TSTP Solution File: GRP227-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP227-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art03.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 299.3s
% Output : Assurance 299.3s
% 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/GRP227-1+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 3 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (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(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c8),sk_c7).
% was split for some strategies as:
% -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c8),sk_c7).
% -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8).
% -equal(inverse(sk_c8),sk_c7).
%
% Starting a split proof attempt with 5 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c8),sk_c7).
% Split part used next: -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c8),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,130189,4,1154,138023,5,1502,138023,1,1502,138023,50,1502,138023,40,1502,138063,0,1502,146729,3,1803,147647,4,1953,148475,5,2103,148476,1,2103,148476,50,2103,148476,40,2103,148516,0,2103,149608,3,2412,149623,4,2555,149759,5,2704,149759,1,2704,149759,50,2704,149759,40,2704,149799,0,2704,179096,3,4209,179857,4,4955,180722,5,5705,180723,1,5705,180723,50,5706,180723,40,5706,180763,0,5706,201409,3,6459,202006,4,6832,202672,5,7207,202673,1,7207,202673,50,7208,202673,40,7208,202713,0,7208,221774,3,7984,222345,4,8334,223080,5,8709,223081,1,8709,223081,50,8709,223081,40,8709,223121,0,8709,281120,3,12619,282100,4,14561,282455,5,16510,282456,1,16510,282456,50,16512,282456,40,16512,282496,0,16512,333745,3,19063,334353,4,20338,334958,5,21613,334959,1,21614,334959,50,21615,334959,40,21615,334999,0,21615,372559,3,23116,373487,4,23866,374136,5,24616,374137,1,24616,374137,50,24617,374137,40,24617,374177,0,24617,389443,3,25371,390418,4,25744,391163,5,26118,391163,1,26118,391163,50,26118,391163,40,26118,391203,0,26118,422589,3,27319,423287,4,27919,423940,1,28519,423940,50,28520,423940,40,28520,423980,0,28520,448187,3,29271,448775,4,29646,449284,5,30021,449285,1,30021,449285,50,30022,449285,40,30022,449285,40,30022,449320,0,30022)
%
%
% START OF PROOF
% 449286 [] equal(X,X).
% 449287 [] equal(multiply(identity,X),X).
% 449288 [] equal(multiply(inverse(X),X),identity).
% 449289 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 449290 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(multiply(Y,X),sk_c7) | -equal(inverse(Y),X).
% 449291 [?] ?
% 449292 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 449293 [?] ?
% 449297 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c6,sk_c8),sk_c7).
% 449298 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c6).
% 449299 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 449303 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c6,sk_c8),sk_c7).
% 449304 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 449305 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 449309 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c6,sk_c8),sk_c7).
% 449310 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 449311 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 449315 [?] ?
% 449316 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 449317 [?] ?
% 449326 [hyper:449290,449292,binarycut:449293,binarycut:449291] equal(inverse(sk_c2),sk_c8).
% 449328 [para:449326.1.1,449288.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 449338 [hyper:449290,449316,binarycut:449317,binarycut:449315] equal(inverse(sk_c1),sk_c8).
% 449341 [para:449338.1.1,449288.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 449350 [hyper:449290,449299,449297,449298] equal(multiply(sk_c2,sk_c8),sk_c3).
% 449387 [hyper:449290,449305,449303,449304] equal(multiply(sk_c8,sk_c3),sk_c7).
% 449400 [hyper:449290,449311,449309,449310] equal(multiply(sk_c1,sk_c7),sk_c8).
% 449401 [para:449288.1.1,449289.1.1.1,demod:449287] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 449402 [para:449328.1.1,449289.1.1.1,demod:449287] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 449409 [para:449350.1.1,449402.1.2.2,demod:449387] equal(sk_c8,sk_c7).
% 449410 [para:449409.1.1,449328.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 449412 [para:449409.1.1,449350.1.1.2] equal(multiply(sk_c2,sk_c7),sk_c3).
% 449413 [para:449409.1.1,449387.1.1.1] equal(multiply(sk_c7,sk_c3),sk_c7).
