TSTP Solution File: GRP371-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP371-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art04.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 298.5s
% Output : Assurance 298.5s
% 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/GRP371-1+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(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11).
% -equal(inverse(sk_c11),sk_c10).
% -equal(multiply(sk_c9,sk_c10),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(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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(55,40,2,118,0,2,102753,5,1503,102753,1,1503,102753,50,1503,102753,40,1503,102816,0,1503,110991,3,1805,112063,4,1954,113026,5,2104,113027,1,2104,113027,50,2104,113027,40,2104,113090,0,2104,115006,3,2406,115050,4,2555,115088,5,2705,115088,1,2705,115088,50,2705,115088,40,2705,115151,0,2705,135278,3,4213,136912,4,4956,138515,5,5706,138516,1,5706,138516,50,5707,138516,40,5707,138579,0,5707,151469,3,6458,152650,4,6833,153911,1,7208,153911,50,7208,153911,40,7208,153974,0,7208,167517,3,8024,168788,4,8334,170425,5,8709,170426,1,8709,170426,50,8709,170426,40,8709,170489,0,8709,211909,3,12610,213789,4,14560,215329,5,16510,215330,1,16510,215330,50,16511,215330,40,16511,215393,0,16511,250072,3,19064,251509,4,20337,252846,1,21612,252846,50,21613,252846,40,21613,252909,0,21613,282990,3,23114,284148,4,23864,285358,5,24614,285359,1,24614,285359,50,24615,285359,40,24615,285422,0,24615,299850,3,25377,301111,4,25743,302961,5,26116,302961,1,26116,302961,50,26116,302961,40,26116,303024,0,26116,323115,3,27317,324320,4,27917,325394,5,28517,325395,1,28517,325395,50,28518,325395,40,28518,325458,0,28518,341299,3,29269,342245,4,29644,343100,1,30019,343100,50,30019,343100,40,30019,343100,40,30019,343209,0,30019)
%
%
% START OF PROOF
% 343101 [] equal(X,X).
% 343102 [] equal(multiply(identity,X),X).
% 343103 [] equal(multiply(inverse(X),X),identity).
% 343104 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 343155 [] -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).
% 343156 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst85,Y).
% 343157 [] -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | $spltprd1($spltcnst86,Y).
% 343158 [] -equal(multiply(X,sk_c10),sk_c11) | $spltprd1($spltcnst87,X).
% 343159 [] -$spltprd1($spltcnst86,X) | -$spltprd1($spltcnst85,X) | -$spltprd1($spltcnst87,X).
% 343170 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 343171 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 343172 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 343173 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 343174 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 343175 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 343180 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c2).
% 343181 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c6),sk_c8).
% 343182 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c7),sk_c6).
% 343183 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c2).
% 343184 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 343185 [?] ?
% 343190 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 343191 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 343192 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 343193 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 343194 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 343195 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 343200 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c11),sk_c10).
% 343201 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 343202 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 343203 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c11),sk_c10).
% 343204 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 343205 [?] ?
% 343324 [hyper:343157,343184,binarycut:343185] equal(inverse(sk_c1),sk_c2) | $spltprd1($spltcnst86,sk_c8).
% 343459 [hyper:343157,343204,binarycut:343205] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst86,sk_c8).
% 343873 [hyper:343156,343180,343181,343182] equal(inverse(sk_c1),sk_c2) | $spltprd1($spltcnst85,sk_c8).
% 343956 [hyper:343158,343183] equal(inverse(sk_c1),sk_c2) | $spltprd1($spltcnst87,sk_c8).
% 343985 [hyper:343159,343956,343873,343324] equal(inverse(sk_c1),sk_c2).
% 344007 [para:343985.1.1,343103.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 344299 [hyper:343156,343200,343201,343202] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst85,sk_c8).
% 345235 [hyper:343158,343203] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst87,sk_c8).
% 345286 [hyper:343159,345235,344299,343459] equal(inverse(sk_c11),sk_c10).
% 345334 [para:345286.1.1,343103.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 347224 [hyper:343155,343175,343173,343174,343171,343170,343172] equal(multiply(sk_c2,sk_c10),sk_c11).
