%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP356-1 : 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 : art10.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 298.6s
% Output : Assurance 298.6s
% 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/GRP356-1+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(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% was split for some strategies as:
% -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8).
% -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8).
% -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% -equal(multiply(sk_c7,sk_c6),sk_c8).
% -equal(multiply(sk_c8,sk_c7),sk_c6).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,786,50,6,826,0,6,1878,50,19,1918,0,19,3151,50,38,3191,0,38,4518,50,53,4558,0,53,5980,50,73,6020,0,73,7582,50,102,7622,0,102,9324,50,148,9364,0,148,11252,50,230,11292,0,230,13366,50,385,13406,0,385,15712,50,640,15752,0,640,18290,50,1074,18290,40,1074,18330,0,1074,28814,3,1375,29502,4,1525,30196,5,1675,30197,1,1675,30197,50,1675,30197,40,1675,30237,0,1675,30502,3,1990,30511,4,2133,30523,5,2276,30523,1,2276,30523,50,2276,30523,40,2276,30563,0,2276,52393,3,3778,53404,4,4527,54023,1,5277,54023,50,5278,54023,40,5278,54063,0,5278,70819,3,6030,71327,4,6404,71862,1,6779,71862,50,6779,71862,40,6779,71902,0,6779,83428,3,7541,84562,4,7905,85929,5,8280,85930,1,8280,85930,50,8280,85930,40,8280,85970,0,8280,160126,3,12182,161166,4,14132,161410,1,16081,161410,50,16083,161410,40,16083,161450,0,16083,220739,3,18637,221575,4,19909,221895,1,21184,221895,50,21186,221895,40,21186,221935,0,21186,262454,3,22688,263105,4,23437,263809,5,24187,263810,1,24187,263810,50,24189,263810,40,24189,263850,0,24189,273692,3,24944,274989,4,25318,275755,5,25690,275756,1,25690,275756,50,25690,275756,40,25690,275796,0,25690,307392,3,26892,308135,4,27491,308789,5,28091,308790,1,28091,308790,50,28092,308790,40,28092,308830,0,28092,331534,3,28843,332199,4,29218,332718,1,29593,332718,50,29593,332718,40,29593,332718,40,29593,332753,0,29593)
%
%
% START OF PROOF
% 332719 [] equal(X,X).
% 332720 [] equal(multiply(identity,X),X).
% 332721 [] equal(multiply(inverse(X),X),identity).
% 332722 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 332723 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 332724 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 332725 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c2),sk_c8).
% 332726 [?] ?
% 332730 [] equal(multiply(sk_c2,sk_c8),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 332731 [] equal(multiply(sk_c2,sk_c8),sk_c6) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 332732 [] equal(multiply(sk_c2,sk_c8),sk_c6) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 332736 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 332737 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 332738 [?] ?
% 332742 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 332743 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 332744 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 332748 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 332749 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 332750 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 332781 [hyper:332723,332725,332724,binarycut:332726] equal(inverse(sk_c2),sk_c8).
% 332788 [para:332781.1.1,332721.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 332808 [hyper:332723,332737,332736,binarycut:332738] equal(inverse(sk_c1),sk_c7).
% 332814 [para:332808.1.1,332721.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 332839 [hyper:332723,332732,332731,332730] equal(multiply(sk_c2,sk_c8),sk_c6).
% 332855 [hyper:332723,332744,332743,332742] equal(multiply(sk_c1,sk_c7),sk_c8).
% 332863 [hyper:332723,332750,332749,332748] equal(multiply(sk_c7,sk_c6),sk_c8).
% 332865 [para:332788.1.1,332722.1.1.1,demod:332720] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 332866 [para:332814.1.1,332722.1.1.1,demod:332720] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 332868 [para:332855.1.1,332722.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c7,X))).
