TSTP Solution File: GRP307-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP307-1 : 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 308.5s
% Output : Assurance 308.5s
% 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/GRP307-1+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 31)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 31)
% (binary-posweight-lex-big-order 30 #f 3 31)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c11,sk_c10),sk_c9) | -equal(inverse(sk_c11),sk_c9) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -equal(multiply(sk_c11,X),sk_c10) | -equal(multiply(Y,sk_c11),X) | -equal(inverse(Y),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(sk_c11,X),sk_c10) | -equal(multiply(Y,sk_c11),X) | -equal(inverse(Y),sk_c11).
% -equal(multiply(sk_c11,sk_c10),sk_c9).
% -equal(inverse(sk_c11),sk_c9).
% -equal(multiply(sk_c9,sk_c10),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(sk_c11,sk_c10),sk_c9) | -equal(inverse(sk_c11),sk_c9) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -equal(multiply(sk_c11,X),sk_c10) | -equal(multiply(Y,sk_c11),X) | -equal(inverse(Y),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(65,40,1,138,0,1,110077,5,1502,110078,1,1502,110078,50,1502,110078,40,1502,110151,0,1502,110740,5,2104,110741,1,2105,110741,50,2105,110741,40,2105,110814,0,2105,111418,5,2706,111421,1,2706,111421,50,2706,111421,40,2706,111494,0,2706,136332,3,4214,137395,4,4957,138331,5,5707,138332,1,5707,138332,50,5708,138332,40,5708,138405,0,5708,154936,3,6459,155634,4,6834,156104,1,7209,156104,50,7209,156104,40,7209,156177,0,7209,157003,5,8713,157004,1,8713,157004,50,8713,157004,40,8713,157077,0,8713,214535,3,12616,215660,4,14564,216500,1,16514,216500,50,16516,216500,40,16516,216573,0,16516,263221,3,19080,264139,4,20342,264813,1,21617,264813,50,21619,264813,40,21619,264886,0,21619,303246,3,23120,303786,4,23870,304486,5,24620,304487,1,24620,304487,50,24621,304487,40,24621,304560,0,24622,305395,5,26126,305396,1,26126,305396,50,26126,305396,40,26126,305469,0,26126,329381,3,27329,330115,4,27927,330647,1,28527,330647,50,28528,330647,40,28528,330720,0,28528,346658,3,29279,347224,4,29654,347802,1,30029,347802,50,30029,347802,40,30029,347802,40,30029,347931,0,30029)
%
%
% START OF PROOF
% 347804 [] equal(multiply(identity,X),X).
% 347805 [] equal(multiply(inverse(X),X),identity).
% 347806 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 347867 [] -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).
% 347868 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst85,Y).
% 347869 [] -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | $spltprd1($spltcnst86,Y).
% 347870 [] -equal(multiply(X,sk_c10),sk_c11) | $spltprd1($spltcnst87,X).
% 347871 [] -$spltprd1($spltcnst86,X) | -$spltprd1($spltcnst85,X) | -$spltprd1($spltcnst87,X).
% 347872 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c11).
% 347873 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 347874 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 347875 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 347876 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 347877 [?] ?
% 347882 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 347883 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(inverse(sk_c6),sk_c8).
% 347884 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(inverse(sk_c7),sk_c6).
% 347885 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 347886 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 347887 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 347892 [] equal(multiply(sk_c11,sk_c2),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 347893 [] equal(multiply(sk_c11,sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 347894 [] equal(multiply(sk_c11,sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 347895 [] equal(multiply(sk_c11,sk_c2),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 347896 [] equal(multiply(sk_c11,sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 347897 [] equal(multiply(sk_c11,sk_c2),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 347902 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 347903 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 347904 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 347905 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 347906 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 347907 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 347912 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c11),sk_c9).
% 347913 [] equal(inverse(sk_c11),sk_c9) | equal(inverse(sk_c6),sk_c8).
% 347914 [] equal(inverse(sk_c11),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 347915 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c11),sk_c9).
% 347916 [] equal(inverse(sk_c11),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 347917 [?] ?
% 347922 [] equal(multiply(sk_c11,sk_c10),sk_c9) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 347923 [] equal(multiply(sk_c11,sk_c10),sk_c9) | equal(inverse(sk_c6),sk_c8).
% 347924 [] equal(multiply(sk_c11,sk_c10),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 347925 [] equal(multiply(sk_c11,sk_c10),sk_c9) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 347926 [] equal(multiply(sk_c11,sk_c10),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 347927 [] equal(multiply(sk_c11,sk_c10),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 347998 [hyper:347869,347876,binarycut:347877] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst86,sk_c8).
% 348092 [hyper:347869,347916,binarycut:347917] equal(inverse(sk_c11),sk_c9) | $spltprd1($spltcnst86,sk_c8).
% 348158 [hyper:347868,347872,347873,347874] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst85,sk_c8).
% 348187 [hyper:347870,347875] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst87,sk_c8).
% 348198 [hyper:347871,348187,348158,347998] equal(inverse(sk_c1),sk_c11).