% 348085 [hyper:343155,343195,343193,343194,343191,343190,343192] equal(multiply(sk_c1,sk_c2),sk_c11).
% 348196 [para:343103.1.1,343104.1.1.1,demod:343102] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 348197 [para:344007.1.1,343104.1.1.1,demod:343102] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 348198 [para:345334.1.1,343104.1.1.1,demod:343102] equal(X,multiply(sk_c10,multiply(sk_c11,X))).
% 348218 [para:348085.1.1,348197.1.2.2] equal(sk_c2,multiply(sk_c2,sk_c11)).
% 348245 [para:344007.1.1,348196.1.2.2] equal(sk_c1,multiply(inverse(sk_c2),identity)).
% 348253 [para:345334.1.1,348196.1.2.2] equal(sk_c11,multiply(inverse(sk_c10),identity)).
% 348256 [para:347224.1.1,348196.1.2.2] equal(sk_c10,multiply(inverse(sk_c2),sk_c11)).
% 348257 [para:348197.1.2,348196.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 348279 [para:348257.1.2,343103.1.1,demod:348085] equal(sk_c11,identity).
% 348285 [para:348279.1.1,345286.1.1.1] equal(inverse(identity),sk_c10).
% 348287 [para:348279.1.1,348218.1.2.2] equal(sk_c2,multiply(sk_c2,identity)).
% 348288 [para:348279.1.1,348198.1.2.2.1,demod:343102] equal(X,multiply(sk_c10,X)).
% 348290 [para:348279.1.1,348256.1.2.2,demod:348245] equal(sk_c10,sk_c1).
% 348295 [para:348290.1.1,348253.1.2.1.1,demod:348287,343985] equal(sk_c11,sk_c2).
% 348300 [para:348295.1.1,345286.1.1.1] equal(inverse(sk_c2),sk_c10).
% 348301 [para:348295.1.1,345334.1.1.2,demod:348288] equal(sk_c2,identity).
% 348307 [para:348301.1.1,347224.1.1.1,demod:343102] equal(sk_c10,sk_c11).
% 348316 [para:348307.1.2,345286.1.1.1] equal(inverse(sk_c10),sk_c10).
% 348361 [hyper:343155,348285,347224,demod:348316,343102,demod:348300,348288,cut:348307,cut:343101,cut:343101,cut:343101] 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(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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
%
%
% 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(55,40,2,118,0,2,102753,5,1503,102753,1,1503,102753,50,1503,102753,40,1503,102816,0,1503,110991,3,1805,112063,4,1954,113026,5,2104,113027,1,2104,113027,50,2104,113027,40,2104,113090,0,2104,115006,3,2406,115050,4,2555,115088,5,2705,115088,1,2705,115088,50,2705,115088,40,2705,115151,0,2705,135278,3,4213,136912,4,4956,138515,5,5706,138516,1,5706,138516,50,5707,138516,40,5707,138579,0,5707,151469,3,6458,152650,4,6833,153911,1,7208,153911,50,7208,153911,40,7208,153974,0,7208,167517,3,8024,168788,4,8334,170425,5,8709,170426,1,8709,170426,50,8709,170426,40,8709,170489,0,8709,211909,3,12610,213789,4,14560,215329,5,16510,215330,1,16510,215330,50,16511,215330,40,16511,215393,0,16511,250072,3,19064,251509,4,20337,252846,1,21612,252846,50,21613,252846,40,21613,252909,0,21613,282990,3,23114,284148,4,23864,285358,5,24614,285359,1,24614,285359,50,24615,285359,40,24615,285422,0,24615,299850,3,25377,301111,4,25743,302961,5,26116,302961,1,26116,302961,50,26116,302961,40,26116,303024,0,26116,323115,3,27317,324320,4,27917,325394,5,28517,325395,1,28517,325395,50,28518,325395,40,28518,325458,0,28518,341299,3,29269,342245,4,29644,343100,1,30019,343100,50,30019,343100,40,30019,343100,40,30019,343209,0,30019,348360,50,30037,348360,30,30037,348360,40,30037,348415,0,30037,348548,50,30037,348603,0,30037)
%
%
% START OF PROOF
% 348550 [] equal(multiply(identity,X),X).
