TSTP Solution File: GRP348-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP348-1 : 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 298.5s
% Output : Assurance 298.5s
% 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/GRP348-1+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(sk_c5,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(Y),sk_c5) | -equal(multiply(Y,sk_c4),sk_c5) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c4,sk_c5),sk_c6) | -equal(inverse(Z),sk_c6) | -equal(multiply(Z,sk_c5),sk_c6).
% was split for some strategies as:
% -equal(inverse(Z),sk_c6) | -equal(multiply(Z,sk_c5),sk_c6).
% -equal(inverse(Y),sk_c5) | -equal(multiply(Y,sk_c4),sk_c5).
% -equal(inverse(X),sk_c6) | -equal(multiply(X,sk_c5),sk_c6).
% -equal(multiply(sk_c5,sk_c6),sk_c4).
% -equal(inverse(sk_c4),sk_c5).
% -equal(multiply(sk_c4,sk_c5),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_c5,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(Y),sk_c5) | -equal(multiply(Y,sk_c4),sk_c5) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c4,sk_c5),sk_c6) | -equal(inverse(Z),sk_c6) | -equal(multiply(Z,sk_c5),sk_c6).
% Split part used next: -equal(inverse(Z),sk_c6) | -equal(multiply(Z,sk_c5),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(25,40,1,54,0,1,395,50,3,424,0,3,780,50,5,809,0,5,1176,50,9,1205,0,9,1579,50,13,1608,0,13,1989,50,19,2018,0,19,2407,50,32,2436,0,32,2834,50,58,2863,0,58,3271,50,115,3300,0,115,3719,50,243,3748,0,243,4179,50,456,4208,0,456,4652,50,871,4652,40,871,4681,0,871,15997,3,1172,16739,4,1322,17409,1,1472,17409,50,1472,17409,40,1472,17438,0,1472,17590,3,1784,17598,4,1929,17606,5,2073,17606,1,2073,17606,50,2073,17606,40,2073,17635,0,2073,38789,3,3574,39964,4,4324,41057,1,5074,41057,50,5074,41057,40,5074,41086,0,5074,54611,3,5826,55504,4,6200,56400,5,6575,56401,1,6575,56401,50,6575,56401,40,6575,56430,0,6575,68913,3,7326,70227,4,7701,70936,1,8076,70936,50,8076,70936,40,8076,70965,0,8076,141128,3,11993,142010,4,13927,143074,5,15877,143075,1,15877,143075,50,15879,143075,40,15879,143104,0,15879,203608,3,18431,204269,4,19705,205044,1,20981,205044,50,20983,205044,40,20983,205073,0,20983,239579,3,22485,240655,4,23234,241475,1,23984,241475,50,23986,241475,40,23986,241504,0,23986,261648,3,24737,262436,4,25112,263002,1,25487,263002,50,25487,263002,40,25487,263031,0,25487,293704,3,26688,294485,4,27288,295129,5,27888,295130,1,27888,295130,50,27889,295130,40,27889,295159,0,27889,316243,3,28640,317023,4,29015,317567,5,29390,317568,1,29390,317568,50,29391,317568,40,29391,317568,40,29391,317593,0,29391)
%
%
% START OF PROOF
% 317569 [] equal(X,X).
% 317573 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 317582 [] equal(multiply(sk_c1,sk_c5),sk_c6) | equal(multiply(sk_c3,sk_c5),sk_c6).
% 317583 [?] ?
% 317586 [?] ?
% 317587 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 317601 [hyper:317573,317587,binarycut:317583] equal(inverse(sk_c3),sk_c6).
% 317603 [hyper:317573,317587,binarycut:317586] equal(inverse(sk_c1),sk_c6).
% 317616 [hyper:317573,317582,demod:317603,cut:317569] equal(multiply(sk_c3,sk_c5),sk_c6).
% 317618 [hyper:317573,317616,demod:317601,cut:317569] 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(sk_c5,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(Y),sk_c5) | -equal(multiply(Y,sk_c4),sk_c5) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c4,sk_c5),sk_c6) | -equal(inverse(Z),sk_c6) | -equal(multiply(Z,sk_c5),sk_c6).
