TSTP Solution File: GRP352-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP352-1 : 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 : art02.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 289.3s
% Output : Assurance 289.3s
% 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/GRP352-1+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 19)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 19)
% (binary-posweight-lex-big-order 30 #f 3 19)
% (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_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c5) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c6),sk_c7) | -equal(inverse(U),sk_c6).
% was split for some strategies as:
% -equal(multiply(U,sk_c6),sk_c7) | -equal(inverse(U),sk_c6).
% -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% -equal(multiply(Y,sk_c6),sk_c5) | -equal(inverse(Y),sk_c6).
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% -equal(multiply(sk_c6,sk_c5),sk_c7).
% -equal(multiply(sk_c6,sk_c7),sk_c5).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c5) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c6),sk_c7) | -equal(inverse(U),sk_c6).
% Split part used next: -equal(multiply(U,sk_c6),sk_c7) | -equal(inverse(U),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,65,0,0,554,50,4,589,0,4,1093,50,7,1128,0,7,1637,50,12,1672,0,12,2187,50,17,2222,0,17,2744,50,23,2779,0,23,3309,50,34,3344,0,35,3882,50,57,3917,0,57,4465,50,107,4500,0,107,5058,50,216,5093,0,217,5663,50,412,5698,0,413,6280,50,779,6280,40,779,6315,0,779,16213,3,1080,17014,4,1230,17741,1,1380,17741,50,1380,17741,40,1380,17776,0,1380,17942,3,1689,17950,4,1832,17958,5,1981,17958,1,1981,17958,50,1981,17958,40,1981,17993,0,1981,43553,3,3483,44631,4,4232,45612,5,4982,45613,1,4982,45613,50,4983,45613,40,4983,45648,0,4983,61174,3,5737,62006,4,6109,62745,1,6484,62745,50,6484,62745,40,6484,62780,0,6484,73989,3,7243,74355,4,7610,75433,5,7985,75434,1,7985,75434,50,7985,75434,40,7985,75469,0,7985,145058,3,11886,145988,4,13837,146778,5,15786,146779,1,15786,146779,50,15789,146779,40,15789,146814,0,15789,207484,3,18341,208204,4,19615,208834,1,20890,208834,50,20892,208834,40,20892,208869,0,20892,255471,3,22408,256123,4,23143,256724,5,23893,256725,1,23893,256725,50,23895,256725,40,23895,256760,0,23895,265609,3,24670,266840,4,25027,267348,5,25396,267348,1,25396,267348,50,25396,267348,40,25396,267383,0,25396,301244,3,26597,301936,4,27197,302455,5,27797,302456,1,27797,302456,50,27798,302456,40,27798,302491,0,27798,328802,3,28550,329313,4,28924,329739,1,29299,329739,50,29300,329739,40,29300,329739,40,29300,329769,0,29300)
%
%
% START OF PROOF
% 329740 [] equal(X,X).
% 329741 [] equal(multiply(identity,X),X).
% 329742 [] equal(multiply(inverse(X),X),identity).
% 329743 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 329744 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6).
% 329745 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 329746 [?] ?
% 329750 [] equal(multiply(sk_c2,sk_c6),sk_c5) | equal(inverse(sk_c4),sk_c6).
% 329751 [] equal(multiply(sk_c2,sk_c6),sk_c5) | equal(multiply(sk_c4,sk_c6),sk_c7).
% 329755 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 329756 [?] ?
% 329760 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 329761 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c6),sk_c7).
% 329765 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 329766 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(multiply(sk_c4,sk_c6),sk_c7).
% 329773 [hyper:329744,329745,binarycut:329746] equal(inverse(sk_c2),sk_c6).
% 329775 [para:329773.1.1,329742.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 329782 [hyper:329744,329755,binarycut:329756] equal(inverse(sk_c1),sk_c7).
% 329783 [para:329782.1.1,329742.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 329790 [hyper:329744,329751,329750] equal(multiply(sk_c2,sk_c6),sk_c5).
% 329798 [hyper:329744,329761,329760] equal(multiply(sk_c1,sk_c7),sk_c6).
% 329801 [hyper:329744,329766,329765] equal(multiply(sk_c6,sk_c5),sk_c7).
