TSTP Solution File: GRP374-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP374-1 : 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 : art02.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 298.9s
% Output : Assurance 298.9s
% 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/GRP374-1+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(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -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(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(inverse(sk_c8),sk_c7).
% -equal(multiply(sk_c8,sk_c6),sk_c7).
% -equal(multiply(sk_c8,sk_c7),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(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -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(41,40,1,87,0,1,1217,50,11,1263,0,11,3142,50,34,3188,0,34,5582,50,64,5628,0,64,8913,50,98,8959,0,98,12479,50,141,12525,0,141,16305,50,197,16351,0,197,20476,50,278,20522,0,278,24993,50,407,25039,0,407,29941,50,610,29987,0,610,35321,50,901,35321,40,901,35367,0,902,46222,3,1203,46917,4,1353,47615,5,1503,47616,1,1503,47616,50,1503,47616,40,1503,47662,0,1503,47939,3,1816,47948,4,1958,47960,5,2104,47960,1,2104,47960,50,2104,47960,40,2104,48006,0,2104,82552,3,3608,83175,4,4355,83870,1,5105,83870,50,5106,83870,40,5106,83916,0,5106,108205,3,5858,108592,4,6232,109132,1,6607,109132,50,6608,109132,40,6608,109178,0,6608,119711,3,7360,120865,4,7734,121969,1,8109,121969,50,8109,121969,40,8109,122015,0,8109,250157,3,12013,251227,4,13961,251563,5,15910,251564,1,15910,251564,50,15913,251564,40,15913,251610,0,15913,339286,3,18465,339984,4,19739,340551,5,21015,340552,1,21015,340552,50,21018,340552,40,21018,340598,0,21018,374585,3,22519,375606,4,23269,376473,5,24019,376474,1,24019,376474,50,24020,376474,40,24020,376520,0,24020,387944,3,24775,388602,4,25146,389681,5,25521,389682,1,25521,389682,50,25521,389682,40,25521,389728,0,25521,421008,3,26723,421819,4,27322,422210,5,27922,422211,1,27922,422211,50,27923,422211,40,27923,422257,0,27923,448270,3,28675,448813,4,29049,449181,1,29424,449181,50,29425,449181,40,29425,449181,40,29425,449222,0,29425)
%
%
% START OF PROOF
% 449182 [] equal(X,X).
% 449183 [] equal(multiply(identity,X),X).
% 449184 [] equal(multiply(inverse(X),X),identity).
% 449185 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 449186 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 449205 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 449206 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c8).
% 449207 [?] ?
% 449211 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 449212 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 449213 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 449217 [] equal(inverse(sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 449218 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c8),sk_c7).
% 449219 [?] ?
% 449298 [hyper:449186,449206,449205,binarycut:449207] equal(inverse(sk_c1),sk_c8).
% 449308 [para:449298.1.1,449184.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 449341 [hyper:449186,449218,449217,binarycut:449219] equal(inverse(sk_c8),sk_c7).
% 449349 [para:449341.1.1,449184.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 449362 [hyper:449186,449213,449212,449211] equal(multiply(sk_c1,sk_c8),sk_c7).
% 449364 [para:449184.1.1,449185.1.1.1,demod:449183] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 449366 [para:449308.1.1,449185.1.1.1,demod:449183] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 449371 [para:449349.1.1,449185.1.1.1,demod:449183] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 449381 [para:449362.1.1,449366.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 449388 [para:449381.1.2,449371.1.2.2,demod:449349] equal(sk_c7,identity).
% 449392 [para:449388.1.1,449371.1.2.1,demod:449183] equal(X,multiply(sk_c8,X)).
