TSTP Solution File: GRP305-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP305-1 : 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 : art09.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 297.5s
% Output : Assurance 297.5s
% 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/GRP305-1+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 19)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 19)
% (binary-posweight-lex-big-order 30 #f 3 19)
% (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(sk_c6,sk_c5),sk_c4) | -equal(multiply(sk_c5,sk_c4),sk_c6) | -equal(inverse(sk_c6),sk_c4) | -equal(multiply(X,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% was split for some strategies as:
% -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6).
% -equal(multiply(X,sk_c6),sk_c4) | -equal(inverse(X),sk_c6).
% -equal(multiply(sk_c6,sk_c5),sk_c4).
% -equal(multiply(sk_c5,sk_c4),sk_c6).
% -equal(inverse(sk_c6),sk_c4).
% -equal(multiply(sk_c5,sk_c6),sk_c4).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c4) | -equal(multiply(sk_c5,sk_c4),sk_c6) | -equal(inverse(sk_c6),sk_c4) | -equal(multiply(X,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% Split part used next: -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,64,0,0,405,50,2,439,0,2,795,50,4,829,0,4,1196,50,8,1230,0,8,1604,50,13,1638,0,13,2020,50,20,2054,0,20,2444,50,33,2478,0,33,2878,50,61,2912,0,61,3322,50,122,3356,0,122,3777,50,258,3811,0,258,4244,50,480,4278,0,480,4724,50,914,4724,40,914,4758,0,914,16086,3,1215,16756,4,1365,17389,1,1515,17389,50,1515,17389,40,1515,17423,0,1515,17573,3,1822,17582,4,1974,17589,5,2116,17589,1,2116,17589,50,2116,17589,40,2116,17623,0,2116,49238,3,3617,50207,4,4367,50892,5,5117,50893,1,5117,50893,50,5118,50893,40,5118,50927,0,5118,68035,3,5869,68963,4,6244,69691,1,6619,69691,50,6619,69691,40,6619,69725,0,6619,78525,3,7371,80116,4,7745,81557,5,8120,81558,1,8120,81558,50,8120,81558,40,8120,81592,0,8120,124601,3,12021,126507,4,13972,128059,5,15921,128060,1,15921,128060,50,15923,128060,40,15923,128094,0,15923,166817,3,18475,168135,4,19749,169186,5,21024,169187,1,21024,169187,50,21026,169187,40,21026,169221,0,21026,204610,3,22527,205237,4,23277,206119,5,24027,206120,1,24027,206120,50,24029,206120,40,24029,206154,0,24029,225358,3,24780,225759,4,25155,226094,5,25530,226095,1,25530,226095,50,25530,226095,40,25530,226129,0,25530,256950,3,26731,257739,4,27331,258366,5,27931,258367,1,27931,258367,50,27932,258367,40,27932,258401,0,27932,281383,3,28684,281987,4,29058,282523,5,29433,282524,1,29433,282524,50,29434,282524,40,29434,282524,40,29434,282554,0,29434,282626,50,29434,282656,0,29434)
%
%
% START OF PROOF
% 282628 [] equal(multiply(identity,X),X).
% 282629 [] equal(multiply(inverse(X),X),identity).
% 282630 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 282631 [] -equal(multiply(X,sk_c4),sk_c5) | -equal(inverse(X),sk_c5).
% 282632 [?] ?
% 282633 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c3),sk_c5).
% 282637 [] equal(multiply(sk_c1,sk_c6),sk_c4) | equal(multiply(sk_c3,sk_c4),sk_c5).
% 282638 [] equal(multiply(sk_c1,sk_c6),sk_c4) | equal(inverse(sk_c3),sk_c5).
% 282642 [?] ?
% 282643 [] equal(inverse(sk_c6),sk_c4) | equal(inverse(sk_c3),sk_c5).
% 282647 [] equal(multiply(sk_c5,sk_c4),sk_c6) | equal(multiply(sk_c3,sk_c4),sk_c5).
% 282648 [] equal(multiply(sk_c5,sk_c4),sk_c6) | equal(inverse(sk_c3),sk_c5).
% 282652 [] equal(multiply(sk_c6,sk_c5),sk_c4) | equal(multiply(sk_c3,sk_c4),sk_c5).
% 282653 [] equal(multiply(sk_c6,sk_c5),sk_c4) | equal(inverse(sk_c3),sk_c5).
% 282659 [hyper:282631,282633,binarycut:282632] equal(inverse(sk_c1),sk_c6).
% 282660 [para:282659.1.1,282629.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 282667 [hyper:282631,282643,binarycut:282642] equal(inverse(sk_c6),sk_c4).
% 282668 [para:282667.1.1,282629.1.1.1] equal(multiply(sk_c4,sk_c6),identity).
% 282671 [hyper:282631,282638,282637] equal(multiply(sk_c1,sk_c6),sk_c4).
% 282677 [hyper:282631,282648,282647] equal(multiply(sk_c5,sk_c4),sk_c6).
% 282683 [hyper:282631,282653,282652] equal(multiply(sk_c6,sk_c5),sk_c4).
% 282684 [para:282629.1.1,282630.1.1.1,demod:282628] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 282685 [para:282660.1.1,282630.1.1.1,demod:282628] equal(X,multiply(sk_c6,multiply(sk_c1,X))).
% 282690 [para:282671.1.1,282685.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c4)).
% 282693 [para:282629.1.1,282684.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 282697 [para:282630.1.1,282684.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 282698 [para:282683.1.1,282684.1.2.2,demod:282667] equal(sk_c5,multiply(sk_c4,sk_c4)).
