TSTP Solution File: GRP369-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP369-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art09.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 298.0s
% Output : Assurance 298.0s
% 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/GRP369-1+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 25)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 25)
% (binary-posweight-lex-big-order 30 #f 3 25)
% (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_c7,sk_c9),sk_c8) | -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9) | -equal(multiply(Z,sk_c7),sk_c9) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% was split for some strategies as:
% -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8).
% -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% -equal(multiply(Z,sk_c7),sk_c9) | -equal(inverse(Z),sk_c7).
% -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9).
% -equal(multiply(sk_c7,sk_c9),sk_c8).
% -equal(inverse(sk_c8),sk_c7).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c9),sk_c8) | -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9) | -equal(multiply(Z,sk_c7),sk_c9) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(47,40,0,100,0,0,894,50,10,947,0,10,1974,50,30,2027,0,30,3171,50,46,3224,0,46,4430,50,65,4483,0,65,5752,50,89,5805,0,90,7166,50,124,7219,0,124,8672,50,178,8725,0,178,10300,50,269,10353,0,269,12050,50,432,12103,0,433,13952,50,665,14005,0,665,16006,50,1098,16006,40,1098,16059,0,1098,27084,3,1399,27759,4,1549,28362,5,1699,28363,1,1699,28363,50,1699,28363,40,1699,28416,0,1699,28723,3,2001,28734,4,2161,28747,5,2300,28747,1,2300,28747,50,2300,28747,40,2300,28800,0,2300,58208,3,3801,58943,4,4551,59706,5,5301,59707,1,5301,59707,50,5302,59707,40,5302,59760,0,5302,78344,3,6053,79057,4,6428,79568,5,6803,79569,1,6803,79569,50,6803,79569,40,6803,79622,0,6803,93455,3,7556,94322,4,7929,95734,5,8304,95735,1,8304,95735,50,8304,95735,40,8304,95788,0,8304,216615,3,12205,217502,4,14156,218411,1,16106,218411,50,16109,218411,40,16109,218464,0,16109,301256,3,18661,301847,4,19935,302420,5,21210,302421,1,21210,302421,50,21213,302421,40,21213,302474,0,21213,347869,3,22715,348636,4,23464,349224,1,24214,349224,50,24215,349224,40,24215,349277,0,24215,362700,3,24972,363871,4,25341,363974,5,25716,363974,1,25716,363974,50,25716,363974,40,25716,364027,0,25716,408464,3,26918,408955,4,27517,409589,1,28117,409589,50,28118,409589,40,28118,409642,0,28118,434655,3,28870,435208,4,29244,435815,1,29619,435815,50,29619,435815,40,29619,435815,40,29620,435862,0,29620)
%
%
% START OF PROOF
% 435817 [] equal(multiply(identity,X),X).
% 435818 [] equal(multiply(inverse(X),X),identity).
% 435819 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 435820 [] -equal(multiply(X,sk_c9),sk_c7) | -equal(inverse(X),sk_c9).
% 435821 [] equal(inverse(sk_c3),sk_c7) | equal(inverse(sk_c6),sk_c9).
% 435822 [?] ?
% 435828 [] equal(multiply(sk_c3,sk_c7),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 435829 [] equal(multiply(sk_c3,sk_c7),sk_c9) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 435835 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 435836 [?] ?
% 435842 [] equal(multiply(sk_c1,sk_c9),sk_c2) | equal(inverse(sk_c6),sk_c9).
% 435843 [] equal(multiply(sk_c1,sk_c9),sk_c2) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 435849 [] equal(multiply(sk_c9,sk_c2),sk_c8) | equal(inverse(sk_c6),sk_c9).
% 435850 [] equal(multiply(sk_c9,sk_c2),sk_c8) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 435856 [] equal(multiply(sk_c7,sk_c9),sk_c8) | equal(inverse(sk_c6),sk_c9).
% 435857 [] equal(multiply(sk_c7,sk_c9),sk_c8) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 435865 [hyper:435820,435821,binarycut:435822] equal(inverse(sk_c3),sk_c7).
% 435866 [para:435865.1.1,435818.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 435871 [hyper:435820,435835,binarycut:435836] equal(inverse(sk_c1),sk_c9).
% 435874 [para:435871.1.1,435818.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 435881 [hyper:435820,435829,435828] equal(multiply(sk_c3,sk_c7),sk_c9).
% 435893 [hyper:435820,435843,435842] equal(multiply(sk_c1,sk_c9),sk_c2).
% 435896 [hyper:435820,435850,435849] equal(multiply(sk_c9,sk_c2),sk_c8).
% 435902 [hyper:435820,435857,435856] equal(multiply(sk_c7,sk_c9),sk_c8).
% 435903 [para:435818.1.1,435819.1.1.1,demod:435817] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 435904 [para:435866.1.1,435819.1.1.1,demod:435817] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 435909 [para:435881.1.1,435904.1.2.2,demod:435902] equal(sk_c7,sk_c8).
% 435910 [para:435909.1.1,435866.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 435914 [para:435909.1.1,435902.1.1.1] equal(multiply(sk_c8,sk_c9),sk_c8).
% 435919 [para:435893.1.1,435903.1.2.2,demod:435896,435871] equal(sk_c9,sk_c8).
% 435928 [para:435914.1.1,435903.1.2.2,demod:435818] equal(sk_c9,identity).
% 435930 [para:435928.1.1,435874.1.1.1,demod:435817] equal(sk_c1,identity).