% 449401 [hyper:449186,449364,449362,demod:449392,449364,demod:449298,cut:449182] 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(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -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 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,1,87,0,1,1217,50,11,1263,0,11,3142,50,34,3188,0,34,5582,50,64,5628,0,64,8913,50,98,8959,0,98,12479,50,141,12525,0,141,16305,50,197,16351,0,197,20476,50,278,20522,0,278,24993,50,407,25039,0,407,29941,50,610,29987,0,610,35321,50,901,35321,40,901,35367,0,902,46222,3,1203,46917,4,1353,47615,5,1503,47616,1,1503,47616,50,1503,47616,40,1503,47662,0,1503,47939,3,1816,47948,4,1958,47960,5,2104,47960,1,2104,47960,50,2104,47960,40,2104,48006,0,2104,82552,3,3608,83175,4,4355,83870,1,5105,83870,50,5106,83870,40,5106,83916,0,5106,108205,3,5858,108592,4,6232,109132,1,6607,109132,50,6608,109132,40,6608,109178,0,6608,119711,3,7360,120865,4,7734,121969,1,8109,121969,50,8109,121969,40,8109,122015,0,8109,250157,3,12013,251227,4,13961,251563,5,15910,251564,1,15910,251564,50,15913,251564,40,15913,251610,0,15913,339286,3,18465,339984,4,19739,340551,5,21015,340552,1,21015,340552,50,21018,340552,40,21018,340598,0,21018,374585,3,22519,375606,4,23269,376473,5,24019,376474,1,24019,376474,50,24020,376474,40,24020,376520,0,24020,387944,3,24775,388602,4,25146,389681,5,25521,389682,1,25521,389682,50,25521,389682,40,25521,389728,0,25521,421008,3,26723,421819,4,27322,422210,5,27922,422211,1,27922,422211,50,27923,422211,40,27923,422257,0,27923,448270,3,28675,448813,4,29049,449181,1,29424,449181,50,29425,449181,40,29425,449181,40,29425,449222,0,29425,449400,50,29425,449400,30,29425,449400,40,29425,449441,0,29425)
%
%
% START OF PROOF
% 449401 [] equal(X,X).
% 449405 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 449427 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 449428 [?] ?
% 449433 [?] ?
% 449434 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 449462 [hyper:449405,449427,binarycut:449433] equal(inverse(sk_c3),sk_c8).
% 449464 [hyper:449405,449427,binarycut:449428] equal(inverse(sk_c1),sk_c8).
% 449489 [hyper:449405,449434,demod:449464,cut:449401] equal(multiply(sk_c3,sk_c8),sk_c7).
% 449491 [hyper:449405,449489,demod:449462,cut:449401] 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 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -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(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,1,87,0,1,1217,50,11,1263,0,11,3142,50,34,3188,0,34,5582,50,64,5628,0,64,8913,50,98,8959,0,98,12479,50,141,12525,0,141,16305,50,197,16351,0,197,20476,50,278,20522,0,278,24993,50,407,25039,0,407,29941,50,610,29987,0,610,35321,50,901,35321,40,901,35367,0,902,46222,3,1203,46917,4,1353,47615,5,1503,47616,1,1503,47616,50,1503,47616,40,1503,47662,0,1503,47939,3,1816,47948,4,1958,47960,5,2104,47960,1,2104,47960,50,2104,47960,40,2104,48006,0,2104,82552,3,3608,83175,4,4355,83870,1,5105,83870,50,5106,83870,40,5106,83916,0,5106,108205,3,5858,108592,4,6232,109132,1,6607,109132,50,6608,109132,40,6608,109178,0,6608,119711,3,7360,120865,4,7734,121969,1,8109,121969,50,8109,121969,40,8109,122015,0,8109,250157,3,12013,251227,4,13961,251563,5,15910,251564,1,15910,251564,50,15913,251564,40,15913,251610,0,15913,339286,3,18465,339984,4,19739,340551,5,21015,340552,1,21015,340552,50,21018,340552,40,21018,340598,0,21018,374585,3,22519,375606,4,23269,376473,5,24019,376474,1,24019,376474,50,24020,376474,40,24020,376520,0,24020,387944,3,24775,388602,4,25146,389681,5,25521,389682,1,25521,389682,50,25521,389682,40,25521,389728,0,25521,421008,3,26723,421819,4,27322,422210,5,27922,422211,1,27922,422211,50,27923,422211,40,27923,422257,0,27923,448270,3,28675,448813,4,29049,449181,1,29424,449181,50,29425,449181,40,29425,449181,40,29425,449222,0,29425,449400,50,29425,449400,30,29425,449400,40,29425,449441,0,29425,449490,50,29425,449490,30,29425,449490,40,29425,449531,0,29429)
%
%
% START OF PROOF
% 449492 [] equal(multiply(identity,X),X).
