TSTP Solution File: GRP290-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP290-1 : 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 297.9s
% Output : Assurance 297.9s
% 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/GRP290-1+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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% was split for some strategies as:
% -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8).
% -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(multiply(sk_c8,sk_c7),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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,717,50,7,757,0,7,1569,50,17,1609,0,17,2506,50,31,2546,0,31,3489,50,42,3529,0,42,4519,50,57,4559,0,57,5617,50,80,5657,0,80,6783,50,117,6823,0,117,8039,50,186,8079,0,186,9385,50,322,9425,0,323,10843,50,541,10883,0,541,12413,50,935,12413,40,935,12453,0,935,22976,3,1236,23645,4,1386,24326,1,1536,24326,50,1536,24326,40,1536,24366,0,1536,24651,3,1843,24662,4,2007,24678,5,2137,24678,1,2137,24678,50,2137,24678,40,2137,24718,0,2137,48521,3,3638,49494,4,4388,50607,1,5138,50607,50,5138,50607,40,5138,50647,0,5138,66475,3,5889,67369,4,6264,68189,1,6639,68189,50,6639,68189,40,6639,68229,0,6639,80749,3,7393,81463,4,7765,82881,1,8140,82881,50,8140,82881,40,8140,82921,0,8140,154075,3,12041,154982,4,13991,155849,5,15941,155850,1,15941,155850,50,15943,155850,40,15943,155890,0,15943,218017,3,18494,218751,4,19769,219531,5,21044,219532,1,21044,219532,50,21046,219532,40,21046,219572,0,21046,253160,3,22550,254194,4,23297,255076,5,24047,255077,1,24047,255077,50,24049,255077,40,24049,255117,0,24049,263929,3,24802,265345,4,25176,265890,5,25550,265890,1,25550,265890,50,25550,265890,40,25550,265930,0,25550,311588,3,26753,312112,4,27351,312434,5,27951,312435,1,27951,312435,50,27953,312435,40,27953,312475,0,27953,345604,3,28704,346055,4,29079,346299,1,29454,346299,50,29455,346299,40,29455,346299,40,29455,346334,0,29455,346419,50,29455,346454,0,29455)
%
%
% START OF PROOF
% 346421 [] equal(multiply(identity,X),X).
% 346422 [] equal(multiply(inverse(X),X),identity).
% 346423 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 346424 [] -equal(multiply(X,sk_c6),sk_c8) | -equal(inverse(X),sk_c6).
% 346425 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 346426 [?] ?
% 346431 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(inverse(sk_c5),sk_c6).
% 346432 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c5,sk_c6),sk_c8).
% 346437 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 346438 [?] ?
% 346443 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 346444 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c5,sk_c6),sk_c8).
% 346449 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c5),sk_c6).
% 346450 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c5,sk_c6),sk_c8).
% 346457 [hyper:346424,346425,binarycut:346426] equal(inverse(sk_c2),sk_c7).
% 346458 [para:346457.1.1,346422.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 346465 [hyper:346424,346437,binarycut:346438] equal(inverse(sk_c1),sk_c8).
% 346466 [para:346465.1.1,346422.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 346470 [hyper:346424,346432,346431] equal(multiply(sk_c2,sk_c7),sk_c6).
% 346477 [hyper:346424,346444,346443] equal(multiply(sk_c1,sk_c8),sk_c7).
% 346483 [hyper:346424,346450,346449] equal(multiply(sk_c8,sk_c7),sk_c6).
% 346484 [para:346422.1.1,346423.1.1.1,demod:346421] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 346485 [para:346458.1.1,346423.1.1.1,demod:346421] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 346486 [para:346466.1.1,346423.1.1.1,demod:346421] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 346488 [para:346477.1.1,346423.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c1,multiply(sk_c8,X))).
% 346490 [para:346470.1.1,346485.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 346492 [para:346477.1.1,346486.1.2.2,demod:346483] equal(sk_c8,sk_c6).
% 346494 [para:346492.1.1,346477.1.1.2] equal(multiply(sk_c1,sk_c6),sk_c7).
% 346495 [para:346492.1.1,346483.1.1.1] equal(multiply(sk_c6,sk_c7),sk_c6).
% 346498 [para:346422.1.1,346484.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 346500 [para:346466.1.1,346484.1.2.2] equal(sk_c1,multiply(inverse(sk_c8),identity)).
% 346502 [para:346423.1.1,346484.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 346506 [para:346484.1.2,346484.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 346509 [para:346495.1.1,346484.1.2.2,demod:346422] equal(sk_c7,identity).
% 346510 [para:346509.1.1,346458.1.1.1,demod:346421] equal(sk_c2,identity).
% 346513 [para:346509.1.1,346485.1.2.1,demod:346421] equal(X,multiply(sk_c2,X)).
