TSTP Solution File: GRP237-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP237-1 : 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 298.7s
% Output : Assurance 298.7s
% 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/GRP237-1+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 23)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 23)
% (binary-posweight-lex-big-order 30 #f 3 23)
% (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_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9) | -equal(multiply(sk_c9,W),sk_c8) | -equal(multiply(X1,sk_c9),W) | -equal(inverse(X1),sk_c9).
% was split for some strategies as:
% -equal(multiply(sk_c9,W),sk_c8) | -equal(multiply(X1,sk_c9),W) | -equal(inverse(X1),sk_c9).
% -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9).
% -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9).
% -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9).
% -equal(inverse(sk_c9),sk_c8).
%
% 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_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9) | -equal(multiply(sk_c9,W),sk_c8) | -equal(multiply(X1,sk_c9),W) | -equal(inverse(X1),sk_c9).
% Split part used next: -equal(multiply(sk_c9,W),sk_c8) | -equal(multiply(X1,sk_c9),W) | -equal(inverse(X1),sk_c9).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,1,87,0,1,296807,5,1502,296808,1,1502,296808,50,1502,296808,40,1502,296854,0,1502,307994,3,1803,308701,4,1953,309354,1,2103,309354,50,2103,309354,40,2103,309400,0,2103,310195,3,2410,310206,4,2562,310267,5,2704,310267,1,2704,310267,50,2704,310267,40,2704,310313,0,2704,329775,3,4207,330761,4,4955,331674,1,5705,331674,50,5705,331674,40,5705,331720,0,5705,341981,3,6456,342932,4,6831,344912,50,7138,344912,40,7138,344958,0,7138,366712,3,7890,367236,4,8264,367644,1,8639,367644,50,8640,367644,40,8640,367690,0,8640,454034,3,12543,454777,4,14491,455147,1,16442,455147,50,16444,455147,40,16444,455193,0,16444,521020,3,19005,521596,4,20270,521948,1,21545,521948,50,21547,521948,40,21547,521994,0,21548,558907,3,23049,559734,4,23799,560276,1,24549,560276,50,24550,560276,40,24550,560322,0,24550,577658,3,25301,578265,4,25676,578837,1,26051,578837,50,26051,578837,40,26051,578883,0,26051,608220,3,27253,608684,4,27852,609049,1,28452,609049,50,28453,609049,40,28453,609095,0,28453,626961,3,29204,627376,4,29579,627848,1,29954,627848,50,29954,627848,40,29954,627848,40,29954,627889,0,29954)
%
%
% START OF PROOF
% 627849 [] equal(X,X).
% 627853 [] -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9).
% 627854 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 627855 [] equal(multiply(sk_c6,sk_c9),sk_c7) | equal(inverse(sk_c2),sk_c9).
% 627856 [?] ?
% 627860 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c6),sk_c9).
% 627861 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 627862 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c9,sk_c7),sk_c8).
% 627866 [?] ?
% 627867 [?] ?
% 627868 [?] ?
% 627925 [hyper:627853,627855,627854,binarycut:627856] equal(inverse(sk_c2),sk_c9).
% 627937 [hyper:627853,627860,demod:627925,cut:627849,binarycut:627866] equal(inverse(sk_c6),sk_c9).
% 627944 [hyper:627853,627861,demod:627925,cut:627849,binarycut:627867] equal(multiply(sk_c6,sk_c9),sk_c7).
% 627958 [hyper:627853,627862,demod:627925,cut:627849,binarycut:627868] equal(multiply(sk_c9,sk_c7),sk_c8).
% 627965 [hyper:627853,627958,627944,demod:627937,cut:627849] 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 23
% 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_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9) | -equal(multiply(sk_c9,W),sk_c8) | -equal(multiply(X1,sk_c9),W) | -equal(inverse(X1),sk_c9).
