TSTP Solution File: GRP278-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP278-1 : 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 : art08.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 298.4s
% Output : Assurance 298.4s
% 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/GRP278-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 17)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 17)
% (binary-posweight-lex-big-order 30 #f 3 17)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c6,sk_c4),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% was split for some strategies as:
% -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6).
% -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6).
% -equal(inverse(sk_c4),sk_c5).
% -equal(multiply(sk_c6,sk_c4),sk_c5).
% -equal(multiply(sk_c5,sk_c6),sk_c4).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c6,sk_c4),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% Split part used next: -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(25,40,0,54,0,0,422,50,2,451,0,2,834,50,5,863,0,5,1257,50,9,1286,0,9,1687,50,14,1716,0,14,2124,50,21,2153,0,21,2569,50,34,2598,0,34,3023,50,60,3052,0,60,3487,50,118,3516,0,118,3962,50,246,3991,0,247,4449,50,459,4478,0,459,4949,50,874,4949,40,874,4978,0,874,15955,3,1175,16721,4,1325,17417,5,1475,17418,1,1475,17418,50,1475,17418,40,1475,17447,0,1475,17602,3,1790,17610,4,1935,17618,5,2076,17618,1,2076,17618,50,2076,17618,40,2076,17647,0,2076,36437,3,3578,37197,4,4327,37834,1,5077,37834,50,5077,37834,40,5077,37863,0,5077,52512,3,5829,53492,4,6203,54359,5,6578,54360,1,6578,54360,50,6578,54360,40,6578,54389,0,6578,66388,3,7331,67403,4,7704,68402,5,8079,68403,1,8079,68403,50,8079,68403,40,8079,68432,0,8079,139460,3,11981,140317,4,13930,141047,1,15880,141047,50,15882,141047,40,15882,141076,0,15882,203981,3,18434,204520,4,19708,205305,5,20984,205306,1,20984,205306,50,20986,205306,40,20986,205335,0,20986,241289,3,22492,242296,4,23237,243173,5,23987,243174,1,23987,243174,50,23989,243174,40,23989,243203,0,23989,254487,3,24740,255399,4,25115,256284,5,25490,256284,1,25490,256284,50,25490,256284,40,25490,256313,0,25490,288630,3,26692,289374,4,27291,290045,1,27891,290045,50,27892,290045,40,27892,290074,0,27892,309850,3,28644,310690,4,29018,311301,5,29393,311302,1,29393,311302,50,29394,311302,40,29394,311302,40,29394,311327,0,29394)
%
%
% START OF PROOF
% 311304 [] equal(multiply(identity,X),X).
% 311305 [] equal(multiply(inverse(X),X),identity).
% 311306 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 311307 [] -equal(multiply(X,sk_c4),sk_c5) | -equal(inverse(X),sk_c5).
% 311308 [] equal(multiply(sk_c6,sk_c4),sk_c5) | equal(multiply(sk_c3,sk_c4),sk_c5).
% 311309 [] equal(multiply(sk_c6,sk_c4),sk_c5) | equal(inverse(sk_c3),sk_c5).
% 311313 [?] ?
% 311314 [] equal(inverse(sk_c4),sk_c5) | equal(inverse(sk_c3),sk_c5).
% 311318 [?] ?
% 311319 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c3),sk_c5).
% 311323 [] equal(multiply(sk_c1,sk_c6),sk_c5) | equal(multiply(sk_c3,sk_c4),sk_c5).
% 311324 [] equal(multiply(sk_c1,sk_c6),sk_c5) | equal(inverse(sk_c3),sk_c5).
% 311331 [hyper:311307,311314,binarycut:311313] equal(inverse(sk_c4),sk_c5).
% 311333 [para:311331.1.1,311305.1.1.1] equal(multiply(sk_c5,sk_c4),identity).
% 311337 [hyper:311307,311319,binarycut:311318] equal(inverse(sk_c1),sk_c6).
% 311338 [para:311337.1.1,311305.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 311347 [hyper:311307,311308,311309] equal(multiply(sk_c6,sk_c4),sk_c5).
% 311356 [hyper:311307,311324,311323] equal(multiply(sk_c1,sk_c6),sk_c5).
