TSTP Solution File: GRP054-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP054-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art02.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 198.2s
% Output : Assurance 198.2s
% 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/GRP054-1+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 12 5)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 12 5)
% (binary-posweight-lex-big-order 30 #f 12 5)
% (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))).
% 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))).
%
% Starting a split proof attempt with 3 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -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))).
% Split part used next: -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
% END OF PROOFPART
% **** EMPTY CLAUSE DERIVED ****
%
%
% timer checkpoints: c(3,40,0,6,0,0,13,50,0,16,0,0,88247,4,754,88315,5,1003,88316,1,1006,88316,50,1010,88316,40,1010,88319,0,1010,99035,3,1239,103312,4,1315,105002,5,1411,105004,1,1411,105004,50,1411,105004,40,1411,105007,0,1411,128569,3,1621,141762,4,1714,152101,5,1812,152109,1,1812,152109,50,1813,152109,40,1813,152112,0,1813,152119,50,1814,152122,0,1827,257540,3,2781,257548,4,3254,257559,5,3748,257559,1,3748,257559,50,3752,257559,40,3752,257562,0,3752,257569,50,3753,257572,0,3769,312368,3,4220,355491,4,4464,393135,5,4670,393155,1,4670,393155,50,4674,393155,40,4674,393158,0,4674,393159,50,4674,393159,40,4674,393162,0,4688,509277,3,7335,581057,4,8605,684745,5,9889,684750,1,9889,684750,50,9891,684750,40,9891,684753,0,9891,770979,3,11850,798200,4,12453,841065,5,13292,841076,1,13292,841076,50,13295,841076,40,13295,841079,0,13295,895613,3,14363,917021,4,14800,951951,5,15296,951953,1,15296,951953,50,15298,951953,40,15298,951956,0,15298,972824,3,15807,995804,4,16065,995804,5,16488,995813,1,16488,995813,50,16490,995813,40,16490,995816,0,16490,1043118,3,17303,1056574,4,17767,1081444,5,18091,1081477,1,18091,1081477,50,18093,1081477,40,18093,1081480,0,18093,1115058,3,18697,1124183,4,18844,1143020,5,19094,1143056,1,19094,1143056,50,19096,1143056,40,19096,1143056,40,19096,1143059,0,19096,1143065,50,19097,1143068,0,19097)
%
%
% START OF PROOF
% 1143067 [] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))),Y).
% 1143068 [] -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
% 1143069 [para:1143067.1.1,1143067.1.1.1.1.1.2.1.1] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(inverse(Y),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(U,V))).
% 1143070 [para:1143069.1.1,1143067.1.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)),Y).
% 1143078 [para:1143070.1.1,1143070.1.1.2] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(U)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y),U).
% 1143091 [para:1143078.1.1,1143067.1.1.1.1.1.2.1] equal(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(inverse(inverse(inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),inverse(multiply(inverse(inverse(Y)),inverse(multiply(multiply(U,V),inverse(multiply(inverse(multiply(U,V)),multiply(U,V))))))))).
% 1143098 [para:1143091.1.2,1143069.1.2.1.1,demod:1143070,1143067] equal(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))).
% 1143106 [para:1143091.1.2,1143091.1.2] equal(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z))),inverse(multiply(inverse(multiply(U,inverse(Y))),multiply(U,Z)))).
% 1143107 [para:1143106.1.1,1143067.1.1.1.1.1.2.1.1,demod:1143067] equal(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)),multiply(inverse(multiply(U,inverse(Y))),multiply(U,Z))).
% 1143124 [para:1143067.1.1,1143107.1.1.1.1.2,demod:1143067] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(multiply(U,Y)),multiply(U,Z))).
% 1143148 [para:1143124.1.1,1143067.1.1.1.1.1.2.1.2.1.2.1] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(multiply(Z,U),inverse(multiply(inverse(multiply(V,U)),multiply(V,U))))))))),multiply(X,multiply(Z,U)))),Y).