% 348551 [] equal(multiply(inverse(X),X),identity).
% 348552 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 348553 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 348560 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 348561 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 348580 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c4),sk_c10).
% 348581 [?] ?
% 348590 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 348591 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 348600 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 348601 [?] ?
% 348610 [hyper:348553,348580,binarycut:348581] equal(inverse(sk_c1),sk_c2).
% 348611 [para:348610.1.1,348551.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 348625 [hyper:348553,348600,binarycut:348601] equal(inverse(sk_c11),sk_c10).
% 348628 [para:348625.1.1,348551.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 348655 [hyper:348553,348561,348560] equal(multiply(sk_c9,sk_c10),sk_c11).
% 348667 [hyper:348553,348591,348590] equal(multiply(sk_c1,sk_c2),sk_c11).
% 348668 [para:348551.1.1,348552.1.1.1,demod:348550] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 348669 [para:348611.1.1,348552.1.1.1,demod:348550] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 348670 [para:348628.1.1,348552.1.1.1,demod:348550] equal(X,multiply(sk_c10,multiply(sk_c11,X))).
% 348671 [para:348655.1.1,348552.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c9,multiply(sk_c10,X))).
% 348677 [para:348551.1.1,348668.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 348683 [para:348669.1.2,348668.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 348685 [para:348668.1.2,348668.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 348688 [para:348628.1.1,348671.1.2.2] equal(multiply(sk_c11,sk_c11),multiply(sk_c9,identity)).
% 348690 [para:348688.1.1,348670.1.2.2] equal(sk_c11,multiply(sk_c10,multiply(sk_c9,identity))).
% 348693 [para:348683.1.2,348551.1.1,demod:348667] equal(sk_c11,identity).
% 348700 [para:348693.1.1,348670.1.2.2.1,demod:348550] equal(X,multiply(sk_c10,X)).
% 348745 [para:348685.1.2,348677.1.2] equal(X,multiply(X,identity)).
% 348752 [para:348745.1.2,348690.1.2.2,demod:348700] equal(sk_c11,sk_c9).
% 348755 [para:348752.1.1,348625.1.1.1] equal(inverse(sk_c9),sk_c10).
% 348763 [hyper:348553,348755,demod:348655,cut:348752] 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 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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(55,40,2,118,0,2,102753,5,1503,102753,1,1503,102753,50,1503,102753,40,1503,102816,0,1503,110991,3,1805,112063,4,1954,113026,5,2104,113027,1,2104,113027,50,2104,113027,40,2104,113090,0,2104,115006,3,2406,115050,4,2555,115088,5,2705,115088,1,2705,115088,50,2705,115088,40,2705,115151,0,2705,135278,3,4213,136912,4,4956,138515,5,5706,138516,1,5706,138516,50,5707,138516,40,5707,138579,0,5707,151469,3,6458,152650,4,6833,153911,1,7208,153911,50,7208,153911,40,7208,153974,0,7208,167517,3,8024,168788,4,8334,170425,5,8709,170426,1,8709,170426,50,8709,170426,40,8709,170489,0,8709,211909,3,12610,213789,4,14560,215329,5,16510,215330,1,16510,215330,50,16511,215330,40,16511,215393,0,16511,250072,3,19064,251509,4,20337,252846,1,21612,252846,50,21613,252846,40,21613,252909,0,21613,282990,3,23114,284148,4,23864,285358,5,24614,285359,1,24614,285359,50,24615,285359,40,24615,285422,0,24615,299850,3,25377,301111,4,25743,302961,5,26116,302961,1,26116,302961,50,26116,302961,40,26116,303024,0,26116,323115,3,27317,324320,4,27917,325394,5,28517,325395,1,28517,325395,50,28518,325395,40,28518,325458,0,28518,341299,3,29269,342245,4,29644,343100,1,30019,343100,50,30019,343100,40,30019,343100,40,30019,343209,0,30019,348360,50,30037,348360,30,30037,348360,40,30037,348415,0,30037,348548,50,30037,348603,0,30037,348762,50,30037,348762,30,30037,348762,40,30037,348817,0,30041,348939,50,30042,348994,0,30042)
%
%
% START OF PROOF
% 348941 [] equal(multiply(identity,X),X).
