TSTP Solution File: GRP234-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP234-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art07.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 297.5s
% Output : Assurance 297.5s
% 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/GRP234-1+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 17)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 17)
% (binary-posweight-lex-big-order 30 #f 3 17)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% was split for some strategies as:
% -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7).
% -equal(inverse(sk_c7),sk_c6).
% -equal(multiply(X,sk_c7),sk_c6).
%
% Starting a split proof attempt with 5 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(25,40,0,55,0,0,1835,50,19,1865,0,19,3861,50,41,3891,0,41,5996,50,67,6026,0,67,8189,50,88,8219,0,88,10441,50,109,10471,0,109,12779,50,138,12809,0,138,15203,50,179,15233,0,179,17741,50,251,17771,0,251,20393,50,386,20423,0,386,23187,50,609,23217,0,609,26123,50,1002,26123,40,1002,26153,0,1002,37390,3,1303,38111,4,1453,38752,1,1603,38752,50,1603,38752,40,1603,38782,0,1603,39048,3,1913,39056,4,2055,39064,5,2204,39064,1,2204,39064,50,2204,39064,40,2204,39094,0,2204,64669,3,3714,65753,4,4455,66621,5,5205,66622,1,5205,66622,50,5205,66622,40,5205,66652,0,5206,85954,3,5960,86559,4,6332,87196,1,6707,87196,50,6707,87196,40,6707,87226,0,6707,105894,3,7460,106487,4,7833,107169,5,8208,107170,1,8208,107170,50,8208,107170,40,8208,107200,0,8208,186865,3,12111,187857,4,14059,188122,1,16010,188122,50,16018,188122,40,16018,188152,0,16018,252949,3,18569,253649,4,19845,254161,1,21119,254161,50,21121,254161,40,21121,254191,0,21121,289566,3,22625,290450,4,23372,291134,1,24122,291134,50,24123,291134,40,24123,291164,0,24123,315817,3,24886,316146,4,25249,316382,1,25624,316382,50,25624,316382,40,25624,316412,0,25624,359170,3,26826,359726,4,27425,359858,1,28025,359858,50,28026,359858,40,28026,359888,0,28026,391802,3,28778,392260,4,29152,392438,1,29527,392438,50,29528,392438,40,29528,392438,40,29528,392463,0,29528)
%
%
% START OF PROOF
% 392439 [] equal(X,X).
% 392440 [] equal(multiply(identity,X),X).
% 392441 [] equal(multiply(inverse(X),X),identity).
% 392442 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 392443 [] -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7).
% 392444 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 392445 [] equal(multiply(sk_c4,sk_c7),sk_c5) | equal(inverse(sk_c2),sk_c7).
% 392446 [?] ?
% 392449 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 392450 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c7),sk_c5).
% 392451 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c7,sk_c5),sk_c6).
% 392459 [] equal(inverse(sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 392460 [] equal(multiply(sk_c4,sk_c7),sk_c5) | equal(inverse(sk_c7),sk_c6).
% 392461 [?] ?
% 392491 [hyper:392443,392445,392444,binarycut:392446] equal(inverse(sk_c2),sk_c7).
% 392506 [para:392491.1.1,392441.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 392539 [hyper:392443,392460,392459,binarycut:392461] equal(inverse(sk_c7),sk_c6).
% 392540 [para:392539.1.1,392441.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 392548 [hyper:392443,392451,392450,392449] equal(multiply(sk_c2,sk_c7),sk_c6).
% 392564 [para:392441.1.1,392442.1.1.1,demod:392440] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 392565 [para:392506.1.1,392442.1.1.1,demod:392440] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 392566 [para:392540.1.1,392442.1.1.1,demod:392440] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 392573 [para:392548.1.1,392565.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 392579 [para:392573.1.2,392566.1.2.2,demod:392540] equal(sk_c6,identity).
% 392582 [para:392579.1.1,392566.1.2.1,demod:392440] equal(X,multiply(sk_c7,X)).
