TSTP Solution File: GRP295-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP295-1 : 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 : art07.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 297.6s
% Output : Assurance 297.6s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP295-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% was split for some strategies as:
% -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7).
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% -equal(multiply(sk_c7,sk_c6),sk_c5).
% -equal(multiply(sk_c7,sk_c5),sk_c6).
% -equal(multiply(sk_c6,sk_c7),sk_c5).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,701,50,5,741,0,5,1382,50,10,1422,0,10,2068,50,16,2108,0,16,2760,50,22,2800,0,22,3459,50,29,3499,0,29,4166,50,42,4206,0,42,4881,50,66,4921,0,66,5606,50,118,5646,0,118,6341,50,231,6381,0,231,7088,50,425,7128,0,425,7847,50,792,7847,40,792,7887,0,792,18446,3,1094,19185,4,1243,19894,1,1393,19894,50,1393,19894,40,1393,19934,0,1393,20161,3,1703,20169,4,1846,20177,5,1994,20177,1,1994,20177,50,1994,20177,40,1994,20217,0,1994,43778,3,3497,44724,4,4245,45172,1,4995,45172,50,4995,45172,40,4995,45212,0,4995,64346,3,5752,64960,4,6121,65466,1,6496,65466,50,6496,65466,40,6496,65506,0,6496,74474,3,7247,75647,4,7622,76865,1,7997,76865,50,7997,76865,40,7997,76905,0,7997,121961,3,11898,123817,4,13848,125132,5,15798,125133,1,15798,125133,50,15800,125133,40,15800,125173,0,15800,167392,3,18351,168708,4,19626,169467,5,20901,169468,1,20901,169468,50,20902,169468,40,20902,169508,0,20902,206495,3,22405,207494,4,23153,208360,5,23906,208361,1,23906,208361,50,23911,208361,40,23911,208401,0,23911,214714,3,24665,215676,4,25041,216010,5,25412,216011,1,25412,216011,50,25412,216011,40,25412,216051,0,25412,241663,3,26614,242650,4,27213,243372,5,27813,243373,1,27813,243373,50,27814,243373,40,27814,243413,0,27814,262702,3,28565,263584,4,28940,264193,5,29315,264194,1,29315,264194,50,29316,264194,40,29316,264194,40,29316,264229,0,29316)
%
%
% START OF PROOF
% 264196 [] equal(multiply(identity,X),X).
% 264197 [] equal(multiply(inverse(X),X),identity).
% 264198 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 264199 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 264200 [?] ?
% 264201 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 264205 [] equal(multiply(sk_c2,sk_c7),sk_c5) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 264206 [] equal(multiply(sk_c2,sk_c7),sk_c5) | equal(inverse(sk_c4),sk_c6).
% 264210 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 264211 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 264215 [?] ?
% 264216 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 264220 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 264221 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 264225 [] equal(multiply(sk_c7,sk_c6),sk_c5) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 264226 [] equal(multiply(sk_c7,sk_c6),sk_c5) | equal(inverse(sk_c4),sk_c6).
% 264232 [hyper:264199,264201,binarycut:264200] equal(inverse(sk_c2),sk_c7).
% 264233 [para:264232.1.1,264197.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 264240 [hyper:264199,264216,binarycut:264215] equal(inverse(sk_c1),sk_c7).
% 264244 [hyper:264199,264206,264205] equal(multiply(sk_c2,sk_c7),sk_c5).
% 264259 [hyper:264199,264210,264211] equal(multiply(sk_c7,sk_c5),sk_c6).
% 264270 [hyper:264199,264220,264221] equal(multiply(sk_c1,sk_c7),sk_c6).
% 264273 [hyper:264199,264225,264226] equal(multiply(sk_c7,sk_c6),sk_c5).
% 264274 [para:264197.1.1,264198.1.1.1,demod:264196] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 264275 [para:264233.1.1,264198.1.1.1,demod:264196] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 264281 [para:264244.1.1,264275.1.2.2,demod:264259] equal(sk_c7,sk_c6).
% 264294 [para:264270.1.1,264274.1.2.2,demod:264273,264240] equal(sk_c7,sk_c5).
% 264303 [para:264294.1.1,264270.1.1.2] equal(multiply(sk_c1,sk_c5),sk_c6).
