TSTP Solution File: GRP216-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP216-1 : 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 : art03.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 277.7s
% Output : Assurance 277.7s
% 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/GRP216-1+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(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(inverse(sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% was split for some strategies as:
% -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6).
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% -equal(inverse(sk_c7),sk_c6).
%
% Starting a split proof attempt with 5 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(inverse(sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(29,40,0,63,0,0,82833,50,872,82833,40,872,82867,0,872,93223,3,1173,93952,4,1323,94648,5,1473,94649,1,1473,94649,50,1473,94649,40,1473,94683,0,1473,95223,3,1784,95234,4,1944,95258,5,2074,95258,1,2074,95258,50,2074,95258,40,2074,95292,0,2074,125401,3,3575,125821,4,4325,126052,5,5075,126053,1,5075,126053,50,5076,126053,40,5076,126087,0,5076,149137,3,5827,149551,4,6202,149865,1,6577,149865,50,6578,149865,40,6578,149899,0,6578,154349,50,6737,154349,40,6737,154383,0,6737,216059,3,10658,217256,4,12588,217728,5,14538,217729,1,14538,217729,50,14540,217729,40,14540,217763,0,14540,266728,3,17091,267656,4,18366,268358,5,19641,268359,1,19641,268359,50,19643,268359,40,19643,268393,0,19643,312014,3,21147,312645,4,21894,312984,1,22644,312984,50,22646,312984,40,22646,313018,0,22646,326127,3,23412,327160,4,23772,328313,5,24147,328314,1,24147,328314,50,24147,328314,40,24147,328348,0,24147,371896,3,25349,372292,4,25948,372698,1,26548,372698,50,26550,372698,40,26550,372732,0,26550,404229,3,27301,404554,4,27676,404852,1,28051,404852,50,28052,404852,40,28052,404852,40,28052,404881,0,28052)
%
%
% START OF PROOF
% 404853 [] equal(X,X).
% 404854 [] equal(multiply(identity,X),X).
% 404855 [] equal(multiply(inverse(X),X),identity).
% 404856 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 404857 [] -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7).
% 404858 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 404859 [] equal(multiply(sk_c4,sk_c7),sk_c5) | equal(inverse(sk_c2),sk_c6).
% 404860 [?] ?
% 404864 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 404865 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c5).
% 404866 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(multiply(sk_c7,sk_c5),sk_c6).
% 404870 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 404871 [] equal(multiply(sk_c4,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 404872 [?] ?
% 404876 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 404877 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c7),sk_c5).
% 404878 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c7,sk_c5),sk_c6).
% 404919 [hyper:404857,404859,404858,binarycut:404860] equal(inverse(sk_c2),sk_c6).
% 404938 [hyper:404857,404871,404870,binarycut:404872] equal(inverse(sk_c1),sk_c7).
% 404945 [para:404938.1.1,404855.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 404961 [hyper:404857,404866,404865,404864] equal(multiply(sk_c2,sk_c6),sk_c7).
% 404982 [hyper:404857,404878,404877,404876] equal(multiply(sk_c1,sk_c7),sk_c6).
% 404986 [para:404855.1.1,404856.1.1.1,demod:404854] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 404988 [para:404945.1.1,404856.1.1.1,demod:404854] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 404996 [para:404961.1.1,404986.1.2.2,demod:404919] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 404999 [para:404996.1.2,404986.1.2.2,demod:404855] equal(sk_c7,identity).
% 405000 [para:404999.1.1,404945.1.1.1,demod:404854] equal(sk_c1,identity).
% 405003 [para:405000.1.1,404938.1.1.1] equal(inverse(identity),sk_c7).
% 405005 [para:405000.1.1,404982.1.1.1,demod:404854] equal(sk_c7,sk_c6).
% 405018 [para:405000.1.1,404988.1.2.2.1,demod:404854] equal(X,multiply(sk_c7,X)).
