TSTP Solution File: GRP320-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP320-1 : 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 : art04.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 298.1s
% Output : Assurance 298.1s
% 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/GRP320-1+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_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7).
% was split for some strategies as:
% -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% -equal(multiply(sk_c7,sk_c8),sk_c6).
% -equal(multiply(sk_c6,sk_c8),sk_c7).
%
% 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_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7).
% Split part used next: -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,868,50,8,908,0,8,1904,50,21,1944,0,21,3041,50,38,3081,0,38,4232,50,51,4272,0,51,5478,50,69,5518,0,69,6804,50,94,6844,0,94,8210,50,135,8250,0,135,9722,50,209,9762,0,210,11340,50,353,11380,0,353,13090,50,581,13130,0,581,14972,50,984,14972,40,984,15012,0,984,25083,3,1285,25816,4,1435,26530,5,1585,26531,1,1585,26531,50,1585,26531,40,1585,26571,0,1585,26878,3,1899,26887,4,2042,26904,5,2186,26904,1,2186,26904,50,2186,26904,40,2186,26944,0,2186,51401,3,3694,52588,4,4437,53645,5,5187,53646,1,5187,53646,50,5187,53646,40,5187,53686,0,5187,70702,3,5938,71406,4,6313,72227,5,6688,72228,1,6688,72228,50,6688,72228,40,6688,72268,0,6688,83182,3,7441,84494,4,7814,86124,5,8189,86125,5,8189,86126,1,8189,86126,50,8189,86126,40,8189,86166,0,8189,162759,3,12094,163523,4,14040,164301,5,15991,164302,1,15991,164302,50,15994,164302,40,15994,164342,0,15994,222713,3,18547,223429,4,19820,224080,5,21095,224081,1,21095,224081,50,21097,224081,40,21097,224121,0,21097,269360,3,22606,270030,4,23348,270787,1,24098,270787,50,24101,270787,40,24101,270827,0,24101,284680,3,24861,285404,4,25227,285955,5,25602,285956,5,25602,285957,1,25602,285957,50,25602,285957,40,25602,285997,0,25602,319584,3,26803,320011,4,27403,320471,1,28003,320471,50,28004,320471,40,28004,320511,0,28004,343325,3,28756,343922,4,29130,344565,5,29505,344566,1,29505,344566,50,29505,344566,40,29505,344566,40,29505,344601,0,29505)
%
%
% START OF PROOF
% 344568 [] equal(multiply(identity,X),X).
% 344569 [] equal(multiply(inverse(X),X),identity).
% 344570 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 344571 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 344573 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 344574 [?] ?
% 344578 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c7).
% 344579 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 344583 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 344584 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 344588 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 344589 [?] ?
% 344593 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 344594 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 344598 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c5),sk_c7).
% 344599 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 344604 [hyper:344571,344573,binarycut:344574] equal(inverse(sk_c2),sk_c8).
% 344605 [para:344604.1.1,344569.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 344611 [hyper:344571,344588,binarycut:344589] equal(inverse(sk_c1),sk_c7).
% 344614 [para:344611.1.1,344569.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 344622 [hyper:344571,344579,344578] equal(multiply(sk_c2,sk_c8),sk_c3).
% 344638 [hyper:344571,344584,344583] equal(multiply(sk_c8,sk_c3),sk_c7).
% 344642 [hyper:344571,344594,344593] equal(multiply(sk_c1,sk_c7),sk_c8).
% 344646 [hyper:344571,344599,344598] equal(multiply(sk_c7,sk_c8),sk_c6).
% 344647 [para:344569.1.1,344570.1.1.1,demod:344568] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 344648 [para:344605.1.1,344570.1.1.1,demod:344568] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 344650 [para:344622.1.1,344570.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c8,X))).
% 344654 [para:344622.1.1,344648.1.2.2,demod:344638] equal(sk_c8,sk_c7).
% 344655 [para:344654.1.2,344614.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 344656 [para:344654.1.2,344642.1.1.2] equal(multiply(sk_c1,sk_c8),sk_c8).
% 344659 [para:344656.1.1,344570.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c8,X))).
% 344661 [para:344605.1.1,344647.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 344664 [para:344642.1.1,344647.1.2.2,demod:344646,344611] equal(sk_c7,sk_c6).