% 264336 [hyper:264199,264303,demod:264240,cut:264281] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,701,50,5,741,0,5,1382,50,10,1422,0,10,2068,50,16,2108,0,16,2760,50,22,2800,0,22,3459,50,29,3499,0,29,4166,50,42,4206,0,42,4881,50,66,4921,0,66,5606,50,118,5646,0,118,6341,50,231,6381,0,231,7088,50,425,7128,0,425,7847,50,792,7847,40,792,7887,0,792,18446,3,1094,19185,4,1243,19894,1,1393,19894,50,1393,19894,40,1393,19934,0,1393,20161,3,1703,20169,4,1846,20177,5,1994,20177,1,1994,20177,50,1994,20177,40,1994,20217,0,1994,43778,3,3497,44724,4,4245,45172,1,4995,45172,50,4995,45172,40,4995,45212,0,4995,64346,3,5752,64960,4,6121,65466,1,6496,65466,50,6496,65466,40,6496,65506,0,6496,74474,3,7247,75647,4,7622,76865,1,7997,76865,50,7997,76865,40,7997,76905,0,7997,121961,3,11898,123817,4,13848,125132,5,15798,125133,1,15798,125133,50,15800,125133,40,15800,125173,0,15800,167392,3,18351,168708,4,19626,169467,5,20901,169468,1,20901,169468,50,20902,169468,40,20902,169508,0,20902,206495,3,22405,207494,4,23153,208360,5,23906,208361,1,23906,208361,50,23911,208361,40,23911,208401,0,23911,214714,3,24665,215676,4,25041,216010,5,25412,216011,1,25412,216011,50,25412,216011,40,25412,216051,0,25412,241663,3,26614,242650,4,27213,243372,5,27813,243373,1,27813,243373,50,27814,243373,40,27814,243413,0,27814,262702,3,28565,263584,4,28940,264193,5,29315,264194,1,29315,264194,50,29316,264194,40,29316,264194,40,29316,264229,0,29316,264335,50,29316,264335,30,29316,264335,40,29316,264370,0,29316,264493,50,29317,264528,0,29322)
%
%
% START OF PROOF
% 264495 [] equal(multiply(identity,X),X).
% 264496 [] equal(multiply(inverse(X),X),identity).
% 264497 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 264498 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 264501 [?] ?
% 264502 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 264506 [] equal(multiply(sk_c2,sk_c7),sk_c5) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 264507 [] equal(multiply(sk_c2,sk_c7),sk_c5) | equal(inverse(sk_c3),sk_c7).
% 264511 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 264512 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 264516 [?] ?
% 264517 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 264521 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 264522 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 264526 [] equal(multiply(sk_c7,sk_c6),sk_c5) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 264527 [] equal(multiply(sk_c7,sk_c6),sk_c5) | equal(inverse(sk_c3),sk_c7).
% 264534 [hyper:264498,264502,binarycut:264501] equal(inverse(sk_c2),sk_c7).
% 264537 [para:264534.1.1,264496.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 264546 [hyper:264498,264517,binarycut:264516] equal(inverse(sk_c1),sk_c7).
% 264549 [para:264546.1.1,264496.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 264557 [hyper:264498,264507,264506] equal(multiply(sk_c2,sk_c7),sk_c5).
% 264573 [hyper:264498,264511,264512] equal(multiply(sk_c7,sk_c5),sk_c6).
% 264577 [hyper:264498,264521,264522] equal(multiply(sk_c1,sk_c7),sk_c6).
% 264581 [hyper:264498,264526,264527] equal(multiply(sk_c7,sk_c6),sk_c5).
% 264582 [para:264496.1.1,264497.1.1.1,demod:264495] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 264583 [para:264537.1.1,264497.1.1.1,demod:264495] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 264584 [para:264549.1.1,264497.1.1.1,demod:264495] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 264585 [para:264557.1.1,264497.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c2,multiply(sk_c7,X))).
% 264589 [para:264557.1.1,264583.1.2.2,demod:264573] equal(sk_c7,sk_c6).
% 264593 [para:264589.1.1,264573.1.1.1] equal(multiply(sk_c6,sk_c5),sk_c6).
% 264599 [para:264496.1.1,264582.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 264600 [para:264537.1.1,264582.1.2.2] equal(sk_c2,multiply(inverse(sk_c7),identity)).
% 264602 [para:264573.1.1,264582.1.2.2] equal(sk_c5,multiply(inverse(sk_c7),sk_c6)).
% 264603 [para:264577.1.1,264582.1.2.2,demod:264581,264546] equal(sk_c7,sk_c5).