% 435934 [para:435928.1.1,435919.1.1] equal(identity,sk_c8).
% 435937 [para:435930.1.1,435871.1.1.1] equal(inverse(identity),sk_c9).
% 435945 [para:435934.1.2,435910.1.1.1,demod:435817] equal(sk_c3,identity).
% 435954 [para:435945.1.1,435865.1.1.1,demod:435937] equal(sk_c9,sk_c7).
% 435968 [hyper:435820,435937,demod:435817,cut:435954] 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 25
% 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_c7,sk_c9),sk_c8) | -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9) | -equal(multiply(Z,sk_c7),sk_c9) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),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 25
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(47,40,0,100,0,0,894,50,10,947,0,10,1974,50,30,2027,0,30,3171,50,46,3224,0,46,4430,50,65,4483,0,65,5752,50,89,5805,0,90,7166,50,124,7219,0,124,8672,50,178,8725,0,178,10300,50,269,10353,0,269,12050,50,432,12103,0,433,13952,50,665,14005,0,665,16006,50,1098,16006,40,1098,16059,0,1098,27084,3,1399,27759,4,1549,28362,5,1699,28363,1,1699,28363,50,1699,28363,40,1699,28416,0,1699,28723,3,2001,28734,4,2161,28747,5,2300,28747,1,2300,28747,50,2300,28747,40,2300,28800,0,2300,58208,3,3801,58943,4,4551,59706,5,5301,59707,1,5301,59707,50,5302,59707,40,5302,59760,0,5302,78344,3,6053,79057,4,6428,79568,5,6803,79569,1,6803,79569,50,6803,79569,40,6803,79622,0,6803,93455,3,7556,94322,4,7929,95734,5,8304,95735,1,8304,95735,50,8304,95735,40,8304,95788,0,8304,216615,3,12205,217502,4,14156,218411,1,16106,218411,50,16109,218411,40,16109,218464,0,16109,301256,3,18661,301847,4,19935,302420,5,21210,302421,1,21210,302421,50,21213,302421,40,21213,302474,0,21213,347869,3,22715,348636,4,23464,349224,1,24214,349224,50,24215,349224,40,24215,349277,0,24215,362700,3,24972,363871,4,25341,363974,5,25716,363974,1,25716,363974,50,25716,363974,40,25716,364027,0,25716,408464,3,26918,408955,4,27517,409589,1,28117,409589,50,28118,409589,40,28118,409642,0,28118,434655,3,28870,435208,4,29244,435815,1,29619,435815,50,29619,435815,40,29619,435815,40,29620,435862,0,29620,435967,50,29620,435967,30,29620,435967,40,29620,436014,0,29620)
%
%
% START OF PROOF
% 435969 [] equal(multiply(identity,X),X).
% 435970 [] equal(multiply(inverse(X),X),identity).
% 435971 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 435972 [] -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8).
% 435975 [] equal(inverse(sk_c3),sk_c7) | equal(inverse(sk_c5),sk_c8).
% 435976 [?] ?
% 435982 [] equal(multiply(sk_c3,sk_c7),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 435983 [] equal(multiply(sk_c3,sk_c7),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 436010 [] equal(multiply(sk_c7,sk_c9),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 436011 [] equal(multiply(sk_c7,sk_c9),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 436018 [hyper:435972,435975,binarycut:435976] equal(inverse(sk_c3),sk_c7).
% 436021 [para:436018.1.1,435970.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 436038 [hyper:435972,435983,435982] equal(multiply(sk_c3,sk_c7),sk_c9).
% 436073 [hyper:435972,436011,436010] equal(multiply(sk_c7,sk_c9),sk_c8).
% 436075 [para:436021.1.1,435971.1.1.1,demod:435969] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 436080 [para:436038.1.1,436075.1.2.2,demod:436073] equal(sk_c7,sk_c8).
% 436082 [para:436080.1.1,436038.1.1.2] equal(multiply(sk_c3,sk_c8),sk_c9).
% 436086 [hyper:435972,436082,demod:436018,cut:436080] 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 25
% 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_c7,sk_c9),sk_c8) | -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9) | -equal(multiply(Z,sk_c7),sk_c9) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),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 25
% 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 25
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(47,40,0,100,0,0,894,50,10,947,0,10,1974,50,30,2027,0,30,3171,50,46,3224,0,46,4430,50,65,4483,0,65,5752,50,89,5805,0,90,7166,50,124,7219,0,124,8672,50,178,8725,0,178,10300,50,269,10353,0,269,12050,50,432,12103,0,433,13952,50,665,14005,0,665,16006,50,1098,16006,40,1098,16059,0,1098,27084,3,1399,27759,4,1549,28362,5,1699,28363,1,1699,28363,50,1699,28363,40,1699,28416,0,1699,28723,3,2001,28734,4,2161,28747,5,2300,28747,1,2300,28747,50,2300,28747,40,2300,28800,0,2300,58208,3,3801,58943,4,4551,59706,5,5301,59707,1,5301,59707,50,5302,59707,40,5302,59760,0,5302,78344,3,6053,79057,4,6428,79568,5,6803,79569,1,6803,79569,50,6803,79569,40,6803,79622,0,6803,93455,3,7556,94322,4,7929,95734,5,8304,95735,1,8304,95735,50,8304,95735,40,8304,95788,0,8304,216615,3,12205,217502,4,14156,218411,1,16106,218411,50,16109,218411,40,16109,218464,0,16109,301256,3,18661,301847,4,19935,302420,5,21210,302421,1,21210,302421,50,21213,302421,40,21213,302474,0,21213,347869,3,22715,348636,4,23464,349224,1,24214,349224,50,24215,349224,40,24215,349277,0,24215,362700,3,24972,363871,4,25341,363974,5,25716,363974,1,25716,363974,50,25716,363974,40,25716,364027,0,25716,408464,3,26918,408955,4,27517,409589,1,28117,409589,50,28118,409589,40,28118,409642,0,28118,434655,3,28870,435208,4,29244,435815,1,29619,435815,50,29619,435815,40,29619,435815,40,29620,435862,0,29620,435967,50,29620,435967,30,29620,435967,40,29620,436014,0,29620,436085,50,29621,436085,30,29621,436085,40,29621,436132,0,29627,436276,50,29627,436323,0,29627)
%
%
% START OF PROOF
% 436278 [] equal(multiply(identity,X),X).