% 392584 [hyper:392443,392564,392548,demod:392582,392564,demod:392491,cut:392439] 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 17
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 17
% clause depth limited to 3
% seconds given: 6
%
%
% 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 17
% clause depth limited to 4
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(25,40,0,55,0,0,1835,50,19,1865,0,19,3861,50,41,3891,0,41,5996,50,67,6026,0,67,8189,50,88,8219,0,88,10441,50,109,10471,0,109,12779,50,138,12809,0,138,15203,50,179,15233,0,179,17741,50,251,17771,0,251,20393,50,386,20423,0,386,23187,50,609,23217,0,609,26123,50,1002,26123,40,1002,26153,0,1002,37390,3,1303,38111,4,1453,38752,1,1603,38752,50,1603,38752,40,1603,38782,0,1603,39048,3,1913,39056,4,2055,39064,5,2204,39064,1,2204,39064,50,2204,39064,40,2204,39094,0,2204,64669,3,3714,65753,4,4455,66621,5,5205,66622,1,5205,66622,50,5205,66622,40,5205,66652,0,5206,85954,3,5960,86559,4,6332,87196,1,6707,87196,50,6707,87196,40,6707,87226,0,6707,105894,3,7460,106487,4,7833,107169,5,8208,107170,1,8208,107170,50,8208,107170,40,8208,107200,0,8208,186865,3,12111,187857,4,14059,188122,1,16010,188122,50,16018,188122,40,16018,188152,0,16018,252949,3,18569,253649,4,19845,254161,1,21119,254161,50,21121,254161,40,21121,254191,0,21121,289566,3,22625,290450,4,23372,291134,1,24122,291134,50,24123,291134,40,24123,291164,0,24123,315817,3,24886,316146,4,25249,316382,1,25624,316382,50,25624,316382,40,25624,316412,0,25624,359170,3,26826,359726,4,27425,359858,1,28025,359858,50,28026,359858,40,28026,359888,0,28026,391802,3,28778,392260,4,29152,392438,1,29527,392438,50,29528,392438,40,29528,392438,40,29528,392463,0,29528,392583,50,29528,392583,30,29528,392583,40,29528,392608,0,29528,392683,50,29528,392708,0,29532)
%
%
% START OF PROOF
% 392685 [] equal(multiply(identity,X),X).
% 392686 [] equal(multiply(inverse(X),X),identity).
% 392687 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 392688 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 392692 [?] ?
% 392693 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 392697 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 392698 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 392702 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 392703 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 392707 [?] ?
% 392708 [] equal(inverse(sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 392715 [hyper:392688,392693,binarycut:392692] equal(inverse(sk_c2),sk_c7).
% 392718 [para:392715.1.1,392686.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 392728 [hyper:392688,392708,binarycut:392707] equal(inverse(sk_c7),sk_c6).
% 392729 [para:392728.1.1,392686.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 392743 [hyper:392688,392697,392698] equal(multiply(sk_c2,sk_c7),sk_c6).
% 392748 [hyper:392688,392702,392703] equal(multiply(sk_c1,sk_c7),sk_c6).
% 392749 [para:392686.1.1,392687.1.1.1,demod:392685] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 392750 [para:392718.1.1,392687.1.1.1,demod:392685] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 392751 [para:392729.1.1,392687.1.1.1,demod:392685] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 392753 [para:392748.1.1,392687.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c1,multiply(sk_c7,X))).
% 392754 [para:392743.1.1,392750.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 392756 [para:392718.1.1,392751.1.2.2] equal(sk_c2,multiply(sk_c6,identity)).
% 392757 [para:392750.1.2,392751.1.2.2] equal(multiply(sk_c2,X),multiply(sk_c6,X)).
% 392758 [para:392754.1.2,392751.1.2.2,demod:392729] equal(sk_c6,identity).
% 392759 [para:392758.1.1,392729.1.1.1,demod:392685] equal(sk_c7,identity).
% 392760 [para:392758.1.1,392754.1.2.2] equal(sk_c7,multiply(sk_c7,identity)).
% 392761 [para:392758.1.1,392751.1.2.1,demod:392685] equal(X,multiply(sk_c7,X)).
% 392763 [para:392686.1.1,392749.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 392764 [para:392728.1.1,392749.1.2.1,demod:392757,392761] equal(X,multiply(sk_c2,X)).