% 449493 [] equal(multiply(inverse(X),X),identity).
% 449494 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 449495 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6).
% 449499 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 449500 [] equal(multiply(sk_c3,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c6).
% 449501 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c2),sk_c6).
% 449505 [?] ?
% 449506 [?] ?
% 449507 [?] ?
% 449539 [hyper:449495,449499,binarycut:449505] equal(inverse(sk_c3),sk_c8).
% 449549 [hyper:449495,449500,binarycut:449506] equal(multiply(sk_c3,sk_c8),sk_c7).
% 449552 [hyper:449495,449501,binarycut:449507] equal(multiply(sk_c8,sk_c7),sk_c6).
% 449553 [para:449493.1.1,449494.1.1.1,demod:449492] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 449573 [para:449549.1.1,449553.1.2.2,demod:449552,449539] equal(sk_c8,sk_c6).
% 449582 [para:449573.1.1,449549.1.1.2] equal(multiply(sk_c3,sk_c6),sk_c7).
% 449626 [hyper:449495,449582,demod:449539,cut:449573] 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(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -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(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(41,40,1,87,0,1,1217,50,11,1263,0,11,3142,50,34,3188,0,34,5582,50,64,5628,0,64,8913,50,98,8959,0,98,12479,50,141,12525,0,141,16305,50,197,16351,0,197,20476,50,278,20522,0,278,24993,50,407,25039,0,407,29941,50,610,29987,0,610,35321,50,901,35321,40,901,35367,0,902,46222,3,1203,46917,4,1353,47615,5,1503,47616,1,1503,47616,50,1503,47616,40,1503,47662,0,1503,47939,3,1816,47948,4,1958,47960,5,2104,47960,1,2104,47960,50,2104,47960,40,2104,48006,0,2104,82552,3,3608,83175,4,4355,83870,1,5105,83870,50,5106,83870,40,5106,83916,0,5106,108205,3,5858,108592,4,6232,109132,1,6607,109132,50,6608,109132,40,6608,109178,0,6608,119711,3,7360,120865,4,7734,121969,1,8109,121969,50,8109,121969,40,8109,122015,0,8109,250157,3,12013,251227,4,13961,251563,5,15910,251564,1,15910,251564,50,15913,251564,40,15913,251610,0,15913,339286,3,18465,339984,4,19739,340551,5,21015,340552,1,21015,340552,50,21018,340552,40,21018,340598,0,21018,374585,3,22519,375606,4,23269,376473,5,24019,376474,1,24019,376474,50,24020,376474,40,24020,376520,0,24020,387944,3,24775,388602,4,25146,389681,5,25521,389682,1,25521,389682,50,25521,389682,40,25521,389728,0,25521,421008,3,26723,421819,4,27322,422210,5,27922,422211,1,27922,422211,50,27923,422211,40,27923,422257,0,27923,448270,3,28675,448813,4,29049,449181,1,29424,449181,50,29425,449181,40,29425,449181,40,29425,449222,0,29425,449400,50,29425,449400,30,29425,449400,40,29425,449441,0,29425,449490,50,29425,449490,30,29425,449490,40,29425,449531,0,29429,449625,50,29429,449625,30,29429,449625,40,29429,449666,0,29429)
%
%
% START OF PROOF
% 449626 [] equal(X,X).
% 449630 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 449652 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 449653 [?] ?
% 449658 [?] ?