% 311357 [para:311305.1.1,311306.1.1.1,demod:311304] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 311358 [para:311333.1.1,311306.1.1.1,demod:311304] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 311359 [para:311338.1.1,311306.1.1.1,demod:311304] equal(X,multiply(sk_c6,multiply(sk_c1,X))).
% 311360 [para:311347.1.1,311306.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c6,multiply(sk_c4,X))).
% 311361 [para:311356.1.1,311306.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c1,multiply(sk_c6,X))).
% 311362 [para:311356.1.1,311359.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c5)).
% 311363 [para:311362.1.2,311306.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c6,multiply(sk_c5,X))).
% 311369 [para:311359.1.2,311357.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c6),X)).
% 311370 [para:311360.1.2,311357.1.2.2,demod:311369] equal(multiply(sk_c4,X),multiply(sk_c1,multiply(sk_c5,X))).
% 311375 [para:311360.1.2,311361.1.2.2,demod:311370,311358] equal(X,multiply(sk_c4,X)).
% 311376 [para:311375.1.2,311358.1.2.2] equal(X,multiply(sk_c5,X)).
% 311377 [para:311375.1.2,311360.1.2.2,demod:311376] equal(X,multiply(sk_c6,X)).
% 311378 [para:311333.1.1,311363.1.2.2,demod:311377,311347] equal(sk_c5,identity).
% 311380 [para:311378.1.1,311333.1.1.1,demod:311304] equal(sk_c4,identity).
% 311381 [para:311378.1.1,311362.1.2.2,demod:311377] equal(sk_c6,identity).
% 311382 [para:311380.1.1,311331.1.1.1] equal(inverse(identity),sk_c5).
% 311385 [para:311381.1.1,311347.1.1.1,demod:311304] equal(sk_c4,sk_c5).
% 311392 [hyper:311307,311382,demod:311304,cut:311385] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 17
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c6,sk_c4),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% Split part used next: -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 17
% clause depth limited to 3
% seconds given: 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 17
% 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 17
% 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 17
% 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 17
% 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 17
% 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 17
% 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 17
% 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 17
% 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(25,40,0,54,0,0,422,50,2,451,0,2,834,50,5,863,0,5,1257,50,9,1286,0,9,1687,50,14,1716,0,14,2124,50,21,2153,0,21,2569,50,34,2598,0,34,3023,50,60,3052,0,60,3487,50,118,3516,0,118,3962,50,246,3991,0,247,4449,50,459,4478,0,459,4949,50,874,4949,40,874,4978,0,874,15955,3,1175,16721,4,1325,17417,5,1475,17418,1,1475,17418,50,1475,17418,40,1475,17447,0,1475,17602,3,1790,17610,4,1935,17618,5,2076,17618,1,2076,17618,50,2076,17618,40,2076,17647,0,2076,36437,3,3578,37197,4,4327,37834,1,5077,37834,50,5077,37834,40,5077,37863,0,5077,52512,3,5829,53492,4,6203,54359,5,6578,54360,1,6578,54360,50,6578,54360,40,6578,54389,0,6578,66388,3,7331,67403,4,7704,68402,5,8079,68403,1,8079,68403,50,8079,68403,40,8079,68432,0,8079,139460,3,11981,140317,4,13930,141047,1,15880,141047,50,15882,141047,40,15882,141076,0,15882,203981,3,18434,204520,4,19708,205305,5,20984,205306,1,20984,205306,50,20986,205306,40,20986,205335,0,20986,241289,3,22492,242296,4,23237,243173,5,23987,243174,1,23987,243174,50,23989,243174,40,23989,243203,0,23989,254487,3,24740,255399,4,25115,256284,5,25490,256284,1,25490,256284,50,25490,256284,40,25490,256313,0,25490,288630,3,26692,289374,4,27291,290045,1,27891,290045,50,27892,290045,40,27892,290074,0,27892,309850,3,28644,310690,4,29018,311301,5,29393,311302,1,29393,311302,50,29394,311302,40,29394,311302,40,29394,311327,0,29394,311391,50,29395,311391,30,29395,311391,40,29395,311416,0,29395,311485,50,29395,311510,0,29401,311623,50,29402,311648,0,29402,311763,50,29404,311788,0,29404,311924,50,29408,311949,0,29412,312092,50,29419,312117,0,29419,312268,50,29433,312293,0,29437,312453,50,29464,312478,0,29464,312648,50,29519,312673,0,29519,312854,50,29636,312854,40,29636,312879,0,29636)
%
%
% START OF PROOF
% 312741 [?] ?