% 332872 [para:332839.1.1,332865.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 332876 [para:332855.1.1,332866.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 332901 [para:332863.1.1,332868.1.2.2,demod:332872] equal(sk_c8,multiply(sk_c1,sk_c8)).
% 332902 [para:332866.1.2,332868.1.2.2] equal(multiply(sk_c8,multiply(sk_c1,X)),multiply(sk_c1,X)).
% 332903 [para:332876.1.2,332868.1.2.2,demod:332855] equal(multiply(sk_c8,sk_c8),sk_c8).
% 332905 [para:332901.1.2,332866.1.2.2,demod:332876] equal(sk_c8,sk_c7).
% 332907 [para:332905.1.2,332866.1.2.1,demod:332902] equal(X,multiply(sk_c1,X)).
% 332908 [para:332905.1.2,332876.1.2.1,demod:332903] equal(sk_c7,sk_c8).
% 332909 [para:332908.1.1,332866.1.2.1,demod:332907] equal(X,multiply(sk_c8,X)).
% 332917 [para:332909.1.2,332788.1.1] equal(sk_c2,identity).
% 332923 [para:332917.1.1,332781.1.1.1] equal(inverse(identity),sk_c8).
% 332927 [hyper:332723,332923,332719,demod:332909,332720,cut:332905] 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: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Z,sk_c8),sk_c7) | -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: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,786,50,6,826,0,6,1878,50,19,1918,0,19,3151,50,38,3191,0,38,4518,50,53,4558,0,53,5980,50,73,6020,0,73,7582,50,102,7622,0,102,9324,50,148,9364,0,148,11252,50,230,11292,0,230,13366,50,385,13406,0,385,15712,50,640,15752,0,640,18290,50,1074,18290,40,1074,18330,0,1074,28814,3,1375,29502,4,1525,30196,5,1675,30197,1,1675,30197,50,1675,30197,40,1675,30237,0,1675,30502,3,1990,30511,4,2133,30523,5,2276,30523,1,2276,30523,50,2276,30523,40,2276,30563,0,2276,52393,3,3778,53404,4,4527,54023,1,5277,54023,50,5278,54023,40,5278,54063,0,5278,70819,3,6030,71327,4,6404,71862,1,6779,71862,50,6779,71862,40,6779,71902,0,6779,83428,3,7541,84562,4,7905,85929,5,8280,85930,1,8280,85930,50,8280,85930,40,8280,85970,0,8280,160126,3,12182,161166,4,14132,161410,1,16081,161410,50,16083,161410,40,16083,161450,0,16083,220739,3,18637,221575,4,19909,221895,1,21184,221895,50,21186,221895,40,21186,221935,0,21186,262454,3,22688,263105,4,23437,263809,5,24187,263810,1,24187,263810,50,24189,263810,40,24189,263850,0,24189,273692,3,24944,274989,4,25318,275755,5,25690,275756,1,25690,275756,50,25690,275756,40,25690,275796,0,25690,307392,3,26892,308135,4,27491,308789,5,28091,308790,1,28091,308790,50,28092,308790,40,28092,308830,0,28092,331534,3,28843,332199,4,29218,332718,1,29593,332718,50,29593,332718,40,29593,332718,40,29593,332753,0,29593,332926,50,29593,332926,30,29593,332926,40,29593,332961,0,29593)
%
%
% START OF PROOF
% 332928 [] equal(multiply(identity,X),X).
% 332929 [] equal(multiply(inverse(X),X),identity).
% 332930 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 332931 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 332935 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 332936 [?] ?
% 332941 [] equal(multiply(sk_c2,sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 332942 [] equal(multiply(sk_c2,sk_c8),sk_c6) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 332947 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 332948 [?] ?
% 332953 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 332954 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 332959 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 332960 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 332968 [hyper:332931,332935,binarycut:332936] equal(inverse(sk_c2),sk_c8).
% 332971 [para:332968.1.1,332929.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 332981 [hyper:332931,332947,binarycut:332948] equal(inverse(sk_c1),sk_c7).