% 449659 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 449687 [hyper:449630,449652,binarycut:449658] equal(inverse(sk_c3),sk_c8).
% 449689 [hyper:449630,449652,binarycut:449653] equal(inverse(sk_c1),sk_c8).
% 449714 [hyper:449630,449659,demod:449689,cut:449626] equal(multiply(sk_c3,sk_c8),sk_c7).
% 449716 [hyper:449630,449714,demod:449687,cut:449626] 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(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -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_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(41,40,1,87,0,1,1217,50,11,1263,0,11,3142,50,34,3188,0,34,5582,50,64,5628,0,64,8913,50,98,8959,0,98,12479,50,141,12525,0,141,16305,50,197,16351,0,197,20476,50,278,20522,0,278,24993,50,407,25039,0,407,29941,50,610,29987,0,610,35321,50,901,35321,40,901,35367,0,902,46222,3,1203,46917,4,1353,47615,5,1503,47616,1,1503,47616,50,1503,47616,40,1503,47662,0,1503,47939,3,1816,47948,4,1958,47960,5,2104,47960,1,2104,47960,50,2104,47960,40,2104,48006,0,2104,82552,3,3608,83175,4,4355,83870,1,5105,83870,50,5106,83870,40,5106,83916,0,5106,108205,3,5858,108592,4,6232,109132,1,6607,109132,50,6608,109132,40,6608,109178,0,6608,119711,3,7360,120865,4,7734,121969,1,8109,121969,50,8109,121969,40,8109,122015,0,8109,250157,3,12013,251227,4,13961,251563,5,15910,251564,1,15910,251564,50,15913,251564,40,15913,251610,0,15913,339286,3,18465,339984,4,19739,340551,5,21015,340552,1,21015,340552,50,21018,340552,40,21018,340598,0,21018,374585,3,22519,375606,4,23269,376473,5,24019,376474,1,24019,376474,50,24020,376474,40,24020,376520,0,24020,387944,3,24775,388602,4,25146,389681,5,25521,389682,1,25521,389682,50,25521,389682,40,25521,389728,0,25521,421008,3,26723,421819,4,27322,422210,5,27922,422211,1,27922,422211,50,27923,422211,40,27923,422257,0,27923,448270,3,28675,448813,4,29049,449181,1,29424,449181,50,29425,449181,40,29425,449181,40,29425,449222,0,29425,449400,50,29425,449400,30,29425,449400,40,29425,449441,0,29425,449490,50,29425,449490,30,29425,449490,40,29425,449531,0,29429,449625,50,29429,449625,30,29429,449625,40,29429,449666,0,29429,449715,50,29429,449715,30,29429,449715,40,29429,449756,0,29429,449896,50,29430,449937,0,29434,450127,50,29438,450168,0,29438,450366,50,29444,450407,0,29448,450613,50,29456,450654,0,29456,450866,50,29467,450907,0,29467,451127,50,29486,451168,0,29490,451396,50,29524,451437,0,29524,451675,50,29594,451716,0,29594,451964,50,29724,451964,40,29724,452005,0,29724)
%
%
% START OF PROOF
% 451966 [] equal(multiply(identity,X),X).
% 451967 [] equal(multiply(inverse(X),X),identity).
% 451968 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 451969 [] -equal(inverse(sk_c8),sk_c7).
% 452000 [?] ?
% 452001 [?] ?
% 452002 [?] ?
% 452003 [?] ?
% 452004 [?] ?
% 452005 [?] ?
% 452020 [input:452000,cut:451969] equal(inverse(sk_c4),sk_c8).
% 452021 [para:452020.1.1,451967.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 452024 [input:452003,cut:451969] equal(inverse(sk_c3),sk_c8).
% 452025 [para:452024.1.1,451967.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 452046 [input:452001,cut:451969] equal(multiply(sk_c4,sk_c8),sk_c5).
% 452048 [input:452002,cut:451969] equal(multiply(sk_c8,sk_c5),sk_c7).
% 452049 [input:452004,cut:451969] equal(multiply(sk_c3,sk_c8),sk_c7).