% 348205 [para:348198.1.1,347805.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 348487 [hyper:347868,347912,347913,347914] equal(inverse(sk_c11),sk_c9) | $spltprd1($spltcnst85,sk_c8).
% 348531 [hyper:347870,347915] equal(inverse(sk_c11),sk_c9) | $spltprd1($spltcnst87,sk_c8).
% 348552 [hyper:347871,348531,348487,348092] equal(inverse(sk_c11),sk_c9).
% 348569 [para:348552.1.1,347805.1.1.1] equal(multiply(sk_c9,sk_c11),identity).
% 348765 [hyper:347867,347887,347885,347886,347883,347882,347884] equal(multiply(sk_c1,sk_c11),sk_c2).
% 349026 [hyper:347867,347897,347895,347896,347893,347892,347894] equal(multiply(sk_c11,sk_c2),sk_c10).
% 349216 [hyper:347867,347907,347905,347906,347903,347902,347904] equal(multiply(sk_c9,sk_c10),sk_c11).
% 349304 [hyper:347867,347927,347925,347926,347923,347922,347924] equal(multiply(sk_c11,sk_c10),sk_c9).
% 349313 [para:348205.1.1,347806.1.1.1,demod:347804] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 349331 [para:348765.1.1,349313.1.2.2,demod:349026] equal(sk_c11,sk_c10).
% 349337 [para:349331.1.1,348552.1.1.1] equal(inverse(sk_c10),sk_c9).
% 349338 [para:349331.1.1,348569.1.1.2,demod:349216] equal(sk_c11,identity).
% 349343 [para:349338.1.1,348205.1.1.1,demod:347804] equal(sk_c1,identity).
% 349344 [para:349338.1.1,348552.1.1.1] equal(inverse(identity),sk_c9).
% 349349 [para:349338.1.1,349313.1.2.1,demod:347804] equal(X,multiply(sk_c1,X)).
% 349350 [para:349338.1.1,349331.1.1] equal(identity,sk_c10).
% 349352 [para:349343.1.1,348198.1.1.1,demod:349344] equal(sk_c9,sk_c11).
% 349353 [para:349343.1.1,348205.1.1.2] equal(multiply(sk_c11,identity),identity).
% 349360 [para:349350.1.2,349304.1.1.2,demod:349353] equal(identity,sk_c9).
% 349365 [para:349352.1.2,348552.1.1.1] equal(inverse(sk_c9),sk_c9).
% 349367 [para:349352.1.2,349304.1.1.1,demod:349216] equal(sk_c11,sk_c9).
% 349376 [para:349360.1.2,349216.1.1.1,demod:347804] equal(sk_c10,sk_c11).
% 349380 [para:349376.1.2,349313.1.2.1,demod:349349] equal(X,multiply(sk_c10,X)).
% 349390 [hyper:347867,349337,347804,demod:349365,349380,demod:349344,349304,cut:349352,cut:349352,cut:349352,cut:349367] 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c11,sk_c10),sk_c9) | -equal(inverse(sk_c11),sk_c9) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -equal(multiply(sk_c11,X),sk_c10) | -equal(multiply(Y,sk_c11),X) | -equal(inverse(Y),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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,1,138,0,1,110077,5,1502,110078,1,1502,110078,50,1502,110078,40,1502,110151,0,1502,110740,5,2104,110741,1,2105,110741,50,2105,110741,40,2105,110814,0,2105,111418,5,2706,111421,1,2706,111421,50,2706,111421,40,2706,111494,0,2706,136332,3,4214,137395,4,4957,138331,5,5707,138332,1,5707,138332,50,5708,138332,40,5708,138405,0,5708,154936,3,6459,155634,4,6834,156104,1,7209,156104,50,7209,156104,40,7209,156177,0,7209,157003,5,8713,157004,1,8713,157004,50,8713,157004,40,8713,157077,0,8713,214535,3,12616,215660,4,14564,216500,1,16514,216500,50,16516,216500,40,16516,216573,0,16516,263221,3,19080,264139,4,20342,264813,1,21617,264813,50,21619,264813,40,21619,264886,0,21619,303246,3,23120,303786,4,23870,304486,5,24620,304487,1,24620,304487,50,24621,304487,40,24621,304560,0,24622,305395,5,26126,305396,1,26126,305396,50,26126,305396,40,26126,305469,0,26126,329381,3,27329,330115,4,27927,330647,1,28527,330647,50,28528,330647,40,28528,330720,0,28528,346658,3,29279,347224,4,29654,347802,1,30029,347802,50,30029,347802,40,30029,347802,40,30029,347931,0,30029,349389,50,30034,349389,30,30034,349389,40,30034,349454,0,30034)
%
%
% START OF PROOF
% 349391 [] equal(multiply(identity,X),X).
% 349392 [] equal(multiply(inverse(X),X),identity).
% 349393 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 349394 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 349401 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 349402 [?] ?
% 349411 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(inverse(sk_c4),sk_c10).
% 349412 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 349421 [] equal(multiply(sk_c11,sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 349422 [] equal(multiply(sk_c11,sk_c2),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 349431 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 349432 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 349441 [] equal(inverse(sk_c11),sk_c9) | equal(inverse(sk_c4),sk_c10).