% 329802 [para:329742.1.1,329743.1.1.1,demod:329741] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 329803 [para:329775.1.1,329743.1.1.1,demod:329741] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 329805 [para:329790.1.1,329743.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c2,multiply(sk_c6,X))).
% 329807 [para:329801.1.1,329743.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c5,X))).
% 329808 [para:329790.1.1,329803.1.2.2,demod:329801] equal(sk_c6,sk_c7).
% 329809 [para:329808.1.1,329775.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 329810 [para:329808.1.1,329790.1.1.2] equal(multiply(sk_c2,sk_c7),sk_c5).
% 329814 [para:329775.1.1,329802.1.2.2] equal(sk_c2,multiply(inverse(sk_c6),identity)).
% 329815 [para:329783.1.1,329802.1.2.2] equal(sk_c1,multiply(inverse(sk_c7),identity)).
% 329816 [para:329798.1.1,329802.1.2.2,demod:329782] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 329817 [para:329801.1.1,329802.1.2.2] equal(sk_c5,multiply(inverse(sk_c6),sk_c7)).
% 329819 [para:329809.1.1,329802.1.2.2,demod:329815] equal(sk_c2,sk_c1).
% 329826 [para:329819.1.1,329810.1.1.1,demod:329798] equal(sk_c6,sk_c5).
% 329827 [para:329826.1.1,329775.1.1.1] equal(multiply(sk_c5,sk_c2),identity).
% 329830 [para:329826.1.1,329803.1.2.1] equal(X,multiply(sk_c5,multiply(sk_c2,X))).
% 329831 [para:329826.1.1,329808.1.1] equal(sk_c5,sk_c7).
% 329835 [para:329805.1.2,329803.1.2.2,demod:329807] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 329836 [para:329803.1.2,329805.1.2.2,demod:329830] equal(X,multiply(sk_c2,X)).
% 329838 [para:329836.1.2,329803.1.2.2,demod:329835] equal(X,multiply(sk_c7,X)).
% 329846 [para:329827.1.1,329802.1.2.2] equal(sk_c2,multiply(inverse(sk_c5),identity)).
% 329848 [para:329846.1.2,329743.1.1.1,demod:329741,329836] equal(X,multiply(inverse(sk_c5),X)).
% 329849 [para:329848.1.2,329742.1.1] equal(sk_c5,identity).
% 329851 [para:329849.1.1,329801.1.1.2,demod:329838,329835] equal(identity,sk_c7).
% 329856 [para:329851.1.2,329817.1.2.2,demod:329814] equal(sk_c5,sk_c2).
% 329857 [para:329856.1.1,329831.1.1] equal(sk_c2,sk_c7).
% 329860 [para:329857.1.1,329773.1.1.1] equal(inverse(sk_c7),sk_c6).
% 329863 [hyper:329744,329860,demod:329816,cut:329740] 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 19
% 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_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c5) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c6),sk_c7) | -equal(inverse(U),sk_c6).
% Split part used next: -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,65,0,0,554,50,4,589,0,4,1093,50,7,1128,0,7,1637,50,12,1672,0,12,2187,50,17,2222,0,17,2744,50,23,2779,0,23,3309,50,34,3344,0,35,3882,50,57,3917,0,57,4465,50,107,4500,0,107,5058,50,216,5093,0,217,5663,50,412,5698,0,413,6280,50,779,6280,40,779,6315,0,779,16213,3,1080,17014,4,1230,17741,1,1380,17741,50,1380,17741,40,1380,17776,0,1380,17942,3,1689,17950,4,1832,17958,5,1981,17958,1,1981,17958,50,1981,17958,40,1981,17993,0,1981,43553,3,3483,44631,4,4232,45612,5,4982,45613,1,4982,45613,50,4983,45613,40,4983,45648,0,4983,61174,3,5737,62006,4,6109,62745,1,6484,62745,50,6484,62745,40,6484,62780,0,6484,73989,3,7243,74355,4,7610,75433,5,7985,75434,1,7985,75434,50,7985,75434,40,7985,75469,0,7985,145058,3,11886,145988,4,13837,146778,5,15786,146779,1,15786,146779,50,15789,146779,40,15789,146814,0,15789,207484,3,18341,208204,4,19615,208834,1,20890,208834,50,20892,208834,40,20892,208869,0,20892,255471,3,22408,256123,4,23143,256724,5,23893,256725,1,23893,256725,50,23895,256725,40,23895,256760,0,23895,265609,3,24670,266840,4,25027,267348,5,25396,267348,1,25396,267348,50,25396,267348,40,25396,267383,0,25396,301244,3,26597,301936,4,27197,302455,5,27797,302456,1,27797,302456,50,27798,302456,40,27798,302491,0,27798,328802,3,28550,329313,4,28924,329739,1,29299,329739,50,29300,329739,40,29300,329739,40,29300,329769,0,29300,329862,50,29300,329862,30,29300,329862,40,29300,329892,0,29300)
%
%
% START OF PROOF
% 329864 [] equal(multiply(identity,X),X).
