%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP109-1 : TPTP v3.4.2. Bugfixed v2.7.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art08.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 0.0s
% Output : Assurance 0.0s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP109-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 7 7)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 7 7)
% (binary-posweight-lex-big-order 30 #f 7 7)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) | -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(a4,b4),multiply(b4,a4)).
% was split for some strategies as:
% -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
% -equal(multiply(multiply(inverse(b2),b2),a2),a2).
% -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% -equal(multiply(a4,b4),multiply(b4,a4)).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(4,40,0,8,0,0,2022,4,751)
%
%
% START OF PROOF
% 5 [] equal(X,X).
% 6 [] equal(double_divide(inverse(double_divide(X,inverse(double_divide(inverse(Y),double_divide(X,Z))))),Z),Y).
% 7 [] equal(multiply(X,Y),inverse(double_divide(Y,X))).
% 8 [] -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) | -equal(multiply(a4,b4),multiply(b4,a4)).
% 9 [para:6.1.1,7.1.2.1,demod:7] equal(multiply(X,multiply(multiply(double_divide(Y,X),inverse(Z)),Y)),inverse(Z)).
% 10 [para:7.1.2,6.1.1.1,demod:7] equal(double_divide(multiply(multiply(double_divide(X,Y),inverse(Z)),X),Y),Z).
% 11 [para:7.1.2,6.1.1.1.1.2.1.1,demod:7] equal(double_divide(multiply(multiply(double_divide(X,Y),multiply(Z,U)),X),Y),double_divide(U,Z)).
% 12 [para:6.1.1,6.1.1.1.1.2.1,demod:7] equal(double_divide(multiply(inverse(X),Y),Z),double_divide(U,multiply(double_divide(U,double_divide(Y,Z)),inverse(X)))).
% 13 [para:6.1.1,6.1.1.1.1.2.1.2,demod:7] equal(double_divide(multiply(multiply(X,inverse(Y)),multiply(multiply(double_divide(Z,U),inverse(X)),Z)),U),Y).
% 14 [para:7.1.2,9.1.1.2.1.2,demod:7] equal(multiply(X,multiply(multiply(double_divide(Y,X),multiply(Z,U)),Y)),multiply(Z,U)).
% 15 [para:6.1.1,9.1.1.2.1.1,demod:7] equal(multiply(X,multiply(multiply(Y,inverse(Z)),multiply(multiply(double_divide(U,X),inverse(Y)),U))),inverse(Z)).
% 17 [para:11.1.1,6.1.1.1.1.2.1.2,demod:7] equal(double_divide(multiply(multiply(double_divide(X,Y),inverse(Z)),multiply(multiply(double_divide(U,V),multiply(Y,X)),U)),V),Z).
% 18 [para:6.1.1,11.1.1.1.1.1,demod:7] equal(double_divide(multiply(multiply(X,multiply(Y,Z)),multiply(multiply(double_divide(U,V),inverse(X)),U)),V),double_divide(Z,Y)).
% 19 [para:11.1.1,9.1.1.2.1.1] equal(multiply(X,multiply(multiply(double_divide(Y,Z),inverse(U)),multiply(multiply(double_divide(V,X),multiply(Z,Y)),V))),inverse(U)).
% 21 [para:6.1.1,14.1.1.2.1.1,demod:7] equal(multiply(X,multiply(multiply(Y,multiply(Z,U)),multiply(multiply(double_divide(V,X),inverse(Y)),V))),multiply(Z,U)).
% 22 [para:9.1.1,14.1.1.2.1] equal(multiply(X,multiply(inverse(Y),Z)),multiply(multiply(double_divide(U,double_divide(Z,X)),inverse(Y)),U)).
% 25 [?] ?
% 26 [para:12.1.2,6.1.1.1.1.2.1.2,demod:7] equal(double_divide(multiply(multiply(double_divide(multiply(inverse(X),Y),Z),inverse(U)),V),multiply(double_divide(V,double_divide(Y,Z)),inverse(X))),U).
