TSTP Solution File: GRP359-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP359-1 : 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 299.1s
% Output : Assurance 299.1s
% 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/GRP359-1+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 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (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_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% was split for some strategies as:
% -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8).
% -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% -equal(multiply(sk_c7,sk_c6),sk_c8).
% -equal(inverse(sk_c8),sk_c6).
% -equal(multiply(sk_c8,sk_c7),sk_c6).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,74,0,0,856,50,6,895,0,6,2444,50,24,2483,0,25,4701,50,54,4740,0,54,7247,50,80,7286,0,80,10177,50,116,10216,0,116,13397,50,165,13436,0,165,17003,50,238,17042,0,238,20995,50,358,21034,0,358,25468,50,568,25507,0,568,30423,50,859,30423,40,859,30462,0,859,42435,3,1160,43053,4,1310,43726,5,1460,43727,1,1460,43727,50,1460,43727,40,1460,43766,0,1461,43985,3,1771,43993,4,1914,44001,5,2062,44001,1,2062,44001,50,2062,44001,40,2062,44040,0,2062,67244,3,3563,68357,4,4313,69113,1,5063,69113,50,5063,69113,40,5063,69152,0,5063,81414,3,5819,82284,4,6189,83162,5,6564,83163,1,6564,83163,50,6564,83163,40,6564,83202,0,6564,100291,3,7315,100467,4,7690,100761,5,8065,100762,1,8065,100762,50,8065,100762,40,8065,100801,0,8065,174510,3,11966,175564,4,13917,176026,1,15866,176026,50,15868,176026,40,15868,176065,0,15868,231568,3,18419,232424,4,19694,232816,1,20969,232816,50,20971,232816,40,20971,232855,0,20971,280407,3,22483,281042,4,23222,281690,5,23972,281691,1,23972,281691,50,23974,281691,40,23974,281730,0,23974,300961,3,24727,301445,4,25100,302108,5,25475,302109,1,25475,302109,50,25475,302109,40,25475,302148,0,25475,331173,3,26677,331881,4,27276,332577,5,27876,332578,1,27876,332578,50,27877,332578,40,27877,332617,0,27877,351003,3,28628,351590,4,29003,351947,1,29378,351947,50,29378,351947,40,29378,351947,40,29378,351982,0,29378)
%
%
% START OF PROOF
% 351948 [] equal(X,X).
% 351952 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 351953 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 351954 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c8).
% 351955 [?] ?
% 351959 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c4),sk_c8).
% 351960 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 351961 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 351965 [?] ?
% 351966 [?] ?
% 351967 [?] ?
% 352010 [hyper:351952,351954,351953,binarycut:351955] equal(inverse(sk_c1),sk_c8).
% 352022 [hyper:351952,351959,demod:352010,cut:351948,binarycut:351965] equal(inverse(sk_c4),sk_c8).
% 352034 [hyper:351952,351960,demod:352010,cut:351948,binarycut:351966] equal(multiply(sk_c4,sk_c8),sk_c5).
% 352056 [hyper:351952,351961,demod:352010,cut:351948,binarycut:351967] equal(multiply(sk_c8,sk_c5),sk_c7).