% Split part used next: -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),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 23
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,1,87,0,1,296807,5,1502,296808,1,1502,296808,50,1502,296808,40,1502,296854,0,1502,307994,3,1803,308701,4,1953,309354,1,2103,309354,50,2103,309354,40,2103,309400,0,2103,310195,3,2410,310206,4,2562,310267,5,2704,310267,1,2704,310267,50,2704,310267,40,2704,310313,0,2704,329775,3,4207,330761,4,4955,331674,1,5705,331674,50,5705,331674,40,5705,331720,0,5705,341981,3,6456,342932,4,6831,344912,50,7138,344912,40,7138,344958,0,7138,366712,3,7890,367236,4,8264,367644,1,8639,367644,50,8640,367644,40,8640,367690,0,8640,454034,3,12543,454777,4,14491,455147,1,16442,455147,50,16444,455147,40,16444,455193,0,16444,521020,3,19005,521596,4,20270,521948,1,21545,521948,50,21547,521948,40,21547,521994,0,21548,558907,3,23049,559734,4,23799,560276,1,24549,560276,50,24550,560276,40,24550,560322,0,24550,577658,3,25301,578265,4,25676,578837,1,26051,578837,50,26051,578837,40,26051,578883,0,26051,608220,3,27253,608684,4,27852,609049,1,28452,609049,50,28453,609049,40,28453,609095,0,28453,626961,3,29204,627376,4,29579,627848,1,29954,627848,50,29954,627848,40,29954,627848,40,29954,627889,0,29954,627964,50,29954,627964,30,29954,627964,40,29954,628005,0,29954)
%
%
% START OF PROOF
% 627966 [] equal(multiply(identity,X),X).
% 627967 [] equal(multiply(inverse(X),X),identity).
% 627968 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 627969 [] -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(Y,X),sk_c9) | -equal(inverse(Y),X).
% 627973 [?] ?
% 627974 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c4),sk_c5).
% 627975 [?] ?
% 627979 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 627980 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c4),sk_c5).
% 627981 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c4,sk_c5),sk_c9).
% 627985 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 627986 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(inverse(sk_c4),sk_c5).
% 627987 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(multiply(sk_c4,sk_c5),sk_c9).
% 627991 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 627992 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(inverse(sk_c4),sk_c5).
% 627993 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(multiply(sk_c4,sk_c5),sk_c9).
% 627997 [?] ?
% 627998 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c4),sk_c5).
% 627999 [?] ?
% 628003 [?] ?
% 628004 [] equal(inverse(sk_c9),sk_c8) | equal(inverse(sk_c4),sk_c5).
% 628005 [?] ?
% 628014 [hyper:627969,627974,binarycut:627975,binarycut:627973] equal(inverse(sk_c2),sk_c9).
% 628017 [para:628014.1.1,627967.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 628030 [hyper:627969,627998,binarycut:627999,binarycut:627997] equal(inverse(sk_c1),sk_c9).
% 628033 [para:628030.1.1,627967.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 628044 [hyper:627969,628004,binarycut:628005,binarycut:628003] equal(inverse(sk_c9),sk_c8).
% 628047 [para:628044.1.1,627967.1.1.1] equal(multiply(sk_c8,sk_c9),identity).
% 628082 [hyper:627969,627981,627979,627980] equal(multiply(sk_c2,sk_c9),sk_c3).
% 628094 [hyper:627969,627987,627985,627986] equal(multiply(sk_c9,sk_c3),sk_c8).
% 628120 [hyper:627969,627993,627991,627992] equal(multiply(sk_c1,sk_c8),sk_c9).
% 628127 [para:627967.1.1,627968.1.1.1,demod:627966] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 628128 [para:628017.1.1,627968.1.1.1,demod:627966] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 628129 [para:628033.1.1,627968.1.1.1,demod:627966] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 628136 [para:628082.1.1,628128.1.2.2,demod:628094] equal(sk_c9,sk_c8).
% 628140 [para:628136.1.1,628047.1.1.2] equal(multiply(sk_c8,sk_c8),identity).