% 449420 [para:449328.1.1,449401.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 449421 [para:449341.1.1,449401.1.2.2,demod:449420] equal(sk_c1,sk_c2).
% 449423 [para:449400.1.1,449401.1.2.2,demod:449338] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 449426 [para:449421.1.1,449400.1.1.1,demod:449412] equal(sk_c3,sk_c8).
% 449432 [para:449426.1.2,449409.1.1] equal(sk_c3,sk_c7).
% 449437 [para:449413.1.1,449401.1.2.2,demod:449288] equal(sk_c3,identity).
% 449440 [para:449437.1.1,449432.1.1] equal(identity,sk_c7).
% 449447 [para:449440.1.2,449410.1.1.1,demod:449287] equal(sk_c2,identity).
% 449450 [para:449447.1.1,449326.1.1.1] equal(inverse(identity),sk_c8).
% 449461 [hyper:449290,449450,demod:449423,449287,cut:449409,cut:449286] 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 21
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c8),sk_c7).
% Split part used next: -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% 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 21
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,130189,4,1154,138023,5,1502,138023,1,1502,138023,50,1502,138023,40,1502,138063,0,1502,146729,3,1803,147647,4,1953,148475,5,2103,148476,1,2103,148476,50,2103,148476,40,2103,148516,0,2103,149608,3,2412,149623,4,2555,149759,5,2704,149759,1,2704,149759,50,2704,149759,40,2704,149799,0,2704,179096,3,4209,179857,4,4955,180722,5,5705,180723,1,5705,180723,50,5706,180723,40,5706,180763,0,5706,201409,3,6459,202006,4,6832,202672,5,7207,202673,1,7207,202673,50,7208,202673,40,7208,202713,0,7208,221774,3,7984,222345,4,8334,223080,5,8709,223081,1,8709,223081,50,8709,223081,40,8709,223121,0,8709,281120,3,12619,282100,4,14561,282455,5,16510,282456,1,16510,282456,50,16512,282456,40,16512,282496,0,16512,333745,3,19063,334353,4,20338,334958,5,21613,334959,1,21614,334959,50,21615,334959,40,21615,334999,0,21615,372559,3,23116,373487,4,23866,374136,5,24616,374137,1,24616,374137,50,24617,374137,40,24617,374177,0,24617,389443,3,25371,390418,4,25744,391163,5,26118,391163,1,26118,391163,50,26118,391163,40,26118,391203,0,26118,422589,3,27319,423287,4,27919,423940,1,28519,423940,50,28520,423940,40,28520,423980,0,28520,448187,3,29271,448775,4,29646,449284,5,30021,449285,1,30021,449285,50,30022,449285,40,30022,449285,40,30022,449320,0,30022,449460,50,30022,449460,30,30022,449460,40,30022,449495,0,30022)
%
%
% START OF PROOF
% 449462 [] equal(multiply(identity,X),X).
% 449463 [] equal(multiply(inverse(X),X),identity).
% 449464 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 449465 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 449469 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 449470 [?] ?
% 449475 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 449476 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 449481 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 449482 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 449487 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 449488 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 449493 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 449494 [?] ?
% 449501 [hyper:449465,449469,binarycut:449470] equal(inverse(sk_c2),sk_c8).
% 449504 [para:449501.1.1,449463.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 449515 [hyper:449465,449493,binarycut:449494] equal(inverse(sk_c1),sk_c8).
% 449518 [para:449515.1.1,449463.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 449538 [hyper:449465,449476,449475] equal(multiply(sk_c2,sk_c8),sk_c3).
% 449545 [hyper:449465,449482,449481] equal(multiply(sk_c8,sk_c3),sk_c7).
% 449552 [hyper:449465,449488,449487] equal(multiply(sk_c1,sk_c7),sk_c8).
% 449553 [para:449463.1.1,449464.1.1.1,demod:449462] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 449554 [para:449504.1.1,449464.1.1.1,demod:449462] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 449559 [para:449538.1.1,449554.1.2.2,demod:449545] equal(sk_c8,sk_c7).