% 352061 [hyper:351952,352056,352034,demod:352022,cut:351948] 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 21
% 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_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,74,0,0,856,50,6,895,0,6,2444,50,24,2483,0,25,4701,50,54,4740,0,54,7247,50,80,7286,0,80,10177,50,116,10216,0,116,13397,50,165,13436,0,165,17003,50,238,17042,0,238,20995,50,358,21034,0,358,25468,50,568,25507,0,568,30423,50,859,30423,40,859,30462,0,859,42435,3,1160,43053,4,1310,43726,5,1460,43727,1,1460,43727,50,1460,43727,40,1460,43766,0,1461,43985,3,1771,43993,4,1914,44001,5,2062,44001,1,2062,44001,50,2062,44001,40,2062,44040,0,2062,67244,3,3563,68357,4,4313,69113,1,5063,69113,50,5063,69113,40,5063,69152,0,5063,81414,3,5819,82284,4,6189,83162,5,6564,83163,1,6564,83163,50,6564,83163,40,6564,83202,0,6564,100291,3,7315,100467,4,7690,100761,5,8065,100762,1,8065,100762,50,8065,100762,40,8065,100801,0,8065,174510,3,11966,175564,4,13917,176026,1,15866,176026,50,15868,176026,40,15868,176065,0,15868,231568,3,18419,232424,4,19694,232816,1,20969,232816,50,20971,232816,40,20971,232855,0,20971,280407,3,22483,281042,4,23222,281690,5,23972,281691,1,23972,281691,50,23974,281691,40,23974,281730,0,23974,300961,3,24727,301445,4,25100,302108,5,25475,302109,1,25475,302109,50,25475,302109,40,25475,302148,0,25475,331173,3,26677,331881,4,27276,332577,5,27876,332578,1,27876,332578,50,27877,332578,40,27877,332617,0,27877,351003,3,28628,351590,4,29003,351947,1,29378,351947,50,29378,351947,40,29378,351947,40,29378,351982,0,29378,352060,50,29379,352060,30,29379,352060,40,29379,352095,0,29379)
%
%
% START OF PROOF
% 352062 [] equal(multiply(identity,X),X).
% 352063 [] equal(multiply(inverse(X),X),identity).
% 352064 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 352065 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 352069 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 352070 [?] ?
% 352075 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c3),sk_c8).
% 352076 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 352081 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 352082 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 352087 [] equal(inverse(sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 352088 [?] ?
% 352093 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 352094 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 352102 [hyper:352065,352069,binarycut:352070] equal(inverse(sk_c1),sk_c8).
% 352105 [para:352102.1.1,352063.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 352115 [hyper:352065,352087,binarycut:352088] equal(inverse(sk_c8),sk_c6).
% 352116 [para:352115.1.1,352063.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 352136 [hyper:352065,352076,352075] equal(multiply(sk_c1,sk_c8),sk_c2).
% 352141 [hyper:352065,352082,352081] equal(multiply(sk_c8,sk_c2),sk_c7).
% 352146 [hyper:352065,352094,352093] equal(multiply(sk_c7,sk_c6),sk_c8).
% 352147 [para:352063.1.1,352064.1.1.1,demod:352062] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 352148 [para:352105.1.1,352064.1.1.1,demod:352062] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 352149 [para:352116.1.1,352064.1.1.1,demod:352062] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 352150 [para:352136.1.1,352064.1.1.1] equal(multiply(sk_c2,X),multiply(sk_c1,multiply(sk_c8,X))).
% 352153 [para:352136.1.1,352148.1.2.2,demod:352141] equal(sk_c8,sk_c7).
% 352154 [para:352153.1.2,352146.1.1.1] equal(multiply(sk_c8,sk_c6),sk_c8).
% 352156 [para:352105.1.1,352149.1.2.2] equal(sk_c1,multiply(sk_c6,identity)).
% 352157 [para:352141.1.1,352149.1.2.2] equal(sk_c2,multiply(sk_c6,sk_c7)).
% 352158 [para:352148.1.2,352149.1.2.2] equal(multiply(sk_c1,X),multiply(sk_c6,X)).
% 352159 [para:352154.1.1,352149.1.2.2,demod:352116] equal(sk_c6,identity).
% 352160 [para:352159.1.1,352116.1.1.1,demod:352062] equal(sk_c8,identity).
% 352163 [para:352159.1.1,352149.1.2.1,demod:352062] equal(X,multiply(sk_c8,X)).
% 352165 [para:352115.1.1,352147.1.2.1,demod:352158,352163] equal(X,multiply(sk_c1,X)).
% 352171 [para:352160.1.1,352136.1.1.2,demod:352165] equal(identity,sk_c2).
% 352180 [para:352141.1.1,352150.1.2.2,demod:352165] equal(multiply(sk_c2,sk_c2),sk_c7).
% 352183 [para:352148.1.2,352150.1.2.2,demod:352165] equal(multiply(sk_c2,X),X).
% 352193 [para:352171.1.2,352180.1.1.2,demod:352183] equal(identity,sk_c7).
% 352194 [para:352193.1.2,352157.1.2.2,demod:352156] equal(sk_c2,sk_c1).