% 329865 [] equal(multiply(inverse(X),X),identity).
% 329866 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 329867 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 329870 [?] ?
% 329871 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 329875 [] equal(multiply(sk_c2,sk_c6),sk_c5) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 329876 [] equal(multiply(sk_c2,sk_c6),sk_c5) | equal(inverse(sk_c3),sk_c7).
% 329880 [?] ?
% 329881 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 329885 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 329886 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 329890 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 329891 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 329896 [hyper:329867,329871,binarycut:329870] equal(inverse(sk_c2),sk_c6).
% 329898 [para:329896.1.1,329865.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 329906 [hyper:329867,329881,binarycut:329880] equal(inverse(sk_c1),sk_c7).
% 329909 [para:329906.1.1,329865.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 329927 [hyper:329867,329875,329876] equal(multiply(sk_c2,sk_c6),sk_c5).
% 329933 [hyper:329867,329885,329886] equal(multiply(sk_c1,sk_c7),sk_c6).
% 329939 [hyper:329867,329890,329891] equal(multiply(sk_c6,sk_c5),sk_c7).
% 329940 [para:329865.1.1,329866.1.1.1,demod:329864] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 329941 [para:329898.1.1,329866.1.1.1,demod:329864] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 329943 [para:329927.1.1,329866.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c2,multiply(sk_c6,X))).
% 329945 [para:329939.1.1,329866.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c5,X))).
% 329946 [para:329927.1.1,329941.1.2.2,demod:329939] equal(sk_c6,sk_c7).
% 329947 [para:329946.1.1,329898.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 329948 [para:329946.1.1,329927.1.1.2] equal(multiply(sk_c2,sk_c7),sk_c5).
% 329953 [para:329909.1.1,329940.1.2.2] equal(sk_c1,multiply(inverse(sk_c7),identity)).
% 329957 [para:329947.1.1,329940.1.2.2,demod:329953] equal(sk_c2,sk_c1).
% 329964 [para:329957.1.1,329948.1.1.1,demod:329933] equal(sk_c6,sk_c5).
% 329968 [para:329964.1.1,329941.1.2.1] equal(X,multiply(sk_c5,multiply(sk_c2,X))).
% 329973 [para:329943.1.2,329941.1.2.2,demod:329945] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 329974 [para:329941.1.2,329943.1.2.2,demod:329968] equal(X,multiply(sk_c2,X)).
% 329976 [para:329974.1.2,329941.1.2.2,demod:329973] equal(X,multiply(sk_c7,X)).
% 329978 [para:329976.1.2,329909.1.1] equal(sk_c1,identity).
% 329980 [para:329978.1.1,329906.1.1.1] equal(inverse(identity),sk_c7).
% 329982 [hyper:329867,329980,demod:329864,cut:329946] 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 19
% 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_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c5) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c6),sk_c7) | -equal(inverse(U),sk_c6).
