TSTP Solution File: GRP293-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP293-1 : 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 : art05.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 296.4s
% Output : Assurance 296.4s
% 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/GRP293-1+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 23)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 23)
% (binary-posweight-lex-big-order 30 #f 3 23)
% (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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -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_c7),sk_c8) | -equal(inverse(Z),sk_c7).
% -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(multiply(sk_c8,sk_c7),sk_c6).
% -equal(multiply(sk_c8,sk_c6),sk_c7).
% -equal(multiply(sk_c7,sk_c8),sk_c6).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -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(41,40,0,87,0,0,1083,50,10,1129,0,10,2941,50,34,2987,0,34,5325,50,61,5371,0,61,7923,50,88,7969,0,88,10736,50,122,10782,0,122,13869,50,169,13915,0,169,17323,50,238,17369,0,238,21203,50,350,21249,0,350,25509,50,549,25555,0,549,30347,50,835,30347,40,835,30393,0,835,42389,3,1136,43058,4,1286,43690,5,1436,43691,1,1436,43691,50,1436,43691,40,1436,43737,0,1436,43926,3,1745,43934,4,1894,43942,5,2037,43942,1,2037,43942,50,2037,43942,40,2037,43988,0,2037,72686,3,3546,73317,4,4288,74148,5,5039,74149,1,5039,74149,50,5040,74149,40,5040,74195,0,5040,95083,3,5796,95310,4,6166,95947,5,6541,95948,1,6541,95948,50,6542,95948,40,6542,95994,0,6542,105619,3,7299,106989,4,7668,108906,5,8043,108907,1,8043,108907,50,8043,108907,40,8043,108953,0,8043,177952,3,11945,179104,4,13894,179907,5,15844,179908,1,15844,179908,50,15847,179908,40,15847,179954,0,15847,237740,3,18398,238528,4,19673,239328,5,20948,239329,1,20948,239329,50,20950,239329,40,20950,239375,0,20950,277791,3,22460,278446,4,23201,278793,5,23951,278794,1,23951,278794,50,23952,278794,40,23952,278840,0,23952,295567,3,24764,296217,4,25078,296854,1,25453,296854,50,25453,296854,40,25453,296900,0,25453,327358,3,26654,328112,4,27254,328676,5,27854,328677,1,27854,328677,50,27855,328677,40,27855,328723,0,27855,348087,3,28607,348777,4,28981,349342,1,29356,349342,50,29356,349342,40,29356,349342,40,29356,349383,0,29356)
%
%
% START OF PROOF
% 349343 [] equal(X,X).
% 349347 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 349348 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 349349 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c2),sk_c8).
% 349350 [?] ?
% 349354 [] equal(multiply(sk_c2,sk_c8),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 349355 [] equal(multiply(sk_c2,sk_c8),sk_c6) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 349356 [] equal(multiply(sk_c2,sk_c8),sk_c6) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 349360 [?] ?
% 349361 [?] ?
% 349362 [?] ?
% 349413 [hyper:349347,349349,349348,binarycut:349350] equal(inverse(sk_c2),sk_c8).
% 349425 [hyper:349347,349354,demod:349413,cut:349343,binarycut:349360] equal(inverse(sk_c4),sk_c8).
% 349437 [hyper:349347,349355,demod:349413,cut:349343,binarycut:349361] equal(multiply(sk_c4,sk_c8),sk_c5).
% 349455 [hyper:349347,349356,demod:349413,cut:349343,binarycut:349362] equal(multiply(sk_c8,sk_c5),sk_c7).