% 352195 [para:352194.1.2,352102.1.1.1] equal(inverse(sk_c2),sk_c8).
% 352197 [hyper:352065,352195,demod:352183,cut:352153] 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 21
% 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_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,74,0,0,856,50,6,895,0,6,2444,50,24,2483,0,25,4701,50,54,4740,0,54,7247,50,80,7286,0,80,10177,50,116,10216,0,116,13397,50,165,13436,0,165,17003,50,238,17042,0,238,20995,50,358,21034,0,358,25468,50,568,25507,0,568,30423,50,859,30423,40,859,30462,0,859,42435,3,1160,43053,4,1310,43726,5,1460,43727,1,1460,43727,50,1460,43727,40,1460,43766,0,1461,43985,3,1771,43993,4,1914,44001,5,2062,44001,1,2062,44001,50,2062,44001,40,2062,44040,0,2062,67244,3,3563,68357,4,4313,69113,1,5063,69113,50,5063,69113,40,5063,69152,0,5063,81414,3,5819,82284,4,6189,83162,5,6564,83163,1,6564,83163,50,6564,83163,40,6564,83202,0,6564,100291,3,7315,100467,4,7690,100761,5,8065,100762,1,8065,100762,50,8065,100762,40,8065,100801,0,8065,174510,3,11966,175564,4,13917,176026,1,15866,176026,50,15868,176026,40,15868,176065,0,15868,231568,3,18419,232424,4,19694,232816,1,20969,232816,50,20971,232816,40,20971,232855,0,20971,280407,3,22483,281042,4,23222,281690,5,23972,281691,1,23972,281691,50,23974,281691,40,23974,281730,0,23974,300961,3,24727,301445,4,25100,302108,5,25475,302109,1,25475,302109,50,25475,302109,40,25475,302148,0,25475,331173,3,26677,331881,4,27276,332577,5,27876,332578,1,27876,332578,50,27877,332578,40,27877,332617,0,27877,351003,3,28628,351590,4,29003,351947,1,29378,351947,50,29378,351947,40,29378,351947,40,29378,351982,0,29378,352060,50,29379,352060,30,29379,352060,40,29379,352095,0,29379,352196,50,29379,352196,30,29379,352196,40,29379,352231,0,29384)
%
%
% START OF PROOF
% 352197 [] equal(X,X).
% 352201 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 352202 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 352203 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c8).
% 352204 [?] ?
% 352208 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c4),sk_c8).
% 352209 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 352210 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 352214 [?] ?
% 352215 [?] ?
% 352216 [?] ?
% 352259 [hyper:352201,352203,352202,binarycut:352204] equal(inverse(sk_c1),sk_c8).
% 352271 [hyper:352201,352208,demod:352259,cut:352197,binarycut:352214] equal(inverse(sk_c4),sk_c8).
% 352283 [hyper:352201,352209,demod:352259,cut:352197,binarycut:352215] equal(multiply(sk_c4,sk_c8),sk_c5).
% 352305 [hyper:352201,352210,demod:352259,cut:352197,binarycut:352216] equal(multiply(sk_c8,sk_c5),sk_c7).