% 264604 [para:264497.1.1,264582.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 264606 [para:264583.1.2,264582.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c7),X)).
% 264608 [para:264582.1.2,264582.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 264610 [para:264603.1.1,264537.1.1.1] equal(multiply(sk_c5,sk_c2),identity).
% 264619 [para:264584.1.2,264582.1.2.2,demod:264606] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 264620 [para:264603.1.1,264584.1.2.1] equal(X,multiply(sk_c5,multiply(sk_c1,X))).
% 264622 [para:264593.1.1,264582.1.2.2,demod:264496] equal(sk_c5,identity).
% 264623 [para:264622.1.1,264573.1.1.2] equal(multiply(sk_c7,identity),sk_c6).
% 264628 [para:264610.1.1,264582.1.2.2] equal(sk_c2,multiply(inverse(sk_c5),identity)).
% 264629 [para:264622.1.1,264610.1.1.1,demod:264495] equal(sk_c2,identity).
% 264632 [para:264583.1.2,264585.1.2.2,demod:264620,264619] equal(X,multiply(sk_c1,X)).
% 264636 [para:264629.1.1,264537.1.1.2,demod:264623] equal(sk_c6,identity).
% 264646 [para:264636.1.1,264602.1.2.2,demod:264600] equal(sk_c5,sk_c2).
% 264647 [para:264646.1.2,264534.1.1.1] equal(inverse(sk_c5),sk_c7).
% 264671 [para:264608.1.2,264496.1.1] equal(multiply(X,inverse(X)),identity).
% 264673 [para:264608.1.2,264599.1.2] equal(X,multiply(X,identity)).
% 264677 [para:264673.1.2,264600.1.2] equal(sk_c2,inverse(sk_c7)).
% 264678 [para:264673.1.2,264599.1.2] equal(X,inverse(inverse(X))).
% 264679 [para:264673.1.2,264628.1.2,demod:264647] equal(sk_c2,sk_c7).
% 264681 [para:264671.1.1,264604.1.2.2.2,demod:264673] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 264684 [para:264583.1.2,264681.1.2.1.1,demod:264632,264619] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 264695 [para:264684.1.2,264608.1.2,demod:264678] equal(multiply(X,sk_c7),X).
% 264696 [para:264589.1.1,264695.1.1.2] equal(multiply(X,sk_c6),X).
% 264700 [hyper:264498,264696,demod:264677,cut:264679] 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 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(Y,sk_c7),sk_c5) | -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
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,701,50,5,741,0,5,1382,50,10,1422,0,10,2068,50,16,2108,0,16,2760,50,22,2800,0,22,3459,50,29,3499,0,29,4166,50,42,4206,0,42,4881,50,66,4921,0,66,5606,50,118,5646,0,118,6341,50,231,6381,0,231,7088,50,425,7128,0,425,7847,50,792,7847,40,792,7887,0,792,18446,3,1094,19185,4,1243,19894,1,1393,19894,50,1393,19894,40,1393,19934,0,1393,20161,3,1703,20169,4,1846,20177,5,1994,20177,1,1994,20177,50,1994,20177,40,1994,20217,0,1994,43778,3,3497,44724,4,4245,45172,1,4995,45172,50,4995,45172,40,4995,45212,0,4995,64346,3,5752,64960,4,6121,65466,1,6496,65466,50,6496,65466,40,6496,65506,0,6496,74474,3,7247,75647,4,7622,76865,1,7997,76865,50,7997,76865,40,7997,76905,0,7997,121961,3,11898,123817,4,13848,125132,5,15798,125133,1,15798,125133,50,15800,125133,40,15800,125173,0,15800,167392,3,18351,168708,4,19626,169467,5,20901,169468,1,20901,169468,50,20902,169468,40,20902,169508,0,20902,206495,3,22405,207494,4,23153,208360,5,23906,208361,1,23906,208361,50,23911,208361,40,23911,208401,0,23911,214714,3,24665,215676,4,25041,216010,5,25412,216011,1,25412,216011,50,25412,216011,40,25412,216051,0,25412,241663,3,26614,242650,4,27213,243372,5,27813,243373,1,27813,243373,50,27814,243373,40,27814,243413,0,27814,262702,3,28565,263584,4,28940,264193,5,29315,264194,1,29315,264194,50,29316,264194,40,29316,264194,40,29316,264229,0,29316,264335,50,29316,264335,30,29316,264335,40,29316,264370,0,29316,264493,50,29317,264528,0,29322,264699,50,29323,264699,30,29323,264699,40,29323,264734,0,29323)
%
%
% START OF PROOF
% 264701 [] equal(multiply(identity,X),X).