% 349464 [hyper:349347,349455,349437,demod:349425,cut:349343] 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 23
% 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -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_c7),sk_c8) | -equal(inverse(Z),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% 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 23
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1083,50,10,1129,0,10,2941,50,34,2987,0,34,5325,50,61,5371,0,61,7923,50,88,7969,0,88,10736,50,122,10782,0,122,13869,50,169,13915,0,169,17323,50,238,17369,0,238,21203,50,350,21249,0,350,25509,50,549,25555,0,549,30347,50,835,30347,40,835,30393,0,835,42389,3,1136,43058,4,1286,43690,5,1436,43691,1,1436,43691,50,1436,43691,40,1436,43737,0,1436,43926,3,1745,43934,4,1894,43942,5,2037,43942,1,2037,43942,50,2037,43942,40,2037,43988,0,2037,72686,3,3546,73317,4,4288,74148,5,5039,74149,1,5039,74149,50,5040,74149,40,5040,74195,0,5040,95083,3,5796,95310,4,6166,95947,5,6541,95948,1,6541,95948,50,6542,95948,40,6542,95994,0,6542,105619,3,7299,106989,4,7668,108906,5,8043,108907,1,8043,108907,50,8043,108907,40,8043,108953,0,8043,177952,3,11945,179104,4,13894,179907,5,15844,179908,1,15844,179908,50,15847,179908,40,15847,179954,0,15847,237740,3,18398,238528,4,19673,239328,5,20948,239329,1,20948,239329,50,20950,239329,40,20950,239375,0,20950,277791,3,22460,278446,4,23201,278793,5,23951,278794,1,23951,278794,50,23952,278794,40,23952,278840,0,23952,295567,3,24764,296217,4,25078,296854,1,25453,296854,50,25453,296854,40,25453,296900,0,25453,327358,3,26654,328112,4,27254,328676,5,27854,328677,1,27854,328677,50,27855,328677,40,27855,328723,0,27855,348087,3,28607,348777,4,28981,349342,1,29356,349342,50,29356,349342,40,29356,349342,40,29356,349383,0,29356,349463,50,29356,349463,30,29356,349463,40,29357,349504,0,29357,349617,50,29357,349658,0,29362)
%
%
% START OF PROOF
% 349619 [] equal(multiply(identity,X),X).
% 349620 [] equal(multiply(inverse(X),X),identity).
% 349621 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 349622 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% 349626 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c3),sk_c7).
% 349627 [?] ?
% 349632 [] equal(multiply(sk_c2,sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 349633 [] equal(multiply(sk_c2,sk_c8),sk_c6) | equal(multiply(sk_c3,sk_c7),sk_c8).
% 349638 [] equal(multiply(sk_c8,sk_c6),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 349639 [] equal(multiply(sk_c8,sk_c6),sk_c7) | equal(multiply(sk_c3,sk_c7),sk_c8).
% 349644 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c7).
% 349645 [?] ?
% 349650 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 349651 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c3,sk_c7),sk_c8).
% 349656 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 349657 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c7),sk_c8).
% 349662 [hyper:349622,349626,binarycut:349627] equal(inverse(sk_c2),sk_c8).
% 349664 [para:349662.1.1,349620.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 349669 [hyper:349622,349644,binarycut:349645] equal(inverse(sk_c1),sk_c8).
% 349670 [para:349669.1.1,349620.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 349690 [hyper:349622,349633,349632] equal(multiply(sk_c2,sk_c8),sk_c6).
% 349695 [hyper:349622,349639,349638] equal(multiply(sk_c8,sk_c6),sk_c7).
% 349700 [hyper:349622,349651,349650] equal(multiply(sk_c1,sk_c8),sk_c7).
% 349705 [hyper:349622,349657,349656] equal(multiply(sk_c8,sk_c7),sk_c6).
% 349706 [para:349620.1.1,349621.1.1.1,demod:349619] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 349707 [para:349664.1.1,349621.1.1.1,demod:349619] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 349708 [para:349670.1.1,349621.1.1.1,demod:349619] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 349709 [para:349690.1.1,349621.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c2,multiply(sk_c8,X))).
% 349713 [para:349690.1.1,349707.1.2.2,demod:349695] equal(sk_c8,sk_c7).
% 349717 [para:349713.1.1,349695.1.1.1] equal(multiply(sk_c7,sk_c6),sk_c7).
% 349718 [para:349713.1.1,349700.1.1.2] equal(multiply(sk_c1,sk_c7),sk_c7).
% 349723 [para:349620.1.1,349706.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 349724 [para:349664.1.1,349706.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 349727 [para:349700.1.1,349706.1.2.2,demod:349705,349669] equal(sk_c8,sk_c6).
% 349728 [para:349621.1.1,349706.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 349729 [para:349705.1.1,349706.1.2.2] equal(sk_c7,multiply(inverse(sk_c8),sk_c6)).
% 349730 [para:349707.1.2,349706.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c8),X)).
% 349732 [para:349706.1.2,349706.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 349743 [para:349708.1.2,349706.1.2.2,demod:349730] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 349744 [para:349727.1.1,349708.1.2.1] equal(X,multiply(sk_c6,multiply(sk_c1,X))).
% 349746 [para:349717.1.1,349706.1.2.2,demod:349620] equal(sk_c6,identity).
% 349756 [para:349707.1.2,349709.1.2.2,demod:349744,349743] equal(X,multiply(sk_c1,X)).
% 349772 [para:349746.1.1,349729.1.2.2,demod:349724] equal(sk_c7,sk_c2).