% 449560 [para:449559.1.1,449504.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 449562 [para:449559.1.1,449538.1.1.2] equal(multiply(sk_c2,sk_c7),sk_c3).
% 449563 [para:449559.1.1,449545.1.1.1] equal(multiply(sk_c7,sk_c3),sk_c7).
% 449568 [para:449504.1.1,449553.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 449569 [para:449518.1.1,449553.1.2.2,demod:449568] equal(sk_c1,sk_c2).
% 449574 [para:449569.1.1,449552.1.1.1,demod:449562] equal(sk_c3,sk_c8).
% 449580 [para:449574.1.2,449559.1.1] equal(sk_c3,sk_c7).
% 449583 [para:449563.1.1,449553.1.2.2,demod:449463] equal(sk_c3,identity).
% 449586 [para:449583.1.1,449580.1.1] equal(identity,sk_c7).
% 449591 [para:449586.1.2,449560.1.1.1,demod:449462] equal(sk_c2,identity).
% 449594 [para:449591.1.1,449501.1.1.1] equal(inverse(identity),sk_c8).
% 449605 [hyper:449465,449594,demod:449462,cut:449559] 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 21
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c8),sk_c7).
% Split part used next: -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% 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 21
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,130189,4,1154,138023,5,1502,138023,1,1502,138023,50,1502,138023,40,1502,138063,0,1502,146729,3,1803,147647,4,1953,148475,5,2103,148476,1,2103,148476,50,2103,148476,40,2103,148516,0,2103,149608,3,2412,149623,4,2555,149759,5,2704,149759,1,2704,149759,50,2704,149759,40,2704,149799,0,2704,179096,3,4209,179857,4,4955,180722,5,5705,180723,1,5705,180723,50,5706,180723,40,5706,180763,0,5706,201409,3,6459,202006,4,6832,202672,5,7207,202673,1,7207,202673,50,7208,202673,40,7208,202713,0,7208,221774,3,7984,222345,4,8334,223080,5,8709,223081,1,8709,223081,50,8709,223081,40,8709,223121,0,8709,281120,3,12619,282100,4,14561,282455,5,16510,282456,1,16510,282456,50,16512,282456,40,16512,282496,0,16512,333745,3,19063,334353,4,20338,334958,5,21613,334959,1,21614,334959,50,21615,334959,40,21615,334999,0,21615,372559,3,23116,373487,4,23866,374136,5,24616,374137,1,24616,374137,50,24617,374137,40,24617,374177,0,24617,389443,3,25371,390418,4,25744,391163,5,26118,391163,1,26118,391163,50,26118,391163,40,26118,391203,0,26118,422589,3,27319,423287,4,27919,423940,1,28519,423940,50,28520,423940,40,28520,423980,0,28520,448187,3,29271,448775,4,29646,449284,5,30021,449285,1,30021,449285,50,30022,449285,40,30022,449285,40,30022,449320,0,30022,449460,50,30022,449460,30,30022,449460,40,30022,449495,0,30022,449604,50,30022,449604,30,30022,449604,40,30022,449639,0,30027)
%
%
% START OF PROOF
% 449605 [] equal(X,X).
% 449606 [] equal(multiply(identity,X),X).
% 449607 [] equal(multiply(inverse(X),X),identity).
% 449608 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 449609 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 449610 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c8).
% 449611 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 449612 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c8).
% 449613 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 449614 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c8).
% 449615 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c8),sk_c7).
% 449616 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c6,sk_c8),sk_c7).
% 449617 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c6).
% 449618 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 449619 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 449620 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 449621 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c8),sk_c7).
% 449622 [?] ?
% 449623 [?] ?
% 449624 [?] ?
% 449625 [?] ?
% 449626 [?] ?
% 449627 [?] ?
% 449697 [hyper:449609,449617,binarycut:449623,binarycut:449611] equal(inverse(sk_c5),sk_c6).
% 449698 [para:449697.1.1,449607.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 449701 [hyper:449609,449619,binarycut:449625,binarycut:449613] equal(inverse(sk_c4),sk_c8).