% 264702 [] equal(multiply(inverse(X),X),identity).
% 264703 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 264704 [] -equal(multiply(X,sk_c7),sk_c5) | -equal(inverse(X),sk_c7).
% 264705 [] equal(multiply(sk_c4,sk_c5),sk_c6) | equal(inverse(sk_c2),sk_c7).
% 264706 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 264707 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 264708 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 264709 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c2),sk_c7).
% 264710 [?] ?
% 264711 [?] ?
% 264712 [?] ?
% 264713 [?] ?
% 264714 [?] ?
% 264737 [hyper:264704,264706,binarycut:264711] equal(inverse(sk_c4),sk_c6).
% 264738 [para:264737.1.1,264702.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 264742 [hyper:264704,264708,binarycut:264713] equal(inverse(sk_c3),sk_c7).
% 264746 [para:264742.1.1,264702.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 264750 [hyper:264704,264705,binarycut:264710] equal(multiply(sk_c4,sk_c5),sk_c6).
% 264753 [hyper:264704,264707,binarycut:264712] equal(multiply(sk_c3,sk_c6),sk_c7).
% 264757 [hyper:264704,264709,binarycut:264714] equal(multiply(sk_c6,sk_c7),sk_c5).
% 264761 [para:264702.1.1,264703.1.1.1,demod:264701] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 264762 [para:264738.1.1,264703.1.1.1,demod:264701] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 264763 [para:264746.1.1,264703.1.1.1,demod:264701] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 264764 [para:264750.1.1,264703.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c4,multiply(sk_c5,X))).
% 264765 [para:264753.1.1,264703.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c6,X))).
% 264766 [para:264757.1.1,264703.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c6,multiply(sk_c7,X))).
% 264767 [para:264750.1.1,264762.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 264768 [para:264767.1.2,264703.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c6,multiply(sk_c6,X))).
% 264769 [para:264753.1.1,264763.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 264772 [para:264738.1.1,264761.1.2.2] equal(sk_c4,multiply(inverse(sk_c6),identity)).
% 264774 [para:264757.1.1,264761.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 264776 [para:264767.1.2,264761.1.2.2,demod:264774] equal(sk_c6,sk_c7).
% 264778 [para:264776.1.2,264746.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 264780 [para:264776.1.2,264769.1.2.1,demod:264757] equal(sk_c6,sk_c5).
% 264781 [para:264776.1.2,264769.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c6)).
% 264784 [para:264780.1.1,264757.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 264788 [para:264778.1.1,264761.1.2.2,demod:264772] equal(sk_c3,sk_c4).
% 264789 [para:264780.1.1,264778.1.1.1] equal(multiply(sk_c5,sk_c3),identity).
% 264791 [para:264788.1.2,264764.1.2.1] equal(multiply(sk_c6,X),multiply(sk_c3,multiply(sk_c5,X))).
% 264794 [para:264780.1.1,264765.1.2.2.1,demod:264791] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 264796 [para:264781.1.2,264703.1.1.1,demod:264768,264794] equal(multiply(sk_c6,X),multiply(sk_c5,X)).
% 264803 [para:264784.1.1,264761.1.2.2,demod:264702] equal(sk_c7,identity).
% 264804 [para:264746.1.1,264766.1.2.2,demod:264796,264789] equal(identity,multiply(sk_c5,identity)).
% 264806 [para:264803.1.1,264746.1.1.1,demod:264701] equal(sk_c3,identity).
% 264807 [para:264803.1.1,264757.1.1.2,demod:264804,264796] equal(identity,sk_c5).
% 264811 [para:264806.1.1,264742.1.1.1] equal(inverse(identity),sk_c7).
% 264817 [para:264807.1.2,264784.1.1.1,demod:264701] equal(sk_c7,sk_c5).