% 332982 [para:332981.1.1,332929.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 333002 [hyper:332931,332942,332941] equal(multiply(sk_c2,sk_c8),sk_c6).
% 333007 [hyper:332931,332954,332953] equal(multiply(sk_c1,sk_c7),sk_c8).
% 333012 [hyper:332931,332960,332959] equal(multiply(sk_c7,sk_c6),sk_c8).
% 333014 [para:332971.1.1,332930.1.1.1,demod:332928] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 333015 [para:332982.1.1,332930.1.1.1,demod:332928] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 333017 [para:333007.1.1,332930.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c7,X))).
% 333019 [para:333002.1.1,333014.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 333021 [para:333007.1.1,333015.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 333040 [para:333012.1.1,333017.1.2.2,demod:333019] equal(sk_c8,multiply(sk_c1,sk_c8)).
% 333041 [para:333015.1.2,333017.1.2.2] equal(multiply(sk_c8,multiply(sk_c1,X)),multiply(sk_c1,X)).
% 333042 [para:333021.1.2,333017.1.2.2,demod:333007] equal(multiply(sk_c8,sk_c8),sk_c8).
% 333044 [para:333040.1.2,333015.1.2.2,demod:333021] equal(sk_c8,sk_c7).
% 333046 [para:333044.1.2,333015.1.2.1,demod:333041] equal(X,multiply(sk_c1,X)).
% 333047 [para:333044.1.2,333021.1.2.1,demod:333042] equal(sk_c7,sk_c8).
% 333048 [para:333047.1.1,333015.1.2.1,demod:333046] equal(X,multiply(sk_c8,X)).
% 333050 [para:333048.1.2,332971.1.1] equal(sk_c2,identity).
% 333056 [para:333050.1.1,332968.1.1.1] equal(inverse(identity),sk_c8).
% 333057 [hyper:332931,333056,demod:332928,cut:333044] 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: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),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: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,786,50,6,826,0,6,1878,50,19,1918,0,19,3151,50,38,3191,0,38,4518,50,53,4558,0,53,5980,50,73,6020,0,73,7582,50,102,7622,0,102,9324,50,148,9364,0,148,11252,50,230,11292,0,230,13366,50,385,13406,0,385,15712,50,640,15752,0,640,18290,50,1074,18290,40,1074,18330,0,1074,28814,3,1375,29502,4,1525,30196,5,1675,30197,1,1675,30197,50,1675,30197,40,1675,30237,0,1675,30502,3,1990,30511,4,2133,30523,5,2276,30523,1,2276,30523,50,2276,30523,40,2276,30563,0,2276,52393,3,3778,53404,4,4527,54023,1,5277,54023,50,5278,54023,40,5278,54063,0,5278,70819,3,6030,71327,4,6404,71862,1,6779,71862,50,6779,71862,40,6779,71902,0,6779,83428,3,7541,84562,4,7905,85929,5,8280,85930,1,8280,85930,50,8280,85930,40,8280,85970,0,8280,160126,3,12182,161166,4,14132,161410,1,16081,161410,50,16083,161410,40,16083,161450,0,16083,220739,3,18637,221575,4,19909,221895,1,21184,221895,50,21186,221895,40,21186,221935,0,21186,262454,3,22688,263105,4,23437,263809,5,24187,263810,1,24187,263810,50,24189,263810,40,24189,263850,0,24189,273692,3,24944,274989,4,25318,275755,5,25690,275756,1,25690,275756,50,25690,275756,40,25690,275796,0,25690,307392,3,26892,308135,4,27491,308789,5,28091,308790,1,28091,308790,50,28092,308790,40,28092,308830,0,28092,331534,3,28843,332199,4,29218,332718,1,29593,332718,50,29593,332718,40,29593,332718,40,29593,332753,0,29593,332926,50,29593,332926,30,29593,332926,40,29593,332961,0,29593,333056,50,29593,333056,30,29593,333056,40,29593,333091,0,29598)
%
%
% START OF PROOF
% 333058 [] equal(multiply(identity,X),X).