% 346514 [para:346509.1.1,346490.1.2.1,demod:346421] equal(sk_c7,sk_c6).
% 346518 [para:346510.1.1,346485.1.2.2.1,demod:346421] equal(X,multiply(sk_c7,X)).
% 346522 [para:346514.1.1,346509.1.1] equal(sk_c6,identity).
% 346525 [para:346522.1.1,346494.1.1.2] equal(multiply(sk_c1,identity),sk_c7).
% 346532 [para:346466.1.1,346488.1.2.2,demod:346525,346518] equal(sk_c1,sk_c7).
% 346533 [para:346532.1.2,346470.1.1.2,demod:346513] equal(sk_c1,sk_c6).
% 346558 [para:346506.1.2,346422.1.1] equal(multiply(X,inverse(X)),identity).
% 346560 [para:346506.1.2,346498.1.2] equal(X,multiply(X,identity)).
% 346562 [para:346560.1.2,346498.1.2] equal(X,inverse(inverse(X))).
% 346564 [para:346560.1.2,346500.1.2] equal(sk_c1,inverse(sk_c8)).
% 346570 [para:346558.1.1,346502.1.2.2.2,demod:346560] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 346572 [para:346485.1.2,346570.1.2.1.1,demod:346513] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 346580 [para:346572.1.2,346506.1.2,demod:346562] equal(multiply(X,sk_c7),X).
% 346581 [para:346514.1.1,346580.1.1.2] equal(multiply(X,sk_c6),X).
% 346584 [hyper:346424,346581,demod:346564,cut:346533] 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 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -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(35,40,1,75,0,1,717,50,7,757,0,7,1569,50,17,1609,0,17,2506,50,31,2546,0,31,3489,50,42,3529,0,42,4519,50,57,4559,0,57,5617,50,80,5657,0,80,6783,50,117,6823,0,117,8039,50,186,8079,0,186,9385,50,322,9425,0,323,10843,50,541,10883,0,541,12413,50,935,12413,40,935,12453,0,935,22976,3,1236,23645,4,1386,24326,1,1536,24326,50,1536,24326,40,1536,24366,0,1536,24651,3,1843,24662,4,2007,24678,5,2137,24678,1,2137,24678,50,2137,24678,40,2137,24718,0,2137,48521,3,3638,49494,4,4388,50607,1,5138,50607,50,5138,50607,40,5138,50647,0,5138,66475,3,5889,67369,4,6264,68189,1,6639,68189,50,6639,68189,40,6639,68229,0,6639,80749,3,7393,81463,4,7765,82881,1,8140,82881,50,8140,82881,40,8140,82921,0,8140,154075,3,12041,154982,4,13991,155849,5,15941,155850,1,15941,155850,50,15943,155850,40,15943,155890,0,15943,218017,3,18494,218751,4,19769,219531,5,21044,219532,1,21044,219532,50,21046,219532,40,21046,219572,0,21046,253160,3,22550,254194,4,23297,255076,5,24047,255077,1,24047,255077,50,24049,255077,40,24049,255117,0,24049,263929,3,24802,265345,4,25176,265890,5,25550,265890,1,25550,265890,50,25550,265890,40,25550,265930,0,25550,311588,3,26753,312112,4,27351,312434,5,27951,312435,1,27951,312435,50,27953,312435,40,27953,312475,0,27953,345604,3,28704,346055,4,29079,346299,1,29454,346299,50,29455,346299,40,29455,346299,40,29455,346334,0,29455,346419,50,29455,346454,0,29455,346583,50,29456,346583,30,29456,346583,40,29457,346618,0,29461)
%
%
% START OF PROOF
% 346584 [] equal(X,X).
% 346585 [] equal(multiply(identity,X),X).
% 346586 [] equal(multiply(inverse(X),X),identity).
% 346587 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 346588 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 346591 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 346592 [] equal(multiply(sk_c3,sk_c8),sk_c4) | equal(inverse(sk_c2),sk_c7).
% 346593 [?] ?
% 346597 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 346598 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c8),sk_c4).
% 346599 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c8,sk_c4),sk_c7).
% 346603 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 346604 [] equal(multiply(sk_c3,sk_c8),sk_c4) | equal(inverse(sk_c1),sk_c8).
% 346605 [?] ?
% 346609 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 346610 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c3,sk_c8),sk_c4).
% 346611 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c8,sk_c4),sk_c7).
% 346615 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 346616 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c8),sk_c4).
% 346617 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c8,sk_c4),sk_c7).
% 346645 [hyper:346588,346592,346591,binarycut:346593] equal(inverse(sk_c2),sk_c7).
% 346646 [para:346645.1.1,346586.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 346662 [hyper:346588,346604,346603,binarycut:346605] equal(inverse(sk_c1),sk_c8).