% 264819 [hyper:264704,264811,demod:264701,cut:264817] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,701,50,5,741,0,5,1382,50,10,1422,0,10,2068,50,16,2108,0,16,2760,50,22,2800,0,22,3459,50,29,3499,0,29,4166,50,42,4206,0,42,4881,50,66,4921,0,66,5606,50,118,5646,0,118,6341,50,231,6381,0,231,7088,50,425,7128,0,425,7847,50,792,7847,40,792,7887,0,792,18446,3,1094,19185,4,1243,19894,1,1393,19894,50,1393,19894,40,1393,19934,0,1393,20161,3,1703,20169,4,1846,20177,5,1994,20177,1,1994,20177,50,1994,20177,40,1994,20217,0,1994,43778,3,3497,44724,4,4245,45172,1,4995,45172,50,4995,45172,40,4995,45212,0,4995,64346,3,5752,64960,4,6121,65466,1,6496,65466,50,6496,65466,40,6496,65506,0,6496,74474,3,7247,75647,4,7622,76865,1,7997,76865,50,7997,76865,40,7997,76905,0,7997,121961,3,11898,123817,4,13848,125132,5,15798,125133,1,15798,125133,50,15800,125133,40,15800,125173,0,15800,167392,3,18351,168708,4,19626,169467,5,20901,169468,1,20901,169468,50,20902,169468,40,20902,169508,0,20902,206495,3,22405,207494,4,23153,208360,5,23906,208361,1,23906,208361,50,23911,208361,40,23911,208401,0,23911,214714,3,24665,215676,4,25041,216010,5,25412,216011,1,25412,216011,50,25412,216011,40,25412,216051,0,25412,241663,3,26614,242650,4,27213,243372,5,27813,243373,1,27813,243373,50,27814,243373,40,27814,243413,0,27814,262702,3,28565,263584,4,28940,264193,5,29315,264194,1,29315,264194,50,29316,264194,40,29316,264194,40,29316,264229,0,29316,264335,50,29316,264335,30,29316,264335,40,29316,264370,0,29316,264493,50,29317,264528,0,29322,264699,50,29323,264699,30,29323,264699,40,29323,264734,0,29323,264818,50,29323,264818,30,29323,264818,40,29323,264853,0,29323)
%
%
% START OF PROOF
% 264820 [] equal(multiply(identity,X),X).
% 264821 [] equal(multiply(inverse(X),X),identity).
% 264822 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 264823 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 264839 [] equal(multiply(sk_c4,sk_c5),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 264840 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 264841 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 264842 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 264843 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 264844 [?] ?
% 264845 [?] ?
% 264846 [?] ?
% 264847 [?] ?
% 264848 [?] ?
% 264862 [hyper:264823,264840,binarycut:264845] equal(inverse(sk_c4),sk_c6).
% 264863 [para:264862.1.1,264821.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 264866 [hyper:264823,264842,binarycut:264847] equal(inverse(sk_c3),sk_c7).
% 264870 [para:264866.1.1,264821.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 264883 [hyper:264823,264839,binarycut:264844] equal(multiply(sk_c4,sk_c5),sk_c6).
% 264886 [hyper:264823,264841,binarycut:264846] equal(multiply(sk_c3,sk_c6),sk_c7).
% 264890 [hyper:264823,264843,binarycut:264848] equal(multiply(sk_c6,sk_c7),sk_c5).
% 264891 [para:264821.1.1,264822.1.1.1,demod:264820] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 264892 [para:264863.1.1,264822.1.1.1,demod:264820] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 264893 [para:264870.1.1,264822.1.1.1,demod:264820] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 264897 [para:264883.1.1,264892.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 264899 [para:264886.1.1,264893.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 264902 [para:264863.1.1,264891.1.2.2] equal(sk_c4,multiply(inverse(sk_c6),identity)).
% 264904 [para:264890.1.1,264891.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 264906 [para:264897.1.2,264891.1.2.2,demod:264904] equal(sk_c6,sk_c7).
% 264908 [para:264906.1.2,264870.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 264910 [para:264906.1.2,264899.1.2.1,demod:264890] equal(sk_c6,sk_c5).
% 264914 [para:264910.1.1,264890.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 264918 [para:264908.1.1,264891.1.2.2,demod:264902] equal(sk_c3,sk_c4).
% 264920 [para:264918.1.2,264862.1.1.1,demod:264866] equal(sk_c7,sk_c6).
% 264931 [para:264914.1.1,264891.1.2.2,demod:264821] equal(sk_c7,identity).
% 264934 [para:264931.1.1,264870.1.1.1,demod:264820] equal(sk_c3,identity).
% 264939 [para:264934.1.1,264866.1.1.1] equal(inverse(identity),sk_c7).
