TSTP Solution File: GRP258-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP258-1 : 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 : art09.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 298.8s
% Output : Assurance 298.8s
% 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/GRP258-1+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 33)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 33)
% (binary-posweight-lex-big-order 30 #f 3 33)
% (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(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(sk_c10,sk_c12),sk_c11) | -equal(multiply(Z,sk_c10),sk_c12) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% was split for some strategies as:
% -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X3),X1) | -equal(inverse(X2),X3) | -equal(multiply(X2,X1),X3).
% -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11).
% -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12).
% -equal(multiply(Z,sk_c10),sk_c12) | -equal(inverse(Z),sk_c10).
% -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11).
% -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12).
% -equal(multiply(sk_c10,sk_c12),sk_c11).
%
% 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(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(sk_c10,sk_c12),sk_c11) | -equal(multiply(Z,sk_c10),sk_c12) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X3),X1) | -equal(inverse(X2),X3) | -equal(multiply(X2,X1),X3).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,0,160,0,0,128098,5,1501,128098,1,1501,128098,50,1501,128098,40,1501,128183,0,1501,137261,3,1803,138226,4,1952,139078,1,2102,139078,50,2102,139078,40,2102,139163,0,2102,140888,3,2419,140900,4,2564,140994,5,2703,140994,1,2703,140994,50,2703,140994,40,2703,141079,0,2703,168889,3,4205,169804,4,4954,170465,5,5704,170466,1,5704,170466,50,5705,170466,40,5705,170551,0,5705,188213,3,6456,188820,4,6831,189205,1,7206,189205,50,7206,189205,40,7206,189290,0,7206,205470,3,7970,206438,4,8332,208010,5,8707,208011,5,8707,208011,1,8707,208011,50,8707,208011,40,8707,208096,0,8707,255440,3,12614,256950,4,14558,257782,5,16508,257783,1,16508,257783,50,16510,257783,40,16510,257868,0,16510,300321,3,19067,301502,4,20336,302073,1,21611,302073,50,21612,302073,40,21612,302158,0,21612,334659,3,23113,335619,4,23863,336596,1,24613,336596,50,24614,336596,40,24614,336681,0,24614,354303,3,25378,355198,4,25740,357242,5,26115,357243,1,26115,357243,50,26115,357243,40,26115,357328,0,26115,379495,3,27316,380524,4,27916,381211,5,28516,381212,1,28516,381212,50,28517,381212,40,28517,381297,0,28517,396649,3,29268,397620,4,29643,398390,1,30018,398390,50,30018,398390,40,30018,398390,40,30018,398539,0,30018)
%
%
% START OF PROOF
% 398392 [] equal(multiply(identity,X),X).
% 398393 [] equal(multiply(inverse(X),X),identity).
% 398394 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 398465 [] -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,X),sk_c12) | -equal(multiply(Z,X),U) | -equal(inverse(Z),U) | -equal(inverse(U),X) | -equal(inverse(Y),X).
% 398466 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst109,Y).
% 398467 [] -equal(multiply(X,Y),sk_c12) | -equal(inverse(X),Y) | $spltprd1($spltcnst110,Y).
% 398468 [] -equal(multiply(X,sk_c11),sk_c12) | $spltprd1($spltcnst111,X).
% 398469 [] -$spltprd1($spltcnst110,X) | -$spltprd1($spltcnst109,X) | -$spltprd1($spltcnst111,X).
% 398470 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c3),sk_c10).
% 398471 [] equal(inverse(sk_c3),sk_c10) | equal(inverse(sk_c7),sk_c9).
% 398472 [] equal(inverse(sk_c3),sk_c10) | equal(inverse(sk_c8),sk_c7).
% 398473 [] equal(multiply(sk_c9,sk_c11),sk_c12) | equal(inverse(sk_c3),sk_c10).
% 398474 [] equal(inverse(sk_c3),sk_c10) | equal(inverse(sk_c6),sk_c9).
% 398475 [?] ?
% 398480 [] equal(multiply(sk_c3,sk_c10),sk_c12) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 398481 [] equal(multiply(sk_c3,sk_c10),sk_c12) | equal(inverse(sk_c7),sk_c9).
% 398482 [] equal(multiply(sk_c3,sk_c10),sk_c12) | equal(inverse(sk_c8),sk_c7).