% 1143180 [para:1143124.1.1,1143078.1.1.1.1.2.1.2.1.2.1] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(U)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(V,Z)),multiply(V,Z))))))))),Y),U).
% 1144157 [para:1143078.1.1,1143148.1.1.1.1.1.2.1.2.1.1,demod:1143180] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(multiply(U,V)),multiply(U,V))))))))),multiply(X,Z))),Y).
% 1144180 [para:1143070.1.1,1144157.1.1.1.1.1.2.1.2.1.2.1.1.1,demod:1143070] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(U),U)))))))),multiply(X,Z))),Y).
% 1144246 [para:1144180.1.1,1143098.1.2.1.1] equal(multiply(inverse(X),inverse(multiply(Y,inverse(multiply(inverse(Z),Z))))),multiply(inverse(X),inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))).
% 1144330 [para:1144246.1.2,1143098.1.2] equal(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,Z)))),inverse(multiply(Z,inverse(multiply(inverse(U),U)))))).
% 1144331 [para:1144246.1.1,1143098.1.2.1.1.1.1.1,demod:1144330] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(X,inverse(multiply(inverse(X),X)))).
% 1144573 [para:1144331.1.1,1143098.1.2.1.1.1.1.1,demod:1144330,slowcut:1143068] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 5
% clause depth limited to 13
% seconds given: 12
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -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))).
% Split part used next: -equal(multiply(multiply(inverse(b2),b2),a2),a2).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 5
% clause depth limited to 12
% seconds given: 12
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 5
% clause depth limited to 13
% seconds given: 12
%
%
% **** EMPTY CLAUSE DERIVED ****
%
%
% timer checkpoints: c(3,40,0,6,0,0,13,50,0,16,0,0,88247,4,754,88315,5,1003,88316,1,1006,88316,50,1010,88316,40,1010,88319,0,1010,99035,3,1239,103312,4,1315,105002,5,1411,105004,1,1411,105004,50,1411,105004,40,1411,105007,0,1411,128569,3,1621,141762,4,1714,152101,5,1812,152109,1,1812,152109,50,1813,152109,40,1813,152112,0,1813,152119,50,1814,152122,0,1827,257540,3,2781,257548,4,3254,257559,5,3748,257559,1,3748,257559,50,3752,257559,40,3752,257562,0,3752,257569,50,3753,257572,0,3769,312368,3,4220,355491,4,4464,393135,5,4670,393155,1,4670,393155,50,4674,393155,40,4674,393158,0,4674,393159,50,4674,393159,40,4674,393162,0,4688,509277,3,7335,581057,4,8605,684745,5,9889,684750,1,9889,684750,50,9891,684750,40,9891,684753,0,9891,770979,3,11850,798200,4,12453,841065,5,13292,841076,1,13292,841076,50,13295,841076,40,13295,841079,0,13295,895613,3,14363,917021,4,14800,951951,5,15296,951953,1,15296,951953,50,15298,951953,40,15298,951956,0,15298,972824,3,15807,995804,4,16065,995804,5,16488,995813,1,16488,995813,50,16490,995813,40,16490,995816,0,16490,1043118,3,17303,1056574,4,17767,1081444,5,18091,1081477,1,18091,1081477,50,18093,1081477,40,18093,1081480,0,18093,1115058,3,18697,1124183,4,18844,1143020,5,19094,1143056,1,19094,1143056,50,19096,1143056,40,19096,1143056,40,19096,1143059,0,19096,1143065,50,19097,1143068,0,19097,1144572,50,19137,1144572,30,19137,1144572,40,19137,1144575,0,19137,1144581,50,19138,1144584,0,19138)
%
%
% START OF PROOF
% 1144583 [] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))),Y).
% 1144584 [] -equal(multiply(multiply(inverse(b2),b2),a2),a2).
% 1144585 [para:1144583.1.1,1144583.1.1.1.1.1.2.1.1] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(inverse(Y),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(U,V))).
% 1144586 [para:1144585.1.1,1144583.1.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)),Y).