% 436279 [] equal(multiply(inverse(X),X),identity).
% 436280 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 436281 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 436286 [] equal(inverse(sk_c3),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 436287 [?] ?
% 436293 [] equal(multiply(sk_c3,sk_c7),sk_c9) | equal(inverse(sk_c4),sk_c8).
% 436294 [] equal(multiply(sk_c3,sk_c7),sk_c9) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 436300 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c4),sk_c8).
% 436301 [?] ?
% 436307 [] equal(multiply(sk_c1,sk_c9),sk_c2) | equal(inverse(sk_c4),sk_c8).
% 436308 [] equal(multiply(sk_c1,sk_c9),sk_c2) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 436314 [] equal(multiply(sk_c9,sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 436315 [] equal(multiply(sk_c9,sk_c2),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 436321 [] equal(multiply(sk_c7,sk_c9),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 436322 [] equal(multiply(sk_c7,sk_c9),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 436330 [hyper:436281,436286,binarycut:436287] equal(inverse(sk_c3),sk_c7).
% 436332 [para:436330.1.1,436279.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 436339 [hyper:436281,436300,binarycut:436301] equal(inverse(sk_c1),sk_c9).
% 436341 [para:436339.1.1,436279.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 436361 [hyper:436281,436294,436293] equal(multiply(sk_c3,sk_c7),sk_c9).
% 436374 [hyper:436281,436308,436307] equal(multiply(sk_c1,sk_c9),sk_c2).
% 436386 [hyper:436281,436315,436314] equal(multiply(sk_c9,sk_c2),sk_c8).
% 436391 [hyper:436281,436322,436321] equal(multiply(sk_c7,sk_c9),sk_c8).
% 436392 [para:436279.1.1,436280.1.1.1,demod:436278] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 436393 [para:436332.1.1,436280.1.1.1,demod:436278] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 436394 [para:436341.1.1,436280.1.1.1,demod:436278] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 436395 [para:436361.1.1,436280.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c3,multiply(sk_c7,X))).
% 436398 [para:436361.1.1,436393.1.2.2,demod:436391] equal(sk_c7,sk_c8).
% 436399 [para:436398.1.1,436332.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 436400 [para:436398.1.1,436361.1.1.2] equal(multiply(sk_c3,sk_c8),sk_c9).
% 436403 [para:436398.1.1,436391.1.1.1] equal(multiply(sk_c8,sk_c9),sk_c8).
% 436406 [para:436279.1.1,436392.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 436407 [para:436332.1.1,436392.1.2.2] equal(sk_c3,multiply(inverse(sk_c7),identity)).
% 436409 [para:436374.1.1,436392.1.2.2,demod:436386,436339] equal(sk_c9,sk_c8).
% 436411 [para:436280.1.1,436392.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 436414 [para:436392.1.2,436392.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 436420 [para:436403.1.1,436392.1.2.2,demod:436279] equal(sk_c9,identity).
% 436422 [para:436420.1.1,436341.1.1.1,demod:436278] equal(sk_c1,identity).
% 436426 [para:436420.1.1,436409.1.1] equal(identity,sk_c8).
% 436429 [para:436422.1.1,436339.1.1.1] equal(inverse(identity),sk_c9).
% 436436 [para:436422.1.1,436394.1.2.2.1,demod:436278] equal(X,multiply(sk_c9,X)).
% 436437 [para:436426.1.2,436399.1.1.1,demod:436278] equal(sk_c3,identity).
% 436438 [para:436426.1.2,436400.1.1.2] equal(multiply(sk_c3,identity),sk_c9).
% 436446 [para:436437.1.1,436330.1.1.1,demod:436429] equal(sk_c9,sk_c7).
% 436450 [para:436332.1.1,436395.1.2.2,demod:436438,436436] equal(sk_c3,sk_c9).
% 436453 [para:436446.1.2,436393.1.2.1,demod:436436] equal(X,multiply(sk_c3,X)).
% 436456 [para:436450.1.2,436409.1.1] equal(sk_c3,sk_c8).
% 436476 [para:436393.1.2,436411.1.2.2.2,demod:436453] equal(X,multiply(inverse(multiply(Y,sk_c7)),multiply(Y,X))).
% 436487 [para:436414.1.2,436279.1.1] equal(multiply(X,inverse(X)),identity).
% 436489 [para:436414.1.2,436406.1.2] equal(X,multiply(X,identity)).
% 436491 [para:436489.1.2,436406.1.2] equal(X,inverse(inverse(X))).
