TSTP Solution File: GRP380-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP380-1 : 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 : art08.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 298.4s
% Output : Assurance 298.4s
% 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/GRP380-1+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 29)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 29)
% (binary-posweight-lex-big-order 30 #f 3 29)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% was split for some strategies as:
% -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X2),W) | -equal(inverse(X1),X2) | -equal(multiply(X1,W),X2).
% -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10).
% -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11).
% -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),sk_c10).
% -equal(inverse(sk_c11),sk_c10).
% -equal(multiply(sk_c10,sk_c9),sk_c11).
%
% 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(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X2),W) | -equal(inverse(X1),X2) | -equal(multiply(X1,W),X2).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,61197,50,922,61197,40,922,61260,0,922,61910,5,1523,61913,1,1523,61913,50,1523,61913,40,1523,61976,0,1523,62631,5,2129,62635,1,2129,62635,50,2129,62635,40,2129,62698,0,2129,88054,3,3630,89069,4,4380,89963,1,5130,89963,50,5130,89963,40,5130,90026,0,5130,106816,3,5881,107546,4,6256,108212,1,6631,108212,50,6631,108212,40,6631,108275,0,6631,109115,5,8137,109115,1,8137,109115,50,8137,109115,40,8137,109178,0,8137,160172,3,12040,161593,4,13988,162879,1,15938,162879,50,15940,162879,40,15940,162942,0,15940,205709,3,18491,206884,4,19766,208029,1,21041,208029,50,21042,208029,40,21042,208092,0,21043,249910,3,22545,250695,4,23294,251586,1,24044,251586,50,24045,251586,40,24045,251649,0,24045,252488,5,25548,252488,1,25549,252488,50,25549,252488,40,25549,252551,0,25549,278694,3,26750,279562,4,27350,280152,5,27950,280153,1,27950,280153,50,27951,280153,40,27951,280216,0,27951,298435,3,28710,298981,4,29077,299535,1,29452,299535,50,29452,299535,40,29452,299535,40,29452,299644,0,29452)
%
%
% START OF PROOF
% 299536 [] equal(X,X).
% 299537 [] equal(multiply(identity,X),X).
% 299538 [] equal(multiply(inverse(X),X),identity).
% 299539 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 299590 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,X),sk_c11) | -equal(multiply(Z,X),U) | -equal(inverse(Z),U) | -equal(inverse(U),X) | -equal(inverse(Y),X).
% 299591 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst85,Y).
% 299592 [] -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | $spltprd1($spltcnst86,Y).
% 299593 [] -equal(multiply(X,sk_c10),sk_c11) | $spltprd1($spltcnst87,X).
% 299594 [] -$spltprd1($spltcnst86,X) | -$spltprd1($spltcnst85,X) | -$spltprd1($spltcnst87,X).
% 299595 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 299596 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 299597 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 299598 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 299599 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 299600 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 299605 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c2).
% 299606 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c6),sk_c8).
% 299607 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c7),sk_c6).
% 299608 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c2).
% 299609 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 299610 [?] ?
% 299615 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 299616 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 299617 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 299618 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 299619 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 299620 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 299625 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 299626 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 299627 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 299628 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 299629 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 299630 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 299635 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c11),sk_c10).
% 299636 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 299637 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 299638 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c11),sk_c10).
% 299639 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 299640 [?] ?
% 299711 [hyper:299592,299609,binarycut:299610] equal(inverse(sk_c1),sk_c2) | $spltprd1($spltcnst86,sk_c8).
% 299799 [hyper:299592,299639,binarycut:299640] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst86,sk_c8).
% 299921 [hyper:299591,299605,299606,299607] equal(inverse(sk_c1),sk_c2) | $spltprd1($spltcnst85,sk_c8).
% 299937 [hyper:299593,299608] equal(inverse(sk_c1),sk_c2) | $spltprd1($spltcnst87,sk_c8).
% 299961 [hyper:299594,299937,299921,299711] equal(inverse(sk_c1),sk_c2).
% 299968 [para:299961.1.1,299538.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 300129 [hyper:299591,299635,299636,299637] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst85,sk_c8).
% 300154 [hyper:299593,299638] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst87,sk_c8).