% 346669 [para:346662.1.1,346586.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 346697 [hyper:346588,346599,346598,346597] equal(multiply(sk_c2,sk_c7),sk_c6).
% 346711 [hyper:346588,346611,346610,346609] equal(multiply(sk_c1,sk_c8),sk_c7).
% 346723 [hyper:346588,346617,346616,346615] equal(multiply(sk_c8,sk_c7),sk_c6).
% 346724 [para:346586.1.1,346587.1.1.1,demod:346585] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 346725 [para:346646.1.1,346587.1.1.1,demod:346585] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 346726 [para:346669.1.1,346587.1.1.1,demod:346585] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 346728 [para:346711.1.1,346587.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c1,multiply(sk_c8,X))).
% 346729 [para:346723.1.1,346587.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c8,multiply(sk_c7,X))).
% 346732 [para:346697.1.1,346725.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 346736 [para:346711.1.1,346726.1.2.2,demod:346723] equal(sk_c8,sk_c6).
% 346737 [para:346736.1.1,346669.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 346738 [para:346736.1.1,346711.1.1.2] equal(multiply(sk_c1,sk_c6),sk_c7).
% 346739 [para:346736.1.1,346723.1.1.1] equal(multiply(sk_c6,sk_c7),sk_c6).
% 346752 [para:346739.1.1,346724.1.2.2,demod:346586] equal(sk_c7,identity).
% 346753 [para:346752.1.1,346646.1.1.1,demod:346585] equal(sk_c2,identity).
% 346756 [para:346752.1.1,346725.1.2.1,demod:346585] equal(X,multiply(sk_c2,X)).
% 346757 [para:346752.1.1,346732.1.2.1,demod:346585] equal(sk_c7,sk_c6).
% 346761 [para:346753.1.1,346725.1.2.2.1,demod:346585] equal(X,multiply(sk_c7,X)).
% 346765 [para:346757.1.1,346752.1.1] equal(sk_c6,identity).
% 346769 [para:346765.1.1,346737.1.1.1,demod:346585] equal(sk_c1,identity).
% 346770 [para:346765.1.1,346738.1.1.2] equal(multiply(sk_c1,identity),sk_c7).
% 346772 [para:346769.1.1,346711.1.1.1,demod:346585] equal(sk_c8,sk_c7).
% 346773 [para:346769.1.1,346726.1.2.2.1,demod:346585] equal(X,multiply(sk_c8,X)).
% 346779 [para:346669.1.1,346728.1.2.2,demod:346770,346761] equal(sk_c1,sk_c7).
% 346780 [para:346779.1.2,346697.1.1.2,demod:346756] equal(sk_c1,sk_c6).
% 346782 [para:346780.1.1,346662.1.1.1] equal(inverse(sk_c6),sk_c8).
% 346783 [hyper:346588,346729,demod:346782,346773,346761,cut:346772,cut:346584] 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),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(35,40,1,75,0,1,717,50,7,757,0,7,1569,50,17,1609,0,17,2506,50,31,2546,0,31,3489,50,42,3529,0,42,4519,50,57,4559,0,57,5617,50,80,5657,0,80,6783,50,117,6823,0,117,8039,50,186,8079,0,186,9385,50,322,9425,0,323,10843,50,541,10883,0,541,12413,50,935,12413,40,935,12453,0,935,22976,3,1236,23645,4,1386,24326,1,1536,24326,50,1536,24326,40,1536,24366,0,1536,24651,3,1843,24662,4,2007,24678,5,2137,24678,1,2137,24678,50,2137,24678,40,2137,24718,0,2137,48521,3,3638,49494,4,4388,50607,1,5138,50607,50,5138,50607,40,5138,50647,0,5138,66475,3,5889,67369,4,6264,68189,1,6639,68189,50,6639,68189,40,6639,68229,0,6639,80749,3,7393,81463,4,7765,82881,1,8140,82881,50,8140,82881,40,8140,82921,0,8140,154075,3,12041,154982,4,13991,155849,5,15941,155850,1,15941,155850,50,15943,155850,40,15943,155890,0,15943,218017,3,18494,218751,4,19769,219531,5,21044,219532,1,21044,219532,50,21046,219532,40,21046,219572,0,21046,253160,3,22550,254194,4,23297,255076,5,24047,255077,1,24047,255077,50,24049,255077,40,24049,255117,0,24049,263929,3,24802,265345,4,25176,265890,5,25550,265890,1,25550,265890,50,25550,265890,40,25550,265930,0,25550,311588,3,26753,312112,4,27351,312434,5,27951,312435,1,27951,312435,50,27953,312435,40,27953,312475,0,27953,345604,3,28704,346055,4,29079,346299,1,29454,346299,50,29455,346299,40,29455,346299,40,29455,346334,0,29455,346419,50,29455,346454,0,29455,346583,50,29456,346583,30,29456,346583,40,29457,346618,0,29461,346782,50,29461,346782,30,29461,346782,40,29461,346817,0,29461,346928,50,29462,346963,0,29462)
%
%
% START OF PROOF
% 346930 [] equal(multiply(identity,X),X).