% 349442 [?] ?
% 349451 [] equal(multiply(sk_c11,sk_c10),sk_c9) | equal(inverse(sk_c4),sk_c10).
% 349452 [] equal(multiply(sk_c11,sk_c10),sk_c9) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 349461 [hyper:349394,349401,binarycut:349402] equal(inverse(sk_c1),sk_c11).
% 349462 [para:349461.1.1,349392.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 349469 [hyper:349394,349441,binarycut:349442] equal(inverse(sk_c11),sk_c9).
% 349470 [para:349469.1.1,349392.1.1.1] equal(multiply(sk_c9,sk_c11),identity).
% 349495 [hyper:349394,349412,349411] equal(multiply(sk_c1,sk_c11),sk_c2).
% 349519 [hyper:349394,349422,349421] equal(multiply(sk_c11,sk_c2),sk_c10).
% 349525 [hyper:349394,349432,349431] equal(multiply(sk_c9,sk_c10),sk_c11).
% 349538 [hyper:349394,349452,349451] equal(multiply(sk_c11,sk_c10),sk_c9).
% 349541 [para:349462.1.1,349393.1.1.1,demod:349391] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 349549 [para:349495.1.1,349541.1.2.2,demod:349519] equal(sk_c11,sk_c10).
% 349551 [para:349549.1.1,349469.1.1.1] equal(inverse(sk_c10),sk_c9).
% 349552 [para:349549.1.1,349470.1.1.2,demod:349525] equal(sk_c11,identity).
% 349555 [para:349549.1.1,349538.1.1.1] equal(multiply(sk_c10,sk_c10),sk_c9).
% 349557 [para:349552.1.1,349462.1.1.1,demod:349391] equal(sk_c1,identity).
% 349558 [para:349552.1.1,349469.1.1.1] equal(inverse(identity),sk_c9).
% 349566 [para:349557.1.1,349461.1.1.1,demod:349558] equal(sk_c9,sk_c11).
% 349590 [para:349566.1.2,349549.1.1] equal(sk_c9,sk_c10).
% 349594 [hyper:349394,349555,demod:349551,cut:349590] 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c11,sk_c10),sk_c9) | -equal(inverse(sk_c11),sk_c9) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -equal(multiply(sk_c11,X),sk_c10) | -equal(multiply(Y,sk_c11),X) | -equal(inverse(Y),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 31
% 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 31
% 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 31
% clause depth limited to 5
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,1,138,0,1,110077,5,1502,110078,1,1502,110078,50,1502,110078,40,1502,110151,0,1502,110740,5,2104,110741,1,2105,110741,50,2105,110741,40,2105,110814,0,2105,111418,5,2706,111421,1,2706,111421,50,2706,111421,40,2706,111494,0,2706,136332,3,4214,137395,4,4957,138331,5,5707,138332,1,5707,138332,50,5708,138332,40,5708,138405,0,5708,154936,3,6459,155634,4,6834,156104,1,7209,156104,50,7209,156104,40,7209,156177,0,7209,157003,5,8713,157004,1,8713,157004,50,8713,157004,40,8713,157077,0,8713,214535,3,12616,215660,4,14564,216500,1,16514,216500,50,16516,216500,40,16516,216573,0,16516,263221,3,19080,264139,4,20342,264813,1,21617,264813,50,21619,264813,40,21619,264886,0,21619,303246,3,23120,303786,4,23870,304486,5,24620,304487,1,24620,304487,50,24621,304487,40,24621,304560,0,24622,305395,5,26126,305396,1,26126,305396,50,26126,305396,40,26126,305469,0,26126,329381,3,27329,330115,4,27927,330647,1,28527,330647,50,28528,330647,40,28528,330720,0,28528,346658,3,29279,347224,4,29654,347802,1,30029,347802,50,30029,347802,40,30029,347802,40,30029,347931,0,30029,349389,50,30034,349389,30,30034,349389,40,30034,349454,0,30034,349593,50,30034,349593,30,30034,349593,40,30034,349658,0,30039,349795,50,30039,349860,0,30039,350006,50,30039,350071,0,30044)
%
%
% START OF PROOF
% 350008 [] equal(multiply(identity,X),X).
% 350009 [] equal(multiply(inverse(X),X),identity).
% 350010 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 350011 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 350020 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 350021 [?] ?
% 350030 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(inverse(sk_c3),sk_c11).
% 350031 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 350040 [] equal(multiply(sk_c11,sk_c2),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 350041 [] equal(multiply(sk_c11,sk_c2),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 350050 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 350051 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 350060 [] equal(inverse(sk_c11),sk_c9) | equal(inverse(sk_c3),sk_c11).
% 350061 [?] ?
% 350086 [hyper:350011,350020,binarycut:350021] equal(inverse(sk_c1),sk_c11).
% 350089 [para:350086.1.1,350009.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 350098 [hyper:350011,350060,binarycut:350061] equal(inverse(sk_c11),sk_c9).