% 1144587 [para:1144585.1.2,1144583.1.1.1] equal(inverse(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)))),Y).
% 1144594 [para:1144586.1.1,1144586.1.1.2] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(U)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y),U).
% 1144607 [para:1144594.1.1,1144583.1.1.1.1.1.2.1] equal(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(inverse(inverse(inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),inverse(multiply(inverse(inverse(Y)),inverse(multiply(multiply(U,V),inverse(multiply(inverse(multiply(U,V)),multiply(U,V))))))))).
% 1144611 [para:1144607.1.2,1144583.1.1.1.1.1,demod:1144586] equal(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),inverse(Y)).
% 1144614 [para:1144607.1.2,1144585.1.2.1.1,demod:1144586,1144583] equal(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))).
% 1144622 [para:1144607.1.2,1144607.1.2] equal(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z))),inverse(multiply(inverse(multiply(U,inverse(Y))),multiply(U,Z)))).
% 1144623 [para:1144622.1.1,1144583.1.1.1.1.1.2.1.1,demod:1144583] equal(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)),multiply(inverse(multiply(U,inverse(Y))),multiply(U,Z))).
% 1144640 [para:1144583.1.1,1144623.1.1.1.1.2,demod:1144583] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(multiply(U,Y)),multiply(U,Z))).
% 1144664 [para:1144640.1.1,1144583.1.1.1.1.1.2.1.2.1.2.1] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(multiply(Z,U),inverse(multiply(inverse(multiply(V,U)),multiply(V,U))))))))),multiply(X,multiply(Z,U)))),Y).
% 1144696 [para:1144640.1.1,1144594.1.1.1.1.2.1.2.1.2.1] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(U)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(V,Z)),multiply(V,Z))))))))),Y),U).
% 1144806 [para:1144583.1.1,1144611.1.1.1.1.1.1.1.1.2,demod:1144583] equal(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),Y).
% 1145673 [para:1144594.1.1,1144664.1.1.1.1.1.2.1.2.1.1,demod:1144696] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(multiply(U,V)),multiply(U,V))))))))),multiply(X,Z))),Y).
% 1145696 [para:1144586.1.1,1145673.1.1.1.1.1.2.1.2.1.2.1.1.1,demod:1144586] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(U),U)))))))),multiply(X,Z))),Y).
% 1145762 [para:1145696.1.1,1144614.1.2.1.1] equal(multiply(inverse(X),inverse(multiply(Y,inverse(multiply(inverse(Z),Z))))),multiply(inverse(X),inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))).
% 1145846 [para:1145762.1.2,1144614.1.2] equal(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,Z)))),inverse(multiply(Z,inverse(multiply(inverse(U),U)))))).
% 1145847 [para:1145762.1.1,1144614.1.2.1.1.1.1.1,demod:1145846] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(X,inverse(multiply(inverse(X),X)))).
% 1146087 [para:1145847.1.1,1144614.1.2.1.1.1.1.1,demod:1145846] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 1146106 [para:1145847.1.1,1144611.1.1.1.1.1.1.1.1,demod:1145846] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))).
% 1146285 [para:1145847.1.2,1145847.1.2] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(X,inverse(multiply(inverse(Z),Z)))).
% 1146367 [para:1146087.1.1,1144614.1.2.1.1.1] equal(X,multiply(inverse(inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(X),inverse(multiply(inverse(inverse(X)),inverse(X))))))).
% 1146602 [para:1146106.1.1,1146087.1.1.1] equal(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)),multiply(inverse(Z),Z)).
% 1146711 [para:1146285.1.1,1146087.1.1] equal(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y))),multiply(inverse(Z),Z)).
% 1147964 [para:1146711.1.1,1145762.1.1,demod:1146367] equal(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))).
% 1148546 [para:1147964.1.1,1146602.1.1.2] equal(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))),multiply(inverse(Z),Z)).