% 282699 [para:282685.1.2,282684.1.2.2,demod:282667] equal(multiply(sk_c1,X),multiply(sk_c4,X)).
% 282700 [para:282690.1.2,282684.1.2.2,demod:282668,282667] equal(sk_c4,identity).
% 282701 [para:282684.1.2,282684.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 282702 [para:282700.1.1,282668.1.1.1,demod:282628] equal(sk_c6,identity).
% 282707 [para:282702.1.1,282660.1.1.1,demod:282628] equal(sk_c1,identity).
% 282708 [para:282702.1.1,282667.1.1.1] equal(inverse(identity),sk_c4).
% 282710 [para:282702.1.1,282683.1.1.1,demod:282628] equal(sk_c5,sk_c4).
% 282711 [para:282702.1.1,282685.1.2.1,demod:282628,282699] equal(X,multiply(sk_c4,X)).
% 282712 [para:282702.1.1,282690.1.2.1,demod:282628] equal(sk_c6,sk_c4).
% 282713 [para:282707.1.1,282659.1.1.1,demod:282708] equal(sk_c4,sk_c6).
% 282716 [para:282710.1.1,282677.1.1.1,demod:282698] equal(sk_c5,sk_c6).
% 282720 [para:282716.1.2,282667.1.1.1] equal(inverse(sk_c5),sk_c4).
% 282723 [para:282716.1.2,282713.1.2] equal(sk_c4,sk_c5).
% 282738 [para:282685.1.2,282697.1.2.2.2,demod:282711,282699] equal(X,multiply(inverse(multiply(Y,sk_c6)),multiply(Y,X))).
% 282742 [para:282701.1.2,282629.1.1] equal(multiply(X,inverse(X)),identity).
% 282744 [para:282701.1.2,282693.1.2] equal(X,multiply(X,identity)).
% 282745 [para:282744.1.2,282693.1.2] equal(X,inverse(inverse(X))).
% 282749 [para:282742.1.1,282738.1.2.2,demod:282744] equal(inverse(X),inverse(multiply(X,sk_c6))).
% 282758 [para:282749.1.2,282693.1.2.1.1,demod:282744,282745] equal(multiply(X,sk_c6),X).
% 282759 [para:282712.1.1,282758.1.1.2] equal(multiply(X,sk_c4),X).
% 282762 [hyper:282631,282759,demod:282720,cut:282723] 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 19
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c4) | -equal(multiply(sk_c5,sk_c4),sk_c6) | -equal(inverse(sk_c6),sk_c4) | -equal(multiply(X,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% Split part used next: -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6).
% 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 19
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,64,0,0,405,50,2,439,0,2,795,50,4,829,0,4,1196,50,8,1230,0,8,1604,50,13,1638,0,13,2020,50,20,2054,0,20,2444,50,33,2478,0,33,2878,50,61,2912,0,61,3322,50,122,3356,0,122,3777,50,258,3811,0,258,4244,50,480,4278,0,480,4724,50,914,4724,40,914,4758,0,914,16086,3,1215,16756,4,1365,17389,1,1515,17389,50,1515,17389,40,1515,17423,0,1515,17573,3,1822,17582,4,1974,17589,5,2116,17589,1,2116,17589,50,2116,17589,40,2116,17623,0,2116,49238,3,3617,50207,4,4367,50892,5,5117,50893,1,5117,50893,50,5118,50893,40,5118,50927,0,5118,68035,3,5869,68963,4,6244,69691,1,6619,69691,50,6619,69691,40,6619,69725,0,6619,78525,3,7371,80116,4,7745,81557,5,8120,81558,1,8120,81558,50,8120,81558,40,8120,81592,0,8120,124601,3,12021,126507,4,13972,128059,5,15921,128060,1,15921,128060,50,15923,128060,40,15923,128094,0,15923,166817,3,18475,168135,4,19749,169186,5,21024,169187,1,21024,169187,50,21026,169187,40,21026,169221,0,21026,204610,3,22527,205237,4,23277,206119,5,24027,206120,1,24027,206120,50,24029,206120,40,24029,206154,0,24029,225358,3,24780,225759,4,25155,226094,5,25530,226095,1,25530,226095,50,25530,226095,40,25530,226129,0,25530,256950,3,26731,257739,4,27331,258366,5,27931,258367,1,27931,258367,50,27932,258367,40,27932,258401,0,27932,281383,3,28684,281987,4,29058,282523,5,29433,282524,1,29433,282524,50,29434,282524,40,29434,282524,40,29434,282554,0,29434,282626,50,29434,282656,0,29434,282761,50,29435,282761,30,29435,282761,40,29435,282791,0,29440)
%
%
% START OF PROOF
% 282763 [] equal(multiply(identity,X),X).
% 282764 [] equal(multiply(inverse(X),X),identity).
% 282765 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 282766 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 282769 [?] ?
% 282770 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c2),sk_c6).
% 282774 [] equal(multiply(sk_c1,sk_c6),sk_c4) | equal(multiply(sk_c2,sk_c5),sk_c6).
% 282775 [] equal(multiply(sk_c1,sk_c6),sk_c4) | equal(inverse(sk_c2),sk_c6).
% 282779 [?] ?
% 282780 [] equal(inverse(sk_c6),sk_c4) | equal(inverse(sk_c2),sk_c6).
% 282784 [] equal(multiply(sk_c5,sk_c4),sk_c6) | equal(multiply(sk_c2,sk_c5),sk_c6).