% 27 [para:6.1.1,12.1.2.2.1,demod:12,7] equal(double_divide(multiply(inverse(X),Y),Z),double_divide(multiply(Z,multiply(inverse(U),Y)),multiply(U,inverse(X)))).
% 28 [para:6.1.1,12.1.2.2.1.2,demod:7] equal(double_divide(multiply(inverse(X),multiply(multiply(double_divide(Y,Z),inverse(U)),Y)),Z),double_divide(V,multiply(double_divide(V,U),inverse(X)))).
% 29 [para:12.1.2,9.1.1.2.1.1] equal(multiply(multiply(double_divide(X,double_divide(Y,Z)),inverse(U)),multiply(multiply(double_divide(multiply(inverse(U),Y),Z),inverse(V)),X)),inverse(V)).
% 30 [para:12.1.2,11.1.1.1.1.1] equal(double_divide(multiply(multiply(double_divide(multiply(inverse(X),Y),Z),multiply(U,V)),W),multiply(double_divide(W,double_divide(Y,Z)),inverse(X))),double_divide(V,U)).
% 31 [para:11.1.1,12.1.2.2.1,demod:25] equal(double_divide(multiply(inverse(X),Y),Z),double_divide(multiply(Z,multiply(multiply(U,V),Y)),multiply(double_divide(V,U),inverse(X)))).
% 32 [para:11.1.1,12.1.2.2.1.2,demod:12] equal(double_divide(multiply(inverse(X),multiply(multiply(double_divide(Y,Z),multiply(U,V)),Y)),Z),double_divide(multiply(inverse(X),V),U)).
% 33 [para:12.1.2,14.1.1.2.1.1] equal(multiply(multiply(double_divide(X,double_divide(Y,Z)),inverse(U)),multiply(multiply(double_divide(multiply(inverse(U),Y),Z),multiply(V,W)),X)),multiply(V,W)).
% 34 [para:12.1.2,12.1.2.2.1.2,demod:12] equal(double_divide(multiply(inverse(X),Y),multiply(double_divide(Y,double_divide(Z,U)),inverse(V))),double_divide(multiply(inverse(X),multiply(inverse(V),Z)),U)).
% 37 [para:9.1.1,13.1.1.1] equal(double_divide(inverse(X),multiply(X,inverse(Y))),Y).
% 43 [para:37.1.1,7.1.2.1] equal(multiply(multiply(X,inverse(Y)),inverse(X)),inverse(Y)).
% 44 [para:7.1.2,37.1.1.1] equal(double_divide(multiply(X,Y),multiply(double_divide(Y,X),inverse(Z))),Z).
% 45 [para:7.1.2,37.1.1.2.2] equal(double_divide(inverse(X),multiply(X,multiply(Y,Z))),double_divide(Z,Y)).
% 55 [para:7.1.2,43.1.1.1.2,demod:7] equal(multiply(multiply(X,multiply(Y,Z)),inverse(X)),multiply(Y,Z)).
% 57 [para:43.1.1,37.1.1.2] equal(double_divide(inverse(multiply(X,inverse(Y))),inverse(Y)),X).
% 58 [para:43.1.1,43.1.1.1] equal(multiply(inverse(X),inverse(multiply(Y,inverse(X)))),inverse(Y)).
% 59 [para:7.1.2,57.1.1.1.1.2,demod:7] equal(double_divide(inverse(multiply(X,multiply(Y,Z))),multiply(Y,Z)),X).
% 71 [?] ?
% 73 [?] ?
% 85 [para:44.1.1,11.1.1.1.1.1] equal(double_divide(multiply(multiply(X,multiply(Y,Z)),multiply(U,V)),multiply(double_divide(V,U),inverse(X))),double_divide(Z,Y)).
% 86 [para:44.1.1,14.1.1.2.1.1] equal(multiply(multiply(double_divide(X,Y),inverse(Z)),multiply(multiply(Z,multiply(U,V)),multiply(Y,X))),multiply(U,V)).
% 102 [?] ?
% 112 [para:9.1.1,55.1.1.1] equal(multiply(inverse(X),inverse(Y)),multiply(multiply(double_divide(Z,Y),inverse(X)),Z)).