% Split part used next: -equal(multiply(Y,sk_c6),sk_c5) | -equal(inverse(Y),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 19
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,65,0,0,554,50,4,589,0,4,1093,50,7,1128,0,7,1637,50,12,1672,0,12,2187,50,17,2222,0,17,2744,50,23,2779,0,23,3309,50,34,3344,0,35,3882,50,57,3917,0,57,4465,50,107,4500,0,107,5058,50,216,5093,0,217,5663,50,412,5698,0,413,6280,50,779,6280,40,779,6315,0,779,16213,3,1080,17014,4,1230,17741,1,1380,17741,50,1380,17741,40,1380,17776,0,1380,17942,3,1689,17950,4,1832,17958,5,1981,17958,1,1981,17958,50,1981,17958,40,1981,17993,0,1981,43553,3,3483,44631,4,4232,45612,5,4982,45613,1,4982,45613,50,4983,45613,40,4983,45648,0,4983,61174,3,5737,62006,4,6109,62745,1,6484,62745,50,6484,62745,40,6484,62780,0,6484,73989,3,7243,74355,4,7610,75433,5,7985,75434,1,7985,75434,50,7985,75434,40,7985,75469,0,7985,145058,3,11886,145988,4,13837,146778,5,15786,146779,1,15786,146779,50,15789,146779,40,15789,146814,0,15789,207484,3,18341,208204,4,19615,208834,1,20890,208834,50,20892,208834,40,20892,208869,0,20892,255471,3,22408,256123,4,23143,256724,5,23893,256725,1,23893,256725,50,23895,256725,40,23895,256760,0,23895,265609,3,24670,266840,4,25027,267348,5,25396,267348,1,25396,267348,50,25396,267348,40,25396,267383,0,25396,301244,3,26597,301936,4,27197,302455,5,27797,302456,1,27797,302456,50,27798,302456,40,27798,302491,0,27798,328802,3,28550,329313,4,28924,329739,1,29299,329739,50,29300,329739,40,29300,329739,40,29300,329769,0,29300,329862,50,29300,329862,30,29300,329862,40,29300,329892,0,29300,329981,50,29300,329981,30,29300,329981,40,29300,330011,0,29306)
%
%
% START OF PROOF
% 329983 [] equal(multiply(identity,X),X).
% 329984 [] equal(multiply(inverse(X),X),identity).
% 329985 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 329986 [] -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6).
% 329987 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 329988 [] equal(multiply(sk_c4,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c6).
% 329989 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c6).
% 329990 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 329991 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c2),sk_c6).
% 329992 [?] ?
% 329993 [?] ?
% 329994 [?] ?
% 329995 [?] ?
% 329996 [?] ?
% 330014 [hyper:329986,329987,binarycut:329992] equal(inverse(sk_c4),sk_c6).
% 330017 [para:330014.1.1,329984.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 330021 [hyper:329986,329990,binarycut:329995] equal(inverse(sk_c3),sk_c7).
% 330022 [para:330021.1.1,329984.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 330025 [hyper:329986,329988,binarycut:329993] equal(multiply(sk_c4,sk_c6),sk_c7).
% 330028 [hyper:329986,329989,binarycut:329994] equal(multiply(sk_c3,sk_c6),sk_c7).
% 330031 [hyper:329986,329991,binarycut:329996] equal(multiply(sk_c6,sk_c7),sk_c5).
% 330032 [para:329984.1.1,329985.1.1.1,demod:329983] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 330033 [para:330017.1.1,329985.1.1.1,demod:329983] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 330034 [para:330022.1.1,329985.1.1.1,demod:329983] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 330035 [para:330025.1.1,329985.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c4,multiply(sk_c6,X))).
% 330038 [para:330025.1.1,330033.1.2.2,demod:330031] equal(sk_c6,sk_c5).
% 330040 [para:330038.1.1,330025.1.1.2] equal(multiply(sk_c4,sk_c5),sk_c7).
% 330042 [para:330038.1.1,330031.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 330047 [para:330028.1.1,330032.1.2.2,demod:330021] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 330056 [para:330042.1.1,330032.1.2.2,demod:329984] equal(sk_c7,identity).
% 330057 [para:330056.1.1,330022.1.1.1,demod:329983] equal(sk_c3,identity).
% 330058 [para:330056.1.1,330031.1.1.2] equal(multiply(sk_c6,identity),sk_c5).
% 330061 [para:330017.1.1,330035.1.2.2] equal(multiply(sk_c7,sk_c4),multiply(sk_c4,identity)).
% 330062 [para:330031.1.1,330035.1.2.2,demod:330040,330047] equal(sk_c6,sk_c7).