% 436492 [para:436489.1.2,436407.1.2] equal(sk_c3,inverse(sk_c7)).
% 436503 [para:436487.1.1,436476.1.2.2,demod:436489] equal(inverse(X),inverse(multiply(X,sk_c7))).
% 436514 [para:436503.1.2,436406.1.2.1.1,demod:436489,436491] equal(multiply(X,sk_c7),X).
% 436519 [para:436398.1.1,436514.1.1.2] equal(multiply(X,sk_c8),X).
% 436523 [hyper:436281,436519,demod:436492,cut:436456] 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 25
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c9),sk_c8) | -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9) | -equal(multiply(Z,sk_c7),sk_c9) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(Z,sk_c7),sk_c9) | -equal(inverse(Z),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 25
% 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 25
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(47,40,0,100,0,0,894,50,10,947,0,10,1974,50,30,2027,0,30,3171,50,46,3224,0,46,4430,50,65,4483,0,65,5752,50,89,5805,0,90,7166,50,124,7219,0,124,8672,50,178,8725,0,178,10300,50,269,10353,0,269,12050,50,432,12103,0,433,13952,50,665,14005,0,665,16006,50,1098,16006,40,1098,16059,0,1098,27084,3,1399,27759,4,1549,28362,5,1699,28363,1,1699,28363,50,1699,28363,40,1699,28416,0,1699,28723,3,2001,28734,4,2161,28747,5,2300,28747,1,2300,28747,50,2300,28747,40,2300,28800,0,2300,58208,3,3801,58943,4,4551,59706,5,5301,59707,1,5301,59707,50,5302,59707,40,5302,59760,0,5302,78344,3,6053,79057,4,6428,79568,5,6803,79569,1,6803,79569,50,6803,79569,40,6803,79622,0,6803,93455,3,7556,94322,4,7929,95734,5,8304,95735,1,8304,95735,50,8304,95735,40,8304,95788,0,8304,216615,3,12205,217502,4,14156,218411,1,16106,218411,50,16109,218411,40,16109,218464,0,16109,301256,3,18661,301847,4,19935,302420,5,21210,302421,1,21210,302421,50,21213,302421,40,21213,302474,0,21213,347869,3,22715,348636,4,23464,349224,1,24214,349224,50,24215,349224,40,24215,349277,0,24215,362700,3,24972,363871,4,25341,363974,5,25716,363974,1,25716,363974,50,25716,363974,40,25716,364027,0,25716,408464,3,26918,408955,4,27517,409589,1,28117,409589,50,28118,409589,40,28118,409642,0,28118,434655,3,28870,435208,4,29244,435815,1,29619,435815,50,29619,435815,40,29619,435815,40,29620,435862,0,29620,435967,50,29620,435967,30,29620,435967,40,29620,436014,0,29620,436085,50,29621,436085,30,29621,436085,40,29621,436132,0,29627,436276,50,29627,436323,0,29627,436522,50,29629,436522,30,29629,436522,40,29629,436569,0,29629,436674,50,29630,436721,0,29635)
%
%
% START OF PROOF
% 436676 [] equal(multiply(identity,X),X).
% 436677 [] equal(multiply(inverse(X),X),identity).
% 436678 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 436679 [] -equal(multiply(X,sk_c7),sk_c9) | -equal(inverse(X),sk_c7).
% 436680 [] equal(inverse(sk_c3),sk_c7) | equal(inverse(sk_c6),sk_c9).
% 436681 [] equal(multiply(sk_c6,sk_c9),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 436682 [] equal(inverse(sk_c3),sk_c7) | equal(inverse(sk_c5),sk_c8).
% 436683 [] equal(multiply(sk_c5,sk_c8),sk_c9) | equal(inverse(sk_c3),sk_c7).
% 436684 [] equal(inverse(sk_c3),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 436685 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 436686 [] equal(inverse(sk_c3),sk_c7) | equal(inverse(sk_c8),sk_c7).
% 436687 [?] ?
% 436688 [?] ?
% 436689 [?] ?
% 436690 [?] ?
% 436691 [?] ?
% 436692 [?] ?
% 436693 [?] ?
% 436724 [hyper:436679,436680,binarycut:436687] equal(inverse(sk_c6),sk_c9).
% 436725 [para:436724.1.1,436677.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 436729 [hyper:436679,436682,binarycut:436689] equal(inverse(sk_c5),sk_c8).
% 436730 [para:436729.1.1,436677.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 436733 [hyper:436679,436684,binarycut:436691] equal(inverse(sk_c4),sk_c8).
% 436736 [hyper:436679,436681,binarycut:436688] equal(multiply(sk_c6,sk_c9),sk_c7).
% 436737 [para:436733.1.1,436677.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 436740 [hyper:436679,436686,binarycut:436693] equal(inverse(sk_c8),sk_c7).
% 436744 [para:436740.1.1,436677.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 436748 [hyper:436679,436683,binarycut:436690] equal(multiply(sk_c5,sk_c8),sk_c9).
% 436751 [hyper:436679,436685,binarycut:436692] equal(multiply(sk_c4,sk_c8),sk_c7).
% 436752 [para:436677.1.1,436678.1.1.1,demod:436676] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 436753 [para:436725.1.1,436678.1.1.1,demod:436676] equal(X,multiply(sk_c9,multiply(sk_c6,X))).
% 436754 [para:436730.1.1,436678.1.1.1,demod:436676] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 436755 [para:436736.1.1,436678.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c9,X))).