% 264947 [hyper:264823,264939,demod:264820,cut:264920] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c7,sk_c6),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,701,50,5,741,0,5,1382,50,10,1422,0,10,2068,50,16,2108,0,16,2760,50,22,2800,0,22,3459,50,29,3499,0,29,4166,50,42,4206,0,42,4881,50,66,4921,0,66,5606,50,118,5646,0,118,6341,50,231,6381,0,231,7088,50,425,7128,0,425,7847,50,792,7847,40,792,7887,0,792,18446,3,1094,19185,4,1243,19894,1,1393,19894,50,1393,19894,40,1393,19934,0,1393,20161,3,1703,20169,4,1846,20177,5,1994,20177,1,1994,20177,50,1994,20177,40,1994,20217,0,1994,43778,3,3497,44724,4,4245,45172,1,4995,45172,50,4995,45172,40,4995,45212,0,4995,64346,3,5752,64960,4,6121,65466,1,6496,65466,50,6496,65466,40,6496,65506,0,6496,74474,3,7247,75647,4,7622,76865,1,7997,76865,50,7997,76865,40,7997,76905,0,7997,121961,3,11898,123817,4,13848,125132,5,15798,125133,1,15798,125133,50,15800,125133,40,15800,125173,0,15800,167392,3,18351,168708,4,19626,169467,5,20901,169468,1,20901,169468,50,20902,169468,40,20902,169508,0,20902,206495,3,22405,207494,4,23153,208360,5,23906,208361,1,23906,208361,50,23911,208361,40,23911,208401,0,23911,214714,3,24665,215676,4,25041,216010,5,25412,216011,1,25412,216011,50,25412,216011,40,25412,216051,0,25412,241663,3,26614,242650,4,27213,243372,5,27813,243373,1,27813,243373,50,27814,243373,40,27814,243413,0,27814,262702,3,28565,263584,4,28940,264193,5,29315,264194,1,29315,264194,50,29316,264194,40,29316,264194,40,29316,264229,0,29316,264335,50,29316,264335,30,29316,264335,40,29316,264370,0,29316,264493,50,29317,264528,0,29322,264699,50,29323,264699,30,29323,264699,40,29323,264734,0,29323,264818,50,29323,264818,30,29323,264818,40,29323,264853,0,29323,264946,50,29323,264946,30,29323,264946,40,29323,264981,0,29328,265084,50,29329,265119,0,29329,265265,50,29332,265300,0,29336,265454,50,29340,265489,0,29340,265651,50,29346,265686,0,29346,265854,50,29354,265889,0,29359,266065,50,29374,266100,0,29374,266284,50,29404,266319,0,29408,266513,50,29466,266548,0,29466,266752,50,29583,266752,40,29583,266787,0,29583)
%
%
% START OF PROOF
% 266753 [] equal(X,X).
% 266754 [] equal(multiply(identity,X),X).
% 266755 [] equal(multiply(inverse(X),X),identity).
% 266756 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 266757 [] -equal(multiply(sk_c7,sk_c6),sk_c5).
% 266783 [?] ?
% 266784 [?] ?
% 266787 [?] ?
% 266826 [input:266784,cut:266757] equal(inverse(sk_c4),sk_c6).
% 266827 [para:266826.1.1,266755.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 266841 [input:266783,cut:266757] equal(multiply(sk_c4,sk_c5),sk_c6).
% 266843 [input:266787,cut:266757] equal(multiply(sk_c6,sk_c7),sk_c5).
% 266847 [para:266755.1.1,266756.1.1.1,demod:266754] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 266866 [para:266827.1.1,266756.1.1.1,demod:266754] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 266895 [para:266841.1.1,266866.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 266947 [para:266843.1.1,266847.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 266953 [para:266895.1.2,266847.1.2.2,demod:266947] equal(sk_c6,sk_c7).