% 350099 [para:350098.1.1,350009.1.1.1] equal(multiply(sk_c9,sk_c11),identity).
% 350123 [hyper:350011,350031,350030] equal(multiply(sk_c1,sk_c11),sk_c2).
% 350140 [hyper:350011,350041,350040] equal(multiply(sk_c11,sk_c2),sk_c10).
% 350147 [hyper:350011,350051,350050] equal(multiply(sk_c9,sk_c10),sk_c11).
% 350155 [para:350009.1.1,350010.1.1.1,demod:350008] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 350156 [para:350089.1.1,350010.1.1.1,demod:350008] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 350157 [para:350099.1.1,350010.1.1.1,demod:350008] equal(X,multiply(sk_c9,multiply(sk_c11,X))).
% 350162 [para:350123.1.1,350156.1.2.2,demod:350140] equal(sk_c11,sk_c10).
% 350164 [para:350162.1.1,350098.1.1.1] equal(inverse(sk_c10),sk_c9).
% 350165 [para:350162.1.1,350099.1.1.2,demod:350147] equal(sk_c11,identity).
% 350170 [para:350165.1.1,350089.1.1.1,demod:350008] equal(sk_c1,identity).
% 350171 [para:350165.1.1,350098.1.1.1] equal(inverse(identity),sk_c9).
% 350179 [para:350170.1.1,350086.1.1.1,demod:350171] equal(sk_c9,sk_c11).
% 350183 [para:350008.1.1,350155.1.2.2,demod:350171] equal(X,multiply(sk_c9,X)).
% 350184 [para:350009.1.1,350155.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 350189 [para:350155.1.2,350155.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 350212 [para:350189.1.2,350009.1.1] equal(multiply(X,inverse(X)),identity).
% 350214 [para:350189.1.2,350184.1.2] equal(X,multiply(X,identity)).
% 350216 [para:350214.1.2,350184.1.2] equal(X,inverse(inverse(X))).
% 350218 [para:350212.1.1,350010.1.1] equal(identity,multiply(X,multiply(Y,inverse(multiply(X,Y))))).
% 350219 [para:350218.1.2,350155.1.2.2,demod:350214] equal(multiply(X,inverse(multiply(Y,X))),inverse(Y)).
% 350231 [para:350219.1.1,350157.1.2.2,demod:350183] equal(inverse(multiply(X,sk_c11)),inverse(X)).
% 350244 [para:350231.1.1,350184.1.2.1.1,demod:350214,350216] equal(multiply(X,sk_c11),X).
% 350245 [hyper:350011,350244,demod:350164,cut:350179] 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 31
% clause depth limited to 5
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c11,sk_c10),sk_c9) | -equal(inverse(sk_c11),sk_c9) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -equal(multiply(sk_c11,X),sk_c10) | -equal(multiply(Y,sk_c11),X) | -equal(inverse(Y),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_c11,X),sk_c10) | -equal(multiply(Y,sk_c11),X) | -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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,1,138,0,1,110077,5,1502,110078,1,1502,110078,50,1502,110078,40,1502,110151,0,1502,110740,5,2104,110741,1,2105,110741,50,2105,110741,40,2105,110814,0,2105,111418,5,2706,111421,1,2706,111421,50,2706,111421,40,2706,111494,0,2706,136332,3,4214,137395,4,4957,138331,5,5707,138332,1,5707,138332,50,5708,138332,40,5708,138405,0,5708,154936,3,6459,155634,4,6834,156104,1,7209,156104,50,7209,156104,40,7209,156177,0,7209,157003,5,8713,157004,1,8713,157004,50,8713,157004,40,8713,157077,0,8713,214535,3,12616,215660,4,14564,216500,1,16514,216500,50,16516,216500,40,16516,216573,0,16516,263221,3,19080,264139,4,20342,264813,1,21617,264813,50,21619,264813,40,21619,264886,0,21619,303246,3,23120,303786,4,23870,304486,5,24620,304487,1,24620,304487,50,24621,304487,40,24621,304560,0,24622,305395,5,26126,305396,1,26126,305396,50,26126,305396,40,26126,305469,0,26126,329381,3,27329,330115,4,27927,330647,1,28527,330647,50,28528,330647,40,28528,330720,0,28528,346658,3,29279,347224,4,29654,347802,1,30029,347802,50,30029,347802,40,30029,347802,40,30029,347931,0,30029,349389,50,30034,349389,30,30034,349389,40,30034,349454,0,30034,349593,50,30034,349593,30,30034,349593,40,30034,349658,0,30039,349795,50,30039,349860,0,30039,350006,50,30039,350071,0,30044,350244,50,30044,350244,30,30044,350244,40,30044,350309,0,30045)
%
%
% START OF PROOF
% 350245 [] equal(X,X).
% 350246 [] equal(multiply(identity,X),X).
% 350247 [] equal(multiply(inverse(X),X),identity).
% 350248 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 350249 [] -equal(multiply(sk_c11,X),sk_c10) | -equal(multiply(Y,sk_c11),X) | -equal(inverse(Y),sk_c11).