% 282785 [] equal(multiply(sk_c5,sk_c4),sk_c6) | equal(inverse(sk_c2),sk_c6).
% 282789 [] equal(multiply(sk_c6,sk_c5),sk_c4) | equal(multiply(sk_c2,sk_c5),sk_c6).
% 282790 [] equal(multiply(sk_c6,sk_c5),sk_c4) | equal(inverse(sk_c2),sk_c6).
% 282797 [hyper:282766,282770,binarycut:282769] equal(inverse(sk_c1),sk_c6).
% 282800 [para:282797.1.1,282764.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 282806 [hyper:282766,282780,binarycut:282779] equal(inverse(sk_c6),sk_c4).
% 282807 [para:282806.1.1,282764.1.1.1] equal(multiply(sk_c4,sk_c6),identity).
% 282814 [hyper:282766,282775,282774] equal(multiply(sk_c1,sk_c6),sk_c4).
% 282826 [hyper:282766,282784,282785] equal(multiply(sk_c5,sk_c4),sk_c6).
% 282830 [hyper:282766,282789,282790] equal(multiply(sk_c6,sk_c5),sk_c4).
% 282831 [para:282764.1.1,282765.1.1.1,demod:282763] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 282832 [para:282800.1.1,282765.1.1.1,demod:282763] equal(X,multiply(sk_c6,multiply(sk_c1,X))).
% 282837 [para:282814.1.1,282832.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c4)).
% 282840 [para:282800.1.1,282831.1.2.2,demod:282806] equal(sk_c1,multiply(sk_c4,identity)).
% 282843 [para:282830.1.1,282831.1.2.2,demod:282806] equal(sk_c5,multiply(sk_c4,sk_c4)).
% 282844 [para:282832.1.2,282831.1.2.2,demod:282806] equal(multiply(sk_c1,X),multiply(sk_c4,X)).
% 282845 [para:282837.1.2,282831.1.2.2,demod:282807,282806] equal(sk_c4,identity).
% 282846 [para:282845.1.1,282807.1.1.1,demod:282763] equal(sk_c6,identity).
% 282853 [para:282846.1.1,282814.1.1.2,demod:282840,282844] equal(sk_c1,sk_c4).
% 282854 [para:282846.1.1,282830.1.1.1,demod:282763] equal(sk_c5,sk_c4).
% 282855 [para:282846.1.1,282832.1.2.1,demod:282763,282844] equal(X,multiply(sk_c4,X)).
% 282858 [para:282853.1.1,282797.1.1.1] equal(inverse(sk_c4),sk_c6).
% 282860 [para:282854.1.1,282826.1.1.1,demod:282843] equal(sk_c5,sk_c6).
% 282869 [hyper:282766,282858,demod:282855,cut:282860] 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 19
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c4) | -equal(multiply(sk_c5,sk_c4),sk_c6) | -equal(inverse(sk_c6),sk_c4) | -equal(multiply(X,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% Split part used next: -equal(multiply(X,sk_c6),sk_c4) | -equal(inverse(X),sk_c6).
% 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 19
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,64,0,0,405,50,2,439,0,2,795,50,4,829,0,4,1196,50,8,1230,0,8,1604,50,13,1638,0,13,2020,50,20,2054,0,20,2444,50,33,2478,0,33,2878,50,61,2912,0,61,3322,50,122,3356,0,122,3777,50,258,3811,0,258,4244,50,480,4278,0,480,4724,50,914,4724,40,914,4758,0,914,16086,3,1215,16756,4,1365,17389,1,1515,17389,50,1515,17389,40,1515,17423,0,1515,17573,3,1822,17582,4,1974,17589,5,2116,17589,1,2116,17589,50,2116,17589,40,2116,17623,0,2116,49238,3,3617,50207,4,4367,50892,5,5117,50893,1,5117,50893,50,5118,50893,40,5118,50927,0,5118,68035,3,5869,68963,4,6244,69691,1,6619,69691,50,6619,69691,40,6619,69725,0,6619,78525,3,7371,80116,4,7745,81557,5,8120,81558,1,8120,81558,50,8120,81558,40,8120,81592,0,8120,124601,3,12021,126507,4,13972,128059,5,15921,128060,1,15921,128060,50,15923,128060,40,15923,128094,0,15923,166817,3,18475,168135,4,19749,169186,5,21024,169187,1,21024,169187,50,21026,169187,40,21026,169221,0,21026,204610,3,22527,205237,4,23277,206119,5,24027,206120,1,24027,206120,50,24029,206120,40,24029,206154,0,24029,225358,3,24780,225759,4,25155,226094,5,25530,226095,1,25530,226095,50,25530,226095,40,25530,226129,0,25530,256950,3,26731,257739,4,27331,258366,5,27931,258367,1,27931,258367,50,27932,258367,40,27932,258401,0,27932,281383,3,28684,281987,4,29058,282523,5,29433,282524,1,29433,282524,50,29434,282524,40,29434,282524,40,29434,282554,0,29434,282626,50,29434,282656,0,29434,282761,50,29435,282761,30,29435,282761,40,29435,282791,0,29440,282868,50,29441,282868,30,29441,282868,40,29441,282898,0,29441)
%
%
% START OF PROOF
% 282870 [] equal(multiply(identity,X),X).
% 282871 [] equal(multiply(inverse(X),X),identity).
% 282872 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 282873 [] -equal(multiply(X,sk_c6),sk_c4) | -equal(inverse(X),sk_c6).
% 282874 [] equal(multiply(sk_c3,sk_c4),sk_c5) | equal(inverse(sk_c1),sk_c6).
