a,1),5(a,1,2)),rewrite([88(3)])].

1430 ((x \ y) * x) / (y * (1 / x)) = x. [para(1394(a,1),6(a,1,1))].

1431 (x \ (y / (1 / x))) * x = x * y. [para(7(a,1),1394(a,1,2)),flip(a)].

1437 ((1 / x) \ y) * (1 / x) = (1 / x) * (y * x). [para(19(a,1),1394(a,1,2,2)),rewrite([126(2),126(6),126(9)]),flip(a)].

1472 x \ (y * (1 / x)) = (x \ y) / x. [para(1429(a,1),5(a,1,2))].

1473 (x * y) * (1 / x) = x * (y / x). [para(5(a,1),1429(a,1,2,1)),flip(a)].

1477 x * ((y * (1 / x)) * z) = (x \ y) * (x * z). [para(1429(a,1),9(a,2,2,1)),rewrite([7(3)]),flip(a)].

1479 (1 / x) * ((1 / x) * y) = (y / x) / x. [para(10(a,1),1429(a,2)),rewrite([1472(4),150(4),191(2)]),flip(a)].

1480 (x / y) * (y / (x / y)) = x * (1 / (x / y)). [para(20(a,1),1429(a,1,2,1))].

1484 x * ((x \ (y / x)) * x) = (y * x) * (1 / x). [para(88(a,1),1429(a,1,2,1)),rewrite([73(3)])].

1488 (x \ y) * (1 / x) = x \ (y / x). [para(191(a,1),1429(a,1,2,1)),rewrite([150(4)]),flip(a)].

1501 (x / (x * y)) * (1 / (x \ (1 / y))) = (x \ (1 / y)) \ (1 / y). [para(991(a,1),1429(a,1,2,1)),rewrite([149(8)]),flip(a)].

1503 (1 / (x \ y)) * (1 / x) = x \ (x / y). [para(1031(a,1),1429(a,1,2,1)),rewrite([150(4)]),flip(a)].

1506 ((x * (1 / y)) / y) / y = y \ ((y \ x) / y). [para(36(a,1),1429(a,2)),rewrite([1479(6),258(3),150(5),1479(12)]),flip(a)].

1507 x * ((x \ y) * ((x \ z) / x)) = (y / x) * (z * (1 / x)). [para(1429(a,1),37(a,1,2)),flip(a)].

1514 ((x / y) * x) * (1 / (x \ y)) = (x / (x \ y)) / (x \ y). [back_rewrite(780),rewrite([1479(8)]),flip(a)].

1543 x \ (y / (1 / x)) = (x \ y) * x. [para(1431(a,1),6(a,1,1)),rewrite([73(2)]),flip(a)].

1550 ((x \ y) \ x) * (x \ y) = (x \ y) * ((x / y) * x). [para(783(a,1),1431(a,1,1,2))].

1578 (x * y) \ (x * (y / x)) = 1 / x. [para(1473(a,1),5(a,1,2))].

1579 (x * (y / x)) / (1 / x) = x * y. [para(1473(a,1),6(a,1,1))].

1586 (1 / x) * (y / (1 / x)) = ((1 / x) * y) * x. [para(19(a,1),1473(a,1,2)),rewrite([126(2),126(6),126(8)]),flip(a)].

1588 (x * (y / x)) / (x * y) = (x * y) / ((x * y) * x). [para(1473(a,1),73(a,1,1)),rewrite([737(10)])].

1628 (1 / (x * y)) \ ((y * x) \ x) = x * (((y * x) \ x) * y). [back_rewrite(412),rewrite([1586(8),9(6),381(4)]),flip(a)].

1650 (x \ y) \ (x \ (y / x)) = 1 / x. [para(1488(a,1),5(a,1,2))].

1656 (x \ (y / x)) / (x \ y) = (x \ y) / ((x \ y) * x). [para(1488(a,1),73(a,1,1)),rewrite([737(10)])].

1674 (x \ y) / (x \ (y / x)) = (x \ y) * ((x / y) * x). [para(1488(a,1),480(a,1,2)),rewrite([1550(8)])].

1702 x * ((x \ y) * x) = y / (1 / x). [para(1543(a,1),4(a,1,2))].

1703 (x / (1 / y)) / ((y \ x) * y) = y. [para(1543(a,1),19(a,1,2))].

1704 (1 / x) \ (y / x) = (1 / x) * (y * x). [para(19(a,1),1543(a,1,2,2)),rewrite([126(2),126(6),126(9),1437(10)])].

1730 (x / y) / (1 / y) = (x * y) * (1 / y). [back_rewrite(1484),rewrite([1702(4)])].

1734 ((x * y) * x) / (y / (1 / x)) = x. [back_rewrite(165),rewrite([1702(5)])].

1735 x * (y / (1 / x)) = (x * y) * x. [back_rewrite(122),rewrite([1702(3)])].

1740 (x * (y * x)) \ (x * y) = 1 / x. [para(6(a,1),1578(a,1,2,2))].

1794 (x * y) / (1 / x) = x * (y * x). [para(6(a,1),1579(a,1,1,2))].

1801 (x \ y) / (1 / x) = x * (y / x). [para(150(a,1),1579(a,1,1))].

1819 (1 / x) / (1 / y) = y * (y / (y * x)). [para(992(a,1),1579(a,1,1,2)),rewrite([4(4)])].

1856 (x \ (y / x)) * ((x \ y) * ((x / y) * x)) = 1 / ((x \ (y / x)) \ (1 / x)). [para(1650(a,1),886(a,1,2,2)),rewrite([1674(13)]),flip(a)].

1868 (x * y) / (1 / y) = x * (y * y). [para(88(a,1),1702(a,1,2,1)),rewrite([25(4)]),flip(a)].

1963 ((x / (1 / y)) * y) \ y = y * (1 / ((y * x) * y)). [para(1735(a,1),381(a,1,2,2)),flip(a)].

1985 (x * (y * y)) \ (x * y) = 1 / y. [para(32(a,1),1740(a,1,2)),rewrite([25(4)])].

2061 (B * (A * x)) / (1 / A) = A * ((B * x) * A). [para(57(a,1),1794(a,1,1))].

2094 ((1 / x) / (x \ y)) * (1 / x) = (x * (y / x)) \ (1 / x). [para(1801(a,1),748(a,1,1)),flip(a)].

2111 x / (1 / (y \ x)) = (x / y) * x. [para(4(a,1),1868(a,1,1)),rewrite([361(8)])].

2112 (x * (y * y)) * (1 / y) = x * y. [para(1868(a,1),7(a,1,1))].

2114 (x * (1 / y)) / y = x * (1 / (y * y)). [para(19(a,1),1868(a,1,2)),rewrite([126(2),126(6),126(8),1073(9)])].

2117 (x * y) / (y \ (x \ y)) = x * (x * y). [para(32(a,1),1868(a,1,1)),rewrite([488(5),91(10),7(6)])].

2151 ((x \ y) * x) / (1 / (y * (1 / x))) = y * (x \ y). [para(1394(a,1),1868(a,1,1)),rewrite([1477(16),1394(13),29(12)])].

2154 (x * y) * (1 / (x * x)) = (x \ (y / x)) * x. [para(1473(a,1),1868(a,1,1)),rewrite([128(6),73(3),1073(9)]),flip(a)].

2161 (x * (1 / (y * y))) / y = y \ ((y \ x) / y). [back_rewrite(1506),rewrite([2114(4)])].

2163 ((x / y) * x) \ x = 1 / (y \ x). [para(4(a,1),1985(a,1,2)),rewrite([361(4)])].

2215 ((x / y) * x) * (1 / (y \ x)) = x. [para(2111(a,1),7(a,1,1))].

2216 (x / (x / y)) * x = x / (1 / y). [para(20(a,1),2111(a,1,2,2)),flip(a)].

2224 x / (1 / (x * (1 / y))) = (x \ y) \ x. [para(393(a,1),2111(a,1,2,2)),rewrite([792(10)])].

2228 (x \ y) / (y * (x / y)) = (y / x) / x. [para(747(a,1),2111(a,2,1)),rewrite([886(5),817(8)])].

2273 (x / (y * y)) * y = x * (1 / y). [para(7(a,1),2112(a,1,1)),flip(a)].

2292 (x * (y * y)) * y = x * (y * (y * y)). [para(2112(a,1),818(a,1,1,2)),rewrite([84(4),9(5),4(2),128(9)]),flip(a)].

2311 1 / ((x \ y) \ y) = (x * y) \ y. [para(19(a,1),2163(a,1,1,1)),flip(a)].

2318 x \ (1 / (y \ x)) = 1 / (x * (x / y)). [para(2163(a,1),394(a,1,2))].

2324 1 / ((x * y) \ y) = (x \ y) \ y. [para(792(a,1),2163(a,1,1)),flip(a)].

2329 (x * (1 / y)) \ x = 1 / ((x * y) \ x). [para(818(a,1),2163(a,1,1))].

2352 (x \ y) * ((y / (x * y)) / (x \ y)) = (x * y) \ y. [back_rewrite(1050),rewrite([2311(10)])].

2357 (x \ y) \ ((y / x) / x) = (x * y) \ y. [back_rewrite(892),rewrite([2311(8)])].

2368 (x * y) * (x / (x * y)) = (x \ y) \ y. [back_rewrite(1033),rewrite([2324(8)])].

2391 ((x / y) / y) * (x * (y / x)) = y \ x. [para(747(a,1),2215(a,1,1,1)),rewrite([817(4),886(6)])].

2410 (x / (1 / y)) / x = x / (x / y). [para(2216(a,1),6(a,1,1))].

2415 x \ (x / (1 / y)) = 1 / (x \ (x / y)). [para(2216(a,1),88(a,1,2)),rewrite([784(8)])].

2422 x / (x / (1 / y)) = (x / y) / x. [para(2216(a,1),747(a,2,2)),rewrite([20(3)]),flip(a)].

2449 (x / (y * y)) \ (x * (1 / y)) = y. [para(2273(a,1),5(a,1,2))].

2450 x * (1 / (y * y)) = x / (y * y). [para(2273(a,1),6(a,1,1)),rewrite([2114(4)])].

2490 x \ ((x \ y) / x) = (y / (x * x)) / x. [back_rewrite(2161),rewrite([2450(4)]),flip(a)].

2493 (x * y) / (x * x) = (x \ (y / x)) * x. [back_rewrite(2154),rewrite([2450(5)])].

2497 (x * (1 / y)) / y = x / (y * y). [back_rewrite(2114),rewrite([2450(8)])].

2566 (x * y) * (y / (x * y)) = x * (1 / (x / y)). [para(32(a,1),2324(a,1,2,1)),rewrite([375(5),1042(6),5(7),88(8),1480(8)])].

2609 (x \ y) / (y / (x * y)) = x * (1 / (x / y)). [back_rewrite(854),rewrite([2566(8)])].

2665 1 / (x \ (1 / y)) = x * (x / (x / y)). [para(2410(a,1),784(a,1,2)),flip(a)].

2669 (x / (x / y)) / (x / (1 / y)) = (x / (1 / y)) \ y. [para(2410(a,1),1031(a,2,1)),rewrite([20(8),128(7)]),flip(a)].

2676 ((x \ y) * x) / (x * y) = (x * y) / (x * (y * x)). [para(1794(a,1),2410(a,2,2)),rewrite([128(5),73(2)])].

2677 (x * (y / x)) / (x \ y) = (x \ y) / ((x \ y) / x). [para(1801(a,1),2410(a,1,1))].

2756 x \ (x / (y * y)) = 1 / (y * y). [para(2450(a,1),5(a,1,2))].

2759 x * (1 / (y * (y * (y * y)))) = x / (y * (y * (y * y))). [para(9(a,1),2450(a,1,2,2)),rewrite([10(3),9(9),10(8)])].

2761 (x / (y * y)) / x = x / (x * (y * y)). [para(2450(a,1),73(a,1,1)),rewrite([737(8)])].

2770 x / (x / (y * y)) = (x \ (y * y)) * x. [para(2450(a,1),480(a,1,2))].

2785 ((x * x) \ y) * (x * x) = (x * x) * (y / (x * x)). [para(2450(a,1),1394(a,1,2)),flip(a)].

2796 (x / (y * y)) / (y * y) = x / (y * (y * (y * y))). [para(2450(a,1),1868(a,1,1)),rewrite([2770(7),15(5),3(5),2450(11),1052(9),9(8),10(7),2759(10)])].

2804 1 / (B * B) = B * (B / A). [back_rewrite(1190),rewrite([2796(9),52(7),53(6),17(3),955(7)]),flip(a)].

2805 A / (B * B) = B * B. [back_rewrite(642),rewrite([2796(14),52(12),53(11),17(8),18(7)])].

2830 (B * B) * (A / B) = B * A. [back_rewrite(981),rewrite([2805(5),2805(15),37(14),51(11),7(13)])].

2831 (B * B) \ (A / B) = B. [back_rewrite(977),rewrite([2805(5)])].

2865 ((B * B) * (x / (B * B))) * (A / B) = (B * B) * (x * B). [para(2831(a,1),86(a,2,2,2)),rewrite([2785(8)])].

2876 x / (B * (B / A)) = x * (B * B). [para(2804(a,1),1702(a,2,2)),rewrite([2785(11),32(12)]),flip(a)].

2879 (B * B) * ((B * B) * x) = x * A. [para(2804(a,1),1868(a,1,2)),rewrite([2876(10),10(8),9(15),10(14),52(14),53(13)])].

2881 (x * A) * (B * (B / A)) = x * (B * B). [para(2804(a,1),2112(a,1,2)),rewrite([9(7),10(6),52(6),53(5)])].

2884 x * (B * (B / A)) = x / (B * B). [para(2804(a,1),2450(a,1,2))].

2889 (x * A) / (B * B) = x * (B * B). [back_rewrite(2881),rewrite([2884(8)])].

2892 (B * B) * (((B * B) * x) * (1 / A)) = x. [back_rewrite(928),rewrite([2884(22),6(20)])].

2908 (x * B) * A = x * (B * A). [para(2830(a,1),25(a,2,2)),rewrite([2865(15),2879(10)])].

2937 (B \ ((B * x) * (A / B))) * B = (x * (B * A)) / B. [back_rewrite(1378),rewrite([2908(14)])].

2944 (x * (B * A)) / A = x * B. [para(2908(a,1),6(a,1,1))].

2945 B * ((B \ x) * A) = x * A. [para(7(a,1),2908(a,1,1)),rewrite([37(8)]),flip(a)].

2981 (x / (B * A)) * B = x / A. [para(7(a,1),2944(a,1,1)),flip(a)].

3003 (B * x) * A = B * (x * A). [para(5(a,1),2945(a,1,2,1)),flip(a)].

3008 B * (A * ((B \ x) * A)) = A * (x * A). [para(2945(a,1),57(a,1,2)),flip(a)].

3013 B * ((A * (B \ x)) * A) = (A * x) * A. [para(180(a,1),2945(a,1,2,1))].

3046 (B * (A * x)) / (1 / A) = B * (A * (x * A)). [back_rewrite(2061),rewrite([3003(13),57(14)])].

3067 (x / A) / B = x / (B * A). [para(2981(a,1),6(a,1,1))].

3138 (x * (y * y)) \ x = 1 / (y * y). [para(6(a,1),2756(a,1,2))].

3179 x * (1 / A) = x / A. [para(2876(a,1),1868(a,1,2)),rewrite([2884(6),2(9),2796(8),52(6),53(5),2884(13),2493(11),3067(8),442(8),524(7),2981(9)]),flip(a)].

3191 (B * B) * (((B * B) * x) / A) = x. [back_rewrite(2892),rewrite([3179(11)])].

3236 x \ (x / A) = 1 / A. [para(3179(a,1),5(a,1,2))].

3239 (x / A) / x = x / (x * A). [para(3179(a,1),73(a,1,1)),rewrite([737(8)])].

3246 x / (x / A) = (x \ A) * x. [para(3179(a,1),480(a,1,2))].

3259 (A \ x) * A = A * (x / A). [para(3179(a,1),1394(a,1,2)),flip(a)].

3260 A \ (x / A) = (A \ x) / A. [para(3179(a,1),1472(a,1,2))].

3263 (x / A) \ (x * ((1 / A) / x)) = 1 / x. [para(3179(a,1),1578(a,1,1))].

3269 (x / A) / (1 / x) = x * ((1 / A) * x). [para(3179(a,1),1794(a,1,1))].

3270 (x / A) / A = x / (A * A). [para(3179(a,1),1868(a,1,1)),rewrite([3246(7),15(5),3(5),3179(11),1052(9),2450(10)])].

3271 (x / (A * A)) \ (x / A) = A. [para(3179(a,1),1985(a,1,1,2)),rewrite([3270(5),2450(6),3179(8),3246(12),15(10),3(10)])].

3278 x / (1 / (A * A)) = x * (A * A). [para(3179(a,1),2450(a,1,2,2)),rewrite([3270(6),2770(7),15(5),3(5),3179(11),3270(9)]),flip(a)].

3309 (x * A) \ x = 1 / A. [para(6(a,1),3236(a,1,2))].

3313 1 / ((x / A) \ (1 / A)) = (x / A) * ((x \ A) * x). [para(3236(a,1),886(a,1,2,2)),rewrite([3246(13)])].

3321 x / (1 / A) = x * A. [para(3309(a,1),19(a,1,2))].

3326 1 / (A / (1 / x)) = x \ (1 / A). [para(3309(a,1),488(a,2,2)),rewrite([73(4),1702(5)])].

3329 1 / (x \ (1 / A)) = A / (1 / x). [para(3309(a,1),886(a,1,2,2)),rewrite([73(9),1702(10)])].

3330 (x * A) / (x * (A * x)) = (x * A) \ A. [para(3309(a,1),1031(a,1,2,2)),rewrite([3246(7),15(5),3(5),73(7),2676(10)]),flip(a)].

3337 (x * A) \ (x / (x * A)) = (1 / A) * (1 / (x * A)). [para(3309(a,1),1488(a,1,1)),flip(a)].

3338 (1 / A) \ ((x * A) \ (x / (x * A))) = 1 / (x * A). [para(3309(a,1),1650(a,1,1))].

3349 B * ((A * x) * A) = B * (A * (x * A)). [back_rewrite(3046),rewrite([3321(8),3003(6)])].

3353 (x / A) * ((x \ A) * x) = A / (1 / (x / A)). [back_rewrite(3313),rewrite([3329(8)]),flip(a)].

3358 (A * x) * A = A * (x * A). [back_rewrite(3013),rewrite([3349(8),3008(8)]),flip(a)].

3362 A * (A * ((1 / A) * x)) = (1 / A) \ x. [para(3321(a,1),150(a,1,2,1)),rewrite([3321(9),10(7),37(8),126(4),37(7),126(5)])].

3363 ((1 / A) \ x) / (A * (A * x)) = 1 / A. [para(3321(a,1),198(a,1,2,1)),rewrite([3321(10),10(8)])].

3368 (1 / A) * (((1 / A) / x) * A) = 1 / ((1 / A) \ x). [para(3321(a,1),784(a,1,2))].

3375 A * (A * x) = x * (A * A). [para(3321(a,1),1868(a,1)),rewrite([10(4)])].

3389 x * (x / (x * A)) = 1 / (x \ A). [para(3239(a,1),784(a,1,2))].

3391 (x / (x * A)) / (x / A) = (x / A) \ (1 / A). [para(3239(a,1),1031(a,2,1)),rewrite([20(6)]),flip(a)].

3392 (1 / (x \ A)) / (x / (x * A)) = x. [para(3239(a,1),1032(a,1,2))].

3407 (x / A) / (x * ((1 / A) * x)) = (x / A) \ (1 / A). [para(3239(a,1),2422(a,2,1)),rewrite([3269(7),3391(14)])].

3413 ((x * A) \ A) * (x * A) = (x \ A) * x. [para(6(a,1),3246(a,1,2)),rewrite([73(3)]),flip(a)].

3416 (A * (1 / x)) * (A * (x / A)) = (A \ x) * ((A / x) * A). [para(393(a,1),3246(a,2,1)),rewrite([3259(4),3259(8),73(10),3260(8),7(10),2677(7),3246(7),1550(7),3259(15)]),flip(a)].

3417 ((x \ A) \ A) * (x \ A) = x * (1 / (x / A)). [para(747(a,1),3246(a,1,2)),rewrite([2609(7)]),flip(a)].

3423 x / (1 / (x / A)) = (x \ A) \ x. [para(3246(a,1),2216(a,1,1,2)),rewrite([792(5)]),flip(a)].

3426 (A \ x) \ (A * (x / A)) = A. [para(3259(a,1),5(a,1,2))].

3430 (A \ x) * (A * (x / A)) = x * (A \ x). [para(3259(a,1),10(a,2,2)),rewrite([4(4)]),flip(a)].

3431 (A * (x / A)) * y = A * (x * (A \ y)). [para(3259(a,1),22(a,2,1)),rewrite([4(5)]),flip(a)].

3432 (A \ x) * (A \ (x \ A)) = x \ (A \ x). [para(3259(a,1),381(a,1,2,2)),rewrite([488(8),4(11)])].

3437 A * ((1 / x) / A) = A / (A * x). [para(3259(a,1),737(a,1))].

3441 A * (x / (A * A)) = A \ x. [para(1472(a,1),3259(a,1,1)),rewrite([7(6),3179(7),3270(7)]),flip(a)].

3452 A \ (A / (A * (A * x))) = (1 / (A * x)) / A. [para(394(a,1),3260(a,2,1)),rewrite([747(7),10(6)])].

3473 (x * A) / (A * A) = x / A. [para(6(a,1),3270(a,1,1)),flip(a)].

3499 (x / (A * A)) * (1 / (x / A)) = (A \ x) \ (x / (A * A)). [para(3271(a,1),393(a,1,1,1)),rewrite([3441(6)]),flip(a)].

3523 A * (1 / (x * A)) = (A * x) \ A. [para(3358(a,1),792(a,1,1,2)),rewrite([818(8)])].

3525 (1 / (A \ x)) * A = A * (A / x). [para(784(a,1),3358(a,1,1)),rewrite([7(13)])].

3543 (x * y) * (A * (A * y)) = y * (A * (A * (y * x))). [para(3375(a,2),9(a,1,2)),rewrite([3375(11,R)])].

3563 x * (1 / (A * (A * x))) = ((A * A) * x) \ x. [para(3375(a,2),381(a,1,2,2))].

3587 (x / (A * (A * x))) / x = x \ (1 / (A * A)). [para(3375(a,2),992(a,1,1,2))].

3652 (A \ (A / x)) \ (1 / (A \ x)) = A. [para(784(a,1),3426(a,1,2))].

3701 (x * A) \ (1 / (A * ((A * x) \ A))) = (x / A) / (x * A). [para(3473(a,1),1031(a,2,1)),rewrite([375(9)])].

3714 (x * A) / (A * (A * (x * A))) = (x / A) / (x * A). [para(3473(a,1),2422(a,2,1)),rewrite([3278(10),3375(8,R)])].

3799 (x * A) * (1 / B) = x * (A / B). [para(2889(a,1),2273(a,1,1)),rewrite([2292(6),52(5)]),flip(a)].

3813 x / (1 / (y * y)) = x * (y * y). [para(3138(a,1),19(a,1,2))].

3823 (x \ (y \ x)) * (x \ (y \ x)) = (y * (y * x)) \ x. [para(25(a,1),3138(a,1,1)),rewrite([32(3),1083(10)]),flip(a)].

3825 (x / (1 / y)) \ (x / y) = 1 / (y * y). [para(37(a,1),3138(a,1,1)),rewrite([1702(3)])].

3851 (x * (y / x)) \ (x \ (y \ x)) = (y * (y * x)) \ x. [back_rewrite(908),rewrite([3823(10)])].

3858 (B * B) * (x / A) = (B * B) \ x. [para(4(a,1),3191(a,1,2,1))].

3859 ((B * B) * x) / A = (B * B) \ x. [para(3191(a,1),5(a,1,2)),flip(a)].

3863 ((B * B) * (x / (B * B))) * y = (B * B) * (x * ((B * B) \ y)). [para(3191(a,1),22(a,1,2,1)),rewrite([3859(15),2785(17)]),flip(a)].

3868 (x * (y / A)) * A = x * y. [para(3191(a,1),25(a,2,2)),rewrite([3859(17),3863(16),191(14),2796(14),52(12),53(11),2879(11)])].

3876 (x * y) / A = x * (y / A). [para(3868(a,1),6(a,1,1))].

3877 (x * y) * A = x * (y * A). [para(6(a,1),3868(a,1,1,2))].

3878 (x / (y / A)) * y = x * A. [para(7(a,1),3868(a,1,1)),flip(a)].

3885 A * (x * (y / (A * A))) = A \ (x * y). [para(3868(a,1),88(a,1,2)),rewrite([3876(9),3270(8)]),flip(a)].

3913 (x * y) / (A * A) = x * (y / (A * A)). [para(3868(a,1),3473(a,1,1)),rewrite([3876(10),3270(9)])].

3965 x * ((x \ y) / A) = y / A. [para(4(a,1),3876(a,1,1)),flip(a)].

3966 x * ((1 / x) / A) = 1 / A. [para(127(a,1),3876(a,1,1)),flip(a)].

3987 (x * (y / A)) * (A * z) = A * ((A \ (x * y)) * z). [para(3876(a,1),37(a,1,1))].

4034 x * ((x \ y) * A) = y * A. [para(4(a,1),3877(a,1,1)),flip(a)].

4039 x * ((1 / x) * A) = A. [para(127(a,1),3877(a,1,1)),rewrite([2(3)]),flip(a)].

4063 (x * y) * ((1 / x) * A) = x * ((y / x) * A). [para(1473(a,1),3877(a,1,1)),rewrite([3877(4)]),flip(a)].

4076 x * ((1 / (y * y)) * A) = (x / (y * y)) * A. [para(2450(a,1),3877(a,1,1)),flip(a)].

4085 (1 / x) * A = x \ A. [para(4039(a,1),5(a,1,2)),flip(a)].

4090 (x / (y * y)) * A = x * ((y * y) \ A). [back_rewrite(4076),rewrite([4085(5)]),flip(a)].

4094 (x * y) * (x \ A) = x * ((y / x) * A). [back_rewrite(4063),rewrite([4085(5)])].

4103 (A \ x) \ A = A * (A / x). [back_rewrite(3525),rewrite([4085(6)])].

4114 A / (x * A) = 1 / x. [para(4085(a,1),6(a,1,1)),rewrite([747(4)])].

4117 A * (A * (1 / x)) = (x \ A) * A. [para(4085(a,1),10(a,1,1)),flip(a)].

4118 (1 / x) \ A = x * A. [para(19(a,1),4085(a,1,1)),rewrite([126(4)]),flip(a)].

4119 A \ (x \ A) = A / (A * x). [para(4085(a,1),88(a,1,2)),rewrite([3437(10)])].

4120 (x \ A) / (A / (A * x)) = A. [para(4085(a,1),89(a,1,1)),rewrite([3437(8)])].

4132 (A * x) / (x * (A * x)) = 1 / x. [para(4085(a,1),1734(a,1,1,1)),rewrite([1488(5),128(8),747(6),799(6)])].

4133 (1 / x) * (A / x) = x \ (A / x). [para(4085(a,1),1735(a,2,1)),rewrite([128(7),1488(10)])].

4149 (A \ x) * (A / (A * x)) = x \ (A \ x). [back_rewrite(3432),rewrite([4119(6)])].

4155 1 / (x / A) = A / x. [para(7(a,1),4114(a,1,2)),flip(a)].

4156 A / (A * (A * x)) = 1 / (x * A). [para(10(a,1),4114(a,1,2))].

4162 1 / (A / x) = x / A. [para(4114(a,1),765(a,1))].

4165 A / (A / (A * x)) = 1 / (A \ (1 / x)). [para(737(a,1),4114(a,1,2))].

4166 A \ (A / (A * x)) = (1 / x) / A. [para(4114(a,1),1031(a,2,1)),rewrite([88(6),488(7),4119(5)])].

4173 A / (1 / (x * A)) = (A / (1 / x)) * A. [para(4114(a,1),2216(a,1,1,2)),flip(a)].

4177 A / (x * (y * A)) = 1 / (x * y). [para(3877(a,1),4114(a,1,2))].

4185 (A \ x) \ (x / (A * A)) = (x / (A * A)) * (A / x). [back_rewrite(3499),rewrite([4155(8)]),flip(a)].

4189 (x \ A) \ x = x / (A / x). [back_rewrite(3423),rewrite([4155(4)]),flip(a)].

4190 ((x \ A) \ A) * (x \ A) = x * (A / x). [back_rewrite(3417),rewrite([4155(11)])].

4192 (x / A) * ((x \ A) * x) = A / (A / x). [back_rewrite(3353),rewrite([4155(11)])].

4197 A \ (1 / (x * A)) = (1 / (A * x)) / A. [back_rewrite(3452),rewrite([4156(7)])].

4198 x \ (1 / A) = (1 / x) / A. [back_rewrite(3326),rewrite([4162(6)]),flip(a)].

4220 (x / A) / (x * ((1 / A) * x)) = (A / x) / A. [back_rewrite(3407),rewrite([4198(14),4155(12)])].

4240 (1 / x) * (A * x) = x * (A / x). [para(4118(a,1),1394(a,2,1)),rewrite([128(7),1473(10)])].

4244 (x / A) * (A / x) = 1. [para(4155(a,1),127(a,1,2))].

4246 (x / A) \ (A / x) = (A / x) / (x / A). [para(4155(a,1),191(a,2,1)),rewrite([126(6),4155(6)])].

4249 x / (x * (A / y)) = (x \ (y / A)) * x. [para(4155(a,1),480(a,1,2,2))].

4251 x / (x * (y / A)) = (x \ (A / y)) * x. [para(4155(a,1),737(a,1,1,2)),flip(a)].

4252 1 / ((x / A) * (x / A)) = (A / x) / (x / A). [para(4155(a,1),1052(a,1,1)),flip(a)].

4254 ((x / A) \ y) * (x / A) = (x / A) * (y * (A / x)). [para(4155(a,1),1394(a,1,2,2)),flip(a)].

4259 (A / x) / (x / A) = (A / x) * (A / x). [para(4155(a,1),1488(a,2,2)),rewrite([126(4),4155(4),4155(6),4246(10)]),flip(a)].

4270 (x / (A / y)) / x = x / (x / (y / A)). [para(4155(a,1),2410(a,1,1,2))].

4271 (x / (y / A)) / x = x / (x / (A / y)). [para(4155(a,1),2422(a,1,2,2)),flip(a)].

4274 1 / (x * (y / A)) = A / (x * y). [para(3876(a,1),4155(a,1,2))].

4275 A / ((x / A) * x) = (A / x) * (A / x). [back_rewrite(4252),rewrite([4274(7),4259(10)])].

4302 (1 / (x \ A)) / A = 1 / ((A / x) * A). [para(2111(a,1),4162(a,1,2)),flip(a)].

4312 (x * A) / y = x / (y / A). [para(3878(a,1),6(a,1,1))].

4361 (x / A) / (x * A) = x / (A * (A * x)). [back_rewrite(3714),rewrite([4312(9),73(8),5(6),10(4)]),flip(a)].

4380 (x \ (A / (A * x))) * x = (x * A) \ A. [back_rewrite(3330),rewrite([4312(6),3876(5),73(4),3259(4),1009(6),4119(4)])].

4411 (x * A) \ (1 / (A * ((A * x) \ A))) = x / (A * (A * x)). [back_rewrite(3701),rewrite([4361(16)])].

4423 x \ (y / A) = (x \ y) / A. [para(3965(a,1),5(a,1,2))].

4427 (((x / y) / y) / A) * y = (x / A) / y. [para(3965(a,1),73(a,1,1)),rewrite([4423(7),191(5)]),flip(a)].

4437 x * ((1 / x) / (A * A)) = 1 / (A * A). [para(1052(a,1),3965(a,2)),rewrite([4423(4),126(2),3270(6)])].

4438 (x / (y / A)) * x = x * (A / (x \ y)). [para(3965(a,1),818(a,1,1,2)),rewrite([4155(9)])].

4441 (A \ x) * (A * y) = A * ((x / A) * y). [para(3965(a,1),25(a,1,2,1)),flip(a)].

4455 x * ((x \ y) / (A * A)) = y / (A * A). [para(3270(a,1),3965(a,2)),rewrite([4423(3),3270(5)])].

4457 x / (x * (A / y)) = ((x \ y) / A) * x. [back_rewrite(4249),rewrite([4423(7)])].

4480 A * ((x / A) * (x / A)) = x * (A \ x). [back_rewrite(3430),rewrite([4441(7)])].

4491 ((1 / (x * x)) / A) * x = (1 / A) / x. [para(3966(a,1),73(a,1,1)),rewrite([4423(9),1075(7)]),flip(a)].

4505 x * (((1 / x) / A) / x) = (1 / A) * (1 / x). [para(3966(a,1),1473(a,1,1)),flip(a)].

4519 x \ (y * A) = (x \ y) * A. [para(4034(a,1),5(a,1,2))].

4523 (((x / y) / y) * A) * y = x / (y / A). [para(4034(a,1),73(a,1,1)),rewrite([4312(3),4519(7),191(5)]),flip(a)].

4603 (A * (A / x)) * (A \ x) = (A \ x) * ((A / x) * A). [para(4103(a,1),1394(a,2,1)),rewrite([786(8)]),flip(a)].

4608 (A / (1 / (A \ x))) / ((A \ x) * ((A / x) * A)) = A \ x. [para(4103(a,1),1703(a,1,2,1)),rewrite([4603(13)])].

4620 1 / ((A * x) \ A) = A * (1 / (x \ A)). [para(4119(a,1),393(a,1,1,1)),rewrite([818(6),2329(6)])].

4622 (x \ A) \ (A / (A * x)) = 1 / ((x \ A) * x). [para(4119(a,1),488(a,2,2)),rewrite([19(7)]),flip(a)].

4623 A / (1 / (A \ x)) = 1 / (A \ (A / x)). [para(784(a,1),4119(a,2,2)),rewrite([748(7),2216(7),2415(6)]),flip(a)].

4625 (x \ A) * (A / (A * x)) = A / (x * x). [para(4119(a,1),29(a,1,1)),rewrite([4119(8),818(10),993(9),1073(6),2450(5),4119(9)]),flip(a)].

4628 (1 / x) * (x \ A) = (A / x) / x. [para(4119(a,1),2111(a,1,2,2)),rewrite([4162(8),73(6),3259(6),2228(7),747(7),4114(7)]),flip(a)].

4629 1 / ((A / (A * x)) \ (x \ A)) = (A * (x \ A)) \ (x \ A). [para(4119(a,1),2311(a,1,2,1))].

4631 (1 / (A \ (A / x))) / ((A \ x) * ((A / x) * A)) = A \ x. [back_rewrite(4608),rewrite([4623(6)])].

4637 (A \ (1 / x)) \ (1 / x) = (A / (A * x)) \ (x \ A). [para(4120(a,1),150(a,1,2,1)),rewrite([4165(10),1501(11)])].

4654 x / (x / (A / x)) = x \ A. [para(4189(a,1),19(a,1,2))].

4655 (A / x) / (A / (A / x)) = x \ (A / x). [para(20(a,1),4189(a,1,1)),flip(a)].

4661 (x / (A / x)) * (x \ A) = (x \ A) * ((x / A) * x). [para(4189(a,1),480(a,2,1)),rewrite([1488(7),1674(6)]),flip(a)].