% 113 [para:9.1.1,55.1.1.1.2,demod:112,43] equal(inverse(X),multiply(Y,multiply(inverse(X),inverse(Y)))).
% 114 [para:14.1.1,55.1.1.1] equal(multiply(multiply(X,Y),inverse(Z)),multiply(multiply(double_divide(U,Z),multiply(X,Y)),U)).
% 128 [para:113.1.2,45.1.1.2.2,demod:37] equal(X,double_divide(multiply(inverse(X),inverse(Y)),Y)).
% 129 [para:7.1.2,128.1.2.1.1] equal(double_divide(X,Y),double_divide(multiply(multiply(Y,X),inverse(Z)),Z)).
% 138 [para:9.1.1,59.1.1.1.1,demod:73,112] equal(multiply(double_divide(inverse(X),inverse(Y)),inverse(Y)),X).
% 167 [para:138.1.1,10.1.1.1.1] equal(double_divide(multiply(X,inverse(X)),inverse(Y)),Y).
% 168 [para:138.1.1,9.1.1.2.1] equal(multiply(inverse(X),multiply(Y,inverse(Y))),inverse(X)).
% 170 [para:138.1.1,14.1.1.2.1.2,demod:138] equal(multiply(X,multiply(multiply(double_divide(Y,X),Z),Y)),Z).
% 178 [para:138.1.1,55.1.1.1.2,demod:138] equal(multiply(multiply(X,Y),inverse(X)),Y).
% 179 [para:138.1.1,59.1.1.1.1.2,demod:138] equal(double_divide(inverse(multiply(X,Y)),Y),X).
% 185 [para:178.1.1,58.1.1.2.1] equal(multiply(inverse(X),inverse(Y)),inverse(multiply(X,Y))).
% 190 [para:138.1.1,178.1.1.1,demod:185,7] equal(multiply(X,inverse(multiply(Y,X))),inverse(Y)).
% 191 [para:179.1.1,6.1.1.1.1.2.1,demod:7] equal(double_divide(multiply(inverse(X),Y),Z),multiply(X,double_divide(Y,Z))).
% 201 [para:178.1.1,179.1.1.1.1] equal(double_divide(inverse(X),inverse(Y)),multiply(Y,X)).
% 206 [para:167.1.1,12.1.2.2.1.2,demod:102,201,168] equal(multiply(X,Y),multiply(Y,X)).
% 217 [para:206.1.1,11.1.1.1.1.2,demod:129,114] equal(double_divide(X,Y),double_divide(Y,X)).
% 237 [para:206.1.1,113.1.2,demod:185] equal(inverse(X),multiply(inverse(multiply(X,Y)),Y)).
% 238 [para:206.1.1,113.1.2.2,demod:185] equal(inverse(X),multiply(Y,inverse(multiply(Y,X)))).
% 239 [para:206.1.1,128.1.2.1,demod:185] equal(X,double_divide(inverse(multiply(Y,X)),Y)).
% 244 [para:206.1.1,138.1.1,demod:201] equal(multiply(inverse(X),multiply(X,Y)),Y).
% 246 [para:206.1.1,167.1.1.1,demod:191] equal(multiply(X,double_divide(X,inverse(Y))),Y).
% 266 [para:19.1.1,178.1.1.1,demod:114,185] equal(inverse(multiply(X,Y)),multiply(multiply(double_divide(Z,U),inverse(X)),multiply(multiply(U,Z),inverse(Y)))).
% 279 [para:217.1.1,12.1.2.2.1.2,demod:7,102,191] equal(multiply(X,double_divide(Y,Z)),double_divide(multiply(Y,Z),inverse(X))).
% 296 [para:15.1.1,239.1.2.1.1,demod:185,112] equal(multiply(multiply(X,inverse(Y)),inverse(multiply(X,Z))),double_divide(inverse(inverse(Y)),Z)).
% 299 [para:113.1.2,239.1.2.1.1,demod:185] equal(inverse(multiply(X,Y)),double_divide(inverse(inverse(X)),Y)).