% 352310 [hyper:352201,352305,352283,demod:352271,cut:352197] 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 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c7,sk_c6),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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,0,74,0,0,856,50,6,895,0,6,2444,50,24,2483,0,25,4701,50,54,4740,0,54,7247,50,80,7286,0,80,10177,50,116,10216,0,116,13397,50,165,13436,0,165,17003,50,238,17042,0,238,20995,50,358,21034,0,358,25468,50,568,25507,0,568,30423,50,859,30423,40,859,30462,0,859,42435,3,1160,43053,4,1310,43726,5,1460,43727,1,1460,43727,50,1460,43727,40,1460,43766,0,1461,43985,3,1771,43993,4,1914,44001,5,2062,44001,1,2062,44001,50,2062,44001,40,2062,44040,0,2062,67244,3,3563,68357,4,4313,69113,1,5063,69113,50,5063,69113,40,5063,69152,0,5063,81414,3,5819,82284,4,6189,83162,5,6564,83163,1,6564,83163,50,6564,83163,40,6564,83202,0,6564,100291,3,7315,100467,4,7690,100761,5,8065,100762,1,8065,100762,50,8065,100762,40,8065,100801,0,8065,174510,3,11966,175564,4,13917,176026,1,15866,176026,50,15868,176026,40,15868,176065,0,15868,231568,3,18419,232424,4,19694,232816,1,20969,232816,50,20971,232816,40,20971,232855,0,20971,280407,3,22483,281042,4,23222,281690,5,23972,281691,1,23972,281691,50,23974,281691,40,23974,281730,0,23974,300961,3,24727,301445,4,25100,302108,5,25475,302109,1,25475,302109,50,25475,302109,40,25475,302148,0,25475,331173,3,26677,331881,4,27276,332577,5,27876,332578,1,27876,332578,50,27877,332578,40,27877,332617,0,27877,351003,3,28628,351590,4,29003,351947,1,29378,351947,50,29378,351947,40,29378,351947,40,29378,351982,0,29378,352060,50,29379,352060,30,29379,352060,40,29379,352095,0,29379,352196,50,29379,352196,30,29379,352196,40,29379,352231,0,29384,352309,50,29384,352309,30,29384,352309,40,29385,352344,0,29385,352450,50,29385,352485,0,29385,352642,50,29388,352677,0,29393,352842,50,29397,352877,0,29397,353050,50,29403,353085,0,29407,353264,50,29416,353299,0,29416,353486,50,29431,353521,0,29431,353716,50,29461,353751,0,29465,353956,50,29524,353991,0,29524,354206,50,29642,354206,40,29642,354241,0,29642)
%
%
% START OF PROOF
% 354152 [?] ?
% 354208 [] equal(multiply(identity,X),X).
% 354209 [] equal(multiply(inverse(X),X),identity).
% 354210 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 354211 [] -equal(multiply(sk_c7,sk_c6),sk_c8).
% 354236 [?] ?
% 354237 [?] ?
% 354238 [?] ?
% 354279 [input:354236,cut:354211] equal(inverse(sk_c4),sk_c8).
% 354280 [para:354279.1.1,354209.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 354294 [input:354237,cut:354211] equal(multiply(sk_c4,sk_c8),sk_c5).
% 354295 [input:354238,cut:354211] equal(multiply(sk_c8,sk_c5),sk_c7).
% 354316 [para:354280.1.1,354210.1.1.1,demod:354208] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 354347 [para:354294.1.1,354316.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 354352 [para:354347.1.2,354295.1.1] equal(sk_c8,sk_c7).
% 354354 [para:354352.1.2,354211.1.1.1,cut:354152] 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 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(inverse(sk_c8),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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,0,74,0,0,856,50,6,895,0,6,2444,50,24,2483,0,25,4701,50,54,4740,0,54,7247,50,80,7286,0,80,10177,50,116,10216,0,116,13397,50,165,13436,0,165,17003,50,238,17042,0,238,20995,50,358,21034,0,358,25468,50,568,25507,0,568,30423,50,859,30423,40,859,30462,0,859,42435,3,1160,43053,4,1310,43726,5,1460,43727,1,1460,43727,50,1460,43727,40,1460,43766,0,1461,43985,3,1771,43993,4,1914,44001,5,2062,44001,1,2062,44001,50,2062,44001,40,2062,44040,0,2062,67244,3,3563,68357,4,4313,69113,1,5063,69113,50,5063,69113,40,5063,69