% 398483 [] equal(multiply(sk_c3,sk_c10),sk_c12) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 398484 [] equal(multiply(sk_c3,sk_c10),sk_c12) | equal(inverse(sk_c6),sk_c9).
% 398485 [] equal(multiply(sk_c3,sk_c10),sk_c12) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 398490 [] equal(multiply(sk_c10,sk_c12),sk_c11) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 398491 [] equal(multiply(sk_c10,sk_c12),sk_c11) | equal(inverse(sk_c7),sk_c9).
% 398492 [] equal(multiply(sk_c10,sk_c12),sk_c11) | equal(inverse(sk_c8),sk_c7).
% 398493 [] equal(multiply(sk_c10,sk_c12),sk_c11) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 398494 [] equal(multiply(sk_c10,sk_c12),sk_c11) | equal(inverse(sk_c6),sk_c9).
% 398495 [] equal(multiply(sk_c10,sk_c12),sk_c11) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 398500 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c2),sk_c11).
% 398501 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c7),sk_c9).
% 398502 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c8),sk_c7).
% 398503 [] equal(multiply(sk_c9,sk_c11),sk_c12) | equal(inverse(sk_c2),sk_c11).
% 398504 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c6),sk_c9).
% 398505 [?] ?
% 398510 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 398511 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(inverse(sk_c7),sk_c9).
% 398512 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(inverse(sk_c8),sk_c7).
% 398513 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 398514 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(inverse(sk_c6),sk_c9).
% 398515 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 398520 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c1),sk_c12).
% 398521 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c7),sk_c9).
% 398522 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c8),sk_c7).
% 398523 [] equal(multiply(sk_c9,sk_c11),sk_c12) | equal(inverse(sk_c1),sk_c12).
% 398524 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c6),sk_c9).
% 398525 [?] ?
% 398530 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 398531 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(inverse(sk_c7),sk_c9).
% 398532 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(inverse(sk_c8),sk_c7).
% 398533 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 398534 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(inverse(sk_c6),sk_c9).
% 398535 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 398630 [hyper:398467,398474,binarycut:398475] equal(inverse(sk_c3),sk_c10) | $spltprd1($spltcnst110,sk_c9).
% 398745 [hyper:398467,398504,binarycut:398505] equal(inverse(sk_c2),sk_c11) | $spltprd1($spltcnst110,sk_c9).
% 398832 [hyper:398467,398524,binarycut:398525] equal(inverse(sk_c1),sk_c12) | $spltprd1($spltcnst110,sk_c9).
% 398928 [hyper:398466,398470,398471,398472] equal(inverse(sk_c3),sk_c10) | $spltprd1($spltcnst109,sk_c9).
% 398980 [hyper:398468,398473] equal(inverse(sk_c3),sk_c10) | $spltprd1($spltcnst111,sk_c9).
% 398994 [hyper:398469,398980,398928,398630] equal(inverse(sk_c3),sk_c10).
% 399011 [para:398994.1.1,398393.1.1.1] equal(multiply(sk_c10,sk_c3),identity).
% 399222 [hyper:398466,398500,398501,398502] equal(inverse(sk_c2),sk_c11) | $spltprd1($spltcnst109,sk_c9).
% 399251 [hyper:398468,398503] equal(inverse(sk_c2),sk_c11) | $spltprd1($spltcnst111,sk_c9).
% 399262 [hyper:398469,399251,399222,398745] equal(inverse(sk_c2),sk_c11).
% 399270 [para:399262.1.1,398393.1.1.1] equal(multiply(sk_c11,sk_c2),identity).
% 399389 [hyper:398466,398520,398521,398522] equal(inverse(sk_c1),sk_c12) | $spltprd1($spltcnst109,sk_c9).
% 399416 [hyper:398468,398523] equal(inverse(sk_c1),sk_c12) | $spltprd1($spltcnst111,sk_c9).
% 399427 [hyper:398469,399416,399389,398832] equal(inverse(sk_c1),sk_c12).
% 399435 [para:399427.1.1,398393.1.1.1] equal(multiply(sk_c12,sk_c1),identity).
% 399800 [hyper:398465,398485,398483,398484,398481,398480,398482] equal(multiply(sk_c3,sk_c10),sk_c12).