% 436756 [para:436737.1.1,436678.1.1.1,demod:436676] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 436757 [para:436744.1.1,436678.1.1.1,demod:436676] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 436762 [para:436677.1.1,436752.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 436763 [para:436725.1.1,436752.1.2.2] equal(sk_c6,multiply(inverse(sk_c9),identity)).
% 436764 [para:436730.1.1,436752.1.2.2,demod:436740] equal(sk_c5,multiply(sk_c7,identity)).
% 436765 [para:436737.1.1,436752.1.2.2,demod:436764,436740] equal(sk_c4,sk_c5).
% 436767 [para:436748.1.1,436752.1.2.2,demod:436729] equal(sk_c8,multiply(sk_c8,sk_c9)).
% 436769 [para:436678.1.1,436752.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 436771 [para:436752.1.2,436752.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 436772 [para:436765.1.2,436748.1.1.1,demod:436751] equal(sk_c7,sk_c9).
% 436776 [para:436764.1.2,436678.1.1.1,demod:436676] equal(multiply(sk_c5,X),multiply(sk_c7,X)).
% 436778 [para:436772.1.1,436764.1.2.1] equal(sk_c5,multiply(sk_c9,identity)).
% 436780 [para:436767.1.2,436752.1.2.2,demod:436744,436740] equal(sk_c9,identity).
% 436781 [para:436780.1.1,436725.1.1.1,demod:436676] equal(sk_c6,identity).
% 436782 [para:436780.1.1,436736.1.1.2] equal(multiply(sk_c6,identity),sk_c7).
% 436787 [para:436781.1.1,436725.1.1.2,demod:436778] equal(sk_c5,identity).
% 436788 [para:436781.1.1,436753.1.2.2.1,demod:436676] equal(X,multiply(sk_c9,X)).
% 436793 [para:436787.1.1,436754.1.2.2.1,demod:436676] equal(X,multiply(sk_c8,X)).
% 436796 [para:436725.1.1,436755.1.2.2,demod:436782,436776] equal(multiply(sk_c5,sk_c6),sk_c7).
% 436798 [para:436755.1.2,436753.1.2.2,demod:436776,436788] equal(X,multiply(sk_c5,X)).
% 436802 [para:436756.1.2,436752.1.2.2,demod:436798,436776,436740] equal(multiply(sk_c4,X),X).
% 436823 [para:436765.1.2,436796.1.1.1,demod:436802] equal(sk_c6,sk_c7).
% 436844 [para:436771.1.2,436677.1.1] equal(multiply(X,inverse(X)),identity).
% 436846 [para:436771.1.2,436762.1.2] equal(X,multiply(X,identity)).
% 436848 [para:436846.1.2,436762.1.2] equal(X,inverse(inverse(X))).
% 436849 [para:436846.1.2,436763.1.2] equal(sk_c6,inverse(sk_c9)).
% 436851 [para:436844.1.1,436769.1.2.2.2,demod:436846] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 436857 [para:436757.1.2,436851.1.2.1.1,demod:436793] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 436868 [para:436857.1.2,436771.1.2,demod:436848] equal(multiply(X,sk_c7),X).
% 436869 [hyper:436679,436868,demod:436849,cut:436823] 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 25
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c9),sk_c8) | -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9) | -equal(multiply(Z,sk_c7),sk_c9) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),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 25
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(47,40,0,100,0,0,894,50,10,947,0,10,1974,50,30,2027,0,30,3171,50,46,3224,0,46,4430,50,65,4483,0,65,5752,50,89,5805,0,90,7166,50,124,7219,0,124,8672,50,178,8725,0,178,10300,50,269,10353,0,269,12050,50,432,12103,0,433,13952,50,665,14005,0,665,16006,50,1098,16006,40,1098,16059,0,1098,27084,3,1399,27759,4,1549,28362,5,1699,28363,1,1699,28363,50,1699,28363,40,1699,28416,0,1699,28723,3,2001,28734,4,2161,28747,5,2300,28747,1,2300,28747,50,2300,28747,40,2300,28800,0,2300,58208,3,3801,58943,4,4551,59706,5,5301,59707,1,5301,59707,50,5302,59707,40,5302,59760,0,5302,78344,3,6053,79057,4,6428,79568,5,6803,79569,1,6803,79569,50,6803,79569,40,6803,79622,0,6803,93455,3,7556,94322,4,7929,95734,5,8304,95735,1,8304,95735,50,8304,95735,40,8304,95788,0,8304,216615,3,12205,217502,4,14156,218411,1,16106,218411,50,16109,218411,40,16109,218464,0,16109,301256,3,18661,301847,4,19935,302420,5,21210,302421,1,21210,302421,50,21213,302421,40,21213,302474,0,21213,347869,3,22715,348636,4,23464,349224,1,24214,349224,50,24215,349224,40,24215,349277,0,24215,362700,3,24972,363871,4,25341,363974,5,25716,363974,1,25716,363974,50,25716,363974,40,25716,364027,0,25716,408464,3,26918,408955,4,27517,409589,1,28117,409589,50,28118,409589,40,28118,409642,0,28118,434655,3,28870,435208,4,29244,435815,1,29619,435815,50,29619,435815,40,29619,435815,40,29620,435862,0,29620,435967,50,29620,435967,30,29620,435967,40,29620,436014,0,29620,436085,50,29621,436085,30,29621,436085,40,29621,436132,0,29627,436276,50,29627,436323,0,29627,436522,50,29629,436522,30,29629,436522,40,29629,436569,0,29629,436674,50,29630,436721,0,29635,436868,50,29636,436868,30,29636,436868,40,29636,436915,0,29636)
%
%
% START OF PROOF
% 436869 [] equal(X,X).