4682 (x / (1 / (x \ A))) / ((x \ A) * ((x / A) * x)) = x \ A. [para(4189(a,1),1703(a,1,2,1)),rewrite([4661(11)])].

4698 (A * (A * x)) / y = x / (y / (A * A)). [para(10(a,1),4312(a,1,1)),rewrite([4312(10),3270(9)])].

4708 (x / A) / y = x / (y * A). [para(4312(a,1),765(a,1,2,1)),rewrite([4312(9),3876(8),6(7),4438(4),4457(5),191(2),4427(5)])].

4716 (A / (A * x)) / (y / A) = (A * (1 / x)) / y. [para(818(a,1),4312(a,1,1)),flip(a)].

4728 x / ((1 / x) / A) = x * (A * x). [para(4312(a,1),1794(a,1))].

4742 (A * (x / A)) / y = (A \ x) / (y / A). [para(3259(a,1),4312(a,1,1))].

4743 (x * (y * A)) / z = (x * y) / (z / A). [para(3877(a,1),4312(a,1,1))].

4751 ((1 / (x * x)) / A) * x = 1 / (x * A). [back_rewrite(4491),rewrite([4708(10)])].

4754 (1 / A) * ((x * A) \ A) = 1 / ((1 / A) \ x). [back_rewrite(3368),rewrite([4708(7),4085(9)])].

4759 (x / A) \ ((A * x) \ x) = 1 / x. [back_rewrite(3263),rewrite([4708(6),381(7)])].

4761 x * ((1 / x) / (x * A)) = (1 / A) * (1 / x). [back_rewrite(4505),rewrite([4708(5)])].

4773 x / (x * ((1 / A) * (x * A))) = (A / x) / A. [back_rewrite(4220),rewrite([4708(8),3877(7),3877(6)])].

4799 x * ((1 / A) * x) = x / (x \ A). [back_rewrite(3269),rewrite([4708(5),4085(4)]),flip(a)].

4818 (B \ ((B * x) * (A / B))) * B = (x * B) / (B / A). [back_rewrite(2937),rewrite([4743(16)])].

4841 (x \ (y \ A)) / A = x \ (1 / y). [para(747(a,1),4423(a,1,2)),rewrite([4114(4)]),flip(a)].

4842 ((1 / x) / A) * x = x / (x * A). [para(4423(a,1),737(a,1,1)),rewrite([126(2)])].

4849 (x / (y * A)) * (y * z) = y * (((y \ x) / A) * z). [para(4423(a,1),37(a,2,2,1)),rewrite([4708(3)])].

4869 x \ (y * (z / A)) = (x \ (y * z)) / A. [para(3876(a,1),4423(a,1,2))].

4870 x \ (y / (A * A)) = (x \ y) / (A * A). [para(4423(a,1),4423(a,2,1)),rewrite([4708(4),4708(10)])].

4884 (x / (A * (A * x))) / x = (1 / x) / (A * A). [back_rewrite(3587),rewrite([4870(12),126(8)])].

4906 ((A \ x) \ x) / (A * A) = (x / (A * A)) * (A / x). [back_rewrite(4185),rewrite([4870(7)])].

4914 x \ (A * (A * y)) = A * (A * (x \ y)). [para(10(a,1),4519(a,1,2)),rewrite([4519(8),10(10)])].

4919 (x \ (1 / y)) * A = x \ (y \ A). [para(792(a,1),4519(a,1,2)),rewrite([4114(7)]),flip(a)].

4924 x \ ((x \ y) \ A) = ((x / y) / x) * A. [para(1031(a,1),4519(a,2,1)),rewrite([4085(5)])].

4928 x \ (y * (x \ A)) = ((x \ y) / x) * A. [para(1472(a,1),4519(a,2,1)),rewrite([3877(5),4085(4)])].

4977 (A \ x) / (y / A) = (A * x) / (y * A). [para(73(a,1),4708(a,1,1)),rewrite([3259(4),4742(5)])].

4982 (x \ A) / (y * A) = (1 / x) / y. [para(747(a,1),4708(a,1,1)),rewrite([4114(4)]),flip(a)].

5005 (x * (y / A)) / z = (x * y) / (z * A). [para(3876(a,1),4708(a,1,1))].

5006 (x / (A * A)) / y = x / (A * (A * y)). [para(4708(a,1),4708(a,1,1)),rewrite([4708(10),10(9)])].

5030 (x \ (x / (x * A))) * x = (1 / (x \ A)) / x. [para(3389(a,1),73(a,1,1)),flip(a)].

5037 x \ (1 / (x / (x * A))) = x / (x / (x \ A)). [para(3389(a,1),992(a,1,1,2)),rewrite([2410(6)]),flip(a)].

5053 x * ((x / (x * A)) * A) = (x \ A) \ A. [para(3389(a,1),3877(a,1,1)),rewrite([4085(6)]),flip(a)].

5088 ((A / (A * x)) \ (1 / x)) / A = x / (x * A). [para(3437(a,1),381(a,2,1)),rewrite([7(11),128(8),4842(5),4423(12)]),flip(a)].

5109 (1 / (x * A)) * ((A / (1 / x)) * A) = (1 / (x * A)) \ ((A * x) \ A). [para(3523(a,1),88(a,1,2)),rewrite([4173(19)]),flip(a)].

5112 ((A * x) \ A) \ (1 / (x * A)) = (1 / (x * A)) * ((x \ A) \ A). [para(3523(a,1),381(a,2,1)),rewrite([4085(11),2324(10)]),flip(a)].

5119 (x * A) * ((A * x) \ A) = (x \ A) * x. [para(3523(a,1),1394(a,1,2)),rewrite([3413(14)])].

5144 (1 / (A \ x)) / A = A \ (A / x). [para(3652(a,1),19(a,1,2))].

5148 (A / x) \ (A \ (A / x)) = (A \ (A / x)) * (A \ x). [para(3652(a,1),393(a,1,1,1)),rewrite([4(6),128(17)])].

5150 (1 / (A \ x)) / ((A \ (A / x)) * (1 / (A \ x))) = 1 / (A \ (A / x)). [para(3652(a,1),747(a,1,1)),rewrite([4623(6)]),flip(a)].

5151 (1 / (A \ (A / x))) * (1 / (A \ x)) = A. [para(3652(a,1),792(a,2)),rewrite([5150(14)])].

5199 B \ (x * (A / B)) = (B \ x) / (B / A). [para(3799(a,1),1472(a,1,2)),rewrite([4519(10),4312(12)])].

5222 (x * B) / (B / A) = x * A. [back_rewrite(4818),rewrite([5199(8),5(4),3878(6)]),flip(a)].

5281 x / (B / A) = (x / B) * A. [para(7(a,1),5222(a,1,1))].

5416 (x / (B * A)) * A = x / B. [para(5281(a,1),4708(a,1)),rewrite([4708(4),7(11)])].

5477 (x / B) / A = x / (B * A). [para(5416(a,1),6(a,1,1))].

5614 (1 / (x * x)) / (y / (x * x)) = (y \ (1 / (x * x))) * (x * x). [para(3813(a,1),747(a,1)),rewrite([2450(13)]),flip(a)].

5632 (1 / (x * x)) / A = 1 / (A * (x * x)). [para(3813(a,1),4162(a,1,2)),flip(a)].

5635 x / ((y * y) \ A) = (x / A) * (y * y). [para(3813(a,1),4708(a,1)),rewrite([4090(9),2(9)]),flip(a)].

5639 (1 / (A * (x * x))) * x = 1 / (x * A). [back_rewrite(4751),rewrite([5632(5)])].

5730 A * ((A * (x \ A)) \ (1 / x)) = 1 / ((x \ A) * x). [para(4117(a,1),2311(a,2,1)),rewrite([5(7),88(8),1586(8),4085(5),375(14)]),flip(a)].

5741 x / ((A \ x) * x) = 1 / (A \ x). [para(4(a,1),4132(a,1,1)),rewrite([4(6)])].

5756 (A * x) * ((1 / x) / (A * x)) = A / (A * x). [para(4132(a,1),784(a,1,2,1)),rewrite([88(15),2566(15),4162(14),488(14),4119(12)])].

5771 x / (x * (x * A)) = 1 / (A * x). [para(3375(a,1),4132(a,1,1)),rewrite([3543(11),4743(12),3876(11),73(10),5(8),10(6),4312(8),3876(7),73(6),5(4)])].

5778 (1 / (x \ A)) * x = x / (A / x). [para(19(a,1),4133(a,1,2)),rewrite([19(11),4189(8)])].

5833 (A * (x \ A)) \ (x \ A) = x / (x * A). [para(4166(a,1),488(a,2,2)),rewrite([4165(11),1501(12),4637(8),4629(9),4423(16),5088(16)])].

5834 (A / (A * x)) \ (x \ A) = 1 / (x / (x * A)). [para(4166(a,1),886(a,1,2,2)),rewrite([4423(10),5088(10),4165(15),1501(16),4637(12)]),flip(a)].

5843 (A \ (1 / x)) \ (1 / x) = 1 / (x / (x * A)). [back_rewrite(4637),rewrite([5834(14)])].

5922 (1 / (A \ x)) * x = (A \ x) \ x. [para(4(a,1),4240(a,1,2)),rewrite([149(12)])].

5926 (A \ x) \ x = x * (A / x). [para(4240(a,1),32(a,2)),rewrite([5756(10),2368(7)])].

5963 (1 / (x * A)) \ ((A * x) \ A) = (x \ A) * x. [para(3523(a,1),4240(a,1,2)),rewrite([128(6),5119(7),4173(13),5109(14)]),flip(a)].

5965 (1 / (A \ x)) * x = x * (A / x). [back_rewrite(5922),rewrite([5926(8)])].

5966 1 / (x / (x * A)) = (x \ A) * x. [back_rewrite(5843),rewrite([5926(7),1586(7),4085(4)]),flip(a)].

5968 (x / (A * A)) * (A / x) = x * ((A / x) / (A * A)). [back_rewrite(4906),rewrite([5926(3),3913(7)]),flip(a)].

5988 x / (x / (x \ A)) = A * (1 / x). [back_rewrite(5037),rewrite([5966(5),88(4),1429(4)]),flip(a)].

6002 (1 / A) * x = A \ x. [para(5926(a,1),19(a,1,2)),rewrite([4457(4),16(1)])].

6009 A * (((x * A) \ A) * x) = (x \ A) * x. [para(394(a,1),5926(a,1,1)),rewrite([1628(9),19(17),3413(14)])].

6010 (A \ x) * ((A / x) * A) = (x \ A) * x. [para(480(a,1),5926(a,2,2)),rewrite([5(6),88(7),1586(7),4085(4),3259(11),3416(12)]),flip(a)].

6011 (x \ (A / x)) * x = 1 / (A \ x). [para(5926(a,1),747(a,1,1)),rewrite([73(4),5741(8)])].

6015 (A * x) \ x = x \ (A \ x). [para(5926(a,1),784(a,2,2)),rewrite([747(5),2352(9),488(8)])].

6031 (A * x) * (x \ (A \ x)) = x. [para(5926(a,1),2215(a,1,2,2)),rewrite([19(3),488(7)])].

6045 x / (x \ A) = x * (A \ x). [back_rewrite(4799),rewrite([6002(4)]),flip(a)].

6046 (x * A) \ A = (A / x) / A. [back_rewrite(4773),rewrite([6002(6),88(4),1009(6),4119(4),4380(6)])].

6048 x * ((1 / x) / (x * A)) = A \ (1 / x). [back_rewrite(4761),rewrite([6002(12)])].

6049 (A \ (A / x)) / A = 1 / ((1 / A) \ x). [back_rewrite(4754),rewrite([6046(7),6002(8),4423(6)])].

6056 (1 / A) \ x = A * x. [back_rewrite(3362),rewrite([6002(6),4(5)]),flip(a)].

6058 (x * A) \ (x / (x * A)) = (1 / (A * x)) / A. [back_rewrite(3337),rewrite([6002(14),4197(12)])].

6074 (1 / (A \ (A / x))) / ((x \ A) * x) = A \ x. [back_rewrite(4631),rewrite([6010(13)])].

6080 1 / ((x \ A) * x) = x / (x * A). [back_rewrite(5833),rewrite([6015(7),4119(6),4622(7)])].

6083 (x / A) \ (x \ (A \ x)) = 1 / x. [back_rewrite(4759),rewrite([6015(5)])].

6092 x / (x * (A \ x)) = A * (1 / x). [back_rewrite(5988),rewrite([6045(3)])].

6100 A * (((A / x) / A) * x) = (x \ A) * x. [back_rewrite(6009),rewrite([6046(5)])].

6122 (A \ (A / x)) / A = 1 / (A * x). [back_rewrite(6049),rewrite([6056(11)])].

6124 x / (A * x) = 1 / A. [back_rewrite(3363),rewrite([6056(4),791(7)])].

6126 (A / x) / (A * A) = 1 / (x * A). [back_rewrite(3338),rewrite([6058(9),4423(10),6056(8),381(6),6046(4),4708(6)])].

6134 A * ((A * (x \ A)) \ (1 / x)) = x / (x * A). [back_rewrite(5730),rewrite([6080(14)])].

6136 (x \ A) \ (A / (A * x)) = x / (x * A). [back_rewrite(4622),rewrite([6080(12)])].

6143 (x / (A * A)) * (A / x) = x \ (A \ x). [back_rewrite(5968),rewrite([6126(13),381(12),6015(10)])].

6144 (A \ x) * (x * y) = x * ((x / A) * y). [para(6002(a,1),9(a,1,1)),rewrite([3179(8)])].

6145 (A \ x) * x = x * (x / A). [para(6002(a,1),10(a,1,1)),rewrite([3179(7)])].

6147 (x / (x * A)) * y = x * (A \ (x \ y)). [para(6002(a,1),86(a,2,2)),rewrite([4423(4),126(2),4842(5)])].

6148 x * (A \ (1 / x)) = x / (x * A). [para(6002(a,1),1394(a,1,2)),rewrite([4423(9),126(7),4842(10)])].

6149 (x / (x * A)) / (A \ (1 / x)) = x. [para(6002(a,1),1430(a,1,2)),rewrite([4423(4),126(2),4842(5)])].

6170 x * (x * (A / (A * x))) = (x \ A) \ A. [back_rewrite(5053),rewrite([6147(5),4119(4)])].

6180 x / (1 / (A * x)) = (x * A) * x. [para(6056(a,1),2111(a,1,2,2)),rewrite([3321(9)])].

6200 (x \ (A \ x)) / x = 1 / (A * x). [para(6015(a,1),747(a,1,1)),rewrite([10(7),5771(8)])].

6201 (1 / (A * x)) * x = x \ (A \ x). [para(6015(a,1),792(a,2)),rewrite([10(3),5771(4)])].

6293 (A / x) * (A \ (A / x)) = (A / x) / x. [para(20(a,1),6045(a,1,2)),flip(a)].

6295 (x \ A) * (x * (A \ x)) = (x \ A) \ A. [para(6045(a,1),88(a,2,2)),rewrite([4(5)]),flip(a)].

6299 (A * x) / (A * (x \ A)) = (x / A) * x. [para(393(a,1),6045(a,1,2)),rewrite([3259(4),5005(9),3877(8),4085(7),3259(11),3259(16),5(17),10(14),7(13)])].

6308 (x \ A) \ A = A / (A / x). [para(6045(a,1),886(a,2,2)),rewrite([191(6),2357(7),6046(5),4155(6),6295(10)]),flip(a)].

6317 x / (1 / (x \ A)) = (A * (1 / x)) * x. [para(6045(a,1),2216(a,1,1,2)),rewrite([6092(4)]),flip(a)].

6320 (x \ A) / (A / (A / x)) = A / (x * x). [para(4119(a,1),6045(a,2,2)),rewrite([6308(6),4625(14)])].

6328 x * (x * (A / (A * x))) = A / (A / x). [back_rewrite(6170),rewrite([6308(10)])].

6330 ((A * x) \ A) \ (1 / (x * A)) = (1 / (x * A)) * (A / (A / x)). [back_rewrite(5112),rewrite([6308(17)])].

6336 (A / (A / x)) * (x \ A) = x * (A / x). [back_rewrite(4190),rewrite([6308(4)])].

6344 ((A * (1 / x)) * x) / ((x \ A) * ((x / A) * x)) = x \ A. [back_rewrite(4682),rewrite([6317(5)])].

6349 A / (A / (A / x)) = x \ A. [para(7(a,1),6046(a,1,1)),rewrite([4271(8)]),flip(a)].

6357 (x * x) / (A / (A / (x / A))) = x * A. [para(6046(a,1),783(a,1,2,2)),rewrite([6(4),4155(9),4743(8),4270(7)])].

6358 1 / (A \ (A / x)) = A * (1 / (x \ A)). [para(818(a,1),6046(a,1,1)),rewrite([2329(6),4620(6),4165(12),5144(14),2415(12)]),flip(a)].

6372 A / (A / (x / A)) = 1 / (x \ A). [para(6046(a,1),2163(a,1)),rewrite([4270(6)])].

6376 A * ((A * x) \ A) = A / x. [para(6046(a,1),4117(a,2,1)),rewrite([3523(7),7(12)])].

6394 (A * (1 / (x \ A))) / ((x \ A) * x) = A \ x. [back_rewrite(6074),rewrite([6358(6)])].

6398 (A * (1 / (x \ A))) * (1 / (A \ x)) = A. [back_rewrite(5151),rewrite([6358(6)])].

6403 A / (1 / (A \ x)) = A * (1 / (x \ A)). [back_rewrite(4623),rewrite([6358(12)])].

6407 (x * x) / (1 / (x \ A)) = x * A. [back_rewrite(6357),rewrite([6372(7)])].

6422 x / (A * (A * x)) = 1 / (A * A). [back_rewrite(4411),rewrite([6376(9),4162(6),4423(5),3309(3),4708(5)]),flip(a)].

6431 (1 / x) / (A * A) = 1 / (A * (A * x)). [back_rewrite(4884),rewrite([6422(5),5006(6)]),flip(a)].

6440 ((A * A) * x) \ x = 1 / (A * A). [back_rewrite(4437),rewrite([6431(6),3563(7)])].

6444 x * (1 / (A * (A * x))) = 1 / (A * A). [back_rewrite(3563),rewrite([6440(12)])].

6488 (A \ x) * (x / A) = x * (x / (A * A)). [para(6145(a,1),3876(a,1,1)),rewrite([3876(5),4708(4)]),flip(a)].

6505 (x \ A) \ (A / (A / x)) = x * (A \ x). [para(6308(a,1),191(a,1,2)),rewrite([19(11),6045(10)])].

6508 A / (x / A) = (x \ A) * A. [para(765(a,1),6308(a,2,2)),rewrite([6046(6),4270(6),6372(6),4118(6)]),flip(a)].

6525 (A / (A / x)) \ (x \ A) = (x \ A) / x. [para(6308(a,1),4189(a,1,1)),rewrite([19(13)])].

6569 (A / x) * (1 / x) = A / (x * x). [para(6349(a,1),191(a,2,1)),rewrite([20(10),748(7),779(7),6320(12)])].

6571 (1 / (x \ A)) * (A / (A / x)) = x * (A \ x). [para(6349(a,1),748(a,1,1)),rewrite([6505(7),4270(9),6508(8),4114(9)]),flip(a)].

6591 A / (A \ x) = A * (x \ A). [para(4(a,1),6376(a,1,2,1)),flip(a)].

6592 (A * x) \ A = A \ (A / x). [para(6376(a,1),5(a,1,2)),flip(a)].

6595 (A \ (A / x)) * (1 / (A \ x)) = (A / x) / x. [para(6376(a,1),10(a,1,1)),rewrite([6592(6),6293(7),6592(7),6592(11),3259(13),784(13)]),flip(a)].

6596 (A \ (A / x)) * ((x \ A) * x) = A / x. [para(6376(a,1),32(a,2)),rewrite([6592(4),6592(8),6592(13),6591(14),20(13),4441(11),6100(11)])].

6612 1 / ((1 / (x * A)) \ (A \ (A / x))) = (A \ (A / x)) * (A \ x). [para(6376(a,1),2311(a,2,1)),rewrite([6592(6),191(7),4708(7),6126(7),6592(9),6592(17),5148(18)])].

6613 (1 / (x * A)) \ (A \ (A / x)) = 1 / ((A \ (A / x)) * (A \ x)). [para(6376(a,1),2324(a,1,2,1)),rewrite([6592(7),5148(8),6592(14),191(15),4708(15),6126(15),6592(17)]),flip(a)].

6617 (A \ (A / x)) \ (1 / (x * A)) = (A \ (A / x)) * (A \ x). [para(6376(a,1),6015(a,1,1)),rewrite([6592(6),5148(7),6592(11),6592(16),191(17),4708(17),6126(17)]),flip(a)].

6633 (1 / (x * A)) * (A / (A / x)) = (A \ (A / x)) * (A \ x). [back_rewrite(6330),rewrite([6592(4),6617(9)]),flip(a)].

6636 1 / ((A \ (A / x)) * (A \ x)) = (x \ A) * x. [back_rewrite(5963),rewrite([6592(8),6613(9)])].

6657 A * (1 / (x * A)) = A \ (A / x). [back_rewrite(3523),rewrite([6592(10)])].

6665 (A \ (A / x)) * (A \ x) = x / (x * A). [back_rewrite(6612),rewrite([6613(10),6636(10),6080(5)]),flip(a)].

6670 (1 / (x * A)) * (A / (A / x)) = x / (x * A). [back_rewrite(6633),rewrite([6665(16)])].

6713 (A * x) * (A \ (A / x)) = A. [para(6592(a,1),4(a,1,2))].

6721 (A * x) \ (A * (1 / (x \ A))) = (A * x) / (A * (x * A)). [para(6592(a,1),1031(a,1,2,2)),rewrite([6358(8),73(13),3259(13),1588(16),3877(15)])].

6757 ((x \ A) * x) / (A * (1 / (x \ A))) = 1 / (A \ x). [para(6713(a,1),1794(a,2,2)),rewrite([4441(7),6100(7),6358(9),3259(16),784(16)])].

6810 x / (x * (y * (z / A))) = (x \ (A / (y * z))) * x. [para(4274(a,1),737(a,1,1,2)),flip(a)].

6813 1 / (x * (y * (z / A))) = A / (x * (y * z)). [para(25(a,1),4274(a,2,2)),rewrite([3876(6),25(7)])].

6924 A / ((A / x) / x) = x * x. [para(4628(a,1),4274(a,2,2)),rewrite([747(7),4114(7),1073(6),2770(5),15(3),3(3)]),flip(a)].

6932 (x * x) * ((A / x) / x) = A. [para(6924(a,1),7(a,1,1))].

6935 (x * x) \ A = (A / x) / x. [para(6924(a,1),20(a,1,1))].

6940 (A * (1 / x)) * (A * (1 / x)) = (A / x) * (A / x). [para(480(a,1),6924(a,1,2,1)),rewrite([3259(5),5005(10),3877(9),4085(8),6299(8),4275(5)]),flip(a)].

6972 x / ((A / y) / y) = (x / A) * (y * y). [back_rewrite(5635),rewrite([6935(3)])].

6977 (x / (y * y)) * A = x * ((A / y) / y). [back_rewrite(4090),rewrite([6935(7)])].

7009 (x * x) \ (A \ (x * x)) = (1 / (x \ A)) / x. [para(6932(a,1),992(a,1,1,2)),rewrite([3876(3),2493(5),4708(3),5030(5),6972(11),6002(11)]),flip(a)].

7029 (A * (1 / x)) * x = x * (1 / (A \ x)). [para(6935(a,1),73(a,2,1)),rewrite([3877(3),2493(5),73(3),88(4),1429(4),37(10),6011(9)])].

7048 (x * (1 / (A \ x))) / ((x \ A) * ((x / A) * x)) = x \ A. [back_rewrite(6344),rewrite([7029(5)])].

7097 (A \ x) / (A \ (A / x)) = x * (x / A). [para(4(a,1),4728(a,2,2)),rewrite([5144(8),6145(10)])].

7112 A \ (x * x) = x / (A / x). [para(37(a,1),4728(a,2)),rewrite([4155(6),4708(7),7(6),6488(9),3885(10)]),flip(a)].

7136 (x * x) \ (x / (A / x)) = (1 / (x \ A)) / x. [back_rewrite(7009),rewrite([7112(4)])].

7161 A * (x / (A / x)) = x * x. [para(7112(a,1),4(a,1,2))].

7169 (A * (1 / x)) / (A * (x / A)) = x \ (A / x). [para(480(a,1),7112(a,2,2)),rewrite([6940(10),7112(7),4655(7),3259(11)]),flip(a)].

7179 (x / (A / x)) * A = A * (x * (x / A)). [para(7112(a,1),1394(a,2,1)),rewrite([3179(6),3876(4)]),flip(a)].

7239 (x \ A) * (x \ A) = A * ((x \ A) / x). [para(19(a,1),7161(a,1,2,2)),flip(a)].

7246 (A / x) * (A / x) = A * (x \ (A / x)). [para(480(a,1),7161(a,1,2,2)),rewrite([3259(9),7169(10),6940(14)]),flip(a)].

7274 (A * (1 / x)) * (A * (1 / x)) = A * (x \ (A / x)). [back_rewrite(6940),rewrite([7246(14)])].

7294 A / ((x / A) * x) = A * (x \ (A / x)). [back_rewrite(4275),rewrite([7246(10)])].

7350 (A / (A * x)) \ (1 / x) = (x \ A) * (x / A). [para(5926(a,1),4841(a,1,1)),rewrite([19(6),3876(5),4119(9)]),flip(a)].

7351 (A * (x \ A)) \ (1 / x) = (x / (x * A)) / A. [para(6015(a,1),4841(a,1,1)),rewrite([4119(6),6136(7)]),flip(a)].

7363 (x \ A) * (x / (A * A)) = x / (x * A). [back_rewrite(5088),rewrite([7350(7),3876(7),4708(6)])].

7364 A * ((x / (x * A)) / A) = x / (x * A). [back_rewrite(6134),rewrite([7351(8)])].

7369 x \ (x / (x * A)) = A \ (1 / x). [para(4842(a,1),88(a,1,2)),rewrite([4708(9),6048(10)])].

7374 (A / (A * x)) / (A * (1 / x)) = x \ (A \ x). [para(818(a,1),4842(a,2,2)),rewrite([4162(6),73(4),3259(4),73(6),4423(4),7(6),4149(7)]),flip(a)].

7383 (1 / (x * A)) / (1 / x) = (x * x) / (x * (x * A)). [para(4842(a,1),1868(a,2)),rewrite([5632(5),5639(6),3877(11)])].

7387 (A / (1 / x)) \ x = x / (x * A). [para(2216(a,1),4842(a,2,2)),rewrite([4162(6),4708(6),6126(6),6670(9),2669(12)]),flip(a)].

7393 (1 / (x \ A)) / x = (A \ (1 / x)) * x. [para(4842(a,1),2450(a,1)),rewrite([6977(8),2(8),6972(7),5632(5),6201(7),7112(4),7136(5),2770(10),15(8),3(8),3876(8),2493(10),4708(8),7369(9)])].

7394 (A \ x) / (A * (x / A)) = x / (x * A). [para(3259(a,1),4842(a,2,2)),rewrite([5144(6),6665(7)]),flip(a)].

7396 ((1 / x) / A) * (x / A) = (x / (x * A)) / A. [para(4842(a,1),3876(a,1,1)),flip(a)].

7398 (A / x) / ((A / x) * A) = x \ (A \ x). [para(4162(a,1),4842(a,1,1,1)),rewrite([4708(4),6143(7)]),flip(a)].

7400 (x * x) / (x * (x * A)) = (A \ (1 / x)) * x. [para(4842(a,1),3813(a,2)),rewrite([5632(5),3813(9),6201(7),7112(4),7136(5),7393(5),3877(9)]),flip(a)].

7445 (x * x) \ (x / (A / x)) = (A \ (1 / x)) * x. [back_rewrite(7136),rewrite([7393(10)])].

7458 (1 / (x * A)) / (1 / x) = (A \ (1 / x)) * x. [back_rewrite(7383),rewrite([7400(12)])].

7465 ((1 / x) / y) \ (x \ A) = y * A. [para(20(a,1),4919(a,1,1)),flip(a)].

7520 (1 / ((A / x) * A)) / y = (1 / (x \ A)) / (y * A). [para(2163(a,1),4982(a,1,1)),flip(a)].

7531 (A / (A / x)) / (y * A) = (1 / (x \ A)) / y. [para(6308(a,1),4982(a,1,1))].

7550 (A \ x) * (A \ (A / x)) = 1 / A. [para(5144(a,1),3966(a,1,2))].

7644 (1 / (x \ A)) * (x / (A / x)) = (x * (A \ x)) / (x \ A). [para(5778(a,1),10(a,2,2)),rewrite([786(5),1514(8),6045(3)]),flip(a)].

7652 1 / ((x / A) * x) = x \ (A / x). [para(5778(a,1),394(a,1,2,1)),rewrite([20(4),786(9)]),flip(a)].

7656 (1 / (x \ A)) \ x = (x \ A) * x. [para(5778(a,1),792(a,1,1,2)),rewrite([4654(4)]),flip(a)].

7683 (1 / (x \ A)) * (x * A) = A * (x * (x / A)). [para(5778(a,1),3877(a,1,1)),rewrite([7179(5)]),flip(a)].

7714 A * (A * (x / (x * A))) = (x \ A) * x. [para(5966(a,1),449(a,2)),rewrite([6147(10),7369(8),191(9),4708(9),6431(9),6444(10),3813(9),3375(7,R)])].

7721 ((x / (x * A)) \ y) * (x / (x * A)) = x * (A \ (x \ (y * ((x \ A) * x)))). [para(5966(a,1),1394(a,1,2,2)),rewrite([6147(8)]),flip(a)].

7730 x / ((y \ A) * y) = x * (y / (y * A)). [para(5966(a,1),1702(a,2,2)),rewrite([7721(11),993(12),6002(11),191(9),4708(9),4455(10),3913(8),3913(7),7363(7)]),flip(a)].

7758 (A * (1 / (x \ A))) * (x / (x * A)) = A \ x. [back_rewrite(6394),rewrite([7730(10)])].

7764 (1 / (A \ x)) / x = x \ (A / x). [para(6011(a,1),6(a,1,1))].

7769 (x \ A) * ((x / A) * x) = A * (x / A). [para(19(a,1),6011(a,1,1,2)),rewrite([4189(3),4661(6),4119(11),4162(12),73(10),3259(10)])].

7794 x * (A / (x * x)) = 1 / (A \ x). [para(6011(a,1),1394(a,2)),rewrite([6569(5)])].

7828 (x * (1 / (A \ x))) / (A * (x / A)) = x \ A. [back_rewrite(7048),rewrite([7769(11)])].

7879 ((x \ (A \ x)) / (x / A)) / (x / A) = (x / A) \ (1 / x). [para(6083(a,1),191(a,1,2)),flip(a)].

7904 (x \ (A \ x)) * A = (x / A) * (x \ A). [para(6083(a,1),4034(a,1,2,1)),rewrite([4085(6)]),flip(a)].

8065 (x \ (A \ x)) / (x / A) = A / (A * x). [para(818(a,1),6149(a,1,1,2)),rewrite([7374(9),4162(10),73(8),3259(8),5(9)])].

8090 (x / A) \ (1 / x) = A / (x * x). [back_rewrite(7879),rewrite([8065(6),4716(7),2497(5)]),flip(a)].

8096 x / (A * (1 / x)) = x * (x / A). [para(7(a,1),6180(a,2,1)),rewrite([488(8),4119(6),4708(7),818(6)])].

8199 (1 / (A * x)) * (x * y) = x * ((1 / (x * A)) * y). [para(6200(a,1),37(a,1,1)),rewrite([191(10),747(9),6124(9),4708(10)])].

8204 (A \ (1 / x)) * x = x * (1 / (A * x)). [para(6200(a,1),1801(a,2,2)),rewrite([191(4),747(3),6124(3),4708(4),7458(7)])].

8266 (x * x) \ (x / (A / x)) = x * (1 / (A * x)). [back_rewrite(7445),rewrite([8204(10)])].

8279 (1 / (x \ A)) / x = x * (1 / (A * x)). [back_rewrite(7393),rewrite([8204(10)])].

8318 (x / A) * (x \ A) = x * ((A / x) / A). [para(6201(a,1),3877(a,1,1)),rewrite([7904(5),8199(12),4085(11),6046(9)])].

8383 (x * A) * (1 / (x \ A)) = x * x. [para(6407(a,1),7(a,1,1))].

8400 1 / ((x * x) \ (1 / (x \ A))) = (x * x) * (1 / (A \ x)). [para(6407(a,1),784(a,1,2,1)),rewrite([2493(5),6011(5)]),flip(a)].

8435 (A * A) * x = A * (A * x). [para(6422(a,1),89(a,1,2,2)),rewrite([2450(15),2493(13),73(10),3259(10),5(11),7(9),73(6),4914(5),16(3),3(4)])].

8514 (A / (x * x)) / x = (A / x) / (x * x). [para(6569(a,1),1868(a,1,1)),rewrite([128(7),1073(11),2450(10)])].

8548 ((1 / x) / A) * (x * y) = x * ((A \ (1 / x)) * y). [para(7369(a,1),37(a,2,2,1)),rewrite([992(4),4423(4),126(2)])].

8723 x \ (A / (A / x)) = x * (A / (A * x)). [para(3392(a,1),7465(a,1,1)),rewrite([6308(4),6147(10),4119(9)])].

8827 1 / (x * (A \ x)) = (x \ A) / x. [para(6349(a,1),7652(a,2,2)),rewrite([4270(7),6508(6),4114(7),6571(10),6525(12)])].

8896 (A * (1 / x)) * (x * y) = x * ((1 / (A \ x)) * y). [para(7794(a,1),9(a,2,2,1)),rewrite([2273(4)])].

8900 (A * (1 / x)) \ x = x * (A \ x). [para(7794(a,1),381(a,1,2,2)),rewrite([128(6),2273(7)]),flip(a)].

9102 (x * (A \ x)) / (x / A) = A / (A / x). [para(8090(a,1),1031(a,1,2,2)),rewrite([4162(7),3876(5),88(6),3246(5),4192(6),4708(9),4085(8),6045(7)]),flip(a)].

9103 (x * x) / (A / (1 / x)) = x / A. [para(8090(a,1),1032(a,1,1,2)),rewrite([4162(5),3876(3),4708(8),4085(7),6045(6),9102(9),5005(8),2216(7)])].

9175 ((A * (x * (x / A))) \ x) * A = 1 / (A \ x). [para(8383(a,1),381(a,1,2,2)),rewrite([2450(6),2493(4),6011(4),7683(11),4519(12)]),flip(a)].

9179 (x * A) \ (1 / (A \ x)) = 1 / (x * x). [para(8383(a,1),394(a,2,2)),rewrite([7683(9),4519(10),9175(10)])].

9194 (A * (x * (x / A))) / (x \ A) = (x \ A) \ (x * x). [para(8383(a,1),1472(a,1,2)),rewrite([4519(9),4189(7),7179(9)]),flip(a)].

9199 (1 / (x \ A)) * (x * x) = (x \ A) \ (x * x). [para(8383(a,1),1794(a,2,2)),rewrite([7683(7),128(11),9194(8)]),flip(a)].

9253 (x / A) \ (x * x) = A / (1 / x). [para(9103(a,1),20(a,1,1))].