% 1148633 [para:1147964.1.1,1147964.1.2.1] equal(multiply(inverse(X),X),inverse(inverse(multiply(inverse(Y),Y)))).
% 1148809 [para:1148633.1.2,1144806.1.1.1.1] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))),Y).
% 1149067 [para:1148633.1.2,1147964.1.1.1] equal(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),Z))).
% 1163351 [para:1147964.1.2,1148809.1.1.1.2.1.2] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,multiply(inverse(Z),Z))))),Y).
% 1163521 [para:1148546.1.2,1148809.1.1.1.2.1.2.1] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,inverse(multiply(inverse(multiply(inverse(Z),Z)),inverse(multiply(inverse(U),U)))))))),Y).
% 1163915 [para:1149067.1.1,1144583.1.1.1.2,demod:1163521] equal(inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))),X).
% 1163939 [para:1149067.1.1,1144586.1.1.2,demod:1163351,1163915] equal(multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))),X).
% 1163945 [para:1149067.1.1,1144587.1.1.1.1.2,demod:1163351,1163915,1163939] equal(inverse(inverse(multiply(X,inverse(multiply(inverse(Y),Y))))),X).
% 1164866 [para:1163915.1.1,1144587.1.1.1.1.1,demod:1163945] equal(inverse(inverse(multiply(X,multiply(inverse(X),Y)))),Y).
% 1165341 [para:1163915.1.1,1148809.1.1.1.2] equal(inverse(multiply(multiply(inverse(X),X),Y)),inverse(Y)).
% 1165435 [para:1146106.1.1,1164866.1.1.1.1.2.1,demod:1165341] equal(inverse(inverse(multiply(inverse(multiply(inverse(X),X)),Y))),Y).
% 1165476 [para:1148633.1.2,1164866.1.1.1.1.2.1,demod:1165435,slowcut:1144584] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 5
% clause depth limited to 13
% seconds given: 12
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -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))).
% Split part used next: -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 5
% clause depth limited to 12
% seconds given: 12
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 5
% clause depth limited to 13
% seconds given: 12
%
%
% **** EMPTY CLAUSE DERIVED ****
%
%
% timer checkpoints: c(3,40,0,6,0,0,13,50,0,16,0,0,88247,4,754,88315,5,1003,88316,1,1006,88316,50,1010,88316,40,1010,88319,0,1010,99035,3,1239,103312,4,1315,105002,5,1411,105004,1,1411,105004,50,1411,105004,40,1411,105007,0,1411,128569,3,1621,141762,4,1714,152101,5,1812,152109,1,1812,152109,50,1813,152109,40,1813,152112,0,1813,152119,50,1814,152122,0,1827,257540,3,2781,257548,4,3254,257559,5,3748,257559,1,3748,257559,50,3752,257559,40,3752,257562,0,3752,257569,50,3753,257572,0,3769,312368,3,4220,355491,4,4464,393135,5,4670,393155,1,4670,393155,50,4674,393155,40,4674,393158,0,4674,393159,50,4674,393159,40,4674,393162,0,4688,509277,3,7335,581057,4,8605,684745,5,9889,684750,1,9889,684750,50,9891,684750,40,9891,684753,0,9891,770979,3,11850,798200,4,12453,841065,5,13292,841076,1,13292,841076,50,13295,841076,40,13295,841079,0,13295,895613,3,14363,917021,4,14800,951951,5,15296,951953,1,15296,951953,50,15298,951953,40,15298,951956,0,15298,972824,3,15807,995804,4,16065,995804,5,16488,995813,1,16488,995813,50,16490,995813,40,16490,995816,0,16490,1043118,3,17303,1056574,4,17767,1081444,5,18091,1081477,1,18091,1081477,50,18093,1081477,40,18093,1081480,0,18093,1115058,3,18697,1124183,4,18844,1143020,5,19094,1143056,1,19094,1143056,50,19096,1143056,40,19096,1143056,40,19096,1143059,0,19096,1143065,50,19097,1143068,0,19097,1144572,50,19137,1144572,30,19137,1144572,40,19137,1144575,0,19137,1144581,50,19138,1144584,0,19138,1165475,50,19509,1165475,30,19509,1165475,40,19509,1165478,0,19509,1165484,50,19509,1165487,0,19509)
%
%
% START OF PROOF
% 1165486 [] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))),Y).