% Split part used next: -equal(inverse(Y),sk_c5) | -equal(multiply(Y,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
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(25,40,1,54,0,1,395,50,3,424,0,3,780,50,5,809,0,5,1176,50,9,1205,0,9,1579,50,13,1608,0,13,1989,50,19,2018,0,19,2407,50,32,2436,0,32,2834,50,58,2863,0,58,3271,50,115,3300,0,115,3719,50,243,3748,0,243,4179,50,456,4208,0,456,4652,50,871,4652,40,871,4681,0,871,15997,3,1172,16739,4,1322,17409,1,1472,17409,50,1472,17409,40,1472,17438,0,1472,17590,3,1784,17598,4,1929,17606,5,2073,17606,1,2073,17606,50,2073,17606,40,2073,17635,0,2073,38789,3,3574,39964,4,4324,41057,1,5074,41057,50,5074,41057,40,5074,41086,0,5074,54611,3,5826,55504,4,6200,56400,5,6575,56401,1,6575,56401,50,6575,56401,40,6575,56430,0,6575,68913,3,7326,70227,4,7701,70936,1,8076,70936,50,8076,70936,40,8076,70965,0,8076,141128,3,11993,142010,4,13927,143074,5,15877,143075,1,15877,143075,50,15879,143075,40,15879,143104,0,15879,203608,3,18431,204269,4,19705,205044,1,20981,205044,50,20983,205044,40,20983,205073,0,20983,239579,3,22485,240655,4,23234,241475,1,23984,241475,50,23986,241475,40,23986,241504,0,23986,261648,3,24737,262436,4,25112,263002,1,25487,263002,50,25487,263002,40,25487,263031,0,25487,293704,3,26688,294485,4,27288,295129,5,27888,295130,1,27888,295130,50,27889,295130,40,27889,295159,0,27889,316243,3,28640,317023,4,29015,317567,5,29390,317568,1,29390,317568,50,29391,317568,40,29391,317568,40,29391,317593,0,29391,317617,50,29391,317617,30,29391,317617,40,29391,317642,0,29391,317696,50,29391,317721,0,29395,317841,50,29396,317866,0,29396)
%
%
% START OF PROOF
% 317833 [?] ?
% 317843 [] equal(multiply(identity,X),X).
% 317844 [] equal(multiply(inverse(X),X),identity).
% 317845 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 317846 [] -equal(multiply(X,sk_c4),sk_c5) | -equal(inverse(X),sk_c5).
% 317847 [?] ?
% 317848 [?] ?
% 317849 [?] ?
% 317850 [?] ?
% 317851 [] equal(multiply(sk_c3,sk_c5),sk_c6) | equal(inverse(sk_c2),sk_c5).
% 317852 [] equal(inverse(sk_c2),sk_c5) | equal(inverse(sk_c3),sk_c6).
% 317853 [] equal(multiply(sk_c4,sk_c5),sk_c6) | equal(inverse(sk_c2),sk_c5).
% 317854 [] equal(inverse(sk_c2),sk_c5) | equal(inverse(sk_c4),sk_c5).
% 317869 [hyper:317846,317852,binarycut:317848] equal(inverse(sk_c3),sk_c6).
% 317870 [para:317869.1.1,317844.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 317874 [hyper:317846,317854,binarycut:317850] equal(inverse(sk_c4),sk_c5).
% 317878 [para:317874.1.1,317844.1.1.1] equal(multiply(sk_c5,sk_c4),identity).
% 317882 [hyper:317846,317851,binarycut:317847] equal(multiply(sk_c3,sk_c5),sk_c6).
% 317885 [hyper:317846,317853,binarycut:317849] equal(multiply(sk_c4,sk_c5),sk_c6).
% 317886 [para:317844.1.1,317845.1.1.1,demod:317843] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 317887 [para:317870.1.1,317845.1.1.1,demod:317843] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 317888 [para:317878.1.1,317845.1.1.1,demod:317843] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 317889 [para:317882.1.1,317845.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c3,multiply(sk_c5,X))).
% 317891 [para:317882.1.1,317887.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 317893 [para:317885.1.1,317888.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c6)).
% 317896 [para:317844.1.1,317886.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 317897 [para:317870.1.1,317886.1.2.2] equal(sk_c3,multiply(inverse(sk_c6),identity)).
% 317898 [para:317878.1.1,317886.1.2.2] equal(sk_c4,multiply(inverse(sk_c5),identity)).
% 317899 [para:317845.1.1,317886.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 317900 [para:317887.1.2,317886.1.2.2] equal(multiply(sk_c3,X),multiply(inverse(sk_c6),X)).