9259 ((A / (1 / x)) / (x * x)) * (A / (1 / x)) = (x / A) \ (A / (1 / x)). [para(9103(a,1),748(a,1,1)),flip(a)].

9276 (x * x) / ((1 / x) / A) = (x * x) * (A / (1 / x)). [para(9103(a,1),2216(a,1,1,2)),rewrite([4438(6),459(4),4162(13)]),flip(a)].

9280 (x * x) * ((A / (1 / x)) / (x * x)) = (x * x) / (x / A). [para(9103(a,1),2410(a,2,2)),rewrite([4162(7),9276(6),73(8),2785(8)])].

9459 (x * y) * (x \ ((y * x) \ z)) = x \ z. [para(4(a,1),339(a,1,2)),flip(a)].

9476 x \ ((y / x) * z) = (x \ y) * (x \ z). [para(150(a,1),339(a,2,1)),rewrite([7(3)])].

9482 (x * y) * (x \ (((y * x) * z) * ((y * x) \ u))) = x \ ((z * (y * x)) * u). [para(22(a,1),339(a,1,2)),flip(a)].

9788 ((A \ x) / A) * x = (x / A) * (x / A). [para(6145(a,1),361(a,1,2)),rewrite([1507(9),3179(6)]),flip(a)].

9812 (x / A) * (1 / (A \ x)) = A * (x / (x * A)). [para(6148(a,1),361(a,1,2)),rewrite([3259(7),7394(8)]),flip(a)].

9861 x * ((x * (y / x)) \ z) = y \ (x * z). [para(7(a,1),375(a,1,1)),flip(a)].

9887 (x / y) \ (y * z) = y * ((y \ x) \ z). [para(150(a,1),375(a,2,2,1)),rewrite([7(3)])].

10080 x * (y * ((z / (y * (x / y))) / (y * (x / y)))) = x \ (y * z). [back_rewrite(1220),rewrite([9861(12)])].

10179 (A * (x \ (A / x))) * (x / A) = A / x. [para(4162(a,1),789(a,1,2)),rewrite([18(4),7246(5),4162(13),4155(12)])].

10215 (x / A) * ((A / (1 / x)) * (A / x)) = (x * x) / (x / A). [para(9103(a,1),789(a,1,2)),rewrite([9259(11),4254(10),9103(17)])].

10339 (x \ A) * ((1 / (x \ A)) \ (x * x)) = x / (1 / ((A / x) * A)). [para(6407(a,1),817(a,2,1)),rewrite([9199(7),19(6),4312(16),4302(15)])].

10369 (x * ((y / (x * z)) / x)) * z = x \ y. [para(7(a,1),1208(a,1,2)),flip(a)].

10373 (x * (y / x)) * (x * (z / x)) = x \ (y * (z * x)). [para(32(a,1),1208(a,1,2,2)),flip(a)].

10379 (x * (y / x)) \ z = x \ (y \ (x * z)). [para(150(a,1),1208(a,2)),rewrite([10080(8)]),flip(a)].

10524 (x * (x * y)) \ y = y \ ((y / x) / x). [back_rewrite(3851),rewrite([10379(5),4(3),191(2)]),flip(a)].

10529 ((1 / x) / (x \ y)) * (1 / x) = x \ (1 / y). [back_rewrite(2094),rewrite([10379(12),127(10),126(9)])].

10618 (x * y) * (x * (1 / y)) = x * ((x \ y) \ y). [para(1214(a,2),9(a,2)),rewrite([9(5),2368(4),818(7)]),flip(a)].

10623 (x \ y) * (x * y) = y * ((x \ y) * x). [para(19(a,1),1214(a,1,2,1)),rewrite([19(6)])].

10665 (x / y) * (1 / (x \ y)) = x * ((x / y) * (1 / y)). [para(784(a,1),1214(a,2,2)),rewrite([779(4)]),flip(a)].

10758 (A / (A / x)) * ((x \ A) * A) = A * (x * (A / x)). [para(6349(a,1),1214(a,1,2,1)),rewrite([6349(20),6336(17)])].

10974 (x * (x * y)) * ((y * x) \ x) = x * (y * (x * ((x * y) \ x))). [para(1262(a,1),339(a,1,2)),rewrite([375(5),375(4),375(3),10(7)]),flip(a)].

10989 (x \ (y / (x \ z))) * x = (x * y) / z. [para(7(a,1),1396(a,1,1,2)),flip(a)].

11086 (x / (y * (y * x))) * (y * x) = y \ x. [para(6(a,1),1421(a,1,1,2,1)),rewrite([792(8)])].

11155 ((x / (1 / y)) / (x / y)) * x = (x / (x / y)) * (x / (1 / y)). [para(2410(a,1),1421(a,2,1)),rewrite([2422(7),7(6)])].

11209 (x * x) * (1 / (A \ x)) = A * (A / (A / x)). [para(5144(a,1),1421(a,1,1,2,1)),rewrite([6595(10),6972(5),17(3),2(3),6403(12),3877(14),4085(13),6308(11)])].

11272 1 / ((x * x) \ (1 / (x \ A))) = A * (A / (A / x)). [back_rewrite(8400),rewrite([11209(14)])].

11310 (x * (y * y)) / (1 / y) = y * (y * (x * y)). [para(1868(a,1),1479(a,2,1)),rewrite([128(4),128(4)]),flip(a)].

11326 (x \ A) * ((x \ A) * (x * x)) = x / (1 / ((A / x) * A)). [para(6407(a,1),1479(a,2,1)),rewrite([128(6),128(8),4312(14),4302(13)])].

11419 (x * A) \ ((x \ A) * x) = A \ (A / x). [para(3309(a,1),1503(a,1,1,2)),rewrite([3246(5),15(3),3(3),6657(6),73(9)]),flip(a)].

11444 (A * (A / (A / x))) / (x * x) = x \ A. [para(6407(a,1),1503(a,2,2)),rewrite([11272(8),2450(10),4519(12),459(10),4085(12)])].

11630 (x * x) / (A * (A / (A / x))) = 1 / (x \ A). [para(7550(a,1),1730(a,2,1)),rewrite([7097(7),6358(9),5005(10),3877(9),4085(8),6308(6),6358(17),37(18),126(12),6002(17),2318(15),381(16),6046(14),4270(14),6508(13),4114(14)])].

11846 (1 / x) / (1 / (y / x)) = (y / x) * ((y / x) / y). [para(7(a,1),1819(a,2,2,2))].

11939 (B * B) * ((B * B) / ((B * B) \ x)) = (A / x) * (B * B). [para(3858(a,1),1819(a,2,2,2)),rewrite([4155(4),2804(7),2876(8)]),flip(a)].

12291 (x / (x * A)) / A = x / (A * (x * A)). [para(9253(a,1),2224(a,2,1)),rewrite([2450(9),4708(7),3877(6),5771(7),128(8),4708(5),3877(4),4423(12),7387(10)]),flip(a)].

12341 ((1 / x) / A) * (x / A) = x / (A * (x * A)). [back_rewrite(7396),rewrite([12291(12)])].

12342 A * (x / (A * (x * A))) = x / (x * A). [back_rewrite(7364),rewrite([12291(6)])].

12374 (1 / (x \ y)) / (y / (y / x)) = (x / y) / x. [para(765(a,1),2228(a,1,2,2)),rewrite([88(3),784(3),789(7),6(9)])].

12398 (x \ y) \ (1 / x) = x \ (1 / (y / x)). [para(1650(a,1),2228(a,1,1)),rewrite([1674(8),1856(9),2111(10),10529(8),1656(8),992(10)]),flip(a)].

12776 (A / x) / (x * x) = A / (x * (x * x)). [para(8096(a,1),2318(a,2,2,2)),rewrite([8900(6),8827(5),2490(4),8514(4),6813(10)])].

12855 (A / (x * x)) / x = A / (x * (x * x)). [back_rewrite(8514),rewrite([12776(8)])].

12890 1 / (x \ (y \ (x * (x * y)))) = x * (y \ ((y / x) / x)). [para(1473(a,1),2329(a,2,2,1)),rewrite([128(5),375(4),10524(3),10379(9)]),flip(a)].

13251 (x / (1 / y)) / (y * y) = x / y. [para(1702(a,1),2493(a,1,1)),rewrite([6(8),191(7),7(8)])].

13357 (x * x) / (x / A) = (x * x) * (A / x). [back_rewrite(9280),rewrite([13251(7)]),flip(a)].

13369 (x / A) * ((A / (1 / x)) * (A / x)) = (x * x) * (A / x). [back_rewrite(10215),rewrite([13357(14)])].

13374 (x / y) \ (x / (1 / y)) = y * y. [para(13251(a,1),20(a,1,1))].

13383 ((x * x) / (y / (1 / x))) * (x * x) = x * ((x \ y) \ x). [para(13251(a,1),748(a,1,1)),rewrite([9887(3)]),flip(a)].

13433 A * (A * (x * (y / (y * A)))) = x / (y / (y * A)). [para(5966(a,1),13251(a,1,1,2)),rewrite([7730(4),6147(11),7369(9),191(10),4708(10),6431(10),6444(11),3813(10),3375(8,R)])].

13445 (x * ((x \ y) \ x)) * (y / x) = (y / (1 / x)) / (y / x). [para(13251(a,1),789(a,1,2)),rewrite([13383(7),13251(13)])].

13456 x / (x \ (y * (y * x))) = (x / y) / y. [para(2228(a,1),13251(a,2)),rewrite([488(5),19(4),10373(5)])].

13486 (x * (1 / y)) * (x * (1 / y)) = y \ (x * (y \ x)). [para(1430(a,1),13374(a,1,1)),rewrite([2151(8)]),flip(a)].

13544 ((x \ y) * x) \ ((x \ y) \ x) = y \ (x * (y \ x)). [para(2224(a,1),13374(a,1,2)),rewrite([480(4),13486(12)])].

13553 ((x \ A) / x) * A = A * (x \ (A / x)). [back_rewrite(7274),rewrite([13486(9),4928(5)])].

13689 x * (x / (x * (y * y))) = 1 / (x \ (y * y)). [para(3813(a,1),2665(a,1,2,2)),rewrite([2(4),3813(8)]),flip(a)].

13804 ((x / y) / y) / x = x / (y * (y * x)). [para(25(a,1),2761(a,2,2)),rewrite([10373(5),13456(4),32(6)])].

14039 (A * x) / (A * (x * A)) = x / (x * A). [para(3431(a,1),4842(a,2,2)),rewrite([488(6),4119(4),992(6),4441(9),12341(8),12342(7),16(11),3(10),1588(10),3877(9)]),flip(a)].

14121 (A * x) \ (A * (1 / (x \ A))) = x / (x * A). [back_rewrite(6721),rewrite([14039(16)])].

14134 1 / (x \ (y * (y * x))) = x \ ((x / y) / y). [para(89(a,1),3825(a,1,2)),rewrite([488(5),2117(4),10524(3),10373(9)]),flip(a)].

14398 (x \ A) * ((x \ A) * (x * y)) = x * (((y / x) / (x / A)) * A). [para(4094(a,1),10(a,1,1)),rewrite([4094(7),4312(4)]),flip(a)].

14485 (A / (1 / x)) * (A / x) = A * (x * (A / x)). [para(6349(a,1),4094(a,2,2,1)),rewrite([2216(6),20(10),10758(16)])].

14502 (x * (1 / (A \ x))) * (A * (1 / (x \ A))) = A * x. [para(8096(a,1),4094(a,2,2,1)),rewrite([7029(5),2329(11),6592(10),6358(11),3877(21),7(20),8896(18),5965(17),32(16)])].

14538 x / (1 / ((A / x) * A)) = x * ((A / x) * A). [back_rewrite(11326),rewrite([14398(7),17(1),4155(4)]),flip(a)].

14540 (x * x) * (A / x) = A * x. [back_rewrite(13369),rewrite([14485(9),37(8),6144(7),4244(6),3(3)]),flip(a)].

14545 (x \ A) * ((1 / (x \ A)) \ (x * x)) = x * ((A / x) * A). [back_rewrite(10339),rewrite([14538(16)])].

14558 (A * x) / (A / x) = x * x. [para(14540(a,1),6(a,1,1))].

14626 (x * x) * (1 / (x * A)) = A \ x. [para(14540(a,1),3913(a,1,1)),rewrite([2493(6),4423(4),7(6),6126(9)]),flip(a)].

14658 (A * (x \ A)) / x = A * ((x \ A) / x). [para(19(a,1),14558(a,1,2)),rewrite([7239(10)])].

14740 (1 / (x \ A)) \ (x * x) = A * (A / (A / x)). [para(14626(a,1),381(a,1,2,2)),rewrite([11209(6),4849(12),126(8),4842(11),3389(10)]),flip(a)].

14814 (x \ A) * (A * (A / (A / x))) = x * ((A / x) * A). [back_rewrite(14545),rewrite([14740(8)])].

15587 (A \ x) * (A \ x) = x * ((A \ x) / A). [para(4480(a,1),73(a,1,1)),rewrite([3876(5),4869(12),9476(10),3876(12),3877(14),7(13)]),flip(a)].

16136 (A * x) * (A * y) = A * ((x * A) * y). [para(4698(a,1),4441(a,2,2,1)),rewrite([5(6),449(11),3321(10)])].

16619 (x \ A) * (x / A) = x * (A / (A * x)). [para(4302(a,1),4924(a,2,1,1)),rewrite([4118(10),6046(10),19(8),4423(7),7656(5),3876(5),7520(16),4085(15),6308(13),12374(14)

,4708(8),6147(10),4119(9)])].

17058 (x * y) / (x \ A) = x * ((y / A) * x). [para(5005(a,1),1794(a,1)),rewrite([4085(5)])].

17145 (1 / (x \ A)) * (x / (A / x)) = x * ((x / A) * (x / A)). [back_rewrite(7644),rewrite([17058(14),9788(13)])].

17955 (A / x) * (1 / (A * x)) = 1 / (x * x). [para(6293(a,1),3876(a,1,1)),rewrite([13804(5),4177(5),6122(11)]),flip(a)].

18086 (A \ (A / x)) \ (A * (1 / (x \ A))) = (A * (1 / (x \ A))) / (A \ (A / x)). [para(6358(a,1),191(a,2,1)),rewrite([126(10),6358(10)])].

18093 (A * (1 / (x \ A))) / (A \ (A / x)) = x * x. [para(6358(a,1),1052(a,1,1)),rewrite([15587(21),6122(20),17955(19),2770(16),15(14),3(14)])].

18102 (A * (1 / (x \ A))) \ (x * x) = A * (1 / (x \ A)). [para(6358(a,1),1650(a,1,2,2)),rewrite([126(6),6358(6),18086(17),18093(17),6358(14)])].

18350 (1 / (A \ x)) * ((x \ A) * x) = (A / x) * A. [para(2111(a,1),6596(a,1,1,2)),rewrite([88(6),784(6),4118(10),1473(13),19(10),2111(14)])].

18975 x / (y / (A * (y * A))) = (x * A) * ((y \ A) * y). [para(7714(a,1),9(a,1,2)),rewrite([16136(15),13433(16),4312(12),12291(11)]),flip(a)].

18981 x / (y / (y * A)) = x * ((y \ A) * y). [para(7714(a,1),25(a,2,2)),rewrite([3987(11),5(6),13433(8)])].

19012 x / (y * (A / y)) = x * (y \ (A \ y)). [para(20(a,1),7730(a,1,2,1)),rewrite([7398(11)])].

19033 x / (y * (A / (A * y))) = (x * A) * (y / (y * A)). [para(7730(a,1),4312(a,1)),rewrite([3876(11),16619(11)]),flip(a)].

19049 (x / A) * ((y \ A) * y) = (x * A) * (y / (y * A)). [para(7730(a,1),4523(a,1,1,1,1)),rewrite([7730(8),10(8),6147(7),993(8),6002(7),191(5),4708(5),4455(6),2273(6),3179(4),3876(11),16619(11),19033(12)])].

19427 (x / A) \ (1 / (x \ A)) = (A * x) / (x * A). [para(8318(a,1),992(a,1,1,2)),rewrite([4708(8),3877(7),7(6),4457(4),16(1),6002(4),4977(5)]),flip(a)].

19607 (A * x) / (x * A) = A * (x / (x * A)). [para(1394(a,1),8723(a,2,2,2)),rewrite([3179(4),3179(8),6508(7),4114(8),19427(7),3179(9),3259(12),4251(13),3259(13),784(13),9812(12)])].

19759 (x * y) \ (x \ z) = x \ ((y * x) \ z). [para(9459(a,1),5(a,1,2))].

19954 (x \ y) \ (y \ x) = y \ (x * (y \ x)). [back_rewrite(13544),rewrite([19759(5),4(3)])].

20455 x \ (A * (x \ (A / x))) = (x \ A) * (x \ (A / x)). [para(7246(a,1),9476(a,1,2))].

20720 x * ((y / (x * z)) / x) = (x \ y) / z. [para(10369(a,1),6(a,1,1)),flip(a)].

20762 x / (y \ (z \ (y * x))) = y * (z / y). [para(10379(a,1),19(a,1,2))].

20905 (x * y) \ (x * (x * (x * y))) = (x \ y) \ (x * y). [para(1794(a,1),10524(a,2,2,1)),rewrite([37(6),126(4),37(7),126(2),1479(6),150(3),1794(9),10(6)]),flip(a)].

20969 (x * y) / (x * z) = (x \ (y / z)) * x. [para(5(a,1),10989(a,1,1,2,2)),flip(a)].

20970 x \ (y / (x \ z)) = ((x * y) / z) / x. [para(10989(a,1),6(a,1,1)),flip(a)].

21203 (x \ y) / (x * y) = y / (x * (x * y)). [para(11086(a,1),6(a,1,1))].

21274 (A * (1 / (x \ A))) / (x * (1 / (A * x))) = x * A. [para(11419(a,1),1032(a,1,1,2)),rewrite([6358(6),7730(12),2368(12),6308(10),7531(13),8279(11)])].

21438 x / (A * (y / (y * A))) = (x * A) * (y / (y * A)). [para(12342(a,1),5006(a,2,2,2)),rewrite([18975(10),2273(6),3179(4),19049(6)]),flip(a)].

21572 x \ (A * (y \ (A / y))) = (x \ ((y \ A) / y)) * A. [para(13553(a,1),4519(a,1,2))].

21596 (A / (x * (x * x))) * A = (x \ A) * (x \ (A / x)). [back_rewrite(20455),rewrite([21572(6),2490(4),12855(4)])].

21652 ((x \ A) * (x \ (A / x))) * x = A * ((x \ A) / x). [para(6145(a,1),13804(a,2,2,2)),rewrite([19(3),6591(4),14658(5),6144(11),6810(12),7294(10),21572(11),2490(9),12855(9),21596(11)]),flip(a)].

22460 x / (y * (1 / (A * y))) = x * (y * (1 / (A \ y))). [para(2450(a,1),18981(a,2,2)),rewrite([6977(8),2(8),6972(7),5632(5),6201(7),7112(4),8266(5),4118(11),3877(9),20969(11),73(9),88(10),1429(10),7029(11)])].

22480 (A * (1 / (x \ A))) * (x * (1 / (A \ x))) = x * A. [back_rewrite(21274),rewrite([22460(12)])].

22885 ((x * y) \ x) \ y = x \ (y * (y * x)). [para(5(a,1),19954(a,1,2)),rewrite([5(6),10(5)])].

23188 x \ ((x \ y) / z) = (y / (x * z)) / x. [para(20720(a,1),5(a,1,2))].

23192 (x / (y * z)) * (y * u) = y * (((y \ x) / z) * u). [para(20720(a,1),9(a,2,2,1)),rewrite([7(4)])].

23193 (x / (y * z)) * y = y * ((y \ x) / z). [para(20720(a,1),10(a,2,2)),rewrite([7(4)])].

23218 (1 / x) / (y / x) = (y \ x) * (1 / x). [para(488(a,1),20720(a,1,2,1)),rewrite([1429(4),126(6)]),flip(a)].

23232 x * ((y / ((x * z) * x)) / x) = (x \ y) / (z / (1 / x)). [para(1735(a,1),20720(a,1,2,1,2))].

23406 (x \ (1 / (y * y))) * (y * y) = (y * y) / (x * (y * y)). [back_rewrite(5614),rewrite([23218(6),2450(6),747(4)]),flip(a)].

23499 (x * x) / (1 / y) = x / (y \ (1 / x)). [para(1985(a,1),20762(a,1,2,2)),rewrite([73(7),1702(8)]),flip(a)].

23500 (1 / x) / (y \ x) = 1 / (y \ (x * x)). [para(2449(a,1),20762(a,1,2,2)),rewrite([2761(7),13689(8)])].

23914 ((x \ A) * x) / (x / (A / x)) = A * ((x \ A) / x). [para(5778(a,1),21203(a,1,2)),rewrite([7656(5),5778(16),17145(15),6810(14),7294(12),21572(13),23188(11),12855(11),21596(13),21652(14)])].

23954 x / (y \ (x * (x * y))) = (y * x) \ y. [para(22885(a,1),19(a,1,2))].

23964 x * (y \ ((y / x) / x)) = x * (((y * x) \ y) / x). [para(22885(a,1),886(a,1,2,2)),rewrite([12890(6)])].

23995 x \ (((y * x) \ y) \ (x * x)) = (x \ y) \ (x * y). [para(375(a,1),22885(a,1,1)),rewrite([10524(3),23964(4),10379(5),20905(10)])].

24288 (1 / x) / (1 / (y / x)) = (y \ x) \ (1 / x). [para(23218(a,1),2216(a,1,1,2)),rewrite([792(10)]),flip(a)].

24334 (x / y) * ((x / y) / x) = (x \ y) \ (1 / y). [back_rewrite(11846),rewrite([24288(6)]),flip(a)].

24366 (B * B) / ((x \ (B * B)) * A) = 1 / (x \ A). [para(2876(a,1),23499(a,2,2,2)),rewrite([2884(11),20969(9),4708(6),442(6),4423(5),126(3),5477(5),23193(7),126(4),5477(6),381(7),59(3),3309(5),4708(6),4085(5),2(14),5005(14)]),flip(a)].

24405 1 / ((x / y) \ (x * x)) = (1 / x) / y. [para(20(a,1),23500(a,1,2)),flip(a)].

24504 (x / y) / ((y \ x) * (y \ x)) = y \ (x \ (y * y)). [para(7(a,1),23954(a,1,2,2,2)),rewrite([9476(4),10379(8)])].

24638 (x / (x / y)) * (x / (1 / y)) = (x / (1 / y)) * y. [para(19(a,1),779(a,2,2)),rewrite([126(2),2410(4),126(4),126(8)])].

24657 ((x / y) / x) * ((x / y) * (1 / y)) = (x / y) / (y * y). [para(779(a,1),2117(a,1,1)),rewrite([20(9),20(6),2497(5),779(9)]),flip(a)].

24665 (x / (1 / y)) / (x / y) = x / ((x / y) * (1 / y)). [para(779(a,1),21203(a,1,2)),rewrite([20(4),779(12),24657(13),2770(10),9887(8),13445(10)]),flip(a)].

24667 ((x \ y) \ (1 / y)) \ (x / y) = ((x / y) / x) * (y * y). [para(779(a,1),23954(a,1,2,2,2)),rewrite([24657(10),2756(7),3813(6),24334(8)]),flip(a)].

24673 (x / ((x / y) * (1 / y))) * x = (x / (1 / y)) * y. [back_rewrite(11155),rewrite([24665(5),24638(12)])].

24959 (((1 / x) * y) * x) \ (1 / x) = (1 / x) \ (y \ (1 / (x * x))). [para(1586(a,1),23954(a,2,1)),rewrite([7(14),9476(10),24504(11),1073(7)]),flip(a)].

25686 x * (y * (x * ((x * y) \ x))) = x * (y * (x / y)). [para(5(a,1),10618(a,2,2,1)),rewrite([381(6),10974(5),88(7)])].

25724 (x * (x * y)) * ((y * x) \ x) = x * (y * (x / y)). [back_rewrite(10974),rewrite([25686(10)])].

25827 (x * ((A / x) * A)) * (1 / (x \ A)) = x * A. [para(11630(a,1),789(a,1,2)),rewrite([11444(8),14814(9),11630(19),23499(16),12398(15),4162(14),4423(13),16(11),3321(14)])].

26403 1 / (x / ((x / y) / x)) = y * (1 / ((y * x) * y)). [para(2410(a,1),873(a,1,1,1)),rewrite([24638(6),20(9),128(8),1963(5),2422(10)]),flip(a)].

26640 (A * (1 / (x \ A))) * ((A / x) * A) = A * ((x \ A) * x). [para(6757(a,1),1214(a,1,2,1)),rewrite([18350(14),6757(30),6398(25),3877(16),10623(16)])].

26641 A * ((A * (x \ (A / x))) * (1 / (x \ A))) = (A / x) * A. [para(6757(a,1),1421(a,2,1)),rewrite([7730(13),7758(13),4441(12),10665(11),3179(10),4708(8),3885(10),7112(6),23914(7),16136(12),13553(6),18350(20)])].

26751 x / (y \ (z * (z * y))) = x * (y \ ((y / z) / z)). [para(10373(a,1),2450(a,1,2,2)),rewrite([14134(5),10373(9)]),flip(a)].

26764 x * (((y * x) \ y) / x) = (y * x) \ y. [back_rewrite(23954),rewrite([26751(4),23964(4)])].

26810 ((x * y) \ x) \ (y * z) = y * (((x * y) \ x) \ z). [para(26764(a,1),375(a,2,2,1)),rewrite([7(4)])].

26814 x \ (y * (y * x)) = y / ((x * y) \ x). [para(26764(a,1),2391(a,1,2)),rewrite([7(9),22885(6)]),flip(a)].

26879 (x \ y) \ (x * y) = x / ((y * x) \ y). [back_rewrite(23995),rewrite([26810(4),22885(3),26814(3),5(5)]),flip(a)].

26971 ((x / y) / x) / (((x / y) / x) * (y * y)) = 1 / (y * y). [para(779(a,1),26814(a,1,2,2)),rewrite([24657(8),2756(5),24334(9),24667(11)]),flip(a)].

27029 x \ ((x / y) * (1 / y)) = 1 / (y * y). [para(779(a,1),26879(a,1,2)),rewrite([20(4),24334(11),24667(13),26971(12)])].

27072 (x / y) * (1 / y) = x / (y * y). [para(27029(a,1),4(a,1,2)),rewrite([2450(4)]),flip(a)].

27114 (x / (1 / y)) * y = x * (y * y). [back_rewrite(24673),rewrite([27072(4),2770(3),10(4),4(3)]),flip(a)].

27157 x * (1 / ((x * y) * x)) = (y * (x * x)) \ x. [back_rewrite(1963),rewrite([27114(4)]),flip(a)].

27181 (x * (y * y)) \ y = 1 / (x / ((x / y) / x)). [back_rewrite(26403),rewrite([27157(10)]),flip(a)].

27245 (x * x) * ((x * x) * y) = x * (x * (x * (x * y))). [para(11310(a,1),27072(a,1,1)),rewrite([128(7),36(4),10(2),27072(11),3813(10),10(8)]),flip(a)].

27307 B * (B * (B * (B * x))) = x * A. [back_rewrite(2879),rewrite([27245(8)])].

27412 B * (B * (B * x)) = (B \ x) * A. [para(4(a,1),27307(a,1,2,2,2))].

27546 ((x * (y * y)) \ y) * (1 / y) = (1 / y) / (x / (1 / y)). [para(27157(a,1),1473(a,1,1)),rewrite([23232(12),126(8)])].

28080 (A * (1 / (x \ A))) * (x * ((A / x) / A)) = A / (A / x). [para(14502(a,1),1628(a,1,2,1)),rewrite([22480(13),14121(13),1704(8),23192(8),126(2),8548(7),737(6),6328(6),14502(22),14121(19),6147(19),5(17),20970(16),3(13)]),flip(a)].

28265 (A / (A / x)) / (x * ((A / x) / A)) = A * (1 / (x \ A)). [para(28080(a,1),6(a,1,1))].

28342 x * ((x * y) * (y / x)) = x * (y * y). [para(1262(a,1),9482(a,2,2)),rewrite([10(3),25724(6),5(5),9(4),5(8)])].

28349 (x * y) * (y / x) = y * y. [para(28342(a,1),5(a,1,2)),rewrite([5(3)]),flip(a)].

28463 x * ((x * y) \ x) = x / y. [para(28349(a,1),5(a,1,2)),rewrite([375(3)])].

28654 x / (x \ y) = x * (y \ x). [para(4(a,1),28463(a,1,2,1)),flip(a)].

28713 x \ (y * y) = y / (x / y). [para(10379(a,1),28463(a,1,2)),rewrite([4(4)])].

28718 1 / (x / ((x / y) / x)) = (1 / x) / y. [para(24405(a,1),28463(a,2)),rewrite([28713(5),2(6),126(6),2(7)])].

28720 (1 / x) / (y / (1 / x)) = y \ (1 / (x * x)). [para(1586(a,1),28463(a,1,2,1)),rewrite([24959(9),4(10)]),flip(a)].

28732 (x * (y * y)) \ y = (1 / x) / y. [para(27181(a,2),28463(a,2)),rewrite([2(6),126(6),28718(6),2(5)]),flip(a)].

28733 (x * (1 / (A \ x))) / (A * (1 / (x \ A))) = A / x. [para(14502(a,1),28463(a,1,2,1)),rewrite([375(13),9179(12),381(9),459(7),1473(8),7764(5),4(4)]),flip(a)].

28775 (B / (x / B)) * A = (A / x) * (B * B). [back_rewrite(11939),rewrite([28654(11),28713(10),27245(12),27412(11),4034(10)])].

29173 (B * B) / ((A / x) * (B * B)) = 1 / (x \ A). [back_rewrite(24366),rewrite([28713(7),28775(9)])].

29191 x / ((A * (1 / (x \ A))) / x) = A * (1 / (x \ A)). [back_rewrite(18102),rewrite([28713(8)])].

29237 x \ (1 / (y * y)) = (1 / x) / (y * y). [back_rewrite(27546),rewrite([28732(3),27072(6),28720(10)]),flip(a)].

29366 (x * x) / (y * (x * x)) = 1 / y. [back_rewrite(23406),rewrite([29237(4),7(6)]),flip(a)].

29430 1 / (x \ A) = x / A. [back_rewrite(29173),rewrite([29366(10),4162(4)]),flip(a)].

29453 A / (A / x) = A * (x / A). [back_rewrite(29191),rewrite([29430(5),5005(5),19607(5),21438(6),2368(6),6308(4),29430(9)])].

29457 x \ A = A / x. [back_rewrite(28733),rewrite([29430(10),7828(10)])].

29465 A * (x / A) = x. [back_rewrite(28265),rewrite([29453(4),5005(10),3877(9),7(8),19012(6),6031(6),29457(4),4162(5)]),flip(a)].

29496 (A / x) * A = A * (A / x). [back_rewrite(26641),rewrite([29457(9),4162(10),10179(9)]),flip(a)].

29497 x * (A * (A / x)) = A * A. [back_rewrite(26640),rewrite([29457(4),4162(5),29465(4),29496(4),29457(8),7(9)])].

29518 A * x = x * A # label(non_clause) # label(goal). [back_rewrite(25827),rewrite([29496(4),29497(5),29457(6),4162(7),8435(6),29465(5)])].

29519 $F. [resolve(29518,a,14,a)].

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

============================== STATISTICS ============================

Given=653. Generated=168288. Kept=29515. proofs=1.

Usable=430. Sos=14362. Demods=14482. Limbo=88, Disabled=14645. Hints=5372.

Kept_by_rule=0, Deleted_by_rule=0.

Forward_subsumed=104321. Back_subsumed=471.

Sos_limit_deleted=34452. Sos_displaced=0. Sos_removed=0.

New_demodulators=28827 (4 lex), Back_demodulated=14163. Back_unit_deleted=0.

Demod_attempts=5908094. Demod_rewrites=895754.

Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.

Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0.

Megabytes=30.99.

User_CPU=8.72, System_CPU=0.26, Wall_clock=9.

============================== end of statistics =====================

============================== end of search =========================

THEOREM PROVED

Exiting with 1 proof.

Process 3366 exit (max_proofs) Tue Oct 6 14:27:44 2009

% Length of proof is 1114.

% Level of proof is 57.

% Maximum clause weight is 42.

% Given clauses 1483.

1 C * (x * C)' = x' # label(non_clause) # label(goal). [goal].

2 1 * x = x. [assumption].

3 x * 1 = x. [assumption].

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

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

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

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

8 x * x' = 1. [assumption].

9 x' * x = 1. [assumption].

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

11 (x * y) * (y * z) = y * ((y * x) * z). [copy(10),flip(a)].

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

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

14 ((x * y) / x) * (x * z) = x * (y * z). [copy(13),flip(a)].

15 B * (B * (B * B)) = A. [assumption].

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

17 A * x = x * A. [copy(16),flip(a)].

18 B * (B * (B * (B * (B * B)))) = C. [assumption].

19 B * (B * A) = C. [copy(18),rewrite([15(9)])].

20 c1' != C * (c1 * C)'. [deny(1)].

21 C * (c1 * C)' != c1'. [copy(20),flip(a)].

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

26 x / (y \ x) = y. [para(4(a,1),6(a,1,1))].

27 (x / y) \ x = y. [para(7(a,1),5(a,1,2))].

29 x \ 1 = x'. [para(8(a,1),5(a,1,2))].

31 x'' = x. [para(9(a,1),5(a,1,2)),rewrite([29(3)])].

32 1 / x = x'. [para(9(a,1),6(a,1,1))].

33 (x \ y) * (((x \ y) * x) * z) = y * ((x \ y) * z). [para(4(a,1),11(a,1,1)),flip(a)].

34 x * ((x * y) * (x \ z)) = (y * x) * z. [para(4(a,1),11(a,1,2)),flip(a)].

35 (x * y) \ (y * ((y * x) * z)) = y * z. [para(11(a,1),5(a,1,2))].

37 x * ((x * (y / x)) * z) = y * (x * z). [para(7(a,1),11(a,1,1)),flip(a)].

38 (x / y) * (((x / y) * z) * y) = (z * (x / y)) * x. [para(7(a,1),11(a,1,2)),flip(a)].

39 x * ((x * y) * x') = y * x. [para(8(a,1),11(a,1,2)),rewrite([3(3)]),flip(a)].

40 x' * ((x' * y) * x) = y * x'. [para(9(a,1),11(a,1,2)),rewrite([3(4)]),flip(a)].

41 (x * ((x * y) * z)) * ((x * z) * u) = (x * z) * (((x * z) * (y * x)) * u). [para(11(a,1),11(a,1,1))].

42 (x * (y * z)) * (z * ((z * y) * u)) = (y * z) * (((y * z) * x) * (z * u)). [para(11(a,1),11(a,1,2))].

46 x * (x * (y / x)) = y * x. [para(7(a,1),12(a,1,1)),flip(a)].

47 (x * (x * y)) * (x * z) = x * ((x * (y * x)) * z). [para(12(a,1),11(a,1,1))].

48 (x * (y * z)) * (z * (z * y)) = (y * z) * (((y * z) * x) * z). [para(12(a,1),11(a,1,2))].

49 (x * ((x * y) * z)) * (x * z) = (x * z) * ((x * z) * (y * x)). [para(11(a,1),12(a,1,1))].

50 (x * (x * y)) * x = x * (x * (y * x)). [para(12(a,1),12(a,1,1))].