% 392766 [para:392687.1.1,392749.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 392769 [para:392749.1.2,392749.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 392770 [para:392759.1.1,392718.1.1.1,demod:392685] equal(sk_c2,identity).
% 392771 [para:392759.1.1,392728.1.1.1] equal(inverse(identity),sk_c6).
% 392773 [para:392759.1.1,392748.1.1.2] equal(multiply(sk_c1,identity),sk_c6).
% 392774 [para:392759.1.1,392754.1.2.1,demod:392685] equal(sk_c7,sk_c6).
% 392775 [para:392770.1.1,392715.1.1.1,demod:392771] equal(sk_c6,sk_c7).
% 392778 [para:392718.1.1,392753.1.2.2,demod:392773,392764,392757] equal(sk_c2,sk_c6).
% 392783 [para:392774.1.1,392760.1.2.1,demod:392756] equal(sk_c7,sk_c2).
% 392789 [para:392769.1.2,392763.1.2] equal(X,multiply(X,identity)).
% 392791 [para:392789.1.2,392773.1.1] equal(sk_c1,sk_c6).
% 392793 [para:392789.1.2,392763.1.2] equal(X,inverse(inverse(X))).
% 392795 [para:392791.1.2,392778.1.2] equal(sk_c2,sk_c1).
% 392798 [para:392718.1.1,392766.1.2.2.2,demod:392789] equal(sk_c2,multiply(inverse(multiply(X,sk_c7)),X)).
% 392801 [para:392748.1.1,392766.1.2.2.2] equal(sk_c7,multiply(inverse(multiply(X,sk_c1)),multiply(X,sk_c6))).
% 392807 [para:392783.1.1,392798.1.2.1.1.2] equal(sk_c2,multiply(inverse(multiply(X,sk_c2)),X)).
% 392811 [para:392807.1.2,392749.1.2.2,demod:392764,392687,392793] equal(X,multiply(X,sk_c2)).
% 392812 [para:392795.1.1,392811.1.2.2] equal(X,multiply(X,sk_c1)).
% 392814 [para:392801.1.2,392749.1.2.2,demod:392793,392812] equal(multiply(X,sk_c6),multiply(X,sk_c7)).
% 392815 [para:392759.1.1,392814.1.2.2,demod:392789] equal(multiply(X,sk_c6),X).
% 392816 [hyper:392688,392815,demod:392728,cut:392775] 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 17
% clause depth limited to 4
% seconds given: 6
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 17
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(25,40,0,55,0,0,1835,50,19,1865,0,19,3861,50,41,3891,0,41,5996,50,67,6026,0,67,8189,50,88,8219,0,88,10441,50,109,10471,0,109,12779,50,138,12809,0,138,15203,50,179,15233,0,179,17741,50,251,17771,0,251,20393,50,386,20423,0,386,23187,50,609,23217,0,609,26123,50,1002,26123,40,1002,26153,0,1002,37390,3,1303,38111,4,1453,38752,1,1603,38752,50,1603,38752,40,1603,38782,0,1603,39048,3,1913,39056,4,2055,39064,5,2204,39064,1,2204,39064,50,2204,39064,40,2204,39094,0,2204,64669,3,3714,65753,4,4455,66621,5,5205,66622,1,5205,66622,50,5205,66622,40,5205,66652,0,5206,85954,3,5960,86559,4,6332,87196,1,6707,87196,50,6707,87196,40,6707,87226,0,6707,105894,3,7460,106487,4,7833,107169,5,8208,107170,1,8208,107170,50,8208,107170,40,8208,107200,0,8208,186865,3,12111,187857,4,14059,188122,1,16010,188122,50,16018,188122,40,16018,188152,0,16018,252949,3,18569,253649,4,19845,254161,1,21119,254161,50,21121,254161,40,21121,254191,0,21121,289566,3,22625,290450,4,23372,291134,1,24122,291134,50,24123,291134,40,24123,291164,0,24123,315817,3,24886,316146,4,25249,316382,1,25624,316382,50,25624,316382,40,25624,316412,0,25624,359170,3,26826,359726,4,27425,359858,1,28025,359858,50,28026,359858,40,28026,359888,0,28026,391802,3,28778,392260,4,29152,392438,1,29527,392438,50,29528,392438,40,29528,392438,40,29528,392463,0,29528,392583,50,29528,392583,30,29528,392583,40,29528,392608,0,29528,392683,50,29528,392708,0,29532,392815,50,29533,392815,30,29533,392815,40,29533,392840,0,29533)
%
%
% START OF PROOF
% 392817 [] equal(multiply(identity,X),X).