% 350251 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 350252 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 350254 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 350255 [] equal(multiply(sk_c5,sk_c8),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 350258 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 350259 [] equal(multiply(sk_c3,sk_c11),sk_c10) | equal(inverse(sk_c1),sk_c11).
% 350261 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(inverse(sk_c6),sk_c8).
% 350262 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(inverse(sk_c7),sk_c6).
% 350264 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 350265 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 350268 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(inverse(sk_c3),sk_c11).
% 350269 [] equal(multiply(sk_c1,sk_c11),sk_c2) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 350271 [?] ?
% 350272 [?] ?
% 350274 [?] ?
% 350275 [?] ?
% 350278 [?] ?
% 350279 [?] ?
% 350377 [hyper:350249,350261,binarycut:350271,binarycut:350251] equal(inverse(sk_c6),sk_c8).
% 350378 [para:350377.1.1,350247.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 350381 [hyper:350249,350262,binarycut:350272,binarycut:350252] equal(inverse(sk_c7),sk_c6).
% 350389 [para:350381.1.1,350247.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 350392 [hyper:350249,350264,binarycut:350274,binarycut:350254] equal(inverse(sk_c5),sk_c8).
% 350393 [para:350392.1.1,350247.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 350408 [hyper:350249,350265,350255,binarycut:350275] equal(multiply(sk_c5,sk_c8),sk_c11).
% 350411 [hyper:350249,350268,binarycut:350278,binarycut:350258] equal(inverse(sk_c3),sk_c11).
% 350432 [hyper:350249,350269,350259,binarycut:350279] equal(multiply(sk_c3,sk_c11),sk_c10).
% 350436 [para:350378.1.1,350248.1.1.1,demod:350246] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 350438 [para:350389.1.1,350248.1.1.1,demod:350246] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 350442 [para:350408.1.1,350248.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 350450 [para:350389.1.1,350436.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 350451 [para:350450.1.2,350248.1.1.1,demod:350246] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 350470 [para:350451.1.1,350438.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 350473 [para:350378.1.1,350470.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 350474 [para:350393.1.1,350470.1.2.2,demod:350473] equal(sk_c5,sk_c6).
% 350478 [para:350474.1.2,350438.1.2.1,demod:350442,350451] equal(X,multiply(sk_c11,X)).
% 350482 [hyper:350249,350478,350432,demod:350478,demod:350411,cut:350245] 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c11,sk_c10),sk_c9) | -equal(inverse(sk_c11),sk_c9) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -equal(multiply(sk_c11,X),sk_c10) | -equal(multiply(Y,sk_c11),X) | -equal(inverse(Y),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_c11,sk_c10),sk_c9).
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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(65,40,1,138,0,1,110077,5,1502,110078,1,1502,110078,50,1502,110078,40,1502,110151,0,1502,110740,5,2104,110741,1,2105,110741,50,2105,110741,40,2105,110814,0,2105,111418,5,2706,111421,1,2706,111421,50,2706,111421,40,2706,111494,0,2706,136332,3,4214,137395,4,4957,138331,5,5707,138332,1,5707,138332,50,5708,138332,40,5708,138405,0,5708,154936,3,6459,155634,4,6834,156104,1,7209,156104,50,7209,156104,40,7209,156177,0,7209,157003,5,8713,157004,1,8713,157004,50,8713,157004,40,8713,157077,0,8713,214535,3,12616,215660,4,14564,216500,1,16514,216500,50,16516,216500,40,16516,216573,0,16516,263221,3,19080,264139,4,20342,264813,1,21617,264813,50,21619,264813,40,21619,264886,0,21619,303246,3,23120,303786,4,23870,304486,5,24620,304487,1,24620,304487,50,24621,304487,40,24621,304560,0,24622,305395,5,26126,305396,1,26126,305396,50,26126,305396,40,26126,305469,0,26126,329381,3,27329,330115,4,27927,330647,1,28527,330647,50,28528,330647,40,28528,330720,0,28528,346658,3,29279,347224,4,29654,347802,1,30029,347802,50,30029,347802,40,30029,347802,40,30029,347931,0,30029,349389,50,30034,349389,30,30034,349389,40,30034,349454,0,30034,349593,50,30034,349593,30,30034,349593,40,30034,349658,0,30039,349795,50,30039,349860,0,30039,350006,50,30039,350071,0,30044,350244,50,30044,350244,30,30044,350244,40,30044,350309,0,30045,350481,50,30045,350481,30,30045,350481,40,30046,350546,0,30050,350760,50,30052,350825,0,30052,351123,50,30057,351188,0,30062,351499,50,30067,351564,0,30067,351888,50,30075,351953,0,30079,352283,50,30090,352348,0,30090,352686,50,30108,352751,0,30112,353097,50,30144,353162,0,30144,353518,50,30211,353583,0,30211,353949,50,30334,353949,40,30334,354014,0,30334)
%
%
% START OF PROOF
% 353795 [?] ?
% 353951 [] equal(multiply(identity,X),X).
% 353952 [] equal(multiply(inverse(X),X),identity).
% 353953 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 353954 [] -equal(multiply(sk_c11,sk_c10),sk_c9).