% 399945 [hyper:398465,398495,398493,398494,398491,398490,398492] equal(multiply(sk_c10,sk_c12),sk_c11).
% 400042 [hyper:398465,398515,398513,398514,398511,398510,398512] equal(multiply(sk_c2,sk_c11),sk_c10).
% 400107 [hyper:398465,398535,398533,398534,398531,398530,398532] equal(multiply(sk_c1,sk_c12),sk_c11).
% 400115 [para:398393.1.1,398394.1.1.1,demod:398392] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 400116 [para:399011.1.1,398394.1.1.1,demod:398392] equal(X,multiply(sk_c10,multiply(sk_c3,X))).
% 400117 [para:399270.1.1,398394.1.1.1,demod:398392] equal(X,multiply(sk_c11,multiply(sk_c2,X))).
% 400118 [para:399435.1.1,398394.1.1.1,demod:398392] equal(X,multiply(sk_c12,multiply(sk_c1,X))).
% 400139 [para:399800.1.1,400116.1.2.2,demod:399945] equal(sk_c10,sk_c11).
% 400140 [para:400139.1.1,399011.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 400141 [para:400139.1.1,399800.1.1.2] equal(multiply(sk_c3,sk_c11),sk_c12).
% 400143 [para:400139.1.1,399945.1.1.1] equal(multiply(sk_c11,sk_c12),sk_c11).
% 400144 [para:400139.1.1,400116.1.2.1] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 400204 [para:400107.1.1,400118.1.2.2] equal(sk_c12,multiply(sk_c12,sk_c11)).
% 400232 [para:399270.1.1,400115.1.2.2] equal(sk_c2,multiply(inverse(sk_c11),identity)).
% 400244 [para:400140.1.1,400115.1.2.2,demod:400232] equal(sk_c3,sk_c2).
% 400245 [para:400143.1.1,400115.1.2.2,demod:398393] equal(sk_c12,identity).
% 400246 [para:400117.1.2,400115.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c11),X)).
% 400249 [para:400144.1.2,400115.1.2.2,demod:400246] equal(multiply(sk_c3,X),multiply(sk_c2,X)).
% 400253 [para:400244.1.1,400141.1.1.1,demod:400042] equal(sk_c10,sk_c12).
% 400255 [para:400245.1.1,399435.1.1.1,demod:398392] equal(sk_c1,identity).
% 400260 [para:400245.1.1,400204.1.2.1,demod:398392] equal(sk_c12,sk_c11).
% 400264 [para:400253.1.2,400245.1.1] equal(sk_c10,identity).
% 400267 [para:400255.1.1,399427.1.1.1] equal(inverse(identity),sk_c12).
% 400272 [para:400260.1.1,400245.1.1] equal(sk_c11,identity).
% 400274 [para:400264.1.1,399011.1.1.1,demod:398392] equal(sk_c3,identity).
% 400275 [para:400264.1.1,399800.1.1.2,demod:400249] equal(multiply(sk_c2,identity),sk_c12).
% 400280 [para:400274.1.1,400141.1.1.1,demod:398392] equal(sk_c11,sk_c12).
% 400677 [hyper:398465,400275,398392,demod:399262,398392,cut:400280,cut:400272,demod:400267,cut:400245,cut:400245] 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 33
% 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(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(sk_c10,sk_c12),sk_c11) | -equal(multiply(Z,sk_c10),sk_c12) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),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 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,0,160,0,0,128098,5,1501,128098,1,1501,128098,50,1501,128098,40,1501,128183,0,1501,137261,3,1803,138226,4,1952,139078,1,2102,139078,50,2102,139078,40,2102,139163,0,2102,140888,3,2419,140900,4,2564,140994,5,2703,140994,1,2703,140994,50,2703,140994,40,2703,141079,0,2703,168889,3,4205,169804,4,4954,170465,5,5704,170466,1,5704,170466,50,5705,170466,40,5705,170551,0,5705,188213,3,6456,188820,4,6831,189205,1,7206,189205,50,7206,189205,40,7206,189290,0,7206,205470,3,7970,206438,4,8332,208010,5,8707,208011,5,8707,208011,1,8707,208011,50,8707,208011,40,8707,208096,0,8707,255440,3,12614,256950,4,14558,257782,5,16508,257783,1,16508,257783,50,16510,257783,40,16510,257868,0,16510,300321,3,19067,301502,4,20336,302073,1,21611,302073,50,21612,302073,40,21612,302158,0,21612,334659,3,23113,335619,4,23863,336596,1,24613,336596,50,24614,336596,40,24614,336681,0,24614,354303,3,25378,355198,4,25740,357242,5,26115,357243,1,26115,357243,50,26115,357243,40,26115,357328,0,26115,379495,3,27316,380524,4,27916,381211,5,28516,381212,1,28516,381212,50,28517,381212,40,28517,381297,0,28517,396649,3,29268,397620,4,29643,398390,1,30018,398390,50,30018,398390,40,30018,398390,40,30018,398539,0,30018,400676,50,30027,400676,30,30027,400676,40,30027,400751,0,30027)
%
%
% START OF PROOF
% 400677 [] equal(X,X).