% 392818 [] equal(multiply(inverse(X),X),identity).
% 392819 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 392820 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 392821 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 392822 [] equal(multiply(sk_c4,sk_c7),sk_c5) | equal(inverse(sk_c2),sk_c7).
% 392823 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c2),sk_c7).
% 392824 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 392825 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 392826 [?] ?
% 392827 [?] ?
% 392828 [?] ?
% 392829 [?] ?
% 392830 [?] ?
% 392843 [hyper:392820,392821,binarycut:392826] equal(inverse(sk_c4),sk_c7).
% 392846 [para:392843.1.1,392818.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 392850 [hyper:392820,392825,binarycut:392830] equal(inverse(sk_c3),sk_c7).
% 392854 [para:392850.1.1,392818.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 392858 [hyper:392820,392822,binarycut:392827] equal(multiply(sk_c4,sk_c7),sk_c5).
% 392861 [hyper:392820,392823,binarycut:392828] equal(multiply(sk_c7,sk_c5),sk_c6).
% 392864 [hyper:392820,392824,binarycut:392829] equal(multiply(sk_c3,sk_c6),sk_c7).
% 392865 [para:392818.1.1,392819.1.1.1,demod:392817] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 392866 [para:392846.1.1,392819.1.1.1,demod:392817] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 392867 [para:392854.1.1,392819.1.1.1,demod:392817] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 392868 [para:392858.1.1,392819.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c4,multiply(sk_c7,X))).
% 392869 [para:392861.1.1,392819.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c5,X))).
% 392870 [para:392864.1.1,392819.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c6,X))).
% 392871 [para:392858.1.1,392866.1.2.2,demod:392861] equal(sk_c7,sk_c6).
% 392872 [para:392871.1.1,392846.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 392874 [para:392871.1.1,392858.1.1.2] equal(multiply(sk_c4,sk_c6),sk_c5).
% 392875 [para:392871.1.1,392861.1.1.1] equal(multiply(sk_c6,sk_c5),sk_c6).
% 392878 [para:392846.1.1,392865.1.2.2] equal(sk_c4,multiply(inverse(sk_c7),identity)).
% 392879 [para:392854.1.1,392865.1.2.2,demod:392878] equal(sk_c3,sk_c4).
% 392882 [para:392866.1.2,392865.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c7),X)).
% 392887 [para:392879.1.2,392874.1.1.1,demod:392864] equal(sk_c7,sk_c5).
% 392888 [para:392867.1.2,392865.1.2.2,demod:392882] equal(multiply(sk_c3,X),multiply(sk_c4,X)).
% 392893 [para:392887.1.1,392866.1.2.1,demod:392888] equal(X,multiply(sk_c5,multiply(sk_c3,X))).
% 392897 [para:392868.1.2,392866.1.2.2,demod:392869] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 392898 [para:392866.1.2,392868.1.2.2,demod:392893,392888] equal(X,multiply(sk_c3,X)).
% 392899 [para:392879.1.2,392868.1.2.1,demod:392870,392897] equal(multiply(sk_c5,X),multiply(sk_c6,X)).
% 392900 [para:392867.1.2,392868.1.2.2,demod:392888,392898] equal(multiply(sk_c5,X),X).
% 392904 [para:392875.1.1,392865.1.2.2,demod:392818] equal(sk_c5,identity).
% 392905 [para:392904.1.1,392861.1.1.2,demod:392900,392899,392897] equal(identity,sk_c6).
% 392907 [para:392905.1.2,392872.1.1.1,demod:392817] equal(sk_c4,identity).