% 344667 [para:344655.1.1,344647.1.2.2,demod:344661] equal(sk_c1,sk_c2).
% 344668 [para:344656.1.1,344647.1.2.2,demod:344646,344611] equal(sk_c8,sk_c6).
% 344669 [para:344664.1.1,344614.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 344673 [para:344667.1.2,344622.1.1.1,demod:344656] equal(sk_c8,sk_c3).
% 344684 [para:344673.1.1,344648.1.2.1] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 344698 [para:344648.1.2,344650.1.2.2,demod:344684] equal(X,multiply(sk_c2,X)).
% 344699 [para:344667.1.2,344650.1.2.1,demod:344659] equal(multiply(sk_c3,X),multiply(sk_c8,X)).
% 344700 [para:344668.1.1,344650.1.2.2.1,demod:344698] equal(multiply(sk_c3,X),multiply(sk_c6,X)).
% 344701 [para:344698.1.2,344648.1.2.2,demod:344700,344699] equal(X,multiply(sk_c6,X)).
% 344704 [para:344701.1.2,344669.1.1] equal(sk_c1,identity).
% 344705 [para:344704.1.1,344611.1.1.1] equal(inverse(identity),sk_c7).
% 344706 [hyper:344571,344705,demod:344568,cut:344664] 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_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7).
% Split part used next: -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,868,50,8,908,0,8,1904,50,21,1944,0,21,3041,50,38,3081,0,38,4232,50,51,4272,0,51,5478,50,69,5518,0,69,6804,50,94,6844,0,94,8210,50,135,8250,0,135,9722,50,209,9762,0,210,11340,50,353,11380,0,353,13090,50,581,13130,0,581,14972,50,984,14972,40,984,15012,0,984,25083,3,1285,25816,4,1435,26530,5,1585,26531,1,1585,26531,50,1585,26531,40,1585,26571,0,1585,26878,3,1899,26887,4,2042,26904,5,2186,26904,1,2186,26904,50,2186,26904,40,2186,26944,0,2186,51401,3,3694,52588,4,4437,53645,5,5187,53646,1,5187,53646,50,5187,53646,40,5187,53686,0,5187,70702,3,5938,71406,4,6313,72227,5,6688,72228,1,6688,72228,50,6688,72228,40,6688,72268,0,6688,83182,3,7441,84494,4,7814,86124,5,8189,86125,5,8189,86126,1,8189,86126,50,8189,86126,40,8189,86166,0,8189,162759,3,12094,163523,4,14040,164301,5,15991,164302,1,15991,164302,50,15994,164302,40,15994,164342,0,15994,222713,3,18547,223429,4,19820,224080,5,21095,224081,1,21095,224081,50,21097,224081,40,21097,224121,0,21097,269360,3,22606,270030,4,23348,270787,1,24098,270787,50,24101,270787,40,24101,270827,0,24101,284680,3,24861,285404,4,25227,285955,5,25602,285956,5,25602,285957,1,25602,285957,50,25602,285957,40,25602,285997,0,25602,319584,3,26803,320011,4,27403,320471,1,28003,320471,50,28004,320471,40,28004,320511,0,28004,343325,3,28756,343922,4,29130,344565,5,29505,344566,1,29505,344566,50,29505,344566,40,29505,344566,40,29505,344601,0,29505,344705,50,29505,344705,30,29505,344705,40,29505,344740,0,29505)
%
%
% START OF PROOF
% 344707 [] equal(multiply(identity,X),X).
% 344708 [] equal(multiply(inverse(X),X),identity).
% 344709 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 344710 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 344714 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 344715 [?] ?
% 344719 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 344720 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 344724 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 344725 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 344729 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 344730 [?] ?
% 344734 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 344735 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 344739 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 344740 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 344746 [hyper:344710,344714,binarycut:344715] equal(inverse(sk_c2),sk_c8).
% 344749 [para:344746.1.1,344708.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 344757 [hyper:344710,344729,binarycut:344730] equal(inverse(sk_c1),sk_c7).
% 344758 [para:344757.1.1,344708.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 344774 [hyper:344710,344720,344719] equal(multiply(sk_c2,sk_c8),sk_c3).
% 344785 [hyper:344710,344725,344724] equal(multiply(sk_c8,sk_c3),sk_c7).