% 312767 [?] ?
% 312856 [] equal(multiply(identity,X),X).
% 312857 [] equal(multiply(inverse(X),X),identity).
% 312858 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 312859 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 312934 [para:312857.1.1,312858.1.1.1,demod:312856] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 312969 [para:312857.1.1,312934.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 313020 [para:312934.1.2,312934.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 313074 [para:313020.1.2,312969.1.2] equal(X,multiply(X,identity)).
% 313081 [para:313074.1.2,312857.1.1] equal(inverse(identity),identity).
% 313083 [para:313081.1.1,312859.2.1,demod:312856,cut:312767,cut:312741] 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 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c6,sk_c4),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% Split part used next: -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 17
% clause depth limited to 3
% seconds given: 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 17
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(25,40,0,54,0,0,422,50,2,451,0,2,834,50,5,863,0,5,1257,50,9,1286,0,9,1687,50,14,1716,0,14,2124,50,21,2153,0,21,2569,50,34,2598,0,34,3023,50,60,3052,0,60,3487,50,118,3516,0,118,3962,50,246,3991,0,247,4449,50,459,4478,0,459,4949,50,874,4949,40,874,4978,0,874,15955,3,1175,16721,4,1325,17417,5,1475,17418,1,1475,17418,50,1475,17418,40,1475,17447,0,1475,17602,3,1790,17610,4,1935,17618,5,2076,17618,1,2076,17618,50,2076,17618,40,2076,17647,0,2076,36437,3,3578,37197,4,4327,37834,1,5077,37834,50,5077,37834,40,5077,37863,0,5077,52512,3,5829,53492,4,6203,54359,5,6578,54360,1,6578,54360,50,6578,54360,40,6578,54389,0,6578,66388,3,7331,67403,4,7704,68402,5,8079,68403,1,8079,68403,50,8079,68403,40,8079,68432,0,8079,139460,3,11981,140317,4,13930,141047,1,15880,141047,50,15882,141047,40,15882,141076,0,15882,203981,3,18434,204520,4,19708,205305,5,20984,205306,1,20984,205306,50,20986,205306,40,20986,205335,0,20986,241289,3,22492,242296,4,23237,243173,5,23987,243174,1,23987,243174,50,23989,243174,40,23989,243203,0,23989,254487,3,24740,255399,4,25115,256284,5,25490,256284,1,25490,256284,50,25490,256284,40,25490,256313,0,25490,288630,3,26692,289374,4,27291,290045,1,27891,290045,50,27892,290045,40,27892,290074,0,27892,309850,3,28644,310690,4,29018,311301,5,29393,311302,1,29393,311302,50,29394,311302,40,29394,311302,40,29394,311327,0,29394,311391,50,29395,311391,30,29395,311391,40,29395,311416,0,29395,311485,50,29395,311510,0,29401,311623,50,29402,311648,0,29402,311763,50,29404,311788,0,29404,311924,50,29408,311949,0,29412,312092,50,29419,312117,0,29419,312268,50,29433,312293,0,29437,312453,50,29464,312478,0,29464,312648,50,29519,312673,0,29519,312854,50,29636,312854,40,29636,312879,0,29636,313082,50,29637,313082,30,29637,313082,40,29637,313107,0,29637,313206,50,29638,313231,0,29643)
%
%
% START OF PROOF
% 313208 [] equal(multiply(identity,X),X).
% 313209 [] equal(multiply(inverse(X),X),identity).
% 313210 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 313211 [] -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6).
% 313222 [] equal(multiply(sk_c3,sk_c4),sk_c5) | equal(inverse(sk_c1),sk_c6).
% 313223 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c3),sk_c5).
% 313224 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(inverse(sk_c1),sk_c6).
% 313225 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c2),sk_c6).
% 313226 [] equal(multiply(sk_c5,sk_c6),sk_c4) | equal(inverse(sk_c1),sk_c6).
% 313227 [?] ?
% 313228 [?] ?
% 313229 [?] ?
% 313230 [?] ?