% 354013 [?] ?
% 354014 [?] ?
% 354110 [input:354013,cut:353954] equal(inverse(sk_c3),sk_c11).
% 354111 [para:354110.1.1,353952.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 354134 [input:354014,cut:353954] equal(multiply(sk_c3,sk_c11),sk_c10).
% 354179 [para:354111.1.1,353953.1.1.1,demod:353951] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 354243 [para:354134.1.1,354179.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 354246 [para:354243.1.2,353954.1.1,cut:353795] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c11,sk_c10),sk_c9) | -equal(inverse(sk_c11),sk_c9) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -equal(multiply(sk_c11,X),sk_c10) | -equal(multiply(Y,sk_c11),X) | -equal(inverse(Y),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_c9).
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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(65,40,1,138,0,1,110077,5,1502,110078,1,1502,110078,50,1502,110078,40,1502,110151,0,1502,110740,5,2104,110741,1,2105,110741,50,2105,110741,40,2105,110814,0,2105,111418,5,2706,111421,1,2706,111421,50,2706,111421,40,2706,111494,0,2706,136332,3,4214,137395,4,4957,138331,5,5707,138332,1,5707,138332,50,5708,138332,40,5708,138405,0,5708,154936,3,6459,155634,4,6834,156104,1,7209,156104,50,7209,156104,40,7209,156177,0,7209,157003,5,8713,157004,1,8713,157004,50,8713,157004,40,8713,157077,0,8713,214535,3,12616,215660,4,14564,216500,1,16514,216500,50,16516,216500,40,16516,216573,0,16516,263221,3,19080,264139,4,20342,264813,1,21617,264813,50,21619,264813,40,21619,264886,0,21619,303246,3,23120,303786,4,23870,304486,5,24620,304487,1,24620,304487,50,24621,304487,40,24621,304560,0,24622,305395,5,26126,305396,1,26126,305396,50,26126,305396,40,26126,305469,0,26126,329381,3,27329,330115,4,27927,330647,1,28527,330647,50,28528,330647,40,28528,330720,0,28528,346658,3,29279,347224,4,29654,347802,1,30029,347802,50,30029,347802,40,30029,347802,40,30029,347931,0,30029,349389,50,30034,349389,30,30034,349389,40,30034,349454,0,30034,349593,50,30034,349593,30,30034,349593,40,30034,349658,0,30039,349795,50,30039,349860,0,30039,350006,50,30039,350071,0,30044,350244,50,30044,350244,30,30044,350244,40,30044,350309,0,30045,350481,50,30045,350481,30,30045,350481,40,30046,350546,0,30050,350760,50,30052,350825,0,30052,351123,50,30057,351188,0,30062,351499,50,30067,351564,0,30067,351888,50,30075,351953,0,30079,352283,50,30090,352348,0,30090,352686,50,30108,352751,0,30112,353097,50,30144,353162,0,30144,353518,50,30211,353583,0,30211,353949,50,30334,353949,40,30334,354014,0,30334,354245,50,30335,354245,30,30335,354245,40,30335,354310,0,30335,354524,50,30337,354589,0,30342,354887,50,30347,354952,0,30347,355263,50,30352,355328,0,30356,355652,50,30364,355717,0,30364,356047,50,30374,356112,0,30379,356450,50,30397,356515,0,30397,356861,50,30429,356926,0,30433,357282,50,30495,357347,0,30495,357713,50,30622,357713,40,30622,357778,0,30622)
%
%
% START OF PROOF
% 357715 [] equal(multiply(identity,X),X).
% 357716 [] equal(multiply(inverse(X),X),identity).
% 357717 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 357718 [] -equal(inverse(sk_c11),sk_c9).
% 357759 [?] ?
% 357760 [?] ?
% 357761 [?] ?
% 357762 [?] ?
% 357763 [?] ?
% 357764 [?] ?
% 357765 [?] ?
% 357766 [?] ?
% 357767 [?] ?
% 357768 [?] ?
% 357796 [input:357760,cut:357718] equal(inverse(sk_c6),sk_c8).
% 357797 [para:357796.1.1,357716.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 357800 [input:357761,cut:357718] equal(inverse(sk_c7),sk_c6).
% 357801 [para:357800.1.1,357716.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 357802 [input:357763,cut:357718] equal(inverse(sk_c5),sk_c8).
% 357803 [para:357802.1.1,357716.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 357806 [input:357765,cut:357718] equal(inverse(sk_c4),sk_c10).
% 357807 [para:357806.1.1,357716.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 357808 [input:357767,cut:357718] equal(inverse(sk_c3),sk_c11).
% 357809 [para:357808.1.1,357716.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 357833 [input:357759,cut:357718] equal(multiply(sk_c7,sk_c8),sk_c6).
% 357834 [input:357762,cut:357718] equal(multiply(sk_c8,sk_c10),sk_c11).
% 357835 [input:357764,cut:357718] equal(multiply(sk_c5,sk_c8),sk_c11).
% 357836 [input:357766,cut:357718] equal(multiply(sk_c4,sk_c10),sk_c9).