% 330067 [para:330057.1.1,330034.1.2.2.1,demod:329983] equal(X,multiply(sk_c7,X)).
% 330069 [para:330062.1.1,330017.1.1.1,demod:330067] equal(sk_c4,identity).
% 330074 [para:330069.1.1,330017.1.1.2,demod:330058] equal(sk_c5,identity).
% 330076 [para:330074.1.1,330040.1.1.2,demod:330067,330061] equal(sk_c4,sk_c7).
% 330078 [para:330076.1.1,330014.1.1.1] equal(inverse(sk_c7),sk_c6).
% 330086 [hyper:329986,330078,demod:330067,cut:330038] 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 19
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c5) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c6),sk_c7) | -equal(inverse(U),sk_c6).
% Split part used next: -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,65,0,0,554,50,4,589,0,4,1093,50,7,1128,0,7,1637,50,12,1672,0,12,2187,50,17,2222,0,17,2744,50,23,2779,0,23,3309,50,34,3344,0,35,3882,50,57,3917,0,57,4465,50,107,4500,0,107,5058,50,216,5093,0,217,5663,50,412,5698,0,413,6280,50,779,6280,40,779,6315,0,779,16213,3,1080,17014,4,1230,17741,1,1380,17741,50,1380,17741,40,1380,17776,0,1380,17942,3,1689,17950,4,1832,17958,5,1981,17958,1,1981,17958,50,1981,17958,40,1981,17993,0,1981,43553,3,3483,44631,4,4232,45612,5,4982,45613,1,4982,45613,50,4983,45613,40,4983,45648,0,4983,61174,3,5737,62006,4,6109,62745,1,6484,62745,50,6484,62745,40,6484,62780,0,6484,73989,3,7243,74355,4,7610,75433,5,7985,75434,1,7985,75434,50,7985,75434,40,7985,75469,0,7985,145058,3,11886,145988,4,13837,146778,5,15786,146779,1,15786,146779,50,15789,146779,40,15789,146814,0,15789,207484,3,18341,208204,4,19615,208834,1,20890,208834,50,20892,208834,40,20892,208869,0,20892,255471,3,22408,256123,4,23143,256724,5,23893,256725,1,23893,256725,50,23895,256725,40,23895,256760,0,23895,265609,3,24670,266840,4,25027,267348,5,25396,267348,1,25396,267348,50,25396,267348,40,25396,267383,0,25396,301244,3,26597,301936,4,27197,302455,5,27797,302456,1,27797,302456,50,27798,302456,40,27798,302491,0,27798,328802,3,28550,329313,4,28924,329739,1,29299,329739,50,29300,329739,40,29300,329739,40,29300,329769,0,29300,329862,50,29300,329862,30,29300,329862,40,29300,329892,0,29300,329981,50,29300,329981,30,29300,329981,40,29300,330011,0,29306,330085,50,29306,330085,30,29306,330085,40,29306,330115,0,29306)
%
%
% START OF PROOF
% 330087 [] equal(multiply(identity,X),X).
% 330088 [] equal(multiply(inverse(X),X),identity).
% 330089 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 330090 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 330101 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 330102 [] equal(multiply(sk_c4,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 330103 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 330104 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 330105 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 330106 [?] ?
% 330107 [?] ?
% 330108 [?] ?
% 330109 [?] ?
% 330110 [?] ?
% 330122 [hyper:330090,330101,binarycut:330106] equal(inverse(sk_c4),sk_c6).
% 330123 [para:330122.1.1,330088.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 330126 [hyper:330090,330104,binarycut:330109] equal(inverse(sk_c3),sk_c7).
% 330130 [para:330126.1.1,330088.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 330137 [hyper:330090,330102,binarycut:330107] equal(multiply(sk_c4,sk_c6),sk_c7).
% 330140 [hyper:330090,330103,binarycut:330108] equal(multiply(sk_c3,sk_c6),sk_c7).
% 330144 [hyper:330090,330105,binarycut:330110] equal(multiply(sk_c6,sk_c7),sk_c5).
% 330145 [para:330088.1.1,330089.1.1.1,demod:330087] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 330146 [para:330123.1.1,330089.1.1.1,demod:330087] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 330147 [para:330130.1.1,330089.1.1.1,demod:330087] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 330148 [para:330137.1.1,330089.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c4,multiply(sk_c6,X))).