% 344792 [hyper:344710,344735,344734] equal(multiply(sk_c1,sk_c7),sk_c8).
% 344799 [hyper:344710,344740,344739] equal(multiply(sk_c7,sk_c8),sk_c6).
% 344800 [para:344708.1.1,344709.1.1.1,demod:344707] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 344801 [para:344749.1.1,344709.1.1.1,demod:344707] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 344803 [para:344774.1.1,344709.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c8,X))).
% 344807 [para:344774.1.1,344801.1.2.2,demod:344785] equal(sk_c8,sk_c7).
% 344808 [para:344807.1.2,344758.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 344809 [para:344807.1.2,344792.1.1.2] equal(multiply(sk_c1,sk_c8),sk_c8).
% 344810 [para:344807.1.2,344799.1.1.1] equal(multiply(sk_c8,sk_c8),sk_c6).
% 344812 [?] ?
% 344814 [para:344749.1.1,344800.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 344816 [para:344785.1.1,344800.1.2.2] equal(sk_c3,multiply(inverse(sk_c8),sk_c7)).
% 344820 [para:344808.1.1,344800.1.2.2,demod:344814] equal(sk_c1,sk_c2).
% 344821 [para:344809.1.1,344800.1.2.2,demod:344799,344757] equal(sk_c8,sk_c6).
% 344826 [para:344820.1.2,344774.1.1.1,demod:344809] equal(sk_c8,sk_c3).
% 344828 [para:344821.1.1,344774.1.1.2] equal(multiply(sk_c2,sk_c6),sk_c3).
% 344837 [para:344826.1.1,344801.1.2.1] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 344840 [para:344826.1.1,344821.1.1] equal(sk_c3,sk_c6).
% 344844 [para:344840.1.1,344785.1.1.2] equal(multiply(sk_c8,sk_c6),sk_c7).
% 344846 [para:344826.1.1,344810.1.1.1] equal(multiply(sk_c3,sk_c8),sk_c6).
% 344851 [para:344801.1.2,344803.1.2.2,demod:344837] equal(X,multiply(sk_c2,X)).
% 344852 [para:344820.1.2,344803.1.2.1,demod:344812] equal(multiply(sk_c3,X),multiply(sk_c8,X)).
% 344853 [para:344821.1.1,344803.1.2.2.1,demod:344851] equal(multiply(sk_c3,X),multiply(sk_c6,X)).
% 344854 [para:344851.1.2,344801.1.2.2,demod:344853,344852] equal(X,multiply(sk_c6,X)).
% 344856 [para:344854.1.2,344800.1.2.2] equal(X,multiply(inverse(sk_c6),X)).
% 344862 [para:344828.1.1,344801.1.2.2,demod:344785] equal(sk_c6,sk_c7).
% 344868 [para:344856.1.2,344708.1.1] equal(sk_c6,identity).
% 344872 [para:344868.1.1,344844.1.1.2,demod:344854,344853,344852] equal(identity,sk_c7).
% 344875 [para:344872.1.2,344816.1.2.2,demod:344814] equal(sk_c3,sk_c2).
% 344876 [para:344875.1.2,344746.1.1.1] equal(inverse(sk_c3),sk_c8).
% 344887 [hyper:344710,344876,demod:344846,cut:344862] 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_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7).