% 357838 [input:357768,cut:357718] equal(multiply(sk_c3,sk_c11),sk_c10).
% 357867 [para:357797.1.1,357717.1.1.1,demod:357715] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 357868 [para:357801.1.1,357717.1.1.1,demod:357715] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 357869 [para:357803.1.1,357717.1.1.1,demod:357715] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 357871 [para:357807.1.1,357717.1.1.1,demod:357715] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 357872 [para:357809.1.1,357717.1.1.1,demod:357715] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 357900 [para:357835.1.1,357717.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 357930 [para:357801.1.1,357867.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 357931 [para:357930.1.2,357717.1.1.1,demod:357715] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 357934 [para:357833.1.1,357868.1.2.2] equal(sk_c8,multiply(sk_c6,sk_c6)).
% 357939 [para:357934.1.2,357867.1.2.2] equal(sk_c6,multiply(sk_c8,sk_c8)).
% 357943 [para:357835.1.1,357869.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 357947 [para:357836.1.1,357871.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 357953 [para:357838.1.1,357872.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 357964 [para:357931.1.1,357868.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 357966 [para:357797.1.1,357964.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 357967 [para:357803.1.1,357964.1.2.2,demod:357966] equal(sk_c5,sk_c6).
% 357975 [para:357967.1.2,357868.1.2.1,demod:357900,357931] equal(X,multiply(sk_c11,X)).
% 357998 [para:357975.1.2,357872.1.2] equal(X,multiply(sk_c3,X)).
% 357999 [para:357975.1.2,357953.1.2] equal(sk_c11,sk_c10).
% 358027 [para:357999.1.1,357943.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c10)).
% 358029 [para:357999.1.1,357872.1.2.1,demod:357998] equal(X,multiply(sk_c10,X)).
% 358040 [para:358029.1.2,357947.1.2] equal(sk_c10,sk_c9).
% 358050 [para:358040.1.1,357834.1.1.2] equal(multiply(sk_c8,sk_c9),sk_c11).
% 358053 [para:358040.1.1,357953.1.2.2,demod:357975] equal(sk_c11,sk_c9).
% 358065 [para:358053.1.1,357943.1.2.2,demod:358050] equal(sk_c8,sk_c11).
% 358087 [para:358065.1.2,357943.1.2.2,demod:357939] equal(sk_c8,sk_c6).
% 358089 [para:358065.1.2,357953.1.2.1,demod:358027] equal(sk_c11,sk_c8).
% 358091 [para:358065.1.2,358053.1.1] equal(sk_c8,sk_c9).
% 358150 [para:358087.1.2,357796.1.1.1] equal(inverse(sk_c8),sk_c8).
% 358156 [para:358089.1.1,357718.1.1.1,demod:358150,cut:358091] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c11,sk_c10),sk_c9) | -equal(inverse(sk_c11),sk_c9) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -equal(multiply(sk_c11,X),sk_c10) | -equal(multiply(Y,sk_c11),X) | -equal(inverse(Y),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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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(65,40,1,138,0,1,110077,5,1502,110078,1,1502,110078,50,1502,110078,40,1502,110151,0,1502,110740,5,2104,110741,1,2105,110741,50,2105,110741,40,2105,110814,0,2105,111418,5,2706,111421,1,2706,111421,50,2706,111421,40,2706,111494,0,2706,136332,3,4214,137395,4,4957,138331,5,5707,138332,1,5707,138332,50,5708,138332,40,5708,138405,0,5708,154936,3,6459,155634,4,6834,156104,1,7209,156104,50,7209,156104,40,7209,156177,0,7209,157003,5,8713,157004,1,8713,157004,50,8713,157004,40,8713,157077,0,8713,214535,3,12616,215660,4,14564,216500,1,16514,216500,50,16516,216500,40,16516,216573,0,16516,263221,3,19080,264139,4,20342,264813,1,21617,264813,50,21619,264813,40,21619,264886,0,21619,303246,3,23120,303786,4,23870,304486,5,24620,304487,1,24620,304487,50,24621,304487,40,24621,304560,0,24622,305395,5,26126,305396,1,26126,305396,50,26126,305396,40,26126,305469,0,26126,329381,3,27329,330115,4,27927,330647,1,28527,330647,50,28528,330647,40,28528,330720,0,28528,346658,3,29279,347224,4,29654,347802,1,30029,347802,50,30029,347802,40,30029,347802,40,30029,347931,0,30029,349389,50,30034,349389,30,30034,349389,40,30034,349454,0,30034,349593,50,30034,349593,30,30034,349593,40,30034,349658,0,30039,349795,50,30039,349860,0,30039,350006,50,30039,350071,0,30044,350244,50,30044,350244,30,30044,350244,40,30044,350309,0,30045,350481,50,30045,350481,30,30045,350481,40,30046,350546,0,30050,350760,50,30052,350825,0,30052,351123,50,30057,351188,0,30062,351499,50,30067,351564,0,30067,351888,50,30075,351953,0,30079,352283,50,30090,352348,0,30090,352686,50,30108,352751,0,30112,353097,50,30144,353162,0,30144,353518,50,30211,353583,0,30211,353949,50,30334,353949,40,30334,354014,0,30334,354245,50,30335,354245,30,30335,354245,40,30335,354310,0,30335,354524,50,30337,354589,0,30342,354887,50,30347,354952,0,30347,355263,50,30352,355328,0,30356,355652,50,30364,355717,0,30364,356047,50,30374,356112,0,30379,356450,50,30397,356515,0,30397,356861,50,30429,356926,0,30433,357282,50,30495,357347,0,30495,357713,50,30622,357713,40,30622,357778,0,30622,358155,50,30624,358155,30,30624,358155,40,30624,358220,0,30624,358434,50,30626,358499,0,30631,358797,50,30635,358862,0,30635,359173,50,30640,359238,0,30644,359562,50,30652,359627,0,30652,359957,50,30662,360022,0,30667,360360,50,30685,360425,0,30685,360771,50,30717,360836,0,30721,361192,50,30784,361257,0,30784,361623,50,30911,361623,40,30911,361688,0,30911)
%
%
% START OF PROOF
% 361455 [?] ?