% 266957 [para:266953.1.2,266757.1.1.1,demod:266895,cut:266753] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c7,sk_c5),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,701,50,5,741,0,5,1382,50,10,1422,0,10,2068,50,16,2108,0,16,2760,50,22,2800,0,22,3459,50,29,3499,0,29,4166,50,42,4206,0,42,4881,50,66,4921,0,66,5606,50,118,5646,0,118,6341,50,231,6381,0,231,7088,50,425,7128,0,425,7847,50,792,7847,40,792,7887,0,792,18446,3,1094,19185,4,1243,19894,1,1393,19894,50,1393,19894,40,1393,19934,0,1393,20161,3,1703,20169,4,1846,20177,5,1994,20177,1,1994,20177,50,1994,20177,40,1994,20217,0,1994,43778,3,3497,44724,4,4245,45172,1,4995,45172,50,4995,45172,40,4995,45212,0,4995,64346,3,5752,64960,4,6121,65466,1,6496,65466,50,6496,65466,40,6496,65506,0,6496,74474,3,7247,75647,4,7622,76865,1,7997,76865,50,7997,76865,40,7997,76905,0,7997,121961,3,11898,123817,4,13848,125132,5,15798,125133,1,15798,125133,50,15800,125133,40,15800,125173,0,15800,167392,3,18351,168708,4,19626,169467,5,20901,169468,1,20901,169468,50,20902,169468,40,20902,169508,0,20902,206495,3,22405,207494,4,23153,208360,5,23906,208361,1,23906,208361,50,23911,208361,40,23911,208401,0,23911,214714,3,24665,215676,4,25041,216010,5,25412,216011,1,25412,216011,50,25412,216011,40,25412,216051,0,25412,241663,3,26614,242650,4,27213,243372,5,27813,243373,1,27813,243373,50,27814,243373,40,27814,243413,0,27814,262702,3,28565,263584,4,28940,264193,5,29315,264194,1,29315,264194,50,29316,264194,40,29316,264194,40,29316,264229,0,29316,264335,50,29316,264335,30,29316,264335,40,29316,264370,0,29316,264493,50,29317,264528,0,29322,264699,50,29323,264699,30,29323,264699,40,29323,264734,0,29323,264818,50,29323,264818,30,29323,264818,40,29323,264853,0,29323,264946,50,29323,264946,30,29323,264946,40,29323,264981,0,29328,265084,50,29329,265119,0,29329,265265,50,29332,265300,0,29336,265454,50,29340,265489,0,29340,265651,50,29346,265686,0,29346,265854,50,29354,265889,0,29359,266065,50,29374,266100,0,29374,266284,50,29404,266319,0,29408,266513,50,29466,266548,0,29466,266752,50,29583,266752,40,29583,266787,0,29583,266956,50,29583,266956,30,29583,266956,40,29583,266991,0,29583,267094,50,29584,267129,0,29588,267275,50,29591,267310,0,29591,267464,50,29594,267499,0,29594,267661,50,29600,267696,0,29604,267864,50,29613,267899,0,29613,268075,50,29629,268110,0,29633,268294,50,29662,268329,0,29662,268523,50,29725,268558,0,29725,268762,50,29842,268762,40,29842,268797,0,29842)
%
%
% START OF PROOF
% 268706 [?] ?
% 268764 [] equal(multiply(identity,X),X).
% 268765 [] equal(multiply(inverse(X),X),identity).
% 268766 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 268767 [] -equal(multiply(sk_c7,sk_c5),sk_c6).
% 268778 [?] ?
% 268779 [?] ?
% 268782 [?] ?
% 268821 [input:268779,cut:268767] equal(inverse(sk_c4),sk_c6).
% 268822 [para:268821.1.1,268765.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 268838 [input:268778,cut:268767] equal(multiply(sk_c4,sk_c5),sk_c6).
% 268843 [input:268782,cut:268767] equal(multiply(sk_c6,sk_c7),sk_c5).
% 268853 [para:268765.1.1,268766.1.1.1,demod:268764] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 268861 [para:268822.1.1,268766.1.1.1,demod:268764] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 268893 [para:268838.1.1,268861.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 268931 [para:268843.1.1,268853.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 268943 [para:268893.1.2,268853.1.2.2,demod:268931] equal(sk_c6,sk_c7).