% 349774 [para:349772.1.1,349718.1.1.2,demod:349756] equal(sk_c2,sk_c7).
% 349791 [para:349732.1.2,349620.1.1] equal(multiply(X,inverse(X)),identity).
% 349793 [para:349732.1.2,349723.1.2] equal(X,multiply(X,identity)).
% 349797 [para:349793.1.2,349724.1.2] equal(sk_c2,inverse(sk_c8)).
% 349798 [para:349793.1.2,349723.1.2] equal(X,inverse(inverse(X))).
% 349801 [para:349791.1.1,349728.1.2.2.2,demod:349793] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 349804 [para:349707.1.2,349801.1.2.1.1,demod:349756,349743] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 349813 [para:349804.1.2,349732.1.2,demod:349798] equal(multiply(X,sk_c8),X).
% 349816 [para:349713.1.1,349813.1.1.2] equal(multiply(X,sk_c7),X).
% 349820 [hyper:349622,349816,demod:349797,cut:349774] 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 23
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Y,sk_c8),sk_c6) | -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 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1083,50,10,1129,0,10,2941,50,34,2987,0,34,5325,50,61,5371,0,61,7923,50,88,7969,0,88,10736,50,122,10782,0,122,13869,50,169,13915,0,169,17323,50,238,17369,0,238,21203,50,350,21249,0,350,25509,50,549,25555,0,549,30347,50,835,30347,40,835,30393,0,835,42389,3,1136,43058,4,1286,43690,5,1436,43691,1,1436,43691,50,1436,43691,40,1436,43737,0,1436,43926,3,1745,43934,4,1894,43942,5,2037,43942,1,2037,43942,50,2037,43942,40,2037,43988,0,2037,72686,3,3546,73317,4,4288,74148,5,5039,74149,1,5039,74149,50,5040,74149,40,5040,74195,0,5040,95083,3,5796,95310,4,6166,95947,5,6541,95948,1,6541,95948,50,6542,95948,40,6542,95994,0,6542,105619,3,7299,106989,4,7668,108906,5,8043,108907,1,8043,108907,50,8043,108907,40,8043,108953,0,8043,177952,3,11945,179104,4,13894,179907,5,15844,179908,1,15844,179908,50,15847,179908,40,15847,179954,0,15847,237740,3,18398,238528,4,19673,239328,5,20948,239329,1,20948,239329,50,20950,239329,40,20950,239375,0,20950,277791,3,22460,278446,4,23201,278793,5,23951,278794,1,23951,278794,50,23952,278794,40,23952,278840,0,23952,295567,3,24764,296217,4,25078,296854,1,25453,296854,50,25453,296854,40,25453,296900,0,25453,327358,3,26654,328112,4,27254,328676,5,27854,328677,1,27854,328677,50,27855,328677,40,27855,328723,0,27855,348087,3,28607,348777,4,28981,349342,1,29356,349342,50,29356,349342,40,29356,349342,40,29356,349383,0,29356,349463,50,29356,349463,30,29356,349463,40,29357,349504,0,29357,349617,50,29357,349658,0,29362,349819,50,29364,349819,30,29364,349819,40,29364,349860,0,29364)
%
%
% START OF PROOF
% 349820 [] equal(X,X).
% 349821 [] equal(multiply(identity,X),X).
% 349822 [] equal(multiply(inverse(X),X),identity).
% 349823 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 349824 [] -equal(multiply(X,sk_c8),sk_c6) | -equal(inverse(X),sk_c8).
% 349825 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 349826 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c2),sk_c8).
% 349827 [] equal(multiply(sk_c8,sk_c5),sk_c7) | equal(inverse(sk_c2),sk_c8).
% 349828 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c3),sk_c7).
% 349829 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(inverse(sk_c2),sk_c8).
% 349830 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c8).
% 349831 [?] ?
% 349832 [?] ?
% 349833 [?] ?
% 349834 [?] ?
% 349835 [?] ?
% 349836 [?] ?
% 349863 [hyper:349824,349825,binarycut:349831] equal(inverse(sk_c4),sk_c8).
% 349866 [para:349863.1.1,349822.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 349870 [hyper:349824,349828,binarycut:349834] equal(inverse(sk_c3),sk_c7).
% 349871 [para:349870.1.1,349822.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 349874 [hyper:349824,349826,binarycut:349832] equal(multiply(sk_c4,sk_c8),sk_c5).
% 349877 [hyper:349824,349827,binarycut:349833] equal(multiply(sk_c8,sk_c5),sk_c7).