% 348942 [] equal(multiply(inverse(X),X),identity).
% 348943 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 348944 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 348953 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 348954 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 348963 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 348964 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 348973 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c3),sk_c11).
% 348974 [?] ?
% 348983 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 348984 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 348993 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 348994 [?] ?
% 349002 [hyper:348944,348973,binarycut:348974] equal(inverse(sk_c1),sk_c2).
% 349003 [para:349002.1.1,348942.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 349011 [hyper:348944,348993,binarycut:348994] equal(inverse(sk_c11),sk_c10).
% 349013 [para:349011.1.1,348942.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 349039 [hyper:348944,348954,348953] equal(multiply(sk_c9,sk_c10),sk_c11).
% 349046 [hyper:348944,348964,348963] equal(multiply(sk_c2,sk_c10),sk_c11).
% 349053 [hyper:348944,348984,348983] equal(multiply(sk_c1,sk_c2),sk_c11).
% 349054 [para:348942.1.1,348943.1.1.1,demod:348941] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 349055 [para:349003.1.1,348943.1.1.1,demod:348941] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 349056 [para:349013.1.1,348943.1.1.1,demod:348941] equal(X,multiply(sk_c10,multiply(sk_c11,X))).
% 349057 [para:349039.1.1,348943.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c9,multiply(sk_c10,X))).
% 349059 [para:349053.1.1,348943.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c1,multiply(sk_c2,X))).
% 349063 [para:348942.1.1,349054.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 349064 [para:349003.1.1,349054.1.2.2] equal(sk_c1,multiply(inverse(sk_c2),identity)).
% 349067 [para:349046.1.1,349054.1.2.2] equal(sk_c10,multiply(inverse(sk_c2),sk_c11)).
% 349068 [para:348943.1.1,349054.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 349069 [para:349055.1.2,349054.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 349071 [para:349054.1.2,349054.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 349074 [para:349013.1.1,349057.1.2.2] equal(multiply(sk_c11,sk_c11),multiply(sk_c9,identity)).
% 349076 [para:349074.1.1,349056.1.2.2] equal(sk_c11,multiply(sk_c10,multiply(sk_c9,identity))).
% 349079 [para:349069.1.2,348942.1.1,demod:349053] equal(sk_c11,identity).
% 349080 [para:349069.1.2,349054.1.2,demod:349059] equal(X,multiply(sk_c11,X)).
% 349082 [para:349069.1.2,349067.1.2] equal(sk_c10,multiply(sk_c1,sk_c11)).
% 349088 [para:349079.1.1,349067.1.2.2,demod:349064] equal(sk_c10,sk_c1).
% 349089 [para:349079.1.1,349074.1.1.1,demod:348941] equal(sk_c11,multiply(sk_c9,identity)).
% 349098 [para:349088.1.1,349076.1.2.1,demod:349082,349089] equal(sk_c11,sk_c10).
% 349107 [para:349098.1.1,349011.1.1.1] equal(inverse(sk_c10),sk_c10).
% 349109 [para:349098.1.1,349074.1.1.2,demod:349089,349080] equal(sk_c10,sk_c11).
% 349127 [para:349071.1.2,348942.1.1] equal(multiply(X,inverse(X)),identity).
% 349129 [para:349071.1.2,349063.1.2] equal(X,multiply(X,identity)).
% 349131 [para:349129.1.2,349063.1.2] equal(X,inverse(inverse(X))).
% 349144 [para:349127.1.1,349068.1.2.2.2,demod:349129] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 349152 [para:349080.1.2,349144.1.2.1.1] equal(inverse(X),multiply(inverse(X),sk_c11)).
% 349155 [para:349152.1.2,349071.1.2,demod:349131] equal(multiply(X,sk_c11),X).