% 346931 [] equal(multiply(inverse(X),X),identity).
% 346932 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 346933 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 346934 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 346935 [] equal(multiply(sk_c5,sk_c6),sk_c8) | equal(inverse(sk_c2),sk_c7).
% 346936 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 346937 [] equal(multiply(sk_c3,sk_c8),sk_c4) | equal(inverse(sk_c2),sk_c7).
% 346938 [] equal(multiply(sk_c8,sk_c4),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 346939 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 346940 [?] ?
% 346941 [?] ?
% 346942 [?] ?
% 346943 [?] ?
% 346944 [?] ?
% 346945 [?] ?
% 346966 [hyper:346933,346934,binarycut:346940] equal(inverse(sk_c5),sk_c6).
% 346967 [para:346966.1.1,346931.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 346971 [hyper:346933,346936,binarycut:346942] equal(inverse(sk_c3),sk_c8).
% 346972 [para:346971.1.1,346931.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 346975 [hyper:346933,346935,binarycut:346941] equal(multiply(sk_c5,sk_c6),sk_c8).
% 346978 [hyper:346933,346937,binarycut:346943] equal(multiply(sk_c3,sk_c8),sk_c4).
% 346981 [hyper:346933,346938,binarycut:346944] equal(multiply(sk_c8,sk_c4),sk_c7).
% 346984 [hyper:346933,346939,binarycut:346945] equal(multiply(sk_c6,sk_c8),sk_c7).
% 346985 [para:346931.1.1,346932.1.1.1,demod:346930] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 346986 [para:346967.1.1,346932.1.1.1,demod:346930] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 346987 [para:346972.1.1,346932.1.1.1,demod:346930] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 346988 [para:346975.1.1,346932.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c5,multiply(sk_c6,X))).
% 346989 [para:346978.1.1,346932.1.1.1] equal(multiply(sk_c4,X),multiply(sk_c3,multiply(sk_c8,X))).
% 346990 [para:346981.1.1,346932.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c4,X))).
% 346991 [para:346984.1.1,346932.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c8,X))).
% 346992 [para:346975.1.1,346986.1.2.2,demod:346984] equal(sk_c6,sk_c7).
% 346993 [para:346978.1.1,346987.1.2.2,demod:346981] equal(sk_c8,sk_c7).
% 346994 [para:346993.1.1,346972.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 346995 [para:346993.1.1,346978.1.1.2] equal(multiply(sk_c3,sk_c7),sk_c4).
% 346996 [para:346993.1.1,346981.1.1.1] equal(multiply(sk_c7,sk_c4),sk_c7).
% 347000 [para:346931.1.1,346985.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 347001 [para:346967.1.1,346985.1.2.2] equal(sk_c5,multiply(inverse(sk_c6),identity)).
% 347002 [para:346972.1.1,346985.1.2.2] equal(sk_c3,multiply(inverse(sk_c8),identity)).
% 347003 [para:346981.1.1,346985.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),sk_c7)).
% 347004 [para:346932.1.1,346985.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 347008 [para:346985.1.2,346985.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 347009 [para:346992.1.2,346994.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 347012 [para:346992.1.2,346995.1.1.2] equal(multiply(sk_c3,sk_c6),sk_c4).
% 347015 [para:346996.1.1,346985.1.2.2,demod:346931] equal(sk_c4,identity).
% 347023 [para:346988.1.2,346986.1.2.2,demod:346991] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 347027 [para:347009.1.1,346985.1.2.2,demod:347001] equal(sk_c3,sk_c5).
% 347028 [?] ?
% 347029 [para:347027.1.2,346966.1.1.1,demod:346971] equal(sk_c8,sk_c6).
% 347030 [para:347027.1.2,346975.1.1.1,demod:347012] equal(sk_c4,sk_c8).
% 347036 [para:347030.1.2,346987.1.2.1] equal(X,multiply(sk_c4,multiply(sk_c3,X))).
% 347039 [para:347030.1.2,347029.1.1] equal(sk_c4,sk_c6).
% 347041 [para:346989.1.2,346987.1.2.2,demod:347023,346990] equal(multiply(sk_c8,X),multiply(sk_c6,X)).
% 347042 [para:346987.1.2,346989.1.2.2,demod:347036] equal(X,multiply(sk_c3,X)).
% 347046 [para:347039.1.1,347015.1.1] equal(sk_c6,identity).
% 347049 [para:347046.1.1,346975.1.1.2,demod:347028] equal(identity,sk_c8).