% 349880 [hyper:349824,349829,binarycut:349835] equal(multiply(sk_c3,sk_c7),sk_c8).
% 349884 [hyper:349824,349830,binarycut:349836] equal(multiply(sk_c7,sk_c8),sk_c6).
% 349886 [para:349822.1.1,349823.1.1.1,demod:349821] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 349887 [para:349866.1.1,349823.1.1.1,demod:349821] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 349889 [para:349874.1.1,349823.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c4,multiply(sk_c8,X))).
% 349890 [para:349877.1.1,349823.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c5,X))).
% 349891 [para:349880.1.1,349823.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c3,multiply(sk_c7,X))).
% 349895 [para:349874.1.1,349887.1.2.2,demod:349877] equal(sk_c8,sk_c7).
% 349896 [para:349895.1.1,349866.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 349897 [para:349895.1.1,349874.1.1.2] equal(multiply(sk_c4,sk_c7),sk_c5).
% 349903 [para:349866.1.1,349886.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 349904 [para:349871.1.1,349886.1.2.2] equal(sk_c3,multiply(inverse(sk_c7),identity)).
% 349905 [para:349877.1.1,349886.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),sk_c7)).
% 349909 [para:349896.1.1,349886.1.2.2,demod:349904] equal(sk_c4,sk_c3).
% 349919 [para:349909.1.1,349897.1.1.1,demod:349880] equal(sk_c8,sk_c5).
% 349923 [para:349919.1.1,349887.1.2.1] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 349924 [para:349919.1.1,349895.1.1] equal(sk_c5,sk_c7).
% 349928 [para:349924.1.2,349884.1.1.1] equal(multiply(sk_c5,sk_c8),sk_c6).
% 349940 [para:349889.1.2,349887.1.2.2,demod:349890] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 349941 [para:349887.1.2,349889.1.2.2,demod:349923] equal(X,multiply(sk_c4,X)).
% 349942 [para:349909.1.1,349889.1.2.1,demod:349891,349940] equal(multiply(sk_c5,X),multiply(sk_c7,X)).
% 349943 [para:349941.1.2,349887.1.2.2,demod:349942,349940] equal(X,multiply(sk_c5,X)).
% 349945 [para:349943.1.2,349886.1.2.2] equal(X,multiply(inverse(sk_c5),X)).
% 349960 [para:349945.1.2,349822.1.1] equal(sk_c5,identity).
% 349961 [para:349960.1.1,349877.1.1.2,demod:349943,349942,349940] equal(identity,sk_c7).
% 349967 [para:349961.1.2,349905.1.2.2,demod:349903] equal(sk_c5,sk_c4).
% 349968 [para:349967.1.2,349863.1.1.1] equal(inverse(sk_c5),sk_c8).
% 349978 [hyper:349824,349968,demod:349928,cut:349820] 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 23
% 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),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 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1083,50,10,1129,0,10,2941,50,34,2987,0,34,5325,50,61,5371,0,61,7923,50,88,7969,0,88,10736,50,122,10782,0,122,13869,50,169,13915,0,169,17323,50,238,17369,0,238,21203,50,350,21249,0,350,25509,50,549,25555,0,549,30347,50,835,30347,40,835,30393,0,835,42389,3,1136,43058,4,1286,43690,5,1436,43691,1,1436,43691,50,1436,43691,40,1436,43737,0,1436,43926,3,1745,43934,4,1894,43942,5,2037,43942,1,2037,43942,50,2037,43942,40,2037,43988,0,2037,72686,3,3546,73317,4,4288,74148,5,5039,74149,1,5039,74149,50,5040,74149,40,5040,74195,0,5040,95083,3,5796,95310,4,6166,95947,5,6541,95948,1,6541,95948,50,6542,95948,40,6542,95994,0,6542,105619,3,7299,106989,4,7668,108906,5,8043,108907,1,8043,108907,50,8043,108907,40,8043,108953,0,8043,177952,3,11945,179104,4,13894,179907,5,15844,179908,1,15844,179908,50,15847,179908,40,15847,179954,0,15847,237740,3,18398,238528,4,19673,239328,5,20948,239329,1,20948,239329,50,20950,239329,40,20950,239375,0,20950,277791,3,22460,278446,4,23201,278793,5,23951,278794,1,23951,278794,50,23952,278794,40,23952,278840,0,23952,295567,3,24764,296217,4,25078,296854,1,25453,296854,50,25453,296854,40,25453,296900,0,25453,327358,3,26654,328112,4,27254,328676,5,27854,328677,1,27854,328677,50,27855,328677,40,27855,328723,0,27855,348087,3,28607,348777,4,28981,349342,1,29356,349342,50,29356,349342,40,29356,349342,40,29356,349383,0,29356,349463,50,29356,349463,30,29356,349463,40,29357,349504,0,29357,349617,50,29357,349658,0,29362,349819,50,29364,349819,30,29364,349819,40,29364,349860,0,29364,349977,50,29364,349977,30,29364,349977,40,29364,350018,0,29364)
%
%
% START OF PROOF
% 349979 [] equal(multiply(identity,X),X).