% 349156 [hyper:348944,349155,demod:349107,cut:349109] 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(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),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
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,2,118,0,2,102753,5,1503,102753,1,1503,102753,50,1503,102753,40,1503,102816,0,1503,110991,3,1805,112063,4,1954,113026,5,2104,113027,1,2104,113027,50,2104,113027,40,2104,113090,0,2104,115006,3,2406,115050,4,2555,115088,5,2705,115088,1,2705,115088,50,2705,115088,40,2705,115151,0,2705,135278,3,4213,136912,4,4956,138515,5,5706,138516,1,5706,138516,50,5707,138516,40,5707,138579,0,5707,151469,3,6458,152650,4,6833,153911,1,7208,153911,50,7208,153911,40,7208,153974,0,7208,167517,3,8024,168788,4,8334,170425,5,8709,170426,1,8709,170426,50,8709,170426,40,8709,170489,0,8709,211909,3,12610,213789,4,14560,215329,5,16510,215330,1,16510,215330,50,16511,215330,40,16511,215393,0,16511,250072,3,19064,251509,4,20337,252846,1,21612,252846,50,21613,252846,40,21613,252909,0,21613,282990,3,23114,284148,4,23864,285358,5,24614,285359,1,24614,285359,50,24615,285359,40,24615,285422,0,24615,299850,3,25377,301111,4,25743,302961,5,26116,302961,1,26116,302961,50,26116,302961,40,26116,303024,0,26116,323115,3,27317,324320,4,27917,325394,5,28517,325395,1,28517,325395,50,28518,325395,40,28518,325458,0,28518,341299,3,29269,342245,4,29644,343100,1,30019,343100,50,30019,343100,40,30019,343100,40,30019,343209,0,30019,348360,50,30037,348360,30,30037,348360,40,30037,348415,0,30037,348548,50,30037,348603,0,30037,348762,50,30037,348762,30,30037,348762,40,30037,348817,0,30041,348939,50,30042,348994,0,30042,349155,50,30043,349155,30,30043,349155,40,30043,349210,0,30048)
%
%
% START OF PROOF
% 349156 [] equal(X,X).
% 349160 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,X),sk_c11) | -equal(inverse(Y),X).
% 349174 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 349175 [?] ?
% 349176 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 349184 [?] ?
% 349185 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 349186 [?] ?
% 349194 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 349195 [?] ?
% 349196 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 349231 [hyper:349160,349185,binarycut:349195,binarycut:349175] equal(inverse(sk_c5),sk_c8).
% 349233 [hyper:349160,349185,binarycut:349186,binarycut:349184] equal(inverse(sk_c1),sk_c2).
% 349327 [hyper:349160,349176,349174,demod:349231,cut:349156] equal(multiply(sk_c2,sk_c10),sk_c11).
% 349355 [hyper:349160,349194,demod:349233,349327,cut:349156,cut:349156] equal(multiply(sk_c8,sk_c10),sk_c11).
% 349368 [hyper:349160,349196,demod:349233,349327,cut:349156,cut:349156] equal(multiply(sk_c5,sk_c8),sk_c11).
% 349370 [hyper:349160,349368,demod:349231,349355,cut:349156,cut:349156] 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(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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(55,40,2,118,0,2,102753,5,1503,102753,1,1503,102753,50,1503,102753,40,1503,102816,0,1503,110991,3,1805,112063,4,1954,113026,5,2104,113027,1,2104,113027,50,2104,113027,40,2104,113090,0,2104,115006,3,2406,115050,4,2555,115088,5,2705,115088,1,2705,115088,50,2705,115088,40,2705,115151,0,2705,135278,3,4213,136912,4,4956,138515,5,5706,138516,1,5706,138516,50,5707,138516,40,5707,138579,0,5707,151469,3,6458,152650,4,6833,153911,1,7208,153911,50,7208,153911,40,7208,153974,0,7208,167517,3,8024,168788,4,8334,170425,5,8709,170426,1,8709,170426,50,8709,170426,40,8709,170489,0,8709,211909,3,12610,213789,4,14560,215329,5,16510,215330,1,16510,215330,50,16511,215330,40,16511,215393,0,16511,250072,3,19064,251509,4,20337,252846,1,21612,252846,50,21613,252846,40,21613,252909,0,21613,282990,3,23114,284148,4,23864,285358,5,24614,285359,1,24614,285359,50,24615,285359,40,24615,285422,0,24615,299850,3,25377,301111,4,25743,302961,5,26116,302961,1,26116,302961,50,26116,302961,40,26116,303024,0,26116,323115,3,27317,324320,4,27917,325394,5,28517,325395,1,28517,325395,50,28518,325395,40,28518,325458,0,28518,341299,3,29269,342245,4,29644,343100,1,30019,343100,50,30019,343100,40,30019,343100,40,30019,343209,0,30019,348360,50,30037,348360,30,30037,348360,40,30037,348415,0,30037,348548,50,30037,348603,0,30037,348762,50,30037,348762,30,30037,348762,40,30037,348817,0,30041,348939,50,30042,348994,0,30042,349155,50,30043,349155,30,30043,349155,40,30043,349210,0,30048,349369,50,30048,349369,30,30048,349369,40,30048,349424,0,30048,349628,50,30050,349683,0,30055,349951,50,30060,350006,0,30060,350282,50,30067,350337,0,30072,350621,50,30081,350676,0,30081,350966,50,30094,351021,0,30098,351319,50,30120,351374,0,30120,351680,50,30157,351735,0,30161,352051,50,30230,352106,0,30230,352432,50,30372,352432,40,30372,352487,0,30372)
%
%
% START OF PROOF
% 352434 [] equal(multiply(identity,X),X).