% 300165 [hyper:299594,300154,300129,299799] equal(inverse(sk_c11),sk_c10).
% 300172 [para:300165.1.1,299538.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 300286 [hyper:299590,299600,299598,299599,299596,299595,299597] equal(multiply(sk_c2,sk_c9),sk_c10).
% 300451 [hyper:299590,299620,299618,299619,299616,299615,299617] equal(multiply(sk_c1,sk_c2),sk_c10).
% 300555 [hyper:299590,299630,299628,299629,299626,299625,299627] equal(multiply(sk_c10,sk_c9),sk_c11).
% 300570 [para:299538.1.1,299539.1.1.1,demod:299537] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 300571 [para:299968.1.1,299539.1.1.1,demod:299537] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 300574 [para:300451.1.1,299539.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c1,multiply(sk_c2,X))).
% 300619 [para:299968.1.1,300570.1.2.2] equal(sk_c1,multiply(inverse(sk_c2),identity)).
% 300625 [para:300286.1.1,300570.1.2.2] equal(sk_c9,multiply(inverse(sk_c2),sk_c10)).
% 300631 [para:300571.1.2,300570.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 300653 [para:300631.1.2,299538.1.1,demod:300451] equal(sk_c10,identity).
% 300656 [para:300631.1.2,300570.1.2,demod:300574] equal(X,multiply(sk_c10,X)).
% 300659 [para:300653.1.1,300172.1.1.1,demod:299537] equal(sk_c11,identity).
% 300660 [para:300653.1.1,300555.1.1.1,demod:299537] equal(sk_c9,sk_c11).
% 300663 [para:300653.1.1,300625.1.2.2,demod:300619] equal(sk_c9,sk_c1).
% 300664 [para:300659.1.1,300165.1.1.1] equal(inverse(identity),sk_c10).
% 300665 [para:300660.1.2,300165.1.1.1] equal(inverse(sk_c9),sk_c10).
% 300667 [para:300663.1.2,299961.1.1.1,demod:300665] equal(sk_c10,sk_c2).
% 300672 [para:300667.1.1,300555.1.1.1,demod:300286] equal(sk_c10,sk_c11).
% 300681 [para:300672.1.2,300165.1.1.1] equal(inverse(sk_c10),sk_c10).
% 300708 [hyper:299590,300664,299537,demod:300656,299537,cut:300672,cut:300672,demod:300664,300681,cut:299536,cut:299536] 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 29
% 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(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10).
% 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,61197,50,922,61197,40,922,61260,0,922,61910,5,1523,61913,1,1523,61913,50,1523,61913,40,1523,61976,0,1523,62631,5,2129,62635,1,2129,62635,50,2129,62635,40,2129,62698,0,2129,88054,3,3630,89069,4,4380,89963,1,5130,89963,50,5130,89963,40,5130,90026,0,5130,106816,3,5881,107546,4,6256,108212,1,6631,108212,50,6631,108212,40,6631,108275,0,6631,109115,5,8137,109115,1,8137,109115,50,8137,109115,40,8137,109178,0,8137,160172,3,12040,161593,4,13988,162879,1,15938,162879,50,15940,162879,40,15940,162942,0,15940,205709,3,18491,206884,4,19766,208029,1,21041,208029,50,21042,208029,40,21042,208092,0,21043,249910,3,22545,250695,4,23294,251586,1,24044,251586,50,24045,251586,40,24045,251649,0,24045,252488,5,25548,252488,1,25549,252488,50,25549,252488,40,25549,252551,0,25549,278694,3,26750,279562,4,27350,280152,5,27950,280153,1,27950,280153,50,27951,280153,40,27951,280216,0,27951,298435,3,28710,298981,4,29077,299535,1,29452,299535,50,29452,299535,40,29452,299535,40,29452,299644,0,29452,300707,50,29455,300707,30,29455,300707,40,29455,300762,0,29455)
%
%
% START OF PROOF
% 300709 [] equal(multiply(identity,X),X).
% 300710 [] equal(multiply(inverse(X),X),identity).
% 300711 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 300712 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 300719 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 300720 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 300729 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c4),sk_c10).
% 300730 [?] ?
% 300739 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 300740 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 300749 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 300750 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 300759 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 300760 [?] ?