% 317902 [para:317886.1.2,317886.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 317904 [para:317888.1.2,317889.1.2.2] equal(multiply(sk_c6,multiply(sk_c4,X)),multiply(sk_c3,X)).
% 317905 [para:317893.1.2,317889.1.2.2,demod:317882,317891] equal(sk_c5,sk_c6).
% 317909 [para:317905.1.1,317888.1.2.1,demod:317904] equal(X,multiply(sk_c3,X)).
% 317910 [para:317905.1.1,317898.1.2.1.1,demod:317897] equal(sk_c4,sk_c3).
% 317952 [para:317900.1.2,317899.1.2.2.2,demod:317909] equal(X,multiply(inverse(multiply(Y,inverse(sk_c6))),multiply(Y,X))).
% 317954 [para:317902.1.2,317844.1.1] equal(multiply(X,inverse(X)),identity).
% 317956 [para:317902.1.2,317896.1.2] equal(X,multiply(X,identity)).
% 317957 [para:317956.1.2,317897.1.2] equal(sk_c3,inverse(sk_c6)).
% 317958 [para:317956.1.2,317898.1.2] equal(sk_c4,inverse(sk_c5)).
% 317960 [para:317956.1.2,317896.1.2] equal(X,inverse(inverse(X))).
% 317980 [para:317954.1.1,317952.1.2.2,demod:317956,317957] equal(inverse(X),inverse(multiply(X,sk_c3))).
% 317988 [para:317980.1.2,317896.1.2.1.1,demod:317956,317960] equal(multiply(X,sk_c3),X).
% 317989 [para:317910.1.2,317988.1.1.2] equal(multiply(X,sk_c4),X).
% 317990 [hyper:317846,317989,demod:317958,cut:317833] 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 5
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(Y),sk_c5) | -equal(multiply(Y,sk_c4),sk_c5) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c4,sk_c5),sk_c6) | -equal(inverse(Z),sk_c6) | -equal(multiply(Z,sk_c5),sk_c6).
% Split part used next: -equal(inverse(X),sk_c6) | -equal(multiply(X,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
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(25,40,1,54,0,1,395,50,3,424,0,3,780,50,5,809,0,5,1176,50,9,1205,0,9,1579,50,13,1608,0,13,1989,50,19,2018,0,19,2407,50,32,2436,0,32,2834,50,58,2863,0,58,3271,50,115,3300,0,115,3719,50,243,3748,0,243,4179,50,456,4208,0,456,4652,50,871,4652,40,871,4681,0,871,15997,3,1172,16739,4,1322,17409,1,1472,17409,50,1472,17409,40,1472,17438,0,1472,17590,3,1784,17598,4,1929,17606,5,2073,17606,1,2073,17606,50,2073,17606,40,2073,17635,0,2073,38789,3,3574,39964,4,4324,41057,1,5074,41057,50,5074,41057,40,5074,41086,0,5074,54611,3,5826,55504,4,6200,56400,5,6575,56401,1,6575,56401,50,6575,56401,40,6575,56430,0,6575,68913,3,7326,70227,4,7701,70936,1,8076,70936,50,8076,70936,40,8076,70965,0,8076,141128,3,11993,142010,4,13927,143074,5,15877,143075,1,15877,143075,50,15879,143075,40,15879,143104,0,15879,203608,3,18431,204269,4,19705,205044,1,20981,205044,50,20983,205044,40,20983,205073,0,20983,239579,3,22485,240655,4,23234,241475,1,23984,241475,50,23986,241475,40,23986,241504,0,23986,261648,3,24737,262436,4,25112,263002,1,25487,263002,50,25487,263002,40,25487,263031,0,25487,293704,3,26688,294485,4,27288,295129,5,27888,295130,1,27888,295130,50,27889,295130,40,27889,295159,0,27889,316243,3,28640,317023,4,29015,317567,5,29390,317568,1,29390,317568,50,29391,317568,40,29391,317568,40,29391,317593,0,29391,317617,50,29391,317617,30,29391,317617,40,29391,317642,0,29391,317696,50,29391,317721,0,29395,317841,50,29396,317866,0,29396,317989,50,29397,317989,30,29397,317989,40,29397,318014,0,29397)
%
%
% START OF PROOF
% 317990 [] equal(X,X).
% 317994 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 318003 [] equal(multiply(sk_c1,sk_c5),sk_c6) | equal(multiply(sk_c3,sk_c5),sk_c6).
% 318004 [?] ?
% 318007 [?] ?