% 352435 [] equal(multiply(inverse(X),X),identity).
% 352436 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 352437 [] -equal(inverse(sk_c11),sk_c10).
% 352478 [?] ?
% 352479 [?] ?
% 352480 [?] ?
% 352481 [?] ?
% 352482 [?] ?
% 352483 [?] ?
% 352484 [?] ?
% 352485 [?] ?
% 352486 [?] ?
% 352487 [?] ?
% 352504 [input:352479,cut:352437] equal(inverse(sk_c6),sk_c8).
% 352505 [para:352504.1.1,352435.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 352507 [input:352480,cut:352437] equal(inverse(sk_c7),sk_c6).
% 352508 [para:352507.1.1,352435.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 352509 [input:352482,cut:352437] equal(inverse(sk_c5),sk_c8).
% 352510 [para:352509.1.1,352435.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 352512 [input:352484,cut:352437] equal(inverse(sk_c4),sk_c10).
% 352513 [para:352512.1.1,352435.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 352514 [input:352486,cut:352437] equal(inverse(sk_c3),sk_c11).
% 352515 [para:352514.1.1,352435.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 352544 [input:352478,cut:352437] equal(multiply(sk_c7,sk_c8),sk_c6).
% 352545 [input:352481,cut:352437] equal(multiply(sk_c8,sk_c10),sk_c11).
% 352547 [input:352483,cut:352437] equal(multiply(sk_c5,sk_c8),sk_c11).
% 352548 [input:352485,cut:352437] equal(multiply(sk_c4,sk_c10),sk_c9).
% 352549 [input:352487,cut:352437] equal(multiply(sk_c3,sk_c11),sk_c10).
% 352569 [para:352505.1.1,352436.1.1.1,demod:352434] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 352570 [para:352508.1.1,352436.1.1.1,demod:352434] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 352571 [para:352510.1.1,352436.1.1.1,demod:352434] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 352573 [para:352513.1.1,352436.1.1.1,demod:352434] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 352574 [para:352515.1.1,352436.1.1.1,demod:352434] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 352606 [para:352547.1.1,352436.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 352624 [para:352508.1.1,352569.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 352625 [para:352624.1.2,352436.1.1.1,demod:352434] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 352629 [para:352544.1.1,352570.1.2.2] equal(sk_c8,multiply(sk_c6,sk_c6)).
% 352632 [para:352629.1.2,352569.1.2.2] equal(sk_c6,multiply(sk_c8,sk_c8)).
% 352638 [para:352547.1.1,352571.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 352644 [para:352548.1.1,352573.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 352650 [para:352549.1.1,352574.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 352652 [para:352625.1.1,352570.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 352653 [para:352505.1.1,352652.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 352654 [para:352510.1.1,352652.1.2.2,demod:352653] equal(sk_c5,sk_c6).
% 352662 [para:352654.1.2,352570.1.2.1,demod:352606,352625] equal(X,multiply(sk_c11,X)).
% 352722 [para:352662.1.2,352574.1.2] equal(X,multiply(sk_c3,X)).