% 405025 [hyper:404857,405003,404853,demod:405018,404854,cut:405005] 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: 6
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(inverse(sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(29,40,0,63,0,0,82833,50,872,82833,40,872,82867,0,872,93223,3,1173,93952,4,1323,94648,5,1473,94649,1,1473,94649,50,1473,94649,40,1473,94683,0,1473,95223,3,1784,95234,4,1944,95258,5,2074,95258,1,2074,95258,50,2074,95258,40,2074,95292,0,2074,125401,3,3575,125821,4,4325,126052,5,5075,126053,1,5075,126053,50,5076,126053,40,5076,126087,0,5076,149137,3,5827,149551,4,6202,149865,1,6577,149865,50,6578,149865,40,6578,149899,0,6578,154349,50,6737,154349,40,6737,154383,0,6737,216059,3,10658,217256,4,12588,217728,5,14538,217729,1,14538,217729,50,14540,217729,40,14540,217763,0,14540,266728,3,17091,267656,4,18366,268358,5,19641,268359,1,19641,268359,50,19643,268359,40,19643,268393,0,19643,312014,3,21147,312645,4,21894,312984,1,22644,312984,50,22646,312984,40,22646,313018,0,22646,326127,3,23412,327160,4,23772,328313,5,24147,328314,1,24147,328314,50,24147,328314,40,24147,328348,0,24147,371896,3,25349,372292,4,25948,372698,1,26548,372698,50,26550,372698,40,26550,372732,0,26550,404229,3,27301,404554,4,27676,404852,1,28051,404852,50,28052,404852,40,28052,404852,40,28052,404881,0,28052,405024,50,28052,405024,30,28052,405024,40,28052,405053,0,28052)
%
%
% START OF PROOF
% 405026 [] equal(multiply(identity,X),X).
% 405027 [] equal(multiply(inverse(X),X),identity).
% 405028 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 405029 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 405033 [?] ?
% 405034 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 405039 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 405040 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 405045 [?] ?
% 405046 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 405051 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 405052 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 405058 [hyper:405029,405034,binarycut:405033] equal(inverse(sk_c2),sk_c6).
% 405074 [hyper:405029,405046,binarycut:405045] equal(inverse(sk_c1),sk_c7).
% 405077 [para:405074.1.1,405027.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 405103 [hyper:405029,405039,405040] equal(multiply(sk_c2,sk_c6),sk_c7).
% 405111 [hyper:405029,405051,405052] equal(multiply(sk_c1,sk_c7),sk_c6).
% 405112 [para:405027.1.1,405028.1.1.1,demod:405026] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 405120 [para:405103.1.1,405112.1.2.2,demod:405058] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 405123 [para:405120.1.2,405112.1.2.2,demod:405027] equal(sk_c7,identity).
% 405124 [para:405123.1.1,405077.1.1.1,demod:405026] equal(sk_c1,identity).
% 405127 [para:405124.1.1,405074.1.1.1] equal(inverse(identity),sk_c7).
% 405129 [para:405124.1.1,405111.1.1.1,demod:405026] equal(sk_c7,sk_c6).
% 405134 [para:405129.1.1,405123.1.1] equal(sk_c6,identity).
% 405142 [para:405134.1.1,405120.1.2.1,demod:405026] equal(sk_c6,sk_c7).
% 405144 [hyper:405029,405127,demod:405026,cut:405142] 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: 6
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(inverse(sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(multiply(Y,sk_c6),sk_c7) | -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: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(29,40,0,63,0,0,82833,50,872,82833,40,872,82867,0,872,93223,3,1173,93952,4,1323,94648,5,1473,94649,1,1473,94649,50,1473,94649,40,1473,94683,0,1473,95223,3,1784,95234,4,1944,95258,5,2074,95258,1,2074,95258,50,2074,95258,40,2074,95292,0,2074,125401,3,3575,125821,4,4325,126052,5,5075,126053,1,5075,126053,50,5076,126053,40,5076,126087,0,5076,149137,3,5827,149551,4,6202,149865,1,6577,149865,50,6578,149865,40,6578,149899,0,6578,154349,50,6737,154349,40,6737,154383,0,6737,216059,3,10658,217256,4,12588,217728,5,14538,217729,1,14538,217729,50,14540,217729,40,14540,217763,0,14540,266728,3,17091,267656,4,18366,268358,5,19641,268359,1,19641,268359,50,19643,268359,40,19643,268393,0,19643,312014,3,21147,312645,4,21894,312984,1,22644,312984,50,22646,312984,40,22646,313018,0,22646,326127,3,23412,327160,4,23772,328313,5,24147,328314,1,24147,328314,50,24147,328314,40,24147,328348,0,24147,371896,3,25349,372292,4,25948,372698,1,26548,372698,50,26550,372698,40,26550,372732,0,26550,404229,3,27301,404554,4,27676,404852,1,28051,404852,50,28052,404852,40,28052,404852,40,28052,404881,0,28052,405024,50,28052,405024,30,28052,405024,40,28052,405053,0,28052,405143,50,28052,405143,30,28052,405143,40,28052,405172,0,28057)
%
%
% START OF PROOF
% 405145 [] equal(multiply(identity,X),X).
% 405146 [] equal(multiply(inverse(X),X),identity).
% 405147 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 405148 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6).