% 300769 [hyper:300712,300729,binarycut:300730] equal(inverse(sk_c1),sk_c2).
% 300770 [para:300769.1.1,300710.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 300784 [hyper:300712,300759,binarycut:300760] equal(inverse(sk_c11),sk_c10).
% 300787 [para:300784.1.1,300710.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 300814 [hyper:300712,300720,300719] equal(multiply(sk_c2,sk_c9),sk_c10).
% 300820 [hyper:300712,300740,300739] equal(multiply(sk_c1,sk_c2),sk_c10).
% 300826 [hyper:300712,300750,300749] equal(multiply(sk_c10,sk_c9),sk_c11).
% 300827 [para:300710.1.1,300711.1.1.1,demod:300709] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 300828 [para:300770.1.1,300711.1.1.1,demod:300709] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 300836 [para:300770.1.1,300827.1.2.2] equal(sk_c1,multiply(inverse(sk_c2),identity)).
% 300838 [para:300814.1.1,300827.1.2.2] equal(sk_c9,multiply(inverse(sk_c2),sk_c10)).
% 300840 [para:300828.1.2,300827.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 300844 [para:300840.1.2,300710.1.1,demod:300820] equal(sk_c10,identity).
% 300848 [para:300844.1.1,300787.1.1.1,demod:300709] equal(sk_c11,identity).
% 300849 [para:300844.1.1,300826.1.1.1,demod:300709] equal(sk_c9,sk_c11).
% 300852 [para:300844.1.1,300838.1.2.2,demod:300836] equal(sk_c9,sk_c1).
% 300853 [para:300848.1.1,300784.1.1.1] equal(inverse(identity),sk_c10).
% 300854 [para:300849.1.2,300784.1.1.1] equal(inverse(sk_c9),sk_c10).
% 300856 [para:300852.1.2,300769.1.1.1,demod:300854] equal(sk_c10,sk_c2).
% 300865 [para:300856.1.1,300826.1.1.1,demod:300814] equal(sk_c10,sk_c11).
% 300873 [para:300849.1.2,300865.1.2] equal(sk_c10,sk_c9).
% 300885 [hyper:300712,300853,demod:300709,cut:300873] 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 29
% 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(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11).
% 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 29
% 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 29
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,61197,50,922,61197,40,922,61260,0,922,61910,5,1523,61913,1,1523,61913,50,1523,61913,40,1523,61976,0,1523,62631,5,2129,62635,1,2129,62635,50,2129,62635,40,2129,62698,0,2129,88054,3,3630,89069,4,4380,89963,1,5130,89963,50,5130,89963,40,5130,90026,0,5130,106816,3,5881,107546,4,6256,108212,1,6631,108212,50,6631,108212,40,6631,108275,0,6631,109115,5,8137,109115,1,8137,109115,50,8137,109115,40,8137,109178,0,8137,160172,3,12040,161593,4,13988,162879,1,15938,162879,50,15940,162879,40,15940,162942,0,15940,205709,3,18491,206884,4,19766,208029,1,21041,208029,50,21042,208029,40,21042,208092,0,21043,249910,3,22545,250695,4,23294,251586,1,24044,251586,50,24045,251586,40,24045,251649,0,24045,252488,5,25548,252488,1,25549,252488,50,25549,252488,40,25549,252551,0,25549,278694,3,26750,279562,4,27350,280152,5,27950,280153,1,27950,280153,50,27951,280153,40,27951,280216,0,27951,298435,3,28710,298981,4,29077,299535,1,29452,299535,50,29452,299535,40,29452,299535,40,29452,299644,0,29452,300707,50,29455,300707,30,29455,300707,40,29455,300762,0,29455,300884,50,29455,300884,30,29455,300884,40,29455,300939,0,29460,301056,50,29460,301111,0,29460)
%
%
% START OF PROOF
% 301058 [] equal(multiply(identity,X),X).
% 301059 [] equal(multiply(inverse(X),X),identity).
% 301060 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 301061 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 301070 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 301071 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 301080 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c3),sk_c11).
% 301081 [?] ?
% 301090 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 301091 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 301100 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 301101 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 301110 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 301111 [?] ?
% 301119 [hyper:301061,301080,binarycut:301081] equal(inverse(sk_c1),sk_c2).