% 400681 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 400718 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c5),sk_c11).
% 400719 [?] ?
% 400728 [?] ?
% 400729 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(multiply(sk_c5,sk_c11),sk_c10).
% 400777 [hyper:400681,400718,binarycut:400728] equal(inverse(sk_c5),sk_c11).
% 400779 [hyper:400681,400718,binarycut:400719] equal(inverse(sk_c2),sk_c11).
% 400811 [hyper:400681,400729,demod:400779,cut:400677] equal(multiply(sk_c5,sk_c11),sk_c10).
% 400813 [hyper:400681,400811,demod:400777,cut:400677] 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 33
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(sk_c10,sk_c12),sk_c11) | -equal(multiply(Z,sk_c10),sk_c12) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12).
% 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 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,0,160,0,0,128098,5,1501,128098,1,1501,128098,50,1501,128098,40,1501,128183,0,1501,137261,3,1803,138226,4,1952,139078,1,2102,139078,50,2102,139078,40,2102,139163,0,2102,140888,3,2419,140900,4,2564,140994,5,2703,140994,1,2703,140994,50,2703,140994,40,2703,141079,0,2703,168889,3,4205,169804,4,4954,170465,5,5704,170466,1,5704,170466,50,5705,170466,40,5705,170551,0,5705,188213,3,6456,188820,4,6831,189205,1,7206,189205,50,7206,189205,40,7206,189290,0,7206,205470,3,7970,206438,4,8332,208010,5,8707,208011,5,8707,208011,1,8707,208011,50,8707,208011,40,8707,208096,0,8707,255440,3,12614,256950,4,14558,257782,5,16508,257783,1,16508,257783,50,16510,257783,40,16510,257868,0,16510,300321,3,19067,301502,4,20336,302073,1,21611,302073,50,21612,302073,40,21612,302158,0,21612,334659,3,23113,335619,4,23863,336596,1,24613,336596,50,24614,336596,40,24614,336681,0,24614,354303,3,25378,355198,4,25740,357242,5,26115,357243,1,26115,357243,50,26115,357243,40,26115,357328,0,26115,379495,3,27316,380524,4,27916,381211,5,28516,381212,1,28516,381212,50,28517,381212,40,28517,381297,0,28517,396649,3,29268,397620,4,29643,398390,1,30018,398390,50,30018,398390,40,30018,398390,40,30018,398539,0,30018,400676,50,30027,400676,30,30027,400676,40,30027,400751,0,30027,400812,50,30027,400812,30,30027,400812,40,30027,400887,0,30032)
%
%
% START OF PROOF
% 400813 [] equal(X,X).
% 400817 [] -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12).
% 400876 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 400877 [?] ?
% 400886 [?] ?
% 400887 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 400928 [hyper:400817,400876,binarycut:400886] equal(inverse(sk_c4),sk_c12).
% 400930 [hyper:400817,400876,binarycut:400877] equal(inverse(sk_c1),sk_c12).
% 400972 [hyper:400817,400887,demod:400930,cut:400813] equal(multiply(sk_c4,sk_c12),sk_c11).