% Split part used next: -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,868,50,8,908,0,8,1904,50,21,1944,0,21,3041,50,38,3081,0,38,4232,50,51,4272,0,51,5478,50,69,5518,0,69,6804,50,94,6844,0,94,8210,50,135,8250,0,135,9722,50,209,9762,0,210,11340,50,353,11380,0,353,13090,50,581,13130,0,581,14972,50,984,14972,40,984,15012,0,984,25083,3,1285,25816,4,1435,26530,5,1585,26531,1,1585,26531,50,1585,26531,40,1585,26571,0,1585,26878,3,1899,26887,4,2042,26904,5,2186,26904,1,2186,26904,50,2186,26904,40,2186,26944,0,2186,51401,3,3694,52588,4,4437,53645,5,5187,53646,1,5187,53646,50,5187,53646,40,5187,53686,0,5187,70702,3,5938,71406,4,6313,72227,5,6688,72228,1,6688,72228,50,6688,72228,40,6688,72268,0,6688,83182,3,7441,84494,4,7814,86124,5,8189,86125,5,8189,86126,1,8189,86126,50,8189,86126,40,8189,86166,0,8189,162759,3,12094,163523,4,14040,164301,5,15991,164302,1,15991,164302,50,15994,164302,40,15994,164342,0,15994,222713,3,18547,223429,4,19820,224080,5,21095,224081,1,21095,224081,50,21097,224081,40,21097,224121,0,21097,269360,3,22606,270030,4,23348,270787,1,24098,270787,50,24101,270787,40,24101,270827,0,24101,284680,3,24861,285404,4,25227,285955,5,25602,285956,5,25602,285957,1,25602,285957,50,25602,285957,40,25602,285997,0,25602,319584,3,26803,320011,4,27403,320471,1,28003,320471,50,28004,320471,40,28004,320511,0,28004,343325,3,28756,343922,4,29130,344565,5,29505,344566,1,29505,344566,50,29505,344566,40,29505,344566,40,29505,344601,0,29505,344705,50,29505,344705,30,29505,344705,40,29505,344740,0,29505,344886,50,29506,344886,30,29506,344886,40,29506,344921,0,29512)
%
%
% START OF PROOF
% 344888 [] equal(multiply(identity,X),X).
% 344889 [] equal(multiply(inverse(X),X),identity).
% 344890 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 344891 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 344892 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c8).
% 344893 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 344894 [] equal(multiply(sk_c5,sk_c7),sk_c6) | equal(inverse(sk_c2),sk_c8).
% 344895 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 344896 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c8).
% 344897 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c6,sk_c8),sk_c7).
% 344898 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c7).
% 344899 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 344900 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 344901 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 344902 [?] ?
% 344903 [?] ?
% 344904 [?] ?
% 344905 [?] ?
% 344906 [?] ?
% 344964 [hyper:344891,344897,344892,binarycut:344902] equal(multiply(sk_c6,sk_c8),sk_c7).
% 344971 [hyper:344891,344898,binarycut:344903,binarycut:344893] equal(inverse(sk_c5),sk_c7).
% 344972 [para:344971.1.1,344889.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 344975 [hyper:344891,344900,binarycut:344905,binarycut:344895] equal(inverse(sk_c4),sk_c8).
% 344985 [hyper:344891,344899,344894,binarycut:344904] equal(multiply(sk_c5,sk_c7),sk_c6).
% 344989 [para:344975.1.1,344889.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 344999 [hyper:344891,344901,344896,binarycut:344906] equal(multiply(sk_c4,sk_c8),sk_c7).
% 345002 [para:344889.1.1,344890.1.1.1,demod:344888] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 345003 [para:344964.1.1,344890.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c8,X))).
% 345004 [para:344972.1.1,344890.1.1.1,demod:344888] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 345006 [para:344989.1.1,344890.1.1.1,demod:344888] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 345012 [para:344985.1.1,345004.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 345016 [para:344999.1.1,345006.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 345021 [para:344964.1.1,345002.1.2.2] equal(sk_c8,multiply(inverse(sk_c6),sk_c7)).
% 345024 [para:345004.1.2,345002.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c7),X)).
% 345033 [para:345016.1.2,345003.1.2.2,demod:344964] equal(multiply(sk_c7,sk_c7),sk_c7).
% 345035 [para:345033.1.1,345002.1.2.2,demod:344985,345024] equal(sk_c7,sk_c6).
% 345040 [para:345035.1.1,345016.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 345041 [para:345035.1.1,345021.1.2.2,demod:344889] equal(sk_c8,identity).
% 345048 [para:345041.1.1,345016.1.2.1,demod:344888] equal(sk_c8,sk_c7).
% 345054 [para:345048.1.2,344985.1.1.2] equal(multiply(sk_c5,sk_c8),sk_c6).
% 345056 [para:345048.1.2,345012.1.2.1,demod:345040] equal(sk_c7,sk_c8).
% 345091 [hyper:344891,345024,demod:344971,345040,345054,345024,cut:345048,cut:345056] 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_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7).