% 392911 [para:392907.1.1,392843.1.1.1] equal(inverse(identity),sk_c7).
% 392912 [hyper:392820,392911,demod:392817,cut:392871] 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 17
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(inverse(sk_c7),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 17
% clause depth limited to 3
% seconds given: 6
%
%
% 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 17
% clause depth limited to 4
% seconds given: 6
%
%
% 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 17
% clause depth limited to 5
% seconds given: 6
%
%
% 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 17
% clause depth limited to 6
% seconds given: 6
%
%
% 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 17
% clause depth limited to 7
% seconds given: 6
%
%
% 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 17
% clause depth limited to 8
% seconds given: 6
%
%
% 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 17
% clause depth limited to 9
% seconds given: 6
%
%
% 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 17
% clause depth limited to 10
% seconds given: 6
%
%
% 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 17
% clause depth limited to 11
% seconds given: 6
%
%
% 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 17
% clause depth limited to 12
% seconds given: 6
%
%
% 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(25,40,0,55,0,0,1835,50,19,1865,0,19,3861,50,41,3891,0,41,5996,50,67,6026,0,67,8189,50,88,8219,0,88,10441,50,109,10471,0,109,12779,50,138,12809,0,138,15203,50,179,15233,0,179,17741,50,251,17771,0,251,20393,50,386,20423,0,386,23187,50,609,23217,0,609,26123,50,1002,26123,40,1002,26153,0,1002,37390,3,1303,38111,4,1453,38752,1,1603,38752,50,1603,38752,40,1603,38782,0,1603,39048,3,1913,39056,4,2055,39064,5,2204,39064,1,2204,39064,50,2204,39064,40,2204,39094,0,2204,64669,3,3714,65753,4,4455,66621,5,5205,66622,1,5205,66622,50,5205,66622,40,5205,66652,0,5206,85954,3,5960,86559,4,6332,87196,1,6707,87196,50,6707,87196,40,6707,87226,0,6707,105894,3,7460,106487,4,7833,107169,5,8208,107170,1,8208,107170,50,8208,107170,40,8208,107200,0,8208,186865,3,12111,187857,4,14059,188122,1,16010,188122,50,16018,188122,40,16018,188152,0,16018,252949,3,18569,253649,4,19845,254161,1,21119,254161,50,21121,254161,40,21121,254191,0,21121,289566,3,22625,290450,4,23372,291134,1,24122,291134,50,24123,291134,40,24123,291164,0,24123,315817,3,24886,316146,4,25249,316382,1,25624,316382,50,25624,316382,40,25624,316412,0,25624,359170,3,26826,359726,4,27425,359858,1,28025,359858,50,28026,359858,40,28026,359888,0,28026,391802,3,28778,392260,4,29152,392438,1,29527,392438,50,29528,392438,40,29528,392438,40,29528,392463,0,29528,392583,50,29528,392583,30,29528,392583,40,29528,392608,0,29528,392683,50,29528,392708,0,29532,392815,50,29533,392815,30,29533,392815,40,29533,392840,0,29533,392911,50,29533,392911,30,29533,392911,40,29533,392936,0,29533,393035,50,29534,393060,0,29539,393198,50,29541,393223,0,29541,393369,50,29545,393394,0,29549,393548,50,29555,393573,0,29555,393733,50,29564,393758,0,29564,393926,50,29579,393951,0,29584,394127,50,29612,394152,0,29612,394338,50,29673,394363,0,29674,394559,50,29790,394584,0,29790,394792,50,30023,394792,40,30023,394817,0,30023)
%
%
% START OF PROOF
% 394794 [] equal(multiply(identity,X),X).
% 394795 [] equal(multiply(inverse(X),X),identity).
% 394796 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 394797 [] -equal(inverse(sk_c7),sk_c6).
% 394813 [?] ?
% 394814 [?] ?
% 394815 [?] ?
% 394816 [?] ?
% 394817 [?] ?
% 394826 [input:394813,cut:394797] equal(inverse(sk_c4),sk_c7).
% 394827 [para:394826.1.1,394795.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 394828 [input:394817,cut:394797] equal(inverse(sk_c3),sk_c7).