% 1165487 [] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% 1165488 [para:1165486.1.1,1165486.1.1.1.1.1.2.1.1] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(inverse(Y),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(U,V))).
% 1165489 [para:1165488.1.1,1165486.1.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)),Y).
% 1165490 [para:1165488.1.2,1165486.1.1.1] equal(inverse(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)))),Y).
% 1165497 [para:1165489.1.1,1165489.1.1.2] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(U)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y),U).
% 1165510 [para:1165497.1.1,1165486.1.1.1.1.1.2.1] equal(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(inverse(inverse(inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),inverse(multiply(inverse(inverse(Y)),inverse(multiply(multiply(U,V),inverse(multiply(inverse(multiply(U,V)),multiply(U,V))))))))).
% 1165513 [para:1165510.1.1,1165486.1.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(multiply(inverse(U),inverse(multiply(Y,inverse(multiply(inverse(Y),Y))))))),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z)))))))),U).
% 1165514 [para:1165510.1.2,1165486.1.1.1.1.1,demod:1165489] equal(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),inverse(Y)).
% 1165517 [para:1165510.1.2,1165488.1.2.1.1,demod:1165489,1165486] equal(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))).
% 1165519 [para:1165489.1.1,1165510.1.2.2.1.2.1.1,demod:1165489] equal(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z))),multiply(inverse(multiply(inverse(multiply(U,inverse(multiply(inverse(inverse(V)),inverse(multiply(W,inverse(multiply(inverse(W),W)))))))),inverse(multiply(inverse(inverse(inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),inverse(multiply(multiply(U,W),inverse(multiply(inverse(multiply(U,W)),multiply(U,W))))))))),inverse(multiply(inverse(inverse(Y)),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))).
% 1165525 [para:1165510.1.2,1165510.1.2] equal(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z))),inverse(multiply(inverse(multiply(U,inverse(Y))),multiply(U,Z)))).
% 1165526 [para:1165525.1.1,1165486.1.1.1.1.1.2.1.1,demod:1165486] equal(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)),multiply(inverse(multiply(U,inverse(Y))),multiply(U,Z))).
% 1165550 [para:1165486.1.1,1165526.1.1.1.1.2,demod:1165486] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(multiply(U,Y)),multiply(U,Z))).
% 1165581 [para:1165550.1.1,1165486.1.1.1.1.1.2.1.2.1.2.1] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(multiply(Z,U),inverse(multiply(inverse(multiply(V,U)),multiply(V,U))))))))),multiply(X,multiply(Z,U)))),Y).
% 1165619 [para:1165550.1.1,1165497.1.1.1.1.2.1.2.1.2.1] equal(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(U)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(V,Z)),multiply(V,Z))))))))),Y),U).
% 1165644 [para:1165550.1.1,1165550.1.1.1.1] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V)),multiply(inverse(multiply(W,multiply(U,Z))),multiply(W,V))).
% 1165645 [para:1165550.1.1,1165550.1.1.2] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,V))),multiply(inverse(multiply(W,Z)),multiply(W,multiply(X,V)))).
% 1165777 [para:1165486.1.1,1165514.1.1.1.1.1.1.1.1.2,demod:1165486] equal(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),Y).
% 1166006 [para:1165645.1.1,1165644.1.1] equal(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U))),multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,U)))).
% 1166724 [para:1165497.1.1,1165581.1.1.1.1.1.2.1.2.1.1,demod:1165619] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(multiply(U,V)),multiply(U,V))))))))),multiply(X,Z))),Y).
% 1166747 [para:1165489.1.1,1166724.1.1.1.1.1.2.1.2.1.2.1.1.1,demod:1165489] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(U),U)))))))),multiply(X,Z))),Y).