% 349980 [] equal(multiply(inverse(X),X),identity).
% 349981 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 349982 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 350001 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 350002 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c8).
% 350003 [] equal(multiply(sk_c8,sk_c5),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 350004 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c7).
% 350005 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 350006 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 350007 [?] ?
% 350008 [?] ?
% 350009 [?] ?
% 350010 [?] ?
% 350011 [?] ?
% 350012 [?] ?
% 350027 [hyper:349982,350001,binarycut:350007] equal(inverse(sk_c4),sk_c8).
% 350031 [para:350027.1.1,349980.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 350035 [hyper:349982,350004,binarycut:350010] equal(inverse(sk_c3),sk_c7).
% 350036 [para:350035.1.1,349980.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 350052 [hyper:349982,350002,binarycut:350008] equal(multiply(sk_c4,sk_c8),sk_c5).
% 350055 [hyper:349982,350003,binarycut:350009] equal(multiply(sk_c8,sk_c5),sk_c7).
% 350059 [hyper:349982,350005,binarycut:350011] equal(multiply(sk_c3,sk_c7),sk_c8).
% 350062 [hyper:349982,350006,binarycut:350012] equal(multiply(sk_c7,sk_c8),sk_c6).
% 350063 [para:349980.1.1,349981.1.1.1,demod:349979] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 350064 [para:350031.1.1,349981.1.1.1,demod:349979] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 350066 [para:350052.1.1,349981.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c4,multiply(sk_c8,X))).
% 350067 [para:350055.1.1,349981.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c5,X))).
% 350068 [para:350059.1.1,349981.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c3,multiply(sk_c7,X))).
% 350070 [para:350052.1.1,350064.1.2.2,demod:350055] equal(sk_c8,sk_c7).
% 350071 [para:350070.1.1,350031.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 350072 [para:350070.1.1,350052.1.1.2] equal(multiply(sk_c4,sk_c7),sk_c5).
% 350078 [para:350031.1.1,350063.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 350079 [para:350036.1.1,350063.1.2.2] equal(sk_c3,multiply(inverse(sk_c7),identity)).
% 350080 [para:350055.1.1,350063.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),sk_c7)).
% 350081 [para:350059.1.1,350063.1.2.2,demod:350062,350035] equal(sk_c7,sk_c6).
% 350084 [para:350071.1.1,350063.1.2.2,demod:350079] equal(sk_c4,sk_c3).
% 350086 [para:350081.1.1,350059.1.1.2] equal(multiply(sk_c3,sk_c6),sk_c8).
% 350094 [para:350084.1.1,350072.1.1.1,demod:350059] equal(sk_c8,sk_c5).
% 350098 [para:350094.1.1,350064.1.2.1] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 350099 [para:350094.1.1,350070.1.1] equal(sk_c5,sk_c7).
% 350103 [para:350099.1.2,350062.1.1.1] equal(multiply(sk_c5,sk_c8),sk_c6).
% 350115 [para:350066.1.2,350064.1.2.2,demod:350067] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 350116 [para:350064.1.2,350066.1.2.2,demod:350098] equal(X,multiply(sk_c4,X)).
% 350117 [para:350084.1.1,350066.1.2.1,demod:350068,350115] equal(multiply(sk_c5,X),multiply(sk_c7,X)).
% 350118 [para:350116.1.2,350064.1.2.2,demod:350117,350115] equal(X,multiply(sk_c5,X)).
% 350119 [para:350084.1.1,350116.1.2.1] equal(X,multiply(sk_c3,X)).
% 350120 [para:350118.1.2,350063.1.2.2] equal(X,multiply(inverse(sk_c5),X)).
% 350125 [para:350086.1.1,350119.1.2] equal(sk_c6,sk_c8).
% 350126 [para:350125.1.2,350070.1.1] equal(sk_c6,sk_c7).
% 350131 [para:350120.1.2,349980.1.1] equal(sk_c5,identity).
% 350132 [para:350131.1.1,350055.1.1.2,demod:350118,350117,350115] equal(identity,sk_c7).