% 400974 [hyper:400817,400972,demod:400928,cut:400813] 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 33
% 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(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(sk_c10,sk_c12),sk_c11) | -equal(multiply(Z,sk_c10),sk_c12) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(Z,sk_c10),sk_c12) | -equal(inverse(Z),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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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(75,40,0,160,0,0,128098,5,1501,128098,1,1501,128098,50,1501,128098,40,1501,128183,0,1501,137261,3,1803,138226,4,1952,139078,1,2102,139078,50,2102,139078,40,2102,139163,0,2102,140888,3,2419,140900,4,2564,140994,5,2703,140994,1,2703,140994,50,2703,140994,40,2703,141079,0,2703,168889,3,4205,169804,4,4954,170465,5,5704,170466,1,5704,170466,50,5705,170466,40,5705,170551,0,5705,188213,3,6456,188820,4,6831,189205,1,7206,189205,50,7206,189205,40,7206,189290,0,7206,205470,3,7970,206438,4,8332,208010,5,8707,208011,5,8707,208011,1,8707,208011,50,8707,208011,40,8707,208096,0,8707,255440,3,12614,256950,4,14558,257782,5,16508,257783,1,16508,257783,50,16510,257783,40,16510,257868,0,16510,300321,3,19067,301502,4,20336,302073,1,21611,302073,50,21612,302073,40,21612,302158,0,21612,334659,3,23113,335619,4,23863,336596,1,24613,336596,50,24614,336596,40,24614,336681,0,24614,354303,3,25378,355198,4,25740,357242,5,26115,357243,1,26115,357243,50,26115,357243,40,26115,357328,0,26115,379495,3,27316,380524,4,27916,381211,5,28516,381212,1,28516,381212,50,28517,381212,40,28517,381297,0,28517,396649,3,29268,397620,4,29643,398390,1,30018,398390,50,30018,398390,40,30018,398390,40,30018,398539,0,30018,400676,50,30027,400676,30,30027,400676,40,30027,400751,0,30027,400812,50,30027,400812,30,30027,400812,40,30027,400887,0,30032,400973,50,30032,400973,30,30032,400973,40,30032,401048,0,30032,401230,50,30034,401305,0,30038,401552,50,30042,401627,0,30042,401882,50,30049,401957,0,30053,402220,50,30062,402295,0,30062,402564,50,30074,402639,0,30079,402916,50,30099,402991,0,30099,403276,50,30135,403351,0,30139,403646,50,30207,403721,0,30207,404026,50,30342,404026,40,30342,404101,0,30342)
%
%
% START OF PROOF
% 403873 [?] ?
% 403885 [?] ?
% 404028 [] equal(multiply(identity,X),X).
% 404029 [] equal(multiply(inverse(X),X),identity).
% 404030 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 404031 [] -equal(multiply(X,sk_c10),sk_c12) | -equal(inverse(X),sk_c10).
% 404286 [para:404029.1.1,404030.1.1.1,demod:404028] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 404399 [para:404029.1.1,404286.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 404573 [para:404286.1.2,404286.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 404739 [para:404573.1.2,404399.1.2] equal(X,multiply(X,identity)).
% 404740 [para:404739.1.2,404029.1.1] equal(inverse(identity),identity).
% 404742 [para:404740.1.1,404031.2.1,demod:404028,cut:403885,cut:403873] 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 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(sk_c10,sk_c12),sk_c11) | -equal(multiply(Z,sk_c10),sk_c12) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),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 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,0,160,0,0,128098,5,1501,128098,1,1501,128098,50,1501,128098,40,1501,128183,0,1501,137261,3,1803,138226,4,1952,139078,1,2102,139078,50,2102,139078,40,2102,139163,0,2102,140888,3,2419,140900,4,2564,140994,5,2703,140994,1,2703,140994,50,2703,140994,40,2703,141079,0,2703,168889,3,4205,169804,4,4954,170465,5,5704,170466,1,5704,170466,50,5705,170466,40,5705,170551,0,5705,188213,3,6456,188820,4,6831,189205,1,7206,189205,50,7206,189205,40,7206,189290,0,7206,205470,3,7970,206438,4,8332,208010,5,8707,208011,5,8707,208011,1,8707,208011,50,8707,208011,40,8707,208096,0,8707,255440,3,12614,256950,4,14558,257782