51 (x / y) * (y * z) = y * ((y \ x) * z). [para(4(a,1),14(a,1,1,1))].

52 ((x * y) / x) * z = x * (y * (x \ z)). [para(4(a,1),14(a,1,2))].

53 ((x * y) / x) \ (x * (y * z)) = x * z. [para(14(a,1),5(a,1,2))].

54 (x * (y * z)) / (x * z) = (x * y) / x. [para(14(a,1),6(a,1,1))].

55 x' * (x * y) = x * (x' * y). [para(8(a,1),14(a,1,1,1)),rewrite([32(2)])].

56 (x * y) / x = x * (y * x'). [para(8(a,1),14(a,1,2)),rewrite([3(4)])].

59 ((x * y)' * (x * (x * y))) * ((x * y)' * y) = 1. [para(9(a,1),14(a,2)),rewrite([56(6),31(5)])].

60 (x * y) * (((x * y) * (x * (z * x'))) * u) = (x * (z * y)) * ((x * y) * u). [para(14(a,1),11(a,1,1)),rewrite([56(9)]),flip(a)].

61 (x * (y * x')) * (((x * (y * x')) * z) * (x * u)) = (z * (x * (y * x'))) * (x * (y * u)). [para(14(a,1),11(a,1,2)),rewrite([56(2),56(9),56(12)]),flip(a)].

65 (x * y) * ((x * y) * (x * (z * x'))) = (x * (z * y)) * (x * y). [para(14(a,1),12(a,1,1)),rewrite([56(8)]),flip(a)].

71 ((x * (y * x')) * (z * (x * (y * x'))')) * (x * (y * u)) = (x * (y * x')) * (z * (x * u)). [para(14(a,1),14(a,1,2)),rewrite([56(2),56(6),56(8),56(14)])].

73 ((x * (y * x')) * (x * (x * (y * x'))')) * ((x * (y * x')) * z) = x * (y * z). [para(14(a,1),14(a,2)),rewrite([56(2),56(6),56(8),56(11)])].

75 (x * (y * z)) / (x * z) = x * (y * x'). [back_rewrite(54),rewrite([56(6)])].

76 (x * (y * x')) \ (x * (y * z)) = x * z. [back_rewrite(53),rewrite([56(2)])].

77 (x * (y * x')) * z = x * (y * (x \ z)). [back_rewrite(52),rewrite([56(2)])].

78 (x * (y * (x * (y * x'))')) * (x * (y * (x \ z))) = x * (y * z). [back_rewrite(73),rewrite([77(9),5(6),77(10)])].

80 (x * (y * (x \ (z * (x * (y * x'))')))) * (x * (y * u)) = x * (y * (x \ (z * (x * u)))). [back_rewrite(71),rewrite([77(9),77(17)])].

81 x * (y * (x \ ((x * (y * (x \ z))) * (x * u)))) = (z * (x * (y * x'))) * (x * (y * u)). [back_rewrite(61),rewrite([77(7),77(9)])].

82 B * (B * B) = B \ A. [para(15(a,1),5(a,1,2)),flip(a)].

83 (B \ A) * B = A. [para(15(a,1),12(a,2)),rewrite([12(5),82(5)])].

84 A \ (x * A) = x. [para(17(a,1),5(a,1,2))].

85 x \ (A * x) = A. [para(17(a,2),5(a,1,2))].

86 x * (A * x') = A. [para(17(a,1),6(a,1,1)),rewrite([56(3)])].

87 A * (x * A') = x. [para(17(a,2),6(a,1,1)),rewrite([56(4)])].

88 A * (x / A) = x. [para(17(a,2),7(a,1))].

89 (x * A) * (x * y) = x * ((x * A) * y). [para(17(a,1),11(a,1,1))].

95 (x * A) * x = x * (x * A). [para(17(a,1),12(a,1,1))].

98 B \ C = B * A. [para(19(a,1),5(a,1,2))].

101 B * ((B * x) * (B * A)) = (x * B) * C. [para(19(a,1),11(a,1,2)),flip(a)].

102 C * (B * x) = B * (C * x). [para(19(a,1),11(a,2,2,1)),rewrite([95(5),19(5)])].

104 C * B = B * C. [para(19(a,1),12(a,2,2)),rewrite([95(5),19(5)])].

110 (x \ y) * (((x \ y) * z) * (((x \ y) * x) * u)) = (z * (x \ y)) * (y * ((x \ y) * u)). [para(33(a,1),11(a,1,2)),flip(a)].

111 (x \ y) * (x * (y * z)) = y * ((x \ y) * (x * z)). [para(11(a,1),33(a,1,2)),rewrite([4(3)])].

117 B \ A = A / B. [para(83(a,1),6(a,1,1)),flip(a)].

120 B * (B * B) = A / B. [back_rewrite(82),rewrite([117(8)])].

121 A \ x = x / A. [para(7(a,1),84(a,1,2))].

125 A * (x * y) = x * (A * y). [para(88(a,1),11(a,2,2,1)),rewrite([17(4,R),88(4)]),flip(a)].

127 ((x \ y) * x) * z = x * (y * (x \ z)). [para(4(a,1),34(a,1,2,1)),flip(a)].

128 x \ ((y * x) * z) = (x * y) * (x \ z). [para(34(a,1),5(a,1,2))].

129 ((x * y) * z) / ((y * x) * (y \ z)) = y. [para(34(a,1),6(a,1,1))].

130 (x / y) * (x * ((x / y) \ z)) = (y * (x / y)) * z. [para(7(a,1),34(a,1,2,1))].

132 x * ((x * y) * ((x * z) * (x \ u))) = (y * x) * ((z * x) * u). [para(34(a,1),11(a,1,2)),flip(a)].

137 (A * x) * y = (x * A) * y. [para(17(a,1),34(a,2,1)),rewrite([34(5)])].

138 x * ((A * x) * (x \ y)) = (A * x) * y. [para(17(a,2),34(a,1,2,1))].

139 B * (C * (B \ x)) = C * x. [para(19(a,1),34(a,1,2,1)),rewrite([95(11),19(11)])].

143 A * (x * (y / A)) = x * y. [para(88(a,1),34(a,1,2,1)),rewrite([121(3),17(9,R),88(9)])].

147 (x \ y) * (((x \ y) * z) * (x * (y * (x \ u)))) = (z * (x \ y)) * (y * ((x \ y) * u)). [back_rewrite(110),rewrite([127(6)])].

152 C \ (B * C) = B. [para(104(a,1),5(a,1,2))].

153 B * (C * B') = C. [para(104(a,1),6(a,1,1)),rewrite([56(5)])].

154 (B * C) * (B * x) = B * ((B * C) * x). [para(104(a,1),11(a,1,1))].

155 (x * C) * (B * C) = C * ((C * x) * B). [para(104(a,1),11(a,1,2))].

156 (B * C) * B = B * (B * C). [para(104(a,1),12(a,1,1))].

162 (x * y) \ (y * z) = y * ((y * x) \ z). [para(4(a,1),35(a,1,2,2))].

163 (x * y) \ y = y * (y * x)'. [para(8(a,1),35(a,1,2,2)),rewrite([3(3)])].

172 (x * A) \ ((A * x) * y) = y. [para(88(a,1),35(a,2)),rewrite([143(9)])].

176 x \ (y * (x * z)) = (x * (y / x)) * z. [para(37(a,1),5(a,1,2))].

177 (x * (y * z)) / ((y * (x / y)) * z) = y. [para(37(a,1),6(a,1,1))].

180 x * ((x * y) * ((x * (z / x)) * u)) = (y * x) * (z * (x * u)). [para(37(a,1),11(a,1,2)),flip(a)].

184 A * (x * y) = x * (y * A). [para(17(a,1),37(a,2,2)),rewrite([88(5)])].

185 x * (A * (x * (y / x))) = y * (x * A). [para(17(a,2),37(a,1,2))].

186 x * (A * y) = x * (y * A). [para(17(a,2),37(a,2,2)),rewrite([17(4,R),185(5)]),flip(a)].

188 (x * y) \ (x * (A * y)) = A. [para(37(a,1),85(a,1,2)),rewrite([88(4)])].

192 x * (y * (((y * (x / y)) * (z / (y * (x / y)))) * u)) = y * (z * ((y * (x / y)) * u)). [para(37(a,1),37(a,1,2)),flip(a)].

197 x * (y * ((x * (x * ((y * (x \ z)) * x'))) * u)) = (z * (x * (y * x'))) * (x * (y * u)). [back_rewrite(81),rewrite([176(6),56(4)])].

198 (x * (y * (x \ (z * (x * (y * x'))')))) * (x * (y * u)) = x * (y * ((x * (z / x)) * u)). [back_rewrite(80),rewrite([176(14)])].

199 B * (A * ((B * x) * B)) = (x * B) * C. [back_rewrite(101),rewrite([184(7,R)])].

201 x \ A = A * x'. [para(86(a,1),5(a,1,2))].

202 A / (A * x') = x. [para(86(a,1),6(a,1,1))].

204 x * (A * ((x * y) * x')) = A * (y * x). [para(86(a,1),11(a,1,2)),rewrite([17(3,R),125(8,R)]),flip(a)].

208 x' * (A * x) = A. [para(31(a,1),86(a,1,2,2))].

209 ((A * x') * x) * y = x * (A * (x \ y)). [para(86(a,1),34(a,1,2,1)),flip(a)].

212 A / B = A * B'. [back_rewrite(117),rewrite([201(3)]),flip(a)].

214 B * (B * B) = A * B'. [back_rewrite(120),rewrite([212(8)])].

216 x / A = x * A'. [para(87(a,1),5(a,1,2)),rewrite([121(2)])].

218 x / A' = A * x. [para(7(a,1),87(a,1,2)),flip(a)].

219 (x * A') * (x * y) = x * ((x * A') * y). [para(87(a,1),11(a,1,1)),rewrite([17(13,R),87(13)]),flip(a)].

221 (x * A') * x = x * (x * A'). [para(87(a,1),12(a,1,1)),rewrite([17(12,R),87(12)]),flip(a)].

222 A * (A' * (A' * x)) = x * A'. [para(12(a,1),87(a,1,2))].

224 A * (x * (y * A')) = x * y. [para(87(a,1),34(a,1,2,1)),rewrite([121(3),216(3),17(11,R),87(11)])].

226 A \ x = x * A'. [back_rewrite(121),rewrite([216(4)])].

227 C * B' = B * A. [para(153(a,1),5(a,1,2)),rewrite([98(3)]),flip(a)].

231 (x / y) * (((x / y) * z) * (((x / y) * u) * y)) = (z * (x / y)) * ((u * (x / y)) * x). [para(38(a,1),11(a,1,2)),flip(a)].

232 (x / (y * z)) * (y * ((y * (x / (y * z))) * z)) = (y * (x / (y * z))) * x. [para(11(a,1),38(a,1,2))].

234 (x / y) * ((A * (x / y)) * y) = (A * (x / y)) * x. [para(17(a,1),38(a,2,1)),rewrite([17(4,R),17(9,R)])].

237 ((((x / y) * z) * y) * (x / y)) * x = (x / y) * (((z * (x / y)) * x) * y). [para(38(a,1),38(a,1,2,1)),flip(a)].

238 x' * A = A * x'. [para(17(a,1),201(a,2)),rewrite([201(2)]),flip(a)].

239 A * (A / x)' = x. [para(201(a,1),27(a,1))].

241 A / (A * x) = x'. [para(31(a,1),202(a,1,2,2))].

256 (x \ y) * x = x * (y * x'). [para(4(a,1),39(a,1,2,1)),flip(a)].

257 x \ (y * x) = (x * y) * x'. [para(39(a,1),5(a,1,2))].

259 (x / y) * (x * (x / y)') = y * (x / y). [para(7(a,1),39(a,1,2,1))].

269 ((x * y) * (x \ z)) * x = x * (((y * x) * z) * x'). [para(34(a,1),39(a,1,2,1)),flip(a)].

272 ((x * (y / x)) * z) * x = x * ((y * (x * z)) * x'). [para(37(a,1),39(a,1,2,1)),flip(a)].

273 (A * x') * x = A. [para(86(a,1),39(a,1,2,1)),rewrite([86(4)]),flip(a)].

277 (A * x) * x' = A. [para(208(a,1),39(a,1,2,1)),rewrite([31(4),208(4)]),flip(a)].

284 (B * C) * C' = B. [back_rewrite(152),rewrite([257(5),104(3)])].

285 (x * A) * x' = A. [back_rewrite(85),rewrite([257(3)])].

289 x * (A * (x \ y)) = A * y. [back_rewrite(209),rewrite([273(4)]),flip(a)].

296 x * (x * A)' = A'. [para(218(a,1),27(a,1,1)),rewrite([163(3)])].

297 A' * ((A * (A' * x)) * y) = x * (A' * y). [para(218(a,1),37(a,1,2,1,2)),rewrite([125(7,R)])].

302 (x * y)' * (x * ((x * (x * y)') * y)) = x * (x * y)'. [para(11(a,1),40(a,1,2))].

314 C \ (B * A) = B'. [para(227(a,1),5(a,1,2))].

317 C * ((C * x) * B') = A * ((x * C) * B). [para(227(a,1),11(a,1,2)),rewrite([184(6,R)]),flip(a)].

318 B' * (B' * C) = A. [para(227(a,1),12(a,1,1)),rewrite([285(6)]),flip(a)].

321 (A / x)' = x * A'. [para(239(a,1),5(a,1,2)),rewrite([226(2)]),flip(a)].

322 x * ((x * A') * (A / x)) = x. [para(239(a,1),40(a,2)),rewrite([321(3),321(6),17(8,R),87(8),219(7)])].

330 (x * ((x * y) * z)) * (z * ((z * x) * u)) = (x * z) * (((x * z) * (y * x)) * (z * u)). [para(11(a,1),41(a,1,2))].

335 (x * ((x * y) * z)) * (z * (z * x)) = (x * z) * (((x * z) * (y * x)) * z). [para(12(a,1),41(a,1,2))].

352 (A * (x * y)) * ((A * y) * z) = (A * y) * (((A * y) * x) * z). [para(87(a,1),41(a,1,1,2,1)),rewrite([17(16,R),87(16)])].

365 (x * A')' = A / x. [para(4(a,1),241(a,1,2)),rewrite([226(4)]),flip(a)].

369 A / x = A * x'. [para(273(a,1),6(a,1,1))].

371 (A * (A * x')) * x = A * A. [para(273(a,1),34(a,1,2)),rewrite([226(5),365(7),369(5),17(8,R)]),flip(a)].

376 (x * A')' = A * x'. [back_rewrite(365),rewrite([369(6)])].

378 A * (A' * x) = x. [back_rewrite(322),rewrite([369(5),125(7,R),204(8)])].

379 (A * x')' = x * A'. [back_rewrite(321),rewrite([369(2)])].

380 A * (A * x)' = x'. [back_rewrite(241),rewrite([369(4)])].

381 A' * (x * y) = x * (A' * y). [back_rewrite(297),rewrite([378(7)])].

382 A' * x = x * A'. [back_rewrite(222),rewrite([378(8)])].

390 (x * y) * (((x * y) * z) * (y * (y * x)')) = (z * (x * y)) * y. [para(8(a,1),42(a,1,2,2)),rewrite([3(4)]),flip(a)].

418 (x * ((x * y) * z))' * ((y * x) * (((y * x) * (x * ((x * y) * z))') * (x * z))) = (y * x) * (x * ((x * y) * z))'. [para(42(a,1),40(a,1,2))].

433 x * (A * (A * x')) = A * A. [para(277(a,1),37(a,1,2)),rewrite([216(6),376(8)]),flip(a)].

434 (x * (A * y)) * (x * y)' = A. [para(37(a,1),277(a,1,1)),rewrite([216(6),87(8)])].

439 B / C' = B * C. [para(284(a,1),6(a,1,1))].

440 C' * ((C' * (B * C)) * x) = B * (C' * x). [para(284(a,1),11(a,1,1)),flip(a)].

442 C' * (C' * (B * C)) = B * C'. [para(284(a,1),12(a,1,1)),flip(a)].

445 C' * (B * C) = B. [para(284(a,1),39(a,1,2,1)),rewrite([154(10),8(9),3(3)]),flip(a)].

450 C' * (B * x) = B * (C' * x). [back_rewrite(440),rewrite([445(8)])].

451 C' * B = B * C'. [back_rewrite(442),rewrite([450(8),9(7),3(5)])].

457 (x * y) * x' = x * (y / x). [para(46(a,1),5(a,1,2)),rewrite([257(2)])].

458 (x * y) / (y * (x / y)) = y. [para(46(a,1),6(a,1,1))].

475 x \ (y * x) = x * (y / x). [back_rewrite(257),rewrite([457(5)])].

476 A' \ x = A * x. [para(4(a,1),378(a,1,2)),flip(a)].

483 A * (x * (A' * y)) = x * y. [para(378(a,1),37(a,2,2)),rewrite([216(4),87(6)])].

488 x * ((x * (x * (y * x'))) * z) = (x * y) * (x * z). [para(4(a,1),47(a,1,1,2)),rewrite([256(5)]),flip(a)].

524 x / (A * x) = A'. [para(476(a,1),26(a,1,2))].

525 (A' * x) * y = (x * A') * y. [para(476(a,1),34(a,1,2,2)),rewrite([125(8,R),125(9,R),378(9)])].

528 x * (A' * x') = A'. [para(4(a,1),524(a,1,2)),rewrite([226(2),56(4)])].

590 (x * A)' = x \ A'. [para(296(a,1),5(a,1,2)),flip(a)].

591 x * (A' / x) = A'. [para(7(a,1),296(a,1,2,1)),rewrite([216(2),457(5)])].

596 x * (A' * (x \ y)) = A' * y. [para(296(a,1),34(a,1,2,1)),rewrite([590(8),256(9),528(10)])].

607 x * (x' * A') = A'. [para(238(a,1),296(a,1,2,1)),rewrite([379(5),55(5)])].

611 B' * C = B * A. [para(318(a,1),5(a,1,2)),rewrite([201(4),31(4),17(3)]),flip(a)].

659 A * ((A * A) * x) = A * (A * (A * x)). [para(273(a,1),49(a,1,1,2)),rewrite([125(6,R),184(14,R),277(13),184(12,R),17(11,R)])].

685 (B * A) / C = B'. [para(611(a,1),6(a,1,1))].

690 (A * x)' = x' * A'. [para(380(a,1),5(a,1,2)),rewrite([226(3)]),flip(a)].

691 (A' * x)' = A * x'. [para(378(a,1),380(a,1,2,1)),flip(a)].

701 x * (x * (x * (y * x'))) = (x * y) * x. [para(4(a,1),50(a,1,1,2)),rewrite([256(4)]),flip(a)].

746 (A' * x) * (A' * y) = A' * ((A' * x) * y). [para(382(a,2),11(a,1,1))].

750 x * (A' * (x * (y / x))) = y * (x * A'). [para(382(a,2),37(a,1,2))].

751 x * (A' * y) = x * (y * A'). [para(382(a,2),37(a,2,2)),rewrite([382(5,R),750(6)]),flip(a)].

800 B * (C' * B') = C'. [para(451(a,1),6(a,1,1)),rewrite([56(6)])].

802 (x * C') * (B * C') = C' * ((C' * x) * B). [para(451(a,1),11(a,1,2))].

821 x \ A' = x' * A'. [para(17(a,2),590(a,1,1)),rewrite([690(3)]),flip(a)].

828 A' / x = x' * A'. [para(591(a,1),5(a,1,2)),rewrite([821(3)]),flip(a)].

832 (x' * A') * x = A'. [para(26(a,1),591(a,1,2)),rewrite([821(3)])].

836 (x * (A' * y)) * (x * y) = (x * y) * (A' * (x * y)). [para(591(a,1),49(a,1,1,2,1)),rewrite([828(11),832(13),382(11,R)])].

840 x * ((x \ y) * (x \ z)) = (y / x) * z. [para(4(a,1),51(a,1,2)),flip(a)].

842 x * ((x \ y) * x') = y / x. [para(51(a,1),6(a,1,1)),rewrite([75(5)])].

850 B * (B * (A * (x * B'))) = (x / B) * C. [para(19(a,1),51(a,1,2)),rewrite([184(11,R),256(10),125(12)]),flip(a)].

855 (x / C) * (B * C) = C * ((C \ x) * B). [para(104(a,1),51(a,1,2))].

864 C * ((C \ x) * B') = A * ((x / C) * B). [para(227(a,1),51(a,1,2)),rewrite([184(6,R)]),flip(a)].

880 (B * C) * (C' * x) = C' * ((C' \ B) * x). [para(439(a,1),51(a,1,1))].

891 (A * x) * (y * A') = A' * ((A * x) * y). [para(382(a,1),51(a,1,2)),rewrite([218(3),476(11)])].

917 A * (A * B') = B * C. [para(214(a,1),50(a,2,2,2)),rewrite([12(8),214(8),125(8,R),457(7),24(5),3(4),17(3),89(7),95(6),19(6),125(14,R),457(13),24(11),3(10),17(9),184(10,R),12(9),214(9)]),flip(a)].

922 (A' * x) * x' = A'. [para(528(a,1),11(a,1)),rewrite([376(11),125(11,R),125(12,R),378(12)]),flip(a)].

934 x * (x' * (x \ y)) = x' * y. [para(4(a,1),55(a,1,2)),flip(a)].

936 x * (x' * x') = x'. [para(55(a,1),6(a,1,1)),rewrite([75(5)])].

937 (x / y) * ((x / y)' * y) = (x / y)' * x. [para(7(a,1),55(a,1,2)),flip(a)].

943 x * ((y / x) / x) = x * (x' * (x' * y)). [para(55(a,1),12(a,2,2)),rewrite([457(3),457(4),55(8)])].

953 C * (C' * B') = B * (A * C'). [para(227(a,1),55(a,1,2)),rewrite([184(6,R),451(5),125(6)]),flip(a)].

964 x * (x * (x' * (y / x))) = x' * (y * x). [para(46(a,1),55(a,1,2)),rewrite([55(7)]),flip(a)].

981 A * (B' * B') = B * B. [para(214(a,1),55(a,1,2)),rewrite([125(7,R),55(14),9(13),3(11)])].

986 (x * (A * y))' = A' * (x * y)'. [para(37(a,1),690(a,1,1)),rewrite([216(7),87(9),382(9,R)])].

989 (x * (A' * y))' = A * (x * y)'. [para(37(a,1),691(a,1,1)),rewrite([218(11),125(11,R),378(11)])].

991 (A' * x) * ((A * x') * y) = (A * x') * ((A' * x) * y). [para(691(a,1),55(a,1,1)),rewrite([691(15)]),flip(a)].

996 B \ C' = C' * B'. [para(800(a,1),5(a,1,2))].

1019 (x * (x * y)) / (y * x) = x * ((x * y) * (y * x)'). [para(11(a,1),56(a,2)),rewrite([12(2)])].

1026 C * (B' * C') = B'. [para(227(a,1),56(a,1,1)),rewrite([685(5)]),flip(a)].

1046 B * (B * (A * C')) = 1. [para(19(a,1),59(a,1,1,1,1)),rewrite([19(8),450(6),9(5),3(3),19(6),184(7,R),451(6),125(7)])].

1059 (B * C) * (B' * C') = 1. [para(284(a,1),59(a,1,1,1,1)),rewrite([284(11),156(7),55(8),55(7),611(6),19(6),284(9)])].

1077 (A' * x') * x = A'. [para(382(a,2),832(a,1,1))].

1115 (x * (y * A')) * ((x * y) * z) = (x * y) * ((x * (y * A')) * z). [para(87(a,1),60(a,2,1,2)),rewrite([86(12),17(10,R),224(10)])].

1193 A' * (B * C) = A * B'. [para(917(a,1),5(a,1,2)),rewrite([226(5),382(6,R)])].

1198 A * (x * (A * B')) = x * (B * C). [para(917(a,1),37(a,2,2)),rewrite([216(4),87(6)])].

1199 B * ((B * A') * C) = A. [para(917(a,1),208(a,1,2)),rewrite([690(5),31(3),219(8)])].

1208 A' * (B * A') = (B * C)'. [para(917(a,1),690(a,1,1)),rewrite([690(9),31(7),382(11,R)]),flip(a)].

1223 x \ x' = x' * x'. [para(936(a,1),5(a,1,2))].

1229 x * (y * ((y * (x / y))' * (y * (x / y))')) = y * (y * (x / y))'. [para(936(a,1),37(a,1,2)),flip(a)].

1239 x * (x' * (x' * x')) = x' * x'. [para(936(a,1),55(a,1,2)),flip(a)].

1241 x' / x = x' * x'. [para(936(a,1),56(a,1,1)),rewrite([12(7),1239(8)])].

1271 (x * (y * A')) * (x * y) = (x * y) * (x * (y * A')). [para(87(a,1),65(a,2,1,2)),rewrite([86(12),17(10,R),224(10)])].

1307 (x * A') * ((A' * x) * y) = A' * ((A' * (y * x)) * x). [para(382(a,1),65(a,1,1)),rewrite([31(11),184(11,R),378(11),746(16)])].

1348 C \ B' = B' * C'. [para(1026(a,1),5(a,1,2))].

1350 (B' * C') * (((B' * C') * C) * x) = B' * ((B' * C') * x). [para(1026(a,1),11(a,1,1)),flip(a)].

1353 ((B' * C') * C) * x = C * (B' * (C \ x)). [para(1026(a,1),34(a,1,2,1)),flip(a)].

1368 C * (C' * (C' * B')) = B' / C. [para(1026(a,1),56(a,1,1)),rewrite([12(13)]),flip(a)].

1373 (B' * C') * (C * (B' * (C \ x))) = B' * ((B' * C') * x). [back_rewrite(1350),rewrite([1353(13)])].

1377 B * (A * C') = B'. [para(1046(a,1),5(a,1,2)),rewrite([29(3)]),flip(a)].

1382 C * (C' * B') = B'. [back_rewrite(953),rewrite([1377(13)])].

1385 (x * y) / (x * z) = x * ((y / z) * x'). [para(7(a,1),75(a,1,1,2))].

1389 x / (x * y) = x * (y' * x'). [para(9(a,1),75(a,1,1,2)),rewrite([3(2)])].

1394 (A * (x * y)) / (y * A) = x. [para(17(a,1),75(a,1,2)),rewrite([87(11)])].

1428 (C' * (x * B)) / (B * C') = C' * (x * C). [para(451(a,1),75(a,1,2)),rewrite([31(15)])].

1445 (C * (x * (B' * C'))) / B' = C * (x * C'). [para(1026(a,1),75(a,1,2))].

1462 B' * B' = A * C'. [para(1377(a,1),5(a,1,2)),rewrite([1223(4)])].

1463 B' / (A * C') = B. [para(1377(a,1),6(a,1,1))].

1478 B * (A * (B' * C')) = A * C'. [para(1377(a,1),55(a,1,2)),rewrite([1462(5),125(12,R)]),flip(a)].

1484 A * (A * C') = B * B. [back_rewrite(981),rewrite([1462(6)])].

1487 (A * C') * (((A * C') \ B') * x) = B * ((A * C') * x). [para(1463(a,1),51(a,1,1)),flip(a)].

1499 (x * (y * x')) \ (x * z) = x * (y \ z). [para(4(a,1),76(a,1,2,2))].

1501 (x * (y * x')) \ x = x * y'. [para(8(a,1),76(a,1,2,2)),rewrite([3(5)])].

1505 A' * (x * (y * A)) = x * y. [para(17(a,1),76(a,1,2,2)),rewrite([86(4),226(5),382(6,R)])].

1527 B' * A' = B * C'. [para(1377(a,1),76(a,1,2)),rewrite([86(6),226(4)])].

1541 (B * A') * C = A * B'. [para(1199(a,1),5(a,1,2)),rewrite([201(3)]),flip(a)].

1551 x' \ x = x * x. [para(31(a,1),1223(a,1,2)),rewrite([31(4),31(4)])].

1562 (x' * x') * x = x'. [para(1241(a,1),7(a,1,1))].

1563 x / x' = x * x. [para(31(a,1),1241(a,1,1)),rewrite([31(4),31(4)])].

1579 (x' * (y * x)) * z = x' * (y * (x' \ z)). [para(31(a,1),77(a,1,1,2,2))].

1596 A * (C * (x * (C \ B))) = C * (x * B'). [para(314(a,1),77(a,2,2,2)),rewrite([184(9,R),77(8)])].

1600 A' * (x * (A * y)) = x * y. [para(476(a,1),77(a,2,2,2)),rewrite([31(5),184(5,R),378(5)]),flip(a)].

1617 x * (y * (x \ (z * (x * (y * x'))'))) = x * (y * (((x \ z) / x') * (y \ x'))). [para(77(a,1),56(a,1,1)),rewrite([1385(7),1385(5),77(8),77(17)]),flip(a)].

1626 x * (y * (((x \ (x * (y * x'))') / x') * (y \ x'))) = (x * (y * x'))'. [para(77(a,1),936(a,1)),rewrite([1617(12)])].

1631 C * (B' * (C \ x)) = B' * x. [para(1026(a,1),77(a,1,1)),flip(a)].

1633 (x * (y * (z * (y \ x')))) * u = x * (y * (z * (y \ (x \ u)))). [para(77(a,1),77(a,1,1,2)),rewrite([77(11)])].

1641 x * (y * (((x \ z) / x') * u)) = x * (y * ((x * (z / x)) * u)). [back_rewrite(198),rewrite([1617(8),1633(11),5(6),5(5)])].

1645 (B' * C') * (B' * x) = B' * ((B' * C') * x). [back_rewrite(1373),rewrite([1631(12)])].

1648 x * (y * ((x * ((x * (y * x'))' / x)) * (y \ x'))) = (x * (y * x'))'. [back_rewrite(1626),rewrite([1641(12)])].

1650 x * (x * x)' = x'. [para(1563(a,1),27(a,1,1)),rewrite([163(2)])].

1652 (x * x) * (x' * y) = x' * ((x * x) * y). [para(1563(a,1),51(a,1,1)),rewrite([1551(7)])].

1657 (x * x)' = x' * x'. [para(1650(a,1),5(a,1,2)),rewrite([1223(2)]),flip(a)].

1672 x * (y * (x * (y * x'))') = x * (y * (x * (y \ x'))). [para(78(a,1),6(a,1,1)),rewrite([1385(6),1385(4),26(2),77(5)]),flip(a)].

1724 (C' / B) * C = B'. [para(1377(a,1),78(a,2)),rewrite([86(8),8(5),3(3),996(7),850(11)])].

1733 C' / B = B' / C. [para(1724(a,1),6(a,1,1)),flip(a)].

1735 C * (B' / C) = B'. [para(1724(a,1),46(a,2)),rewrite([1733(6),943(9),1368(11)])].

1750 B' / C = B' * C'. [para(1735(a,1),5(a,1,2)),rewrite([1348(4)]),flip(a)].

1761 C' / B = B' * C'. [back_rewrite(1733),rewrite([1750(8)])].

1764 C' * B' = B' * C'. [para(1382(a,1),5(a,1,2)),rewrite([1348(4)]),flip(a)].

1777 B \ C' = B' * C'. [back_rewrite(996),rewrite([1764(9)])].

1778 B * (B' * C') = C'. [back_rewrite(800),rewrite([1764(6)])].

1820 B * (B * C) = A * A. [para(214(a,1),89(a,1,2)),rewrite([125(8,R),457(7),369(5),86(7),89(11),95(10),19(10)]),flip(a)].

1834 (B * C) * B = A * A. [back_rewrite(156),rewrite([1820(10)])].

1863 B * ((B \ x) * (B * C)) = A * (A * (x / B)). [para(1820(a,1),51(a,1,2)),rewrite([184(6,R),17(5,R)]),flip(a)].

1868 (B * C) \ (A * A) = B. [para(1834(a,1),5(a,1,2))].

1971 B' \ (A * C') = B'. [para(1462(a,1),5(a,1,2))].

1983 B' * (B' * (x * B)) = A * ((x / B') * C'). [para(1462(a,1),51(a,1,2)),rewrite([125(8,R),256(16),31(15)]),flip(a)].

1987 A' * (B * B) = A * C'. [para(1484(a,1),5(a,1,2)),rewrite([226(5),382(6,R)])].

1991 (A * C') * (B * B) = A * ((B * B) * C'). [para(1484(a,1),12(a,1,1)),rewrite([125(8,R),17(18,R),1484(18)]),flip(a)].

1992 A * (x * (A * C')) = x * (B * B). [para(1484(a,1),37(a,2,2)),rewrite([216(4),87(6)])].

2088 (x * B') * (B * C') = B' * (A' * (B' * x)). [para(1527(a,1),11(a,1,2)),rewrite([382(16,R)])].

2095 C' * (B' * x) = B' * (C' * x). [para(1527(a,1),47(a,1,1,2)),rewrite([55(7),1778(7),382(15),1527(15),55(15),1778(15)])].

2102 B * (B * C') = A'. [para(1527(a,1),607(a,1,2))].

2242 (A * C') * B = B'. [para(1462(a,1),1562(a,1,1))].

2244 (A * C') \ B' = B. [para(2242(a,1),5(a,1,2))].

2255 (A * C') * (B * x) = B * ((A * C') * x). [back_rewrite(1487),rewrite([2244(11)])].

2256 A * ((B * B) * C') = 1. [back_rewrite(1991),rewrite([2255(8),2242(7),8(4)]),flip(a)].

2266 (x' * x') * ((x * x) * y) = (x * x) * ((x' * x') * y). [para(1657(a,1),55(a,1,1)),rewrite([1657(9)])].

2279 C * A' = B * B. [para(1462(a,1),1657(a,1,1)),rewrite([690(5),31(3),31(7),31(8)])].

2306 (x * C) * (B * B) = C * (A' * (C * x)). [para(2279(a,1),11(a,1,2)),rewrite([382(12,R)])].

2308 (B * B) * C = A * A. [para(2279(a,1),12(a,2,2)),rewrite([382(4),2279(4),102(10),104(9),1820(10)])].

2322 (x / C) * (B * B) = A' * x. [para(2279(a,1),51(a,1,2)),rewrite([382(12,R),596(13)])].

2323 (B * B) / C = A'. [para(2279(a,1),56(a,1,1)),rewrite([528(12)])].

2327 (x * A') * (B * B) = A' * ((A' * x) * C). [para(2323(a,1),38(a,1,1)),rewrite([2323(7),2323(13)]),flip(a)].

2378 A * (A * A) = C * C. [para(2308(a,1),50(a,1,1,2)),rewrite([184(7,R),17(6,R),125(6),17(5),19(6),2306(7),17(6,R),125(7,R),382(6),2279(6),125(6),17(5),19(6),102(14),10

4(13),1820(14),184(13,R),17(12,R),125(12),17(11),19(12),125(10,R),2308(9)]),flip(a)].

2387 A' * (C * C) = A * A. [para(2378(a,1),5(a,1,2)),rewrite([226(5),382(6,R)])].

2392 A * (x * (A * A)) = x * (C * C). [para(2378(a,1),37(a,2,2)),rewrite([216(4),87(6)])].

2403 A' * (A' * A') = C' * C'. [para(2378(a,1),690(a,1,1)),rewrite([1657(4),1657(9),382(13,R)]),flip(a)].

2535 A * ((x / (A * y)) * y) = x. [para(125(a,2),7(a,1))].

2541 x * (A * ((x * y) * (x \ z))) = A * ((y * x) * z). [para(34(a,1),125(a,1,2)),flip(a)].