% 347050 [para:347046.1.1,346986.1.2.1,demod:346930] equal(X,multiply(sk_c5,X)).
% 347051 [para:347046.1.1,346988.1.2.2.1,demod:347050,346930,347041] equal(multiply(sk_c6,X),X).
% 347056 [para:347049.1.2,346984.1.1.2,demod:347051] equal(identity,sk_c7).
% 347065 [para:347056.1.2,347003.1.2.2,demod:347002] equal(sk_c4,sk_c3).
% 347081 [para:347065.1.2,346971.1.1.1] equal(inverse(sk_c4),sk_c8).
% 347082 [para:347039.1.1,347081.1.1.1] equal(inverse(sk_c6),sk_c8).
% 347095 [para:347008.1.2,346931.1.1] equal(multiply(X,inverse(X)),identity).
% 347097 [para:347008.1.2,347000.1.2] equal(X,multiply(X,identity)).
% 347098 [para:347097.1.2,347000.1.2] equal(X,inverse(inverse(X))).
% 347107 [para:347095.1.1,347004.1.2.2.2,demod:347097] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 347110 [para:346987.1.2,347107.1.2.1.1,demod:347042] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 347119 [para:347110.1.2,347008.1.2,demod:347098] equal(multiply(X,sk_c8),X).
% 347120 [para:346993.1.1,347119.1.1.2] equal(multiply(X,sk_c7),X).
% 347124 [hyper:346933,347120,demod:347082,cut:346993] 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 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),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(35,40,1,75,0,1,717,50,7,757,0,7,1569,50,17,1609,0,17,2506,50,31,2546,0,31,3489,50,42,3529,0,42,4519,50,57,4559,0,57,5617,50,80,5657,0,80,6783,50,117,6823,0,117,8039,50,186,8079,0,186,9385,50,322,9425,0,323,10843,50,541,10883,0,541,12413,50,935,12413,40,935,12453,0,935,22976,3,1236,23645,4,1386,24326,1,1536,24326,50,1536,24326,40,1536,24366,0,1536,24651,3,1843,24662,4,2007,24678,5,2137,24678,1,2137,24678,50,2137,24678,40,2137,24718,0,2137,48521,3,3638,49494,4,4388,50607,1,5138,50607,50,5138,50607,40,5138,50647,0,5138,66475,3,5889,67369,4,6264,68189,1,6639,68189,50,6639,68189,40,6639,68229,0,6639,80749,3,7393,81463,4,7765,82881,1,8140,82881,50,8140,82881,40,8140,82921,0,8140,154075,3,12041,154982,4,13991,155849,5,15941,155850,1,15941,155850,50,15943,155850,40,15943,155890,0,15943,218017,3,18494,218751,4,19769,219531,5,21044,219532,1,21044,219532,50,21046,219532,40,21046,219572,0,21046,253160,3,22550,254194,4,23297,255076,5,24047,255077,1,24047,255077,50,24049,255077,40,24049,255117,0,24049,263929,3,24802,265345,4,25176,265890,5,25550,265890,1,25550,265890,50,25550,265890,40,25550,265930,0,25550,311588,3,26753,312112,4,27351,312434,5,27951,312435,1,27951,312435,50,27953,312435,40,27953,312475,0,27953,345604,3,28704,346055,4,29079,346299,1,29454,346299,50,29455,346299,40,29455,346299,40,29455,346334,0,29455,346419,50,29455,346454,0,29455,346583,50,29456,346583,30,29456,346583,40,29457,346618,0,29461,346782,50,29461,346782,30,29461,346782,40,29461,346817,0,29461,346928,50,29462,346963,0,29462,347123,50,29464,347123,30,29464,347123,40,29464,347158,0,29468)
%
%
% START OF PROOF
% 347124 [] equal(X,X).
% 347125 [] equal(multiply(identity,X),X).
% 347126 [] equal(multiply(inverse(X),X),identity).
% 347127 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 347128 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 347141 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 347142 [] equal(multiply(sk_c5,sk_c6),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 347143 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 347144 [] equal(multiply(sk_c3,sk_c8),sk_c4) | equal(inverse(sk_c1),sk_c8).
% 347145 [] equal(multiply(sk_c8,sk_c4),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 347146 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 347147 [?] ?
% 347148 [?] ?
% 347149 [?] ?
% 347150 [?] ?
% 347151 [?] ?
% 347152 [?] ?
% 347165 [hyper:347128,347141,binarycut:347147] equal(inverse(sk_c5),sk_c6).
% 347166 [para:347165.1.1,347126.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 347169 [hyper:347128,347143,binarycut:347149] equal(inverse(sk_c3),sk_c8).
% 347173 [para:347169.1.1,347126.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 347184 [hyper:347128,347142,binarycut:347148] equal(multiply(sk_c5,sk_c6),sk_c8).