% 1166819 [para:1166747.1.1,1165517.1.2.1.1] equal(multiply(inverse(X),inverse(multiply(Y,inverse(multiply(inverse(Z),Z))))),multiply(inverse(X),inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))).
% 1166903 [para:1166819.1.2,1165517.1.2] equal(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,Z)))),inverse(multiply(Z,inverse(multiply(inverse(U),U)))))).
% 1166904 [para:1166819.1.1,1165517.1.2.1.1.1.1.1,demod:1166903] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(X,inverse(multiply(inverse(X),X)))).
% 1166929 [para:1166819.1.1,1165514.1.1.1.1.1.1.1.1,demod:1166903] equal(inverse(multiply(X,inverse(multiply(inverse(X),X)))),inverse(multiply(X,inverse(multiply(inverse(Y),Y))))).
% 1167153 [para:1166904.1.1,1165517.1.2.1.1.1.1.1,demod:1166903] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 1167174 [para:1166904.1.1,1165514.1.1.1.1.1.1.1.1,demod:1166903] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))).
% 1167363 [para:1166904.1.2,1166904.1.2] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(X,inverse(multiply(inverse(Z),Z)))).
% 1167503 [para:1167153.1.1,1165517.1.2.1.1.1] equal(X,multiply(inverse(inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(X),inverse(multiply(inverse(inverse(X)),inverse(X))))))).
% 1168131 [para:1167174.1.1,1167153.1.1.1] equal(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)),multiply(inverse(Z),Z)).
% 1168133 [para:1167174.1.1,1167174.1.1.1.1] equal(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),Z))).
% 1168384 [para:1167363.1.1,1167153.1.1] equal(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y))),multiply(inverse(Z),Z)).
% 1170310 [para:1168384.1.1,1166819.1.1,demod:1167503] equal(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))).
% 1170900 [para:1170310.1.2,1166904.1.2.2] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(X,multiply(inverse(Z),Z))).
% 1170938 [para:1170310.1.1,1168131.1.1.2] equal(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))),multiply(inverse(Z),Z)).
% 1171033 [para:1170310.1.1,1170310.1.2.1] equal(multiply(inverse(X),X),inverse(inverse(multiply(inverse(Y),Y)))).
% 1171556 [para:1171033.1.2,1165777.1.1.1.1] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))),Y).
% 1171557 [para:1171033.1.1,1165777.1.1.1.1.1.1] equal(inverse(multiply(inverse(inverse(inverse(inverse(multiply(inverse(X),X))))),inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))),Y).
% 1171843 [para:1171033.1.2,1170310.1.1.1] equal(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),Z))).
% 1192361 [para:1170310.1.2,1171556.1.1.1.2.1.2] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,multiply(inverse(Z),Z))))),Y).
% 1192538 [para:1170938.1.2,1171556.1.1.1.2.1.2.1] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,inverse(multiply(inverse(multiply(inverse(Z),Z)),inverse(multiply(inverse(U),U)))))))),Y).
% 1192590 [para:1165550.1.1,1192361.1.1.1.2.1] equal(inverse(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,U))))),inverse(multiply(inverse(U),Z))).
% 1192985 [para:1171843.1.1,1165486.1.1.1.2,demod:1192538] equal(inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))),X).
% 1193009 [para:1171843.1.1,1165489.1.1.2,demod:1192361,1192985] equal(multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))),X).
% 1193015 [para:1171843.1.1,1165490.1.1.1.1.2,demod:1192361,1192985,1193009] equal(inverse(inverse(multiply(X,inverse(multiply(inverse(Y),Y))))),X).
% 1193151 [para:1171843.1.2,1165517.1.2.1.1,demod:1192985] equal(X,multiply(inverse(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(Z),Z)))),X)).