% 449712 [hyper:449609,449616,449610,binarycut:449622] equal(multiply(sk_c6,sk_c8),sk_c7).
% 449718 [para:449701.1.1,449607.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 449726 [hyper:449609,449621,binarycut:449627,binarycut:449615] equal(inverse(sk_c8),sk_c7).
% 449727 [para:449726.1.1,449607.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 449731 [hyper:449609,449618,449612,binarycut:449624] equal(multiply(sk_c5,sk_c6),sk_c7).
% 449744 [hyper:449609,449620,449614,binarycut:449626] equal(multiply(sk_c4,sk_c8),sk_c7).
% 449749 [para:449607.1.1,449608.1.1.1,demod:449606] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 449750 [para:449698.1.1,449608.1.1.1,demod:449606] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 449752 [para:449718.1.1,449608.1.1.1,demod:449606] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 449758 [para:449731.1.1,449750.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 449765 [para:449718.1.1,449749.1.2.2,demod:449726] equal(sk_c4,multiply(sk_c7,identity)).
% 449767 [para:449744.1.1,449749.1.2.2,demod:449701] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 449769 [para:449765.1.2,449608.1.1.1,demod:449606] equal(multiply(sk_c4,X),multiply(sk_c7,X)).
% 449772 [para:449767.1.2,449749.1.2.2,demod:449727,449726] equal(sk_c7,identity).
% 449773 [para:449772.1.1,449727.1.1.1,demod:449606] equal(sk_c8,identity).
% 449774 [para:449772.1.1,449758.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 449775 [para:449772.1.1,449765.1.2.1,demod:449606] equal(sk_c4,identity).
% 449777 [para:449773.1.1,449712.1.1.2,demod:449774] equal(sk_c6,sk_c7).
% 449779 [para:449773.1.1,449744.1.1.2,demod:449765,449769] equal(sk_c4,sk_c7).
% 449789 [para:449777.1.1,449712.1.1.1,demod:449727] equal(identity,sk_c7).
% 449793 [para:449779.1.1,449701.1.1.1] equal(inverse(sk_c7),sk_c8).
% 449796 [para:449775.1.1,449752.1.2.2.1,demod:449606] equal(X,multiply(sk_c8,X)).
% 449802 [hyper:449609,449793,449605,demod:449796,449727,cut:449789] 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 21
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c8),sk_c7).
% Split part used next: -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8).
% 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 21
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,130189,4,1154,138023,5,1502,138023,1,1502,138023,50,1502,138023,40,1502,138063,0,1502,146729,3,1803,147647,4,1953,148475,5,2103,148476,1,2103,148476,50,2103,148476,40,2103,148516,0,2103,149608,3,2412,149623,4,2555,149759,5,2704,149759,1,2704,149759,50,2704,149759,40,2704,149799,0,2704,179096,3,4209,179857,4,4955,180722,5,5705,180723,1,5705,180723,50,5706,180723,40,5706,180763,0,5706,201409,3,6459,202006,4,6832,202672,5,7207,202673,1,7207,202673,50,7208,202673,40,7208,202713,0,7208,221774,3,7984,222345,4,8334,223080,5,8709,223081,1,8709,223081,50,8709,223081,40,8709,223121,0,8709,281120,3,12619,282100,4,14561,282455,5,16510,282456,1,16510,282456,50,16512,282456,40,16512,282496,0,16512,333745,3,19063,334353,4,20338,334958,5,21613,334959,1,21614,334959,50,21615,334959,40,21615,334999,0,21615,372559,3,23116,373487,4,23866,374136,5,24616,374137,1,24616,374137,50,24617,374137,40,24617,374177,0,24617,389443,3,25371,390418,4,25744,391163,5,26118,391163,1,26118,391163,50,26118,391163,40,26118,391203,0,26118,422589,3,27319,423287,4,27919,423940,1,28519,423940,50,28520,423940,40,28520,423980,0,28520,448187,3,29271,448775,4,29646,449284,5,30021,449285,1,30021,449285,50,30022,449285,40,30022,449285,40,30022,449320,0,30022,449460,50,30022,449460,30,30022,449460,40,30022,449495,0,30022,449604,50,30022,449604,30,30022,449604,40,30022,449639,0,30027,449801,50,30028,449801,30,30028,449801,40,30028,449836,0,30028)
%
%
% START OF PROOF
% 449803 [] equal(multiply(identity,X),X).