% 436870 [] equal(multiply(identity,X),X).
% 436871 [] equal(multiply(inverse(X),X),identity).
% 436872 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 436873 [] -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9).
% 436888 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 436889 [] equal(multiply(sk_c6,sk_c9),sk_c7) | equal(inverse(sk_c1),sk_c9).
% 436890 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 436891 [] equal(multiply(sk_c5,sk_c8),sk_c9) | equal(inverse(sk_c1),sk_c9).
% 436892 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c4),sk_c8).
% 436893 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c9).
% 436894 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c8),sk_c7).
% 436895 [] equal(multiply(sk_c1,sk_c9),sk_c2) | equal(inverse(sk_c6),sk_c9).
% 436896 [] equal(multiply(sk_c1,sk_c9),sk_c2) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 436897 [] equal(multiply(sk_c1,sk_c9),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 436898 [] equal(multiply(sk_c1,sk_c9),sk_c2) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 436899 [] equal(multiply(sk_c1,sk_c9),sk_c2) | equal(inverse(sk_c4),sk_c8).
% 436900 [] equal(multiply(sk_c1,sk_c9),sk_c2) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 436901 [] equal(multiply(sk_c1,sk_c9),sk_c2) | equal(inverse(sk_c8),sk_c7).
% 436902 [?] ?
% 436903 [?] ?
% 436904 [?] ?
% 436905 [?] ?
% 436906 [?] ?
% 436907 [?] ?
% 436908 [?] ?
% 436988 [hyper:436873,436895,binarycut:436902,binarycut:436888] equal(inverse(sk_c6),sk_c9).
% 437004 [para:436988.1.1,436871.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 437012 [hyper:436873,436897,binarycut:436904,binarycut:436890] equal(inverse(sk_c5),sk_c8).
% 437013 [para:437012.1.1,436871.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 437017 [hyper:436873,436899,binarycut:436906,binarycut:436892] equal(inverse(sk_c4),sk_c8).
% 437018 [para:437017.1.1,436871.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 437021 [hyper:436873,436901,binarycut:436908,binarycut:436894] equal(inverse(sk_c8),sk_c7).
% 437025 [hyper:436873,436896,436889,binarycut:436903] equal(multiply(sk_c6,sk_c9),sk_c7).
% 437028 [para:437021.1.1,436871.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 437034 [hyper:436873,436898,436891,binarycut:436905] equal(multiply(sk_c5,sk_c8),sk_c9).
% 437038 [hyper:436873,436900,436893,binarycut:436907] equal(multiply(sk_c4,sk_c8),sk_c7).
% 437039 [para:436871.1.1,436872.1.1.1,demod:436870] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 437040 [para:437004.1.1,436872.1.1.1,demod:436870] equal(X,multiply(sk_c9,multiply(sk_c6,X))).
% 437049 [para:437025.1.1,437040.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c7)).
% 437053 [para:437004.1.1,437039.1.2.2] equal(sk_c6,multiply(inverse(sk_c9),identity)).
% 437054 [para:437013.1.1,437039.1.2.2,demod:437021] equal(sk_c5,multiply(sk_c7,identity)).
% 437055 [para:437018.1.1,437039.1.2.2,demod:437054,437021] equal(sk_c4,sk_c5).
% 437057 [para:437034.1.1,437039.1.2.2,demod:437012] equal(sk_c8,multiply(sk_c8,sk_c9)).
% 437058 [para:437038.1.1,437039.1.2.2,demod:437017] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 437060 [para:437055.1.2,437034.1.1.1,demod:437038] equal(sk_c7,sk_c9).
% 437061 [para:437060.1.1,437028.1.1.1] equal(multiply(sk_c9,sk_c8),identity).
% 437068 [para:437061.1.1,437039.1.2.2,demod:437053] equal(sk_c8,sk_c6).
% 437071 [para:437068.1.2,437025.1.1.1,demod:437057] equal(sk_c8,sk_c7).
% 437073 [para:437071.1.2,437060.1.1] equal(sk_c8,sk_c9).
% 437074 [para:437071.1.2,437049.1.2.2,demod:437061] equal(sk_c9,identity).
% 437079 [para:437073.1.2,437049.1.2.1,demod:437058] equal(sk_c9,sk_c8).
% 437080 [para:437074.1.1,437004.1.1.1,demod:436870] equal(sk_c6,identity).
% 437090 [para:437080.1.1,436988.1.1.1] equal(inverse(identity),sk_c9).
% 437092 [para:437080.1.1,437040.1.2.2.1,demod:436870] equal(X,multiply(sk_c9,X)).