% 452050 [input:452005,cut:451969] equal(multiply(sk_c8,sk_c7),sk_c6).
% 452067 [para:451967.1.1,451968.1.1.1,demod:451966] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 452069 [para:452021.1.1,451968.1.1.1,demod:451966] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 452071 [para:452025.1.1,451968.1.1.1,demod:451966] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 452091 [para:452048.1.1,451968.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c5,X))).
% 452113 [para:452046.1.1,452069.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 452117 [para:452113.1.2,452048.1.1] equal(sk_c8,sk_c7).
% 452118 [para:452113.1.2,451968.1.1.1,demod:452091] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 452119 [para:452117.1.1,451969.1.1.1] -equal(inverse(sk_c7),sk_c7).
% 452136 [para:452117.1.1,452046.1.1.2] equal(multiply(sk_c4,sk_c7),sk_c5).
% 452138 [para:452117.1.1,452048.1.1.1] equal(multiply(sk_c7,sk_c5),sk_c7).
% 452139 [para:452117.1.1,452049.1.1.2] equal(multiply(sk_c3,sk_c7),sk_c7).
% 452140 [para:452117.1.1,452050.1.1.1] equal(multiply(sk_c7,sk_c7),sk_c6).
% 452161 [para:452049.1.1,452071.1.2.2,demod:452140,452118] equal(sk_c8,sk_c6).
% 452162 [para:452139.1.1,452071.1.2.2,demod:452140,452118] equal(sk_c7,sk_c6).
% 452165 [para:452161.1.1,452021.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 452215 [para:452021.1.1,452067.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 452217 [para:452025.1.1,452067.1.2.2,demod:452215] equal(sk_c3,sk_c4).
% 452253 [para:452138.1.1,452067.1.2.2,demod:451967] equal(sk_c5,identity).
% 452265 [para:452217.1.2,452136.1.1.1,demod:452139] equal(sk_c7,sk_c5).
% 452269 [para:452253.1.1,452048.1.1.2,demod:452118] equal(multiply(sk_c7,identity),sk_c7).
% 452280 [para:452265.1.1,452162.1.1] equal(sk_c5,sk_c6).
% 452285 [para:452280.1.1,452253.1.1] equal(sk_c6,identity).
% 452294 [para:452285.1.1,452165.1.1.1,demod:451966] equal(sk_c4,identity).
% 452300 [para:452294.1.1,452020.1.1.1] equal(inverse(identity),sk_c8).
% 452301 [para:452294.1.1,452021.1.1.2,demod:452269,452118] equal(sk_c7,identity).
% 452306 [para:452301.1.1,452119.1.1.1,demod:452300,cut:452117] 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(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -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_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(41,40,1,87,0,1,1217,50,11,1263,0,11,3142,50,34,3188,0,34,5582,50,64,5628,0,64,8913,50,98,8959,0,98,12479,50,141,12525,0,141,16305,50,197,16351,0,197,20476,50,278,20522,0,278,24993,50,407,25039,0,407,29941,50,610,29987,0,610,35321,50,901,35321,40,901,35367,0,902,46222,3,1203,46917,4,1353,47615,5,1503,47616,1,1503,47616,50,1503,47616,40,1503,47662,0,1503,47939,3,1816,47948,4,1958,47960,5,2104,47960,1,2104,47960,50,2104,47960,40,2104,48006,0,2104,82552,3,3608,83175,4,4355,83870,1,5105,83870,50,5106,83870,40,5106,83916,0,5106,108205,3,5858,108592,4,6232,109132,1,6607,109132,50,6608,109132,40,6608,109178,0,6608,119711,3,7360,120865,4,7734,121969,1,8109,121969,50,8109,121969,40,8109,122015,0,8109,250157,3,12013,251227,4,13961,251563,5,15910,251564,1,15910,251564,50,15913,251564,40,15913,251610,0,15913,339286,3,18465,339984,4,19739,340551,5,21015,340552,1,21015,340552,50,21018,340552,40,21018,340598,0,21018,374585,3