% 333059 [] equal(multiply(inverse(X),X),identity).
% 333060 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 333061 [] -equal(multiply(X,sk_c8),sk_c6) | -equal(inverse(X),sk_c8).
% 333062 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 333063 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c2),sk_c8).
% 333064 [] equal(multiply(sk_c8,sk_c5),sk_c7) | equal(inverse(sk_c2),sk_c8).
% 333065 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 333066 [] equal(multiply(sk_c3,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c8).
% 333067 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c2),sk_c8).
% 333068 [?] ?
% 333069 [?] ?
% 333070 [?] ?
% 333071 [?] ?
% 333072 [?] ?
% 333073 [?] ?
% 333094 [hyper:333061,333062,binarycut:333068] equal(inverse(sk_c4),sk_c8).
% 333097 [para:333094.1.1,333059.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 333101 [hyper:333061,333065,binarycut:333071] equal(inverse(sk_c3),sk_c8).
% 333105 [para:333101.1.1,333059.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 333109 [hyper:333061,333063,binarycut:333069] equal(multiply(sk_c4,sk_c8),sk_c5).
% 333112 [hyper:333061,333064,binarycut:333070] equal(multiply(sk_c8,sk_c5),sk_c7).
% 333115 [hyper:333061,333066,binarycut:333072] equal(multiply(sk_c3,sk_c8),sk_c7).
% 333118 [hyper:333061,333067,binarycut:333073] equal(multiply(sk_c8,sk_c7),sk_c6).
% 333119 [para:333059.1.1,333060.1.1.1,demod:333058] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 333120 [para:333097.1.1,333060.1.1.1,demod:333058] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 333121 [para:333105.1.1,333060.1.1.1,demod:333058] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 333122 [para:333109.1.1,333060.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c4,multiply(sk_c8,X))).
% 333123 [para:333112.1.1,333060.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c5,X))).
% 333124 [para:333115.1.1,333060.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c8,X))).
% 333131 [para:333115.1.1,333121.1.2.2,demod:333118] equal(sk_c8,sk_c6).
% 333137 [para:333120.1.2,333119.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c8),X)).
% 333138 [para:333121.1.2,333119.1.2.2,demod:333137] equal(multiply(sk_c3,X),multiply(sk_c4,X)).
% 333150 [para:333122.1.2,333120.1.2.2,demod:333123] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 333162 [para:333120.1.2,333124.1.2.2,demod:333121,333150,333138] equal(X,multiply(sk_c3,X)).
% 333163 [para:333121.1.2,333124.1.2.2,demod:333150,333162] equal(multiply(sk_c8,X),X).
% 333164 [para:333163.1.1,333097.1.1] equal(sk_c4,identity).
% 333169 [para:333164.1.1,333094.1.1.1] equal(inverse(identity),sk_c8).