% 282875 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c3),sk_c5).
% 282876 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(inverse(sk_c1),sk_c6).
% 282877 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c2),sk_c6).
% 282878 [] equal(multiply(sk_c5,sk_c6),sk_c4) | equal(inverse(sk_c1),sk_c6).
% 282879 [?] ?
% 282880 [?] ?
% 282881 [?] ?
% 282882 [?] ?
% 282883 [?] ?
% 282901 [hyper:282873,282875,binarycut:282880] equal(inverse(sk_c3),sk_c5).
% 282902 [para:282901.1.1,282871.1.1.1] equal(multiply(sk_c5,sk_c3),identity).
% 282906 [hyper:282873,282877,binarycut:282882] equal(inverse(sk_c2),sk_c6).
% 282910 [para:282906.1.1,282871.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 282914 [hyper:282873,282874,binarycut:282879] equal(multiply(sk_c3,sk_c4),sk_c5).
% 282917 [hyper:282873,282876,binarycut:282881] equal(multiply(sk_c2,sk_c5),sk_c6).
% 282921 [hyper:282873,282878,binarycut:282883] equal(multiply(sk_c5,sk_c6),sk_c4).
% 282923 [para:282871.1.1,282872.1.1.1,demod:282870] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 282924 [para:282902.1.1,282872.1.1.1,demod:282870] equal(X,multiply(sk_c5,multiply(sk_c3,X))).
% 282931 [para:282914.1.1,282924.1.2.2] equal(sk_c4,multiply(sk_c5,sk_c5)).
% 282936 [para:282917.1.1,282923.1.2.2,demod:282906] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 282937 [para:282921.1.1,282923.1.2.2] equal(sk_c6,multiply(inverse(sk_c5),sk_c4)).
% 282939 [para:282931.1.2,282923.1.2.2,demod:282937] equal(sk_c5,sk_c6).
% 282944 [para:282939.1.2,282936.1.2.1,demod:282921] equal(sk_c5,sk_c4).
% 282948 [para:282944.1.1,282921.1.1.1] equal(multiply(sk_c4,sk_c6),sk_c4).
% 282965 [para:282948.1.1,282923.1.2.2,demod:282871] equal(sk_c6,identity).
% 282968 [para:282965.1.1,282910.1.1.1,demod:282870] equal(sk_c2,identity).
% 282970 [para:282965.1.1,282939.1.2] equal(sk_c5,identity).
% 282973 [para:282968.1.1,282906.1.1.1] equal(inverse(identity),sk_c6).
% 282979 [para:282970.1.1,282921.1.1.1,demod:282870] equal(sk_c6,sk_c4).
% 282984 [hyper:282873,282973,demod:282870,cut:282979] 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 19
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c4) | -equal(multiply(sk_c5,sk_c4),sk_c6) | -equal(inverse(sk_c6),sk_c4) | -equal(multiply(X,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% Split part used next: -equal(multiply(sk_c6,sk_c5),sk_c4).
% 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 19
% clause depth limited to 3
% seconds given: 4
%
%
% 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 19
% clause depth limited to 4
% seconds given: 4
%
%
% 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 19
% clause depth limited to 5
% seconds given: 4
%
%
% 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 19
% clause depth limited to 6
% seconds given: 4
%
%
% 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 19
% clause depth limited to 7
% seconds given: 4
%
%
% 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 19
% clause depth limited to 8
% seconds given: 4
%
%
% 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 19
% clause depth limited to 9
% seconds given: 4
%
%
% 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 19
% clause depth limited to 10
% seconds given: 4
%
%
% 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 19
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,64,0,0,405,50,2,439,0,2,795,50,4,829,0,4,1196,50,8,1230,0,8,1604,50,13,1638,0,13,2020,50,20,2054,0,20,2444,50,33,2478,0,33,2878,50,61,2912,0,61,3322,50,122,3356,0,122,3777,50,258,3811,0,258,4244,50,480,4278,0,480,4724,50,914,4724,40,914,4758,0,914,16086,3,1215,16756,4,1365,17389,1,1515,17389,50,1515,17389,40,1515,17423,0,1515,17573,3,1822,17582,4,1974,17589,5,2116,17589,1,2116,17589,50,2116,17589,40,2116,17623,0,2116,49238,3,3617,50207,4,4367,50892,5,5117,50893,1,5117,50893,50,5118,50893,40,5118,50927,0,5118,68035,3,5869,68963,4,6244,69691,1,6619,69691,50,6619,69691,40,6619,69725,0,6619,78525,3,7371,80116,4,7745,81557,5,8120,81558,1,8120,81558,50,8120,81558,40,8120,81592,0,8120,124601,3,12021,126507,4,13972,128059,5,15921,128060,1,15921,128060,50,15923,128060,40,15923,128094,0,15923,166817,3,18475,168135,4,19749,169186,5,21024,169187,1,21024,169187,50,21026,169187,40,21026,169221,0,21026,204610,3,22527,205237,4,23277,206119,5,24027,206120,1,24027,206120,50,24029,206120,40,24029,206154,0,24029,225358,3,24780,225759,4,25155,226094,5,25530,226095,1,25530,226095,50,25530,226095,40,25530,226129,0,25530,256950,3,26731,257739,4,27331,258366,5,27931,258367,1,27931,258367,50,27932,258367,40,27932,258401,0,27932,281383,3,28684,281987,4,29058,282523,5,29433,282524,1,29433,282524,50,29434,282524,40,29434,282524,40,29434,282554,0,29434,282626,50,29434,282656,0,29434,282761,50,29435,282761,30,29435,282761,40,29435,282791,0,29440,282868,50,29441,282868,30,29441,282868,40,29441,282898,0,29441,282983,50,29441,282983,30,29441,282983,40,29441,283013,0,29441,283115,50,29441,283145,0,29446,283289,50,29448,283319,0,29448,283471,50,29452,283501,0,29456,283661,50,29461,283691,0,29461,283857,50,29470,283887,0,29470,284061,50,29485,284091,0,29490,284273,50,29519,284303,0,29519,284495,50,29581,284525,0,29581,284727,50,29697,284727,40,29697,284757,0,29697)
%
%
% START OF PROOF
% 284728 [] equal(X,X).