% 449804 [] equal(multiply(inverse(X),X),identity).
% 449805 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 449806 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c8).
% 449828 [?] ?
% 449829 [?] ?
% 449830 [?] ?
% 449834 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 449835 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 449836 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c8),sk_c7).
% 449852 [hyper:449806,449834,binarycut:449828] equal(inverse(sk_c4),sk_c8).
% 449859 [para:449852.1.1,449804.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 449863 [hyper:449806,449836,binarycut:449830] equal(inverse(sk_c8),sk_c7).
% 449864 [para:449863.1.1,449804.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 449880 [hyper:449806,449835,binarycut:449829] equal(multiply(sk_c4,sk_c8),sk_c7).
% 449881 [para:449804.1.1,449805.1.1.1,demod:449803] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 449883 [para:449859.1.1,449805.1.1.1,demod:449803] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 449890 [para:449880.1.1,449883.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 449893 [para:449859.1.1,449881.1.2.2,demod:449863] equal(sk_c4,multiply(sk_c7,identity)).
% 449897 [para:449883.1.2,449881.1.2.2,demod:449863] equal(multiply(sk_c4,X),multiply(sk_c7,X)).
% 449899 [para:449890.1.2,449881.1.2.2,demod:449864,449863] equal(sk_c7,identity).
% 449900 [para:449899.1.1,449864.1.1.1,demod:449803] equal(sk_c8,identity).
% 449903 [para:449900.1.1,449859.1.1.1,demod:449803] equal(sk_c4,identity).
% 449904 [para:449900.1.1,449863.1.1.1] equal(inverse(identity),sk_c7).
% 449906 [para:449900.1.1,449880.1.1.2,demod:449893,449897] equal(sk_c4,sk_c7).
% 449907 [para:449900.1.1,449883.1.2.1,demod:449803,449897] equal(X,multiply(sk_c7,X)).
% 449909 [para:449903.1.1,449852.1.1.1,demod:449904] equal(sk_c7,sk_c8).
% 449916 [para:449906.1.1,449852.1.1.1] equal(inverse(sk_c7),sk_c8).
% 449922 [hyper:449806,449916,demod:449907,cut:449909] 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 21
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,W),sk_c7) | -equal(inverse(V),W) | -equal(multiply(W,sk_c8),sk_c7).
% Split part used next: -equal(inverse(sk_c8),sk_c7).
% 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 21
% clause depth limited to 3
% seconds given: 6
%
%
% 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 21
% clause depth limited to 4
% seconds given: 6
%
%
% 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 21
% clause depth limited to 5
% seconds given: 6
%
%
% 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 21
% clause depth limited to 6
% seconds given: 6
%
%
% 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 21
% clause depth limited to 7
% seconds given: 6
%
%
% 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 21
% clause depth limited to 8
% seconds given: 6
%
%
% 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 21
% clause depth limited to 9
% seconds given: 6
%
%
% 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 21
% clause depth limited to 10
% seconds given: 6
%
%
% 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 21
% clause depth limited to 11
% seconds given: 6
%
%
% 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 21
% clause depth limited to 12