% 301 [para:138.1.1,239.1.2.1.1,demod:201] equal(inverse(X),double_divide(inverse(Y),multiply(X,Y))).
% 306 [para:244.1.1,15.1.1,demod:238,71,112] equal(inverse(inverse(inverse(X))),inverse(X)).
% 307 [para:15.1.1,244.1.1.2,demod:299,296,112,185] equal(inverse(multiply(X,Y)),inverse(multiply(Y,X))).
% 310 [para:244.1.1,45.1.1.2,demod:299] equal(inverse(multiply(X,Y)),double_divide(Y,X)).
% 314 [para:138.1.1,244.1.1.2,demod:310,201] equal(multiply(double_divide(X,Y),X),inverse(Y)).
% 319 [para:244.1.1,244.1.1.2] equal(multiply(inverse(inverse(X)),Y),multiply(X,Y)).
% 320 [para:306.1.1,6.1.1.1.1.2.1.1,demod:310,201,102,7] equal(double_divide(double_divide(X,Y),X),inverse(inverse(Y))).
% 322 [?] ?
% 323 [para:306.1.1,13.1.1.1.2.1.2,demod:322,310,185,112,319] equal(inverse(inverse(X)),X).
% 325 [para:306.1.1,17.1.1.1.1.2,demod:323,310,266,114] equal(double_divide(double_divide(X,Y),X),Y).
% 326 [para:306.1.1,113.1.2.2.1,demod:310,185,323] equal(inverse(X),multiply(Y,double_divide(Y,X))).
% 328 [para:306.1.1,167.1.1.1.2,demod:279,323] equal(multiply(X,double_divide(Y,inverse(Y))),X).
% 331 [para:323.1.1,13.1.1.1.1.2,demod:310,185,112] equal(double_divide(multiply(multiply(X,Y),double_divide(Z,X)),Z),inverse(Y)).
% 333 [para:323.1.1,37.1.1.1,demod:310,185] equal(double_divide(X,double_divide(Y,X)),Y).
% 340 [para:323.1.1,113.1.2.2.1,demod:323] equal(X,multiply(Y,multiply(X,inverse(Y)))).
% 344 [para:323.1.1,138.1.1.1.2,demod:323] equal(multiply(double_divide(inverse(X),Y),Y),X).
% 345 [para:323.1.1,178.1.1.2] equal(multiply(multiply(inverse(X),Y),X),Y).
% 348 [para:323.1.1,244.1.1.1] equal(multiply(X,multiply(inverse(X),Y)),Y).
% 377 [para:37.1.1,325.1.1.1] equal(double_divide(X,inverse(Y)),multiply(Y,inverse(X))).
% 382 [para:45.1.1,325.1.1.1] equal(double_divide(double_divide(X,Y),inverse(Z)),multiply(Z,multiply(Y,X))).
% 385 [para:167.1.1,325.1.1.1,demod:377] equal(double_divide(X,double_divide(Y,inverse(Y))),inverse(X)).
% 388 [para:325.1.1,217.1.1] equal(X,double_divide(Y,double_divide(Y,X))).
% 389 [para:217.1.1,325.1.1.1] equal(double_divide(double_divide(X,Y),Y),X).
% 392 [para:333.1.1,7.1.2.1] equal(multiply(double_divide(X,Y),Y),inverse(X)).
% 394 [para:6.1.1,333.1.1.2,demod:377,7] equal(double_divide(X,Y),multiply(double_divide(Y,multiply(X,Z)),Z)).
% 397 [para:13.1.1,333.1.1.2,demod:394,7,377] equal(double_divide(X,Y),multiply(double_divide(Y,inverse(Z)),double_divide(X,Z))).
% 403 [para:18.1.1,333.1.1.2,demod:394,7,377] equal(double_divide(X,double_divide(Y,Z)),multiply(multiply(U,multiply(Z,Y)),double_divide(X,U))).
% 412 [para:45.1.1,388.1.2.2] equal(multiply(X,multiply(Y,Z)),double_divide(inverse(X),double_divide(Z,Y))).