152,0,5063,81414,3,5819,82284,4,6189,83162,5,6564,83163,1,6564,83163,50,6564,83163,40,6564,83202,0,6564,100291,3,7315,100467,4,7690,100761,5,8065,100762,1,8065,100762,50,8065,100762,40,8065,100801,0,8065,174510,3,11966,175564,4,13917,176026,1,15866,176026,50,15868,176026,40,15868,176065,0,15868,231568,3,18419,232424,4,19694,232816,1,20969,232816,50,20971,232816,40,20971,232855,0,20971,280407,3,22483,281042,4,23222,281690,5,23972,281691,1,23972,281691,50,23974,281691,40,23974,281730,0,23974,300961,3,24727,301445,4,25100,302108,5,25475,302109,1,25475,302109,50,25475,302109,40,25475,302148,0,25475,331173,3,26677,331881,4,27276,332577,5,27876,332578,1,27876,332578,50,27877,332578,40,27877,332617,0,27877,351003,3,28628,351590,4,29003,351947,1,29378,351947,50,29378,351947,40,29378,351947,40,29378,351982,0,29378,352060,50,29379,352060,30,29379,352060,40,29379,352095,0,29379,352196,50,29379,352196,30,29379,352196,40,29379,352231,0,29384,352309,50,29384,352309,30,29384,352309,40,29385,352344,0,29385,352450,50,29385,352485,0,29385,352642,50,29388,352677,0,29393,352842,50,29397,352877,0,29397,353050,50,29403,353085,0,29407,353264,50,29416,353299,0,29416,353486,50,29431,353521,0,29431,353716,50,29461,353751,0,29465,353956,50,29524,353991,0,29524,354206,50,29642,354206,40,29642,354241,0,29642,354353,50,29642,354353,30,29642,354353,40,29642,354388,0,29642,354494,50,29643,354529,0,29647,354686,50,29650,354721,0,29650,354886,50,29653,354921,0,29653,355094,50,29659,355129,0,29664,355308,50,29673,355343,0,29673,355530,50,29689,355565,0,29693,355760,50,29723,355795,0,29723,356000,50,29787,356035,0,29787,356250,50,29905,356250,40,29905,356285,0,29905)
%
%
% START OF PROOF
% 356144 [?] ?
% 356252 [] equal(multiply(identity,X),X).
% 356253 [] equal(multiply(inverse(X),X),identity).
% 356254 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 356255 [] -equal(inverse(sk_c8),sk_c6).
% 356277 [?] ?
% 356278 [?] ?
% 356279 [?] ?
% 356296 [input:356277,cut:356255] equal(inverse(sk_c3),sk_c8).
% 356297 [para:356296.1.1,356253.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 356311 [input:356278,cut:356255] equal(multiply(sk_c3,sk_c8),sk_c7).
% 356312 [input:356279,cut:356255] equal(multiply(sk_c8,sk_c7),sk_c6).
% 356332 [para:356297.1.1,356254.1.1.1,demod:356252] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 356377 [para:356311.1.1,356332.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 356380 [para:356377.1.2,356312.1.1] equal(sk_c8,sk_c6).
% 356382 [para:356380.1.2,356255.1.2,cut:356144] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,0,74,0,0,856,50,6,895,0,6,2444,50,24,2483,0,25,4701,50,54,4740,0,54,7247,50,80,7286,0,80,10177,50,116,10216,0,116,13397,50,165,13436,0,165,17003,50,238,17042,0,238,20995,50,358,21034,0,358,25468,50,568,25507,0,568,30423,50,859,30423,40,859,30462,0,859,42435,3,1160,43053,4,1310,43726,5,1460,43727,1,1460,43727,50,1460,43727,40,1460,43766,0,1461,43985,3,1771,43993,4,1914,44001,5,2062,44001,1,2062,44001,50,2062,44001,40,2062,44040,0,2062,67244,3,3563,68357,4,4313,69113,1,5063,69113,50,5063,69113,40,5063,69152,0,5063,81414,3,5819,82284,4,6189,83162,5,6564,83163,1,6564,83163,50,6564,83163,40,6564,83202,0,6564,100291,3,7315,100467,4,7690,100761,5,8065,100762,1,8065,100762,50,8065,100762,40,8065,100801,0,8065,174510,3,11966,175564,4,13917,176026,1,15866,176026,50,15868,176026,40,15868,176065,0,15868,231568,3,18419,232424,4,19694,232816,1,20969,232816,50,20971,232816,40,20971,232855,0,20971,280407,3,22483,281042,4,23222,281690,5,23972,281691,1,23972,281691,50,23974,281691,40,23974,281730,0,23974,300961,3,24727,301445,4,25100,302108,5,25475,302109,1,25475,302109,50,25475,302109,40,25475,302148,0,25475,331173,3,26677,331881