,22519,375606,4,23269,376473,5,24019,376474,1,24019,376474,50,24020,376474,40,24020,376520,0,24020,387944,3,24775,388602,4,25146,389681,5,25521,389682,1,25521,389682,50,25521,389682,40,25521,389728,0,25521,421008,3,26723,421819,4,27322,422210,5,27922,422211,1,27922,422211,50,27923,422211,40,27923,422257,0,27923,448270,3,28675,448813,4,29049,449181,1,29424,449181,50,29425,449181,40,29425,449181,40,29425,449222,0,29425,449400,50,29425,449400,30,29425,449400,40,29425,449441,0,29425,449490,50,29425,449490,30,29425,449490,40,29425,449531,0,29429,449625,50,29429,449625,30,29429,449625,40,29429,449666,0,29429,449715,50,29429,449715,30,29429,449715,40,29429,449756,0,29429,449896,50,29430,449937,0,29434,450127,50,29438,450168,0,29438,450366,50,29444,450407,0,29448,450613,50,29456,450654,0,29456,450866,50,29467,450907,0,29467,451127,50,29486,451168,0,29490,451396,50,29524,451437,0,29524,451675,50,29594,451716,0,29594,451964,50,29724,451964,40,29724,452005,0,29724,452305,50,29725,452305,30,29725,452305,40,29725,452346,0,29725,452486,50,29726,452527,0,29730,452717,50,29734,452758,0,29734,452956,50,29739,452997,0,29739,453203,50,29746,453244,0,29750,453456,50,29761,453497,0,29761,453717,50,29779,453758,0,29784,453986,50,29818,454027,0,29818,454265,50,29888,454306,0,29888,454554,50,30018,454554,40,30018,454595,0,30018)
%
%
% START OF PROOF
% 454497 [?] ?
% 454556 [] equal(multiply(identity,X),X).
% 454557 [] equal(multiply(inverse(X),X),identity).
% 454558 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 454559 [] -equal(multiply(sk_c8,sk_c6),sk_c7).
% 454572 [?] ?
% 454573 [?] ?
% 454574 [?] ?
% 454626 [input:454572,cut:454559] equal(inverse(sk_c4),sk_c8).
% 454627 [para:454626.1.1,454557.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 454655 [input:454573,cut:454559] equal(multiply(sk_c4,sk_c8),sk_c5).
% 454656 [input:454574,cut:454559] equal(multiply(sk_c8,sk_c5),sk_c7).
% 454679 [para:454627.1.1,454558.1.1.1,demod:454556] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 454719 [para:454655.1.1,454679.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 454724 [para:454719.1.2,454656.1.1] equal(sk_c8,sk_c7).
% 454726 [para:454724.1.1,454559.1.1.1,cut:454497] 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(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -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 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(41,40,1,87,0,1,1217,50,11,1263,0,11,3142,50,34,3188,0,34,5582,50,64,5628,0,64,8913,50,98,8959,0,98,12479,50,141,12525,0,141,16305,50,197,16351,0,197,20476,50,278,20522,0,278,24993,50,407,25039,0,407,29941,50,610,29987,0,610,35321,50,901,35321,40,901,35367,0,902,46222,3,1203,46917,4,1353,47615,5,1503,47616,1,1503,47616,50,1503,47616,40,1503,47662,0,1503,47939,3,1816,47948,4,1958,47960,5,2104,47960,1,2104,47960,50,2104,47960,40,2104,48006,0,2104,82552,3,3608,83175,4,4355,83870,1,5105,83870,50,5106,83870,40,5106,83916,0,5106,108205,3,5858,108592,4,6232,109132,1,6607,109132,50,6608,109132,40,6608,109178,0,6608,119711,3,7360,120865,4,7734,121969,1,8109,121969,50,8109,121969,40,8109,122015,0,8109,250157,3,12013,251227,4,13961,251563,5,15910,251564,1,15910,251564,50,15913,251564,40,15913,251610,0,15913,339286,3,18465,339984,4,19739,340551,5,21015,340552,1,21015,340552,50,