% 432 [para:21.1.1,244.1.1.2,demod:403,394,7,377] equal(multiply(inverse(X),multiply(Y,Z)),double_divide(X,double_divide(Z,Y))).
% 438 [para:389.1.1,7.1.2.1] equal(multiply(X,double_divide(Y,X)),inverse(Y)).
% 440 [para:6.1.1,389.1.1.1,demod:7,310,412] equal(double_divide(X,Y),multiply(double_divide(multiply(Y,Z),X),Z)).
% 447 [para:167.1.1,389.1.1.1,demod:377] equal(double_divide(X,inverse(X)),double_divide(Y,inverse(Y))).
% 452 [para:10.1.1,22.1.2.1.1,demod:397,394,7,377] equal(multiply(X,multiply(inverse(Y),Z)),double_divide(double_divide(Z,X),Y)).
% 462 [para:22.1.2,179.1.1.1.1,demod:377,7,452] equal(double_divide(multiply(X,double_divide(Y,Z)),U),double_divide(X,multiply(double_divide(Y,Z),U))).
% 472 [para:333.1.1,22.1.2.1.1,demod:377,452] equal(double_divide(double_divide(X,Y),Z),multiply(double_divide(Z,inverse(X)),Y)).
% 481 [para:246.1.1,244.1.1.2] equal(multiply(inverse(X),Y),double_divide(X,inverse(Y))).
% 497 [para:217.1.1,328.1.1.2] equal(multiply(X,double_divide(inverse(Y),Y)),X).
% 526 [para:6.1.1,344.1.1.1,demod:310,412] equal(multiply(X,Y),double_divide(Z,double_divide(multiply(Y,Z),X))).
% 528 [para:19.1.1,345.1.1.1,demod:392,472,7,377,481] equal(double_divide(X,inverse(Y)),multiply(double_divide(X,multiply(Z,U)),multiply(multiply(Z,U),Y))).
% 530 [para:348.1.1,11.1.1.1.1,demod:7] equal(double_divide(multiply(X,Y),Z),double_divide(X,multiply(Z,Y))).
% 535 [para:392.1.1,45.1.1.2,demod:530,279,7] equal(multiply(X,double_divide(Y,multiply(X,Z))),double_divide(Z,Y)).
% 538 [para:497.1.1,206.1.1] equal(X,multiply(double_divide(inverse(Y),Y),X)).
% 542 [para:190.1.1,10.1.1.1.1,demod:481] equal(double_divide(double_divide(X,inverse(Y)),Z),multiply(X,double_divide(Y,Z))).
% 543 [para:190.1.1,13.1.1.1.1,demod:481,394,7,377] equal(double_divide(double_divide(X,multiply(Y,Z)),Z),multiply(X,Y)).
% 548 [para:7.1.2,201.1.1.2] equal(double_divide(inverse(X),multiply(Y,Z)),multiply(double_divide(Z,Y),X)).
% 573 [para:26.1.1,333.1.1.2,demod:310,542,481,7,377] equal(double_divide(double_divide(X,multiply(double_divide(Y,Z),U)),V),multiply(double_divide(V,double_divide(double_divide(Y,Z),X)),U)).
% 598 [para:238.1.2,44.1.1.2,demod:279] equal(multiply(X,double_divide(Y,Z)),multiply(double_divide(Z,Y),X)).
% 602 [para:7.1.2,27.1.2.1.2.1,demod:528,530,7,377,542,481] equal(multiply(X,double_divide(Y,Z)),double_divide(Z,double_divide(X,inverse(Y)))).
% 606 [para:19.1.1,27.1.2.1.2,demod:542,462,602,481,528,392,472,7,377] equal(double_divide(X,multiply(double_divide(Y,Z),U)),multiply(Y,multiply(Z,double_divide(X,U)))).
% 611 [para:27.1.2,333.1.1.2,demod:535,542,481,377] equal(double_divide(double_divide(X,Y),Z),multiply(Y,double_divide(Z,inverse(X)))).