% 628141 [para:628136.1.1,628082.1.1.2] equal(multiply(sk_c2,sk_c8),sk_c3).
% 628142 [para:628136.1.1,628094.1.1.1] equal(multiply(sk_c8,sk_c3),sk_c8).
% 628149 [para:628017.1.1,628127.1.2.2,demod:628044] equal(sk_c2,multiply(sk_c8,identity)).
% 628150 [para:628033.1.1,628127.1.2.2,demod:628149,628044] equal(sk_c1,sk_c2).
% 628154 [para:628128.1.2,628127.1.2.2,demod:628044] equal(multiply(sk_c2,X),multiply(sk_c8,X)).
% 628167 [para:628136.1.1,628129.1.2.1,demod:628154] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 628168 [para:628129.1.2,628127.1.2.2,demod:628154,628044] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 628169 [para:628141.1.1,627968.1.1.1,demod:628167,628168,628154] equal(multiply(sk_c3,X),X).
% 628170 [para:628150.1.2,628141.1.1.1,demod:628120] equal(sk_c9,sk_c3).
% 628175 [para:628170.1.1,628033.1.1.1,demod:628169] equal(sk_c1,identity).
% 628176 [para:628170.1.1,628044.1.1.1] equal(inverse(sk_c3),sk_c8).
% 628177 [para:628170.1.1,628047.1.1.2,demod:628142] equal(sk_c8,identity).
% 628180 [para:628170.1.1,628128.1.2.1,demod:628169,628168] equal(X,multiply(sk_c1,X)).
% 628184 [para:628175.1.1,628120.1.1.1,demod:627966] equal(sk_c8,sk_c9).
% 628186 [para:628177.1.1,628120.1.1.2,demod:628180] equal(identity,sk_c9).
% 628193 [hyper:627969,628176,demod:628140,628169,cut:628184,cut:628186] 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 23
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9) | -equal(multiply(sk_c9,W),sk_c8) | -equal(multiply(X1,sk_c9),W) | -equal(inverse(X1),sk_c9).
% Split part used next: -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),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 23
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,1,87,0,1,296807,5,1502,296808,1,1502,296808,50,1502,296808,40,1502,296854,0,1502,307994,3,1803,308701,4,1953,309354,1,2103,309354,50,2103,309354,40,2103,309400,0,2103,310195,3,2410,310206,4,2562,310267,5,2704,310267,1,2704,310267,50,2704,310267,40,2704,310313,0,2704,329775,3,4207,330761,4,4955,331674,1,5705,331674,50,5705,331674,40,5705,331720,0,5705,341981,3,6456,342932,4,6831,344912,50,7138,344912,40,7138,344958,0,7138,366712,3,7890,367236,4,8264,367644,1,8639,367644,50,8640,367644,40,8640,367690,0,8640,454034,3,12543,454777,4,14491,455147,1,16442,455147,50,16444,455147,40,16444,455193,0,16444,521020,3,19005,521596,4,20270,521948,1,21545,521948,50,21547,521948,40,21547,521994,0,21548,558907,3,23049,559734,4,23799,560276,1,24549,560276,50,24550,560276,40,24550,560322,0,24550,577658,3,25301,578265,4,25676,578837,1,26051,578837,50,26051,578837,40,26051,578883,0,26051,608220,3,27253,608684,4,27852,609049,1,28452,609049,50,28453,609049,40,28453,609095,0,28453,626961,3,29204,627376,4,29579,627848,1,29954,627848,50,29954,627848,40,29954,627848,40,29954,627889,0,29954,627964,50,29954,627964,30,29954,627964,40,29954,628005,0,29954,628192,50,29954,628192,30,29954,628192,40,29954,628233,0,29960)
%
%
% START OF PROOF
% 628193 [] equal(X,X).
% 628197 [] -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9).
% 628198 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 628199 [] equal(multiply(sk_c6,sk_c9),sk_c7) | equal(inverse(sk_c2),sk_c9).
% 628200 [?] ?
% 628204 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c6),sk_c9).