% 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
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,868,50,8,908,0,8,1904,50,21,1944,0,21,3041,50,38,3081,0,38,4232,50,51,4272,0,51,5478,50,69,5518,0,69,6804,50,94,6844,0,94,8210,50,135,8250,0,135,9722,50,209,9762,0,210,11340,50,353,11380,0,353,13090,50,581,13130,0,581,14972,50,984,14972,40,984,15012,0,984,25083,3,1285,25816,4,1435,26530,5,1585,26531,1,1585,26531,50,1585,26531,40,1585,26571,0,1585,26878,3,1899,26887,4,2042,26904,5,2186,26904,1,2186,26904,50,2186,26904,40,2186,26944,0,2186,51401,3,3694,52588,4,4437,53645,5,5187,53646,1,5187,53646,50,5187,53646,40,5187,53686,0,5187,70702,3,5938,71406,4,6313,72227,5,6688,72228,1,6688,72228,50,6688,72228,40,6688,72268,0,6688,83182,3,7441,84494,4,7814,86124,5,8189,86125,5,8189,86126,1,8189,86126,50,8189,86126,40,8189,86166,0,8189,162759,3,12094,163523,4,14040,164301,5,15991,164302,1,15991,164302,50,15994,164302,40,15994,164342,0,15994,222713,3,18547,223429,4,19820,224080,5,21095,224081,1,21095,224081,50,21097,224081,40,21097,224121,0,21097,269360,3,22606,270030,4,23348,270787,1,24098,270787,50,24101,270787,40,24101,270827,0,24101,284680,3,24861,285404,4,25227,285955,5,25602,285956,5,25602,285957,1,25602,285957,50,25602,285957,40,25602,285997,0,25602,319584,3,26803,320011,4,27403,320471,1,28003,320471,50,28004,320471,40,28004,320511,0,28004,343325,3,28756,343922,4,29130,344565,5,29505,344566,1,29505,344566,50,29505,344566,40,29505,344566,40,29505,344601,0,29505,344705,50,29505,344705,30,29505,344705,40,29505,344740,0,29505,344886,50,29506,344886,30,29506,344886,40,29506,344921,0,29512,345090,50,29513,345090,30,29513,345090,40,29513,345125,0,29513)
%
%
% START OF PROOF
% 345092 [] equal(multiply(identity,X),X).
% 345093 [] equal(multiply(inverse(X),X),identity).
% 345094 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 345095 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% 345111 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 345112 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 345113 [] equal(multiply(sk_c5,sk_c7),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 345114 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 345115 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 345116 [?] ?
% 345117 [?] ?
% 345118 [?] ?
% 345119 [?] ?
% 345120 [?] ?
% 345132 [hyper:345095,345112,binarycut:345117] equal(inverse(sk_c5),sk_c7).
% 345136 [para:345132.1.1,345093.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 345140 [hyper:345095,345114,binarycut:345119] equal(inverse(sk_c4),sk_c8).
% 345141 [para:345140.1.1,345093.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 345147 [hyper:345095,345111,binarycut:345116] equal(multiply(sk_c6,sk_c8),sk_c7).
% 345150 [hyper:345095,345113,binarycut:345118] equal(multiply(sk_c5,sk_c7),sk_c6).
% 345154 [hyper:345095,345115,binarycut:345120] equal(multiply(sk_c4,sk_c8),sk_c7).
% 345155 [para:345093.1.1,345094.1.1.1,demod:345092] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 345156 [para:345136.1.1,345094.1.1.1,demod:345092] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 345157 [para:345141.1.1,345094.1.1.1,demod:345092] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 345158 [para:345147.1.1,345094.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c8,X))).
% 345159 [para:345150.1.1,345094.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c5,multiply(sk_c7,X))).
% 345161 [para:345150.1.1,345156.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 345163 [para:345154.1.1,345157.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 345168 [para:345147.1.1,345155.1.2.2] equal(sk_c8,multiply(inverse(sk_c6),sk_c7)).
% 345169 [para:345156.1.2,345155.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c7),X)).
% 345173 [para:345163.1.2,345158.1.2.2,demod:345147] equal(multiply(sk_c7,sk_c7),sk_c7).
% 345176 [para:345173.1.1,345155.1.2.2,demod:345150,345169] equal(sk_c7,sk_c6).
% 345177 [para:345176.1.1,345136.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 345179 [para:345176.1.1,345156.1.2.1] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 345182 [?] ?