% 313231 [?] ?
% 313238 [hyper:313211,313223,binarycut:313228] equal(inverse(sk_c3),sk_c5).
% 313239 [para:313238.1.1,313209.1.1.1] equal(multiply(sk_c5,sk_c3),identity).
% 313242 [hyper:313211,313225,binarycut:313230] equal(inverse(sk_c2),sk_c6).
% 313246 [para:313242.1.1,313209.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 313255 [hyper:313211,313222,binarycut:313227] equal(multiply(sk_c3,sk_c4),sk_c5).
% 313258 [hyper:313211,313224,binarycut:313229] equal(multiply(sk_c2,sk_c5),sk_c6).
% 313262 [hyper:313211,313226,binarycut:313231] equal(multiply(sk_c5,sk_c6),sk_c4).
% 313263 [para:313209.1.1,313210.1.1.1,demod:313208] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 313264 [para:313239.1.1,313210.1.1.1,demod:313208] equal(X,multiply(sk_c5,multiply(sk_c3,X))).
% 313265 [para:313246.1.1,313210.1.1.1,demod:313208] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 313266 [para:313255.1.1,313210.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c3,multiply(sk_c4,X))).
% 313267 [para:313258.1.1,313210.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c2,multiply(sk_c5,X))).
% 313268 [para:313262.1.1,313210.1.1.1] equal(multiply(sk_c4,X),multiply(sk_c5,multiply(sk_c6,X))).
% 313269 [para:313255.1.1,313264.1.2.2] equal(sk_c4,multiply(sk_c5,sk_c5)).
% 313273 [para:313209.1.1,313263.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 313274 [para:313239.1.1,313263.1.2.2] equal(sk_c3,multiply(inverse(sk_c5),identity)).
% 313276 [para:313262.1.1,313263.1.2.2] equal(sk_c6,multiply(inverse(sk_c5),sk_c4)).
% 313277 [para:313210.1.1,313263.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 313278 [para:313264.1.2,313263.1.2.2] equal(multiply(sk_c3,X),multiply(inverse(sk_c5),X)).
% 313279 [para:313269.1.2,313263.1.2.2,demod:313276] equal(sk_c5,sk_c6).
% 313281 [para:313263.1.2,313263.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 313282 [para:313279.1.2,313246.1.1.1] equal(multiply(sk_c5,sk_c2),identity).
% 313293 [para:313282.1.1,313267.1.2.2,demod:313246] equal(identity,multiply(sk_c2,identity)).
% 313300 [para:313268.1.2,313263.1.2.2,demod:313266,313278] equal(multiply(sk_c6,X),multiply(sk_c5,X)).
% 313303 [para:313293.1.2,313210.1.1.1,demod:313208] equal(X,multiply(sk_c2,X)).
% 313305 [para:313303.1.2,313265.1.2.2,demod:313300] equal(X,multiply(sk_c5,X)).
% 313310 [para:313305.1.2,313268.1.2,demod:313305,313300] equal(multiply(sk_c4,X),X).
% 313312 [para:313310.1.1,313263.1.2.2] equal(X,multiply(inverse(sk_c4),X)).
% 313314 [para:313312.1.2,313209.1.1] equal(sk_c4,identity).
% 313321 [para:313314.1.1,313276.1.2.2,demod:313274] equal(sk_c6,sk_c3).
% 313322 [para:313321.1.1,313279.1.2] equal(sk_c5,sk_c3).
% 313350 [para:313322.1.2,313238.1.1.1] equal(inverse(sk_c5),sk_c5).
% 313357 [para:313281.1.2,313209.1.1] equal(multiply(X,inverse(X)),identity).
% 313359 [para:313281.1.2,313273.1.2] equal(X,multiply(X,identity)).
% 313360 [para:313359.1.2,313273.1.2] equal(X,inverse(inverse(X))).
% 313362 [para:313357.1.1,313277.1.2.2.2,demod:313359] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 313367 [para:313265.1.2,313362.1.2.1.1,demod:313303] equal(inverse(X),multiply(inverse(X),sk_c6)).
% 313377 [para:313367.1.2,313281.1.2,demod:313360] equal(multiply(X,sk_c6),X).