% 284729 [] equal(multiply(identity,X),X).
% 284730 [] equal(multiply(inverse(X),X),identity).
% 284731 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 284732 [] -equal(multiply(sk_c6,sk_c5),sk_c4).
% 284753 [?] ?
% 284754 [?] ?
% 284757 [?] ?
% 284792 [input:284754,cut:284732] equal(inverse(sk_c3),sk_c5).
% 284793 [para:284792.1.1,284730.1.1.1] equal(multiply(sk_c5,sk_c3),identity).
% 284804 [input:284753,cut:284732] equal(multiply(sk_c3,sk_c4),sk_c5).
% 284806 [input:284757,cut:284732] equal(multiply(sk_c5,sk_c6),sk_c4).
% 284807 [para:284730.1.1,284731.1.1.1,demod:284729] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 284822 [para:284793.1.1,284731.1.1.1,demod:284729] equal(X,multiply(sk_c5,multiply(sk_c3,X))).
% 284843 [para:284804.1.1,284822.1.2.2] equal(sk_c4,multiply(sk_c5,sk_c5)).
% 284890 [para:284806.1.1,284807.1.2.2] equal(sk_c6,multiply(inverse(sk_c5),sk_c4)).
% 284894 [para:284843.1.2,284807.1.2.2,demod:284890] equal(sk_c5,sk_c6).
% 284898 [para:284894.1.2,284732.1.1.1,demod:284843,cut:284728] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c4) | -equal(multiply(sk_c5,sk_c4),sk_c6) | -equal(inverse(sk_c6),sk_c4) | -equal(multiply(X,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% Split part used next: -equal(multiply(sk_c5,sk_c4),sk_c6).
% 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 19
% clause depth limited to 3
% seconds given: 4
%
%
% 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 19
% clause depth limited to 4
% seconds given: 4
%
%
% 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 19
% clause depth limited to 5
% seconds given: 4
%
%
% 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 19
% clause depth limited to 6
% seconds given: 4
%
%
% 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 19
% clause depth limited to 7
% seconds given: 4
%
%
% 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 19
% clause depth limited to 8
% seconds given: 4
%
%
% 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 19
% clause depth limited to 9
% seconds given: 4
%
%
% 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 19
% clause depth limited to 10
% seconds given: 4
%
%
% 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 19
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,64,0,0,405,50,2,439,0,2,795,50,4,829,0,4,1196,50,8,1230,0,8,1604,50,13,1638,0,13,2020,50,20,2054,0,20,2444,50,33,2478,0,33,2878,50,61,2912,0,61,3322,50,122,3356,0,122,3777,50,258,3811,0,258,4244,50,480,4278,0,480,4724,50,914,4724,40,914,4758,0,914,16086,3,1215,16756,4,1365,17389,1,1515,17389,50,1515,17389,40,1515,17423,0,1515,17573,3,1822,17582,4,1974,17589,5,2116,17589,1,2116,17589,50,2116,17589,40,2116,17623,0,2116,49238,3,3617,50207,4,4367,50892,5,5117,50893,1,5117,50893,50,5118,50893,40,5118,50927,0,5118,68035,3,5869,68963,4,6244,69691,1,6619,69691,50,6619,69691,40,6619,69725,0,6619,78525,3,7371,80116,4,7745,81557,5,8120,81558,1,8120,81558,50,8120,81558,40,8120,81592,0,8120,124601,3,12021,126507,4,13972,128059,5,15921,128060,1,15921,128060,50,15923,128060,40,15923,128094,0,15923,166817,3,18475,168135,4,19749,169186,5,21024,169187,1,21024,169187,50,21026,169187,40,21026,169221,0,21026,204610,3,22527,205237,4,23277,206119,5,24027,206120,1,24027,206120,50,24029,206120,40,24029,206154,0,24029,225358,3,24780,225759,4,25155,226094,5,25530,226095,1,25530,226095,50,25530,226095,40,25530,226129,0,25530,256950,3,26731,257739,4,27331,258366,5,27931,258367,1,27931,258367,50,27932,258367,40,27932,258401,0,27932,281383,3,28684,281987,4,29058,282523,5,29433,282524,1,29433,282524,50,29434,282524,40,29434,282524,40,29434,282554,0,29434,282626,50,29434,282656,0,29434,282761,50,29435,282761,30,29435,282761,40,29435,282791,0,29440,282868,50,29441,282868,30,29441,282868,40,29441,282898,0,29441,282983,50,29441,282983,30,29441,282983,40,29441,283013,0,29441,283115,50,29441,283145,0,29446,283289,50,29448,283319,0,29448,283471,50,29452,283501,0,29456,283661,50,29461,283691,0,29461,283857,50,29470,283887,0,29470,284061,50,29485,284091,0,29490,284273,50,29519,284303,0,29519,284495,50,29581,284525,0,29581,284727,50,29697,284727,40,29697,284757,0,29697,284897,50,29698,284897,30,29698,284897,40,29698,284927,0,29698,285029,50,29698,285059,0,29703,285203,50,29705,285233,0,29705,285385,50,29709,285415,0,29709,285575,50,29715,285605,0,29719,285771,50,29728,285801,0,29728,285975,50,29743,286005,0,29748,286187,50,29777,286217,0,29777,286409,50,29839,286439,0,29839,286641,50,29956,286641,40,29956,286671,0,29956)
%
%
% START OF PROOF
% 286585 [?] ?