% 437134 [hyper:436873,437090,436869,demod:437092,436870,cut:437079] 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 25
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c9),sk_c8) | -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9) | -equal(multiply(Z,sk_c7),sk_c9) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(sk_c7,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 25
% 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 25
% 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 25
% 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 25
% 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 25
% 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 25
% 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 25
% 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 25
% 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 25
% 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(47,40,0,100,0,0,894,50,10,947,0,10,1974,50,30,2027,0,30,3171,50,46,3224,0,46,4430,50,65,4483,0,65,5752,50,89,5805,0,90,7166,50,124,7219,0,124,8672,50,178,8725,0,178,10300,50,269,10353,0,269,12050,50,432,12103,0,433,13952,50,665,14005,0,665,16006,50,1098,16006,40,1098,16059,0,1098,27084,3,1399,27759,4,1549,28362,5,1699,28363,1,1699,28363,50,1699,28363,40,1699,28416,0,1699,28723,3,2001,28734,4,2161,28747,5,2300,28747,1,2300,28747,50,2300,28747,40,2300,28800,0,2300,58208,3,3801,58943,4,4551,59706,5,5301,59707,1,5301,59707,50,5302,59707,40,5302,59760,0,5302,78344,3,6053,79057,4,6428,79568,5,6803,79569,1,6803,79569,50,6803,79569,40,6803,79622,0,6803,93455,3,7556,94322,4,7929,95734,5,8304,95735,1,8304,95735,50,8304,95735,40,8304,95788,0,8304,216615,3,12205,217502,4,14156,218411,1,16106,218411,50,16109,218411,40,16109,218464,0,16109,301256,3,18661,301847,4,19935,302420,5,21210,302421,1,21210,302421,50,21213,302421,40,21213,302474,0,21213,347869,3,22715,348636,4,23464,349224,1,24214,349224,50,24215,349224,40,24215,349277,0,24215,362700,3,24972,363871,4,25341,363974,5,25716,363974,1,25716,363974,50,25716,363974,40,25716,364027,0,25716,408464,3,26918,408955,4,27517,409589,1,28117,409589,50,28118,409589,40,28118,409642,0,28118,434655,3,28870,435208,4,29244,435815,1,29619,435815,50,29619,435815,40,29619,435815,40,29620,435862,0,29620,435967,50,29620,435967,30,29620,435967,40,29620,436014,0,29620,436085,50,29621,436085,30,29621,436085,40,29621,436132,0,29627,436276,50,29627,436323,0,29627,436522,50,29629,436522,30,29629,436522,40,29629,436569,0,29629,436674,50,29630,436721,0,29635,436868,50,29636,436868,30,29636,436868,40,29636,436915,0,29636,437133,50,29637,437133,30,29637,437133,40,29637,437180,0,29642,437296,50,29643,437343,0,29643,437520,50,29646,437567,0,29646,437752,50,29650,437799,0,29654,437992,50,29659,438039,0,29660,438238,50,29669,438285,0,29673,438492,50,29690,438539,0,29690,438754,50,29720,438801,0,29720,439026,50,29783,439073,0,29783,439308,50,29902,439308,40,29902,439355,0,29902)
%
%
% START OF PROOF
% 439215 [?] ?
% 439310 [] equal(multiply(identity,X),X).
% 439311 [] equal(multiply(inverse(X),X),identity).
% 439312 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 439313 [] -equal(multiply(sk_c7,sk_c9),sk_c8).
% 439351 [?] ?
% 439352 [?] ?
% 439355 [?] ?
% 439422 [input:439351,cut:439313] equal(inverse(sk_c5),sk_c8).
% 439423 [para:439422.1.1,439311.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 439428 [input:439355,cut:439313] equal(inverse(sk_c8),sk_c7).
% 439429 [para:439428.1.1,439311.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 439442 [input:439352,cut:439313] equal(multiply(sk_c5,sk_c8),sk_c9).
% 439475 [para:439423.1.1,439312.1.1.1,demod:439310] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 439481 [para:439429.1.1,439312.1.1.1,demod:439310] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 439514 [para:439442.1.1,439475.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c9)).
% 439523 [para:439423.1.1,439481.1.2.2] equal(sk_c5,multiply(sk_c7,identity)).
% 439526 [para:439514.1.2,439481.1.2.2,demod:439429] equal(sk_c9,identity).
% 439536 [para:439526.1.1,439313.1.1.2,demod:439523,cut:439215] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c9),sk_c8) | -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9) | -equal(multiply(Z,sk_c7),sk_c9) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(inverse(sk_c8),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 25
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(47,40,0,100,0,0,894,50,10,947,0,10,1974,50,30,2027,0,30,3171,50,46,3224,0,46,4430,50,65,4483,0,65,5752,50,89,5805,0,90,7166,50,124,7219,0,124,8672,50,178,8725,0,178,10300,50,269,10353,0,269,12050,50,432,12103,0,433,13952,50,665,14005,0,665,16006,50,1098,16006,40,1098,16059,0,1098,27084,3,1399,27759,4,1549,28362,5,1699,28363,1,1699,28363,50,1699,28363,40,1699,28416,0,1699,28723,3,2001,28734,4,2161,28747,5,2300,28747,1,2300,28747,50,2300,28747,40,2300,28800,0,2300,58208,3,3801,58943,4,4551,59706,5,5301,59707,1,5301,59707,50,5302,59707,40,5302,59760,0,5302,78344,3,6053,79057,4,6428,79568,5,6803,79569,1,6803,79569,50,6803,79569,40,6803,79622,0,6803,93455,3,7556,94322,4,7929,95734,5,8304,95735,1,8304,95735,50,8304,95735,40,8304,95788,0,8304,216615,3,12205,217502,4,14156,218411,1,16106,218411,50,16109,218411,40,16109,218464,0,16109,301256,3,18661,301847,4,19935,302420,5,21210,302421,1,21210,302421,50,21213,302421,40,21213,302474,0,21213,347869,3,22715,348636,4,23464,349224,1,24214,349224,50,24215,349224,40,24215,349277,0,24215,362700,3,24972,363871,4,25341,363974,5,25716,363974,1,25716,363974,50,25716,363974,40,25716,364027,0,25716,408464,3,26918,408955,4,27517,409589,1,28117,409589,50,28118,409589,40,28118,409642,0,28118,434655,3,28870,435208,4,29244,435815,1,29619,435815,50,29619,435815,40,29619,435815,40,29620,435862,0,29620,435967,50,29620,435967,30,29620,435967,40,29620,436014,0,29620,436085,50,29621,436085,30,29621,436085,40,29621,436132,0,29627,436276,50,29627,436323,0,29627,436522,50,29629,436522,30,29629,436522,40,29629,436569,0,29629,436674,50,29630,436721,0,29635,436868,50,29636,436868,30,29636,436868,40,29636,436915,0,29636,437133,50,29637,437133,30,29637,437133,40,29637,437180,0,29642,437296,50,29643,437343,0,29643,437520,50,29646,437567,0,29646,437752,50,29650,437799,0,29654,437992,50,29659,438039,0,29660,438238,50,29669,438285,0,29673,438492,50,29690,438539,0,29690,438754,50,29720,438801,0,29720,439026,50,29783,439073,0,29783,439308,50,29902,439308,40,29902,439355,0,29902,439535,50,29903,439535,30,29903,439535,40,29903,439582,0,29903)
%
%
% START OF PROOF
% 439537 [] equal(multiply(identity,X),X).