2598 A * (A * (A * x)) = x * (C * C). [para(125(a,1),50(a,2,2)),rewrite([17(6,R),2392(12)])].

2650 A * ((A * A) * x) = x * (C * C). [back_rewrite(659),rewrite([2598(12)])].

2687 B' * (B' * C') = A * (C' * C'). [para(1778(a,1),111(a,1,2)),rewrite([1223(4),1462(5),12(7),17(6,R),125(7,R),1223(13),1462(14),802(18),17(15,R),2242(17),1764(14)]),flip(a)].

2693 (x * (y / x)) * (x \ z) = x \ (y * z). [para(7(a,1),128(a,1,2,1)),flip(a)].

2698 (x * A) * (y * A') = A' * ((A * x) * y). [para(17(a,1),128(a,2,1)),rewrite([128(5),226(4),891(6),226(10)]),flip(a)].

2701 B \ (C * x) = C * (B \ x). [para(19(a,1),128(a,2,1)),rewrite([95(6),19(6)])].

2709 x \ (A * y) = A * (x \ y). [para(86(a,1),128(a,2,1)),rewrite([273(4)])].

2719 C \ B = B * C'. [para(284(a,1),128(a,1,2)),rewrite([104(6),1223(10),880(12),256(12),31(11),450(11),9(10),3(8),451(7)])].

2738 x \ (A' * y) = A' * (x \ y). [para(528(a,1),128(a,2,1)),rewrite([1077(5)])].

2741 x' \ ((x * (y / x)) * z) = (x * (x' * y)) * (x' \ z). [para(55(a,1),128(a,2,1)),rewrite([457(4)])].

2742 (x * y) * (x' * A') = A' * (x * (y / x)). [para(821(a,1),128(a,2,2)),rewrite([382(4,R),2738(5),475(4)]),flip(a)].

2750 x \ (x' * y) = x' * (x \ y). [para(936(a,1),128(a,2,1)),rewrite([1562(4)])].

2796 A * (B' \ C') = B'. [back_rewrite(1971),rewrite([2709(7)])].

2797 A * (A * (B * C)') = B. [back_rewrite(1868),rewrite([2709(7),201(6)])].

2803 A * (C * (x * (B * C'))) = C * (x * B'). [back_rewrite(1596),rewrite([2719(5)])].

3010 x * ((x * y) * (A' * (x * (z / x)))) = (y * x) * (A' * (z * x)). [para(382(a,2),132(a,2,2)),rewrite([821(5),2742(7)])].

3020 x * (A' * ((x * y) * (x \ z))) = A' * ((y * x) * z). [para(528(a,1),132(a,1,2,1)),rewrite([1077(12)])].

3128 (B * B) * C' = A'. [para(2256(a,1),5(a,1,2)),rewrite([29(3)]),flip(a)].

3129 C' * (A' * x) = A' * (C' * x). [para(2256(a,1),42(a,1,1)),rewrite([450(9),451(8),2102(9),2(8),3128(12),3128(14),17(12,R),8(12),2(13)])].

3140 A' * ((A' * x) * (C * C)) = A * x. [para(2387(a,1),11(a,1,2)),rewrite([184(7,R),17(6,R),87(6)]),flip(a)].

3141 A' * (x * (C * C)) = (A * A) * x. [para(2387(a,1),34(a,1,2,1)),rewrite([476(8),125(8,R),2650(8),382(13,R),2387(13)])].

3151 A * (C' * C') = A' * A'. [para(2387(a,1),691(a,1,1)),rewrite([1657(4),1657(10)]),flip(a)].

3161 A' * ((A * A) * x) = A * x. [back_rewrite(3140),rewrite([3141(10),1652(7)])].

3165 B' * (B' * C') = A' * A'. [back_rewrite(2687),rewrite([3151(15)])].

3383 B' \ C' = B * C'. [para(2796(a,1),5(a,1,2)),rewrite([226(4),1527(5)]),flip(a)].

3384 A * (x * (B * C')) = x * B'. [para(2796(a,1),37(a,2,2)),rewrite([216(4),87(6),3383(6)])].

3528 A * (B * C)' = B * A'. [para(2797(a,1),5(a,1,2)),rewrite([226(3)]),flip(a)].

3536 (x * A) * ((A * x) \ y) = y. [para(137(a,1),4(a,1))].

3537 (A * x) * ((x * A) \ y) = y. [para(137(a,2),4(a,1))].

3679 B * ((C * (B \ x)) * B') = (C * x) / B. [para(139(a,1),56(a,1,1)),flip(a)].

3693 (A * x) \ y = (x * A) \ y. [para(4(a,1),172(a,1,2)),flip(a)].

3729 (A * A) * x = A * (A * x). [para(138(a,1),17(a,1)),rewrite([226(9),2698(11),3161(11),17(8,R)])].

3778 (A * B') * C' = A * (B' * C'). [para(3383(a,1),138(a,1,2,2)),rewrite([2088(11),17(10,R),125(11,R),382(10),1527(10),125(10),1377(10),1462(7),125(7,R)]),flip(a)].

3794 A' * (x * (C * C)) = A * (A * x). [back_rewrite(3141),rewrite([3729(11)])].

3860 (A * x) * (((A * x) * y) * x) = A * ((y * (A * x)) * (x * x)). [para(184(a,2),48(a,1,2)),rewrite([125(7,R)]),flip(a)].

3877 (x * (y * A))' = A' * (x * y)'. [para(184(a,1),690(a,1,1)),rewrite([382(9,R)])].

3961 (x * (y * A)) / (A * y) = x. [para(186(a,1),6(a,1,1))].

4027 (A * B') \ (B * C) = A. [para(214(a,1),188(a,1,1)),rewrite([125(10),17(9),19(10)])].

4138 x * ((A * (x \ y)) * x') = (A * y) / x. [para(289(a,1),56(a,1,1)),flip(a)].

4144 x * (x' * (C * C)) = C * C. [para(2378(a,1),289(a,2)),rewrite([2709(5),201(4),2598(7)])].

4332 (x \ y) * (x / (x \ y)) = (x \ y) \ y. [para(4(a,1),475(a,1,2)),flip(a)].

4333 x * (x' * (x' * y)) = x \ y. [para(7(a,1),475(a,1,2)),rewrite([943(4)]),flip(a)].

4408 x * ((y / x) / x) = x \ y. [back_rewrite(943),rewrite([4333(8)])].

4556 (B * C)' = B' * C'. [para(1059(a,1),5(a,1,2)),rewrite([29(5)])].

4571 A * (B' * C') = B * A'. [back_rewrite(3528),rewrite([4556(5)])].

4577 A' * (B * A') = B' * C'. [back_rewrite(1208),rewrite([4556(11)])].

4583 (A * B') * C' = B * A'. [back_rewrite(3778),rewrite([4571(14)])].

4588 B * (B * A') = A * C'. [back_rewrite(1478),rewrite([4571(8)])].

4601 B' * (B' * (C' * C')) = A' * (A' * C'). [para(4556(a,1),1657(a,2,1)),rewrite([155(7),104(4),1834(6),184(5,R),17(4,R),986(6),690(6),382(7,R),4556(17),1645(19),12(18),1764(17),2095(18)]),flip(a)].

4857 (A * x) / (y * A) = x / y. [para(7(a,1),1394(a,1,1,2))].

5012 A' * (x * (B * B)) = x * (A * C'). [para(1987(a,1),37(a,2,2)),rewrite([218(7),125(7,R),378(7)])].

5032 A * ((B * B) \ C') = A'. [para(1987(a,1),475(a,1,2)),rewrite([2709(8),828(17),1657(15),1462(16),382(18,R),125(18,R),378(18),3128(14)])].

5103 (x / (A * y)) * y = x * A'. [para(2535(a,1),5(a,1,2)),rewrite([226(2)]),flip(a)].

5104 A * (A * (x / (A * A))) = x. [para(17(a,2),2535(a,1,2,1,2)),rewrite([17(7,R)])].

5288 C * (A' * A') = A * C'. [para(1026(a,1),2701(a,1,2)),rewrite([1223(4),1462(5),2750(12),1777(11),3165(13)]),flip(a)].

5306 x \ (y * A) = A * (x \ y). [para(17(a,1),2709(a,1,2))].

5309 x \ (y * (A * z)) = A * (x \ (y * z)). [para(37(a,1),2709(a,1,2)),rewrite([216(8),87(10)])].

5310 A * (A * (x \ B')) = x \ (B * C). [para(917(a,1),2709(a,1,2)),rewrite([2709(10)]),flip(a)].

5312 x \ (C * C) = x' * (C * C). [para(2378(a,1),2709(a,1,2)),rewrite([5306(9),201(8),2598(11)])].

5315 x \ (y * (z * A)) = A * (x \ (y * z)). [para(184(a,1),2709(a,1,2))].

5344 x * ((x * y) \ (x \ z)) = (y * x) \ z. [para(4(a,1),162(a,1,2)),flip(a)].

5345 x * ((x * (y / x)) \ z) = y \ (x * z). [para(7(a,1),162(a,1,1)),flip(a)].

5388 (A * B') \ (B * x) = B * ((A * B') \ x). [para(214(a,1),162(a,2,2,1)),rewrite([12(5),214(5)])].

5400 x' \ (x * y) = x * (x' \ y). [para(936(a,1),162(a,2,2,1)),rewrite([1562(4)])].

5485 (x * y) * (y / (x * y)) = y * (x * (y * (y * x)')). [para(162(a,1),475(a,1)),rewrite([162(3),163(2)]),flip(a)].

5520 B * ((A * B') \ C) = A. [back_rewrite(4027),rewrite([5388(8)])].

5529 (x * ((A * B') \ B)) * (B * (((A * B') \ B) * C)) = ((A * B') \ B) * ((((A * B') \ B) * x) * (B * C)). [para(5520(a,1),147(a,1,2,2,2)),rewrite([17(19,R),917(19)]),flip(a)].

5568 (x \ y) * (x * (y * x'))' = y \ (x \ y). [para(4(a,1),163(a,1,1)),rewrite([256(5)]),flip(a)].

5569 x * (x * (y / x))' = y \ x. [para(7(a,1),163(a,1,1)),flip(a)].

5571 (x * (x * y)) \ x = x * (x * (y * x))'. [para(12(a,1),163(a,1,1))].

5580 (A * B') \ B = A * C'. [para(214(a,1),163(a,2,2,1)),rewrite([12(5),214(5),690(12),31(10),4588(12)])].

5630 x * (y * ((y * (x / y))' * (y * (x / y))')) = x \ y. [back_rewrite(1229),rewrite([5569(13)])].

5639 (A * C') * (((A * C') * x) * (B * C)) = A * ((x * (A * C')) * B). [back_rewrite(5529),rewrite([5580(6),5580(12),273(12),184(9,R),5580(15),5580(19)]),flip(a)].

5725 (x * A') * ((A' * x) \ y) = y. [para(3537(a,1),130(a,2)),rewrite([216(2),216(5),216(8),17(11,R),87(11),5344(9)])].

5741 (x' * (y / x')) * x = x' \ y. [para(9(a,1),176(a,1,2,2)),rewrite([3(3)]),flip(a)].

5742 (x * ((x * y)' / x)) * y = x'. [para(9(a,1),176(a,1,2)),rewrite([29(2)]),flip(a)].

5749 C \ (x * (B * C)) = (C * (x / C)) * B. [para(104(a,1),176(a,1,2,2))].

5754 (C * (x / C)) * B' = A * (C \ (x * B)). [para(227(a,1),176(a,1,2,2)),rewrite([5315(6)]),flip(a)].

5773 x \ (y * A') = A' * (x \ y). [para(607(a,1),176(a,1,2,2)),rewrite([2742(11),4408(9)])].

5782 (x * (y / x))' = x \ (y \ x). [para(936(a,1),176(a,2)),rewrite([5630(9)]),flip(a)].

5784 x \ (y * (y * (x * (x * (z * x'))))) = (x * (z * (y / x))) * (x * (y / x)). [para(65(a,1),176(a,2)),rewrite([37(7)])].

5811 A' * (x * (y * (A * z))) = x * (y * z). [para(125(a,1),176(a,1,2,2)),rewrite([226(6),382(7,R),216(10),87(12)])].

5849 A * (A * (x * B')) = x * (B * C). [para(1193(a,1),176(a,1,2,2)),rewrite([5309(8),476(7),218(12),125(12,R),378(12)])].

5861 A * (A * (x * C')) = x * (B * B). [para(1987(a,1),176(a,1,2,2)),rewrite([5309(8),476(7),218(12),125(12,R),378(12)])].

6173 (x * y) * (A' * (z * y)) = (x * y) * (z * (y * A')). [para(382(a,2),180(a,1,2,2)),rewrite([3010(8)])].

6260 (x * y) * (z * (A * u)) = A * ((x * y) * (z * u)). [para(289(a,1),180(a,2,2,2)),rewrite([125(7,R),2693(6),125(6,R),2541(7)]),flip(a)].

6374 x \ (x \ y) = (y / x) / x. [para(4408(a,1),5(a,1,2))].

6379 x * (y * ((z / (y * (x / y))) / (y * (x / y)))) = x \ (y * z). [para(4408(a,1),37(a,1,2)),rewrite([5345(4)]),flip(a)].

6386 x * (x' * ((y / x) / x)) = x' * (x \ y). [para(4408(a,1),55(a,1,2)),flip(a)].

6387 x * (((y / x) / x) * x') = (x \ y) / x. [para(4408(a,1),56(a,1,1)),flip(a)].

6410 ((x / y) / y) * (y / ((x / y) / y)) = ((x / y) / y) \ (y \ x). [para(4408(a,1),475(a,1,2)),flip(a)].

6423 (x / y) \ y = y * (y \ x)'. [para(4408(a,1),163(a,2,2,1)),rewrite([7(3)])].

6426 (x * (y / x)) \ z = x \ (y \ (x * z)). [para(4408(a,1),176(a,2)),rewrite([6379(8)]),flip(a)].

6430 (A * A) \ x = x / (A * A). [para(4408(a,1),3729(a,1)),rewrite([5104(16)])].

6540 (x * A') / y = x / (y * A). [para(4(a,1),4857(a,1,1)),rewrite([226(5)]),flip(a)].

6541 (A * x) / y = x / (y * A'). [para(7(a,1),4857(a,1,2)),rewrite([216(5)])].

6545 (x * (A * y)) / (z * A) = (x * y) / z. [para(37(a,1),4857(a,1,1)),rewrite([216(9),87(11)])].

6546 (A' * x) / y = x / (y * A). [para(378(a,1),4857(a,1,1)),flip(a)].

6548 x / (A' * A') = A * (A * x). [para(832(a,1),4857(a,1,2)),rewrite([218(5)]),flip(a)].

6550 (B * B) / (x * A) = C' / (x * A'). [para(1484(a,1),4857(a,1,1)),rewrite([6541(11)])].

6555 (x * A) / y = x / (y * A'). [para(184(a,2),4857(a,1,1)),rewrite([6545(7),6541(3)]),flip(a)].

6585 x * ((A * (x \ y)) * x') = y / (x * A'). [back_rewrite(4138),rewrite([6541(9)])].

7252 (B * B) \ C' = A' * A'. [para(5032(a,1),5(a,1,2)),rewrite([1223(4)]),flip(a)].

7297 x * (x * (A * (y / x))) = y * (x * A). [para(37(a,1),185(a,1,2)),rewrite([216(3),87(5),216(4),87(6),216(8),87(10)])].

7464 A * (x * (y * (A' * z))) = x * (y * z). [para(192(a,1),378(a,1,2)),rewrite([828(4),607(6),828(10),607(12),828(12),607(14),218(12),125(12,R),378(12)])].

7477 (x * (y * (A * z)))' = A' * (x * (y * z))'. [para(192(a,1),690(a,1,1)),rewrite([369(2),86(4),369(7),86(9),369(8),86(10),216(8),87(10),382(11,R)])].

7487 x * (A' * (A' * (x \ y))) = A' * (y * A'). [para(922(a,1),192(a,2,2,2)),rewrite([218(7),125(7,R),378(7),218(7),125(7,R),378(7),218(7),690(7),2742(9),4408(7)])].

7693 x * (x * (y / (x * A'))) = (y * A) * x. [para(87(a,1),197(a,1,2)),rewrite([6585(6),86(10),8(12),3(10)])].

7753 (x / y) / y = y' * (y' * x). [para(936(a,1),197(a,2,2)),rewrite([457(10),56(8),12(8),4333(9),2750(5),6374(4),6386(6),4333(6),6374(2),936(6),12(6)])].

7949 (x' * (x' * y)) * (x / (x' * (x' * y))) = (x' * (x' * y)) \ (x \ y). [back_rewrite(6410),rewrite([7753(2),7753(6),7753(12)])].

7963 x \ (y * x') = (x \ y) / x. [back_rewrite(6387),rewrite([7753(2),50(6),4333(7)])].

7973 x \ (x \ y) = x' * (x' * y). [back_rewrite(6374),rewrite([7753(4)])].

8136 (x * x) / (A * x) = x * A'. [para(219(a,1),3961(a,1,1)),rewrite([17(5,R),87(5)])].

8289 (x / (y * A')) * y = A * x. [para(7(a,1),224(a,1,2)),flip(a)].

8301 A * (x * (B * B)) = x * C. [para(2279(a,1),224(a,1,2,2))].

8304 (x * y) * (z * A') = A' * ((x * y) * z). [para(224(a,1),128(a,2,1)),rewrite([17(7,R),224(7),226(4),382(5,R),226(8)]),flip(a)].

8383 A' * (x * C) = x * (B * B). [para(8301(a,1),5(a,1,2)),rewrite([226(4),382(5,R)])].

8384 (x / (B * B)) * C = A * x. [para(7(a,1),8301(a,1,2)),flip(a)].

8401 (x * (B * B)) \ (x * C) = A. [para(8301(a,1),475(a,1,2)),rewrite([369(17),125(19,R),8(18),3(10)])].

8410 C * (C * (x / (B * B))) = (A * x) * C. [para(8384(a,1),12(a,1,1)),flip(a)].

8424 (x / (A * C')) * C = A * (A * x). [para(125(a,2),8384(a,2)),rewrite([6541(6),382(6,R),1987(6)])].

8435 C * (C * (x / (B * B)))' = (A * x) \ C. [para(8384(a,1),163(a,1,1)),flip(a)].

8447 (B * (B * (x * B'))) \ ((x / B) * C) = A. [para(51(a,1),8401(a,1,1)),rewrite([256(5)])].

8547 (x \ y) \ (x * (y * x')) = x. [para(256(a,1),5(a,1,2))].

8549 (x * (x * y)') * (y * x) = x * ((x * y) * (y * x)'). [para(11(a,1),256(a,2)),rewrite([163(2)])].

8574 x * ((x \ y) / x) = y * x'. [para(256(a,1),475(a,1,2)),rewrite([5(4)]),flip(a)].

8639 (x' * (C * C)) * x = C * C. [para(371(a,1),34(a,1,2)),rewrite([2378(5),226(6),376(8),17(10,R),2598(10)]),flip(a)].

8677 x / (A * A) = x * (A' * A'). [para(371(a,1),163(a,1,1)),rewrite([6430(4),433(10),1657(8)])].

8911 (x * y) \ (x * (y / x)) = x'. [para(457(a,1),5(a,1,2))].

8912 (x * (y / x)) / x' = x * y. [para(457(a,1),6(a,1,1))].

8917 (x' * y) * x = x' * (y / x'). [para(31(a,1),457(a,1,2))].

8925 x * (x * ((y / x) * x')) = (y * x) * x'. [para(46(a,1),457(a,1,1)),rewrite([56(6)]),flip(a)].

8931 x \ (y / x) = (x \ y) * x'. [para(457(a,1),50(a,2,2,2)),rewrite([55(4),55(5),4333(5),55(8),55(9),4333(9)]),flip(a)].

8954 (A * (x * y)) * x' = x * (y / (x * A')). [para(125(a,2),457(a,1,1)),rewrite([6541(8)])].

8955 x \ (y * (x / y)) = (x * y) * (x \ y'). [para(457(a,1),128(a,1,2))].

9010 x' * ((C * C) / x') = C * C. [back_rewrite(8639),rewrite([8917(6)])].

9013 x * (x * (x' * y)) = x' \ y. [back_rewrite(5741),rewrite([8917(5),7753(5),31(3),31(3),55(4),55(3)])].

9040 x' \ (y / x) = x' * (y * x). [back_rewrite(964),rewrite([9013(5)])].

9289 B * (C * ((B \ x) * B')) = C * (x / B). [para(842(a,1),102(a,1,2)),flip(a)].

9326 x' * (x' * (y * x)) = y / x. [para(842(a,1),256(a,2)),rewrite([7973(2),8917(5),56(5),31(4)])].

9336 A * ((x / B') * C') = x / B. [back_rewrite(1983),rewrite([9326(8)]),flip(a)].

9341 (x * y) * (A' * z) = A' * ((x * y) * z). [para(1505(a,1),11(a,2,2,1)),rewrite([382(6,R),1505(6)])].

9342 (x * A') * ((x * A') * y) = A' * ((y * (x * A')) * x). [para(38(a,1),1505(a,1,2)),rewrite([216(4),216(10),216(13)]),flip(a)].

9362 (x * y) * (z * (A' * u)) = A' * ((x * y) * (z * u)). [para(1505(a,1),180(a,1,2,1)),rewrite([218(8),125(8,R),378(8),382(12,R),1505(12)]),flip(a)].

9407 (x * y) * (z * (y * A')) = A' * ((x * y) * (z * y)). [back_rewrite(6173),rewrite([9341(6)]),flip(a)].

9423 (x * (A' * y)) * (x * y) = A' * ((x * y) * (x * y)). [back_rewrite(836),rewrite([9341(12)])].

9464 (x * (y * A')) * (x * y) = A' * ((x * y) * (x * y)). [back_rewrite(1271),rewrite([9407(12)])].

9751 (x * (A' * A')) * ((B * B) * ((A' * (A' * ((B * B) * x))) * C)) = (A' * (A' * ((B * B) * x))) * x. [para(2308(a,1),232(a,1,1,2)),rewrite([8677(4),2308(17),8677(16),9362(19),8304(18),2308(31),8677(30),9362(33),8304(32)])].

10171 (C * C) * x = x * (C * C). [para(4144(a,1),12(a,2,2)),rewrite([8917(6),9010(7)])].

10198 (x * (C * C)) * x = x * (x * (C * C)). [para(4144(a,1),50(a,1,1,2)),rewrite([8917(11),9010(12)])].

10200 (C * C) / x = x' * (C * C). [para(4144(a,1),56(a,1,1)),rewrite([10198(11),4333(12),5312(8)])].

10213 (C * C) * (x * (C' * C')) = x. [para(4144(a,1),129(a,1,2,1)),rewrite([8917(6),10200(6),31(3),55(6),4144(6),1385(10),26(5),1657(7)])].

10237 (C * C) \ (x * y) = x * ((C * C) \ y). [para(4144(a,1),162(a,2,2,1)),rewrite([8917(6),10200(6),31(3),55(6),4144(6)])].

10239 (C * C) \ x = x * (C' * C'). [para(4144(a,1),163(a,2,2,1)),rewrite([8917(6),10200(6),31(3),55(6),4144(6),1657(8)])].

10242 (C * C) * (x * (C * C))' = x'. [para(4144(a,1),177(a,1,1)),rewrite([1563(6),55(6),9(5),3(5),10200(8),10171(9,R)])].

10284 (x * y) * (C' * C') = x * (y * (C' * C')). [back_rewrite(10237),rewrite([10239(5),10239(11)])].

10335 (C * C) * (x / (C * C)) = x. [para(10171(a,1),5(a,1,2)),rewrite([475(8)])].

10412 (C * C) * (x / C) = C * (C * (x * C')). [para(10171(a,2),51(a,1)),rewrite([256(11)])].

10414 x' * ((C * C) * x) = C * C. [para(10171(a,2),55(a,1,2)),rewrite([4144(12)])].

10508 (C * C) * ((C * C) * x)' = x'. [para(10171(a,1),163(a,2)),rewrite([5312(8),10171(9,R),10242(9),10171(10,R)]),flip(a)].

10546 ((C * C) * x) * x' = C * C. [para(10171(a,2),457(a,1,1)),rewrite([10200(10),4144(12)])].

10600 x / (C * C) = x * (C' * C'). [para(10335(a,1),5(a,1,2)),rewrite([10239(4)]),flip(a)].

10624 x * ((C' * C') / x) = C' * C'. [para(10335(a,1),163(a,1,1)),rewrite([10600(4),5(7),10600(9),10600(15),10171(21,R),10213(21),457(13)]),flip(a)].

10647 A * (x * (B' * C')) = x * (B * A'). [para(4571(a,1),37(a,2,2)),rewrite([216(4),87(6)])].

10666 A' * (x * (B * A')) = x * (B' * C'). [para(4571(a,1),176(a,1,2,2)),rewrite([226(7),382(8,R),216(11),87(13)])].

10676 (A * B') * (((A * B') * x) * C') = A' * ((x * (A * B')) * B). [para(4583(a,1),11(a,1,2)),rewrite([8304(10)]),flip(a)].

10690 A' * ((A' * ((x * (A * B')) * B)) * B) = (A' * ((x * B') * B)) * B. [para(4583(a,1),49(a,1,2)),rewrite([10676(13),8304(15),4583(22),4583(26),6260(29),125(30,R),9342(29),8304(26),378(30)])].

10873 x * (x * (y / (A * x))) = (y * A') * x. [para(5103(a,1),12(a,1,1)),flip(a)].

11094 C * ((C \ x) * (A' * A')) = A * ((x / C) * C'). [para(5288(a,1),51(a,1,2)),rewrite([125(7,R)]),flip(a)].

11183 (x * ((x / y) / x)) * (x / y)' = (x * y) * (x \ y'). [para(259(a,1),176(a,1,2)),rewrite([8955(3)]),flip(a)].

11651 (x \ (y \ x))' = x * (y / x). [para(5782(a,1),31(a,1,1))].

11746 (x \ y) * ((x \ y) \ y)' = x' * (x' * y). [para(26(a,1),6423(a,1,1)),rewrite([7973(2)]),flip(a)].

11813 x * ((A' * (x * y)) * x') = (A' * y) * x. [para(382(a,1),272(a,2,2,1)),rewrite([828(3),607(5),382(8,R)]),flip(a)].

11978 A' * (A' * (A' * x)) = x * (C' * C'). [para(95(a,1),6540(a,2,2)),rewrite([8677(7),11(9),382(8,R),2378(14),10600(13)])].

11979 (B * B) / x = C / (x * A). [para(2279(a,1),6540(a,1,1))].

11986 A' * (A' * (x' * A')) = (C' * C') / x. [para(221(a,1),6540(a,1,1)),rewrite([2403(8),6540(14),17(12,R),828(13),3877(11),690(11),382(16,R)]),flip(a)].

12028 C / (A * (x * A)) = C' / (x * A'). [back_rewrite(6550),rewrite([11979(6),17(5,R)])].

12038 C / (A * (A * x)) = C' / (x * A'). [para(12(a,1),11979(a,2,2)),rewrite([11979(6),17(5,R),12028(6)]),flip(a)].

12039 C / (A * (x \ (B * B))) = x. [para(11979(a,1),26(a,1)),rewrite([17(7,R)])].

12052 A * (x \ (B * B)) = x \ C. [para(12039(a,1),27(a,1,1)),flip(a)].

12165 x \ (B * B) = A' * (x \ C). [para(12052(a,1),5(a,1,2)),rewrite([226(4),382(5,R)]),flip(a)].

12197 x / (C' * C') = x * (C * C). [para(221(a,1),6541(a,2,2)),rewrite([6548(8),2598(6),2403(12)]),flip(a)].

12666 (A * ((B * B) * (x * C'))) * C' = A' * (A' * ((B * B) * x)). [para(7252(a,1),77(a,2,2,2)),rewrite([1657(7),1462(8),6260(9),9362(22),8304(21)])].

12831 (x \ (y / x')) / x = x \ y. [para(7(a,1),7963(a,1,2)),flip(a)].

12845 (x * y) * (x' * x') = x * ((y / x) * x'). [para(7963(a,1),128(a,1)),rewrite([475(2),56(3),1223(7)]),flip(a)].

12879 x * (((x \ y) / x) * x') = (y * x') / x. [para(7963(a,1),842(a,1,2,1))].

12902 (A' * A') * x = A' * (x * A'). [para(4(a,1),8136(a,1,2)),rewrite([226(2),226(5),8304(7),221(6),6546(8),1385(7),216(5),382(6,R),11813(9),226(8),382(12,R)])].

12909 A' * (A' * (x * A')) = x * (C' * C'). [para(50(a,1),8136(a,2)),rewrite([9362(13),12(12),382(11,R),9362(12),9341(11),12(10),11978(13),10284(10),10284(9),4333(18),22

6(12),1385(14),218(12),483(11),457(8),10624(7)]),flip(a)].

12962 (C' * C') / x = x' * (C' * C'). [back_rewrite(11986),rewrite([12909(10)]),flip(a)].

12989 C * (C' * ((C * x) * B')) = A * (C' * ((x * C) * B)). [para(317(a,1),55(a,1,2)),rewrite([125(9,R)]),flip(a)].

13108 (A' * x) * (B * B) = A' * ((A' * x) * C). [para(8383(a,1),11(a,2)),rewrite([382(7),2279(7),2327(7)]),flip(a)].

13112 A' * (A' * (x * C)) = x * (A * C'). [para(8383(a,1),12(a,2,2)),rewrite([382(5,R),382(8,R),5012(15)])].

13113 (B * B) * ((B * B) * x) = A' * ((A' * (x * C)) * C). [para(8383(a,2),12(a,1,1)),rewrite([13108(9)]),flip(a)].

13466 (x' * (x' * y)) \ (y / x) = x. [para(842(a,1),8547(a,1,2)),rewrite([7973(2)])].

13638 (x \ y) * (x * z) = x * ((y * x') * z). [para(8574(a,1),11(a,2,2,1)),rewrite([7(3)])].

13649 x * (x' * ((x \ y) / x)) = x' * (y * x'). [para(8574(a,1),55(a,1,2)),flip(a)].

13683 (x \ y) \ x = x * (y * x')'. [para(8574(a,1),163(a,2,2,1)),rewrite([7(3)])].

13954 B * (B * ((x * B') * C)) = A * (A * (x / B)). [back_rewrite(1863),rewrite([13638(7)])].

14511 (x * (y * x)) \ (x * y) = x'. [para(6(a,1),8911(a,1,2,2))].

14579 (x * y) / x' = x * (y * x). [para(6(a,1),8912(a,1,1,2))].

14594 (x \ y) / (x * (x' * y)) = x'. [para(8912(a,1),458(a,1,2,2)),rewrite([457(4),7753(2),4333(5),55(4)])].

14596 x' \ (x \ y) = x * (x' * y). [para(8912(a,1),475(a,2,2)),rewrite([457(5),7753(3),4333(6),55(6)])].

14611 (x * (x' * y))' = x * (x' * y'). [para(8912(a,1),5782(a,1,1,2)),rewrite([55(3),6426(9),8(7),29(7),14596(8)])].

14613 (x * y) \ x' = x \ (y * x)'. [para(8912(a,1),6423(a,1,1)),rewrite([5400(8),9040(7),14611(9),55(10),4333(10)])].

15863 ((C * C) * x) * (x' / ((C * C) * x)) = x'. [para(10414(a,1),475(a,1,2)),rewrite([5312(8),10171(9,R),10508(9)]),flip(a)].

15881 ((C * C) * x') * x = C * C. [para(31(a,1),10546(a,1,2))].

15920 (C * C) * ((C' * C') * x) = x. [para(10546(a,1),302(a,1,1,1)),rewrite([1657(4),10546(19),1657(17),10284(19),10213(19),8(11),3(11),2266(10),10546(20),1657(18),10284(20),10213(20)])].

15923 ((C * C) * x)' = x' * (C' * C'). [para(10546(a,1),8911(a,1,1)),rewrite([15863(14),10239(5)]),flip(a)].

16540 (B * A') * ((A' * ((B * A') * x)) * (B * C)) = (A' * x) * B. [para(1541(a,1),330(a,1,2,2)),rewrite([86(14),17(10,R),378(10),382(9),382(13),8304(17)]),flip(a)].

16705 x * ((x / y) / x) = (x \ y)'. [para(27(a,1),11651(a,1,1,2)),flip(a)].

16744 (x \ y)' * (x / y)' = (x * y) * (x \ y'). [back_rewrite(11183),rewrite([16705(3)])].

16779 (x * y) * (B * B) = A' * ((x * y) * C). [para(12165(a,1),34(a,1,2,2)),rewrite([9341(7),3020(8)]),flip(a)].

17088 x \ (y / x') = x * (y * x'). [para(12831(a,1),7(a,1,1)),rewrite([256(2)]),flip(a)].

17394 (x * (y * y)) \ (x * y) = y'. [para(37(a,1),14511(a,1,1)),rewrite([46(5)])].

17492 (A' * ((x * y) * (x * y))) \ (x * y) = (x * (y * A'))'. [para(224(a,1),14511(a,1,1,2)),rewrite([9464(6),17(12,R),224(12)])].

17499 (x * (y * A'))' = A * (x * y)'. [para(483(a,1),14511(a,1,1,2)),rewrite([9423(6),17(12,R),483(12),17492(8),989(10)])].

17558 x * (x * (y * x')) = y / x'. [para(4(a,1),14579(a,1,1)),rewrite([256(4)]),flip(a)].

17562 (x' * y) / x = x' * (y * x'). [para(31(a,1),14579(a,1,2))].

17563 (x * y) / y' = x * (y * y). [para(37(a,1),14579(a,2)),rewrite([46(3)])].

17739 (C * C) * (x / C) = x / C'. [back_rewrite(10412),rewrite([17558(13)])].

17750 (x / y) / y' = (x * y) * y'. [back_rewrite(8925),rewrite([17558(5)])].

17758 (x / B') \ ((x / B) * C) = A. [back_rewrite(8447),rewrite([17558(7)])].

17858 (x * (y * (z / x))) * (x * (z / x)) = x \ (z * (z * (y / x'))). [back_rewrite(5784),rewrite([17558(4)]),flip(a)].

17873 (x * y) * x = x * (y / x'). [back_rewrite(701),rewrite([17558(4)]),flip(a)].

17875 (x * y) * (x * z) = x * ((y / x') * z). [back_rewrite(488),rewrite([17558(4)]),flip(a)].

18391 B * (B * (A * (x / B'))) = (x * B) * C. [back_rewrite(199),rewrite([17873(6),125(8)])].

18406 x * (((y * (z / x)) / x') * (z / x)) = x \ (z * (z * (y / x'))). [back_rewrite(17858),rewrite([17875(6)])].

19277 (x * y) * ((x * y) * (z * x)) = x * ((((x * z) * y) / x') * y). [back_rewrite(49),rewrite([17875(5)]),flip(a)].

19782 x \ (x \ y)' = (x / y) / x. [para(16705(a,1),5(a,1,2))].

19786 (x / y) * (x * z) = x * ((x \ y)' * z). [para(16705(a,1),11(a,2,2,1)),rewrite([7(3)])].

19788 (x / y) * x = x * (x \ y)'. [para(16705(a,1),12(a,2,2)),rewrite([7(3)])].

19806 x * (x' * ((x / y) / x)) = x' * (x \ y)'. [para(16705(a,1),55(a,1,2)),flip(a)].