% 394829 [para:394828.1.1,394795.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 394839 [input:394814,cut:394797] equal(multiply(sk_c4,sk_c7),sk_c5).
% 394840 [input:394815,cut:394797] equal(multiply(sk_c7,sk_c5),sk_c6).
% 394841 [input:394816,cut:394797] equal(multiply(sk_c3,sk_c6),sk_c7).
% 394852 [para:394795.1.1,394796.1.1.1,demod:394794] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 394854 [para:394827.1.1,394796.1.1.1,demod:394794] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 394855 [para:394829.1.1,394796.1.1.1,demod:394794] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 394865 [para:394840.1.1,394796.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c5,X))).
% 394879 [para:394839.1.1,394854.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c5)).
% 394915 [para:394879.1.2,394840.1.1] equal(sk_c7,sk_c6).
% 394916 [para:394879.1.2,394796.1.1.1,demod:394865] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 394918 [para:394915.1.1,394797.1.1.1] -equal(inverse(sk_c6),sk_c6).
% 394934 [para:394841.1.1,394855.1.2.2,demod:394916] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 394950 [para:394934.1.2,394852.1.2.2,demod:394795] equal(sk_c7,identity).
% 394954 [para:394950.1.1,394827.1.1.1,demod:394794] equal(sk_c4,identity).
% 394968 [para:394950.1.1,394915.1.1] equal(identity,sk_c6).
% 394971 [para:394954.1.1,394826.1.1.1] equal(inverse(identity),sk_c7).
% 394989 [para:394968.1.2,394918.1.1.1,demod:394971,cut:394915] 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(inverse(sk_c7),sk_c6) | -equal(multiply(X,sk_c7),sk_c6) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(multiply(X,sk_c7),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 17
% clause depth limited to 3
% seconds given: 6
%
%
% 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 17
% clause depth limited to 4
% seconds given: 6
%
%
% **** EMPTY CLAUSE DERIVED ****
%
%
% timer checkpoints: c(25,40,0,55,0,0,1835,50,19,1865,0,19,3861,50,41,3891,0,41,5996,50,67,6026,0,67,8189,50,88,8219,0,88,10441,50,109,10471,0,109,12779,50,138,12809,0,138,15203,50,179,15233,0,179,17741,50,251,17771,0,251,20393,50,386,20423,0,386,23187,50,609,23217,0,609,26123,50,1002,26123,40,1002,26153,0,1002,37390,3,1303,38111,4,1453,38752,1,1603,38752,50,1603,38752,40,1603,38782,0,1603,39048,3,1913,39056,4,2055,39064,5,2204,39064,1,2204,39064,50,2204,39064,40,2204,39094,0,2204,64669,3,3714,65753,4,4455,66621,5,5205,66622,1,5205,66622,50,5205,66622,40,5205,66652,0,5206,85954,3,5960,86559,4,6332,87196,1,6707,87196,50,6707,87196,40,6707,87226,0,6707,105894,3,7460,106487,4,7833,107169,5,8208,107170,1,8208,107170,50,8208,107170,40,8208,107200,0,8208,186865,3,12111,187857,4,14059,188122,1,16010,188122,50,16018,188122,40,16018,188152,0,16018,252949,3,18569,253649,4,19845,254161,1,21119,254161,50,21121,254161,40,21121,254191,0,21121,289566,3,22625,290450,4,23372,291134,1,24122,291134,50,24123,291134,40,24123,291164,0,24123,315817,3,24886,316146,4,25249,316382,1,25624,316382,50,25624,316382,40,25624,316412,0,25624,359170,3,26826,359726,4,27425,359858,1,28025,359858,50,28026,359858,40,28026,359888,0,28026,391802,3,28778,392260,4,29152,392438,1,29527,392438,50,29528,392438,40,29528,392438,40,29528,392463,0,29528,392583,50,29528,392583,30,29528,392583,40,29528,392608,0,29528,392683,50,29528,392708,0,29532,392815,50,29533,392815,30,29533,392815,40,29533,392840,0,29533,392911,50,29533,392911,30,29533,392911,40,29533,392936,0,29533,393035,50,29534,393060,0,29539,393198,50,29541,393223,0,29541,393369,50,29545,393394,0,29549,393548,50,29555,393573,0,29555,393733,50,29564,393758,0,29564,393926,50,29579,393951,0,29584,394127,50,29612,394152,0,29612,394338,50,29673,394363,0,29674,394559,50,29790,394584,0,29790,394792,50,30023,394792,40,30023,394817,0,30023,394988,50,30024,394988,30,30024,394988,40,30024,395013,0,30024,395112,50,30025,395137,0,30029)
%
%
% START OF PROOF
% 395114 [] equal(multiply(identity,X),X).