% 347187 [hyper:347128,347144,binarycut:347150] equal(multiply(sk_c3,sk_c8),sk_c4).
% 347191 [hyper:347128,347145,binarycut:347151] equal(multiply(sk_c8,sk_c4),sk_c7).
% 347195 [hyper:347128,347146,binarycut:347152] equal(multiply(sk_c6,sk_c8),sk_c7).
% 347197 [para:347126.1.1,347127.1.1.1,demod:347125] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 347198 [para:347166.1.1,347127.1.1.1,demod:347125] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 347199 [para:347173.1.1,347127.1.1.1,demod:347125] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 347200 [para:347184.1.1,347127.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c5,multiply(sk_c6,X))).
% 347201 [para:347187.1.1,347127.1.1.1] equal(multiply(sk_c4,X),multiply(sk_c3,multiply(sk_c8,X))).
% 347202 [para:347191.1.1,347127.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c4,X))).
% 347205 [para:347195.1.1,347127.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c8,X))).
% 347206 [para:347184.1.1,347198.1.2.2,demod:347195] equal(sk_c6,sk_c7).
% 347207 [para:347187.1.1,347199.1.2.2,demod:347191] equal(sk_c8,sk_c7).
% 347208 [para:347207.1.1,347173.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 347209 [para:347207.1.1,347187.1.1.2] equal(multiply(sk_c3,sk_c7),sk_c4).
% 347210 [para:347207.1.1,347191.1.1.1] equal(multiply(sk_c7,sk_c4),sk_c7).
% 347214 [para:347166.1.1,347197.1.2.2] equal(sk_c5,multiply(inverse(sk_c6),identity)).
% 347215 [para:347173.1.1,347197.1.2.2] equal(sk_c3,multiply(inverse(sk_c8),identity)).
% 347216 [para:347191.1.1,347197.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),sk_c7)).
% 347220 [para:347206.1.2,347208.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 347223 [para:347206.1.2,347209.1.1.2] equal(multiply(sk_c3,sk_c6),sk_c4).
% 347226 [para:347210.1.1,347197.1.2.2,demod:347126] equal(sk_c4,identity).
% 347234 [para:347200.1.2,347198.1.2.2,demod:347205] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 347238 [para:347220.1.1,347197.1.2.2,demod:347214] equal(sk_c3,sk_c5).
% 347239 [?] ?
% 347240 [para:347238.1.2,347165.1.1.1,demod:347169] equal(sk_c8,sk_c6).
% 347241 [para:347238.1.2,347184.1.1.1,demod:347223] equal(sk_c4,sk_c8).
% 347242 [para:347238.1.2,347200.1.2.1] equal(multiply(sk_c8,X),multiply(sk_c3,multiply(sk_c6,X))).
% 347250 [para:347241.1.2,347240.1.1] equal(sk_c4,sk_c6).
% 347252 [para:347201.1.2,347199.1.2.2,demod:347234,347202] equal(multiply(sk_c8,X),multiply(sk_c6,X)).
% 347254 [para:347207.1.1,347201.1.2.2.1,demod:347252,347242,347234] equal(multiply(sk_c4,X),multiply(sk_c6,X)).
% 347257 [para:347250.1.1,347226.1.1] equal(sk_c6,identity).
% 347260 [para:347257.1.1,347184.1.1.2,demod:347239] equal(identity,sk_c8).
% 347261 [para:347257.1.1,347198.1.2.1,demod:347125] equal(X,multiply(sk_c5,X)).
% 347262 [para:347257.1.1,347200.1.2.2.1,demod:347261,347125,347252] equal(multiply(sk_c6,X),X).
% 347267 [para:347260.1.2,347195.1.1.2,demod:347262] equal(identity,sk_c7).
% 347275 [para:347267.1.2,347216.1.2.2,demod:347215] equal(sk_c4,sk_c3).
% 347276 [para:347275.1.2,347169.1.1.1] equal(inverse(sk_c4),sk_c8).