% 361625 [] equal(multiply(identity,X),X).
% 361626 [] equal(multiply(inverse(X),X),identity).
% 361627 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 361628 [] -equal(multiply(sk_c9,sk_c10),sk_c11).
% 361660 [?] ?
% 361661 [?] ?
% 361663 [?] ?
% 361664 [?] ?
% 361665 [?] ?
% 361666 [?] ?
% 361667 [?] ?
% 361668 [?] ?
% 361751 [input:361660,cut:361628] equal(inverse(sk_c6),sk_c8).
% 361752 [para:361751.1.1,361626.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 361753 [input:361661,cut:361628] equal(inverse(sk_c7),sk_c6).
% 361754 [para:361753.1.1,361626.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 361756 [input:361663,cut:361628] equal(inverse(sk_c5),sk_c8).
% 361757 [para:361756.1.1,361626.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 361758 [input:361665,cut:361628] equal(inverse(sk_c4),sk_c10).
% 361759 [para:361758.1.1,361626.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 361762 [input:361667,cut:361628] equal(inverse(sk_c3),sk_c11).
% 361763 [para:361762.1.1,361626.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 361796 [input:361664,cut:361628] equal(multiply(sk_c5,sk_c8),sk_c11).
% 361797 [input:361666,cut:361628] equal(multiply(sk_c4,sk_c10),sk_c9).
% 361798 [input:361668,cut:361628] equal(multiply(sk_c3,sk_c11),sk_c10).
% 361824 [para:361752.1.1,361627.1.1.1,demod:361625] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 361825 [para:361754.1.1,361627.1.1.1,demod:361625] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 361831 [para:361759.1.1,361627.1.1.1,demod:361625] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 361834 [para:361763.1.1,361627.1.1.1,demod:361625] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 361867 [para:361796.1.1,361627.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 361875 [para:361754.1.1,361824.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 361876 [para:361875.1.2,361627.1.1.1,demod:361625] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 361897 [para:361797.1.1,361831.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 361903 [para:361798.1.1,361834.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 361916 [para:361876.1.1,361825.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 361919 [para:361752.1.1,361916.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 361920 [para:361757.1.1,361916.1.2.2,demod:361919] equal(sk_c5,sk_c6).
% 361928 [para:361920.1.2,361825.1.2.1,demod:361867,361876] equal(X,multiply(sk_c11,X)).
% 361951 [para:361928.1.2,361834.1.2] equal(X,multiply(sk_c3,X)).
% 361953 [para:361928.1.2,361903.1.2] equal(sk_c11,sk_c10).
% 361995 [para:361953.1.1,361834.1.2.1,demod:361951] equal(X,multiply(sk_c10,X)).
% 362006 [para:361995.1.2,361831.1.2] equal(X,multiply(sk_c4,X)).
% 362007 [para:361995.1.2,361897.1.2] equal(sk_c10,sk_c9).
% 362008 [para:361897.1.2,361995.1.2] equal(sk_c9,sk_c10).
% 362016 [para:362007.1.1,361831.1.2.1,demod:362006] equal(X,multiply(sk_c9,X)).
% 362018 [para:362008.1.2,361628.1.1.2,demod:362016,cut:361455] 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: 33766
% derived clauses: 4550557
% kept clauses: 210877
% kept size sum: 758686
% kept mid-nuclei: 91369
% kept new demods: 6827
% forw unit-subs: 1742425
% forw double-subs: 2208403
% forw overdouble-subs: 215404
% backward subs: 18928
% fast unit cutoff: 29623
% full unit cutoff: 0
% dbl unit cutoff: 25815
% real runtime : 310.94
% process. runtime: 309.12
% specific non-discr-tree subsumption statistics:
% tried: 102527901
% length fails: 16221270
% strength fails: 32258437
% predlist fails: 433553
% aux str. fails: 14421481
% by-lit fails: 19272072
% full subs tried: 5311509
% full subs fail: 5228325
%
% ; 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/GRP307-1+eq_r.in")
%
%------------------------------------------------------------------------------