% 628205 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 628206 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c9,sk_c7),sk_c8).
% 628210 [?] ?
% 628211 [?] ?
% 628212 [?] ?
% 628269 [hyper:628197,628199,628198,binarycut:628200] equal(inverse(sk_c2),sk_c9).
% 628281 [hyper:628197,628204,demod:628269,cut:628193,binarycut:628210] equal(inverse(sk_c6),sk_c9).
% 628288 [hyper:628197,628205,demod:628269,cut:628193,binarycut:628211] equal(multiply(sk_c6,sk_c9),sk_c7).
% 628302 [hyper:628197,628206,demod:628269,cut:628193,binarycut:628212] equal(multiply(sk_c9,sk_c7),sk_c8).
% 628309 [hyper:628197,628302,628288,demod:628281,cut:628193] 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 23
% 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_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9) | -equal(multiply(sk_c9,W),sk_c8) | -equal(multiply(X1,sk_c9),W) | -equal(inverse(X1),sk_c9).
% Split part used next: -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),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 23
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,1,87,0,1,296807,5,1502,296808,1,1502,296808,50,1502,296808,40,1502,296854,0,1502,307994,3,1803,308701,4,1953,309354,1,2103,309354,50,2103,309354,40,2103,309400,0,2103,310195,3,2410,310206,4,2562,310267,5,2704,310267,1,2704,310267,50,2704,310267,40,2704,310313,0,2704,329775,3,4207,330761,4,4955,331674,1,5705,331674,50,5705,331674,40,5705,331720,0,5705,341981,3,6456,342932,4,6831,344912,50,7138,344912,40,7138,344958,0,7138,366712,3,7890,367236,4,8264,367644,1,8639,367644,50,8640,367644,40,8640,367690,0,8640,454034,3,12543,454777,4,14491,455147,1,16442,455147,50,16444,455147,40,16444,455193,0,16444,521020,3,19005,521596,4,20270,521948,1,21545,521948,50,21547,521948,40,21547,521994,0,21548,558907,3,23049,559734,4,23799,560276,1,24549,560276,50,24550,560276,40,24550,560322,0,24550,577658,3,25301,578265,4,25676,578837,1,26051,578837,50,26051,578837,40,26051,578883,0,26051,608220,3,27253,608684,4,27852,609049,1,28452,609049,50,28453,609049,40,28453,609095,0,28453,626961,3,29204,627376,4,29579,627848,1,29954,627848,50,29954,627848,40,29954,627848,40,29954,627889,0,29954,627964,50,29954,627964,30,29954,627964,40,29954,628005,0,29954,628192,50,29954,628192,30,29954,628192,40,29954,628233,0,29960,628308,50,29961,628308,30,29961,628308,40,29961,628349,0,29961)
%
%
% START OF PROOF
% 628310 [] equal(multiply(identity,X),X).
% 628311 [] equal(multiply(inverse(X),X),identity).
% 628312 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 628313 [] -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c9).
% 628332 [?] ?
% 628333 [?] ?
% 628334 [?] ?
% 628335 [?] ?
% 628336 [?] ?
% 628337 [?] ?
% 628338 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 628339 [] equal(multiply(sk_c6,sk_c9),sk_c7) | equal(inverse(sk_c1),sk_c9).
% 628340 [] equal(multiply(sk_c9,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c9).
% 628341 [] equal(multiply(sk_c5,sk_c8),sk_c9) | equal(inverse(sk_c1),sk_c9).
% 628342 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c4),sk_c5).
% 628343 [] equal(multiply(sk_c4,sk_c5),sk_c9) | equal(inverse(sk_c1),sk_c9).
% 628358 [hyper:628313,628338,binarycut:628332] equal(inverse(sk_c6),sk_c9).
% 628362 [para:628358.1.1,628311.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 628366 [hyper:628313,628342,binarycut:628336] equal(inverse(sk_c4),sk_c5).
% 628385 [hyper:628313,628339,binarycut:628333] equal(multiply(sk_c6,sk_c9),sk_c7).