% 333170 [hyper:333061,333169,demod:333058,cut:333131] 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: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),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: 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 21
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,786,50,6,826,0,6,1878,50,19,1918,0,19,3151,50,38,3191,0,38,4518,50,53,4558,0,53,5980,50,73,6020,0,73,7582,50,102,7622,0,102,9324,50,148,9364,0,148,11252,50,230,11292,0,230,13366,50,385,13406,0,385,15712,50,640,15752,0,640,18290,50,1074,18290,40,1074,18330,0,1074,28814,3,1375,29502,4,1525,30196,5,1675,30197,1,1675,30197,50,1675,30197,40,1675,30237,0,1675,30502,3,1990,30511,4,2133,30523,5,2276,30523,1,2276,30523,50,2276,30523,40,2276,30563,0,2276,52393,3,3778,53404,4,4527,54023,1,5277,54023,50,5278,54023,40,5278,54063,0,5278,70819,3,6030,71327,4,6404,71862,1,6779,71862,50,6779,71862,40,6779,71902,0,6779,83428,3,7541,84562,4,7905,85929,5,8280,85930,1,8280,85930,50,8280,85930,40,8280,85970,0,8280,160126,3,12182,161166,4,14132,161410,1,16081,161410,50,16083,161410,40,16083,161450,0,16083,220739,3,18637,221575,4,19909,221895,1,21184,221895,50,21186,221895,40,21186,221935,0,21186,262454,3,22688,263105,4,23437,263809,5,24187,263810,1,24187,263810,50,24189,263810,40,24189,263850,0,24189,273692,3,24944,274989,4,25318,275755,5,25690,275756,1,25690,275756,50,25690,275756,40,25690,275796,0,25690,307392,3,26892,308135,4,27491,308789,5,28091,308790,1,28091,308790,50,28092,308790,40,28092,308830,0,28092,331534,3,28843,332199,4,29218,332718,1,29593,332718,50,29593,332718,40,29593,332718,40,29593,332753,0,29593,332926,50,29593,332926,30,29593,332926,40,29593,332961,0,29593,333056,50,29593,333056,30,29593,333056,40,29593,333091,0,29598,333169,50,29598,333169,30,29598,333169,40,29598,333204,0,29598,333308,50,29599,333343,0,29599)
%
%
% START OF PROOF
% 333310 [] equal(multiply(identity,X),X).
% 333311 [] equal(multiply(inverse(X),X),identity).
% 333312 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 333313 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% 333326 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 333327 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 333328 [] equal(multiply(sk_c8,sk_c5),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 333329 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 333330 [] equal(multiply(sk_c3,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 333331 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 333332 [?] ?
% 333333 [?] ?
% 333334 [?] ?
% 333335 [?] ?
% 333336 [?] ?
% 333337 [?] ?
% 333349 [hyper:333313,333326,binarycut:333332] equal(inverse(sk_c4),sk_c8).
% 333350 [para:333349.1.1,333311.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 333353 [hyper:333313,333329,binarycut:333335] equal(inverse(sk_c3),sk_c8).
% 333354 [para:333353.1.1,333311.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 333362 [hyper:333313,333327,binarycut:333333] equal(multiply(sk_c4,sk_c8),sk_c5).
% 333365 [hyper:333313,333328,binarycut:333334] equal(multiply(sk_c8,sk_c5),sk_c7).
% 333369 [hyper:333313,333330,binarycut:333336] equal(multiply(sk_c3,sk_c8),sk_c7).
% 333372 [hyper:333313,333331,binarycut:333337] equal(multiply(sk_c8,sk_c7),sk_c6).
% 333373 [para:333311.1.1,333312.1.1.1,demod:333310] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 333374 [para:333350.1.1,333312.1.1.1,demod:333310] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 333375 [para:333354.1.1,333312.1.1.1,demod:333310] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 333376 [para:333362.1.1,333312.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c4,multiply(sk_c8,X))).
% 333377 [para:333365.1.1,333312.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c5,X))).
% 333378 [para:333369.1.1,333312.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c8,X))).
% 333380 [para:333362.1.1,333374.1.2.2,demod:333365] equal(sk_c8,sk_c7).
% 333385 [para:333311.1.1,333373.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 333386 [para:333350.1.1,333373.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 333389 [para:333312.1.1,333373.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 333390 [para:333372.1.1,333373.1.2.2] equal(sk_c7,multiply(inverse(sk_c8),sk_c6)).
% 333391 [para:333374.1.2,333373.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c8),X)).
% 333392 [para:333375.1.2,333373.1.2.2,demod:333391] equal(multiply(sk_c3,X),multiply(sk_c4,X)).