% 301120 [para:301119.1.1,301059.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 301128 [hyper:301061,301110,binarycut:301111] equal(inverse(sk_c11),sk_c10).
% 301130 [para:301128.1.1,301059.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 301156 [hyper:301061,301071,301070] equal(multiply(sk_c2,sk_c9),sk_c10).
% 301163 [hyper:301061,301091,301090] equal(multiply(sk_c1,sk_c2),sk_c10).
% 301170 [hyper:301061,301101,301100] equal(multiply(sk_c10,sk_c9),sk_c11).
% 301171 [para:301059.1.1,301060.1.1.1,demod:301058] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 301172 [para:301120.1.1,301060.1.1.1,demod:301058] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 301173 [para:301130.1.1,301060.1.1.1,demod:301058] equal(X,multiply(sk_c10,multiply(sk_c11,X))).
% 301176 [para:301170.1.1,301060.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c10,multiply(sk_c9,X))).
% 301180 [para:301059.1.1,301171.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 301181 [para:301120.1.1,301171.1.2.2] equal(sk_c1,multiply(inverse(sk_c2),identity)).
% 301183 [para:301156.1.1,301171.1.2.2] equal(sk_c9,multiply(inverse(sk_c2),sk_c10)).
% 301184 [para:301170.1.1,301171.1.2.2] equal(sk_c9,multiply(inverse(sk_c10),sk_c11)).
% 301185 [para:301060.1.1,301171.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 301186 [para:301172.1.2,301171.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 301187 [para:301173.1.2,301171.1.2.2] equal(multiply(sk_c11,X),multiply(inverse(sk_c10),X)).
% 301188 [para:301171.1.2,301171.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 301190 [para:301184.1.2,301060.1.1.1,demod:301187] equal(multiply(sk_c9,X),multiply(sk_c11,multiply(sk_c11,X))).
% 301191 [para:301186.1.2,301059.1.1,demod:301163] equal(sk_c10,identity).
% 301196 [para:301191.1.1,301170.1.1.1,demod:301058] equal(sk_c9,sk_c11).
% 301198 [para:301191.1.1,301173.1.2.1,demod:301058] equal(X,multiply(sk_c11,X)).
% 301199 [para:301191.1.1,301183.1.2.2,demod:301181] equal(sk_c9,sk_c1).
% 301201 [para:301196.1.2,301128.1.1.1] equal(inverse(sk_c9),sk_c10).
% 301205 [para:301199.1.2,301119.1.1.1,demod:301201] equal(sk_c10,sk_c2).
% 301208 [para:301176.1.2,301171.1.2.2,demod:301187,301198] equal(multiply(sk_c9,X),X).
% 301213 [para:301205.1.1,301170.1.1.1,demod:301156] equal(sk_c10,sk_c11).
% 301219 [para:301213.1.2,301128.1.1.1] equal(inverse(sk_c10),sk_c10).
% 301248 [para:301188.1.2,301059.1.1] equal(multiply(X,inverse(X)),identity).
% 301250 [para:301188.1.2,301180.1.2] equal(X,multiply(X,identity)).
% 301258 [para:301250.1.2,301180.1.2] equal(X,inverse(inverse(X))).
% 301259 [para:301248.1.1,301185.1.2.2.2,demod:301250] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 301265 [para:301190.1.2,301259.1.2.1.1,demod:301208,301198] equal(inverse(X),multiply(inverse(X),sk_c11)).
% 301277 [para:301265.1.2,301188.1.2,demod:301258] equal(multiply(X,sk_c11),X).
% 301278 [hyper:301061,301277,demod:301219,cut:301213] 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 29
% 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(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),sk_c10).