% 345183 [para:345177.1.1,345155.1.2.2] equal(sk_c5,multiply(inverse(sk_c6),identity)).
% 345187 [para:345156.1.2,345159.1.2.2,demod:345179] equal(X,multiply(sk_c5,X)).
% 345188 [para:345187.1.2,345156.1.2.2] equal(X,multiply(sk_c7,X)).
% 345189 [para:345187.1.2,345159.1.2,demod:345188] equal(multiply(sk_c6,X),X).
% 345194 [para:345189.1.1,345147.1.1] equal(sk_c8,sk_c7).
% 345195 [para:345147.1.1,345189.1.1] equal(sk_c7,sk_c8).
% 345196 [para:345189.1.1,345155.1.2.2] equal(X,multiply(inverse(sk_c6),X)).
% 345202 [para:345194.1.2,345150.1.1.2,demod:345187] equal(sk_c8,sk_c6).
% 345205 [para:345196.1.2,345093.1.1] equal(sk_c6,identity).
% 345206 [para:345205.1.1,345161.1.2.2,demod:345188] equal(sk_c7,identity).
% 345214 [para:345206.1.1,345168.1.2.2,demod:345183] equal(sk_c8,sk_c5).
% 345216 [para:345214.1.1,345202.1.1] equal(sk_c5,sk_c6).
% 345219 [para:345216.1.1,345132.1.1.1] equal(inverse(sk_c6),sk_c7).
% 345222 [hyper:345095,345219,demod:345182,cut:345195] 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 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7).
% Split part used next: -equal(multiply(sk_c7,sk_c8),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(35,40,1,75,0,1,868,50,8,908,0,8,1904,50,21,1944,0,21,3041,50,38,3081,0,38,4232,50,51,4272,0,51,5478,50,69,5518,0,69,6804,50,94,6844,0,94,8210,50,135,8250,0,135,9722,50,209,9762,0,210,11340,50,353,11380,0,353,13090,50,581,13130,0,581,14972,50,984,14972,40,984,15012,0,984,25083,3,1285,25816,4,1435,26530,5,1585,26531,1,1585,26531,50,1585,26531,40,1585,26571,0,1585,26878,3,1899,26887,4,2042,26904,5,2186,26904,1,2186,26904,50,2186,26904,40,2186,26944,0,2186,51401,3,3694,52588,4,4437,53645,5,5187,53646,1,5187,53646,50,5187,53646,40,5187,53686,0,5187,70702,3,5938,71406,4,6313,72227,5,6688,72228,1,6688,72228,50,6688,72228,40,6688,72268,0,6688,83182,3,7441,84494,4,7814,86124,5,8189,86125,5,8189,86126,1,8189,86126,50,8189,86126,40,8189,86166,0,8189,162759,3,12094,163523,4,14040,164301,5,15991,164302,1,15991,164302,50,15994,164302,40,15994,164342,0,15994,222713,3,18547,223429,4,19820,224080,5,21095,224081,1,21095,224081,50,21097,224081,40,21097,224121,0,21097,269360,3,22606,270030,4,23348,270787,1,24098,270787,50,24101,270787,40,24101,270827,0,24101,284680,3,24861,285404,4,25227,285955,5,25602,285956,5,25602,285957,1,25602,285957,50,25602,285957,40,25602,285997,0,25602,319584,3,26803,320011,4,27403,320471,1,28003,320471,50,28004,320471,40,28004,320511,0,28004,343325,3,28756,343922,4,29130,344565,5,29505,344566,1,29505,344566,50,29505,344566,40,29505,344566,40,29505,344601,0,29505,344705,50,29505,344705,30,29505,344705,40,29505,344740,0,29505,344886,50,29506,344886,30,29506,344886,40,29506,344921,0,29512,345090,50,29513,345090,30,29513,345090,40,29513,345125,0,29513,345221,50,29514,345221,30,29514,345221,40,29514,345256,0,29514,345370,50,29514,345405,0,29519,345579,50,29521,345614,0,29521,345804,50,29524,345839,0,29528,346042,50,29533,346077,0,29533,346286,50,29540,346321,0,29540,346538,50,29554,346573,0,29559,346798,50,29585,346833,0,29585,347068,50,29643,347103,0,29643,347348,50,29754,347348,40,29754,347383,0,29754)
%
%
% START OF PROOF
% 347203 [?] ?