% 350138 [para:350132.1.2,350080.1.2.2,demod:350078] equal(sk_c5,sk_c4).
% 350139 [para:350138.1.2,350027.1.1.1] equal(inverse(sk_c5),sk_c8).
% 350149 [hyper:349982,350139,demod:350103,cut:350126] 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 23
% 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(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,0,87,0,0,1083,50,10,1129,0,10,2941,50,34,2987,0,34,5325,50,61,5371,0,61,7923,50,88,7969,0,88,10736,50,122,10782,0,122,13869,50,169,13915,0,169,17323,50,238,17369,0,238,21203,50,350,21249,0,350,25509,50,549,25555,0,549,30347,50,835,30347,40,835,30393,0,835,42389,3,1136,43058,4,1286,43690,5,1436,43691,1,1436,43691,50,1436,43691,40,1436,43737,0,1436,43926,3,1745,43934,4,1894,43942,5,2037,43942,1,2037,43942,50,2037,43942,40,2037,43988,0,2037,72686,3,3546,73317,4,4288,74148,5,5039,74149,1,5039,74149,50,5040,74149,40,5040,74195,0,5040,95083,3,5796,95310,4,6166,95947,5,6541,95948,1,6541,95948,50,6542,95948,40,6542,95994,0,6542,105619,3,7299,106989,4,7668,108906,5,8043,108907,1,8043,108907,50,8043,108907,40,8043,108953,0,8043,177952,3,11945,179104,4,13894,179907,5,15844,179908,1,15844,179908,50,15847,179908,40,15847,179954,0,15847,237740,3,18398,238528,4,19673,239328,5,20948,239329,1,20948,239329,50,20950,239329,40,20950,239375,0,20950,277791,3,22460,278446,4,23201,278793,5,23951,278794,1,23951,278794,50,23952,278794,40,23952,278840,0,23952,295567,3,24764,296217,4,25078,296854,1,25453,296854,50,25453,296854,40,25453,296900,0,25453,327358,3,26654,328112,4,27254,328676,5,27854,328677,1,27854,328677,50,27855,328677,40,27855,328723,0,27855,348087,3,28607,348777,4,28981,349342,1,29356,349342,50,29356,349342,40,29356,349342,40,29356,349383,0,29356,349463,50,29356,349463,30,29356,349463,40,29357,349504,0,29357,349617,50,29357,349658,0,29362,349819,50,29364,349819,30,29364,349819,40,29364,349860,0,29364,349977,50,29364,349977,30,29364,349977,40,29364,350018,0,29364,350148,50,29365,350148,30,29365,350148,40,29365,350189,0,29369,350324,50,29370,350365,0,29370,350545,50,29374,350586,0,29378,350774,50,29382,350815,0,29383,351011,50,29389,351052,0,29389,351254,50,29399,351295,0,29403,351505,50,29420,351546,0,29420,351764,50,29451,351805,0,29455,352033,50,29516,352074,0,29516,352312,50,29640,352312,40,29640,352353,0,29641)
%
%
% START OF PROOF
% 352126 [?] ?
% 352314 [] equal(multiply(identity,X),X).
% 352315 [] equal(multiply(inverse(X),X),identity).
% 352316 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 352317 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 352348 [?] ?
% 352349 [?] ?
% 352350 [?] ?
% 352396 [input:352348,cut:352317] equal(inverse(sk_c4),sk_c8).
% 352397 [para:352396.1.1,352315.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 352414 [input:352349,cut:352317] equal(multiply(sk_c4,sk_c8),sk_c5).
% 352415 [input:352350,cut:352317] equal(multiply(sk_c8,sk_c5),sk_c7).
% 352440 [para:352397.1.1,352316.1.1.1,demod:352314] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 352478 [para:352414.1.1,352440.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 352484 [para:352478.1.2,352415.1.1] equal(sk_c8,sk_c7).