% 620 [para:328.1.1,27.1.2.1.2,demod:606,602,542,377,385,7,481] equal(double_divide(inverse(X),Y),double_divide(Z,multiply(double_divide(Z,X),Y))).
% 623 [para:237.1.2,27.1.2.1.2,demod:310,377,542,481] equal(multiply(X,double_divide(Y,Z)),multiply(U,double_divide(Z,double_divide(X,double_divide(Y,U))))).
% 626 [para:301.1.2,6.1.1.1.1.2.1.2,demod:530,412,310,201] equal(double_divide(double_divide(X,multiply(Y,Z)),multiply(X,Y)),Z).
% 650 [para:307.1.1,201.1.1.1,demod:382,310] equal(multiply(X,multiply(Y,Z)),multiply(X,multiply(Z,Y))).
% 670 [para:45.1.1,320.1.1.1,demod:7,530,310,382] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Z),Y)).
% 674 [para:26.1.1,320.1.1.1,demod:530,310,377,388,606,7,670,542,481] equal(multiply(double_divide(X,Y),multiply(Z,U)),double_divide(X,multiply(double_divide(U,Z),Y))).
% 676 [para:6.1.1,28.1.1.1.2.1.1,demod:543,481,388,472,394,7,530,310,412,377] equal(multiply(X,Y),double_divide(Z,double_divide(X,multiply(Y,Z)))).
% 683 [para:44.1.1,28.1.2.2.1,demod:472,543,481,310,314,530,674,670,7,377] equal(multiply(X,double_divide(Y,multiply(Z,U))),double_divide(Z,double_divide(double_divide(Y,U),X))).
% 738 [para:29.1.1,178.1.1.1,demod:573,683,542,481,674,670,7,377] equal(double_divide(X,double_divide(Y,multiply(double_divide(Z,U),V))),double_divide(double_divide(V,multiply(double_divide(X,U),Y)),Z)).
% 826 [para:19.1.1,31.1.2.1,demod:392,548,432,670,412,620,738,7,481,310,314,674] equal(double_divide(X,double_divide(inverse(Y),Z)),multiply(double_divide(X,Y),Z)).
% 829 [para:244.1.1,31.1.2.1,demod:7,377,542,310,481] equal(multiply(X,double_divide(Y,double_divide(Z,U))),double_divide(Y,double_divide(X,multiply(U,Z)))).
% 846 [para:31.1.2,438.1.1.2,demod:530,310,670,676,674,542,481,7,377] equal(multiply(double_divide(X,Y),double_divide(Z,U)),double_divide(U,multiply(Y,multiply(X,Z)))).
% 848 [para:538.1.2,31.1.2.1,demod:620,674,530,7,670,377,392,826,542,481] equal(double_divide(X,inverse(Y)),double_divide(Z,multiply(double_divide(Y,Z),X))).
% 851 [para:238.1.2,31.1.2.2,demod:683,279,670,530,310] equal(double_divide(double_divide(X,double_divide(Y,Z)),multiply(U,V)),double_divide(Z,double_divide(double_divide(U,multiply(V,Y)),X))).
% 855 [para:29.1.1,31.1.2.1,demod:301,530,846,670,548,606,676,542,7,377,481] equal(double_divide(X,multiply(double_divide(Y,Z),U)),multiply(Z,multiply(double_divide(X,U),Y))).
% 871 [para:178.1.1,32.1.1.1.2.1.2,demod:310,185,314,462,602,7,481,848,674,670] equal(double_divide(X,inverse(Y)),double_divide(double_divide(Z,Y),multiply(Z,X))).
% 900 [para:21.1.1,170.1.1.2.1,demod:403,394,7,377,670] equal(multiply(X,multiply(Y,multiply(Z,U))),double_divide(double_divide(Z,X),double_divide(U,Y))).
% 905 [para:170.1.1,32.1.1.1.2.1,demod:683,530,7,620,542,481,432] equal(double_divide(double_divide(X,double_divide(Y,Z)),U),double_divide(Z,double_divide(double_divide(U,Y),X))).