19816 x \ ((x / y) * z) = (x \ y)' * (x \ z). [para(16705(a,1),128(a,2,1)),rewrite([7(3)])].

19841 (x / y) \ (x * z) = x * ((x \ y)' \ z). [para(16705(a,1),162(a,2,2,1)),rewrite([7(3)])].

19855 x \ (x / y) = (x \ y)' * x'. [para(16705(a,1),457(a,1,1)),rewrite([7753(7),4333(10)]),flip(a)].

19866 (x * (C' * C'))' = x' * (C * C). [para(16705(a,1),10171(a,1)),rewrite([10239(4),10200(11),10600(16),10284(18),1652(17),457(16),24(14),3(13),9(12),3(10)])].

21017 (x * (y * y)) * y' = x * y. [para(17394(a,1),4(a,1,2))].

21018 (x * (x \ y)') \ x = (y \ x)'. [para(4(a,1),17394(a,1,2)),rewrite([840(4),19788(2)])].

21019 (x \ (y * y))' * (x \ y) = y'. [para(7(a,1),17394(a,1,1)),rewrite([19816(4)])].

21080 A * (((C * C) * (x / (B * B))) \ x) = C'. [para(8384(a,1),17394(a,1,2)),rewrite([10171(8,R),2709(11)])].

21100 x * ((x * (C * C)) \ C) = C'. [para(10171(a,2),17394(a,1,1)),rewrite([162(7)])].

21110 (x * (y * y)) * y = x * (y * (y * y)). [para(17394(a,1),6423(a,2,2,1)),rewrite([1385(4),1389(2),936(4),1499(7),5400(3),1551(2),31(7)]),flip(a)].

21118 (A' * (x * C)) \ (x * B) = B'. [para(8383(a,2),17394(a,1,1))].

21128 (C * C) * (x' * ((C * C) * (x * (x * (C * C)))))' = x' * (C' * C'). [para(10414(a,1),17394(a,1,2)),rewrite([17875(10),1657(8),12197(10),17873(9),10200(9),31(6),5312(15),10171(16,R),15923(21)])].

21375 x / (y \ x)' = x * (x \ y)'. [para(4(a,1),17563(a,1,1)),rewrite([840(7),19788(5)])].

21379 (x * y') / y = x * (y' * y'). [para(31(a,1),17563(a,1,2))].

21435 x / (B * B) = A * (x / C). [para(2322(a,1),17563(a,1,1)),rewrite([1657(7),1462(8),6546(8),17(6,R),1484(6),17875(13),1563(11),17873(12),1563(12),214(12),86(12),17(8,R)])].

21460 x' * ((C * C) * (x * (x * (C * C)))) = (C * C) * (x * (C * C)). [para(10414(a,1),17563(a,1,1)),rewrite([15923(8),10200(11),19866(8),31(2),10171(8,R),17875(18),1657(16),12197(18),17873(17),10200(17),31(14)]),flip(a)].

21473 x * (((x \ y) / x) * x') = y * (x' * x'). [back_rewrite(12879),rewrite([21379(8)])].

21479 A * ((A * (x / C')) \ x) = C'. [back_rewrite(21080),rewrite([21435(8),125(9,R),17739(8)])].

21524 (A * x) \ C = A' * (x \ C). [back_rewrite(8435),rewrite([21435(6),125(7,R),690(8),5782(6),382(8,R),596(9)]),flip(a)].

21539 (A * x) * C = A * (x * C). [back_rewrite(8410),rewrite([21435(6),125(7,R),125(8,R),46(7)]),flip(a)].

21544 (x * (C * C))' = x' * (C' * C'). [back_rewrite(21128),rewrite([21460(14),15923(12),10213(15)])].

21633 (A * (x / C)) \ x = B * B. [para(21435(a,1),27(a,1,1))].

21635 (A' * x) * C = x * (B * B). [para(21435(a,1),46(a,1,2,2)),rewrite([125(11,R),125(12,R),13113(11),7(9),378(10)])].

21645 A * (x / (A * C)) = x / C. [para(21435(a,1),6540(a,1)),rewrite([6540(6),17(4,R),17(11,R),125(11),17(10),19(11)])].

21700 (B * B) * ((B * B) * x) = A' * (A' * (C * (C * x))). [back_rewrite(13113),rewrite([21635(17),16779(16),12(16)])].

21704 (A' * (A' * ((B * B) * x))) * x = (x * A') * ((x * (A' * A')) * C). [back_rewrite(9751),rewrite([21635(21),16779(20),21635(20),17873(19),1657(18),1462(19),9341(22),21700(21),11978(24),12845(21),56(16),5103(16),457(15),6540(13),17(11,R),10873(14),1115(12)]),flip(a)].

21724 (x * A) * C = A * (x * C). [para(17(a,1),21539(a,1,1))].

21727 (x * (A * y)) * C = A * ((x * y) * C). [para(37(a,1),21539(a,1,1)),rewrite([216(9),87(11)])].

21740 (x * A) * (x \ C) = A * C. [para(21539(a,1),128(a,1,2)),rewrite([176(5),369(2),86(4)]),flip(a)].

21836 x * ((x * A) \ C) = B * B. [para(6(a,1),21633(a,1,1,2)),rewrite([162(5)])].

21922 A' * (A' * (C * (C * (x / (A * C'))))) = x * C. [para(2279(a,1),335(a,1,2,2)),rewrite([21635(7),5012(7),102(10),104(9),1820(10),184(9,R),17(8,R),1992(8),8301(6),382(6),2279(6),382(9),2279(9),8304(12),21635(14),17873(13),1657(12),1462(13),21700(15)]),flip(a)].

22052 A * ((x * A') * C') = x * C'. [para(5288(a,1),335(a,1,2,2)),rewrite([12902(11),21635(13),16779(12),17875(14),31(7),216(6),12902(13),382(12,R),13112(13),125(10,R),125(11,R),378(11),125(12,R),8(11),3(9),17(8,R),21635(15),1987(14),21635(19),1987(18),9362(23),8304(22),21635(25),16779(24),21635(24),16779(23),13112(25),125(22,R),125(23,R),3860(22),10284(21),11(20),17(16,R),12(19),17(18,R),125(19,R),3151(19),3129(18),382(17,R),7464(20),483(16)])].

22102 x / (A * C) = A' * (x / C). [para(21645(a,1),5(a,1,2)),rewrite([226(4),382(5,R)]),flip(a)].

22182 C / (A' * (x \ C)) = x * A. [para(21740(a,1),6(a,1,1)),rewrite([6541(6),382(6,R)])].

22191 (A * (C / x)) * x = A * C. [para(27(a,1),21740(a,1,2)),rewrite([17(4,R)])].

22260 (x * A') * (x \ C) = B * B. [para(7(a,1),21836(a,1,2,1)),rewrite([216(2)])].

22515 C / (x * A') = A * (C / x). [para(22191(a,1),6(a,1,1)),rewrite([6541(4)])].

22518 (A * C) * x = A * (C * x). [para(22191(a,1),12(a,1,1)),rewrite([7297(10),184(8,R)])].

22538 (A * (C / x)) * (x * (x \ C)') = A * x. [para(22191(a,1),128(a,1,2)),rewrite([2709(6),27(5),17(6,R),6423(9)]),flip(a)].

22566 (A * (C / (x * A))) * x = C. [para(22191(a,1),1505(a,1,2)),rewrite([125(6,R),382(5),2279(5),125(5),17(4),19(5)]),flip(a)].

22570 (A * x) * (C / x) = A * (x * (C / x)). [para(22191(a,1),269(a,2,2,1)),rewrite([17(4,R),6423(7),22538(9),22518(14),125(15,R),19786(14),16744(14),34(14),457(10)])].

22832 A * (C / (x * A)) = C / x. [para(22566(a,1),6(a,1,1)),flip(a)].

22849 (A * (C' / (x * A'))) * x = B * B. [para(22566(a,1),1505(a,1,2)),rewrite([382(4),2279(4),17(9,R),12028(10)]),flip(a)].

22850 (x * A') * C = A' * (x * C). [para(22566(a,1),231(a,2,2)),rewrite([17(4,R),524(5),17(6,R),524(7),17(9,R),524(10),17(9,R),8(9),17(9,R),2(10),125(9,R),21635(8),8301(8),17(9,R),524(10)]),flip(a)].

23040 C / (x * A) = A' * (C / x). [para(22832(a,1),5(a,1,2)),rewrite([226(4),382(5,R)]),flip(a)].

23041 A * (C' / (x * A')) = A' * (C / x). [para(12(a,1),22832(a,1,2,2)),rewrite([12038(7),23040(12)])].

23044 C / (A * x) = A' * (C / x). [para(137(a,1),22832(a,1,2,2)),rewrite([17(6,R),12028(7),23041(8)]),flip(a)].

23089 (B * B) / x = A' * (C / x). [back_rewrite(11979),rewrite([23040(8)])].

23090 (A' * (C / x)) * x = B * B. [back_rewrite(22849),rewrite([23041(8)])].

23095 A' * (A' * (C / x)) = C' / (x * A'). [back_rewrite(12038),rewrite([23044(6),23044(6)])].

23102 (x / C') / (x / C) = C * C. [para(17739(a,1),6(a,1,1))].

23109 (C * C) * (x * (y / C)) = x * (y / C'). [para(17739(a,1),37(a,2,2)),rewrite([10600(10),10213(13)])].

23129 (x / C) \ (x / C') = C * C. [para(17739(a,1),475(a,1,2)),rewrite([10200(14),4144(16)])].

23132 (x / C') \ (x / C) = (x / C) * (x / C')'. [para(17739(a,1),163(a,1,1)),rewrite([51(14),256(13),17558(15)])].

23144 x / (A * C') = A' * (x / C'). [para(6540(a,1),17739(a,1,2)),rewrite([17(6,R),22102(7),9341(9),17739(8),6540(12),17(10,R)]),flip(a)].

23147 (x / C) * (x / C')' = C' * C'. [para(17739(a,1),8911(a,1,1)),rewrite([10600(12),10213(15),23132(6),1657(11)])].

23174 A' * (A' * (C * (C * (A' * (x / C'))))) = x * C. [back_rewrite(21922),rewrite([23144(11)])].

23188 (x / C') * (B * B) = A * (A * x). [back_rewrite(8424),rewrite([23144(5),21635(8)])].

23190 (x / C') \ (x / C) = C' * C'. [back_rewrite(23132),rewrite([23147(13)])].

23191 (x / B) * C = A * (x / B'). [para(17758(a,1),4(a,1,2)),rewrite([17(5,R)]),flip(a)].

23198 B * (B * (A * (x * B'))) = A * (x / B'). [back_rewrite(850),rewrite([23191(13)])].

23268 x * ((x \ y) / x') = y * x. [para(4(a,1),17873(a,1,1)),flip(a)].

23269 (x * y) \ (x * (y / x')) = x. [para(17873(a,1),5(a,1,2))].

23300 (x * (x' * (y / x))) * z = x * ((x' * y) * (x \ z)). [para(17873(a,1),77(a,1,1,2)),rewrite([31(3)])].

23331 (x * (y / x')) \ x = x * (x * (x * y))'. [para(17873(a,1),163(a,1,1))].

23500 x * ((x \ y)' * x') = x / y. [para(19782(a,1),256(a,1,1)),rewrite([7(3)]),flip(a)].

23502 x * ((C' * C') * x') = C' * C'. [para(5312(a,1),19782(a,1,2,1)),rewrite([21544(6),31(2),5(7),10600(9),56(12)]),flip(a)].

23505 x \ ((x \ y) / x)' = (x / (y * x')) / x. [para(7963(a,1),19782(a,1,2,1))].

23576 x * (x * (x / y))' = (y \ x)'. [para(19788(a,1),163(a,1,1)),rewrite([21018(4)]),flip(a)].

23692 (x / (y * y)) * y = x * y'. [para(7(a,1),21017(a,1,1)),flip(a)].

23696 (x * (y' * y')) * y = x * y'. [para(31(a,1),21017(a,1,2))].

23720 (x * (A * C')) * B = x * B'. [para(1462(a,1),21017(a,1,1,2)),rewrite([31(8)])].

23752 (x / C) * B = (A' * x) * B'. [para(2322(a,1),21017(a,1,1)),flip(a)].

23812 (A * C') * (((A * C') * x) * (B * C)) = A * (x * B'). [back_rewrite(5639),rewrite([23720(22)])].

23815 C * ((C \ x) * B') = A * ((A' * x) * B'). [back_rewrite(864),rewrite([23752(12)])].

23818 (x * (C * C)) \ C = x \ C'. [para(21100(a,1),5(a,1,2)),flip(a)].

23872 (x * (A * y)) \ C = A' * ((x * y) \ C). [para(37(a,1),21524(a,1,1)),rewrite([216(10),87(12)])].

23905 (x * (B * B)) * C = C * (C * (A' * x)). [para(21635(a,1),12(a,1,1))].

23906 A' * (A' * (C * (C * x))) = A * ((x * C') * C). [para(12(a,1),21635(a,2)),rewrite([5012(7),21727(7),21700(15)]),flip(a)].

23909 (x * (A' * y)) * C = A' * ((x * y) * C). [para(37(a,1),21635(a,1,1)),rewrite([218(11),125(11,R),378(11),16779(11)])].

23983 A * (((A' * (x / C')) * C') * C) = x * C. [back_rewrite(23174),rewrite([23906(16)])].

23998 (A' * (A' * ((B * B) * x))) * x = x * (x * C'). [back_rewrite(21704),rewrite([23909(22),22850(21),13112(22),17875(20),828(15),31(13),125(19,R),22052(19)])].

24077 C / (A' * x) = A * (C / x). [para(27(a,1),22182(a,1,2,2)),rewrite([17(9,R)])].

24226 (A' * x) * (x \ C) = B * B. [para(22260(a,1),34(a,2)),rewrite([476(10),125(10,R),125(11,R),378(11)])].

24390 C / (x * (A * y)) = A' * (C / (x * y)). [para(37(a,1),23044(a,1,2)),rewrite([216(11),87(13)])].

24402 (A' * (C / x)) * (x * y) = x * ((A' * (x \ C)) * y). [para(23089(a,1),51(a,1,1)),rewrite([12165(11)])].

24404 A * ((B * B) * x) = C * x. [para(23089(a,1),185(a,1,2,2,2)),rewrite([483(8),46(4),184(8,R)]),flip(a)].

24451 A' * (A' * ((B * B) * x)) = C * (x * (C' * C')). [back_rewrite(12666),rewrite([24404(9),457(8),21379(6)]),flip(a)].

24470 (C * (x * (C' * C'))) * x = x * (x * C'). [back_rewrite(23998),rewrite([24451(10)])].

24494 C * ((B * B) \ x) = A * x. [para(4(a,1),24404(a,1,2)),flip(a)].

24495 (B * B) * x = A' * (C * x). [para(24404(a,1),5(a,1,2)),rewrite([226(4),382(5,R)]),flip(a)].

24509 (C * x) / (A * x) = B * B. [para(24404(a,1),177(a,1,1)),rewrite([21435(10),369(9),1484(11),17875(9),1563(7),17873(8),1563(8),214(8),86(8)])].

24521 C * ((x / C) * C') = C * (x * (C' * C')). [back_rewrite(24451),rewrite([24495(8),11978(11),12845(8)])].

24802 (B * B) \ x = A * (C \ x). [para(24494(a,1),5(a,1,2)),rewrite([2709(4)]),flip(a)].

24813 x / (A' * ((C \ x) \ x)) = A * (C \ x). [para(24494(a,1),458(a,1,1)),rewrite([24802(6),24802(11),23044(12),9341(14),22570(13),4332(12),125(10,R),378(10),6541(6),382(6,R),24802(11)])].

24819 (A * x) * C' = A * (x * C'). [para(24494(a,1),457(a,1,1)),rewrite([24802(10),6541(12),2279(12),21435(12),125(13,R),8574(12)])].

24895 (C * (x * A')) / x = B * B. [para(4(a,1),24509(a,1,2)),rewrite([226(3)])].

25113 (C / x) * (A' * (C * (C / x)')) = (x * A') * (C / x). [para(23090(a,1),269(a,2,2,1)),rewrite([382(5,R),6423(8),24402(10),922(9),24495(15)]),flip(a)].

25141 (x / C) \ (C' * C') = (x / C')'. [para(23102(a,1),5782(a,1,1,2)),rewrite([51(6),256(5),17558(7),23190(12)]),flip(a)].

25155 ((x / C) / (x / C')) / (x / C) = (x / C')'. [para(23129(a,1),19782(a,1,2,1)),rewrite([1657(6),25141(8)]),flip(a)].

25349 A * ((x * C') * C) = A * x. [para(6(a,1),23191(a,2,2)),rewrite([21379(5),1462(5),21727(7)])].

25411 x / C' = x * C. [back_rewrite(23983),rewrite([25349(13),378(8)])].

25421 ((x / C) / (x * C)) / (x / C) = (x * C)'. [back_rewrite(25155),rewrite([25411(5),25411(11)])].

25503 A' * (C * (C * x)) = A * (A * x). [back_rewrite(23188),rewrite([25411(3),16779(6),12(6)])].

25555 (C * C) * (x * (y / C)) = x * (y * C). [back_rewrite(23109),rewrite([25411(10)])].

25600 A * ((A * (x * C)) \ x) = C'. [back_rewrite(21479),rewrite([25411(5)])].

25676 (x * C') * C = x. [para(25411(a,1),6(a,1))].

25677 (x * C) * C' = x. [para(25411(a,1),7(a,1,1))].

25678 (x * C) \ x = C'. [para(25411(a,1),27(a,1,1))].

25681 x / C = x * C'. [para(25411(a,1),46(a,1,2,2)),rewrite([9326(8)])].

25682 (x * C) * (C' * y) = C' * ((C' \ x) * y). [para(25411(a,1),51(a,1,1))].

25692 (C' * (x * C))' = C' \ (x \ C'). [para(25411(a,1),5782(a,1,1,2))].

25693 (x * C) \ C' = C' * (C' \ x)'. [para(25411(a,1),6423(a,1,1))].

25699 (x \ C')' = C / x'. [para(25411(a,1),16705(a,1,2,1)),rewrite([56(3),17558(5)]),flip(a)].

25700 C' * ((C' / x) * C) = (C' \ x)'. [para(25411(a,1),16705(a,1,2))].

25701 C * (C * x) = x * (C * C). [para(25411(a,1),17563(a,1)),rewrite([12(4)])].

25725 (C * C) * (x * (y * C')) = x * (y * C). [back_rewrite(25555),rewrite([25681(5)])].

25765 (x * C')' * (C' * C') = (x * C)'. [back_rewrite(25421),rewrite([25681(2),1385(6),25681(4),23502(8),25681(7),12962(9)])].

25801 C * (x * (C' * C')) = C \ x. [back_rewrite(24521),rewrite([25681(3),12(7),4333(8)]),flip(a)].

25872 x / (A * C) = A' * (x * C'). [back_rewrite(22102),rewrite([25681(8)])].

25935 C * ((C \ x) * (A' * A')) = A * (C' * (C' * x)). [back_rewrite(11094),rewrite([25681(13),12(17)])].

25965 C * (x * (B' * C')) = A * (C \ (x * B)). [back_rewrite(5754),rewrite([25681(3),77(8),1348(5)])].

25966 C \ (x * (B * C)) = C * (x * (B * C')). [back_rewrite(5749),rewrite([25681(9),77(13),2719(10)])].

25979 (x * C') * (B * C) = C * ((C \ x) * B). [back_rewrite(855),rewrite([25681(2)])].

26082 (C \ x) * x = x * (x * C'). [back_rewrite(24470),rewrite([25801(8)])].

26088 (C \ (x * B)) / (B * C') = C * (x * C'). [back_rewrite(1445),rewrite([25965(8),6541(9),1527(9)])].

26106 (x * C') \ x = C. [para(25676(a,1),5(a,1,2))].

26107 C * (C * (x * (C \ y))) = x * (C * y). [para(25676(a,1),11(a,1,1)),rewrite([77(10)]),flip(a)].

26110 (C' * (x * C')) * x = x * (C' * (C' \ x')'). [para(25676(a,1),38(a,1,2)),rewrite([25681(2),25681(5),17875(7),19788(7),25681(13)]),flip(a)].

26134 (x * C') * (C / (x * C')) = x * (x * C')'. [para(25676(a,1),457(a,1,1)),flip(a)].

26139 (C' * C') * (x * (C' * C')) = C' * (C' * ((C' * C') * x)). [para(25676(a,1),237(a,2,2)),rewrite([25681(4),25681(12),10284(14),936(13),12(12),25681(16),25681(21)]),flip(a)].

26158 C' * ((C' \ x)' * C) = C' / x. [para(19788(a,1),25676(a,1,1)),rewrite([8917(9),25411(9)])].

26183 C * ((x * C) * (C \ y)) = (C * x) * y. [para(25677(a,1),77(a,1,1,2)),flip(a)].

26185 C' * (x * (C * (C * y))) = C' \ (x * y). [para(25677(a,1),128(a,1,2,1)),rewrite([1579(13),7973(12),31(9),31(10)]),flip(a)].

26216 C' * ((C' \ x) * (x * C)) = x / (x * C)'. [para(25677(a,1),14579(a,1,1)),rewrite([25682(12)]),flip(a)].

26279 (C / x')' = x \ C'. [para(25678(a,1),5782(a,2,2)),rewrite([56(3),17558(5)])].

26288 (x * C') * (C * y) = C * ((C \ x) * y). [para(25681(a,1),51(a,1,1))].

26297 (C * (x * C'))' = C \ (x \ C). [para(25681(a,1),5782(a,1,1,2))].

26300 (A' * x) * C' = A' * (x * C'). [para(25681(a,1),6546(a,1)),rewrite([17(9,R),25872(10)])].

26302 (x \ C)' = C' / x'. [para(25681(a,1),16705(a,1,2,1)),rewrite([56(4),17558(6)]),flip(a)].

26303 C * ((C / x) * C') = (C \ x)'. [para(25681(a,1),16705(a,1,2))].

26412 (C' / x')' = x \ C. [para(26106(a,1),5782(a,2,2)),rewrite([56(4),17558(6)])].

26435 (C' * (C' * x)')' = C / (x * C')'. [para(163(a,1),25699(a,1,1))].

26455 (C / x)' = x' \ C'. [para(31(a,1),26279(a,1,1,2))].

26477 (C / x) * (A' * (C * (x' \ C'))) = (x * A') * (C / x). [back_rewrite(25113),rewrite([26455(8)])].

26507 (C * (C * x)')' = C' / (x * C)'. [para(163(a,1),26302(a,1,1))].

26513 (x \ C) * (C * (C * (C' / x'))) = C * C. [para(26302(a,1),4144(a,1,2,1)),rewrite([25701(10,R)])].

26523 ((C * C) * (C' / x')) * (x \ C) = C * C. [para(26302(a,1),15881(a,1,1,2))].

26535 (C' / x)' = x' \ C. [para(31(a,1),26412(a,1,1,2))].

26615 (x' \ C) * (C' / x) = 1. [para(26535(a,1),9(a,1,1))].

26639 (x' \ C) * ((C * C) * (C' / x)) = C * C. [para(26535(a,1),10414(a,1,1))].

26693 (C * C) * x = C * (C * x). [para(25701(a,2),46(a,2)),rewrite([10600(10),25725(13),9(7),3(5)])].

26708 C' * (x * (C * C)) = C' \ x. [para(25701(a,1),55(a,1,2)),rewrite([55(13),9013(14)])].

26710 x * (C * (C * x')) = C * C. [para(25701(a,2),55(a,2,2)),rewrite([55(6),4144(6)]),flip(a)].

26711 (C * (C * x)) / x = C * C. [para(25701(a,2),56(a,1,1)),rewrite([26693(10),26710(11)])].

26940 (C * (C * (C' / x'))) * (x \ C) = C * C. [back_rewrite(26523),rewrite([26693(8)])].

27099 (x' \ C) * (C * (C * (C' / x))) = C * C. [back_rewrite(26639),rewrite([26693(10)])].

27264 (C * (C * x))' = x' * (C' * C'). [back_rewrite(15923),rewrite([26693(4)])].

27265 C * (C * ((C' * C') * x)) = x. [back_rewrite(15920),rewrite([26693(10)])].

27681 (x \ y) / x' = x * (y / x). [para(23268(a,1),5(a,1,2)),rewrite([475(2)]),flip(a)].

27696 (x * x) * (((x * x) \ y) / (x' * x')) = y * (x * x). [para(1657(a,1),23268(a,1,2,2))].

27827 (C * x) \ (C * (x * C)) = C. [para(25411(a,1),23269(a,1,2,2))].

27926 x / (y * y) = x * (y' * y'). [para(23692(a,1),6(a,1,1)),rewrite([21379(3)]),flip(a)].

27991 (x * x) * ((x * x) * (y * (x' * x'))) = y * (x * x). [back_rewrite(27696),rewrite([27926(7),31(5),31(5),256(5),1657(4)])].

28033 (x * (C * C)) * (x \ C') = C. [para(23818(a,1),4(a,1,2))].

28035 C \ (C * x)' = C' * (C' \ x)'. [para(11(a,1),23818(a,1,1)),rewrite([17873(5),25411(5),5571(8),12(6),27264(8),25801(11),25693(10)])].

28036 C / (x \ C') = x * (C * C). [para(23818(a,1),26(a,1,2))].

28039 C' * (C' * x)' = C * (C * x)'. [para(51(a,1),23818(a,1,1)),rewrite([256(5),17558(7),25411(3),163(4),25681(7),163(11)]),flip(a)].

28053 (C * (x * C))' = C \ (x \ C'). [para(23818(a,1),5782(a,2,2)),rewrite([25681(7),21017(8)])].

28077 C' / (x * C)' = C / (x * C')'. [back_rewrite(26435),rewrite([28039(7),26507(6)])].

28084 (C * (C * x)')' = C / (x * C')'. [back_rewrite(26507),rewrite([28077(12)])].

28098 C / (x * (B * B)) = A * (C / (x * C)). [para(8383(a,1),24077(a,1,2))].

28141 x * ((x \ y) * (A' * z)) = x * (A' * ((x \ y) * z)). [para(381(a,2),51(a,2,2)),rewrite([51(6)])].

28252 C * (A' * (C * x)) = A * (A * x). [para(25701(a,1),381(a,1,2)),rewrite([3794(7)]),flip(a)].

28253 C * (C * (A' * x)) = A * (A * x). [para(381(a,2),26693(a,1)),rewrite([26693(6),25503(7)]),flip(a)].

28260 A * (C' * (C' * x)) = A' * (x * A'). [back_rewrite(25935),rewrite([28141(10),382(8,R),7487(10)]),flip(a)].

28301 (x * (B * B)) * C = A * (A * x). [back_rewrite(23905),rewrite([28253(13)])].

28504 C * (C * (x * A')) = A * (A * x). [para(24895(a,1),234(a,1,1)),rewrite([24895(10),125(8),17(7),19(8),24495(6),25503(7),24895(11),125(9),17(8),19(9)]),flip(a)].

28549 A * ((x * (A * C)) \ x) = C'. [para(37(a,1),25600(a,1,2,1)),rewrite([216(8),87(10)])].

28675 C \ x = C' * x. [para(26082(a,1),6(a,1,1)),rewrite([56(5),457(5),46(5)]),flip(a)].

28683 C * (C' * x) = x. [para(26082(a,1),3536(a,1,1)),rewrite([1484(6),201(7),1484(9),24802(7),28675(6),125(9,R),24495(8),378(10)])].

28749 (C * (x * C))' = C' * (x \ C'). [back_rewrite(28053),rewrite([28675(10)])].

28751 C' * (C' \ x)' = C' * (C * x)'. [back_rewrite(28035),rewrite([28675(5)]),flip(a)].

28821 C * ((C / x) * C') = (C' * x)'. [back_rewrite(26303),rewrite([28675(9)])].

28824 (C * (x * C'))' = C' * (x \ C). [back_rewrite(26297),rewrite([28675(10)])].

28826 (x * C') * (C * y) = C * ((C' * x) * y). [back_rewrite(26288),rewrite([28675(9)])].

28839 (C' \ x) * y = (C * x) * y. [back_rewrite(26183),rewrite([28675(5),25682(7),28683(9)])].

28854 C * (C * (x * (C' * y))) = x * (C * y). [back_rewrite(26107),rewrite([28675(4)])].

28860 C' * (x * C) = C * (x * C'). [back_rewrite(26088),rewrite([28675(4),1428(10)])].

28873 (x * C') * (B * C) = C * ((C' * x) * B). [back_rewrite(25979),rewrite([28675(10)])].

28877 C' * (x * (B * C)) = C * (x * (B * C')). [back_rewrite(25966),rewrite([28675(6)])].

28987 x / (A' * (x * (x * C')')) = A * (C' * x). [back_rewrite(24813),rewrite([28675(4),163(6),28675(12)])].

29013 C * ((C' * x) * B') = A * ((A' * x) * B'). [back_rewrite(23815),rewrite([28675(3)])].

29173 A * (C' * ((x * C) * B)) = (C * x) * B'. [back_rewrite(12989),rewrite([28683(10)]),flip(a)].

29191 (C' * (x * C')) * x = x * (C' * (C * x')'). [back_rewrite(26110),rewrite([28751(15)])].

29195 (x * C) \ C' = C' * (C * x)'. [back_rewrite(25693),rewrite([28751(12)])].

29206 C' \ (x * x) = x / (x * C)'. [back_rewrite(26216),rewrite([28839(8),11(7),12(6),26185(8)])].

29213 (x * C) * (C' * y) = C' * ((C * x) * y). [back_rewrite(25682),rewrite([28839(12)])].

29237 C * ((C' \ x)' * C') = C' / x. [back_rewrite(26158),rewrite([28860(9)])].

29240 (C' \ x)' = (C * x)'. [back_rewrite(25700),rewrite([28860(8),19788(7),28751(8),28683(8)]),flip(a)].

29243 C' \ (x \ C') = C' * (x \ C). [back_rewrite(25692),rewrite([28860(5),28824(6)]),flip(a)].

29272 C * ((C * x)' * C') = C' / x. [back_rewrite(29237),rewrite([29240(5)])].

29278 x / (C' * x) = C. [para(28675(a,1),26(a,1,2))].

29280 (C * x) * (C' * y) = C' * ((x * C) * y). [para(28675(a,1),128(a,1)),rewrite([28675(10)]),flip(a)].

29284 C' * (x * (C * y)) = C * (x * (C' * y)). [para(28675(a,1),176(a,1)),rewrite([25681(9),77(12),28675(9)])].

29286 (C' * (x \ C))' = C * (x * C'). [para(28675(a,1),11651(a,1,1)),rewrite([25681(9)])].

29287 (C / x) * C' = C * (C * x)'. [para(28675(a,1),19782(a,1,2,1)),rewrite([28675(6),28039(7),25681(9)]),flip(a)].

29303 C' \ x = C * x. [back_rewrite(26708),rewrite([29284(7),9(5),3(3)]),flip(a)].

29316 C * (C * (C * x)') = (C' * x)'. [back_rewrite(28821),rewrite([29287(6)])].

29342 C' * (x \ C) = C * (x \ C'). [back_rewrite(29243),rewrite([29303(6)]),flip(a)].

29354 x / (x * C)' = C * (x * x). [back_rewrite(29206),rewrite([29303(4)]),flip(a)].

29381 (C * (x \ C'))' = C * (x * C'). [back_rewrite(29286),rewrite([29342(5)])].

29385 (C * (x * C'))' = C * (x \ C'). [back_rewrite(28824),rewrite([29342(11)])].

29406 (C' * x) * (C * y) = C * ((x * C') * y). [para(34(a,1),28683(a,1,2)),rewrite([29303(12)]),flip(a)].

29415 (C' * x) * (C / (C' * x)) = x * (x * C')'. [para(28683(a,1),475(a,1,2)),rewrite([163(4)]),flip(a)].

29418 C * ((x * C') * (x \ C')) = x * (C' / x). [para(28683(a,1),163(a,1,1)),rewrite([475(4),8917(12),25411(12),28860(12),29385(13),29406(13)]),flip(a)].

29419 x / (C * x) = C'. [para(28683(a,1),177(a,1,1)),rewrite([1563(6),25701(6,R),8(5),3(3)])].

29425 (C' / x) * C = C * (C * x)'. [para(16705(a,1),28683(a,1,2)),rewrite([29303(4),25411(11)]),flip(a)].

29426 x * (x * (x * C'))' = (C' * x)'. [para(28683(a,1),17394(a,1,2)),rewrite([17875(8),31(6),25681(5),17873(7),28683(10),23331(6)])].

29513 (C * (x * C')) / (x * C) = C'. [para(46(a,1),29419(a,1,2)),rewrite([25681(3)])].

29524 (C * x) / (x * (C * C)) = C'. [para(25701(a,1),29419(a,1,2))].

29812 x * ((C' / x') * (C * x')) = C / (x * C')'. [para(26106(a,1),27681(a,1,1)),rewrite([1389(13),31(12),17875(14)]),flip(a)].

29841 (x * A') * (((x * A') * y) * x') = A' * (y * (x * A')). [para(382(a,1),390(a,1,2,2,2,1)),rewrite([376(13),125(13,R),378(13),382(17,R)])].

30031 (x * (C * x')) / (C / x') = (x \ C') * C. [para(28033(a,1),14579(a,2,2)),rewrite([13638(8),25701(8,R),28683(7),25699(8)])].

30046 C * (C * (C' / x)) = C / x. [para(27(a,1),28036(a,1,2)),rewrite([25701(9,R)]),flip(a)].

30059 (x' \ C) * (C / x) = C * C. [back_rewrite(27099),rewrite([30046(10)])].

30060 (C / x') * (x \ C) = C * C. [back_rewrite(26940),rewrite([30046(8)])].

30062 (x \ C) * (C / x') = C * C. [back_rewrite(26513),rewrite([30046(10)])].

30114 (x * (A * C)) * C' = A * x. [para(28549(a,1),77(a,2,2)),rewrite([986(10),378(12),434(8)]),flip(a)].

30348 C' * (x * (x * C)) = C * (x * (x * C')). [para(29524(a,1),232(a,1,1)),rewrite([29524(9),25701(9,R),17558(9),25411(5),29524(13),28826(12),12(11)])].

30452 (C' * x)' * C = C * (C / x). [para(30046(a,1),12(a,2,2)),rewrite([17873(7),25411(7),29425(6),29316(7)])].

30453 C * ((C * x)' * C) = C / x. [para(30046(a,1),12(a,2)),rewrite([29425(5),17873(7),25411(7)])].

30455 C * (C * (x * (C' / y))) = x * (C / y). [para(30046(a,1),37(a,2,2)),rewrite([25681(4),17875(12),25411(8),25676(7)])].

30462 C' * (C / x) = C * (C' / x). [para(30046(a,1),55(a,1,2)),rewrite([55(14),28683(14)])].

30464 (C / x) * (C' * y) = C' * ((C' * x)' * y). [para(30046(a,1),128(a,2,1)),rewrite([17873(8),25411(8),29425(7),29316(8),28675(7),28675(12)]),flip(a)].

30479 C' * (x * (C / y)) = C * (x * (C' / y)). [para(30046(a,1),176(a,1,2,2)),rewrite([28675(5),25681(9),17875(17),25411(13),25676(12)])].

30501 (C / x) / (C' / x) = C * C. [para(30046(a,1),26711(a,1,1))].

30502 A * (A * (C' / x)) = A' * (C / x). [para(30046(a,1),381(a,1,2)),rewrite([28252(15)]),flip(a)].

30503 (C * (C' / x)) / (C / x) = C'. [para(30046(a,1),29419(a,1,2))].