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,130189,4,1154,138023,5,1502,138023,1,1502,138023,50,1502,138023,40,1502,138063,0,1502,146729,3,1803,147647,4,1953,148475,5,2103,148476,1,2103,148476,50,2103,148476,40,2103,148516,0,2103,149608,3,2412,149623,4,2555,149759,5,2704,149759,1,2704,149759,50,2704,149759,40,2704,149799,0,2704,179096,3,4209,179857,4,4955,180722,5,5705,180723,1,5705,180723,50,5706,180723,40,5706,180763,0,5706,201409,3,6459,202006,4,6832,202672,5,7207,202673,1,7207,202673,50,7208,202673,40,7208,202713,0,7208,221774,3,7984,222345,4,8334,223080,5,8709,223081,1,8709,223081,50,8709,223081,40,8709,223121,0,8709,281120,3,12619,282100,4,14561,282455,5,16510,282456,1,16510,282456,50,16512,282456,40,16512,282496,0,16512,333745,3,19063,334353,4,20338,334958,5,21613,334959,1,21614,334959,50,21615,334959,40,21615,334999,0,21615,372559,3,23116,373487,4,23866,374136,5,24616,374137,1,24616,374137,50,24617,374137,40,24617,374177,0,24617,389443,3,25371,390418,4,25744,391163,5,26118,391163,1,26118,391163,50,26118,391163,40,26118,391203,0,26118,422589,3,27319,423287,4,27919,423940,1,28519,423940,50,28520,423940,40,28520,423980,0,28520,448187,3,29271,448775,4,29646,449284,5,30021,449285,1,30021,449285,50,30022,449285,40,30022,449285,40,30022,449320,0,30022,449460,50,30022,449460,30,30022,449460,40,30022,449495,0,30022,449604,50,30022,449604,30,30022,449604,40,30022,449639,0,30027,449801,50,30028,449801,30,30028,449801,40,30028,449836,0,30028,449921,50,30029,449921,30,30029,449921,40,30029,449956,0,30029,450046,50,30029,450081,0,30034,450219,50,30036,450254,0,30036,450400,50,30040,450435,0,30045,450600,50,30051,450635,0,30051,450806,50,30061,450841,0,30061,451020,50,30078,451055,0,30082,451243,50,30113,451278,0,30113,451476,50,30179,451511,0,30179,451720,50,30304,451755,0,30304,451976,4,30532)
%
%
% START OF PROOF
% 451722 [] equal(multiply(identity,X),X).
% 451723 [] equal(multiply(inverse(X),X),identity).
% 451724 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 451725 [] -equal(inverse(sk_c8),sk_c7).
% 451731 [?] ?
% 451737 [?] ?
% 451743 [?] ?
% 451749 [?] ?
% 451755 [?] ?
% 451759 [input:451731,cut:451725] equal(inverse(sk_c2),sk_c8).
% 451760 [para:451759.1.1,451723.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 451764 [input:451755,cut:451725] equal(inverse(sk_c1),sk_c8).
% 451765 [para:451764.1.1,451723.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 451770 [input:451737,cut:451725] equal(multiply(sk_c2,sk_c8),sk_c3).
% 451773 [input:451743,cut:451725] equal(multiply(sk_c8,sk_c3),sk_c7).
% 451777 [input:451749,cut:451725] equal(multiply(sk_c1,sk_c7),sk_c8).
% 451788 [para:451723.1.1,451724.1.1.1,demod:451722] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 451789 [para:451760.1.1,451724.1.1.1,demod:451722] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 451790 [para:451765.1.1,451724.1.1.1,demod:451722] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 451791 [para:451770.1.1,451724.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c8,X))).
% 451792 [para:451773.1.1,451724.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c3,X))).
% 451794 [para:451770.1.1,451789.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c3)).
% 451795 [para:451794.1.2,451773.1.1] equal(sk_c8,sk_c7).
% 451796 [para:451794.1.2,451724.1.1.1,demod:451792] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 451798 [para:451723.1.1,451788.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 451799 [para:451760.1.1,451788.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 451800 [para:451765.1.1,451788.1.2.2,demod:451799] equal(sk_c1,sk_c2).
% 451804 [para:451724.1.1,451788.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 451805 [para:451789.1.2,451788.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c8),X)).
% 451807 [para:451788.1.2,451788.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 451810 [para:451795.1.1,451770.1.1.2] equal(multiply(sk_c2,sk_c7),sk_c3).
% 451814 [para:451790.1.2,451788.1.2.2,demod:451805] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 451816 [para:451800.1.1,451777.1.1.1,demod:451810] equal(sk_c3,sk_c8).
% 451821 [para:451816.1.2,451789.1.2.1] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 451827 [para:451789.1.2,451791.1.2.2,demod:451821] equal(X,multiply(sk_c2,X)).