% 268947 [para:268943.1.2,268767.1.1.1,cut:268706] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c6,sk_c7),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,701,50,5,741,0,5,1382,50,10,1422,0,10,2068,50,16,2108,0,16,2760,50,22,2800,0,22,3459,50,29,3499,0,29,4166,50,42,4206,0,42,4881,50,66,4921,0,66,5606,50,118,5646,0,118,6341,50,231,6381,0,231,7088,50,425,7128,0,425,7847,50,792,7847,40,792,7887,0,792,18446,3,1094,19185,4,1243,19894,1,1393,19894,50,1393,19894,40,1393,19934,0,1393,20161,3,1703,20169,4,1846,20177,5,1994,20177,1,1994,20177,50,1994,20177,40,1994,20217,0,1994,43778,3,3497,44724,4,4245,45172,1,4995,45172,50,4995,45172,40,4995,45212,0,4995,64346,3,5752,64960,4,6121,65466,1,6496,65466,50,6496,65466,40,6496,65506,0,6496,74474,3,7247,75647,4,7622,76865,1,7997,76865,50,7997,76865,40,7997,76905,0,7997,121961,3,11898,123817,4,13848,125132,5,15798,125133,1,15798,125133,50,15800,125133,40,15800,125173,0,15800,167392,3,18351,168708,4,19626,169467,5,20901,169468,1,20901,169468,50,20902,169468,40,20902,169508,0,20902,206495,3,22405,207494,4,23153,208360,5,23906,208361,1,23906,208361,50,23911,208361,40,23911,208401,0,23911,214714,3,24665,215676,4,25041,216010,5,25412,216011,1,25412,216011,50,25412,216011,40,25412,216051,0,25412,241663,3,26614,242650,4,27213,243372,5,27813,243373,1,27813,243373,50,27814,243373,40,27814,243413,0,27814,262702,3,28565,263584,4,28940,264193,5,29315,264194,1,29315,264194,50,29316,264194,40,29316,264194,40,29316,264229,0,29316,264335,50,29316,264335,30,29316,264335,40,29316,264370,0,29316,264493,50,29317,264528,0,29322,264699,50,29323,264699,30,29323,264699,40,29323,264734,0,29323,264818,50,29323,264818,30,29323,264818,40,29323,264853,0,29323,264946,50,29323,264946,30,29323,264946,40,29323,264981,0,29328,265084,50,29329,265119,0,29329,265265,50,29332,265300,0,29336,265454,50,29340,265489,0,29340,265651,50,29346,265686,0,29346,265854,50,29354,265889,0,29359,266065,50,29374,266100,0,29374,266284,50,29404,266319,0,29408,266513,50,29466,266548,0,29466,266752,50,29583,266752,40,29583,266787,0,29583,266956,50,29583,266956,30,29583,266956,40,29583,266991,0,29583,267094,50,29584,267129,0,29588,267275,50,29591,267310,0,29591,267464,50,29594,267499,0,29594,267661,50,29600,267696,0,29604,267864,50,29613,267899,0,29613,268075,50,29629,268110,0,29633,268294,50,29662,268329,0,29662,268523,50,29725,268558,0,29725,268762,50,29842,268762,40,29842,268797,0,29842,268946,50,29842,268946,30,29842,268946,40,29842,268981,0,29842,269081,50,29843,269116,0,29847,269268,50,29850,269303,0,29850,269465,50,29854,269500,0,29854,269674,50,29862,269709,0,29866,269889,50,29877,269924,0,29877,270112,50,29896,270147,0,29900,270344,50,29934,270379,0,29934,270586,50,30004,270621,0,30004,270839,50,30135,270839,40,30135,270874,0,30135)
%
%
% START OF PROOF
% 270681 [?] ?
% 270841 [] equal(multiply(identity,X),X).
% 270842 [] equal(multiply(inverse(X),X),identity).
% 270843 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 270844 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 270849 [?] ?
% 270854 [?] ?
% 270859 [?] ?
% 270891 [input:270849,cut:270844] equal(inverse(sk_c2),sk_c7).
% 270892 [para:270891.1.1,270842.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 270911 [input:270854,cut:270844] equal(multiply(sk_c2,sk_c7),sk_c5).
% 270924 [input:270859,cut:270844] equal(multiply(sk_c7,sk_c5),sk_c6).
% 270937 [para:270892.1.1,270843.1.1.1,demod:270841] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 270976 [para:270911.1.1,270937.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c5)).
% 270981 [para:270976.1.2,270924.1.1] equal(sk_c7,sk_c6).
% 270983 [para:270981.1.1,270844.1.1.2,cut:270681] 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: 37784
% derived clauses: 6744314
% kept clauses: 225440
% kept size sum: 280042
% kept mid-nuclei: 4224
% kept new demods: 5381
% forw unit-subs: 2696330
% forw double-subs: 3554633
% forw overdouble-subs: 223680
% backward subs: 11761
% fast unit cutoff: 26120
% full unit cutoff: 0
% dbl unit cutoff: 6111
% real runtime : 304.4
% process. runtime: 301.35
% specific non-discr-tree subsumption statistics:
% tried: 38619342
% length fails: 5405975
% strength fails: 10798804
% predlist fails: 1548255
% aux str. fails: 4721799
% by-lit fails: 10135533
% full subs tried: 1330806
% full subs fail: 1241802
%
% ; 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/GRP295-1+eq_r.in")
%
%------------------------------------------------------------------------------