% 395115 [] equal(multiply(inverse(X),X),identity).
% 395116 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 395117 [] -equal(multiply(X,sk_c7),sk_c6).
% 395123 [?] ?
% 395124 [?] ?
% 395125 [?] ?
% 395126 [?] ?
% 395127 [?] ?
% 395145 [input:395123,cut:395117] equal(inverse(sk_c4),sk_c7).
% 395146 [para:395145.1.1,395115.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 395147 [input:395127,cut:395117] equal(inverse(sk_c3),sk_c7).
% 395148 [para:395147.1.1,395115.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 395151 [input:395124,cut:395117] equal(multiply(sk_c4,sk_c7),sk_c5).
% 395155 [input:395125,cut:395117] equal(multiply(sk_c7,sk_c5),sk_c6).
% 395156 [input:395126,cut:395117] equal(multiply(sk_c3,sk_c6),sk_c7).
% 395160 [para:395115.1.1,395116.1.1.1,demod:395114] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 395161 [para:395146.1.1,395116.1.1.1,demod:395114] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 395162 [para:395148.1.1,395116.1.1.1,demod:395114] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 395164 [para:395155.1.1,395116.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c5,X))).
% 395166 [para:395151.1.1,395161.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c5)).
% 395168 [para:395166.1.2,395116.1.1.1,demod:395164] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 395170 [para:395115.1.1,395160.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 395176 [para:395116.1.1,395160.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 395177 [para:395161.1.2,395160.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c7),X)).
% 395179 [para:395160.1.2,395160.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 395189 [para:395156.1.1,395162.1.2.2,demod:395168] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 395190 [para:395162.1.2,395160.1.2.2,demod:395177] equal(multiply(sk_c3,X),multiply(sk_c4,X)).
% 395204 [para:395189.1.2,395160.1.2.2,demod:395115] equal(sk_c7,identity).
% 395210 [para:395204.1.1,395161.1.2.1,demod:395114,395190] equal(X,multiply(sk_c3,X)).
% 395252 [para:395179.1.2,395115.1.1] equal(multiply(X,inverse(X)),identity).
% 395254 [para:395179.1.2,395170.1.2] equal(X,multiply(X,identity)).
% 395255 [para:395254.1.2,395170.1.2] equal(X,inverse(inverse(X))).
% 395259 [para:395252.1.1,395176.1.2.2.2,demod:395254] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 395261 [para:395161.1.2,395259.1.2.1.1,demod:395210,395190] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 395270 [para:395261.1.2,395179.1.2,demod:395255,slowcut:395117] 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 17
% clause depth limited to 4
% seconds given: 6
%
%
% Split attempt finished with SUCCESS.
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 27140
% derived clauses: 6154313
% kept clauses: 336880
% kept size sum: 444013
% kept mid-nuclei: 21448
% kept new demods: 2921
% forw unit-subs: 1726187
% forw double-subs: 3633971
% forw overdouble-subs: 395502
% backward subs: 11125
% fast unit cutoff: 29977
% full unit cutoff: 148
% dbl unit cutoff: 8626
% real runtime : 303.13
% process. runtime: 300.30
% specific non-discr-tree subsumption statistics:
% tried: 15471886
% length fails: 1943519
% strength fails: 3755277
% predlist fails: 452157
% aux str. fails: 2172879
% by-lit fails: 1514462
% full subs tried: 1927805
% full subs fail: 1769964
%
% ; 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/GRP234-1+eq_r.in")
%
%------------------------------------------------------------------------------