,5,16508,257783,1,16508,257783,50,16510,257783,40,16510,257868,0,16510,300321,3,19067,301502,4,20336,302073,1,21611,302073,50,21612,302073,40,21612,302158,0,21612,334659,3,23113,335619,4,23863,336596,1,24613,336596,50,24614,336596,40,24614,336681,0,24614,354303,3,25378,355198,4,25740,357242,5,26115,357243,1,26115,357243,50,26115,357243,40,26115,357328,0,26115,379495,3,27316,380524,4,27916,381211,5,28516,381212,1,28516,381212,50,28517,381212,40,28517,381297,0,28517,396649,3,29268,397620,4,29643,398390,1,30018,398390,50,30018,398390,40,30018,398390,40,30018,398539,0,30018,400676,50,30027,400676,30,30027,400676,40,30027,400751,0,30027,400812,50,30027,400812,30,30027,400812,40,30027,400887,0,30032,400973,50,30032,400973,30,30032,400973,40,30032,401048,0,30032,401230,50,30034,401305,0,30038,401552,50,30042,401627,0,30042,401882,50,30049,401957,0,30053,402220,50,30062,402295,0,30062,402564,50,30074,402639,0,30079,402916,50,30099,402991,0,30099,403276,50,30135,403351,0,30139,403646,50,30207,403721,0,30207,404026,50,30342,404026,40,30342,404101,0,30342,404741,50,30343,404741,30,30343,404741,40,30343,404816,0,30343)
%
%
% START OF PROOF
% 404742 [] equal(X,X).
% 404746 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 404783 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c5),sk_c11).
% 404784 [?] ?
% 404793 [?] ?
% 404794 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(multiply(sk_c5,sk_c11),sk_c10).
% 404842 [hyper:404746,404783,binarycut:404793] equal(inverse(sk_c5),sk_c11).
% 404844 [hyper:404746,404783,binarycut:404784] equal(inverse(sk_c2),sk_c11).
% 404876 [hyper:404746,404794,demod:404844,cut:404742] equal(multiply(sk_c5,sk_c11),sk_c10).
% 404878 [hyper:404746,404876,demod:404842,cut:404742] 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 33
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(sk_c10,sk_c12),sk_c11) | -equal(multiply(Z,sk_c10),sk_c12) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12).
% 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 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,0,160,0,0,128098,5,1501,128098,1,1501,128098,50,1501,128098,40,1501,128183,0,1501,137261,3,1803,138226,4,1952,139078,1,2102,139078,50,2102,139078,40,2102,139163,0,2102,140888,3,2419,140900,4,2564,140994,5,2703,140994,1,2703,140994,50,2703,140994,40,2703,141079,0,2703,168889,3,4205,169804,4,4954,170465,5,5704,170466,1,5704,170466,50,5705,170466,40,5705,170551,0,5705,188213,3,6456,188820,4,6831,189205,1,7206,189205,50,7206,189205,40,7206,189290,0,7206,205470,3,7970,206438,4,8332,208010,5,8707,208011,5,8707,208011,1,8707,208011,50,8707,208011,40,8707,208096,0,8707,255440,3,12614,256950,4,14558,257782,5,16508,257783,1,16508,257783,50,16510,257783,40,16510,257868,0,16510,300321,3,19067,301502,4,20336,302073,1,21611,302073,50,21612,302073,40,21612,302158,0,21612,334659,3,23113,335619,4,23863,336596,1,24613,336596,50,24614,336596,40,24614,336681,0,24614,354303,3,25378,355198,4,25740,357242,5,26115,357243,1,26115,357243,50,26115,357243,40,26115,357328,0,26115,379495,3,27316,380524,4,27916,381211,5,28516,381212,1,28516,381212,50,28517,381212,40,28517,381297,0,28517,396649,3,29268,397620,4,29643,398390,1,30018,398390,50,30018,398390,40,30018,398390,40,30018,398539,0,30018,400676,50,30027,400676,30,30027,400676,40,30027,400751,0,30027,400812,50,30027,400812,30,30027,400812,40,30027,400887,0,30032,400973,50,30032,400973,30,30032,400973,40,30032,401048,0,30032,401230,50,30034,401305,0,30038,401552,50,30042,401627,0,30042,401882,50,30049,401957,0,30053,402220,50,30062,402295,0,30062,402564,50,30074,402639,0,30079,402916,50,30099,402991,0,30099,403276,50,30135,403351,0,30139,403646,50,30207,403721,0,30207,404026,50,30342,404026,40,30342,404101,0,30342,404741,50,30343,404741,30,30343,404741,40,30343,404816,0,30343,404877,50,30344,404877,30,30344,404877,40,30344,404952,0,30349)
%
%
% START OF PROOF
% 404878 [] equal(X,X).