% 347350 [] equal(multiply(identity,X),X).
% 347351 [] equal(multiply(inverse(X),X),identity).
% 347352 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 347353 [] -equal(multiply(sk_c7,sk_c8),sk_c6).
% 347379 [?] ?
% 347380 [?] ?
% 347381 [?] ?
% 347382 [?] ?
% 347383 [?] ?
% 347422 [input:347380,cut:347353] equal(inverse(sk_c5),sk_c7).
% 347423 [para:347422.1.1,347351.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 347425 [input:347382,cut:347353] equal(inverse(sk_c4),sk_c8).
% 347426 [para:347425.1.1,347351.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 347437 [input:347379,cut:347353] equal(multiply(sk_c6,sk_c8),sk_c7).
% 347438 [input:347381,cut:347353] equal(multiply(sk_c5,sk_c7),sk_c6).
% 347439 [input:347383,cut:347353] equal(multiply(sk_c4,sk_c8),sk_c7).
% 347443 [para:347351.1.1,347352.1.1.1,demod:347350] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 347462 [para:347423.1.1,347352.1.1.1,demod:347350] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 347463 [para:347426.1.1,347352.1.1.1,demod:347350] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 347491 [para:347438.1.1,347462.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 347498 [para:347439.1.1,347463.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 347541 [para:347437.1.1,347443.1.2.2] equal(sk_c8,multiply(inverse(sk_c6),sk_c7)).
% 347548 [para:347462.1.2,347443.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c7),X)).
% 347549 [para:347491.1.2,347443.1.2.2,demod:347548] equal(sk_c6,multiply(sk_c5,sk_c7)).
% 347552 [para:347443.1.2,347443.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 347554 [para:347541.1.2,347443.1.2.2,demod:347552] equal(sk_c7,multiply(sk_c6,sk_c8)).
% 347561 [para:347548.1.2,347351.1.1,demod:347549] equal(sk_c6,identity).
% 347570 [para:347561.1.1,347437.1.1.1,demod:347350] equal(sk_c8,sk_c7).
% 347572 [para:347561.1.1,347554.1.2.1,demod:347350] equal(sk_c7,sk_c8).
% 347588 [para:347570.1.2,347498.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c8)).
% 347593 [para:347572.1.1,347353.1.1.1,demod:347588,cut:347203] 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_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7).
% Split part used next: -equal(multiply(sk_c6,sk_c8),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 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(35,40,1,75,0,1,868,50,8,908,0,8,1904,50,21,1944,0,21,3041,50,38,3081,0,38,4232,50,51,4272,0,51,5478,50,69,5518,0,69,6804,50,94,6844,0,94,8210,50,135,8250,0,135,9722,50,209,9762,0,210,11340,50,353,11380,0,353,13090,50,581,13130,0,581,14972,50,984,14972,40,984,15012,0,984,25083,3,1285,25816,4,1435,26530,5,1585,26531,1,1585,26531,50,1585,26531,40,1585,26571,0,1585,26878,3,1899,26887,4,2042,26904,5,2186,26904,1,2186,26904,50,2186,26904,40,2186,26944,0,2186,51401,3,3694,52588,4,4437,53645,5,5187,53646,1,5187,53646,50,5187,53646,40,5187,53686,0,5187,70702,3,5938,71406,4,6313,72227,5,6688,72228,1,6688,72228,50,6688,72228,40,6688,72268,0,6688,83182,3,7441,84494,4,7814,86124,5,8189,86125,5,8189,86126,1,8189,86126,50,8189,86126,40,8189,86166,0,8189,162759,3,12094,163523,4,14040,164301,5,15991,164302,1,15991,164302,50,15994,164302,40,15994,164342,0,15994,222713,3,18547,223429,4,19820,224080,5,21095,224081,1,21095,224081,50,21097,224081,40,21097,224121,0,21097,269360,3,22606,270030,4,23348,270787,1,24098,270787,50,24101,270787,40,24101,270827,0,24101,284680,3,24861,285404,4,25227,285955,5,25602,285956,5,25602,285957,1,25602,285957,50,25602,285957,40,25602,285997,0,25602,319584,3,26803,320011,4,27403,320471,1,28003,320471,50,28004,320471,40