% 1193633 [para:1171843.1.1,1165513.1.1.1.1.2.1.1.1.1.1,demod:1192985,1192590,1171557] equal(multiply(inverse(multiply(X,Y)),inverse(multiply(inverse(Z),inverse(multiply(multiply(X,Y),inverse(multiply(inverse(multiply(X,Y)),multiply(X,Y)))))))),Z).
% 1193758 [para:1171843.1.2,1165519.1.2.1.1.1.1.2.1.1.1,demod:1193009,1192590,1193633,1193015,1193151] equal(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z))),multiply(inverse(Z),inverse(Y))).
% 1193956 [para:1192985.1.1,1165490.1.1.1.1.1,demod:1193015] equal(inverse(inverse(multiply(X,multiply(inverse(X),Y)))),Y).
% 1194212 [para:1170310.1.2,1192985.1.1.1.2] equal(inverse(multiply(inverse(X),multiply(inverse(Y),Y))),X).
% 1194440 [para:1192985.1.1,1171556.1.1.1.2] equal(inverse(multiply(multiply(inverse(X),X),Y)),inverse(Y)).
% 1194534 [para:1167174.1.1,1193956.1.1.1.1.2.1,demod:1194440] equal(inverse(inverse(multiply(inverse(multiply(inverse(X),X)),Y))),Y).
% 1194562 [para:1168133.1.2,1193956.1.1.1.1.2.1,demod:1194440,1194212] equal(inverse(inverse(X)),X).
% 1194574 [para:1171033.1.2,1193956.1.1.1.1.2.1,demod:1194534] equal(multiply(multiply(inverse(X),X),Y),Y).
% 1194804 [para:1166929.1.1,1194562.1.1.1,demod:1193015] equal(X,multiply(X,inverse(multiply(inverse(X),X)))).
% 1194805 [para:1166929.1.2,1194562.1.1.1,demod:1194562,1194804] equal(X,multiply(X,inverse(multiply(inverse(Y),Y)))).
% 1194834 [para:1194562.1.1,1170900.1.2.2.1,demod:1194805] equal(X,multiply(X,multiply(Y,inverse(Y)))).
% 1194909 [para:1194562.1.1,1193956.1.1.1.1.2.1,demod:1194562] equal(multiply(inverse(X),multiply(X,Y)),Y).
% 1194943 [para:1194574.1.1,1165525.1.1.1.1.1,demod:1193758,1194574,1194562] equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))).
% 1194944 [para:1194574.1.1,1165526.1.1.1.1,demod:1194574,1194562] equal(multiply(X,Y),multiply(inverse(multiply(Z,inverse(X))),multiply(Z,Y))).
% 1194946 [para:1194574.1.1,1165550.1.1.1.1,demod:1194574] equal(multiply(inverse(X),Y),multiply(inverse(multiply(Z,X)),multiply(Z,Y))).
% 1194970 [para:1194834.1.2,1165525.1.1.1,demod:1194944,1194562] equal(multiply(X,inverse(Y)),inverse(multiply(Y,inverse(X)))).
% 1194987 [para:1194834.1.2,1166006.1.1.1.1,demod:1194970,1194946,1194909] equal(multiply(X,Y),multiply(multiply(X,inverse(Z)),multiply(Z,Y))).
% 1195019 [para:1194909.1.1,1165526.1.1.2,demod:1194987,1194970,1194562,1194943,slowcut:1165487] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 5
% clause depth limited to 13
% seconds given: 12
%
%
% old unit clauses discarded
%
% Split attempt finished with SUCCESS.
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 2749
% derived clauses: 3046995
% kept clauses: 431481
% kept size sum: 0
% kept mid-nuclei: 2
% kept new demods: 35266
% forw unit-subs: 1675784
% forw double-subs: 1267
% forw overdouble-subs: 14
% backward subs: 791
% fast unit cutoff: 22
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 201.13
% process. runtime: 199.10
% specific non-discr-tree subsumption statistics:
% tried: 15
% length fails: 1
% strength fails: 0
% 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/GRP054-1+eq_r.in")
%
%------------------------------------------------------------------------------