% 628388 [hyper:628313,628340,binarycut:628334] equal(multiply(sk_c9,sk_c7),sk_c8).
% 628395 [hyper:628313,628341,binarycut:628335] equal(multiply(sk_c5,sk_c8),sk_c9).
% 628401 [hyper:628313,628343,binarycut:628337] equal(multiply(sk_c4,sk_c5),sk_c9).
% 628402 [para:628311.1.1,628312.1.1.1,demod:628310] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 628403 [para:628362.1.1,628312.1.1.1,demod:628310] equal(X,multiply(sk_c9,multiply(sk_c6,X))).
% 628409 [para:628385.1.1,628403.1.2.2,demod:628388] equal(sk_c9,sk_c8).
% 628420 [para:628401.1.1,628402.1.2.2,demod:628366] equal(sk_c5,multiply(sk_c5,sk_c9)).
% 628428 [para:628409.1.1,628420.1.2.2,demod:628395] equal(sk_c5,sk_c9).
% 628429 [para:628420.1.2,628402.1.2.2,demod:628311] equal(sk_c9,identity).
% 628432 [para:628428.1.2,628388.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c8).
% 628436 [para:628429.1.1,628362.1.1.1,demod:628310] equal(sk_c6,identity).
% 628438 [para:628429.1.1,628388.1.1.1,demod:628310] equal(sk_c7,sk_c8).
% 628445 [para:628436.1.1,628358.1.1.1] equal(inverse(identity),sk_c9).
% 628449 [para:628438.1.2,628395.1.1.2,demod:628432] equal(sk_c8,sk_c9).
% 628475 [hyper:628313,628445,demod:628310,cut:628449] 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 23
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9) | -equal(multiply(sk_c9,W),sk_c8) | -equal(multiply(X1,sk_c9),W) | -equal(inverse(X1),sk_c9).
% Split part used next: -equal(inverse(sk_c9),sk_c8).
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% clause depth limited to 12
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,1,87,0,1,296807,5,1502,296808,1,1502,296808,50,1502,296808,40,1502,296854,0,1502,307994,3,1803,308701,4,1953,309354,1,2103,309354,50,2103,309354,40,2103,309400,0,2103,310195,3,2410,310206,4,2562,310267,5,2704,310267,1,2704,310267,50,2704,310267,40,2704,310313,0,2704,329775,3,4207,330761,4,4955,331674,1,5705,331674,50,5705,331674,40,5705,331720,0,5705,341981,3,6456,342932,4,6831,344912,50,7138,344912,40,7138,344958,0,7138,366712,3,7890,367236,4,8264,367644,1,8639,367644,50,8640,367644,40,8640,367690,0,8640,454034,3,12543,454777,4,14491,455147,1,16442,455147,50,16444,455147,40,16444,455193,0,16444,521020,3,19005,521596,4,20270,521948,1,21545,521948,50,21547,521948,40,21547,521994,0,21548,558907,3,23049,559734,4,23799,560276,1,24549,560276,50,24550,560276,40,24550,560322,0,24550,577658,3,25301,578265,4,25676,578837,1,26051,578837,50,26051,578837,40,26051,578883,0,26051,608220,3,27253,608684,4,27852,609049,1,28452,609049,50,28453,609049,40,28453,609095,0,28453,626961,3,29204,627376,4,29579,627848,1,29954,627848,50,29954,627848,40,29954,627848,40,29954,627889,0,29954,627964,50,29954,627964,30,29954,627964,40,29954,628005,0,29954,628192,50,29954,628192,30,29954,628192,40,29954,628233,0,29960,628308,50,29961,628308,30,29961,628308,40,29961,628349,0,29961,628474,50,29961,628474,30,29961,628474,40,29961,628515,0,29961,628650,50,29962,628691,0,29967,628873,50,29970,628914,0,29970,629104,50,29975,629145,0,29979,629343,50,29986,629384,0,29986,629588,50,29996,629629,0,29996,629841,50,30014,629882,0,30019,630102,50,30051,630143,0,30051,630373,50,30117,630414,0,30117,630654,50,30239,630695,0,30239,630947,4,30471)
%
%
% START OF PROOF
% 630656 [] equal(multiply(identity,X),X).