% 333393 [para:333373.1.2,333373.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 333405 [para:333376.1.2,333374.1.2.2,demod:333377] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 333417 [para:333374.1.2,333378.1.2.2,demod:333375,333405,333392] equal(X,multiply(sk_c3,X)).
% 333418 [para:333375.1.2,333378.1.2.2,demod:333405,333417] equal(multiply(sk_c8,X),X).
% 333425 [para:333405.1.2,333373.1.2.2,demod:333418] equal(X,multiply(inverse(sk_c7),X)).
% 333439 [para:333425.1.2,333311.1.1] equal(sk_c7,identity).
% 333440 [para:333439.1.1,333372.1.1.2,demod:333418] equal(identity,sk_c6).
% 333447 [para:333440.1.2,333390.1.2.2,demod:333386] equal(sk_c7,sk_c4).
% 333452 [para:333447.1.1,333380.1.2] equal(sk_c8,sk_c4).
% 333456 [para:333393.1.2,333311.1.1] equal(multiply(X,inverse(X)),identity).
% 333458 [para:333393.1.2,333385.1.2] equal(X,multiply(X,identity)).
% 333462 [para:333452.1.2,333349.1.1.1] equal(inverse(sk_c8),sk_c8).
% 333466 [para:333458.1.2,333385.1.2] equal(X,inverse(inverse(X))).
% 333472 [para:333456.1.1,333389.1.2.2.2,demod:333458] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 333487 [para:333405.1.2,333472.1.2.1.1,demod:333418] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 333496 [para:333487.1.2,333393.1.2,demod:333466] equal(multiply(X,sk_c7),X).
% 333497 [hyper:333313,333496,demod:333462,cut:333380] 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 4
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c7,sk_c6),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: 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,0,75,0,0,786,50,6,826,0,6,1878,50,19,1918,0,19,3151,50,38,3191,0,38,4518,50,53,4558,0,53,5980,50,73,6020,0,73,7582,50,102,7622,0,102,9324,50,148,9364,0,148,11252,50,230,11292,0,230,13366,50,385,13406,0,385,15712,50,640,15752,0,640,18290,50,1074,18290,40,1074,18330,0,1074,28814,3,1375,29502,4,1525,30196,5,1675,30197,1,1675,30197,50,1675,30197,40,1675,30237,0,1675,30502,3,1990,30511,4,2133,30523,5,2276,30523,1,2276,30523,50,2276,30523,40,2276,30563,0,2276,52393,3,3778,53404,4,4527,54023,1,5277,54023,50,5278,54023,40,5278,54063,0,5278,70819,3,6030,71327,4,6404,71862,1,6779,71862,50,6779,71862,40,6779,71902,0,6779,83428,3,7541,84562,4,7905,85929,5,8280,85930,1,8280,85930,50,8280,85930,40,8280,85970,0,8280,160126,3,12182,161166,4,14132,161410,1,16081,161410,50,16083,161410,40,16083,161450,0,16083,220739,3,18637,221575,4,19909,221895,1,21184,221895,50,21186,221895,40,21186,221935,0,21186,262454,3,22688,263105,4,23437,263809,5,24187,263810,1,24187,263810,50,24189,263810,40,24189,263850,0,24189,273692,3,24944,274989,4,25318,275755,5,25690,275756,1,25690,275756,50,25690,275756,40,25690,275796,0,25690,307392,3,26892,308135,4,27491,308789,5,28091,308790,1,28091,308790,50,28092,308790,40,28092,308830,0,28092,331534,3,28843,332199,4,29218,332718,1,29593,332718,50,29593,332718,40,29593,332718,40,29593,332753,0,29593,332926,50,29593,332926,30,29593,332926,40,29593,332961,0,29593,333056,50,29593,333056,30,29593,333056,40,29593,333091,0,29598,333169,50,29598,333169,30,29598,333169,40,29598,333204,0,29598,333308,50,29599,333343,0,29599,333496,50,29601,333496,30,29601,333496,40,29601,333531,0,29606,333637,50,29606,333672,0,29606,333829,50,29609,333864,0,29614,334029,50,29618,334064,0,29618,334237,50,29624,334272,0,29624,334451,50,29633,334486,0,29638,334673,50,29654,334708,0,29654,334903,50,29683,334938,0,29688,335143,50,29746,335178,0,29746,335393,50,29864,335393,40,29864,335428,0,29864)
%
%
% START OF PROOF
% 335339 [?] ?