% 286643 [] equal(multiply(identity,X),X).
% 286644 [] equal(multiply(inverse(X),X),identity).
% 286645 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 286646 [] -equal(multiply(sk_c5,sk_c4),sk_c6).
% 286662 [?] ?
% 286663 [?] ?
% 286666 [?] ?
% 286702 [input:286663,cut:286646] equal(inverse(sk_c3),sk_c5).
% 286703 [para:286702.1.1,286644.1.1.1] equal(multiply(sk_c5,sk_c3),identity).
% 286711 [input:286662,cut:286646] equal(multiply(sk_c3,sk_c4),sk_c5).
% 286715 [input:286666,cut:286646] equal(multiply(sk_c5,sk_c6),sk_c4).
% 286719 [para:286644.1.1,286645.1.1.1,demod:286643] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 286732 [para:286703.1.1,286645.1.1.1,demod:286643] equal(X,multiply(sk_c5,multiply(sk_c3,X))).
% 286751 [para:286711.1.1,286732.1.2.2] equal(sk_c4,multiply(sk_c5,sk_c5)).
% 286791 [para:286715.1.1,286719.1.2.2] equal(sk_c6,multiply(inverse(sk_c5),sk_c4)).
% 286798 [para:286751.1.2,286719.1.2.2,demod:286791] equal(sk_c5,sk_c6).
% 286802 [para:286798.1.2,286646.1.2,cut:286585] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c4) | -equal(multiply(sk_c5,sk_c4),sk_c6) | -equal(inverse(sk_c6),sk_c4) | -equal(multiply(X,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% Split part used next: -equal(inverse(sk_c6),sk_c4).
% 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 19
% clause depth limited to 3
% seconds given: 4
%
%
% 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 19
% clause depth limited to 4
% seconds given: 4
%
%
% 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 19
% clause depth limited to 5
% seconds given: 4
%
%
% 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 19
% clause depth limited to 6
% seconds given: 4
%
%
% 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 19
% clause depth limited to 7
% seconds given: 4
%
%
% 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 19
% clause depth limited to 8
% seconds given: 4
%
%
% 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 19
% clause depth limited to 9
% seconds given: 4
%
%
% 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 19
% clause depth limited to 10
% seconds given: 4
%
%
% 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 19
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,64,0,0,405,50,2,439,0,2,795,50,4,829,0,4,1196,50,8,1230,0,8,1604,50,13,1638,0,13,2020,50,20,2054,0,20,2444,50,33,2478,0,33,2878,50,61,2912,0,61,3322,50,122,3356,0,122,3777,50,258,3811,0,258,4244,50,480,4278,0,480,4724,50,914,4724,40,914,4758,0,914,16086,3,1215,16756,4,1365,17389,1,1515,17389,50,1515,17389,40,1515,17423,0,1515,17573,3,1822,17582,4,1974,17589,5,2116,17589,1,2116,17589,50,2116,17589,40,2116,17623,0,2116,49238,3,3617,50207,4,4367,50892,5,5117,50893,1,5117,50893,50,5118,50893,40,5118,50927,0,5118,68035,3,5869,68963,4,6244,69691,1,6619,69691,50,6619,69691,40,6619,69725,0,6619,78525,3,7371,80116,4,7745,81557,5,8120,81558,1,8120,81558,50,8120,81558,40,8120,81592,0,8120,124601,3,12021,126507,4,13972,128059,5,15921,128060,1,15921,128060,50,15923,128060,40,15923,128094,0,15923,166817,3,18475,168135,4,19749,169186,5,21024,169187,1,21024,169187,50,21026,169187,40,21026,169221,0,21026,204610,3,22527,205237,4,23277,206119,5,24027,206120,1,24027,206120,50,24029,206120,40,24029,206154,0,24029,225358,3,24780,225759,4,25155,226094,5,25530,226095,1,25530,226095,50,25530,226095,40,25530,226129,0,25530,256950,3,26731,257739,4,27331,258366,5,27931,258367,1,27931,258367,50,27932,258367,40,27932,258401,0,27932,281383,3,28684,281987,4,29058,282523,5,29433,282524,1,29433,282524,50,29434,282524,40,29434,282524,40,29434,282554,0,29434,282626,50,29434,282656,0,29434,282761,50,29435,282761,30,29435,282761,40,29435,282791,0,29440,282868,50,29441,282868,30,29441,282868,40,29441,282898,0,29441,282983,50,29441,282983,30,29441,282983,40,29441,283013,0,29441,283115,50,29441,283145,0,29446,283289,50,29448,283319,0,29448,283471,50,29452,283501,0,29456,283661,50,29461,283691,0,29461,283857,50,29470,283887,0,29470,284061,50,29485,284091,0,29490,284273,50,29519,284303,0,29519,284495,50,29581,284525,0,29581,284727,50,29697,284727,40,29697,284757,0,29697,284897,50,29698,284897,30,29698,284897,40,29698,284927,0,29698,285029,50,29698,285059,0,29703,285203,50,29705,285233,0,29705,285385,50,29709,285415,0,29709,285575,50,29715,285605,0,29719,285771,50,29728,285801,0,29728,285975,50,29743,286005,0,29748,286187,50,29777,286217,0,29777,286409,50,29839,286439,0,29839,286641,50,29956,286641,40,29956,286671,0,29956,286801,50,29956,286801,30,29956,286801,40,29956,286831,0,29956,286933,50,29957,286963,0,29961,287107,50,29964,287137,0,29964,287289,50,29968,287319,0,29968,287479,50,29973,287509,0,29978,287675,50,29986,287705,0,29987,287879,50,30002,287909,0,30007,288091,50,30036,288121,0,30036,288313,50,30098,288343,0,30098,288545,50,30215,288545,40,30215,288575,0,30215)
%
%
% START OF PROOF
% 288547 [] equal(multiply(identity,X),X).