% 352723 [para:352662.1.2,352650.1.2] equal(sk_c11,sk_c10).
% 352729 [para:352723.1.1,352638.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c10)).
% 352730 [para:352723.1.1,352574.1.2.1,demod:352722] equal(X,multiply(sk_c10,X)).
% 352735 [para:352730.1.2,352644.1.2] equal(sk_c10,sk_c9).
% 352750 [para:352735.1.1,352545.1.1.2] equal(multiply(sk_c8,sk_c9),sk_c11).
% 352753 [para:352735.1.1,352650.1.2.2,demod:352662] equal(sk_c11,sk_c9).
% 352761 [para:352753.1.1,352638.1.2.2,demod:352750] equal(sk_c8,sk_c11).
% 352765 [para:352761.1.2,352549.1.1.2,demod:352722] equal(sk_c8,sk_c10).
% 352766 [para:352761.1.2,352638.1.2.2,demod:352632] equal(sk_c8,sk_c6).
% 352768 [para:352761.1.2,352650.1.2.1,demod:352729] equal(sk_c11,sk_c8).
% 352783 [para:352766.1.2,352504.1.1.1] equal(inverse(sk_c8),sk_c8).
% 352789 [para:352768.1.1,352437.1.1.1,demod:352783,cut:352765] 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(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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_c9,sk_c10),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(55,40,2,118,0,2,102753,5,1503,102753,1,1503,102753,50,1503,102753,40,1503,102816,0,1503,110991,3,1805,112063,4,1954,113026,5,2104,113027,1,2104,113027,50,2104,113027,40,2104,113090,0,2104,115006,3,2406,115050,4,2555,115088,5,2705,115088,1,2705,115088,50,2705,115088,40,2705,115151,0,2705,135278,3,4213,136912,4,4956,138515,5,5706,138516,1,5706,138516,50,5707,138516,40,5707,138579,0,5707,151469,3,6458,152650,4,6833,153911,1,7208,153911,50,7208,153911,40,7208,153974,0,7208,167517,3,8024,168788,4,8334,170425,5,8709,170426,1,8709,170426,50,8709,170426,40,8709,170489,0,8709,211909,3,12610,213789,4,14560,215329,5,16510,215330,1,16510,215330,50,16511,215330,40,16511,215393,0,16511,250072,3,19064,251509,4,20337,252846,1,21612,252846,50,21613,252846,40,21613,252909,0,21613,282990,3,23114,284148,4,23864,285358,5,24614,285359,1,24614,285359,50,24615,285359,40,24615,285422,0,24615,299850,3,25377,301111,4,25743,302961,5,26116,302961,1,26116,302961,50,26116,302961,40,26116,303024,0,26116,323115,3,27317,324320,4,27917,325394,5,28517,325395,1,28517,325395,50,28518,325395,40,28518,325458,0,28518,341299,3,29269,342245,4,29644,343100,1,30019,343100,50,30019,343100,40,30019,343100,40,30019,343209,0,30019,348360,50,30037,348360,30,30037,348360,40,30037,348415,0,30037,348548,50,30037,348603,0,30037,348762,50,30037,348762,30,30037,348762,40,30037,348817,0,30041,348939,50,30042,348994,0,30042,349155,50,30043,349155,30,30043,349155,40,30043,349210,0,30048,349369,50,30048,349369,30,30048,349369,40,30048,349424,0,30048,349628,50,30050,349683,0,30055,349951,50,30060,350006,0,30060,350282,50,30067,350337,0,30072,350621,50,30081,350676,0,30081,350966,50,30094,351021,0,30098,351319,50,30120,351374,0,30120,351680,50,30157,351735,0,30161,352051,50,30230,352106,0,30230,352432,50,30372,352432,40,30372,352487,0,30372,352788,50,30373,352788,30,30373,352788,40,30373,352843,0,30373,353051,50,30375,353106,0,30379,353371,50,30384,353426,0,30384,353699,50,30392,353754,0,30397,354035,50,30406,354090,0,30406,354377,50,30418,354432,0,30423,354727,50,30444,354782,0,30444,355085,50,30480,355140,0,30485,355453,50,30554,355508,0,30554,355831,50,30691,355831,40,30691,355886,0,30691)
%
%
% START OF PROOF
% 355694 [?] ?