% 318008 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 318022 [hyper:317994,318008,binarycut:318004] equal(inverse(sk_c3),sk_c6).
% 318024 [hyper:317994,318008,binarycut:318007] equal(inverse(sk_c1),sk_c6).
% 318037 [hyper:317994,318003,demod:318024,cut:317990] equal(multiply(sk_c3,sk_c5),sk_c6).
% 318039 [hyper:317994,318037,demod:318022,cut:317990] 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 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(Y),sk_c5) | -equal(multiply(Y,sk_c4),sk_c5) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c4,sk_c5),sk_c6) | -equal(inverse(Z),sk_c6) | -equal(multiply(Z,sk_c5),sk_c6).
% 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(25,40,1,54,0,1,395,50,3,424,0,3,780,50,5,809,0,5,1176,50,9,1205,0,9,1579,50,13,1608,0,13,1989,50,19,2018,0,19,2407,50,32,2436,0,32,2834,50,58,2863,0,58,3271,50,115,3300,0,115,3719,50,243,3748,0,243,4179,50,456,4208,0,456,4652,50,871,4652,40,871,4681,0,871,15997,3,1172,16739,4,1322,17409,1,1472,17409,50,1472,17409,40,1472,17438,0,1472,17590,3,1784,17598,4,1929,17606,5,2073,17606,1,2073,17606,50,2073,17606,40,2073,17635,0,2073,38789,3,3574,39964,4,4324,41057,1,5074,41057,50,5074,41057,40,5074,41086,0,5074,54611,3,5826,55504,4,6200,56400,5,6575,56401,1,6575,56401,50,6575,56401,40,6575,56430,0,6575,68913,3,7326,70227,4,7701,70936,1,8076,70936,50,8076,70936,40,8076,70965,0,8076,141128,3,11993,142010,4,13927,143074,5,15877,143075,1,15877,143075,50,15879,143075,40,15879,143104,0,15879,203608,3,18431,204269,4,19705,205044,1,20981,205044,50,20983,205044,40,20983,205073,0,20983,239579,3,22485,240655,4,23234,241475,1,23984,241475,50,23986,241475,40,23986,241504,0,23986,261648,3,24737,262436,4,25112,263002,1,25487,263002,50,25487,263002,40,25487,263031,0,25487,293704,3,26688,294485,4,27288,295129,5,27888,295130,1,27888,295130,50,27889,295130,40,27889,295159,0,27889,316243,3,28640,317023,4,29015,317567,5,29390,317568,1,29390,317568,50,29391,317568,40,29391,317568,40,29391,317593,0,29391,317617,50,29391,317617,30,29391,317617,40,29391,317642,0,29391,317696,50,29391,317721,0,29395,317841,50,29396,317866,0,29396,317989,50,29397,317989,30,29397,317989,40,29397,318014,0,29397,318038,50,29397,318038,30,29397,318038,40,29397,318063,0,29401,318128,50,29401,318153,0,29401,318262,50,29403,318287,0,29407,318406,50,29410,318431,0,29410,318558,50,29414,318583,0,29414,318716,50,29421,318741,0,29425,318882,50,29438,318907,0,29438,319056,50,29463,319081,0,29467,319240,50,29519,319265,0,29519,319434,50,29625,319434,40,29625,319459,0,29625)
%
%
% START OF PROOF
% 319362 [?] ?
% 319436 [] equal(multiply(identity,X),X).
% 319437 [] equal(multiply(inverse(X),X),identity).
% 319438 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 319439 [] -equal(multiply(sk_c5,sk_c6),sk_c4).
% 319458 [?] ?
% 319459 [?] ?
% 319493 [input:319459,cut:319439] equal(inverse(sk_c4),sk_c5).
% 319494 [para:319493.1.1,319437.1.1.1] equal(multiply(sk_c5,sk_c4),identity).
% 319501 [input:319458,cut:319439] equal(multiply(sk_c4,sk_c5),sk_c6).
% 319518 [para:319494.1.1,319438.1.1.1,demod:319436] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 319537 [para:319501.1.1,319518.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c6)).
% 319538 [para:319537.1.2,319439.1.1,cut:319362] 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_c5,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(Y),sk_c5) | -equal(multiply(Y,sk_c4),sk_c5) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c4,sk_c5),sk_c6) | -equal(inverse(Z),sk_c6) | -equal(multiply(Z,sk_c5),sk_c6).