% 405149 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 405150 [] equal(multiply(sk_c4,sk_c7),sk_c5) | equal(inverse(sk_c2),sk_c6).
% 405151 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c2),sk_c6).
% 405152 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c6).
% 405153 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 405154 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c7),sk_c6).
% 405155 [?] ?
% 405156 [?] ?
% 405157 [?] ?
% 405158 [?] ?
% 405159 [?] ?
% 405160 [?] ?
% 405175 [hyper:405148,405149,binarycut:405155] equal(inverse(sk_c4),sk_c7).
% 405176 [para:405175.1.1,405146.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 405180 [hyper:405148,405153,binarycut:405159] equal(inverse(sk_c3),sk_c7).
% 405181 [para:405180.1.1,405146.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 405184 [hyper:405148,405154,binarycut:405160] equal(inverse(sk_c7),sk_c6).
% 405189 [hyper:405148,405150,binarycut:405156] equal(multiply(sk_c4,sk_c7),sk_c5).
% 405191 [para:405184.1.1,405146.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 405195 [hyper:405148,405151,binarycut:405157] equal(multiply(sk_c7,sk_c5),sk_c6).
% 405199 [hyper:405148,405152,binarycut:405158] equal(multiply(sk_c3,sk_c6),sk_c7).
% 405203 [para:405146.1.1,405147.1.1.1,demod:405145] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 405204 [para:405176.1.1,405147.1.1.1,demod:405145] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 405206 [para:405189.1.1,405147.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c4,multiply(sk_c7,X))).
% 405208 [para:405195.1.1,405147.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c5,X))).
% 405209 [para:405199.1.1,405147.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c6,X))).
% 405210 [para:405189.1.1,405204.1.2.2,demod:405195] equal(sk_c7,sk_c6).
% 405212 [para:405176.1.1,405203.1.2.2,demod:405184] equal(sk_c4,multiply(sk_c6,identity)).
% 405213 [para:405181.1.1,405203.1.2.2,demod:405212,405184] equal(sk_c3,sk_c4).
% 405217 [para:405204.1.2,405203.1.2.2,demod:405184] equal(multiply(sk_c4,X),multiply(sk_c6,X)).
% 405223 [para:405210.1.1,405204.1.2.1,demod:405217] equal(X,multiply(sk_c6,multiply(sk_c6,X))).
% 405233 [para:405206.1.2,405204.1.2.2,demod:405208] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 405235 [para:405210.1.1,405206.1.2.2.1,demod:405223,405217] equal(multiply(sk_c5,X),X).
% 405236 [para:405213.1.2,405206.1.2.1,demod:405209,405233,405235] equal(X,multiply(sk_c6,X)).
% 405238 [para:405236.1.2,405191.1.1] equal(sk_c7,identity).
% 405239 [para:405236.1.2,405212.1.2] equal(sk_c4,identity).
% 405242 [para:405238.1.1,405184.1.1.1] equal(inverse(identity),sk_c6).
% 405247 [para:405239.1.1,405175.1.1.1,demod:405242] equal(sk_c6,sk_c7).
% 405261 [hyper:405148,405242,demod:405145,cut:405247] 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: 6
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(inverse(sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(multiply(X,sk_c7),sk_c6) | -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: 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 19
% clause depth limited to 4
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(29,40,0,63,0,0,82833,50,872,82833,40,872,82867,0,872,93223,3,1173,93952,4,1323,94648,5,1473,94649,1,1473,94649,50,1473,94649,40,1473,94683,0,1473,95223,3,1784,95234,4,1944,95258,5,2074,95258,1,2074,95258,50,2074,95258,40,2074,95292,0,2074,125401,3,3575,125821,4,4325,126052,5,5075,126053,1,5075,126053,50,5076,126053,40,5076,126087,0,5076,149137,3,5827,149551,4,6202,149865,1,6577,149865,50,6578,149865,40,6578,149899,0,6578,154349,50,6737,154349,40,6737,154383,0,6737,216059,3,10658,217256,4,12588,217728,5,14538,217729,1,14538,217729,50,14540,217729,40,14540,217763,0,14540,266728,3,17091,267656,4,18366,268358,5,19641,268359,1,19641,268359,50,19643,268359,40,19643,268393,0,19643,312014,3,21147,312645,4,21894,312984,1,22644,312984,50,22646,312984,40,22646,313018,0,22646,326127,3,23412,327160,4,23772,328313,5,24147,328314,1,24147,328314,50,24147,328314,40,24147,328348,0,24147,371896,3,25349,372292,4,25948,372698,1,26548,372698,50,26550,372698,40,26550,372732,0,26550,404229,3,27301,404554,4,27676,404852,1,28051,404852,50,28052,404852,40,28052,404852,40,28052,404881,0,28052,405024,50,28052,405024,30,28052,405024,40,28052,405053,0,28052,405143,50,28052,405143,30,28052,405143,40,28052,405172,0,28057,405260,50,28057,405260,30,28057,405260,40,28057,405289,0,28057,405382,50,28058,405411,0,28058)
%
%
% START OF PROOF
% 405384 [] equal(multiply(identity,X),X).