% 355833 [] equal(multiply(identity,X),X).
% 355834 [] equal(multiply(inverse(X),X),identity).
% 355835 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 355836 [] -equal(multiply(sk_c9,sk_c10),sk_c11).
% 355838 [?] ?
% 355839 [?] ?
% 355841 [?] ?
% 355842 [?] ?
% 355843 [?] ?
% 355844 [?] ?
% 355845 [?] ?
% 355846 [?] ?
% 355906 [input:355838,cut:355836] equal(inverse(sk_c6),sk_c8).
% 355907 [para:355906.1.1,355834.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 355920 [input:355839,cut:355836] equal(inverse(sk_c7),sk_c6).
% 355921 [para:355920.1.1,355834.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 355922 [input:355841,cut:355836] equal(inverse(sk_c5),sk_c8).
% 355923 [para:355922.1.1,355834.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 355924 [input:355843,cut:355836] equal(inverse(sk_c4),sk_c10).
% 355925 [para:355924.1.1,355834.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 355927 [input:355845,cut:355836] equal(inverse(sk_c3),sk_c11).
% 355928 [para:355927.1.1,355834.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 355932 [input:355842,cut:355836] equal(multiply(sk_c5,sk_c8),sk_c11).
% 355941 [input:355844,cut:355836] equal(multiply(sk_c4,sk_c10),sk_c9).
% 355947 [input:355846,cut:355836] equal(multiply(sk_c3,sk_c11),sk_c10).
% 355984 [para:355907.1.1,355835.1.1.1,demod:355833] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 355985 [para:355921.1.1,355835.1.1.1,demod:355833] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 355987 [para:355925.1.1,355835.1.1.1,demod:355833] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 355989 [para:355928.1.1,355835.1.1.1,demod:355833] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 355993 [para:355932.1.1,355835.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 356024 [para:355921.1.1,355984.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 356025 [para:356024.1.2,355835.1.1.1,demod:355833] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 356035 [para:355941.1.1,355987.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 356040 [para:355947.1.1,355989.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 356042 [para:356025.1.1,355985.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 356043 [para:355907.1.1,356042.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 356044 [para:355923.1.1,356042.1.2.2,demod:356043] equal(sk_c5,sk_c6).
% 356051 [para:356044.1.2,355985.1.2.1,demod:355993,356025] equal(X,multiply(sk_c11,X)).
% 356055 [para:356051.1.2,355989.1.2] equal(X,multiply(sk_c3,X)).
% 356056 [para:356051.1.2,356040.1.2] equal(sk_c11,sk_c10).
% 356074 [para:356056.1.1,355989.1.2.1,demod:356055] equal(X,multiply(sk_c10,X)).
% 356088 [para:356074.1.2,355987.1.2] equal(X,multiply(sk_c4,X)).
% 356089 [para:356074.1.2,356035.1.2] equal(sk_c10,sk_c9).
% 356090 [para:356035.1.2,356074.1.2] equal(sk_c9,sk_c10).
% 356104 [para:356089.1.1,355987.1.2.1,demod:356088] equal(X,multiply(sk_c9,X)).
% 356106 [para:356090.1.2,355836.1.1.2,demod:356104,cut:355694] 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: 49803
% derived clauses: 3748867
% kept clauses: 180121
% kept size sum: 231481
% kept mid-nuclei: 79166
% kept new demods: 5341
% forw unit-subs: 957727
% forw double-subs: 2264161
% forw overdouble-subs: 141716
% backward subs: 16367
% fast unit cutoff: 37863
% full unit cutoff: 0
% dbl unit cutoff: 44725
% real runtime : 308.80
% process. runtime: 306.90
% specific non-discr-tree subsumption statistics:
% tried: 32987276
% length fails: 3988686
% strength fails: 12207280
% predlist fails: 2254599
% aux str. fails: 3586796
% by-lit fails: 5856291
% full subs tried: 2287202
% full subs fail: 2185685
%
% ; 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/GRP371-1+eq_r.in")
%
%------------------------------------------------------------------------------