% 922 [para:340.1.2,33.1.1.2.1,demod:310,542,481,530,620,674,7,377] equal(double_divide(X,double_divide(Y,multiply(Z,U))),multiply(Z,double_divide(double_divide(U,Y),X))).
% 925 [para:348.1.1,33.1.1.2.1,demod:310,542,481,530,620,674,7,377] equal(double_divide(X,double_divide(Y,multiply(Z,U))),multiply(double_divide(double_divide(U,Y),X),Z)).
% 983 [para:394.1.2,394.1.2.1.2] equal(double_divide(double_divide(X,multiply(Y,Z)),U),multiply(double_divide(U,double_divide(Y,X)),Z)).
% 989 [para:11.1.1,34.1.1.2.1.2,demod:925,530,905,670,7,310,314,674,606,676,542,462,602,377,983,481] equal(double_divide(X,multiply(double_divide(Y,Z),U)),double_divide(double_divide(V,Z),double_divide(Y,double_divide(X,multiply(U,V))))).
% 994 [para:323.1.1,34.1.1.1.1,demod:611,481,323,394,530,462,602,377,983] equal(double_divide(X,double_divide(double_divide(Y,Z),U)),double_divide(double_divide(double_divide(Y,X),U),Z)).
% 997 [para:310.1.1,34.1.1.1.1,demod:548,846,481,310,394,530,462,602,377,983] equal(double_divide(double_divide(X,Y),double_divide(double_divide(Z,U),V)),double_divide(double_divide(X,multiply(Y,V)),multiply(U,Z))).
% 1016 [para:314.1.1,440.1.2.1.1] equal(double_divide(X,double_divide(Y,Z)),multiply(double_divide(inverse(Z),X),Y)).
% 1050 [para:31.1.2,526.1.2.2,demod:611,848,855,530,542,481,670,7,377] equal(multiply(double_divide(X,multiply(Y,Z)),U),double_divide(Y,double_divide(double_divide(Z,X),U))).
% 1062 [para:30.1.1,535.1.1.2,demod:606,846,623,997,412,530,905,994,925,683,855,670,542,481,983] equal(double_divide(double_divide(X,multiply(Y,double_divide(Z,U))),V),double_divide(Z,double_divide(X,multiply(double_divide(V,U),Y)))).
% 1110 [para:598.1.1,30.1.1.1.1.2,demod:1016,438,871,530,826,620,462,602,377,994,738,905,1062,851,683,829,983,674,670,542,481] equal(double_divide(double_divide(X,Y),double_divide(Z,double_divide(U,X))),double_divide(double_divide(Y,Z),U)).
% 1336 [para:85.1.1,331.1.1.1.2,demod:994,922,900,670,925,530,905,846,983,1050,7,377] equal(double_divide(double_divide(X,multiply(Y,multiply(Z,U))),double_divide(double_divide(Z,multiply(V,Y)),double_divide(W,double_divide(double_divide(X,U),V)))),inverse(W)).
% 1353 [para:86.1.1,626.1.1.1.2,demod:922,900,670,530,1110,683,7,377] equal(double_divide(double_divide(X,multiply(Y,Z)),double_divide(U,V)),double_divide(double_divide(Z,X),double_divide(Y,multiply(U,V)))).
% 2023 [input:8,cut:206] -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
% 2024 [para:1336.1.2,2023.1.1.1.1,demod:670,325,472,481,326,279,871,989,388,922,1353,cut:5,cut:650,cut:447] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 7
% clause depth limited to 7
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 388
% derived clauses: 172471
% kept clauses: 2011
% kept size sum: 37571
% kept mid-nuclei: 2
% kept new demods: 994
% forw unit-subs: 170277
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 43
% fast unit cutoff: 2
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.56
% process. runtime: 7.52
% specific non-discr-tree subsumption statistics:
% tried: 2
% length fails: 0
% strength fails: 2
% predlist fails: 0
% aux str. fails: 0
% by-lit fails: 0
% full subs tried: 0
% full subs fail: 0
%
% ; program args: ("/home/graph/tptp/Systems/Gandalf---c-2.6/gandalf" "-time" "600" "/home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP109-1+eq_r.in")
%
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