% 439538 [] equal(multiply(inverse(X),X),identity).
% 439539 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 439540 [] -equal(inverse(sk_c8),sk_c7).
% 439547 [?] ?
% 439554 [?] ?
% 439561 [?] ?
% 439568 [?] ?
% 439575 [?] ?
% 439582 [?] ?
% 439587 [input:439547,cut:439540] equal(inverse(sk_c3),sk_c7).
% 439588 [para:439587.1.1,439538.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 439593 [input:439561,cut:439540] equal(inverse(sk_c1),sk_c9).
% 439594 [para:439593.1.1,439538.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 439599 [input:439554,cut:439540] equal(multiply(sk_c3,sk_c7),sk_c9).
% 439607 [input:439568,cut:439540] equal(multiply(sk_c1,sk_c9),sk_c2).
% 439612 [input:439575,cut:439540] equal(multiply(sk_c9,sk_c2),sk_c8).
% 439617 [input:439582,cut:439540] equal(multiply(sk_c7,sk_c9),sk_c8).
% 439627 [para:439538.1.1,439539.1.1.1,demod:439537] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 439628 [para:439588.1.1,439539.1.1.1,demod:439537] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 439629 [para:439594.1.1,439539.1.1.1,demod:439537] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 439630 [para:439599.1.1,439539.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c3,multiply(sk_c7,X))).
% 439634 [para:439599.1.1,439628.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c9)).
% 439635 [para:439634.1.2,439617.1.1] equal(sk_c7,sk_c8).
% 439638 [para:439635.1.1,439599.1.1.2] equal(multiply(sk_c3,sk_c8),sk_c9).
% 439639 [para:439635.1.1,439617.1.1.1] equal(multiply(sk_c8,sk_c9),sk_c8).
% 439654 [para:439639.1.1,439627.1.2.2,demod:439538] equal(sk_c9,identity).
% 439655 [para:439654.1.1,439594.1.1.1,demod:439537] equal(sk_c1,identity).
% 439660 [para:439655.1.1,439594.1.1.2] equal(multiply(sk_c9,identity),identity).
% 439661 [para:439655.1.1,439607.1.1.1,demod:439537] equal(sk_c9,sk_c2).
% 439665 [para:439655.1.1,439629.1.2.2.1,demod:439537] equal(X,multiply(sk_c9,X)).
% 439669 [para:439661.1.1,439654.1.1] equal(sk_c2,identity).
% 439672 [para:439669.1.1,439612.1.1.2,demod:439660] equal(identity,sk_c8).
% 439675 [para:439672.1.2,439638.1.1.2] equal(multiply(sk_c3,identity),sk_c9).
% 439676 [para:439672.1.2,439639.1.1.1,demod:439537] equal(sk_c9,sk_c8).
% 439677 [para:439588.1.1,439630.1.2.2,demod:439675,439665] equal(sk_c3,sk_c9).
% 439689 [para:439677.1.2,439676.1.1] equal(sk_c3,sk_c8).
% 439694 [para:439689.1.1,439587.1.1.1,cut:439540] 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 25
% clause depth limited to 3
% seconds given: 4
%
%
% Split attempt finished with SUCCESS.
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 31383
% derived clauses: 4778883
% kept clauses: 344832
% kept size sum: 931719
% kept mid-nuclei: 12145
% kept new demods: 3152
% forw unit-subs: 1498404
% forw double-subs: 2548149
% forw overdouble-subs: 291295
% backward subs: 9656
% fast unit cutoff: 25537
% full unit cutoff: 0
% dbl unit cutoff: 6276
% real runtime : 301.27
% process. runtime: 299.3
% specific non-discr-tree subsumption statistics:
% tried: 29885264
% length fails: 3326162
% strength fails: 9717936
% predlist fails: 1438224
% aux str. fails: 3087841
% by-lit fails: 5008152
% full subs tried: 1626641
% full subs fail: 1510238
%
% ; 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/GRP369-1+eq_r.in")
%
%------------------------------------------------------------------------------