% 313378 [hyper:313211,313377,demod:313350,cut:313279] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 17
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c6,sk_c4),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% Split part used next: -equal(inverse(sk_c4),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 17
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(25,40,0,54,0,0,422,50,2,451,0,2,834,50,5,863,0,5,1257,50,9,1286,0,9,1687,50,14,1716,0,14,2124,50,21,2153,0,21,2569,50,34,2598,0,34,3023,50,60,3052,0,60,3487,50,118,3516,0,118,3962,50,246,3991,0,247,4449,50,459,4478,0,459,4949,50,874,4949,40,874,4978,0,874,15955,3,1175,16721,4,1325,17417,5,1475,17418,1,1475,17418,50,1475,17418,40,1475,17447,0,1475,17602,3,1790,17610,4,1935,17618,5,2076,17618,1,2076,17618,50,2076,17618,40,2076,17647,0,2076,36437,3,3578,37197,4,4327,37834,1,5077,37834,50,5077,37834,40,5077,37863,0,5077,52512,3,5829,53492,4,6203,54359,5,6578,54360,1,6578,54360,50,6578,54360,40,6578,54389,0,6578,66388,3,7331,67403,4,7704,68402,5,8079,68403,1,8079,68403,50,8079,68403,40,8079,68432,0,8079,139460,3,11981,140317,4,13930,141047,1,15880,141047,50,15882,141047,40,15882,141076,0,15882,203981,3,18434,204520,4,19708,205305,5,20984,205306,1,20984,205306,50,20986,205306,40,20986,205335,0,20986,241289,3,22492,242296,4,23237,243173,5,23987,243174,1,23987,243174,50,23989,243174,40,23989,243203,0,23989,254487,3,24740,255399,4,25115,256284,5,25490,256284,1,25490,256284,50,25490,256284,40,25490,256313,0,25490,288630,3,26692,289374,4,27291,290045,1,27891,290045,50,27892,290045,40,27892,290074,0,27892,309850,3,28644,310690,4,29018,311301,5,29393,311302,1,29393,311302,50,29394,311302,40,29394,311302,40,29394,311327,0,29394,311391,50,29395,311391,30,29395,311391,40,29395,311416,0,29395,311485,50,29395,311510,0,29401,311623,50,29402,311648,0,29402,311763,50,29404,311788,0,29404,311924,50,29408,311949,0,29412,312092,50,29419,312117,0,29419,312268,50,29433,312293,0,29437,312453,50,29464,312478,0,29464,312648,50,29519,312673,0,29519,312854,50,29636,312854,40,29636,312879,0,29636,313082,50,29637,313082,30,29637,313082,40,29637,313107,0,29637,313206,50,29638,313231,0,29643,313377,50,29644,313377,30,29644,313377,40,29644,313402,0,29644)
%
%
% START OF PROOF
% 313379 [] equal(multiply(identity,X),X).
% 313380 [] equal(multiply(inverse(X),X),identity).
% 313381 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 313382 [] -equal(inverse(sk_c4),sk_c5).
% 313388 [?] ?
% 313389 [?] ?
% 313390 [?] ?
% 313391 [?] ?
% 313392 [?] ?
% 313403 [input:313389,cut:313382] equal(inverse(sk_c3),sk_c5).
% 313404 [para:313403.1.1,313380.1.1.1] equal(multiply(sk_c5,sk_c3),identity).
% 313406 [input:313391,cut:313382] equal(inverse(sk_c2),sk_c6).
% 313407 [para:313406.1.1,313380.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 313412 [input:313388,cut:313382] equal(multiply(sk_c3,sk_c4),sk_c5).
% 313413 [input:313390,cut:313382] equal(multiply(sk_c2,sk_c5),sk_c6).
% 313414 [input:313392,cut:313382] equal(multiply(sk_c5,sk_c6),sk_c4).
% 313425 [para:313380.1.1,313381.1.1.1,demod:313379] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 313426 [para:313404.1.1,313381.1.1.1,demod:313379] equal(X,multiply(sk_c5,multiply(sk_c3,X))).
% 313429 [para:313413.1.1,313381.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c2,multiply(sk_c5,X))).
% 313431 [para:313412.1.1,313426.1.2.2] equal(sk_c4,multiply(sk_c5,sk_c5)).