% 630657 [] equal(multiply(inverse(X),X),identity).
% 630658 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 630659 [] -equal(inverse(sk_c9),sk_c8).
% 630690 [?] ?
% 630691 [?] ?
% 630692 [?] ?
% 630693 [?] ?
% 630694 [?] ?
% 630695 [?] ?
% 630701 [input:630690,cut:630659] equal(inverse(sk_c6),sk_c9).
% 630702 [para:630701.1.1,630657.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 630704 [input:630694,cut:630659] equal(inverse(sk_c4),sk_c5).
% 630705 [para:630704.1.1,630657.1.1.1] equal(multiply(sk_c5,sk_c4),identity).
% 630720 [input:630691,cut:630659] equal(multiply(sk_c6,sk_c9),sk_c7).
% 630722 [input:630692,cut:630659] equal(multiply(sk_c9,sk_c7),sk_c8).
% 630723 [input:630693,cut:630659] equal(multiply(sk_c5,sk_c8),sk_c9).
% 630724 [input:630695,cut:630659] equal(multiply(sk_c4,sk_c5),sk_c9).
% 630734 [para:630657.1.1,630658.1.1.1,demod:630656] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 630735 [para:630702.1.1,630658.1.1.1,demod:630656] equal(X,multiply(sk_c9,multiply(sk_c6,X))).
% 630736 [para:630705.1.1,630658.1.1.1,demod:630656] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 630738 [para:630722.1.1,630658.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c9,multiply(sk_c7,X))).
% 630739 [para:630723.1.1,630658.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c5,multiply(sk_c8,X))).
% 630740 [para:630724.1.1,630658.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c4,multiply(sk_c5,X))).
% 630741 [para:630720.1.1,630735.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c7)).
% 630742 [para:630741.1.2,630722.1.1] equal(sk_c9,sk_c8).
% 630743 [para:630741.1.2,630658.1.1.1,demod:630738] equal(multiply(sk_c9,X),multiply(sk_c8,X)).
% 630744 [para:630742.1.1,630702.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 630746 [para:630742.1.1,630722.1.1.1] equal(multiply(sk_c8,sk_c7),sk_c8).
% 630749 [para:630657.1.1,630734.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 630751 [para:630705.1.1,630734.1.2.2] equal(sk_c4,multiply(inverse(sk_c5),identity)).
% 630756 [para:630658.1.1,630734.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 630760 [para:630734.1.2,630734.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 630764 [para:630746.1.1,630734.1.2.2,demod:630657] equal(sk_c7,identity).
% 630765 [para:630764.1.1,630722.1.1.2,demod:630743] equal(multiply(sk_c8,identity),sk_c8).
% 630766 [para:630724.1.1,630736.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c9)).
% 630767 [para:630736.1.2,630734.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c5),X)).
% 630768 [para:630766.1.2,630658.1.1.1,demod:630739,630743] equal(multiply(sk_c5,X),multiply(sk_c8,X)).
% 630769 [para:630742.1.1,630766.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c8)).
% 630770 [para:630766.1.2,630734.1.2.2,demod:630767] equal(sk_c9,multiply(sk_c4,sk_c5)).
% 630771 [para:630769.1.2,630723.1.1] equal(sk_c5,sk_c9).
% 630773 [para:630771.1.2,630702.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 630774 [para:630771.1.2,630720.1.1.2] equal(multiply(sk_c6,sk_c5),sk_c7).
% 630777 [para:630771.1.2,630742.1.1] equal(sk_c5,sk_c8).
% 630780 [para:630777.1.2,630765.1.1.1] equal(multiply(sk_c5,identity),sk_c8).