% 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(25,40,1,54,0,1,395,50,3,424,0,3,780,50,5,809,0,5,1176,50,9,1205,0,9,1579,50,13,1608,0,13,1989,50,19,2018,0,19,2407,50,32,2436,0,32,2834,50,58,2863,0,58,3271,50,115,3300,0,115,3719,50,243,3748,0,243,4179,50,456,4208,0,456,4652,50,871,4652,40,871,4681,0,871,15997,3,1172,16739,4,1322,17409,1,1472,17409,50,1472,17409,40,1472,17438,0,1472,17590,3,1784,17598,4,1929,17606,5,2073,17606,1,2073,17606,50,2073,17606,40,2073,17635,0,2073,38789,3,3574,39964,4,4324,41057,1,5074,41057,50,5074,41057,40,5074,41086,0,5074,54611,3,5826,55504,4,6200,56400,5,6575,56401,1,6575,56401,50,6575,56401,40,6575,56430,0,6575,68913,3,7326,70227,4,7701,70936,1,8076,70936,50,8076,70936,40,8076,70965,0,8076,141128,3,11993,142010,4,13927,143074,5,15877,143075,1,15877,143075,50,15879,143075,40,15879,143104,0,15879,203608,3,18431,204269,4,19705,205044,1,20981,205044,50,20983,205044,40,20983,205073,0,20983,239579,3,22485,240655,4,23234,241475,1,23984,241475,50,23986,241475,40,23986,241504,0,23986,261648,3,24737,262436,4,25112,263002,1,25487,263002,50,25487,263002,40,25487,263031,0,25487,293704,3,26688,294485,4,27288,295129,5,27888,295130,1,27888,295130,50,27889,295130,40,27889,295159,0,27889,316243,3,28640,317023,4,29015,317567,5,29390,317568,1,29390,317568,50,29391,317568,40,29391,317568,40,29391,317593,0,29391,317617,50,29391,317617,30,29391,317617,40,29391,317642,0,29391,317696,50,29391,317721,0,29395,317841,50,29396,317866,0,29396,317989,50,29397,317989,30,29397,317989,40,29397,318014,0,29397,318038,50,29397,318038,30,29397,318038,40,29397,318063,0,29401,318128,50,29401,318153,0,29401,318262,50,29403,318287,0,29407,318406,50,29410,318431,0,29410,318558,50,29414,318583,0,29414,318716,50,29421,318741,0,29425,318882,50,29438,318907,0,29438,319056,50,29463,319081,0,29467,319240,50,29519,319265,0,29519,319434,50,29625,319434,40,29625,319459,0,29625,319537,50,29625,319537,30,29625,319537,40,29625,319562,0,29625)
%
%
% START OF PROOF
% 319539 [] equal(multiply(identity,X),X).
% 319540 [] equal(multiply(inverse(X),X),identity).
% 319541 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 319542 [] -equal(inverse(sk_c4),sk_c5).
% 319546 [?] ?
% 319550 [?] ?
% 319554 [?] ?
% 319558 [?] ?
% 319562 [?] ?
% 319565 [input:319550,cut:319542] equal(inverse(sk_c2),sk_c5).
% 319566 [para:319565.1.1,319540.1.1.1] equal(multiply(sk_c5,sk_c2),identity).
% 319568 [input:319558,cut:319542] equal(inverse(sk_c1),sk_c6).
% 319569 [para:319568.1.1,319540.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 319571 [input:319546,cut:319542] equal(multiply(sk_c2,sk_c4),sk_c5).
% 319575 [input:319554,cut:319542] equal(multiply(sk_c1,sk_c5),sk_c6).
% 319580 [input:319562,cut:319542] equal(multiply(sk_c5,sk_c6),sk_c4).
% 319585 [para:319540.1.1,319541.1.1.1,demod:319539] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 319586 [para:319566.1.1,319541.1.1.1,demod:319539] equal(X,multiply(sk_c5,multiply(sk_c2,X))).
% 319587 [para:319569.1.1,319541.1.1.1,demod:319539] equal(X,multiply(sk_c6,multiply(sk_c1,X))).
% 319589 [para:319575.1.1,319541.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c1,multiply(sk_c5,X))).
% 319590 [para:319580.1.1,319541.1.1.1] equal(multiply(sk_c4,X),multiply(sk_c5,multiply(sk_c6,X))).
% 319591 [para:319571.1.1,319586.1.2.2] equal(sk_c4,multiply(sk_c5,sk_c5)).