% 352486 [para:352484.1.1,352317.1.1.1,cut:352126] 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -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_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,0,87,0,0,1083,50,10,1129,0,10,2941,50,34,2987,0,34,5325,50,61,5371,0,61,7923,50,88,7969,0,88,10736,50,122,10782,0,122,13869,50,169,13915,0,169,17323,50,238,17369,0,238,21203,50,350,21249,0,350,25509,50,549,25555,0,549,30347,50,835,30347,40,835,30393,0,835,42389,3,1136,43058,4,1286,43690,5,1436,43691,1,1436,43691,50,1436,43691,40,1436,43737,0,1436,43926,3,1745,43934,4,1894,43942,5,2037,43942,1,2037,43942,50,2037,43942,40,2037,43988,0,2037,72686,3,3546,73317,4,4288,74148,5,5039,74149,1,5039,74149,50,5040,74149,40,5040,74195,0,5040,95083,3,5796,95310,4,6166,95947,5,6541,95948,1,6541,95948,50,6542,95948,40,6542,95994,0,6542,105619,3,7299,106989,4,7668,108906,5,8043,108907,1,8043,108907,50,8043,108907,40,8043,108953,0,8043,177952,3,11945,179104,4,13894,179907,5,15844,179908,1,15844,179908,50,15847,179908,40,15847,179954,0,15847,237740,3,18398,238528,4,19673,239328,5,20948,239329,1,20948,239329,50,20950,239329,40,20950,239375,0,20950,277791,3,22460,278446,4,23201,278793,5,23951,278794,1,23951,278794,50,23952,278794,40,23952,278840,0,23952,295567,3,24764,296217,4,25078,296854,1,25453,296854,50,25453,296854,40,25453,296900,0,25453,327358,3,26654,328112,4,27254,328676,5,27854,328677,1,27854,328677,50,27855,328677,40,27855,328723,0,27855,348087,3,28607,348777,4,28981,349342,1,29356,349342,50,29356,349342,40,29356,349342,40,29356,349383,0,29356,349463,50,29356,349463,30,29356,349463,40,29357,349504,0,29357,349617,50,29357,349658,0,29362,349819,50,29364,349819,30,29364,349819,40,29364,349860,0,29364,349977,50,29364,349977,30,29364,349977,40,29364,350018,0,29364,350148,50,29365,350148,30,29365,350148,40,29365,350189,0,29369,350324,50,29370,350365,0,29370,350545,50,29374,350586,0,29378,350774,50,29382,350815,0,29383,351011,50,29389,351052,0,29389,351254,50,29399,351295,0,29403,351505,50,29420,351546,0,29420,351764,50,29451,351805,0,29455,352033,50,29516,352074,0,29516,352312,50,29640,352312,40,29640,352353,0,29641,352485,50,29641,352485,30,29641,352485,40,29641,352526,0,29641,352661,50,29642,352702,0,29647,352882,50,29650,352923,0,29650,353111,50,29654,353152,0,29654,353348,50,29661,353389,0,29665,353591,50,29675,353632,0,29675,353842,50,29692,353883,0,29696,354101,50,29727,354142,0,29727,354370,50,29792,354411,0,29792,354649,50,29912,354649,40,29912,354690,0,29912)
%
%
% START OF PROOF
% 354593 [?] ?
% 354651 [] equal(multiply(identity,X),X).
% 354652 [] equal(multiply(inverse(X),X),identity).
% 354653 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 354654 [] -equal(multiply(sk_c8,sk_c6),sk_c7).
% 354667 [?] ?
% 354668 [?] ?
% 354669 [?] ?
% 354715 [input:354667,cut:354654] equal(inverse(sk_c4),sk_c8).
% 354716 [para:354715.1.1,354652.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 354739 [input:354668,cut:354654] equal(multiply(sk_c4,sk_c8),sk_c5).
% 354740 [input:354669,cut:354654] equal(multiply(sk_c8,sk_c5),sk_c7).
% 354761 [para:354716.1.1,354653.1.1.1,demod:354651] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 354801 [para:354739.1.1,354761.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 354805 [para:354801.1.2,354740.1.1] equal(sk_c8,sk_c7).