% 313434 [para:313404.1.1,313425.1.2.2] equal(sk_c3,multiply(inverse(sk_c5),identity)).
% 313435 [para:313407.1.1,313425.1.2.2] equal(sk_c2,multiply(inverse(sk_c6),identity)).
% 313438 [para:313414.1.1,313425.1.2.2] equal(sk_c6,multiply(inverse(sk_c5),sk_c4)).
% 313440 [para:313431.1.2,313425.1.2.2,demod:313438] equal(sk_c5,sk_c6).
% 313441 [para:313440.1.2,313407.1.1.1] equal(multiply(sk_c5,sk_c2),identity).
% 313443 [para:313441.1.1,313425.1.2.2,demod:313434] equal(sk_c2,sk_c3).
% 313444 [para:313443.1.2,313403.1.1.1] equal(inverse(sk_c2),sk_c5).
% 313463 [para:313441.1.1,313429.1.2.2,demod:313407] equal(identity,multiply(sk_c2,identity)).
% 313464 [para:313463.1.2,313381.1.1.1,demod:313379] equal(X,multiply(sk_c2,X)).
% 313469 [para:313464.1.2,313425.1.2.2,demod:313444] equal(X,multiply(sk_c5,X)).
% 313471 [para:313469.1.2,313414.1.1] equal(sk_c6,sk_c4).
% 313477 [para:313471.1.1,313435.1.2.1.1] equal(sk_c2,multiply(inverse(sk_c4),identity)).
% 313478 [para:313477.1.2,313381.1.1.1,demod:313379,313464] equal(X,multiply(inverse(sk_c4),X)).
% 313479 [para:313478.1.2,313380.1.1] equal(sk_c4,identity).
% 313482 [para:313479.1.1,313438.1.2.2,demod:313434] equal(sk_c6,sk_c3).
% 313490 [para:313482.1.1,313471.1.1] equal(sk_c3,sk_c4).
% 313495 [para:313490.1.1,313403.1.1.1,cut:313382] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 17
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c6,sk_c4),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% Split part used next: -equal(multiply(sk_c6,sk_c4),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 17
% 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 17
% 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 17
% 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 17
% 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 17
% 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 17
% 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 17
% 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 17
% 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 17
% 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(25,40,0,54,0,0,422,50,2,451,0,2,834,50,5,863,0,5,1257,50,9,1286,0,9,1687,50,14,1716,0,14,2124,50,21,2153,0,21,2569,50,34,2598,0,34,3023,50,60,3052,0,60,3487,50,118,3516,0,118,3962,50,246,3991,0,247,4449,50,459,4478,0,459,4949,50,874,4949,40,874,4978,0,874,15955,3,1175,16721,4,1325,17417,5,1475,17418,1,1475,17418,50,1475,17418,40,1475,17447,0,1475,17602,3,1790,17610,4,1935,17618,5,2076,17618,1,2076,17618,50,2076,17618,40,2076,17647,0,2076,36437,3,3578,37197,4,4327,37834,1,5077,37834,50,5077,37834,40,5077,37863,0,5077,52512,3,5829,53492,4,6203,54359,5,6578,54360,1,6578,54360,50,6578,54360,40,6578,54389,0,6578,66388,3,7331,67403,4,7704,68402,5,8079,68403,1,8079,68403,50,8079,68403,40,8079,68432,0,8079,139460,3,11981,140317,4,13930,141047,1,15880,141047,50,15882,141047,40,15882,141076,0,15882,203981,3,18434,204520,4,19708,205305,5,20984,205306,1,20984,205306,50,20986,205306,40,20986,205335,0,20986,241289,3,22492,242296,4,23237,243173,5,23987,243174,1,23987,243174,50,23989,243174,40,23989,243203,0,23989,254487,3,24740,255399,4,25115,256284,5,25490,256284,1,25490,256284,50,25490,256284,40,25490,256313,0,25490,288630,3,26692,289374,4,27291,290045,1,27891,290045,50,27892,290045,40,27892,290074,0,27892,309850,3,28644,310690,4,29018,311301,5,29393,311302,1,29393,311302,50,29394,311302,40,29394,311302,40,29394,311327,0,29394,311391,50,29395,311391,30,29395,311391,40,29395,311416,0,29395,311485,50,29395,311510,0,29401,311623,50,29402,311648,0,29402,311763,50,29404,311788,0,29404,311924,50,29408,311949,0,29412,312092,50,29419,312117,0,29419,312268,50,29433,312293,0,29437,312453,50,29464,312478,0,29464,312648,50,29519,312673,0,29519,312854,50,29636,312854,40,29636,312879,0,29636,313082,50,29637,313082,30,29637,313082,40,29637,313107,0,29637,313206,50,29638,313231,0,29643,313377,50,29644,313377,30,29644,313377,40,29644,313402,0,29644,313494,50,29645,313494,30,29645,313494,40,29645,313519,0,29645,313618,50,29646,313643,0,29650,313781,50,29653,313806,0,29653,313952,50,29656,313977,0,29661,314131,50,29666,314156,0,29666,314316,50,29674,314341,0,29674,314509,50,29689,314534,0,29693,314710,50,29722,314735,0,29722,314921,50,29783,314946,0,29783,315142,50,29899,315142,40,29899,315167,0,29899)
%
%
% START OF PROOF
% 315088 [?] ?