% 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,61197,50,922,61197,40,922,61260,0,922,61910,5,1523,61913,1,1523,61913,50,1523,61913,40,1523,61976,0,1523,62631,5,2129,62635,1,2129,62635,50,2129,62635,40,2129,62698,0,2129,88054,3,3630,89069,4,4380,89963,1,5130,89963,50,5130,89963,40,5130,90026,0,5130,106816,3,5881,107546,4,6256,108212,1,6631,108212,50,6631,108212,40,6631,108275,0,6631,109115,5,8137,109115,1,8137,109115,50,8137,109115,40,8137,109178,0,8137,160172,3,12040,161593,4,13988,162879,1,15938,162879,50,15940,162879,40,15940,162942,0,15940,205709,3,18491,206884,4,19766,208029,1,21041,208029,50,21042,208029,40,21042,208092,0,21043,249910,3,22545,250695,4,23294,251586,1,24044,251586,50,24045,251586,40,24045,251649,0,24045,252488,5,25548,252488,1,25549,252488,50,25549,252488,40,25549,252551,0,25549,278694,3,26750,279562,4,27350,280152,5,27950,280153,1,27950,280153,50,27951,280153,40,27951,280216,0,27951,298435,3,28710,298981,4,29077,299535,1,29452,299535,50,29452,299535,40,29452,299535,40,29452,299644,0,29452,300707,50,29455,300707,30,29455,300707,40,29455,300762,0,29455,300884,50,29455,300884,30,29455,300884,40,29455,300939,0,29460,301056,50,29460,301111,0,29460,301277,50,29461,301277,30,29461,301277,40,29461,301332,0,29466)
%
%
% START OF PROOF
% 301279 [] equal(multiply(identity,X),X).
% 301280 [] equal(multiply(inverse(X),X),identity).
% 301281 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 301282 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,X),sk_c10) | -equal(inverse(Y),X).
% 301284 [?] ?
% 301285 [?] ?
% 301286 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 301287 [?] ?
% 301288 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 301289 [?] ?
% 301290 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 301291 [?] ?
% 301292 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 301294 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c6),sk_c8).
% 301295 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c7),sk_c6).
% 301296 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c2).
% 301297 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 301298 [] equal(multiply(sk_c5,sk_c8),sk_c11) | equal(inverse(sk_c1),sk_c2).
% 301299 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c4),sk_c10).
% 301300 [] equal(multiply(sk_c4,sk_c10),sk_c9) | equal(inverse(sk_c1),sk_c2).
% 301301 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c3),sk_c11).
% 301302 [] equal(multiply(sk_c3,sk_c11),sk_c10) | equal(inverse(sk_c1),sk_c2).
% 301304 [?] ?
% 301305 [?] ?
% 301306 [?] ?
% 301307 [?] ?
% 301308 [?] ?
% 301309 [?] ?
% 301310 [?] ?
% 301311 [?] ?
% 301312 [?] ?
% 301337 [hyper:301282,301294,binarycut:301304,binarycut:301284] equal(inverse(sk_c6),sk_c8).
% 301340 [para:301337.1.1,301280.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 301344 [hyper:301282,301295,binarycut:301305,binarycut:301285] equal(inverse(sk_c7),sk_c6).
% 301348 [para:301344.1.1,301280.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 301352 [hyper:301282,301297,binarycut:301307,binarycut:301287] equal(inverse(sk_c5),sk_c8).
% 301361 [para:301352.1.1,301280.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 301365 [hyper:301282,301299,binarycut:301309,binarycut:301289] equal(inverse(sk_c4),sk_c10).
% 301378 [hyper:301282,301301,binarycut:301311,binarycut:301291] equal(inverse(sk_c3),sk_c11).
% 301384 [para:301378.1.1,301280.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 301396 [hyper:301282,301296,binarycut:301306,binarycut:301286] equal(multiply(sk_c8,sk_c10),sk_c11).
% 301404 [hyper:301282,301298,binarycut:301308,binarycut:301288] equal(multiply(sk_c5,sk_c8),sk_c11).
% 301407 [hyper:301282,301300,binarycut:301310,binarycut:301290] equal(multiply(sk_c4,sk_c10),sk_c9).
% 301418 [hyper:301282,301302,binarycut:301312,binarycut:301292] equal(multiply(sk_c3,sk_c11),sk_c10).
% 301422 [para:301280.1.1,301281.1.1.1,demod:301279] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 301423 [para:301340.1.1,301281.1.1.1,demod:301279] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 301424 [para:301348.1.1,301281.1.1.1,demod:301279] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 301427 [para:301384.1.1,301281.1.1.1,demod:301279] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 301430 [para:301404.1.1,301281.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 301435 [para:301348.1.1,301423.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 301439 [para:301340.1.1,301422.1.2.2] equal(sk_c6,multiply(inverse(sk_c8),identity)).