% 630787 [para:630773.1.1,630734.1.2.2,demod:630751] equal(sk_c6,sk_c4).
% 630793 [para:630787.1.1,630774.1.1.1,demod:630770] equal(sk_c9,sk_c7).
% 630798 [para:630793.1.1,630771.1.2] equal(sk_c5,sk_c7).
% 630800 [para:630744.1.1,630739.1.2.2,demod:630780,630702] equal(identity,sk_c8).
% 630801 [para:630798.1.2,630764.1.1] equal(sk_c5,identity).
% 630807 [para:630801.1.1,630736.1.2.1,demod:630656] equal(X,multiply(sk_c4,X)).
% 630809 [para:630736.1.2,630740.1.2.2,demod:630768,630743,630807] equal(multiply(sk_c5,X),X).
% 630854 [para:630760.1.2,630657.1.1] equal(multiply(X,inverse(X)),identity).
% 630856 [para:630760.1.2,630749.1.2] equal(X,multiply(X,identity)).
% 630857 [para:630856.1.2,630749.1.2] equal(X,inverse(inverse(X))).
% 630865 [para:630854.1.1,630756.1.2.2.2,demod:630856] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 630876 [para:630865.1.2,630865.1.2.1.1,demod:630857] equal(inverse(X),multiply(Y,inverse(multiply(X,Y)))).
% 630883 [para:630876.1.2,630658.1.1] equal(inverse(X),multiply(Y,multiply(Z,inverse(multiply(X,multiply(Y,Z)))))).
% 630885 [para:630658.1.1,630876.1.2.2.1] equal(inverse(multiply(X,Y)),multiply(Z,inverse(multiply(X,multiply(Y,Z))))).
% 630891 [para:630883.1.2,630658.1.1,demod:630658] equal(inverse(X),multiply(Y,multiply(Z,multiply(U,inverse(multiply(X,multiply(Y,multiply(Z,U)))))))).
% 630895 [para:630658.1.1,630885.1.2.2.1,demod:630658] equal(inverse(multiply(X,multiply(Y,Z))),multiply(U,inverse(multiply(X,multiply(Y,multiply(Z,U)))))).
% 630900 [para:630891.1.2,630658.1.1,demod:630658] equal(inverse(X),multiply(Y,multiply(Z,multiply(U,multiply(V,inverse(multiply(X,multiply(Y,multiply(Z,multiply(U,V)))))))))).
% 630905 [para:630658.1.1,630895.1.2.2.1,demod:630658] equal(inverse(multiply(X,multiply(Y,multiply(Z,U)))),multiply(V,inverse(multiply(X,multiply(Y,multiply(Z,multiply(U,V))))))).
% 630911 [para:630900.1.2,630658.1.1,demod:630658] equal(inverse(X),multiply(Y,multiply(Z,multiply(U,multiply(V,multiply(W,inverse(multiply(X,multiply(Y,multiply(Z,multiply(U,multiply(V,W)))))))))))).
% 630948 [para:630911.1.1,630659.1.1,demod:630854,630876,630885,630895,630905,630809,630768,630743,cut:630800] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 12
% seconds given: 6
%
%
% Split attempt finished with SUCCESS.
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 32602
% derived clauses: 4661535
% kept clauses: 290649
% kept size sum: 15102
% kept mid-nuclei: 224380
% kept new demods: 2331
% forw unit-subs: 932559
% forw double-subs: 2902977
% forw overdouble-subs: 246018
% backward subs: 24019
% fast unit cutoff: 31930
% full unit cutoff: 0
% dbl unit cutoff: 76685
% real runtime : 306.40
% process. runtime: 304.70
% specific non-discr-tree subsumption statistics:
% tried: 20619484
% length fails: 2589778
% strength fails: 6106514
% predlist fails: 1018974
% aux str. fails: 2365497
% by-lit fails: 3050940
% full subs tried: 1744847
% full subs fail: 1610085
%
% ; 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/GRP237-1+eq_r.in")
%
%------------------------------------------------------------------------------