% 315144 [] equal(multiply(identity,X),X).
% 315145 [] equal(multiply(inverse(X),X),identity).
% 315146 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 315147 [] -equal(multiply(sk_c6,sk_c4),sk_c5).
% 315148 [?] ?
% 315149 [?] ?
% 315152 [?] ?
% 315171 [input:315148,cut:315147] equal(multiply(sk_c3,sk_c4),sk_c5).
% 315181 [input:315149,cut:315147] equal(inverse(sk_c3),sk_c5).
% 315182 [para:315181.1.1,315145.1.1.1] equal(multiply(sk_c5,sk_c3),identity).
% 315192 [input:315152,cut:315147] equal(multiply(sk_c5,sk_c6),sk_c4).
% 315209 [para:315145.1.1,315146.1.1.1,demod:315144] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 315211 [para:315182.1.1,315146.1.1.1,demod:315144] equal(X,multiply(sk_c5,multiply(sk_c3,X))).
% 315226 [para:315171.1.1,315211.1.2.2] equal(sk_c4,multiply(sk_c5,sk_c5)).
% 315241 [para:315192.1.1,315209.1.2.2] equal(sk_c6,multiply(inverse(sk_c5),sk_c4)).
% 315257 [para:315226.1.2,315209.1.2.2,demod:315241] equal(sk_c5,sk_c6).
% 315263 [para:315257.1.2,315147.1.1.1,cut:315088] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c6,sk_c4),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(Z),sk_c5) | -equal(multiply(Z,sk_c4),sk_c5).
% Split part used next: -equal(multiply(sk_c5,sk_c6),sk_c4).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 17
% clause depth limited to 3
% seconds given: 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 17
% 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 17
% 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 17
% 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 17
% 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 17
% 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 17
% 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 17
% 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 17
% 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(25,40,0,54,0,0,422,50,2,451,0,2,834,50,5,863,0,5,1257,50,9,1286,0,9,1687,50,14,1716,0,14,2124,50,21,2153,0,21,2569,50,34,2598,0,34,3023,50,60,3052,0,60,3487,50,118,3516,0,118,3962,50,246,3991,0,247,4449,50,459,4478,0,459,4949,50,874,4949,40,874,4978,0,874,15955,3,1175,16721,4,1325,17417,5,1475,17418,1,1475,17418,50,1475,17418,40,1475,17447,0,1475,17602,3,1790,17610,4,1935,17618,5,2076,17618,1,2076,17618,50,2076,17618,40,2076,17647,0,2076,36437,3,3578,37197,4,4327,37834,1,5077,37834,50,5077,37834,40,5077,37863,0,5077,52512,3,5829,53492,4,6203,54359,5,6578,54360,1,6578,54360,50,6578,54360,40,6578,54389,0,6578,66388,3,7331,67403,4,7704,68402,5,8079,68403,1,8079,68403,50,8079,68403,40,8079,68432,0,8079,139460,3,11981,140317,4,13930,141047,1,15880,141047,50,15882,141047,40,15882,141076,0,15882,203981,3,18434,204520,4,19708,205305,5,20984,205306,1,20984,205306,50,20986,205306,40,20986,205335,0,20986,241289,3,22492,242296,4,23237,243173,5,23987,243174,1,23987,243174,50,23989,243174,40,23989,243203,0,23989,254487,3,24740,255399,4,25115,256284,5,25490,256284,1,25490,256284,50,25490,256284,40,25490,256313,0,25490,288630,3,26692,289374,4,27291,290045,1,27891,290045,50,27892,290045,40,27892,290074,0,27892,309850,3,28644,310690,4,29018,311301,5,29393,311302,1,29393,311302,50,29394,311302,40,29394,311302,