% 347277 [hyper:347128,347276,demod:347195,347254,cut:347124] 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% 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(35,40,1,75,0,1,717,50,7,757,0,7,1569,50,17,1609,0,17,2506,50,31,2546,0,31,3489,50,42,3529,0,42,4519,50,57,4559,0,57,5617,50,80,5657,0,80,6783,50,117,6823,0,117,8039,50,186,8079,0,186,9385,50,322,9425,0,323,10843,50,541,10883,0,541,12413,50,935,12413,40,935,12453,0,935,22976,3,1236,23645,4,1386,24326,1,1536,24326,50,1536,24326,40,1536,24366,0,1536,24651,3,1843,24662,4,2007,24678,5,2137,24678,1,2137,24678,50,2137,24678,40,2137,24718,0,2137,48521,3,3638,49494,4,4388,50607,1,5138,50607,50,5138,50607,40,5138,50647,0,5138,66475,3,5889,67369,4,6264,68189,1,6639,68189,50,6639,68189,40,6639,68229,0,6639,80749,3,7393,81463,4,7765,82881,1,8140,82881,50,8140,82881,40,8140,82921,0,8140,154075,3,12041,154982,4,13991,155849,5,15941,155850,1,15941,155850,50,15943,155850,40,15943,155890,0,15943,218017,3,18494,218751,4,19769,219531,5,21044,219532,1,21044,219532,50,21046,219532,40,21046,219572,0,21046,253160,3,22550,254194,4,23297,255076,5,24047,255077,1,24047,255077,50,24049,255077,40,24049,255117,0,24049,263929,3,24802,265345,4,25176,265890,5,25550,265890,1,25550,265890,50,25550,265890,40,25550,265930,0,25550,311588,3,26753,312112,4,27351,312434,5,27951,312435,1,27951,312435,50,27953,312435,40,27953,312475,0,27953,345604,3,28704,346055,4,29079,346299,1,29454,346299,50,29455,346299,40,29455,346299,40,29455,346334,0,29455,346419,50,29455,346454,0,29455,346583,50,29456,346583,30,29456,346583,40,29457,346618,0,29461,346782,50,29461,346782,30,29461,346782,40,29461,346817,0,29461,346928,50,29462,346963,0,29462,347123,50,29464,347123,30,29464,347123,40,29464,347158,0,29468,347276,50,29468,347276,30,29468,347276,40,29468,347311,0,29468,347416,50,29468,347451,0,29474,347615,50,29477,347650,0,29477,347821,50,29480,347856,0,29480,348035,50,29485,348070,0,29490,348255,50,29499,348290,0,29499,348483,50,29515,348518,0,29519,348719,50,29549,348754,0,29549,348965,50,29611,349000,0,29611,349221,50,29729,349221,40,29729,349256,0,29729)
%
%
% START OF PROOF
% 349165 [?] ?
% 349223 [] equal(multiply(identity,X),X).
% 349224 [] equal(multiply(inverse(X),X),identity).
% 349225 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 349226 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 349251 [?] ?
% 349252 [?] ?
% 349253 [?] ?
% 349254 [?] ?
% 349255 [?] ?
% 349256 [?] ?
% 349294 [input:349251,cut:349226] equal(inverse(sk_c5),sk_c6).
% 349295 [para:349294.1.1,349224.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 349297 [input:349253,cut:349226] equal(inverse(sk_c3),sk_c8).
% 349298 [para:349297.1.1,349224.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 349309 [input:349252,cut:349226] equal(multiply(sk_c5,sk_c6),sk_c8).
% 349310 [input:349254,cut:349226] equal(multiply(sk_c3,sk_c8),sk_c4).
% 349311 [input:349255,cut:349226] equal(multiply(sk_c8,sk_c4),sk_c7).
% 349312 [input:349256,cut:349226] equal(multiply(sk_c6,sk_c8),sk_c7).
% 349331 [para:349295.1.1,349225.1.1.1,demod:349223] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 349334 [para:349298.1.1,349225.1.1.1,demod:349223] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 349354 [para:349312.1.1,349225.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c8,X))).
% 349362 [para:349309.1.1,349331.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c8)).
% 349368 [para:349362.1.2,349225.1.1.1,demod:349354] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 349384 [para:349310.1.1,349334.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c4)).
% 349390 [para:349384.1.2,349311.1.1] equal(sk_c8,sk_c7).