30555 C * (C * (x \ C')) = x \ C. [para(30060(a,1),5(a,1,2)),rewrite([5312(7),26455(4),31(2),25701(7,R)])].

30895 C / (C' * x) = C * (x' * C). [para(4(a,1),30453(a,1,2,1,1)),rewrite([28675(8)]),flip(a)].

30906 C * (C * ((x \ C') * C)) = C / (x * C'). [para(5782(a,1),30453(a,1,2,1)),rewrite([28675(5),29342(6),17873(8),25411(8),25681(12)])].

30909 (C * (C * x)') \ (C / x) = C. [para(30453(a,1),27827(a,1,2))].

30911 C * ((x * C') * (x' * C)) = x * (x * C')'. [back_rewrite(29415),rewrite([30895(8),29406(9)])].

30914 x / (C' / (x \ C)) = C * C. [para(26(a,1),30501(a,1,1))].

30935 (x \ C) / (C * (x \ C')) = C. [para(30555(a,1),6(a,1,1))].

30942 C * (C * (x * (y \ C'))) = x * (y \ C). [para(30555(a,1),37(a,2,2)),rewrite([25681(4),17875(12),25411(8),25676(7)])].

30948 (x \ C') * C = (x \ C) * C'. [para(30555(a,1),56(a,1,1)),rewrite([25681(4),457(14),25681(12),17558(15),25411(11)]),flip(a)].

30957 (x \ C) \ (C * (x \ C')) = (x \ C) * (C' / (x \ C)). [para(30555(a,1),163(a,1,1)),rewrite([17873(20),25411(20),30948(19),29385(21),17875(21),25411(15),30948(14),29418(21)])].

30966 (x \ C) / (C * (x * C')) = (x \ C) * (C' / (C' / x')). [para(30555(a,1),17563(a,1,1)),rewrite([29381(8),17875(20),25411(16),30948(15),30942(21),17873(16),26302(15)])].

30983 C / (x * C') = (x \ C) * C. [back_rewrite(30906),rewrite([30948(7),17558(9),25411(5)]),flip(a)].

30985 (x * (C * x')) / (C / x') = (x \ C) * C'. [back_rewrite(30031),rewrite([30948(13)])].

30992 (x * C') * ((x \ C) * C) = x * (x * C')'. [back_rewrite(26134),rewrite([30983(8)])].

31033 (C / x) * (C / (x * C')') = C * ((C * x) * (x * C)'). [para(30909(a,1),8574(a,1,2,1)),rewrite([1389(12),31(10),457(11),25681(9),17558(12),25411(8),8549(8),28084(16)]),flip(a)].

31043 C' / (x \ C) = x * (C' * C'). [para(30914(a,1),27(a,1,1)),rewrite([10239(4)]),flip(a)].

31053 (x \ C) \ (C * (x \ C')) = x * (C' * x'). [back_rewrite(30957),rewrite([31043(15),13638(17),12845(17),25681(12),12(16),4333(17),28675(11)])].

31215 C * (x * (C' * (C * x)')) = (x * (x * C')')'. [para(30983(a,1),5782(a,1,1,2)),rewrite([30992(8),7963(14),28675(11),25681(14),17873(15),31(14),25681(13),475(16),5485(16),28039(15),29284(15)]),flip(a)].

31223 C / (x * C) = (x \ C) * C'. [para(21017(a,1),30983(a,1,2)),rewrite([23818(10),30948(9)])].

31240 C / (x * (B * B)) = A * ((x \ C) * C'). [back_rewrite(28098),rewrite([31223(11)])].

32003 ((A' * x) \ y) * (x * A') = A * ((A' * x) * (y * x')). [para(751(a,1),256(a,1)),rewrite([691(15),6260(16)])].

32382 (x \ y) / y = y / (x * y). [para(46(a,1),1389(a,1,2)),rewrite([5782(5),842(7)]),flip(a)].

32435 C * ((C * x) * (x * C)') = x * (C * x'). [para(25677(a,1),1389(a,1,2)),rewrite([56(3),31(9),11(12)]),flip(a)].

32437 C / (x * (C * C)) = C' / x. [para(25701(a,1),1389(a,1,2)),rewrite([29272(14)])].

32442 x / (A' * (x * y)) = x * ((A * y') * x'). [para(381(a,2),1389(a,1,2)),rewrite([691(9)])].

32445 C' / (C' / x) = C / (C / x). [para(30046(a,1),1389(a,1,2)),rewrite([29272(15)]),flip(a)].

32457 x * ((x' * (x \ y))' * x') = x / (x' * y). [para(934(a,1),1389(a,1,2)),flip(a)].

32470 (C / x) * (C / (x * C')') = x * (C * x'). [back_rewrite(31033),rewrite([32435(17)])].

32474 (A * C') * x = A * (C' * x). [back_rewrite(28987),rewrite([32442(9),31(6),8954(7),7693(8),17(4,R)])].

32478 (x \ C) / (C * (x * C')) = (x \ C) * (C / (C / x')). [back_rewrite(30966),rewrite([32445(17)])].

32541 C * ((A * (C' * x)) * B') = A * (x * B'). [back_rewrite(23812),rewrite([32474(9),32474(14),28877(13),2803(14)])].

32649 (x / (y * x)) \ (y \ x) = x. [para(32382(a,1),27(a,1,1))].

32654 x * (x * (x / (y * x))) = (y \ x) * x. [para(32382(a,1),46(a,1,2,2))].

32678 (x * (x / (y * x)))' = x \ ((y \ x) \ x). [para(32382(a,1),5782(a,1,1,2))].

32687 x * (y * (((x * x) / y')' * (y \ x'))) = x' / (x * y). [para(14511(a,1),32382(a,1,1)),rewrite([17875(8),17563(7),17873(7),1385(10),1389(8),77(12)]),flip(a)].

32694 (x / (y * x)) * (y \ x) = y' * (y' * x). [para(32382(a,1),19788(a,1,1)),rewrite([11746(9)])].

32698 C' / (x * C') = (x \ C) * C'. [para(32382(a,1),25411(a,1)),rewrite([30948(11)])].

32706 C' / (A * x) = A' * (C' / x). [para(30114(a,1),32382(a,2,2)),rewrite([25411(10),30948(9),23872(6),163(6),26300(11),457(10),25681(8),29272(10)]),flip(a)].

32763 (A * ((x \ C) * C')) \ ((A' * x) \ (x \ C)) = x \ C. [para(24226(a,1),32649(a,1,1,2)),rewrite([27926(6),1462(7),125(7,R)])].

32780 C' / (x * C) = (x \ C') * C'. [para(11(a,1),32437(a,1,2)),rewrite([17873(6),25411(6),1389(8),28749(6),17873(10),31(9),25681(8),28683(11)]),flip(a)].

32792 (x * (C' / x)) * C = (C' / x) * (C * x). [para(32437(a,1),232(a,1,1)),rewrite([32437(9),25701(11,R),30455(11),46(7),32437(12)]),flip(a)].

32803 C' / (x * A') = A * (C' / x). [para(32437(a,1),22515(a,2,2)),rewrite([382(8,R),3794(8),24390(6),23044(6),23095(8)])].

32810 C' / (A' * x) = A * (C' / x). [para(525(a,1),32437(a,1,2)),rewrite([25701(8,R),28504(8),24390(6),23044(6),23095(8),32803(6)]),flip(a)].

32916 (x * y) \ x = x * (y / x')'. [para(7(a,1),1501(a,1,1,2))].

32927 x * ((y' / x') * (y * x')) = x * (y * (x * (y \ x'))). [para(1501(a,1),256(a,1,1)),rewrite([17875(6),17875(16),6(11),1672(13)])].

32984 x * (C * (x * (C' * x'))) = C / (x * C')'. [back_rewrite(29812),rewrite([32927(9),28675(4)])].

33490 A * (x * (y * (B * C'))) = x * (y * B'). [para(3384(a,1),37(a,2,2)),rewrite([216(4),87(6)])].

33588 x * ((x' * (x' * y))' * x') = x / (x \ y). [para(4333(a,1),1389(a,1,2)),flip(a)].

33922 (A' * ((x * y') * y)) * y = x / (A * y'). [para(5725(a,1),14579(a,1,1)),rewrite([376(4),32003(15),125(16,R),1307(15),378(16)]),flip(a)].

33936 A' * ((A' * ((x * (A * B')) * B)) * B) = x / (A * B'). [back_rewrite(10690),rewrite([33922(25)])].

33961 x * ((x * y)' / x) = x' / y. [para(5742(a,1),6(a,1,1)),flip(a)].

34051 (x * (y * x'))' = x * (y \ x'). [back_rewrite(1648),rewrite([33961(6),32694(7),4333(6)]),flip(a)].

34093 x * ((y * x') * (y \ x')) = y \ (x \ y). [back_rewrite(5568),rewrite([34051(5),13638(5)])].

34104 x \ (B * C') = A' * (x \ B'). [para(1527(a,1),5773(a,1,2))].

34217 (x * y)' * ((x * y)' * x) = x * ((y' * (x' * y')) * x'). [para(1389(a,1),7753(a,1,1)),rewrite([1385(6),17562(4)]),flip(a)].

34488 (x / y) / (y' * (x * y)) = y'. [para(9040(a,1),26(a,1,2))].

34577 (x / y) * (y' * (x * y)) = y' * (x * x). [para(9326(a,1),12(a,1,1)),rewrite([17873(13),31(12),6(11),17875(11),31(9),6(8)])].

34678 x' * ((x' * (y * x))' * x) = x' / (y / x). [para(9326(a,1),1389(a,1,2)),rewrite([31(10)]),flip(a)].

34687 (x * (x' * y')) * ((x * (x' * y')) * (x' \ y)) = x * ((x' * y)' * x'). [para(9013(a,1),9326(a,1,2,2)),rewrite([14611(4),14611(8),1389(16)])].

34712 (x / B') * C' = A' * (x / B). [para(9336(a,1),5(a,1,2)),rewrite([226(4),382(5,R)]),flip(a)].

34721 A * ((x / (A * B')) * C') = x / (B * A). [para(6540(a,1),9336(a,1,2,1)),rewrite([17(5,R),6540(15)])].

34785 (C' * C') * x = C' * (C' * x). [para(10239(a,1),934(a,1,2,2)),rewrite([1657(7),26139(15),1652(16),1652(15),26693(14),27265(14),1657(10)]),flip(a)].

35071 (x' * (x' * y)) \ (x \ y) = (y / x) * (x' * (x' * y))'. [para(13466(a,1),8574(a,1,2,1)),rewrite([7949(10)])].

35314 (A * x') \ ((A' * x) \ y) = (A * x') * ((A' * x) * y). [para(691(a,1),14596(a,1,1)),rewrite([691(15),991(16)])].

35325 (x * (x' * y)) * (x' \ z) = x * (x' * (y * (x * z))). [para(176(a,1),14596(a,1,2)),rewrite([2741(5)])].

35348 (C * (C * x)') * ((C / (x * C')') * (C / x)) = (x * C')'. [para(30909(a,1),14596(a,1,2)),rewrite([28084(6),27(8),28084(15)]),flip(a)].

35360 x * ((x' * y)' * x') = x * (x' * (x / y)). [back_rewrite(34687),rewrite([35325(11),17875(11),56(5),31(4),17875(10),31(5),6(4),9326(6)]),flip(a)].

35366 x * (x' * (x / (x' * y))) = x / (x \ y). [back_rewrite(33588),rewrite([35360(8)])].

35367 x * (x' * (x / (x \ y))) = x / (x' * y). [back_rewrite(32457),rewrite([35360(7)])].

35372 (x' * y) \ x = x' \ (y * x')'. [para(31(a,1),14613(a,1,2))].

35419 (x / y) / x = x' * (x' * y)'. [para(8574(a,1),14613(a,1,1)),rewrite([163(4),7(8),19782(8)]),flip(a)].

35551 x \ ((x \ y) / x)' = x' * (x' * (y * x'))'. [back_rewrite(23505),rewrite([35419(8)])].

35588 x \ (x' * y)' = x' * (x \ y)'. [back_rewrite(19806),rewrite([35419(3),4333(8)])].

35595 x \ (x \ y)' = x' * (x' * y)'. [back_rewrite(19782),rewrite([35419(5)])].

35632 x * (x' * (x' \ y)') = (x * y)'. [para(19788(a,1),17088(a,2,2)),rewrite([35419(4),31(2),31(2),5(4)]),flip(a)].

35643 (x * (y * x')) / (y / x') = (y / x') / (x * (y / x')). [para(17088(a,1),32382(a,1,1))].

35654 (C / x') / (x * (C / x')) = (x \ C) * C'. [back_rewrite(30985),rewrite([35643(8)])].

35807 (x * y) \ (x * z) = x * ((y / x') \ z). [para(17558(a,1),162(a,2,2,1)),rewrite([17873(4),6(4)])].

35846 x / (y / x') = (y \ x') * x. [para(17558(a,1),1389(a,1,2)),rewrite([34051(7),457(8),46(8)])].

35847 (x / y') / (y * (x / y')) = (x * y') / (y * (x * y')). [para(17558(a,1),32382(a,2,2)),rewrite([5(4),35643(12)]),flip(a)].

35856 x \ (x * y)' = x' * (x' \ y)'. [para(17558(a,1),14613(a,1,1)),rewrite([6423(4),17873(9),6(9)]),flip(a)].

36029 x * ((y / x') \ (y / x)) = x'. [back_rewrite(8911),rewrite([35807(4)])].

36060 (C * x') / (x * (C * x')) = (x \ C) * C'. [back_rewrite(35654),rewrite([35847(8)])].

36113 x' * ((x' * y)' * x) = x * ((x \ y)' / x). [para(19788(a,1),17750(a,2,1)),rewrite([35419(2),56(7),31(6),457(11)])].

36165 x' / (y / x) = (y \ x) * x'. [back_rewrite(34678),rewrite([36113(7),475(2),5782(3),8574(4)]),flip(a)].

36404 (x \ C) \ C = C / (x * C')'. [para(30935(a,1),19855(a,1,2)),rewrite([31053(12),34051(10),29303(8),26302(11),77(13),17088(10),32984(12)])].

36410 (C * x)' * C' = C' * (C' / x). [para(32437(a,1),19855(a,1,2)),rewrite([28675(5),176(12),25681(9),17873(13),25411(13),25676(12)]),flip(a)].

36661 (x \ (y * y))' = y' / (x \ y). [para(21019(a,1),6(a,1,1)),flip(a)].

36663 x' * (((y * y) / x) \ y) = y'. [para(27(a,1),21019(a,1,1,1))].

36743 (x * C) \ ((x * A) * B) = B'. [para(137(a,1),21118(a,1,2)),rewrite([21539(6),125(7,R),378(7)])].

36847 (x * C) * B' = (x * A) * B. [para(36743(a,1),4(a,1,2))].

36908 (A * x) * B' = x * (A * B'). [para(8289(a,1),36847(a,1,1)),rewrite([2279(9),27926(9),1462(10),17(12,R),1992(12),21110(11),214(10)])].

36921 (A * (x / B)) * B = A * x. [para(23191(a,1),36847(a,1,1)),rewrite([36908(8),125(8,R),7(7),17(6,R)]),flip(a)].

36976 (A' * x) * (B * C) = A * (x * B'). [back_rewrite(32541),rewrite([36908(9),125(9,R),125(10,R),29013(9),5849(10)])].

37026 (A' * x) * B = x * (B * A'). [back_rewrite(16540),rewrite([36976(16),125(15,R),29841(14),10666(9),10647(8)]),flip(a)].

37036 x / (A * B') = A' * (x / B'). [back_rewrite(33936),rewrite([37026(14),11(14),382(13,R),5811(13),17558(9)]),flip(a)].

37049 x / (B * A) = A' * (x / B). [back_rewrite(34721),rewrite([37036(6),26300(10),34712(9),4333(10),226(4),382(5,R)]),flip(a)].

37118 A * ((A * (x / B)) \ x) = B. [para(36921(a,1),5(a,1,2)),rewrite([2709(7)])].

37119 x / (B * A') = A * (x / B). [para(36921(a,1),6(a,1,1)),rewrite([6541(4)])].

37120 (A * x) * B = A * (x * B). [para(6(a,1),36921(a,1,1,2))].

37379 (A * (x / B)) \ x = B * A'. [para(37118(a,1),5(a,1,2)),rewrite([226(3)]),flip(a)].

37381 (x * A) * B = A * (x * B). [para(37118(a,1),11(a,1,2)),rewrite([37379(12),8304(12),37120(11),125(12,R),378(12)])].

37430 (x * C) * B' = A * (x * B). [back_rewrite(36847),rewrite([37381(9)])].

37463 (x * A) * (x \ B) = B * A. [para(37120(a,1),128(a,1,2)),rewrite([176(5),369(2),86(4),17(3)]),flip(a)].

37475 (x * C) * B = x * (B * C). [para(8301(a,1),37120(a,1,1)),rewrite([21110(11),214(10),1198(11)])].

37529 (C * x) * B' = C * (x * B'). [back_rewrite(29173),rewrite([37475(7),28877(8),33490(9)]),flip(a)].

37616 (C * x) / B = C * (x / B). [back_rewrite(3679),rewrite([37529(8),9289(9)]),flip(a)].

37765 (A * (B / x)) * x = B * A. [para(27(a,1),37463(a,1,2)),rewrite([17(4,R)])].

37855 x * ((C / x') \ (B * C)) = B. [para(37475(a,1),5(a,1,2)),rewrite([35807(7)])].

37856 (x * (B * C)) / B = x * C. [para(37475(a,1),6(a,1,1))].

37857 C * ((C' * x) * B) = x * B. [para(7(a,1),37475(a,1,1)),rewrite([25681(4),28873(9)]),flip(a)].

37867 A * ((x / B') * B) = B * ((B \ x) * C). [para(51(a,1),37475(a,2)),rewrite([23191(4),37120(7)])].

37911 (x * C') * (B * C) = x * B. [back_rewrite(28873),rewrite([37857(14)])].

37936 C * ((A * (x / B')) \ x) = B. [para(37616(a,1),27(a,1,1)),rewrite([35807(7),25411(6),23191(5)])].

38141 B / (x * A') = A * (B / x). [para(37765(a,1),6(a,1,1)),rewrite([6555(4)])].

38320 (x / (B * C)) * C = x / B. [para(7(a,1),37856(a,1,1)),flip(a)].

38500 x / (B * C) = (x / B) * C'. [para(38320(a,1),6(a,1,1)),rewrite([25681(4)]),flip(a)].

38586 (A' * (x / B)) \ x = B * A. [para(37049(a,1),27(a,1,1))].

38616 A * (A * (x / B)) = x / (B' * C'). [para(37119(a,1),6541(a,1)),rewrite([6541(5),37119(6),382(13,R),4577(13)])].

38635 B * (B * ((x * B') * C)) = x / (B' * C'). [back_rewrite(13954),rewrite([38616(15)])].

38951 (C / x') \ (B * C) = x \ B. [para(37855(a,1),5(a,1,2)),flip(a)].

39069 C * (x * ((x * A) \ B')) = B. [para(6(a,1),37936(a,1,2,1,2)),rewrite([162(7)])].

39123 ((x / B) * C') \ x = B * C. [para(38500(a,1),27(a,1,1))].

39271 (C / x') * (x \ B) = B * C. [para(38951(a,1),4(a,1,2))].

39272 (B * C) / (x \ B) = C / x'. [para(38951(a,1),26(a,1,2))].

39309 x * ((x * A) \ B') = B * C'. [para(39069(a,1),5(a,1,2)),rewrite([28675(3),451(4)]),flip(a)].

39377 (C / (B / x)') * x = B * C. [para(27(a,1),39271(a,1,2))].

39415 (B * C) / x = C / (B / x)'. [para(27(a,1),39272(a,1,2))].

39712 C / (B / (x * ((C / (B / x)') / x)))' = x. [para(39377(a,1),458(a,1,1)),rewrite([39415(11)])].

39735 (C / (B / x)') / x = x' * (x' * (B * C)). [para(39377(a,1),9326(a,1,2,2)),flip(a)].

39737 C / (B / (x \ (B * C)))' = x. [back_rewrite(39712),rewrite([39735(8),4333(10)])].

39807 (B / (x \ (B * C)))' = x \ C. [para(39737(a,1),27(a,1,1)),flip(a)].

39810 (x \ C) * (C * (C * x)') = x' * (x' * C). [para(39737(a,1),6423(a,1,1)),rewrite([39807(7),7973(3),39807(12),39807(14),36404(11),26455(14),31(12),163(13),28039(14)]),flip(a)].

39865 x / (x * (x * y)')' = y \ x. [para(475(a,1),21375(a,2,2,1)),rewrite([163(2),5782(8),4(8)])].

39890 C / (C / x') = C * (C * x)'. [para(23818(a,1),21375(a,1,2,1)),rewrite([25699(5),176(12),25681(9),17873(13),25411(13),25676(12)])].

39961 (x \ C) / (C * (x * C')) = x' * (x' * C). [back_rewrite(32478),rewrite([39890(15),39810(16)])].

40027 x' / (x \ y) = x * (y' / x). [para(14596(a,1),23500(a,1,2,1,1)),rewrite([14611(5),31(7),17873(6),56(6),31(5),55(7),9326(6)]),flip(a)].

40072 (x * (x / y))' = x \ (y \ x)'. [para(23576(a,1),5(a,1,2)),flip(a)].

40073 ((x \ y) \ y)' = y * (y * x)'. [para(26(a,1),23576(a,1,2,1,2)),flip(a)].

40094 (x * (x * C')')' = x * (x * C)'. [para(29278(a,1),23576(a,1,2,1,2)),rewrite([163(8)]),flip(a)].

40149 x \ ((y \ x) \ x) = x' * (x' \ (x * y)')'. [back_rewrite(32678),rewrite([40072(4),163(2),35856(5)]),flip(a)].

40167 C * (x * (C' * (C * x)')) = x * (x * C)'. [back_rewrite(31215),rewrite([40094(15)])].

40266 (x * (A * y)) * C' = A * ((x * y) * C'). [para(37(a,1),24819(a,1,1)),rewrite([216(10),87(12)])].

40714 ((x * x) * (y * (x' * x')))' = (x * x) \ (y \ (x * x)). [para(27926(a,1),5782(a,1,1,2))].

40798 x / (B' * C') = (x / B') * C. [para(51(a,1),28301(a,1,1)),rewrite([256(5),17558(7),38616(11)]),flip(a)].

40820 B * (B * ((x * B') * C)) = (x / B') * C. [back_rewrite(38635),rewrite([40798(15)])].

40872 (x * (C / x)) * C' = (C' / x) * (C * x). [para(28860(a,1),176(a,1,2)),rewrite([176(6),32792(12)])].

40968 (C * (C' / x)) \ (C / x) = x * (C * x'). [para(29287(a,1),163(a,2,2,1)),rewrite([30462(5),28084(16),32470(17)])].

40977 (C * (C * x)') * (C / x) = (C / x) * x'. [para(29287(a,1),17873(a,1,1)),rewrite([26455(15),26(17)])].

41074 x * (x' * ((x' \ C) * (C' * (C * x)'))) = C'. [para(29513(a,1),842(a,2)),rewrite([162(10),162(9),29195(8),40167(11),12(10),34217(10),29191(11),31(8),17875(12),51(12)])].

41111 (C * (C / x)) / (C' * x)' = (C' * x)' * x. [para(30452(a,1),56(a,1,1)),rewrite([31(19),28683(18)])].

41153 (C * (C' / x)) * (x * (C' * x')) = C' / x. [para(30503(a,1),19788(a,1,1)),rewrite([55(8),28683(8),40968(16),34051(13),28675(11)]),flip(a)].

41172 (C * (x * C')') / (C' * x)' = x * (x * C')'. [para(30895(a,1),27681(a,2,2)),rewrite([35372(5),29303(7),29406(20),30911(20)])].

42079 (x * y)' * (x * z) = x * ((x' / y) * z). [para(33961(a,1),11(a,2,2,1)),rewrite([7(4)])].

42082 (x * y)' * x = x * (x' / y). [para(33961(a,1),12(a,2,2)),rewrite([7(4)])].

42086 (x / y) * (((x / y)' / z) * y) = ((x / y) * z)' * x. [para(33961(a,1),38(a,1,2,1)),rewrite([7(13)])].

42122 (x * y)' \ x = x * (x' / y)'. [para(33961(a,1),163(a,2,2,1)),rewrite([7(4)])].

42155 A' * ((x * A') * (C / x)) = x' / (A' * (x \ C)). [para(24226(a,1),33961(a,1,2,1,1)),rewrite([1657(7),1462(8),6541(11),382(11,R),32810(12),32810(10),30502(10),17875(9),31(5),216(4),691(13),6541(15),382(15,R)])].

42158 (x' \ C) * (C' * (C' * (C' / x))) = (C' / x) / (C / x). [para(30059(a,1),33961(a,1,2,1,1)),rewrite([1657(7),12962(12),26302(7),31(7),19786(12),29303(8),36410(11),26302(17),31(17)])].

42165 x' / (A' * (x \ y)) = x * (y' / (x * A')). [para(596(a,1),33961(a,1,2,1,1)),rewrite([691(4),6541(4)]),flip(a)].

42345 A' * ((x * A') * (C / x)) = x * (A * (C' / x)). [back_rewrite(42155),rewrite([42165(16),32803(15)])].

42679 x' * ((x / (y * x)) * (y * y)) = x' * (x / (y * x))'. [para(34488(a,1),9040(a,1,2)),rewrite([42122(6),31(3),34577(14),42079(13),31(8)]),flip(a)].

42707 (x' * (y * x))' = x' * (y \ x). [para(34488(a,1),34488(a,1,1)),rewrite([34577(10),42079(9),31(4),42679(7),1389(7),31(5),31(5),19788(4),475(3),5782(4),4(4)]),flip(a)].

43309 x \ ((y / x) \ (y / x')) = x. [para(36029(a,1),4333(a,1,2,2)),rewrite([31(3),9(2),3(2),31(2)]),flip(a)].

43379 C * (((x \ C) * C') \ (x' * (x' * C'))) = C * (x \ C'). [para(30935(a,1),43309(a,1,2,1)),rewrite([29381(14),39961(14),28675(12),30348(13),35807(14),25411(7),30948(6)])].

43531 x * ((C * x)' * x) = C' * x. [para(30935(a,1),36165(a,1,2)),rewrite([29381(6),25681(7),457(8),25681(6),12(7),4333(8),28675(2),31053(11),29381(14),77(14),176(11),40872(11),29284(12),19786(11),29303(9),28683(12)]),flip(a)].

43716 (x' / (y \ x))' = y \ (x * x). [para(36661(a,1),31(a,1,1))].

43733 B / (x \ B') = A' * (C / x'). [para(1462(a,1),36661(a,1,1,2)),rewrite([2709(5),690(6),25699(4),382(6,R),31(9)]),flip(a)].

43841 ((x * x) / y) \ x = y' \ x'. [para(36663(a,1),5(a,1,2)),flip(a)].

43898 (x * A) * (x \ B') = A * B'. [para(36908(a,1),128(a,1,2)),rewrite([5(6)]),flip(a)].

44760 (x * A) \ B' = A' * (x \ B'). [para(39309(a,1),5(a,1,2)),rewrite([34104(5)]),flip(a)].

44802 (x * (x * y)')' = (y \ x) \ x. [para(39865(a,1),27(a,1,1)),flip(a)].

44803 x \ (y * x)' = x' / (x \ y')'. [para(55(a,1),39865(a,1,2,1,2,1)),rewrite([14611(6),55(7),4333(7),14613(8)]),flip(a)].

45001 (x' * y) \ x = x / (x' \ y')'. [back_rewrite(35372),rewrite([44803(8),31(5)])].

45027 (x * y) \ x' = x' / (x \ y')'. [back_rewrite(14613),rewrite([44803(6)])].

45182 (x \ (y \ x)')' = x * (x / y). [para(40072(a,1),31(a,1,1))].

45211 (x * (x * C'))' = x' / (C' / x'). [para(25681(a,1),40072(a,1,1,2)),rewrite([28675(7),44803(10),31(9),26302(9)])].

45274 x' / (x / y) = (y \ x)' * x'. [para(40072(a,1),33961(a,1,2,1)),rewrite([8574(5)]),flip(a)].

45290 x * (x' / (C' / x')) = (C' * x)'. [back_rewrite(29426),rewrite([45211(5)])].

45378 x' \ (x * y)' = x * (x' \ y)'. [para(9013(a,1),40073(a,2,2,1)),rewrite([32916(4),56(4),31(3),42707(4),32916(5),56(5),31(4),42707(5),14611(6),40073(4),55(5),9013(6)])].

45430 x \ ((y \ x) \ x) = x' * (x * (x' \ y)')'. [back_rewrite(40149),rewrite([45378(8)])].

45882 (x \ C) * ((C' / x') / (C / x')) = x \ C'. [para(30062(a,1),42082(a,1,1,1)),rewrite([1657(4),34785(8),29342(7),55(8),28683(8),26302(8)]),flip(a)].

45919 (C / (x * C')') * (C / x) = (C / x) * ((x' \ C) * C'). [para(29287(a,1),42082(a,1,1,1)),rewrite([44802(6),36404(4),26455(14),25411(18),30948(17)])].

45953 (C * (C * x)') * ((C / x) * ((x' \ C) * C')) = (x * C')'. [back_rewrite(35348),rewrite([45919(14)])].

46057 (C * x)' * x = x * (C' / x). [para(43531(a,1),5(a,1,2)),rewrite([475(4)]),flip(a)].

46077 x * (x' * (C * x)) = C * x. [para(43531(a,1),9326(a,1,2,2)),rewrite([46057(4),5782(5),29303(3),475(3),46057(7),5782(8),29303(6),475(6),19277(11),18406(12),14579(7),28854(8),5(4),46057(6),1389(7),26535(6),256(7),31(6)]),flip(a)].

46097 x' * (C * x) = x * (C / x). [para(46077(a,1),5(a,1,2)),rewrite([475(3)]),flip(a)].

46114 x' \ C = x * C. [para(46077(a,1),272(a,2,2,1)),rewrite([1563(3),55(3),9(2),3(2),457(5),6(3),31(7),12(6),55(7),55(6),9013(7)]),flip(a)].

46131 (x \ C) * C' = x'. [para(46077(a,1),14594(a,1,2,2)),rewrite([31(2),5(5),36060(8)])].

46159 (x * C')' = C / x. [back_rewrite(45953),rewrite([46114(10),25677(12),7(8),17873(7),25411(7),42082(6),30046(7)]),flip(a)].

46201 C' * (C' * ((x * C) * (C' / x))) = (C' / x) / (C / x). [back_rewrite(42158),rewrite([46114(3),29213(12),29280(11)])].

46203 x * (x' * C') = C'. [back_rewrite(41074),rewrite([46114(4),29213(10),8(9),3(5)])].

46335 (x * C) * (C' / x) = 1. [back_rewrite(26615),rewrite([46114(3)])].

46361 C * (x \ C') = C * (x' * C'). [back_rewrite(43379),rewrite([46131(6),5(9)]),flip(a)].

46411 x \ C = x' * C. [back_rewrite(32763),rewrite([46131(6),35314(10),24226(9),16779(7),21539(7),125(8,R),378(8)]),flip(a)].

46414 C' / (x * C') = x'. [back_rewrite(32698),rewrite([46411(8),25677(12)])].

46434 C / (x * (B * B)) = A * x'. [back_rewrite(31240),rewrite([46411(9),25677(13)])].

46552 (C' * x)' * x = x * (C / x). [back_rewrite(41172),rewrite([46159(5),41111(9),46159(9)])].

46669 (x * C)' = C' / x. [back_rewrite(25765),rewrite([46159(4),30464(8),42082(9),31(7),30462(7),55(8),28683(8)]),flip(a)].

46699 (C / x) * (A' * (C * (x * C'))) = (x * A') * (C / x). [back_rewrite(26477),rewrite([46361(10),31(7)])].

46705 (C' / x) / (C / x) = C' * C'. [back_rewrite(46201),rewrite([46335(10),3(6)]),flip(a)].

46785 x \ C' = x' * C'. [back_rewrite(45882),rewrite([46411(2),46705(11),10284(9),936(8)]),flip(a)].

47136 C * (C' / c1) != c1'. [back_rewrite(21),rewrite([46669(5)])].

47320 x / (C' / x) = C * (x * x). [back_rewrite(29354),rewrite([46669(3)])].

47485 (C / x)' = x * C'. [back_rewrite(26455),rewrite([46785(7),31(5)])].

47633 C' / (x * C) = C' * (C' * x'). [back_rewrite(32780),rewrite([46785(8),12(12)])].

47712 x * (C * (x' * x')) = (C' * x)'. [back_rewrite(45290),rewrite([47320(6)])].

47740 x / (C / x) = x * (C * x')'. [para(46411(a,1),13683(a,1,1)),rewrite([45001(4),46785(4),31(2),46159(4)])].

47861 (C * x) * (((C * x) * y) * (x * (C' / x))) = (y * (C * x)) * x. [para(46669(a,1),390(a,1,2,2,2))].

47957 x * (x' * ((C * x) * x')) = (C * x) * x'. [para(46335(a,1),418(a,1,1,1,2)),rewrite([3(2),46335(11),3(7),47861(13),46097(5),17873(5),17750(5),55(7),46335(15),3(11)])].

47971 (C / x) * x' = C * (x' * x'). [para(46414(a,1),8931(a,1,2)),rewrite([45027(5),31(4),46411(3),46669(5),47320(6),46785(11),46159(9),29287(10),46159(14),40977(13)]),flip(a)].

47997 (C * (C * x)') * (C / x) = C * (x' * x'). [back_rewrite(40977),rewrite([47971(12)])].

48045 x' * ((C * x) * x') = (C' * x)'. [para(46097(a,1),14579(a,1,1)),rewrite([31(5),56(4),47971(4),47712(6)]),flip(a)].

48066 (C * x) * x' = x * (C' * x)'. [back_rewrite(47957),rewrite([48045(6)]),flip(a)].

48070 x * (x' * (C' * x)') = (C' * x)'. [back_rewrite(48045),rewrite([48066(5),55(7)])].

48674 (x / (y \ x'))' = y \ (x' * x'). [para(31(a,1),43716(a,1,1,1))].

48675 x * ((x \ y)' \ x) = (x' / y)'. [para(27(a,1),43716(a,1,1,2)),rewrite([19841(6)]),flip(a)].

49051 (x * x) / y = x / (y' \ x'). [para(43841(a,1),26(a,1,2)),flip(a)].

49065 (C / x) * (x' \ B') = B * A. [para(43841(a,1),37463(a,1,2)),rewrite([49051(4),43733(6),31(5),17(7,R),378(7)])].

49129 (x * (y' \ x))' = x' / (x * y). [back_rewrite(32687),rewrite([49051(3),31(2),48674(4),840(8),49051(4),31(4),19788(6),35632(8)])].

49162 x * ((x * A') \ B') = A * B'. [para(7(a,1),43898(a,1,1)),rewrite([216(2)])].

49168 (A * (B' / x)) * x = A * B'. [para(27(a,1),43898(a,1,2)),rewrite([17(5,R)])].

49325 (x / y) * (y' * (y' * x))' = x * (y / x). [para(256(a,1),44802(a,1,1,2,1)),rewrite([34051(5),13638(5),34093(6),11651(3),7973(4),35071(8)]),flip(a)].