,28004,320511,0,28004,343325,3,28756,343922,4,29130,344565,5,29505,344566,1,29505,344566,50,29505,344566,40,29505,344566,40,29505,344601,0,29505,344705,50,29505,344705,30,29505,344705,40,29505,344740,0,29505,344886,50,29506,344886,30,29506,344886,40,29506,344921,0,29512,345090,50,29513,345090,30,29513,345090,40,29513,345125,0,29513,345221,50,29514,345221,30,29514,345221,40,29514,345256,0,29514,345370,50,29514,345405,0,29519,345579,50,29521,345614,0,29521,345804,50,29524,345839,0,29528,346042,50,29533,346077,0,29533,346286,50,29540,346321,0,29540,346538,50,29554,346573,0,29559,346798,50,29585,346833,0,29585,347068,50,29643,347103,0,29643,347348,50,29754,347348,40,29754,347383,0,29754,347592,50,29754,347592,30,29754,347592,40,29754,347627,0,29754,347740,50,29755,347775,0,29760,347938,50,29763,347973,0,29763,348145,50,29767,348180,0,29767,348372,50,29773,348407,0,29778,348606,50,29788,348641,0,29789,348848,50,29807,348883,0,29811,349099,50,29845,349134,0,29845,349360,50,29914,349395,0,29914,349632,50,30044,349632,40,30044,349667,0,30044)
%
%
% START OF PROOF
% 349634 [] equal(multiply(identity,X),X).
% 349635 [] equal(multiply(inverse(X),X),identity).
% 349636 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 349637 [] -equal(multiply(sk_c6,sk_c8),sk_c7).
% 349638 [?] ?
% 349643 [?] ?
% 349648 [?] ?
% 349653 [?] ?
% 349658 [?] ?
% 349663 [?] ?
% 349671 [input:349638,cut:349637] equal(inverse(sk_c2),sk_c8).
% 349672 [para:349671.1.1,349635.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 349691 [input:349653,cut:349637] equal(inverse(sk_c1),sk_c7).
% 349692 [para:349691.1.1,349635.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 349693 [input:349643,cut:349637] equal(multiply(sk_c2,sk_c8),sk_c3).
% 349710 [input:349648,cut:349637] equal(multiply(sk_c8,sk_c3),sk_c7).
% 349713 [input:349658,cut:349637] equal(multiply(sk_c1,sk_c7),sk_c8).
% 349716 [input:349663,cut:349637] equal(multiply(sk_c7,sk_c8),sk_c6).
% 349724 [para:349672.1.1,349636.1.1.1,demod:349634] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 349732 [para:349692.1.1,349636.1.1.1,demod:349634] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 349745 [para:349710.1.1,349636.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c3,X))).
% 349760 [para:349693.1.1,349724.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c3)).
% 349763 [para:349760.1.2,349710.1.1] equal(sk_c8,sk_c7).
% 349764 [para:349760.1.2,349636.1.1.1,demod:349745] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 349778 [para:349763.1.2,349716.1.1.1] equal(multiply(sk_c8,sk_c8),sk_c6).
% 349789 [para:349713.1.1,349732.1.2.2,demod:349778,349764] equal(sk_c7,sk_c6).
% 349791 [para:349789.1.1,349637.1.2] -equal(multiply(sk_c6,sk_c8),sk_c6).
% 349804 [para:349789.1.1,349716.1.1.1,cut:349791] 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: 33248
% derived clauses: 5158228
% kept clauses: 298712
% kept size sum: 772975
% kept mid-nuclei: 11535
% kept new demods: 4142
% forw unit-subs: 1649821
% forw double-subs: 2769750
% forw overdouble-subs: 388519
% backward subs: 11708
% fast unit cutoff: 21883
% full unit cutoff: 0
% dbl unit cutoff: 7307
% real runtime : 302.59
% process. runtime: 300.43
% specific non-discr-tree subsumption statistics:
% tried: 38059694
% length fails: 3966096
% strength fails: 11142134
% predlist fails: 3006024
% aux str. fails: 6071698
% by-lit fails: 7543995
% full subs tried: 2064378
% full subs fail: 1939532
%
% ; 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/GRP320-1+eq_r.in")
%
%------------------------------------------------------------------------------