40,29394,311327,0,29394,311391,50,29395,311391,30,29395,311391,40,29395,311416,0,29395,311485,50,29395,311510,0,29401,311623,50,29402,311648,0,29402,311763,50,29404,311788,0,29404,311924,50,29408,311949,0,29412,312092,50,29419,312117,0,29419,312268,50,29433,312293,0,29437,312453,50,29464,312478,0,29464,312648,50,29519,312673,0,29519,312854,50,29636,312854,40,29636,312879,0,29636,313082,50,29637,313082,30,29637,313082,40,29637,313107,0,29637,313206,50,29638,313231,0,29643,313377,50,29644,313377,30,29644,313377,40,29644,313402,0,29644,313494,50,29645,313494,30,29645,313494,40,29645,313519,0,29645,313618,50,29646,313643,0,29650,313781,50,29653,313806,0,29653,313952,50,29656,313977,0,29661,314131,50,29666,314156,0,29666,314316,50,29674,314341,0,29674,314509,50,29689,314534,0,29693,314710,50,29722,314735,0,29722,314921,50,29783,314946,0,29783,315142,50,29899,315142,40,29899,315167,0,29899,315262,50,29899,315262,30,29899,315262,40,29899,315287,0,29899,315360,50,29900,315385,0,29904,315501,50,29905,315526,0,29905,315657,50,29907,315682,0,29907,315826,50,29910,315851,0,29915,316001,50,29920,316026,0,29920,316184,50,29931,316209,0,29935,316375,50,29958,316400,0,29958,316576,50,30006,316601,0,30006,316787,50,30107,316787,40,30107,316812,0,30107)
%
%
% START OF PROOF
% 316728 [?] ?
% 316789 [] equal(multiply(identity,X),X).
% 316790 [] equal(multiply(inverse(X),X),identity).
% 316791 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 316792 [] -equal(multiply(sk_c5,sk_c6),sk_c4).
% 316807 [?] ?
% 316812 [?] ?
% 316842 [input:316807,cut:316792] equal(inverse(sk_c1),sk_c6).
% 316843 [para:316842.1.1,316790.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 316854 [input:316812,cut:316792] equal(multiply(sk_c1,sk_c6),sk_c5).
% 316856 [para:316790.1.1,316791.1.1.1,demod:316789] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 316869 [para:316843.1.1,316791.1.1.1,demod:316789] equal(X,multiply(sk_c6,multiply(sk_c1,X))).
% 316886 [para:316854.1.1,316869.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c5)).
% 316921 [para:316869.1.2,316856.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c6),X)).
% 316922 [para:316886.1.2,316856.1.2.2,demod:316921] equal(sk_c5,multiply(sk_c1,sk_c6)).
% 316944 [para:316921.1.2,316790.1.1,demod:316922] equal(sk_c5,identity).
% 316948 [para:316944.1.1,316792.1.1.1,demod:316789,cut:316728] 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: 34775
% derived clauses: 6513140
% kept clauses: 276360
% kept size sum: 978026
% kept mid-nuclei: 2287
% kept new demods: 4718
% forw unit-subs: 2282464
% forw double-subs: 3621308
% forw overdouble-subs: 288570
% backward subs: 13800
% fast unit cutoff: 19257
% full unit cutoff: 0
% dbl unit cutoff: 5991
% real runtime : 303.0
% process. runtime: 301.8
% specific non-discr-tree subsumption statistics:
% tried: 34097176
% length fails: 3451394
% strength fails: 10610179
% predlist fails: 1105182
% aux str. fails: 5700190
% by-lit fails: 7045590
% full subs tried: 1434909
% full subs fail: 1338847
%
% ; 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/GRP278-1+eq_r.in")
%
%------------------------------------------------------------------------------