% 301440 [para:301361.1.1,301422.1.2.2,demod:301439] equal(sk_c5,sk_c6).
% 301445 [para:301404.1.1,301422.1.2.2,demod:301352] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 301446 [para:301407.1.1,301422.1.2.2,demod:301365] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 301450 [para:301435.1.2,301281.1.1.1,demod:301279] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 301459 [para:301440.1.2,301424.1.2.1,demod:301430,301450] equal(X,multiply(sk_c11,X)).
% 301466 [para:301459.1.2,301384.1.1] equal(sk_c3,identity).
% 301467 [para:301459.1.2,301422.1.2.2] equal(X,multiply(inverse(sk_c11),X)).
% 301468 [para:301466.1.1,301378.1.1.1] equal(inverse(identity),sk_c11).
% 301469 [para:301466.1.1,301418.1.1.1,demod:301279] equal(sk_c11,sk_c10).
% 301472 [para:301469.1.1,301445.1.2.2,demod:301396] equal(sk_c8,sk_c11).
% 301480 [para:301472.1.2,301459.1.2.1] equal(X,multiply(sk_c8,X)).
% 301481 [para:301472.1.2,301469.1.1] equal(sk_c8,sk_c10).
% 301491 [para:301481.1.2,301446.1.2.1,demod:301480] equal(sk_c10,sk_c9).
% 301500 [para:301427.1.2,301422.1.2.2,demod:301467] equal(multiply(sk_c3,X),X).
% 301513 [para:301491.1.1,301396.1.1.2,demod:301480] equal(sk_c9,sk_c11).
% 301532 [para:301513.1.2,301418.1.1.2,demod:301500] equal(sk_c9,sk_c10).
% 301579 [hyper:301282,301468,demod:301459,301279,cut:301469,cut:301532] 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 29
% 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(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(inverse(sk_c11),sk_c10).
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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(55,40,0,118,0,0,61197,50,922,61197,40,922,61260,0,922,61910,5,1523,61913,1,1523,61913,50,1523,61913,40,1523,61976,0,1523,62631,5,2129,62635,1,2129,62635,50,2129,62635,40,2129,62698,0,2129,88054,3,3630,89069,4,4380,89963,1,5130,89963,50,5130,89963,40,5130,90026,0,5130,106816,3,5881,107546,4,6256,108212,1,6631,108212,50,6631,108212,40,6631,108275,0,6631,109115,5,8137,109115,1,8137,109115,50,8137,109115,40,8137,109178,0,8137,160172,3,12040,161593,4,13988,162879,1,15938,162879,50,15940,162879,40,15940,162942,0,15940,205709,3,18491,206884,4,19766,208029,1,21041,208029,50,21042,208029,40,21042,208092,0,21043,249910,3,22545,250695,4,23294,251586,1,24044,251586,50,24045,251586,40,24045,251649,0,24045,252488,5,25548,252488,1,25549,252488,50,25549,252488,40,25549,252551,0,25549,278694,3,26750,279562,4,27350,280152,5,27950,280153,1,27950,280153,50,27951,280153,40,27951,280216,0,27951,298435,3,28710,298981,4,29077,299535,1,29452,299535,50,29452,299535,40,29452,299535,40,29452,299644,0,29452,300707,50,29455,300707,30,29455,300707,40,29455,300762,0,29455,300884,50,29455,300884,30,29455,300884,40,29455,300939,0,29460,301056,50,29460,301111,0,29460,301277,50,29461,301277,30,29461,301277,40,29461,301332,0,29466,301578,50,29468,301578,30,29468,301578,40,29468,301633,0,29468,301837,50,29470,301892,0,29475,302160,50,29480,302215,0,29480,302491,50,29487,302546,0,29492,302830,50,29501,302885,0,29501,303175,50,29514,303230,0,29518,303528,50,29539,303583,0,29539,303889,50,29575,303944,0,29580,304260,50,29649,304315,0,29649,304641,50,29786,304641,40,29786,304696,0,29786)
%
%
% START OF PROOF
% 304643 [] equal(multiply(identity,X),X).
% 304644 [] equal(multiply(inverse(X),X),identity).
% 304645 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 304646 [] -equal(inverse(sk_c11),sk_c10).