% 335395 [] equal(multiply(identity,X),X).
% 335396 [] equal(multiply(inverse(X),X),identity).
% 335397 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 335398 [] -equal(multiply(sk_c7,sk_c6),sk_c8).
% 335423 [?] ?
% 335424 [?] ?
% 335425 [?] ?
% 335466 [input:335423,cut:335398] equal(inverse(sk_c4),sk_c8).
% 335467 [para:335466.1.1,335396.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 335481 [input:335424,cut:335398] equal(multiply(sk_c4,sk_c8),sk_c5).
% 335482 [input:335425,cut:335398] equal(multiply(sk_c8,sk_c5),sk_c7).
% 335503 [para:335467.1.1,335397.1.1.1,demod:335395] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 335534 [para:335481.1.1,335503.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 335539 [para:335534.1.2,335482.1.1] equal(sk_c8,sk_c7).
% 335541 [para:335539.1.2,335398.1.1.1,cut:335339] 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_c7,sk_c6),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,sk_c7),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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,0,75,0,0,786,50,6,826,0,6,1878,50,19,1918,0,19,3151,50,38,3191,0,38,4518,50,53,4558,0,53,5980,50,73,6020,0,73,7582,50,102,7622,0,102,9324,50,148,9364,0,148,11252,50,230,11292,0,230,13366,50,385,13406,0,385,15712,50,640,15752,0,640,18290,50,1074,18290,40,1074,18330,0,1074,28814,3,1375,29502,4,1525,30196,5,1675,30197,1,1675,30197,50,1675,30197,40,1675,30237,0,1675,30502,3,1990,30511,4,2133,30523,5,2276,30523,1,2276,30523,50,2276,30523,40,2276,30563,0,2276,52393,3,3778,53404,4,4527,54023,1,5277,54023,50,5278,54023,40,5278,54063,0,5278,70819,3,6030,71327,4,6404,71862,1,6779,71862,50,6779,71862,40,6779,71902,0,6779,83428,3,7541,84562,4,7905,85929,5,8280,85930,1,8280,85930,50,8280,85930,40,8280,85970,0,8280,160126,3,12182,161166,4,14132,161410,1,16081,161410,50,16083,161410,40,16083,161450,0,16083,220739,3,18637,221575,4,19909,221895,1,21184,221895,50,21186,221895,40,21186,221935,0,21186,262454,3,22688,263105,4,23437,263809,5,24187,263810,1,24187,263810,50,24189,263810,40,24189,263850,0,24189,273692,3,24944,274989,4,25318,275755,5,25690,275756,1,25690,275756,50,25690,275756,40,25690,275796,0,25690,307392,3,26892,308135,4,27491,308789,5,28091,308790,1,28091,308790,50,28092,308790,40,28092,308830,0,28092,331534,3,28843,332199,4,29218,332718,1,29593,332718,50,29593,332718,40,29593,332718,40,29593,332753,0,29593,332926,50,29593,332926,30,29593,332926,40,29593,332961,0,29593,333056,50,29593,333056,30,29593,333056,40,29593,333091,0,29598,333169,50,29598,333169,30,29598,333169,40,29598,333204,0,29598,333308,50,29599,333343,0,29599,333496,50,29601,333496,30,29601,333496,40,29601,333531,0,29606,333637,50,29606,333672,0,29606,333829,50,29609,333864,0,29614,334029,50,29618,334064,0,29618,334237,50,29624,334272,0,29624,334451,50,29633,334486,0,29638,334673,50,29654,334708,0,29654,334903,50,29683,334938,0,29688,335143,50,29746,335178,0,29746,335393,50,29864,335393,40,29864,335428,0,29864,335540,50,29864,335540,30,29864,335540,40,29864,335575,0,29864,335676,50,29865,335711,0,29869,335858,50,29871,335893,0,29871,336048,50,29874,336083,0,29874,336246,50,29879,336281,0,29883,336450,50,29891,336485,0,29891,336662,50,29905,336697,0,29909,336882,50,29937,336917,0,29937,337112,50,29998,337147,0,29998,337352,50,30112,337352,40,30112,337387,0,30112)
%
%
% START OF PROOF
% 337279 [?] ?