% 451828 [para:451790.1.2,451791.1.2.2,demod:451827,451814] equal(multiply(sk_c3,X),X).
% 451830 [para:451827.1.2,451789.1.2.2,demod:451796] equal(X,multiply(sk_c7,X)).
% 451831 [para:451828.1.1,451788.1.2.2] equal(X,multiply(inverse(sk_c3),X)).
% 451840 [para:451831.1.2,451723.1.1] equal(sk_c3,identity).
% 451841 [para:451840.1.1,451773.1.1.2,demod:451830,451796] equal(identity,sk_c7).
% 451851 [para:451723.1.1,451804.1.2.2] equal(X,multiply(inverse(multiply(inverse(multiply(Y,X)),Y)),identity)).
% 451865 [para:451807.1.2,451723.1.1] equal(multiply(X,inverse(X)),identity).
% 451867 [para:451807.1.2,451798.1.2] equal(X,multiply(X,identity)).
% 451882 [para:451851.1.2,451867.1.2] equal(inverse(multiply(inverse(multiply(X,Y)),X)),Y).
% 451885 [para:451865.1.1,451804.1.2.2.2,demod:451867] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 451908 [para:451882.1.1,451885.1.2.1] equal(inverse(X),multiply(Y,inverse(multiply(X,Y)))).
% 451911 [para:451908.1.2,451724.1.1] equal(inverse(X),multiply(Y,multiply(Z,inverse(multiply(X,multiply(Y,Z)))))).
% 451913 [para:451724.1.1,451908.1.2.2.1] equal(inverse(multiply(X,Y)),multiply(Z,inverse(multiply(X,multiply(Y,Z))))).
% 451922 [para:451911.1.2,451724.1.1,demod:451724] equal(inverse(X),multiply(Y,multiply(Z,multiply(U,inverse(multiply(X,multiply(Y,multiply(Z,U)))))))).
% 451924 [para:451724.1.1,451913.1.2.2.1,demod:451724] equal(inverse(multiply(X,multiply(Y,Z))),multiply(U,inverse(multiply(X,multiply(Y,multiply(Z,U)))))).
% 451931 [para:451922.1.2,451724.1.1,demod:451724] equal(inverse(X),multiply(Y,multiply(Z,multiply(U,multiply(V,inverse(multiply(X,multiply(Y,multiply(Z,multiply(U,V)))))))))).
% 451934 [para:451724.1.1,451924.1.2.2.1,demod:451724] equal(inverse(multiply(X,multiply(Y,multiply(Z,U)))),multiply(V,inverse(multiply(X,multiply(Y,multiply(Z,multiply(U,V))))))).
% 451942 [para:451931.1.2,451724.1.1,demod:451724] equal(inverse(X),multiply(Y,multiply(Z,multiply(U,multiply(V,multiply(W,inverse(multiply(X,multiply(Y,multiply(Z,multiply(U,multiply(V,W)))))))))))).
% 451977 [para:451942.1.1,451725.1.1,demod:451865,451908,451913,451924,451934,451830,451796,cut:451841] 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 21
% clause depth limited to 12
% seconds given: 6
%
%
% Split attempt finished with SUCCESS.
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 28658
% derived clauses: 5606784
% kept clauses: 285248
% kept size sum: 14087
% kept mid-nuclei: 127052
% kept new demods: 2115
% forw unit-subs: 1553360
% forw double-subs: 3116885
% forw overdouble-subs: 457214
% backward subs: 9959
% fast unit cutoff: 31706
% full unit cutoff: 0
% dbl unit cutoff: 8165
% real runtime : 306.38
% process. runtime: 305.31
% specific non-discr-tree subsumption statistics:
% tried: 34240509
% length fails: 2295516
% strength fails: 15856834
% predlist fails: 1768924
% aux str. fails: 3109482
% by-lit fails: 3744603
% full subs tried: 4259886
% full subs fail: 4082290
%
% ; 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/GRP227-1+eq_r.in")
%
%------------------------------------------------------------------------------