% 354807 [para:354805.1.1,354654.1.1.1,cut:354593] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c8),sk_c6) | -equal(inverse(Y),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -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_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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,0,87,0,0,1083,50,10,1129,0,10,2941,50,34,2987,0,34,5325,50,61,5371,0,61,7923,50,88,7969,0,88,10736,50,122,10782,0,122,13869,50,169,13915,0,169,17323,50,238,17369,0,238,21203,50,350,21249,0,350,25509,50,549,25555,0,549,30347,50,835,30347,40,835,30393,0,835,42389,3,1136,43058,4,1286,43690,5,1436,43691,1,1436,43691,50,1436,43691,40,1436,43737,0,1436,43926,3,1745,43934,4,1894,43942,5,2037,43942,1,2037,43942,50,2037,43942,40,2037,43988,0,2037,72686,3,3546,73317,4,4288,74148,5,5039,74149,1,5039,74149,50,5040,74149,40,5040,74195,0,5040,95083,3,5796,95310,4,6166,95947,5,6541,95948,1,6541,95948,50,6542,95948,40,6542,95994,0,6542,105619,3,7299,106989,4,7668,108906,5,8043,108907,1,8043,108907,50,8043,108907,40,8043,108953,0,8043,177952,3,11945,179104,4,13894,179907,5,15844,179908,1,15844,179908,50,15847,179908,40,15847,179954,0,15847,237740,3,18398,238528,4,19673,239328,5,20948,239329,1,20948,239329,50,20950,239329,40,20950,239375,0,20950,277791,3,22460,278446,4,23201,278793,5,23951,278794,1,23951,278794,50,23952,278794,40,23952,278840,0,23952,295567,3,24764,296217,4,25078,296854,1,25453,296854,50,25453,296854,40,25453,296900,0,25453,327358,3,26654,328112,4,27254,328676,5,27854,328677,1,27854,328677,50,27855,328677,40,27855,328723,0,27855,348087,3,28607,348777,4,28981,349342,1,29356,349342,50,29356,349342,40,29356,349342,40,29356,349383,0,29356,349463,50,29356,349463,30,29356,349463,40,29357,349504,0,29357,349617,50,29357,349658,0,29362,349819,50,29364,349819,30,29364,349819,40,29364,349860,0,29364,349977,50,29364,349977,30,29364,349977,40,29364,350018,0,29364,350148,50,29365,350148,30,29365,350148,40,29365,350189,0,29369,350324,50,29370,350365,0,29370,350545,50,29374,350586,0,29378,350774,50,29382,350815,0,29383,351011,50,29389,351052,0,29389,351254,50,29399,351295,0,29403,351505,50,29420,351546,0,29420,351764,50,29451,351805,0,29455,352033,50,29516,352074,0,29516,352312,50,29640,352312,40,29640,352353,0,29641,352485,50,29641,352485,30,29641,352485,40,29641,352526,0,29641,352661,50,29642,352702,0,29647,352882,50,29650,352923,0,29650,353111,50,29654,353152,0,29654,353348,50,29661,353389,0,29665,353591,50,29675,353632,0,29675,353842,50,29692,353883,0,29696,354101,50,29727,354142,0,29727,354370,50,29792,354411,0,29792,354649,50,29912,354649,40,29912,354690,0,29912,354806,50,29913,354806,30,29913,354806,40,29913,354847,0,29913,354956,50,29914,354997,0,29918,355154,50,29921,355195,0,29921,355360,50,29925,355401,0,29925,355574,50,29931,355615,0,29935,355794,50,29944,355835,0,29944,356022,50,29960,356063,0,29965,356258,50,29995,356299,0,29995,356504,50,30058,356545,0,30058,356760,50,30176,356760,40,30176,356801,0,30176)
%
%
% START OF PROOF
% 356599 [?] ?
% 356762 [] equal(multiply(identity,X),X).
% 356763 [] equal(multiply(inverse(X),X),identity).
% 356764 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 356765 [] -equal(multiply(sk_c7,sk_c8),sk_c6).
% 356771 [?] ?
% 356777 [?] ?
% 356783 [?] ?
% 356820 [input:356771,cut:356765] equal(inverse(sk_c2),sk_c8).
% 356821 [para:356820.1.1,356763.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 356852 [input:356777,cut:356765] equal(multiply(sk_c2,sk_c8),sk_c6).
% 356857 [input:356783,cut:356765] equal(multiply(sk_c8,sk_c6),sk_c7).
% 356870 [para:356821.1.1,356764.1.1.1,demod:356762] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 356920 [para:356852.1.1,356870.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 356926 [para:356920.1.2,356857.1.1] equal(sk_c8,sk_c7).
% 356928 [para:356926.1.1,356765.1.1.2,cut:356599] 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: 36145
% derived clauses: 6830568
% kept clauses: 289058
% kept size sum: 282803
% kept mid-nuclei: 17971
% kept new demods: 5595
% forw unit-subs: 3276665
% forw double-subs: 2965360
% forw overdouble-subs: 239289
% backward subs: 12597
% fast unit cutoff: 29915
% full unit cutoff: 0
% dbl unit cutoff: 15943
% real runtime : 305.66
% process. runtime: 301.77
% specific non-discr-tree subsumption statistics:
% tried: 33243602
% length fails: 2776913
% strength fails: 8901770
% predlist fails: 3239115
% aux str. fails: 5014371
% by-lit fails: 7204656
% full subs tried: 1541364
% full subs fail: 1444202
%
% ; 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/GRP293-1+eq_r.in")
%
%------------------------------------------------------------------------------