% 304687 [?] ?
% 304688 [?] ?
% 304689 [?] ?
% 304690 [?] ?
% 304691 [?] ?
% 304692 [?] ?
% 304693 [?] ?
% 304694 [?] ?
% 304695 [?] ?
% 304696 [?] ?
% 304713 [input:304688,cut:304646] equal(inverse(sk_c6),sk_c8).
% 304714 [para:304713.1.1,304644.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 304716 [input:304689,cut:304646] equal(inverse(sk_c7),sk_c6).
% 304717 [para:304716.1.1,304644.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 304718 [input:304691,cut:304646] equal(inverse(sk_c5),sk_c8).
% 304719 [para:304718.1.1,304644.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 304721 [input:304693,cut:304646] equal(inverse(sk_c4),sk_c10).
% 304722 [para:304721.1.1,304644.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 304723 [input:304695,cut:304646] equal(inverse(sk_c3),sk_c11).
% 304724 [para:304723.1.1,304644.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 304753 [input:304687,cut:304646] equal(multiply(sk_c7,sk_c8),sk_c6).
% 304754 [input:304690,cut:304646] equal(multiply(sk_c8,sk_c10),sk_c11).
% 304756 [input:304692,cut:304646] equal(multiply(sk_c5,sk_c8),sk_c11).
% 304757 [input:304694,cut:304646] equal(multiply(sk_c4,sk_c10),sk_c9).
% 304758 [input:304696,cut:304646] equal(multiply(sk_c3,sk_c11),sk_c10).
% 304778 [para:304714.1.1,304645.1.1.1,demod:304643] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 304779 [para:304717.1.1,304645.1.1.1,demod:304643] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 304780 [para:304719.1.1,304645.1.1.1,demod:304643] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 304782 [para:304722.1.1,304645.1.1.1,demod:304643] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 304783 [para:304724.1.1,304645.1.1.1,demod:304643] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 304815 [para:304756.1.1,304645.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 304833 [para:304717.1.1,304778.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 304834 [para:304833.1.2,304645.1.1.1,demod:304643] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 304838 [para:304753.1.1,304779.1.2.2] equal(sk_c8,multiply(sk_c6,sk_c6)).
% 304841 [para:304838.1.2,304778.1.2.2] equal(sk_c6,multiply(sk_c8,sk_c8)).
% 304847 [para:304756.1.1,304780.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 304853 [para:304757.1.1,304782.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 304868 [para:304758.1.1,304783.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 304870 [para:304834.1.1,304779.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 304871 [para:304714.1.1,304870.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 304872 [para:304719.1.1,304870.1.2.2,demod:304871] equal(sk_c5,sk_c6).
% 304880 [para:304872.1.2,304779.1.2.1,demod:304815,304834] equal(X,multiply(sk_c11,X)).
% 304940 [para:304880.1.2,304783.1.2] equal(X,multiply(sk_c3,X)).
% 304941 [para:304880.1.2,304868.1.2] equal(sk_c11,sk_c10).
% 304947 [para:304941.1.1,304847.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c10)).
% 304948 [para:304941.1.1,304783.1.2.1,demod:304940] equal(X,multiply(sk_c10,X)).
% 304958 [para:304948.1.2,304853.1.2] equal(sk_c10,sk_c9).
% 304968 [para:304958.1.1,304754.1.1.2] equal(multiply(sk_c8,sk_c9),sk_c11).
% 304971 [para:304958.1.1,304868.1.2.2,demod:304880] equal(sk_c11,sk_c9).
% 304974 [para:304971.1.1,304847.1.2.2,demod:304968] equal(sk_c8,sk_c11).
% 304979 [para:304974.1.2,304758.1.1.2,demod:304940] equal(sk_c8,sk_c10).
% 304980 [para:304974.1.2,304847.1.2.2,demod:304841] equal(sk_c8,sk_c6).
% 304982 [para:304974.1.2,304868.1.2.1,demod:304947] equal(sk_c11,sk_c8).
% 304995 [para:304980.1.2,304713.1.1.1] equal(inverse(sk_c8),sk_c8).
% 305001 [para:304982.1.1,304646.1.1.1,demod:304995,cut:304979] 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(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(sk_c10,sk_c9),sk_c11).