% 319594 [para:319566.1.1,319585.1.2.2] equal(sk_c2,multiply(inverse(sk_c5),identity)).
% 319595 [para:319569.1.1,319585.1.2.2] equal(sk_c1,multiply(inverse(sk_c6),identity)).
% 319598 [para:319580.1.1,319585.1.2.2] equal(sk_c6,multiply(inverse(sk_c5),sk_c4)).
% 319600 [para:319591.1.2,319585.1.2.2,demod:319598] equal(sk_c5,sk_c6).
% 319601 [para:319600.1.1,319566.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 319603 [para:319600.1.1,319580.1.1.1] equal(multiply(sk_c6,sk_c6),sk_c4).
% 319604 [para:319600.1.1,319586.1.2.1] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 319607 [para:319601.1.1,319585.1.2.2,demod:319595] equal(sk_c2,sk_c1).
% 319608 [para:319607.1.1,319565.1.1.1] equal(inverse(sk_c1),sk_c5).
% 319613 [para:319575.1.1,319587.1.2.2,demod:319603] equal(sk_c5,sk_c4).
% 319620 [para:319613.1.1,319600.1.1] equal(sk_c4,sk_c6).
% 319629 [para:319586.1.2,319589.1.2.2,demod:319604] equal(X,multiply(sk_c1,X)).
% 319630 [para:319589.1.2,319585.1.2.2,demod:319590,319608] equal(multiply(sk_c5,X),multiply(sk_c4,X)).
% 319633 [para:319629.1.2,319585.1.2.2,demod:319630,319608] equal(X,multiply(sk_c4,X)).
% 319634 [para:319633.1.2,319585.1.2.2] equal(X,multiply(inverse(sk_c4),X)).
% 319642 [para:319634.1.2,319540.1.1] equal(sk_c4,identity).
% 319648 [para:319642.1.1,319598.1.2.2,demod:319594] equal(sk_c6,sk_c2).
% 319649 [para:319648.1.1,319620.1.2] equal(sk_c4,sk_c2).
% 319653 [para:319649.1.2,319565.1.1.1,cut:319542] 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 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c5,sk_c6),sk_c4) | -equal(inverse(X),sk_c6) | -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(Y),sk_c5) | -equal(multiply(Y,sk_c4),sk_c5) | -equal(inverse(sk_c4),sk_c5) | -equal(multiply(sk_c4,sk_c5),sk_c6) | -equal(inverse(Z),sk_c6) | -equal(multiply(Z,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c4,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(25,40,1,54,0,1,395,50,3,424,0,3,780,50,5,809,0,5,1176,50,9,1205,0,9,1579,50,13,1608,0,13,1989,50,19,2018,0,19,2407,50,32,2436,0,32,2834,50,58,2863,0,58,3271,50,115,3300,0,115,3719,50,243,3748,0,243,4179,50,456,4208,0,456,4652,50,871,4652,40,871,4681,0,871,15997,3,1172,16739,4,1322,17409,1,1472,17409,50,1472,17409,40,1472,17438,0,1472,17590,3,1784,17598,4,1929,17606,5,2073,17606,1,2073,17606,50,2073,17606,40,2073,17635,0,2073,38789,3,3574,39964,4,4324,41057,1,5074,41057,50,5074,41057,40,5074,41086,0,5074,54611,3,5826,55504,4,6200,56400,5,6575,56401,1,6575,56401,50,6575,56401,40,6575,56430,0,6575,68913,3,7326,70227,4,7701,70936,1,8076,70936,50,8076,70936,40,8076,70965,0,8076,141128,3,11993,142010,4,13927,143074,5,15877,143075,1,15877,143075,50,15879,143075,40,15879,143104,0,15879,203608,3,18431,204269,4,19705,205044,1,20981,205044,50,20983,205044,40,20983,205073,0,20983,239579,3,22485,240655,4,23234,241475,1,23984,241475,50,23986,241475,40,23986,241504,0,23986,261648,3,24737,262436,4,25112,263002,1,25487,263002,50,25487,263002,40,25487,263031,0,25487,293704,3,26688,294485,4,27288,295129,5,27888,295130,1,27888,295130,50,27889,295130,40,27889,295159,0,27889,316243,3,28640,317023,4,29015,317567,5,29390,317568,1,29390,317568,50,29391,317568,40,29391,317568,40,29391,317593,0,29391,317617,50,29391,317617,30,29391,317617,40,29391,317642,0,29391,317696,50,29391,317721,0,29395,317841,50,29396,317866,0,29396,317989,50,29397,317989,30,29397,317989,40,29397,318014,0,29397,318038,50,29397,318038,30,29397,318038,40,29397,318063,0,29401,318128,50,29401,318153,0,29401,318262,50,29403,318287,0,29407,318406,50,29410,318431,0,29410,318558,50,29414,318583,0,29414,318716,50,29421,318741,0,29425,318882,50,29438,318907,0,29438,319056,50,29463,319081,0,29467,319240,50,29519,319265,0,29519,319434,50,29625,319434,40,29625,319459,0,29625,319537,50,29625,319537,30,29625,319537,40,29625,319562,0,29625,319652,50,29625,319652,30,29625,319652,40,29625,319677,0,29630,319774,50,29630,319799,0,29630,319960,50,29633,319985,0,29633,320163,50,29635,320188,0,29640,320379,50,29644,320404,0,29644,320601,50,29651,320626,0,29656,320831,50,29669,320856,0,29669,321069,50,29695,321094,0,29695,321317,50,29752,321342,0,29752,321575,50,29861,321575,40,29861,321600,0,29862)
%
%
% START OF PROOF
% 321576 [] equal(X,X).