% 330151 [para:330137.1.1,330146.1.2.2,demod:330144] equal(sk_c6,sk_c5).
% 330153 [para:330151.1.1,330137.1.1.2] equal(multiply(sk_c4,sk_c5),sk_c7).
% 330155 [para:330151.1.1,330144.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 330160 [para:330140.1.1,330145.1.2.2,demod:330126] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 330169 [para:330155.1.1,330145.1.2.2,demod:330088] equal(sk_c7,identity).
% 330170 [para:330169.1.1,330130.1.1.1,demod:330087] equal(sk_c3,identity).
% 330175 [para:330144.1.1,330148.1.2.2,demod:330153,330160] equal(sk_c6,sk_c7).
% 330178 [para:330170.1.1,330126.1.1.1] equal(inverse(identity),sk_c7).
% 330180 [para:330170.1.1,330147.1.2.2.1,demod:330087] equal(X,multiply(sk_c7,X)).
% 330182 [para:330175.1.1,330123.1.1.1,demod:330180] equal(sk_c4,identity).
% 330186 [para:330182.1.1,330122.1.1.1,demod:330178] equal(sk_c7,sk_c6).
% 330192 [hyper:330090,330178,demod:330087,cut:330186] 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 19
% 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_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c5) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c6),sk_c7) | -equal(inverse(U),sk_c6).
% Split part used next: -equal(multiply(sk_c6,sk_c5),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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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(30,40,0,65,0,0,554,50,4,589,0,4,1093,50,7,1128,0,7,1637,50,12,1672,0,12,2187,50,17,2222,0,17,2744,50,23,2779,0,23,3309,50,34,3344,0,35,3882,50,57,3917,0,57,4465,50,107,4500,0,107,5058,50,216,5093,0,217,5663,50,412,5698,0,413,6280,50,779,6280,40,779,6315,0,779,16213,3,1080,17014,4,1230,17741,1,1380,17741,50,1380,17741,40,1380,17776,0,1380,17942,3,1689,17950,4,1832,17958,5,1981,17958,1,1981,17958,50,1981,17958,40,1981,17993,0,1981,43553,3,3483,44631,4,4232,45612,5,4982,45613,1,4982,45613,50,4983,45613,40,4983,45648,0,4983,61174,3,5737,62006,4,6109,62745,1,6484,62745,50,6484,62745,40,6484,62780,0,6484,73989,3,7243,74355,4,7610,75433,5,7985,75434,1,7985,75434,50,7985,75434,40,7985,75469,0,7985,145058,3,11886,145988,4,13837,146778,5,15786,146779,1,15786,146779,50,15789,146779,40,15789,146814,0,15789,207484,3,18341,208204,4,19615,208834,1,20890,208834,50,20892,208834,40,20892,208869,0,20892,255471,3,22408,256123,4,23143,256724,5,23893,256725,1,23893,256725,50,23895,256725,40,23895,256760,0,23895,265609,3,24670,266840,4,25027,267348,5,25396,267348,1,25396,267348,50,25396,267348,40,25396,267383,0,25396,301244,3,26597,301936,4,27197,302455,5,27797,302456,1,27797,302456,50,27798,302456,40,27798,302491,0,27798,328802,3,28550,329313,4,28924,329739,1,29299,329739,50,29300,329739,40,29300,329739,40,29300,329769,0,29300,329862,50,29300,329862,30,29300,329862,40,29300,329892,0,29300,329981,50,29300,329981,30,29300,329981,40,29300,330011,0,29306,330085,50,29306,330085,30,29306,330085,40,29306,330115,0,29306,330191,50,29306,330191,30,29306,330191,40,29306,330221,0,29306,330310,50,29306,330340,0,29312,330480,50,29314,330510,0,29314,330658,50,29318,330688,0,29323,330844,50,29328,330874,0,29328,331036,50,29337,331066,0,29337,331236,50,29352,331266,0,29356,331444,50,29384,331474,0,29384,331662,50,29444,331692,0,29444,331890,50,29558,331890,40,29558,331920,0,29558)
%
%
% START OF PROOF
% 331892 [] equal(multiply(identity,X),X).