21018,340552,40,21018,340598,0,21018,374585,3,22519,375606,4,23269,376473,5,24019,376474,1,24019,376474,50,24020,376474,40,24020,376520,0,24020,387944,3,24775,388602,4,25146,389681,5,25521,389682,1,25521,389682,50,25521,389682,40,25521,389728,0,25521,421008,3,26723,421819,4,27322,422210,5,27922,422211,1,27922,422211,50,27923,422211,40,27923,422257,0,27923,448270,3,28675,448813,4,29049,449181,1,29424,449181,50,29425,449181,40,29425,449181,40,29425,449222,0,29425,449400,50,29425,449400,30,29425,449400,40,29425,449441,0,29425,449490,50,29425,449490,30,29425,449490,40,29425,449531,0,29429,449625,50,29429,449625,30,29429,449625,40,29429,449666,0,29429,449715,50,29429,449715,30,29429,449715,40,29429,449756,0,29429,449896,50,29430,449937,0,29434,450127,50,29438,450168,0,29438,450366,50,29444,450407,0,29448,450613,50,29456,450654,0,29456,450866,50,29467,450907,0,29467,451127,50,29486,451168,0,29490,451396,50,29524,451437,0,29524,451675,50,29594,451716,0,29594,451964,50,29724,451964,40,29724,452005,0,29724,452305,50,29725,452305,30,29725,452305,40,29725,452346,0,29725,452486,50,29726,452527,0,29730,452717,50,29734,452758,0,29734,452956,50,29739,452997,0,29739,453203,50,29746,453244,0,29750,453456,50,29761,453497,0,29761,453717,50,29779,453758,0,29784,453986,50,29818,454027,0,29818,454265,50,29888,454306,0,29888,454554,50,30018,454554,40,30018,454595,0,30018,454725,50,30018,454725,30,30018,454725,40,30018,454766,0,30018,454877,50,30019,454918,0,30023,455067,50,30025,455108,0,30025,455265,50,30028,455306,0,30028,455471,50,30033,455512,0,30038,455683,50,30046,455724,0,30046,455903,50,30061,455944,0,30065,456131,50,30092,456172,0,30092,456369,50,30153,456410,0,30153,456617,50,30266,456617,40,30266,456658,0,30266)
%
%
% START OF PROOF
% 456493 [?] ?
% 456619 [] equal(multiply(identity,X),X).
% 456620 [] equal(multiply(inverse(X),X),identity).
% 456621 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 456622 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 456646 [?] ?
% 456652 [?] ?
% 456701 [input:456646,cut:456622] equal(inverse(sk_c1),sk_c8).
% 456702 [para:456701.1.1,456620.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 456730 [input:456652,cut:456622] equal(multiply(sk_c1,sk_c8),sk_c7).
% 456748 [para:456702.1.1,456621.1.1.1,demod:456619] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 456791 [para:456730.1.1,456748.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 456792 [para:456791.1.2,456622.1.1,cut:456493] 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: 33403
% derived clauses: 6103230
% kept clauses: 328478
% kept size sum: 473527
% kept mid-nuclei: 23320
% kept new demods: 5657
% forw unit-subs: 2095847
% forw double-subs: 3332538
% forw overdouble-subs: 219824
% backward subs: 10324
% fast unit cutoff: 30940
% full unit cutoff: 0
% dbl unit cutoff: 16630
% real runtime : 304.12
% process. runtime: 302.66
% specific non-discr-tree subsumption statistics:
% tried: 38862891
% length fails: 3627386
% strength fails: 10721778
% predlist fails: 2403411
% aux str. fails: 5538730
% by-lit fails: 7912446
% full subs tried: 1187108
% full subs fail: 1094368
%
% ; 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/GRP374-1+eq_r.in")
%
%------------------------------------------------------------------------------