% 349392 [para:349390.1.1,349226.1.1.1,demod:349368,cut:349165] 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% 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(35,40,1,75,0,1,717,50,7,757,0,7,1569,50,17,1609,0,17,2506,50,31,2546,0,31,3489,50,42,3529,0,42,4519,50,57,4559,0,57,5617,50,80,5657,0,80,6783,50,117,6823,0,117,8039,50,186,8079,0,186,9385,50,322,9425,0,323,10843,50,541,10883,0,541,12413,50,935,12413,40,935,12453,0,935,22976,3,1236,23645,4,1386,24326,1,1536,24326,50,1536,24326,40,1536,24366,0,1536,24651,3,1843,24662,4,2007,24678,5,2137,24678,1,2137,24678,50,2137,24678,40,2137,24718,0,2137,48521,3,3638,49494,4,4388,50607,1,5138,50607,50,5138,50607,40,5138,50647,0,5138,66475,3,5889,67369,4,6264,68189,1,6639,68189,50,6639,68189,40,6639,68229,0,6639,80749,3,7393,81463,4,7765,82881,1,8140,82881,50,8140,82881,40,8140,82921,0,8140,154075,3,12041,154982,4,13991,155849,5,15941,155850,1,15941,155850,50,15943,155850,40,15943,155890,0,15943,218017,3,18494,218751,4,19769,219531,5,21044,219532,1,21044,219532,50,21046,219532,40,21046,219572,0,21046,253160,3,22550,254194,4,23297,255076,5,24047,255077,1,24047,255077,50,24049,255077,40,24049,255117,0,24049,263929,3,24802,265345,4,25176,265890,5,25550,265890,1,25550,265890,50,25550,265890,40,25550,265930,0,25550,311588,3,26753,312112,4,27351,312434,5,27951,312435,1,27951,312435,50,27953,312435,40,27953,312475,0,27953,345604,3,28704,346055,4,29079,346299,1,29454,346299,50,29455,346299,40,29455,346299,40,29455,346334,0,29455,346419,50,29455,346454,0,29455,346583,50,29456,346583,30,29456,346583,40,29457,346618,0,29461,346782,50,29461,346782,30,29461,346782,40,29461,346817,0,29461,346928,50,29462,346963,0,29462,347123,50,29464,347123,30,29464,347123,40,29464,347158,0,29468,347276,50,29468,347276,30,29468,347276,40,29468,347311,0,29468,347416,50,29468,347451,0,29474,347615,50,29477,347650,0,29477,347821,50,29480,347856,0,29480,348035,50,29485,348070,0,29490,348255,50,29499,348290,0,29499,348483,50,29515,348518,0,29519,348719,50,29549,348754,0,29549,348965,50,29611,349000,0,29611,349221,50,29729,349221,40,29729,349256,0,29729,349391,50,29729,349391,30,29729,349391,40,29729,349426,0,29729,349526,50,29730,349561,0,29734,349707,50,29737,349742,0,29737,349896,50,29740,349931,0,29740,350093,50,29745,350128,0,29749,350296,50,29757,350331,0,29757,350507,50,29772,350542,0,29777,350726,50,29805,350761,0,29805,350955,50,29866,350990,0,29866,351194,50,29981,351194,40,29981,351229,0,29981)
%
%
% START OF PROOF
% 351141 [?] ?
% 351196 [] equal(multiply(identity,X),X).
% 351197 [] equal(multiply(inverse(X),X),identity).
% 351198 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 351199 [] -equal(multiply(sk_c6,sk_c8),sk_c7).
% 351205 [?] ?
% 351211 [?] ?
% 351217 [?] ?
% 351223 [?] ?
% 351229 [?] ?
% 351248 [input:351205,cut:351199] equal(inverse(sk_c2),sk_c7).
% 351249 [para:351248.1.1,351197.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 351261 [input:351217,cut:351199] equal(inverse(sk_c1),sk_c8).
% 351262 [para:351261.1.1,351197.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 351277 [input:351211,cut:351199] equal(multiply(sk_c2,sk_c7),sk_c6).
% 351281 [input:351223,cut:351199] equal(multiply(sk_c1,sk_c8),sk_c7).
% 351285 [input:351229,cut:351199] equal(multiply(sk_c8,sk_c7),sk_c6).
% 351286 [para:351197.1.1,351198.1.1.1,demod:351196] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 351290 [para:351249.1.1,351198.1.1.1,demod:351196] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 351298 [para:351262.1.1,351198.1.1.1,demod:351196] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 351331 [para:351277.1.1,351290.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 351338 [para:351281.1.1,351298.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 351344 [para:351338.1.2,351285.1.1] equal(sk_c8,sk_c6).
% 351369 [para:351344.1.1,351285.1.1.1] equal(multiply(sk_c6,sk_c7),sk_c6).
% 351434 [para:351369.1.1,351286.1.2.2,demod:351197] equal(sk_c7,identity).
% 351453 [para:351434.1.1,351331.1.2.1,demod:351196] equal(sk_c7,sk_c6).
% 351461 [para:351453.1.1,351199.1.2,cut:351141] 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: 32746
% derived clauses: 5306522
% kept clauses: 303542
% kept size sum: 512462
% kept mid-nuclei: 9057
% kept new demods: 4290
% forw unit-subs: 1764804
% forw double-subs: 2824199
% forw overdouble-subs: 367424
% backward subs: 9222
% fast unit cutoff: 24223
% full unit cutoff: 0
% dbl unit cutoff: 7505
% real runtime : 302.23
% process. runtime: 299.80
% specific non-discr-tree subsumption statistics:
% tried: 39072385
% length fails: 4355205
% strength fails: 12367005
% predlist fails: 3647156
% aux str. fails: 4638293
% by-lit fails: 7682968
% full subs tried: 1464457
% full subs fail: 1302030
%
% ; 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/GRP290-1+eq_r.in")
%
%------------------------------------------------------------------------------