% 321577 [] equal(multiply(identity,X),X).
% 321578 [] equal(multiply(inverse(X),X),identity).
% 321579 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 321580 [] -equal(multiply(sk_c4,sk_c5),sk_c6).
% 321583 [?] ?
% 321587 [?] ?
% 321591 [?] ?
% 321595 [?] ?
% 321599 [?] ?
% 321618 [input:321583,cut:321580] equal(multiply(sk_c2,sk_c4),sk_c5).
% 321621 [input:321587,cut:321580] equal(inverse(sk_c2),sk_c5).
% 321622 [para:321621.1.1,321578.1.1.1] equal(multiply(sk_c5,sk_c2),identity).
% 321630 [input:321595,cut:321580] equal(inverse(sk_c1),sk_c6).
% 321631 [para:321630.1.1,321578.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 321636 [input:321591,cut:321580] equal(multiply(sk_c1,sk_c5),sk_c6).
% 321642 [input:321599,cut:321580] equal(multiply(sk_c5,sk_c6),sk_c4).
% 321644 [para:321578.1.1,321579.1.1.1,demod:321577] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 321651 [para:321622.1.1,321579.1.1.1,demod:321577] equal(X,multiply(sk_c5,multiply(sk_c2,X))).
% 321657 [para:321631.1.1,321579.1.1.1,demod:321577] equal(X,multiply(sk_c6,multiply(sk_c1,X))).
% 321672 [para:321618.1.1,321651.1.2.2] equal(sk_c4,multiply(sk_c5,sk_c5)).
% 321677 [para:321636.1.1,321657.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 321709 [para:321642.1.1,321644.1.2.2] equal(sk_c6,multiply(inverse(sk_c5),sk_c4)).
% 321713 [para:321672.1.2,321644.1.2.2,demod:321709] equal(sk_c5,sk_c6).
% 321733 [para:321713.1.1,321642.1.1.1,demod:321677] equal(sk_c5,sk_c4).
% 321754 [para:321733.1.1,321672.1.2.1] equal(sk_c4,multiply(sk_c4,sk_c5)).
% 321757 [para:321733.1.1,321713.1.1] equal(sk_c4,sk_c6).
% 321759 [para:321757.1.2,321580.1.2,demod:321754,cut:321576] 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: 35828
% derived clauses: 6771439
% kept clauses: 281422
% kept size sum: 960803
% kept mid-nuclei: 2222
% kept new demods: 3678
% forw unit-subs: 2146907
% forw double-subs: 4016538
% forw overdouble-subs: 285009
% backward subs: 10189
% fast unit cutoff: 19063
% full unit cutoff: 0
% dbl unit cutoff: 3944
% real runtime : 300.35
% process. runtime: 298.61
% specific non-discr-tree subsumption statistics:
% tried: 16114936
% length fails: 1462585
% strength fails: 2381856
% predlist fails: 1786959
% aux str. fails: 2724801
% by-lit fails: 2803990
% full subs tried: 1560241
% full subs fail: 1470018
%
% ; 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/GRP348-1+eq_r.in")
%
%------------------------------------------------------------------------------