% 331893 [] equal(multiply(inverse(X),X),identity).
% 331894 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 331895 [] -equal(multiply(sk_c6,sk_c5),sk_c7).
% 331916 [?] ?
% 331917 [?] ?
% 331918 [?] ?
% 331919 [?] ?
% 331920 [?] ?
% 331954 [input:331916,cut:331895] equal(inverse(sk_c4),sk_c6).
% 331955 [para:331954.1.1,331893.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 331956 [input:331919,cut:331895] equal(inverse(sk_c3),sk_c7).
% 331957 [para:331956.1.1,331893.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 331967 [input:331917,cut:331895] equal(multiply(sk_c4,sk_c6),sk_c7).
% 331968 [input:331918,cut:331895] equal(multiply(sk_c3,sk_c6),sk_c7).
% 331969 [input:331920,cut:331895] equal(multiply(sk_c6,sk_c7),sk_c5).
% 331970 [para:331893.1.1,331894.1.1.1,demod:331892] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 331983 [para:331955.1.1,331894.1.1.1,demod:331892] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 331984 [para:331957.1.1,331894.1.1.1,demod:331892] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 332001 [para:331969.1.1,331894.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c6,multiply(sk_c7,X))).
% 332006 [para:331967.1.1,331983.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 332013 [para:332006.1.2,331969.1.1] equal(sk_c6,sk_c5).
% 332014 [para:332006.1.2,331894.1.1.1,demod:332001] equal(multiply(sk_c6,X),multiply(sk_c5,X)).
% 332035 [para:332013.1.1,331967.1.1.2] equal(multiply(sk_c4,sk_c5),sk_c7).
% 332036 [para:332013.1.1,331968.1.1.2] equal(multiply(sk_c3,sk_c5),sk_c7).
% 332037 [para:332013.1.1,331969.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 332040 [para:332035.1.1,331894.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c4,multiply(sk_c5,X))).
% 332052 [para:331968.1.1,331984.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 332096 [para:331983.1.2,331970.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c6),X)).
% 332101 [para:332037.1.1,331970.1.2.2,demod:331893] equal(sk_c7,identity).
% 332104 [para:332014.1.1,331970.1.2.2,demod:332040,332096] equal(X,multiply(sk_c7,X)).
% 332112 [para:332101.1.1,331957.1.1.1,demod:331892] equal(sk_c3,identity).
% 332119 [para:332101.1.1,332052.1.2.1,demod:331892] equal(sk_c6,sk_c7).
% 332126 [para:332112.1.1,332036.1.1.1,demod:331892] equal(sk_c5,sk_c7).
% 332127 [para:332119.1.1,331895.1.1.1,demod:332104,cut:332126] 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_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c5) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c6),sk_c7) | -equal(inverse(U),sk_c6).
% Split part used next: -equal(multiply(sk_c6,sk_c7),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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(30,40,0,65,0,0,554,50,4,589,0,4,1093,50,7,1128,0,7,1637,50,12,1672,0,12,2187,50,17,2222,0,17,2744,50,23,2779,0,23,3309,50,34,3344,0,35,3882,50,57,3917,0,57,4465,50,107,4500,0,107,5058,50,216,5093,0,217,5663,50,412,5698,0,413,6280,50,779,6280,40,779,6315,0,779,16213,3,1080,17014,4,1230,17741,1,1380,17741,50,1380,17741,40,1380,17776,0,1380,17942,3,1689,17950,4,1832,17958,5,1981,17958,1,1981,17958,50,1981,17958,40,1981,17993,0,1981,43553,3,3483,44631,4,4232,45612,5,4982,45613,1,4982,45613,50,4983,45613,40,4983,45648,0,4983,61174,3,5737,62006,4,6109,62745,1,6484,62745,50,6484,62745,40,6484,62780,0,6484,73989,3,7243,74355,4,7610,75433,5,7985,75434,1,7985,75434,50,7985,75434,40,7985,75469,0,7985,145058,3,11886,145988,4,13837,146778,5,15786,146779,1,15786,146779,50,15789,146779,40,15789,146814,0,15789,207484,3,18341,208204,4,19615,208834,1,20890,208834,50,20892,208834,40,20892,208869,0,20892,255471