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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(55,40,0,118,0,0,61197,50,922,61197,40,922,61260,0,922,61910,5,1523,61913,1,1523,61913,50,1523,61913,40,1523,61976,0,1523,62631,5,2129,62635,1,2129,62635,50,2129,62635,40,2129,62698,0,2129,88054,3,3630,89069,4,4380,89963,1,5130,89963,50,5130,89963,40,5130,90026,0,5130,106816,3,5881,107546,4,6256,108212,1,6631,108212,50,6631,108212,40,6631,108275,0,6631,109115,5,8137,109115,1,8137,109115,50,8137,109115,40,8137,109178,0,8137,160172,3,12040,161593,4,13988,162879,1,15938,162879,50,15940,162879,40,15940,162942,0,15940,205709,3,18491,206884,4,19766,208029,1,21041,208029,50,21042,208029,40,21042,208092,0,21043,249910,3,22545,250695,4,23294,251586,1,24044,251586,50,24045,251586,40,24045,251649,0,24045,252488,5,25548,252488,1,25549,252488,50,25549,252488,40,25549,252551,0,25549,278694,3,26750,279562,4,27350,280152,5,27950,280153,1,27950,280153,50,27951,280153,40,27951,280216,0,27951,298435,3,28710,298981,4,29077,299535,1,29452,299535,50,29452,299535,40,29452,299535,40,29452,299644,0,29452,300707,50,29455,300707,30,29455,300707,40,29455,300762,0,29455,300884,50,29455,300884,30,29455,300884,40,29455,300939,0,29460,301056,50,29460,301111,0,29460,301277,50,29461,301277,30,29461,301277,40,29461,301332,0,29466,301578,50,29468,301578,30,29468,301578,40,29468,301633,0,29468,301837,50,29470,301892,0,29475,302160,50,29480,302215,0,29480,302491,50,29487,302546,0,29492,302830,50,29501,302885,0,29501,303175,50,29514,303230,0,29518,303528,50,29539,303583,0,29539,303889,50,29575,303944,0,29580,304260,50,29649,304315,0,29649,304641,50,29786,304641,40,29786,304696,0,29786,305000,50,29787,305000,30,29787,305000,40,29787,305055,0,29787,305259,50,29789,305314,0,29793,305582,50,29798,305637,0,29798,305913,50,29805,305968,0,29810,306252,50,29819,306307,0,29819,306597,50,29832,306652,0,29836,306950,50,29857,307005,0,29857,307311,50,29892,307366,0,29897,307682,50,29965,307737,0,29965,308063,50,30101,308063,40,30101,308118,0,30101)
%
%
% START OF PROOF
% 307854 [?] ?
% 308065 [] equal(multiply(identity,X),X).
% 308066 [] equal(multiply(inverse(X),X),identity).
% 308067 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 308068 [] -equal(multiply(sk_c10,sk_c9),sk_c11).
% 308105 [?] ?
% 308106 [?] ?
% 308192 [input:308105,cut:308068] equal(inverse(sk_c4),sk_c10).
% 308193 [para:308192.1.1,308066.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 308222 [input:308106,cut:308068] equal(multiply(sk_c4,sk_c10),sk_c9).
% 308257 [para:308193.1.1,308067.1.1.1,demod:308065] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 308306 [para:308222.1.1,308257.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 308307 [para:308306.1.2,308068.1.1,cut:307854] 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: 32738
% derived clauses: 4596699
% kept clauses: 208196
% kept size sum: 729414
% kept mid-nuclei: 56162
% kept new demods: 5092
% forw unit-subs: 1605832
% forw double-subs: 2490781
% forw overdouble-subs: 177166
% backward subs: 14136
% fast unit cutoff: 30535
% full unit cutoff: 0
% dbl unit cutoff: 11046
% real runtime : 302.96
% process. runtime: 301.2
% specific non-discr-tree subsumption statistics:
% tried: 133393598
% length fails: 25730499
% strength fails: 38090675
% predlist fails: 283261
% aux str. fails: 23692043
% by-lit fails: 21328540
% full subs tried: 5168062
% full subs fail: 5075188
%
% ; 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/GRP380-1+eq_r.in")
%
%------------------------------------------------------------------------------