% 404882 [] -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12).
% 404941 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 404942 [?] ?
% 404951 [?] ?
% 404952 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 404993 [hyper:404882,404941,binarycut:404951] equal(inverse(sk_c4),sk_c12).
% 404995 [hyper:404882,404941,binarycut:404942] equal(inverse(sk_c1),sk_c12).
% 405037 [hyper:404882,404952,demod:404995,cut:404878] equal(multiply(sk_c4,sk_c12),sk_c11).
% 405039 [hyper:404882,405037,demod:404993,cut:404878] 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 33
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(sk_c10,sk_c12),sk_c11) | -equal(multiply(Z,sk_c10),sk_c12) | -equal(inverse(Z),sk_c10) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(sk_c10,sk_c12),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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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(75,40,0,160,0,0,128098,5,1501,128098,1,1501,128098,50,1501,128098,40,1501,128183,0,1501,137261,3,1803,138226,4,1952,139078,1,2102,139078,50,2102,139078,40,2102,139163,0,2102,140888,3,2419,140900,4,2564,140994,5,2703,140994,1,2703,140994,50,2703,140994,40,2703,141079,0,2703,168889,3,4205,169804,4,4954,170465,5,5704,170466,1,5704,170466,50,5705,170466,40,5705,170551,0,5705,188213,3,6456,188820,4,6831,189205,1,7206,189205,50,7206,189205,40,7206,189290,0,7206,205470,3,7970,206438,4,8332,208010,5,8707,208011,5,8707,208011,1,8707,208011,50,8707,208011,40,8707,208096,0,8707,255440,3,12614,256950,4,14558,257782,5,16508,257783,1,16508,257783,50,16510,257783,40,16510,257868,0,16510,300321,3,19067,301502,4,20336,302073,1,21611,302073,50,21612,302073,40,21612,302158,0,21612,334659,3,23113,335619,4,23863,336596,1,24613,336596,50,24614,336596,40,24614,336681,0,24614,354303,3,25378,355198,4,25740,357242,5,26115,357243,1,26115,357243,50,26115,357243,40,26115,357328,0,26115,379495,3,27316,380524,4,27916,381211,5,28516,381212,1,28516,381212,50,28517,381212,40,28517,381297,0,28517,396649,3,29268,397620,4,29643,398390,1,30018,398390,50,30018,398390,40,30018,398390,40,30018,398539,0,30018,400676,50,30027,400676,30,30027,400676,40,30027,400751,0,30027,400812,50,30027,400812,30,30027,400812,40,30027,400887,0,30032,400973,50,30032,400973,30,30032,400973,40,30032,401048,0,30032,401230,50,30034,401305,0,30038,401552,50,30042,401627,0,30042,401882,50,30049,401957,0,30053,402220,50,30062,402295,0,30062,402564,50,30074,402639,0,30079,402916,50,30099,402991,0,30099,403276,50,30135,403351,0,30139,403646,50,30207,403721,0,30207,404026,50,30342,404026,40,30342,404101,0,30342,404741,50,30343,404741,30,30343,404741,40,30343,404816,0,30343,404877,50,30344,404877,30,30344,404877,40,30344,404952,0,30349,405038,50,30349,405038,30,30349,405038,40,30349,405113,0,30349,405341,50,30351,405416,0,30355,405703,50,30361,405778,0,30361,406073,50,30368,406148,0,30373,406451,50,30383,406526,0,30383,406835,50,30396,406910,0,30400,407227,50,30422,407302,0,30422,407627,50,30459,407702,0,30463,408037,50,30533,408112,0,30533,408457,50,30671,408457,40,30671,408532,0,30671)
%
%
% START OF PROOF
% 408459 [] equal(multiply(identity,X),X).
% 408460 [] equal(multiply(inverse(X),X),identity).
% 408461 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 408462 [] -equal(multiply(sk_c10,sk_c12),sk_c11).
% 408484 [?] ?
% 408485 [?] ?
% 408487 [?] ?
% 408488 [?] ?