,4,27276,332577,5,27876,332578,1,27876,332578,50,27877,332578,40,27877,332617,0,27877,351003,3,28628,351590,4,29003,351947,1,29378,351947,50,29378,351947,40,29378,351947,40,29378,351982,0,29378,352060,50,29379,352060,30,29379,352060,40,29379,352095,0,29379,352196,50,29379,352196,30,29379,352196,40,29379,352231,0,29384,352309,50,29384,352309,30,29384,352309,40,29385,352344,0,29385,352450,50,29385,352485,0,29385,352642,50,29388,352677,0,29393,352842,50,29397,352877,0,29397,353050,50,29403,353085,0,29407,353264,50,29416,353299,0,29416,353486,50,29431,353521,0,29431,353716,50,29461,353751,0,29465,353956,50,29524,353991,0,29524,354206,50,29642,354206,40,29642,354241,0,29642,354353,50,29642,354353,30,29642,354353,40,29642,354388,0,29642,354494,50,29643,354529,0,29647,354686,50,29650,354721,0,29650,354886,50,29653,354921,0,29653,355094,50,29659,355129,0,29664,355308,50,29673,355343,0,29673,355530,50,29689,355565,0,29693,355760,50,29723,355795,0,29723,356000,50,29787,356035,0,29787,356250,50,29905,356250,40,29905,356285,0,29905,356381,50,29905,356381,30,29905,356381,40,29905,356416,0,29905,356505,50,29906,356540,0,29910,356678,50,29913,356713,0,29913,356859,50,29916,356894,0,29916,357047,50,29922,357082,0,29926,357242,50,29934,357277,0,29934,357445,50,29949,357480,0,29954,357657,50,29984,357692,0,29984,357879,50,30048,357914,0,30048,358112,50,30172,358112,40,30172,358147,0,30172)
%
%
% START OF PROOF
% 358038 [?] ?
% 358114 [] equal(multiply(identity,X),X).
% 358115 [] equal(multiply(inverse(X),X),identity).
% 358116 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 358117 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 358123 [?] ?
% 358129 [?] ?
% 358135 [?] ?
% 358141 [?] ?
% 358147 [?] ?
% 358166 [input:358123,cut:358117] equal(inverse(sk_c1),sk_c8).
% 358167 [para:358166.1.1,358115.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 358183 [input:358141,cut:358117] equal(inverse(sk_c8),sk_c6).
% 358184 [para:358183.1.1,358115.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 358195 [input:358129,cut:358117] equal(multiply(sk_c1,sk_c8),sk_c2).
% 358199 [input:358135,cut:358117] equal(multiply(sk_c8,sk_c2),sk_c7).
% 358203 [input:358147,cut:358117] equal(multiply(sk_c7,sk_c6),sk_c8).
% 358208 [para:358167.1.1,358116.1.1.1,demod:358114] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 358218 [para:358184.1.1,358116.1.1.1,demod:358114] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 358249 [para:358195.1.1,358208.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c2)).
% 358255 [para:358249.1.2,358199.1.1] equal(sk_c8,sk_c7).
% 358263 [para:358255.1.2,358203.1.1.1] equal(multiply(sk_c8,sk_c6),sk_c8).
% 358283 [para:358263.1.1,358218.1.2.2,demod:358184] equal(sk_c6,identity).
% 358292 [para:358283.1.1,358184.1.1.1,demod:358114] equal(sk_c8,identity).
% 358301 [para:358292.1.1,358117.1.1.1,demod:358114,cut:358038] 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: 36957
% derived clauses: 5612295
% kept clauses: 288790
% kept size sum: 34128
% kept mid-nuclei: 19885
% kept new demods: 4928
% forw unit-subs: 1462346
% forw double-subs: 3521482
% forw overdouble-subs: 267808
% backward subs: 25994
% fast unit cutoff: 15259
% full unit cutoff: 0
% dbl unit cutoff: 15252
% real runtime : 302.90
% process. runtime: 301.72
% specific non-discr-tree subsumption statistics:
% tried: 22985709
% length fails: 2147688
% strength fails: 5300296
% predlist fails: 1463875
% aux str. fails: 4536952
% by-lit fails: 4225476
% full subs tried: 1026471
% full subs fail: 936955
%
% ; 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/GRP359-1+eq_r.in")
%
%------------------------------------------------------------------------------