% 405385 [] equal(multiply(inverse(X),X),identity).
% 405386 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 405387 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 405400 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 405401 [] equal(multiply(sk_c4,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 405402 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 405403 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 405404 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 405405 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c7),sk_c6).
% 405406 [?] ?
% 405407 [?] ?
% 405408 [?] ?
% 405409 [?] ?
% 405410 [?] ?
% 405411 [?] ?
% 405420 [hyper:405387,405400,binarycut:405406] equal(inverse(sk_c4),sk_c7).
% 405424 [para:405420.1.1,405385.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 405428 [hyper:405387,405404,binarycut:405410] equal(inverse(sk_c3),sk_c7).
% 405433 [para:405428.1.1,405385.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 405437 [hyper:405387,405405,binarycut:405411] equal(inverse(sk_c7),sk_c6).
% 405438 [para:405437.1.1,405385.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 405443 [hyper:405387,405401,binarycut:405407] equal(multiply(sk_c4,sk_c7),sk_c5).
% 405447 [hyper:405387,405402,binarycut:405408] equal(multiply(sk_c7,sk_c5),sk_c6).
% 405450 [hyper:405387,405403,binarycut:405409] equal(multiply(sk_c3,sk_c6),sk_c7).
% 405451 [para:405385.1.1,405386.1.1.1,demod:405384] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 405452 [para:405424.1.1,405386.1.1.1,demod:405384] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 405453 [para:405433.1.1,405386.1.1.1,demod:405384] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 405454 [para:405438.1.1,405386.1.1.1,demod:405384] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 405458 [para:405443.1.1,405452.1.2.2,demod:405447] equal(sk_c7,sk_c6).
% 405460 [para:405385.1.1,405451.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 405461 [para:405424.1.1,405451.1.2.2,demod:405437] equal(sk_c4,multiply(sk_c6,identity)).
% 405462 [para:405433.1.1,405451.1.2.2,demod:405461,405437] equal(sk_c3,sk_c4).
% 405464 [para:405447.1.1,405451.1.2.2,demod:405437] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 405465 [para:405450.1.1,405451.1.2.2,demod:405428] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 405466 [para:405386.1.1,405451.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 405467 [para:405452.1.2,405451.1.2.2,demod:405437] equal(multiply(sk_c4,X),multiply(sk_c6,X)).
% 405468 [para:405451.1.2,405451.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 405471 [para:405458.1.1,405437.1.1.1] equal(inverse(sk_c6),sk_c6).
% 405474 [para:405458.1.1,405452.1.2.1,demod:405467] equal(X,multiply(sk_c6,multiply(sk_c6,X))).
% 405475 [para:405453.1.2,405451.1.2.2,demod:405437] equal(multiply(sk_c3,X),multiply(sk_c6,X)).
% 405477 [para:405462.1.2,405452.1.2.2.1,demod:405475] equal(X,multiply(sk_c7,multiply(sk_c6,X))).
% 405479 [para:405454.1.2,405451.1.2.2,demod:405471] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 405480 [para:405464.1.2,405386.1.1.1,demod:405474] equal(multiply(sk_c5,X),X).
% 405482 [para:405465.1.2,405386.1.1.1,demod:405477,405479] equal(multiply(sk_c6,X),X).
% 405483 [para:405465.1.2,405451.1.2.2,demod:405464,405437] equal(sk_c7,sk_c5).
% 405490 [para:405483.1.1,405465.1.2.1,demod:405480] equal(sk_c6,sk_c7).
% 405522 [para:405468.1.2,405385.1.1] equal(multiply(X,inverse(X)),identity).
% 405524 [para:405468.1.2,405460.1.2] equal(X,multiply(X,identity)).
% 405525 [para:405524.1.2,405460.1.2] equal(X,inverse(inverse(X))).
% 405526 [para:405522.1.1,405466.1.2.2.2,demod:405524] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 405528 [para:405452.1.2,405526.1.2.1.1,demod:405482,405467] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 405536 [para:405528.1.2,405468.1.2,demod:405525] equal(multiply(X,sk_c7),X).