% 288548 [] equal(multiply(inverse(X),X),identity).
% 288549 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 288550 [] -equal(inverse(sk_c6),sk_c4).
% 288561 [?] ?
% 288562 [?] ?
% 288563 [?] ?
% 288564 [?] ?
% 288565 [?] ?
% 288584 [input:288562,cut:288550] equal(inverse(sk_c3),sk_c5).
% 288585 [para:288584.1.1,288548.1.1.1] equal(multiply(sk_c5,sk_c3),identity).
% 288586 [input:288564,cut:288550] equal(inverse(sk_c2),sk_c6).
% 288587 [para:288586.1.1,288548.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 288594 [input:288561,cut:288550] equal(multiply(sk_c3,sk_c4),sk_c5).
% 288595 [input:288563,cut:288550] equal(multiply(sk_c2,sk_c5),sk_c6).
% 288597 [input:288565,cut:288550] equal(multiply(sk_c5,sk_c6),sk_c4).
% 288612 [para:288548.1.1,288549.1.1.1,demod:288547] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 288614 [para:288585.1.1,288549.1.1.1,demod:288547] equal(X,multiply(sk_c5,multiply(sk_c3,X))).
% 288615 [para:288587.1.1,288549.1.1.1,demod:288547] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 288639 [para:288594.1.1,288614.1.2.2] equal(sk_c4,multiply(sk_c5,sk_c5)).
% 288642 [para:288595.1.1,288615.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 288661 [para:288597.1.1,288612.1.2.2] equal(sk_c6,multiply(inverse(sk_c5),sk_c4)).
% 288678 [para:288639.1.2,288612.1.2.2,demod:288661] equal(sk_c5,sk_c6).
% 288683 [para:288678.1.2,288550.1.1.1] -equal(inverse(sk_c5),sk_c4).
% 288693 [para:288678.1.2,288642.1.2.1] equal(sk_c5,multiply(sk_c5,sk_c6)).
% 288708 [para:288693.1.2,288597.1.1] equal(sk_c5,sk_c4).
% 288713 [para:288708.1.1,288597.1.1.1] equal(multiply(sk_c4,sk_c6),sk_c4).
% 288734 [para:288713.1.1,288612.1.2.2,demod:288548] equal(sk_c6,identity).
% 288736 [para:288734.1.1,288587.1.1.1,demod:288547] equal(sk_c2,identity).
% 288742 [para:288734.1.1,288678.1.2] equal(sk_c5,identity).
% 288745 [para:288736.1.1,288586.1.1.1] equal(inverse(identity),sk_c6).
% 288752 [para:288742.1.1,288597.1.1.1,demod:288547] equal(sk_c6,sk_c4).
% 288754 [para:288742.1.1,288683.1.1.1,demod:288745,cut:288752] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c4) | -equal(multiply(sk_c5,sk_c4),sk_c6) | -equal(inverse(sk_c6),sk_c4) | -equal(multiply(X,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% Split part used next: -equal(multiply(sk_c5,sk_c6),sk_c4).