,3,22408,256123,4,23143,256724,5,23893,256725,1,23893,256725,50,23895,256725,40,23895,256760,0,23895,265609,3,24670,266840,4,25027,267348,5,25396,267348,1,25396,267348,50,25396,267348,40,25396,267383,0,25396,301244,3,26597,301936,4,27197,302455,5,27797,302456,1,27797,302456,50,27798,302456,40,27798,302491,0,27798,328802,3,28550,329313,4,28924,329739,1,29299,329739,50,29300,329739,40,29300,329739,40,29300,329769,0,29300,329862,50,29300,329862,30,29300,329862,40,29300,329892,0,29300,329981,50,29300,329981,30,29300,329981,40,29300,330011,0,29306,330085,50,29306,330085,30,29306,330085,40,29306,330115,0,29306,330191,50,29306,330191,30,29306,330191,40,29306,330221,0,29306,330310,50,29306,330340,0,29312,330480,50,29314,330510,0,29314,330658,50,29318,330688,0,29323,330844,50,29328,330874,0,29328,331036,50,29337,331066,0,29337,331236,50,29352,331266,0,29356,331444,50,29384,331474,0,29384,331662,50,29444,331692,0,29444,331890,50,29558,331890,40,29558,331920,0,29558,332126,50,29559,332126,30,29559,332126,40,29559,332156,0,29559,332252,50,29560,332282,0,29564,332426,50,29567,332456,0,29567,332608,50,29570,332638,0,29570,332798,50,29575,332828,0,29579,332994,50,29588,333024,0,29588,333198,50,29603,333228,0,29608,333410,50,29636,333440,0,29636,333632,50,29697,333662,0,29697,333864,50,29812,333864,40,29812,333894,0,29812)
%
%
% START OF PROOF
% 333733 [?] ?
% 333866 [] equal(multiply(identity,X),X).
% 333867 [] equal(multiply(inverse(X),X),identity).
% 333868 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 333869 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 333874 [?] ?
% 333879 [?] ?
% 333884 [?] ?
% 333889 [?] ?
% 333894 [?] ?
% 333911 [input:333874,cut:333869] equal(inverse(sk_c2),sk_c6).
% 333912 [para:333911.1.1,333867.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 333921 [input:333884,cut:333869] equal(inverse(sk_c1),sk_c7).
% 333922 [para:333921.1.1,333867.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 333935 [input:333879,cut:333869] equal(multiply(sk_c2,sk_c6),sk_c5).
% 333940 [input:333889,cut:333869] equal(multiply(sk_c1,sk_c7),sk_c6).
% 333943 [input:333894,cut:333869] equal(multiply(sk_c6,sk_c5),sk_c7).
% 333948 [para:333912.1.1,333868.1.1.1,demod:333866] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 333954 [para:333922.1.1,333868.1.1.1,demod:333866] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 333980 [para:333935.1.1,333948.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c5)).
% 333985 [para:333980.1.2,333943.1.1] equal(sk_c6,sk_c7).
% 333987 [para:333985.1.1,333869.1.1.1] -equal(multiply(sk_c7,sk_c7),sk_c5).
% 334017 [para:333940.1.1,333954.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 334019 [para:333985.1.1,334017.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c7)).
% 334020 [para:334019.1.2,333987.1.1,cut:333733] 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: 32559
% derived clauses: 5532420
% kept clauses: 293996
% kept size sum: 343192
% kept mid-nuclei: 3328
% kept new demods: 3849
% forw unit-subs: 1666747
% forw double-subs: 3132979
% forw overdouble-subs: 398937
% backward subs: 12544
% fast unit cutoff: 23272
% full unit cutoff: 0
% dbl unit cutoff: 5770
% real runtime : 299.21
% process. runtime: 298.12
% specific non-discr-tree subsumption statistics:
% tried: 36786523
% length fails: 3920775
% strength fails: 9839003
% predlist fails: 3116340
% aux str. fails: 4434409
% by-lit fails: 8478333
% full subs tried: 1449057
% full subs fail: 1333122
%
% ; 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/GRP352-1+eq_r.in")
%
%------------------------------------------------------------------------------