49344 x * (x' * ((y \ x) \ x)) = (x * (x' \ y)')'. [para(9013(a,1),44802(a,1,1,2,1)),rewrite([32916(9),56(9),31(8),42707(9),32916(10),56(10),31(9),42707(10)]),flip(a)].

49425 x * (x / (x / y)) = (x \ y')'. [para(27(a,1),45182(a,1,1,2,1)),flip(a)].

49430 (x' * (x * (x' \ y)')')' = x * (x / (y * x)). [para(163(a,1),45182(a,1,1,2,1)),rewrite([44802(4),45430(3)])].

50024 x * ((x' * C) * (C * x')') = C * (x * C'). [para(47740(a,1),457(a,2,2)),rewrite([7(3),47485(4),51(13),46411(7)]),flip(a)].

50045 (x * A') * (C / x) = x * (A' * (C / x)). [para(47740(a,1),750(a,1,2,2,2)),rewrite([51(12),46411(6),50024(13),46699(11),382(11,R)])].

50051 A' * (x * (A' * (C / x))) = x * (A * (C' / x)). [back_rewrite(42345),rewrite([50045(8)])].

50472 x * ((x' * (x' * y)) * (x \ z)) = ((x \ y) / x) * z. [para(7973(a,1),840(a,1,2,1))].

50747 (C / x') * (x \ B') = B * A. [para(31(a,1),49065(a,1,2,1))].

50837 (A * (B' / (A * x))) * x = B'. [para(49168(a,1),1600(a,1,2)),rewrite([125(7,R),382(6),1527(6),125(6),1377(6)]),flip(a)].

50908 x / (x / y) = x' * (x' * y')'. [para(49425(a,1),5(a,1,2)),rewrite([35595(4)]),flip(a)].

50925 (x' * (x' \ y)')' = (y' * x')' / x'. [para(1389(a,1),49425(a,1,2,2)),rewrite([1389(5),17558(8),35856(9)]),flip(a)].

51704 (C / (B' / x)') * x = B * A. [para(27(a,1),50747(a,1,2))].

51739 A * (B' / (A * x)) = B' / x. [para(50837(a,1),6(a,1,1)),flip(a)].

52078 C / (B' / x)' = A * (B / x). [para(51704(a,1),6(a,1,1)),rewrite([6555(4),38141(5)]),flip(a)].

52134 B' / (x * (A' * y)) = A * (B' / (x * y)). [para(483(a,1),51739(a,1,2,2)),flip(a)].

52237 (B / x)' * (B * B) = (B' / x)'. [para(52078(a,1),27(a,1,1)),rewrite([46411(6),690(5),382(6,R),21635(8)])].

52418 A * (A * (x * B)') = (x * (B' * C'))'. [para(4577(a,1),989(a,1,1,2)),rewrite([17499(14)]),flip(a)].

52517 (x * (B * C)) * C' = A' * ((x * B') * C). [para(1198(a,1),24819(a,1,1)),rewrite([40266(16),5861(17),16779(14)])].

52743 (A * x) \ (B * C) = A * (x \ B'). [para(3693(a,1),5310(a,1,2,2)),rewrite([44760(7),378(9)]),flip(a)].

52768 (x \ (B * C)) * B' = (x \ B') * (B * C). [para(5310(a,1),36908(a,1,1)),rewrite([125(17,R),36908(16),125(16,R),5849(17)])].

53766 (x * x) \ (y \ (x * x)) = (x * x) * (y \ (x' * x')). [para(1657(a,1),34051(a,1,1,2,2)),rewrite([40714(7),1657(7)])].

54602 x / (x * y)' = x * (y' * x')'. [para(42122(a,1),842(a,1,2,1)),rewrite([31(9),17875(8),42079(10),42086(9),19788(4),50925(6),7(8)]),flip(a)].

56328 (C * (x' * x')) / (C' * x)' = x'. [para(47971(a,1),458(a,1,1)),rewrite([17750(10),48066(10),55(12),48070(12)])].

56551 (x \ y)' \ x = x \ (x' / y)'. [para(48675(a,1),5(a,1,2)),flip(a)].

56552 (x' / (x * y))' = x * (y' \ x). [para(5(a,1),48675(a,1,2,1,1)),flip(a)].

56557 (x * x) * ((x * x) * (y' \ (x' * x'))) = y' \ (x * x). [para(1657(a,1),48675(a,2,1,1)),rewrite([56551(6),1657(4),49051(6),31(6),43716(7),53766(6),49051(13),31(13),43716(14)])].

56579 (x / (x \ y))' = x \ (y' \ x'). [para(14596(a,1),48675(a,1,2,1,1)),rewrite([14611(5),45027(7),35588(7),54602(9),31(6),31(6),256(5),34051(7),55(7),55(8),4333(8),31(6)]),flip(a)].

56683 (x' * (y * y))' = (y / x)' / y. [para(7(a,1),49129(a,2,2)),rewrite([9040(4),34577(5)])].

56687 (x * (y \ x))' = x' / (x * y'). [para(31(a,1),49129(a,1,1,2,1))].

56836 (A * x) * (((A * x) * y) * (x \ B')) = (y * x) * (B * C). [para(49162(a,1),352(a,1,2)),rewrite([125(8,R),36908(7),125(7,R),5849(8),382(15,R),125(15,R),378(15)]),flip(a)].

57853 (B / x)' * C = A * (B' / x)'. [para(52237(a,1),125(a,1,2)),rewrite([125(14),17(13),19(14)]),flip(a)].

58078 (x * (A * y)) * (B * C) = A * ((x * y) * (B * C)). [para(52743(a,1),34(a,1,2,2)),rewrite([125(11,R),125(12,R),56836(11)]),flip(a)].

58226 C * ((C * (C' / x)) * (x * (C' / x))) = x'. [para(29316(a,1),1019(a,1,2)),rewrite([17873(12),25411(12),42082(11),30046(12),47997(8),56328(10),17873(13),25411(13),42082(12),30046(13),29316(15),31(13),30464(12),46552(13),30479(12),17875(13),25411(8),42082(7)]),flip(a)].

58987 (x' * (x \ y))' \ x = x' * (x \ (y' \ x)). [para(1389(a,1),56551(a,2,2,1)),rewrite([2750(3),31(9),42707(10),2750(10)])].

59062 (x / (x' * y))' = x' * (y' \ x'). [para(31(a,1),56552(a,1,1,1))].

59214 (x \ (y' \ x'))' = x / (x \ y). [para(56579(a,1),31(a,1,1))].

59279 (x * (y * y))' = (y / x')' / y. [para(31(a,1),56683(a,1,1,1))].

59349 (x / y)' / (x * (y / x)) = x'. [para(13466(a,1),56687(a,1,1,2)),rewrite([7(2),49325(10)]),flip(a)].

59434 (x / (y * x))' / (x * y) = x'. [para(6(a,1),59349(a,1,2,2))].

59435 x * (x' * (y / x)) = (x / y)'. [para(59349(a,1),7(a,1,1)),rewrite([55(4)])].

59518 x' * (y * x) = x * (x / y)'. [para(59349(a,1),937(a,1,1)),rewrite([59349(6),31(3),46(4),59349(8),31(5)])].

59541 x * ((x' * y) * (x \ z)) = (x / y)' * z. [back_rewrite(23300),rewrite([59435(4)]),flip(a)].

59542 x \ (y' \ x') = x' * (y * x'). [back_rewrite(13649),rewrite([59435(5),56579(3)])].

59636 x * (x' * (x / y)') = y / x. [back_rewrite(9326),rewrite([59518(4),55(5)])].

59652 ((x \ y) / x) * z = (x' * (y' \ x')) * z. [back_rewrite(50472),rewrite([59541(7),59062(4)]),flip(a)].

59693 (x' * (y * x'))' = x / (x \ y). [back_rewrite(59214),rewrite([59542(4)])].

59710 x' \ (y' * y') = x * (y' * y'). [back_rewrite(21473),rewrite([59652(4),17873(7),31(6),59435(7),48674(5)])].

59721 x \ ((x \ y) / x)' = x' * (x / (x \ y)). [back_rewrite(35551),rewrite([59693(10)])].

59730 x' \ (y * y) = x * (y * y). [back_rewrite(56557),rewrite([59710(7),27991(8)]),flip(a)].

59746 x \ (y * y) = x' * (y * y). [para(31(a,1),59730(a,1,1))].

59866 (x' / (y \ x))' = y' * (x * x). [back_rewrite(43716),rewrite([59746(6)])].

59874 (x / y)' / x = x' / (y \ x). [back_rewrite(36661),rewrite([59746(2),59279(4),31(2)])].

60001 (x * y)' * (y * y) = y * (y * (x / y')'). [para(59746(a,1),162(a,1)),rewrite([32916(6)])].

60023 (x / (y * x))' = x * (x' * y). [para(59434(a,1),7(a,1,1)),rewrite([55(3)]),flip(a)].

60129 x' / (y \ x) = x' * (x \ y). [para(59435(a,1),56(a,1,1)),rewrite([59874(3),17873(8),31(7),7753(6),4333(10),2750(6)])].

60130 x' * (y / x') = x * (y' \ x'). [para(56(a,1),59435(a,1,2,2)),rewrite([55(5),9013(6),475(4),1389(6),34051(9)])].

60143 x * (x * (x * (x / y)')) = x * (y' \ x). [para(14579(a,1),59435(a,1,2,2)),rewrite([31(3),55(5),55(4),59518(3),56552(9)])].

60147 x \ (y' \ x) = x * (x / y)'. [para(27681(a,1),59435(a,1,2,2)),rewrite([31(3),46(4),59518(3),40027(6),5782(7)]),flip(a)].

60154 x \ (x' / y)' = x * (y' \ x'). [para(59435(a,1),2750(a,1,2)),rewrite([31(7),5(9),60130(8)])].

60206 (x \ y) / x = x' * (y' \ x'). [para(17562(a,1),59435(a,1,2,2)),rewrite([4333(7),7963(3),59062(6)])].

60353 (x' * (x \ y))' = y' * (x * x). [back_rewrite(59866),rewrite([60129(3)])].

60489 (x' * (y * y)) \ y = x / y. [back_rewrite(58987),rewrite([60353(4),60147(8),55(9),59636(9)])].

60520 (x \ y)' \ x = x * (y' \ x'). [back_rewrite(56551),rewrite([60154(7)])].

60544 x' * (x / (x \ y)) = y' * x. [back_rewrite(59721),rewrite([60206(2),56687(6),31(2),31(3),19855(4),2750(3),60353(4),21017(5)]),flip(a)].

60648 x / (x' * y) = x * (y' * x). [back_rewrite(35367),rewrite([60544(4)]),flip(a)].

60750 x / (x \ y) = x * (y \ x). [back_rewrite(35366),rewrite([60648(4),55(5),59518(4),60143(6),31(2)]),flip(a)].

60784 x * (x' * (y \ x)) = y' * x. [back_rewrite(60544),rewrite([60750(3),55(4)])].

60853 (x * (x' \ y)')' = (y \ x)' * x. [back_rewrite(49344),rewrite([60784(5)]),flip(a)].

60881 x * (x / (y * x)) = x' \ y'. [back_rewrite(49430),rewrite([60853(6),59518(5),21375(3),44802(6),60520(3),32916(5),32382(5),60023(6),31(3),55(4),9013(5)]),flip(a)].

60893 (x \ y) * y = y * (y' \ x'). [back_rewrite(32654),rewrite([60881(3)]),flip(a)].

60943 x * (x * (y / x')') = x / y. [para(5(a,1),60750(a,1,2)),rewrite([32916(3)]),flip(a)].

61033 (x * y)' * (y * y) = y / x. [back_rewrite(60001),rewrite([60943(9)])].

61201 (x' * C) * (x / B) = B * A. [para(60489(a,1),37463(a,1,2)),rewrite([17(7,R),8301(7)])].

61239 (x \ B') * B = C * (C * x)'. [para(60489(a,1),43733(a,1,2)),rewrite([35846(5),1462(14),986(15),46159(15),24077(15),50908(13),31(14),28039(15),125(15,R),378(15)])].

61335 (x * B)' * C = A * (B / x). [para(61033(a,1),8301(a,1,2)),flip(a)].

61377 (x * (B' * C'))' = (B / x) * C. [para(61033(a,1),28301(a,1,1)),rewrite([52418(11)]),flip(a)].

61395 C / (B / x) = A * (x * B). [para(61033(a,1),46434(a,1,2)),rewrite([31(9)])].

61533 A * (A * (x * B)') = (B / x) * C. [back_rewrite(52418),rewrite([61377(14)])].

61788 B * (A * (B' \ x')) = C / x. [para(26(a,1),61395(a,1,2)),rewrite([60893(7),125(10)]),flip(a)].

61811 B * ((B \ x) * C) = x * C. [para(35846(a,1),61395(a,1,2)),rewrite([61239(6),1389(7),31(5),457(6),25681(4),17558(7),25411(3),37867(9)]),flip(a)].

61835 A' * (C' / (x * B)) = A' * ((B' / x) * C'). [para(61395(a,1),45274(a,1,2)),rewrite([32706(7),46411(12),57853(13),690(15),31(13),382(14,R),26300(17)])].

61955 (B * x) * C = B * (x * C). [para(5(a,1),61811(a,1,2,1)),flip(a)].

61963 (x * C) / B = A * (x / B'). [para(61811(a,1),56(a,1,1)),rewrite([37430(12),256(10),125(12),23198(13)])].

61976 (x * C) / B' = (x / B') * C. [para(61811(a,1),14579(a,1,1)),rewrite([37475(12),13638(12),40820(14)])].

61977 (x * B) * C = x * (B * C). [para(61811(a,1),17873(a,1,1)),rewrite([37475(4),61976(12),27681(10),61955(11),23191(10),18391(13)]),flip(a)].

62280 (x * (B * C))' = C' / (x * B). [para(61977(a,1),46669(a,1,1))].

62284 (x * B') * C = A * (x * B). [para(23696(a,1),61977(a,1,1)),rewrite([1462(10),58078(14),37911(13)])].

62293 (x * (B * C)) * C' = x * B. [back_rewrite(52517),rewrite([62284(14),125(14,R),378(14)])].

62652 x * ((C / x) / B) = B * A. [para(47485(a,1),61201(a,1,1,1)),rewrite([25676(5)])].

62667 (C / x) / B = A * (x \ B). [para(62652(a,1),5(a,1,2)),rewrite([5306(4)]),flip(a)].

62710 (x \ B) \ (C / x) = B * A. [para(62667(a,1),38586(a,1,1,2)),rewrite([125(7,R),378(7)])].

62767 A' * (C / x) = B * (B' \ x'). [para(62710(a,1),596(a,1,2,2)),rewrite([184(8,R),382(7),125(8),8(7),3(5),60893(4)]),flip(a)].

62828 A' * (x * (B * (B' \ x'))) = x * (A * (C' / x)). [back_rewrite(50051),rewrite([62767(7)])].

63001 C * (C * (x * B))' = A * (B / (x * C)). [para(37475(a,1),61335(a,1,1,1)),rewrite([62280(5),29425(7)])].

63111 x * ((x \ B) * C) = B * C. [para(61963(a,1),39123(a,1,1,1)),rewrite([24819(8),34712(7),378(7),19841(5),46411(5),31(4)])].

63148 x \ (B * C) = (x \ B) * C. [para(63111(a,1),5(a,1,2))].

63186 C' / (x * B) = (B' / x) * C'. [para(63111(a,1),989(a,1,1,2)),rewrite([62280(5),476(10),17(9),21724(11),125(11),7477(13),62280(13),61835(14),378(16)])].

63275 (x \ B') * (B * C) = C / x. [back_rewrite(52768),rewrite([63148(4),37430(7),60893(5),125(8),61788(8)]),flip(a)].

63371 (x * (B * C))' = (B' / x) * C'. [back_rewrite(62280),rewrite([63186(10)])].

63475 C / (x * B') = (B / x) * C. [para(62284(a,1),61033(a,1,1,1)),rewrite([690(5),382(6,R),25701(10,R),28253(10),61533(7)]),flip(a)].

63547 (C * (x * B))' = C' * (B' / x). [para(62293(a,1),34051(a,1,1,2)),rewrite([46785(13),63371(11),12(15),4333(16),28675(10)])].

63554 A * (B / (x * C)) = B' / x. [back_rewrite(63001),rewrite([63547(6),28683(8)]),flip(a)].

63819 C / (B' / x) = x * (B * C). [para(27(a,1),63275(a,1,1)),flip(a)].

63966 ((B / x) * C) * (x * B') = C. [para(63475(a,1),7(a,1,1))].

63987 C' / (B / x) = (x * B') * C'. [para(63475(a,1),47485(a,1,1)),rewrite([46669(5)])].

64119 B' / (x * C') = A * (B / x). [para(7(a,1),63554(a,1,2,2)),rewrite([25681(8)]),flip(a)].

64244 (x * B') * C' = x * (B' * C'). [para(23696(a,1),63819(a,2)),rewrite([46669(7),1761(7),46669(12),1761(12),17875(14),31(10),1761(9),12(13),1764(12),2095(13),4601(14),52134(13),52134(11),64119(9),2598(9),25701(7,R),1389(8),36410(9),63987(8),28683(11),46669(10),1761(10)])].

64268 C' / (B / x) = x * (B' * C'). [back_rewrite(63987),rewrite([64244(11)])].

64515 x * (C' / x) = x * (C' * x'). [para(63966(a,1),33961(a,1,2,1,1)),rewrite([47633(11),29213(14),29280(13),457(12),61395(10),125(11,R),51(10),60893(9),125(14,R),125(15,R),28260(15),382(12,R),62828(12),1600(9),46669(9),64268(9),1385(14),56(12),31(11),451(10),55(11),46203(11)])].

64544 C * (C' / x) = x'. [back_rewrite(58226),rewrite([64515(10),41153(12)])].

64545 $F. [resolve(64544,a,47136,a)].

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

============================== STATISTICS ============================

Given=1483. Generated=1181553. Kept=64538. proofs=1.

Usable=833. Sos=19919. Demods=17999. Limbo=29, Disabled=43771. Hints=0.

Kept_by_rule=0, Deleted_by_rule=187415.

Forward_subsumed=524785. Back_subsumed=576.

Sos_limit_deleted=404815. Sos_displaced=8754. Sos_removed=0.

New_demodulators=59522 (15 lex), Back_demodulated=34426. Back_unit_deleted=0.

Demod_attempts=98531512. Demod_rewrites=11437746.

Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.

Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0.

Megabytes=66.00.

User_CPU=157.94, System_CPU=1.45, Wall_clock=159.

============================== end of statistics =====================

============================== end of search =========================

THEOREM PROVED

Exiting with 1 proof.

Process 3393 exit (max_proofs) Tue Oct 6 14:35:22 2009

% Length of proof is 137.

% Level of proof is 22.

% Maximum clause weight is 38.

% Given clauses 154.

1 (x * y) * (C * C) = x * (y * (C * C)) # label(non_clause) # label(goal). [goal].

2 1 * x = x. [assumption].

3 x * 1 = x. [assumption].

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

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

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

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

8 x * x' = 1. [assumption].

9 x' * x = 1. [assumption].

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

11 (x * y) * (y * z) = y * ((y * x) * z). [copy(10),flip(a)].

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

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

14 ((x * y) / x) * (x * z) = x * (y * z). [copy(13),flip(a)].

15 C * (x * C)' = x'. [assumption].

16 (c1 * c2) * (C * C) != c1 * (c2 * (C * C)). [deny(1)].

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

21 x / (y \ x) = y. [para(4(a,1),6(a,1,1))].

22 (x / y) \ x = y. [para(7(a,1),5(a,1,2))].

24 x \ 1 = x'. [para(8(a,1),5(a,1,2))].

26 x'' = x. [para(9(a,1),5(a,1,2)),rewrite([24(3)])].

29 x * ((x * y) * (x \ z)) = (y * x) * z. [para(4(a,1),11(a,1,2)),flip(a)].

30 (x * y) \ (y * ((y * x) * z)) = y * z. [para(11(a,1),5(a,1,2))].

32 x * ((x * (y / x)) * z) = y * (x * z). [para(7(a,1),11(a,1,1)),flip(a)].

34 x * ((x * y) * x') = y * x. [para(8(a,1),11(a,1,2)),rewrite([3(3)]),flip(a)].

41 x * (x * (y / x)) = y * x. [para(7(a,1),12(a,1,1)),flip(a)].

46 (x / y) * (y * z) = y * ((y \ x) * z). [para(4(a,1),14(a,1,1,1))].

47 ((x * y) / x) * z = x * (y * (x \ z)). [para(4(a,1),14(a,1,2))].

49 (x * (y * z)) / (x * z) = (x * y) / x. [para(14(a,1),6(a,1,1))].

51 (x * y) / x = x * (y * x'). [para(8(a,1),14(a,1,2)),rewrite([3(4)])].

70 (x * (y * z)) / (x * z) = x * (y * x'). [back_rewrite(49),rewrite([51(6)])].

72 (x * (y * x')) * z = x * (y * (x \ z)). [back_rewrite(47),rewrite([51(2)])].

77 (x * C)' = C \ x'. [para(15(a,1),5(a,1,2)),flip(a)].

78 (x / C)' = C * x'. [para(7(a,1),15(a,1,2,1)),flip(a)].

84 C * ((C \ x) * x') = 1. [para(78(a,1),8(a,1,2)),rewrite([46(6)])].

86 (C * x')' = x / C. [para(78(a,1),26(a,1,1))].

89 (C * x)' = x' / C. [para(26(a,1),86(a,1,1,2))].

95 (x * C')' / C = C * (x' / C). [para(89(a,1),78(a,2,2)),rewrite([51(4),89(6)])].

96 (C \ x) * x' = C'. [para(84(a,1),5(a,1,2)),rewrite([24(3)]),flip(a)].

101 x * (x' / C) = C'. [para(5(a,1),96(a,1,1)),rewrite([89(3)])].

102 C \ x = C' / x'. [para(96(a,1),6(a,1,1)),flip(a)].

107 (x * C)' = C' / x. [back_rewrite(77),rewrite([102(6),26(7)])].

108 x \ C' = x' / C. [para(101(a,1),5(a,1,2))].

121 x \ (y * x) = x * (y / x). [para(41(a,1),5(a,1,2))].

122 (x * y) / (y * (x / y)) = y. [para(41(a,1),6(a,1,1))].

129 x * ((y / x) / x) = x \ y. [para(7(a,1),121(a,1,2)),flip(a)].

131 x * (x' / x) = x'. [para(9(a,1),121(a,1,2)),rewrite([24(2)]),flip(a)].

136 x \ x' = x' / x. [para(131(a,1),5(a,1,2))].

144 x' \ x = x / x'. [para(26(a,1),136(a,1,2)),rewrite([26(4)])].

155 x \ (x \ y) = (y / x) / x. [para(129(a,1),5(a,1,2))].

163 x * (x' * (x' * y)) = x \ y. [para(5(a,1),155(a,1,2)),rewrite([51(3),51(5),12(5)]),flip(a)].

172 (x \ y) * x = x * (y * x'). [para(4(a,1),34(a,1,2,1)),flip(a)].

174 (x * y) * x' = x * (y / x). [para(34(a,1),5(a,1,2)),rewrite([121(2)]),flip(a)].

184 x * (x' * x') = x'. [para(131(a,1),34(a,1,2,1)),rewrite([7(7)])].

185 x * ((x \ y) * x') = y / x. [para(129(a,1),34(a,1,2,1)),rewrite([7(7)])].

194 x' / x = x' * x'. [para(184(a,1),5(a,1,2)),rewrite([136(2)])].

204 x \ x' = x' * x'. [back_rewrite(136),rewrite([194(4)])].

207 x / x' = x * x. [para(26(a,1),194(a,1,1)),rewrite([26(4),26(4)])].

214 x' \ x = x * x. [back_rewrite(144),rewrite([207(4)])].

229 (x * (y * x')) \ (x * y) = x. [para(51(a,1),22(a,1,1))].

242 (x * (y / x)) / x' = x * y. [para(174(a,1),6(a,1,1))].

250 (x' * y) * x = x' * (y / x'). [para(26(a,1),174(a,1,2))].

276 (x * y) \ (x * (y / x')) = x. [para(7(a,1),229(a,1,1,2))].

300 (x * y) / x' = x * (y * x). [para(6(a,1),242(a,1,1,2))].

332 (x * y) * x = x * (y / x'). [para(276(a,1),4(a,1,2))].

365 x * (x * (y * x')) = y / x'. [para(4(a,1),300(a,1,1)),rewrite([172(4)]),flip(a)].

369 (x' * y) / x = x' * (y * x'). [para(26(a,1),300(a,1,2))].

447 (x / y) / y = y' * (y' * x). [para(163(a,1),5(a,1,2)),rewrite([155(2)])].

459 x \ (y / x') = x * (y * x'). [para(41(a,1),163(a,1,2)),flip(a)].

461 x \ (y * x') = (x \ y) / x. [para(163(a,1),51(a,1,1)),rewrite([332(8),26(7),369(6),163(9)]),flip(a)].

475 x \ (x \ y) = x' * (x' * y). [back_rewrite(155),rewrite([447(4)])].

493 (x * y) * (x * z) = x * ((y / x') * z). [para(365(a,1),11(a,2,2,1)),rewrite([332(4),6(4)])].

502 (x / y') / y = (x * y') * y. [para(365(a,1),51(a,1,1)),rewrite([174(8),41(8)])].

593 C' / (x * C') = C * (x / C')'. [para(502(a,1),78(a,1,1)),rewrite([107(6)])].

627 x' * ((x / C) * x') = C' / x. [para(101(a,1),369(a,1,1)),rewrite([26(6)]),flip(a)].

669 (x * y) \ (y * z) = y * ((y * x) \ z). [para(4(a,1),30(a,1,2,2))].

670 (x * y) \ y = y * (y * x)'. [para(8(a,1),30(a,1,2,2)),rewrite([3(3)])].

685 x * (x * (y / x))' = y \ x. [para(7(a,1),670(a,1,1)),flip(a)].

716 (x * (y / x))' = x \ (y \ x). [para(685(a,1),5(a,1,2)),flip(a)].

717 x \ C = x' / C'. [para(685(a,1),78(a,2)),rewrite([51(6),89(8),95(8),78(4),51(6),365(8)]),flip(a)].

742 x * (x' / C') = C. [para(717(a,1),4(a,1,2))].

753 x' * (x / C') = C. [para(26(a,1),742(a,1,2,1))].

766 C / (x / C') = x'. [para(753(a,1),6(a,1,1))].

775 C' / (x' * ((x / C') / x))' = x'. [para(753(a,1),276(a,1,1)),rewrite([26(7),102(8)])].

777 x' * ((x / C') / x) = C * x'. [para(753(a,1),332(a,1,1)),rewrite([26(9)]),flip(a)].

783 C' / (x / C) = x'. [back_rewrite(775),rewrite([777(8),89(6),26(4)])].

785 (x * C')' = C / x. [para(6(a,1),766(a,1,2)),flip(a)].

800 (C / x) / C = C * (x' / C). [back_rewrite(95),rewrite([785(4)])].

804 C * (C' / x) = x'. [para(783(a,1),185(a,2)),rewrite([108(7),78(5),51(7),78(11),493(12),6(10),46(8),102(3),46(9),108(6),26(4),627(7)])].

813 (C / x)' = x * C'. [para(785(a,1),26(a,1,1))].

821 C / (C * x) = C * (x' * C'). [para(174(a,1),785(a,1,1)),rewrite([716(5),717(3),459(6)]),flip(a)].

858 C * (C * (x / C')') = C / x. [para(785(a,1),804(a,2)),rewrite([593(7)])].

908 (x \ (y \ x))' = x * (y / x). [para(716(a,1),26(a,1,1))].

951 x * ((x / y) / x) = (x \ y)'. [para(22(a,1),908(a,1,1,2)),flip(a)].

981 x \ (x \ y)' = (x / y) / x. [para(951(a,1),5(a,1,2))].

987 (x / y) * x = x * (x \ y)'. [para(951(a,1),12(a,2,2)),rewrite([7(3)])].

991 (x * x)' = x' * x'. [para(194(a,1),951(a,1,2,1)),rewrite([51(6),26(5),9(4),3(4),214(5)]),flip(a)].

1058 ((x * x) * y) * (x' * x') = (x * x) * (y / (x * x)). [para(991(a,1),174(a,1,2))].

1059 (x * x) * (((x * x) \ y) * (x' * x')) = y / (x * x). [para(991(a,1),185(a,1,2,2))].

1104 (x / y) \ (x * (x \ y)') = x. [para(987(a,1),5(a,1,2))].

1138 (x / (y * x)) \ (y \ x) = x. [para(121(a,1),1104(a,1,2,2,1)),rewrite([716(5),4(5)])].

1163 (x \ y) / y = y / (x * y). [para(1138(a,1),21(a,1,2))].

1209 (x * C) * C' = C * (x' / C')'. [para(1163(a,1),78(a,1,1)),rewrite([813(5),717(8)])].

1404 (x * y) / y' = x * (y * y). [para(32(a,1),300(a,2)),rewrite([41(3)])].

1422 (x * y') / y = x * (y' * y'). [para(32(a,1),369(a,2)),rewrite([41(6)])].

1520 (x * y) * (x' * x') = x * ((y / x) * x'). [para(174(a,1),1404(a,1,1)),rewrite([26(4),51(3)]),flip(a)].

1574 (x * (C' * C'))' = C * (C / x). [para(1422(a,1),78(a,1,1)),rewrite([785(12)])].

1599 (x' * x') * (x * y) = x * ((x' * x') * y). [para(194(a,1),46(a,1,1)),rewrite([204(7)])].

1600 (x * x) * (x' * y) = x' * ((x * x) * y). [para(207(a,1),46(a,1,1)),rewrite([214(7)])].

1622 (x * (y' * y')) * (y * z) = y * (((y \ x) / y) * z). [para(461(a,1),46(a,2,2,1)),rewrite([1422(3)])].

1851 C * (C / x') = x * (C * C). [para(1209(a,1),365(a,1,2,2)),rewrite([858(10),1404(10)])].

1875 C * (C / (x / (C * C))') = x. [para(1851(a,2),7(a,1))].

1883 (C * C) * ((C * C) * x) = C * (((C / x') / C') * C). [para(1851(a,2),12(a,1,1)),rewrite([493(9)]),flip(a)].

1887 (c1 * c2) * (C * C) != c1 * (C * (C / c2')). [para(1851(a,2),16(a,2,2))].

1891 (C * C) * (x / (C * C)) = C * ((C * C) \ (C / x')). [para(1851(a,2),121(a,1,2)),rewrite([669(9)]),flip(a)].

1895 (C * C) * (x * (C' * C')) = C * (C / ((C * C) \ x)'). [para(1851(a,2),172(a,1)),rewrite([991(16)]),flip(a)].

1920 (C' * C') * (x / (C' * C')) = C * (C / ((C' * C') * x)'). [para(1851(a,2),250(a,1)),rewrite([991(6),991(15),991(20)]),flip(a)].

1926 (x * y) * (C * C) = C * (C / (x * y)'). [para(1851(a,2),29(a,2)),rewrite([29(7)])].

1948 c1 * (C * (C / c2')) != C * (C / (c1 * c2)'). [back_rewrite(1887),rewrite([1926(7)]),flip(a)].

2063 C * ((x * C) * (C' / y')) = (C / x') * y. [para(1209(a,1),72(a,1,1,2)),rewrite([858(9),102(9)]),flip(a)].

2371 (C' * C') * (x * (C * C)) = C * ((C' * C') * (C / x')). [para(1851(a,1),1599(a,1,2))].

2471 (x * x) * (y / (x * x)) = (x * x) * (y * (x' * x')). [para(1059(a,1),12(a,2,2)),rewrite([1622(8),7(5),4(4),172(4),991(3)]),flip(a)].

2511 C * (C / ((C' * C') * x)') = C * ((C' * C') * (C / x')). [back_rewrite(1920),rewrite([2471(12),26(8),26(9),2371(10)]),flip(a)].

2512 C * ((C * C) \ (C / x')) = C * (C / ((C * C) \ x)'). [back_rewrite(1891),rewrite([2471(8),1895(10)]),flip(a)].

2516 ((x * x) * y) * (x' * x') = (x * x) * (y * (x' * x')). [back_rewrite(1058),rewrite([2471(10)])].

2530 C * ((C * C) * (C / ((C * C) \ x)')) = C * (C / x'). [para(1883(a,1),51(a,1,1)),rewrite([70(14),7(10),991(16),2516(18),1895(18),493(18),207(10)]),flip(a)].

2573 C * ((C' * C') * (C / ((C' * C') * x)')) = x * (C' * C'). [para(1895(a,1),5(a,1,2)),rewrite([669(13),2512(13),475(10),991(6),991(11),2511(17)])].

2577 (C * C) * ((C * (C / ((C * C) \ x)')) * y) = x * ((C * C) * y). [para(1895(a,1),11(a,2,2,1)),rewrite([1926(10),1574(9),821(7),813(5),12(8),163(9),102(3),804(6),26(2)]),flip(a)].

2581 (C * (C / ((C * C) \ x)')) / ((x * (C' * C')) * ((C * C) / (x * (C' * C')))) = x * (C' * C'). [para(1895(a,1),122(a,1,1))].

2597 x \ (C * C) = (C * C) / x. [para(1895(a,1),670(a,2,2,1)),rewrite([1926(10),1574(9),821(7),813(5),12(8),163(9),102(3),804(6),26(2),89(17),813(15),1422(17),1895(19),981(15),1875(17)])].

2604 x / (C * C) = x * (C' * C'). [para(1895(a,1),46(a,2)),rewrite([1600(13),174(12),19(10),3(9),9(8),3(6),475(14),991(10),991(15),2511(21),2573(21)])].

3298 x * ((C * C) / x) = C * C. [para(2597(a,1),4(a,1,2))].

3315 (C * C) \ x = x * (C' * C'). [back_rewrite(2581),rewrite([3298(26),2604(13),1520(15),800(10),26(8),174(12),447(10),163(13),102(7),804(10),26(6)])].

3366 (C * C) * (x * y) = x * ((C * C) * y). [back_rewrite(2577),rewrite([3315(9),1574(12),821(10),813(8),12(11),163(12),102(6),804(9),26(5)])].

3374 (C * C) * x = C * (C / x'). [back_rewrite(2530),rewrite([3315(9),1574(12),821(10),813(8),12(11),163(12),102(6),2063(10),207(4)])].

3462 C * (C / (x * y)') = x * (C * (C / y')). [back_rewrite(3366),rewrite([3374(5),3374(10)])].

3463 $F. [resolve(3462,a,1948,a(flip))].

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

============================== STATISTICS ============================

Given=154. Generated=10713. Kept=3459. proofs=1.

Usable=127. Sos=2242. Demods=2423. Limbo=88, Disabled=1014. Hints=515.

Kept_by_rule=0, Deleted_by_rule=0.

Forward_subsumed=7254. Back_subsumed=17.

Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.

New_demodulators=3399 (0 lex), Back_demodulated=984. Back_unit_deleted=0.

Demod_attempts=271934. Demod_rewrites=38856.

Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.

Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0.

Megabytes=5.36.

User_CPU=0.46, System_CPU=0.02, Wall_clock=1.

============================== end of statistics =====================

============================== end of search =========================

THEOREM PROVED

Exiting with 1 proof.

Process 3413 exit (max_proofs) Tue Oct 6 14:35:32 2009