% 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 19
% clause depth limited to 3
% seconds given: 4
%
%
% 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 19
% clause depth limited to 4
% seconds given: 4
%
%
% 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 19
% clause depth limited to 5
% seconds given: 4
%
%
% 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 19
% clause depth limited to 6
% seconds given: 4
%
%
% 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 19
% clause depth limited to 7
% seconds given: 4
%
%
% 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 19
% clause depth limited to 8
% seconds given: 4
%
%
% 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 19
% clause depth limited to 9
% seconds given: 4
%
%
% 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 19
% clause depth limited to 10
% seconds given: 4
%
%
% 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 19
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,64,0,0,405,50,2,439,0,2,795,50,4,829,0,4,1196,50,8,1230,0,8,1604,50,13,1638,0,13,2020,50,20,2054,0,20,2444,50,33,2478,0,33,2878,50,61,2912,0,61,3322,50,122,3356,0,122,3777,50,258,3811,0,258,4244,50,480,4278,0,480,4724,50,914,4724,40,914,4758,0,914,16086,3,1215,16756,4,1365,17389,1,1515,17389,50,1515,17389,40,1515,17423,0,1515,17573,3,1822,17582,4,1974,17589,5,2116,17589,1,2116,17589,50,2116,17589,40,2116,17623,0,2116,49238,3,3617,50207,4,4367,50892,5,5117,50893,1,5117,50893,50,5118,50893,40,5118,50927,0,5118,68035,3,5869,68963,4,6244,69691,1,6619,69691,50,6619,69691,40,6619,69725,0,6619,78525,3,7371,80116,4,7745,81557,5,8120,81558,1,8120,81558,50,8120,81558,40,8120,81592,0,8120,124601,3,12021,126507,4,13972,128059,5,15921,128060,1,15921,128060,50,15923,128060,40,15923,128094,0,15923,166817,3,18475,168135,4,19749,169186,5,21024,169187,1,21024,169187,50,21026,169187,40,21026,169221,0,21026,204610,3,22527,205237,4,23277,206119,5,24027,206120,1,24027,206120,50,24029,206120,40,24029,206154,0,24029,225358,3,24780,225759,4,25155,226094,5,25530,226095,1,25530,226095,50,25530,226095,40,25530,226129,0,25530,256950,3,26731,257739,4,27331,258366,5,27931,258367,1,27931,258367,50,27932,258367,40,27932,258401,0,27932,281383,3,28684,281987,4,29058,282523,5,29433,282524,1,29433,282524,50,29434,282524,40,29434,282524,40,29434,282554,0,29434,282626,50,29434,282656,0,29434,282761,50,29435,282761,30,29435,282761,40,29435,282791,0,29440,282868,50,29441,282868,30,29441,282868,40,29441,282898,0,29441,282983,50,29441,282983,30,29441,282983,40,29441,283013,0,29441,283115,50,29441,283145,0,29446,283289,50,29448,283319,0,29448,283471,50,29452,283501,0,29456,283661,50,29461,283691,0,29461,283857,50,29470,283887,0,29470,284061,50,29485,284091,0,29490,284273,50,29519,284303,0,29519,284495,50,29581,284525,0,29581,284727,50,29697,284727,40,29697,284757,0,29697,284897,50,29698,284897,30,29698,284897,40,29698,284927,0,29698,285029,50,29698,285059,0,29703,285203,50,29705,285233,0,29705,285385,50,29709,285415,0,29709,285575,50,29715,285605,0,29719,285771,50,29728,285801,0,29728,285975,50,29743,286005,0,29748,286187,50,29777,286217,0,29777,286409,50,29839,286439,0,29839,286641,50,29956,286641,40,29956,286671,0,29956,286801,50,29956,286801,30,29956,286801,40,29956,286831,0,29956,286933,50,29957,286963,0,29961,287107,50,29964,287137,0,29964,287289,50,29968,287319,0,29968,287479,50,29973,287509,0,29978,287675,50,29986,287705,0,29987,287879,50,30002,287909,0,30007,288091,50,30036,288121,0,30036,288313,50,30098,288343,0,30098,288545,50,30215,288545,40,30215,288575,0,30215,288753,50,30216,288753,30,30216,288753,40,30216,288783,0,30216,288860,50,30217,288890,0,30221,288997,50,30223,289027,0,30223,289147,50,30226,289177,0,30226,289304,50,30230,289334,0,30234,289468,50,30242,289498,0,30242,289640,50,30256,289670,0,30261,289821,50,30290,289851,0,30290,290012,50,30352,290042,0,30352,290214,50,30471,290214,40,30471,290244,0,30471)
%
%
% START OF PROOF
% 290105 [?] ?
% 290216 [] equal(multiply(identity,X),X).
% 290217 [] equal(multiply(inverse(X),X),identity).
% 290218 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 290219 [] -equal(multiply(sk_c5,sk_c6),sk_c4).
% 290224 [?] ?
% 290229 [?] ?
% 290234 [?] ?
% 290239 [?] ?
% 290261 [input:290224,cut:290219] equal(inverse(sk_c1),sk_c6).
% 290262 [para:290261.1.1,290217.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 290273 [input:290234,cut:290219] equal(inverse(sk_c6),sk_c4).
% 290274 [para:290273.1.1,290217.1.1.1] equal(multiply(sk_c4,sk_c6),identity).
% 290281 [input:290229,cut:290219] equal(multiply(sk_c1,sk_c6),sk_c4).
% 290290 [input:290239,cut:290219] equal(multiply(sk_c5,sk_c4),sk_c6).
% 290299 [para:290262.1.1,290218.1.1.1,demod:290216] equal(X,multiply(sk_c6,multiply(sk_c1,X))).
% 290306 [para:290274.1.1,290218.1.1.1,demod:290216] equal(X,multiply(sk_c4,multiply(sk_c6,X))).
% 290330 [para:290281.1.1,290299.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c4)).
% 290341 [para:290330.1.2,290306.1.2.2,demod:290274] equal(sk_c4,identity).
% 290346 [para:290341.1.1,290274.1.1.1,demod:290216] equal(sk_c6,identity).
% 290352 [para:290341.1.1,290290.1.1.2] equal(multiply(sk_c5,identity),sk_c6).
% 290356 [para:290346.1.1,290219.1.1.2,demod:290352,cut:290105] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split attempt finished with SUCCESS.
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 38637
% derived clauses: 6926908
% kept clauses: 248699
% kept size sum: 379396
% kept mid-nuclei: 2426
% kept new demods: 6353
% forw unit-subs: 2624612
% forw double-subs: 3787305
% forw overdouble-subs: 218819
% backward subs: 10504
% fast unit cutoff: 18172
% full unit cutoff: 0
% dbl unit cutoff: 4472
% real runtime : 307.50
% process. runtime: 304.72
% specific non-discr-tree subsumption statistics:
% tried: 29363333
% length fails: 4006192
% strength fails: 7186375
% predlist fails: 1042644
% aux str. fails: 3921537
% by-lit fails: 7399765
% full subs tried: 1269208
% full subs fail: 1191434
%
% ; 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/GRP305-1+eq_r.in")
%
%------------------------------------------------------------------------------