% 408489 [?] ?
% 408490 [?] ?
% 408491 [?] ?
% 408492 [?] ?
% 408599 [input:408484,cut:408462] equal(inverse(sk_c7),sk_c9).
% 408600 [para:408599.1.1,408460.1.1.1] equal(multiply(sk_c9,sk_c7),identity).
% 408601 [input:408485,cut:408462] equal(inverse(sk_c8),sk_c7).
% 408602 [para:408601.1.1,408460.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 408603 [input:408487,cut:408462] equal(inverse(sk_c6),sk_c9).
% 408604 [para:408603.1.1,408460.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 408606 [input:408489,cut:408462] equal(inverse(sk_c5),sk_c11).
% 408607 [para:408606.1.1,408460.1.1.1] equal(multiply(sk_c11,sk_c5),identity).
% 408609 [input:408491,cut:408462] equal(inverse(sk_c4),sk_c12).
% 408610 [para:408609.1.1,408460.1.1.1] equal(multiply(sk_c12,sk_c4),identity).
% 408644 [input:408488,cut:408462] equal(multiply(sk_c6,sk_c9),sk_c12).
% 408648 [input:408490,cut:408462] equal(multiply(sk_c5,sk_c11),sk_c10).
% 408652 [input:408492,cut:408462] equal(multiply(sk_c4,sk_c12),sk_c11).
% 408690 [para:408600.1.1,408461.1.1.1,demod:408459] equal(X,multiply(sk_c9,multiply(sk_c7,X))).
% 408691 [para:408602.1.1,408461.1.1.1,demod:408459] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 408695 [para:408607.1.1,408461.1.1.1,demod:408459] equal(X,multiply(sk_c11,multiply(sk_c5,X))).
% 408700 [para:408610.1.1,408461.1.1.1,demod:408459] equal(X,multiply(sk_c12,multiply(sk_c4,X))).
% 408723 [para:408644.1.1,408461.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c6,multiply(sk_c9,X))).
% 408756 [para:408602.1.1,408690.1.2.2] equal(sk_c8,multiply(sk_c9,identity)).
% 408757 [para:408756.1.2,408461.1.1.1,demod:408459] equal(multiply(sk_c8,X),multiply(sk_c9,X)).
% 408778 [para:408648.1.1,408695.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 408784 [para:408652.1.1,408700.1.2.2] equal(sk_c12,multiply(sk_c12,sk_c11)).
% 408786 [para:408757.1.1,408691.1.2.2] equal(X,multiply(sk_c7,multiply(sk_c9,X))).
% 408788 [para:408600.1.1,408786.1.2.2] equal(sk_c7,multiply(sk_c7,identity)).
% 408790 [para:408604.1.1,408786.1.2.2,demod:408788] equal(sk_c6,sk_c7).
% 408798 [para:408790.1.2,408691.1.2.1,demod:408723,408757] equal(X,multiply(sk_c12,X)).
% 408806 [para:408798.1.2,408700.1.2] equal(X,multiply(sk_c4,X)).
% 408807 [para:408798.1.2,408784.1.2] equal(sk_c12,sk_c11).
% 408827 [para:408807.1.1,408700.1.2.1,demod:408806] equal(X,multiply(sk_c11,X)).
% 408835 [para:408827.1.2,408778.1.2] equal(sk_c11,sk_c10).
% 408837 [para:408835.1.2,408462.1.1.1,demod:408827,cut:408807] 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: 40196
% derived clauses: 3927409
% kept clauses: 220279
% kept size sum: 38303
% kept mid-nuclei: 124785
% kept new demods: 5030
% forw unit-subs: 1347248
% forw double-subs: 1995532
% forw overdouble-subs: 184171
% backward subs: 23923
% fast unit cutoff: 35527
% full unit cutoff: 0
% dbl unit cutoff: 20394
% real runtime : 308.31
% process. runtime: 306.72
% specific non-discr-tree subsumption statistics:
% tried: 24334213
% length fails: 3122576
% strength fails: 7480561
% predlist fails: 1548850
% aux str. fails: 2057966
% by-lit fails: 3779726
% full subs tried: 2646122
% full subs fail: 2526198
%
% ; 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/GRP258-1+eq_r.in")
%
%------------------------------------------------------------------------------