% 337354 [] equal(multiply(identity,X),X).
% 337355 [] equal(multiply(inverse(X),X),identity).
% 337356 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 337357 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 337363 [?] ?
% 337369 [?] ?
% 337375 [?] ?
% 337381 [?] ?
% 337387 [?] ?
% 337406 [input:337363,cut:337357] equal(inverse(sk_c2),sk_c8).
% 337407 [para:337406.1.1,337355.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 337419 [input:337375,cut:337357] equal(inverse(sk_c1),sk_c7).
% 337420 [para:337419.1.1,337355.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 337435 [input:337369,cut:337357] equal(multiply(sk_c2,sk_c8),sk_c6).
% 337439 [input:337381,cut:337357] equal(multiply(sk_c1,sk_c7),sk_c8).
% 337443 [input:337387,cut:337357] equal(multiply(sk_c7,sk_c6),sk_c8).
% 337444 [para:337355.1.1,337356.1.1.1,demod:337354] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 337448 [para:337407.1.1,337356.1.1.1,demod:337354] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 337456 [para:337420.1.1,337356.1.1.1,demod:337354] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 337489 [para:337435.1.1,337448.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 337496 [para:337439.1.1,337456.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 337503 [para:337407.1.1,337444.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 337546 [para:337448.1.2,337444.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c8),X)).
% 337547 [para:337489.1.2,337444.1.2.2,demod:337546] equal(sk_c6,multiply(sk_c2,sk_c8)).
% 337573 [para:337546.1.2,337355.1.1,demod:337547] equal(sk_c6,identity).
% 337582 [para:337573.1.1,337443.1.1.2] equal(multiply(sk_c7,identity),sk_c8).
% 337590 [para:337582.1.1,337356.1.1.1,demod:337354] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 337601 [para:337590.1.2,337420.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 337603 [para:337590.1.2,337496.1.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 337604 [para:337601.1.1,337444.1.2.2,demod:337503] equal(sk_c1,sk_c2).
% 337610 [para:337604.1.2,337406.1.1.1] equal(inverse(sk_c1),sk_c8).
% 337636 [para:337610.1.1,337419.1.1] equal(sk_c8,sk_c7).
% 337638 [para:337636.1.2,337357.1.1.2,demod:337603,cut:337279] 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: 32232
% derived clauses: 6345832
% kept clauses: 285250
% kept size sum: 310198
% kept mid-nuclei: 14754
% kept new demods: 4056
% forw unit-subs: 2501031
% forw double-subs: 3224467
% forw overdouble-subs: 284702
% backward subs: 13524
% fast unit cutoff: 30133
% full unit cutoff: 0
% dbl unit cutoff: 6662
% real runtime : 302.93
% process. runtime: 301.13
% specific non-discr-tree subsumption statistics:
% tried: 40280519
% length fails: 4208094
% strength fails: 12976147
% predlist fails: 3869376
% aux str. fails: 6563353
% by-lit fails: 6526724
% full subs tried: 1282926
% full subs fail: 1176600
%
% ; 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/GRP356-1+eq_r.in")
%
%------------------------------------------------------------------------------