% 405537 [hyper:405387,405536,demod:405471,cut:405490] 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 4
% seconds given: 6
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(inverse(sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(sk_c7,U),sk_c6) | -equal(multiply(V,sk_c7),U) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(inverse(sk_c7),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% clause depth limited to 12
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(29,40,0,63,0,0,82833,50,872,82833,40,872,82867,0,872,93223,3,1173,93952,4,1323,94648,5,1473,94649,1,1473,94649,50,1473,94649,40,1473,94683,0,1473,95223,3,1784,95234,4,1944,95258,5,2074,95258,1,2074,95258,50,2074,95258,40,2074,95292,0,2074,125401,3,3575,125821,4,4325,126052,5,5075,126053,1,5075,126053,50,5076,126053,40,5076,126087,0,5076,149137,3,5827,149551,4,6202,149865,1,6577,149865,50,6578,149865,40,6578,149899,0,6578,154349,50,6737,154349,40,6737,154383,0,6737,216059,3,10658,217256,4,12588,217728,5,14538,217729,1,14538,217729,50,14540,217729,40,14540,217763,0,14540,266728,3,17091,267656,4,18366,268358,5,19641,268359,1,19641,268359,50,19643,268359,40,19643,268393,0,19643,312014,3,21147,312645,4,21894,312984,1,22644,312984,50,22646,312984,40,22646,313018,0,22646,326127,3,23412,327160,4,23772,328313,5,24147,328314,1,24147,328314,50,24147,328314,40,24147,328348,0,24147,371896,3,25349,372292,4,25948,372698,1,26548,372698,50,26550,372698,40,26550,372732,0,26550,404229,3,27301,404554,4,27676,404852,1,28051,404852,50,28052,404852,40,28052,404852,40,28052,404881,0,28052,405024,50,28052,405024,30,28052,405024,40,28052,405053,0,28052,405143,50,28052,405143,30,28052,405143,40,28052,405172,0,28057,405260,50,28057,405260,30,28057,405260,40,28057,405289,0,28057,405382,50,28058,405411,0,28058,405536,50,28059,405536,30,28059,405536,40,28059,405565,0,28064,405640,50,28064,405669,0,28064,405786,50,28066,405815,0,28071,405940,50,28074,405969,0,28074,406102,50,28078,406131,0,28078,406270,50,28086,406299,0,28090,406446,50,28104,406475,0,28104,406630,50,28131,406659,0,28135,406824,50,28190,406853,0,28190,407028,50,28300,407057,0,28300,407244,50,28527,407244,40,28527,407273,0,28527)
%
%
% START OF PROOF
% 407124 [?] ?
% 407246 [] equal(multiply(identity,X),X).
% 407247 [] equal(multiply(inverse(X),X),identity).
% 407248 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 407249 [] -equal(inverse(sk_c7),sk_c6).
% 407255 [?] ?
% 407261 [?] ?
% 407282 [input:407255,cut:407249] equal(inverse(sk_c2),sk_c6).
% 407283 [para:407282.1.1,407247.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 407299 [input:407261,cut:407249] equal(multiply(sk_c2,sk_c6),sk_c7).
% 407317 [para:407247.1.1,407248.1.1.1,demod:407246] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 407319 [para:407283.1.1,407248.1.1.1,demod:407246] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 407346 [para:407299.1.1,407319.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 407385 [para:407319.1.2,407317.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c6),X)).
% 407387 [para:407346.1.2,407317.1.2.2,demod:407385] equal(sk_c7,multiply(sk_c2,sk_c6)).
% 407412 [para:407385.1.2,407247.1.1,demod:407387] equal(sk_c7,identity).
% 407415 [para:407412.1.1,407249.1.1.1,cut:407124] 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: 25029
% derived clauses: 6201664
% kept clauses: 298081
% kept size sum: 447798
% kept mid-nuclei: 78397
% kept new demods: 2095
% forw unit-subs: 1897338
% forw double-subs: 3484637
% forw overdouble-subs: 269678
% backward subs: 13557
% fast unit cutoff: 32568
% full unit cutoff: 0
% dbl unit cutoff: 5745
% real runtime : 287.89
% process. runtime: 285.28
% specific non-discr-tree subsumption statistics:
% tried: 15860348
% length fails: 1950033
% strength fails: 4348864
% predlist fails: 483347
% aux str. fails: 2033261
% by-lit fails: 1457085
% full subs tried: 2064454
% full subs fail: 1912251
%
% ; 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/GRP216-1+eq_r.in")
%
%------------------------------------------------------------------------------