TSTP Solution File: GRP361-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP361-1 : 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 : art03.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 297.7s
% Output : Assurance 297.7s
% 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/GRP361-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c5),sk_c7) | -equal(inverse(U),sk_c5).
% was split for some strategies as:
% -equal(multiply(U,sk_c5),sk_c7) | -equal(inverse(U),sk_c5).
% -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7).
% -equal(multiply(sk_c6,sk_c5),sk_c7).
% -equal(inverse(sk_c7),sk_c5).
% -equal(multiply(sk_c6,sk_c7),sk_c5).
% -equal(multiply(sk_c5,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(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c5),sk_c7) | -equal(inverse(U),sk_c5).
% Split part used next: -equal(multiply(U,sk_c5),sk_c7) | -equal(inverse(U),sk_c5).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,74,0,0,863,50,8,902,0,8,2405,50,32,2444,0,32,4304,50,64,4343,0,64,6385,50,91,6424,0,91,8649,50,125,8688,0,125,11185,50,172,11224,0,172,13994,50,240,14033,0,240,17165,50,353,17204,0,353,20698,50,547,20737,0,547,24683,50,836,24683,40,836,24722,0,836,35612,3,1137,36348,4,1287,37044,5,1437,37044,1,1437,37044,50,1437,37044,40,1437,37083,0,1437,37366,3,1751,37375,4,1895,37388,5,2038,37388,1,2038,37388,50,2038,37388,40,2038,37427,0,2038,64830,3,3539,65304,4,4289,65721,1,5039,65721,50,5040,65721,40,5040,65760,0,5040,84884,3,5791,85466,4,6166,86050,5,6541,86051,1,6541,86051,50,6542,86051,40,6542,86090,0,6542,100193,3,7601,100368,4,7668,101040,1,8043,101040,50,8043,101040,40,8043,101079,0,8043,158943,3,11946,159910,4,13894,161045,1,15844,161045,50,15846,161045,40,15846,161084,0,15846,210928,3,18399,211628,4,19672,212114,1,20947,212114,50,20949,212114,40,20949,212153,0,20949,263190,3,22450,263723,4,23201,264315,5,23950,264316,1,23950,264316,50,23951,264316,40,23951,264355,0,23952,273259,3,24712,274860,4,25078,275759,5,25453,275759,1,25453,275759,50,25453,275759,40,25453,275798,0,25453,324517,3,26654,324958,4,27254,325302,1,27854,325302,50,27856,325302,40,27856,325341,0,27856,359665,3,28607,360039,4,28982,360276,1,29357,360276,50,29358,360276,40,29358,360276,40,29358,360311,0,29358)
%
%
% START OF PROOF
% 360277 [] equal(X,X).
% 360278 [] equal(multiply(identity,X),X).
% 360279 [] equal(multiply(inverse(X),X),identity).
% 360280 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 360281 [] -equal(multiply(X,sk_c5),sk_c7) | -equal(inverse(X),sk_c5).
% 360282 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c5).
% 360283 [?] ?
% 360288 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c4),sk_c5).
% 360289 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c4,sk_c5),sk_c7).
% 360294 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c5).
% 360295 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(multiply(sk_c4,sk_c5),sk_c7).
% 360300 [] equal(inverse(sk_c7),sk_c5) | equal(inverse(sk_c4),sk_c5).
% 360301 [?] ?
% 360306 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(inverse(sk_c4),sk_c5).
% 360307 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(multiply(sk_c4,sk_c5),sk_c7).
% 360314 [hyper:360281,360282,binarycut:360283] equal(inverse(sk_c1),sk_c7).
% 360315 [para:360314.1.1,360279.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 360323 [hyper:360281,360300,binarycut:360301] equal(inverse(sk_c7),sk_c5).
% 360331 [hyper:360281,360289,360288] equal(multiply(sk_c1,sk_c7),sk_c2).
% 360337 [hyper:360281,360295,360294] equal(multiply(sk_c7,sk_c2),sk_c6).
% 360346 [hyper:360281,360307,360306] equal(multiply(sk_c6,sk_c5),sk_c7).
% 360351 [para:360315.1.1,360280.1.1.1,demod:360278] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 360356 [para:360331.1.1,360351.1.2.2,demod:360337] equal(sk_c7,sk_c6).
% 360357 [para:360356.1.2,360346.1.1.1] equal(multiply(sk_c7,sk_c5),sk_c7).
% 360358 [hyper:360281,360357,demod:360323,cut:360277] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c5),sk_c7) | -equal(inverse(U),sk_c5).
% Split part used next: -equal(inverse(Z),sk_c7) | -equal(multiply(Z,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 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,74,0,0,863,50,8,902,0,8,2405,50,32,2444,0,32,4304,50,64,4343,0,64,6385,50,91,6424,0,91,8649,50,125,8688,0,125,11185,50,172,11224,0,172,13994,50,240,14033,0,240,17165,50,353,17204,0,353,20698,50,547,20737,0,547,24683,50,836,24683,40,836,24722,0,836,35612,3,1137,36348,4,1287,37044,5,1437,37044,1,1437,37044,50,1437,37044,40,1437,37083,0,1437,37366,3,1751,37375,4,1895,37388,5,2038,37388,1,2038,37388,50,2038,37388,40,2038,37427,0,2038,64830,3,3539,65304,4,4289,65721,1,5039,65721,50,5040,65721,40,5040,65760,0,5040,84884,3,5791,85466,4,6166,86050,5,6541,86051,1,6541,86051,50,6542,86051,40,6542,86090,0,6542,100193,3,7601,100368,4,7668,101040,1,8043,101040,50,8043,101040,40,8043,101079,0,8043,158943,3,11946,159910,4,13894,161045,1,15844,161045,50,15846,161045,40,15846,161084,0,15846,210928,3,18399,211628,4,19672,212114,1,20947,212114,50,20949,212114,40,20949,212153,0,20949,263190,3,22450,263723,4,23201,264315,5,23950,264316,1,23950,264316,50,23951,264316,40,23951,264355,0,23952,273259,3,24712,274860,4,25078,275759,5,25453,275759,1,25453,275759,50,25453,275759,40,25453,275798,0,25453,324517,3,26654,324958,4,27254,325302,1,27854,325302,50,27856,325302,40,27856,325341,0,27856,359665,3,28607,360039,4,28982,360276,1,29357,360276,50,29358,360276,40,29358,360276,40,29358,360311,0,29358,360357,50,29358,360357,30,29358,360357,40,29358,360392,0,29358,360483,50,29358,360518,0,29363)
%
%
% START OF PROOF
% 360485 [] equal(multiply(identity,X),X).
% 360486 [] equal(multiply(inverse(X),X),identity).
% 360487 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 360488 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 360491 [?] ?
% 360492 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 360497 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 360498 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c3),sk_c7).
% 360503 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 360504 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 360509 [?] ?
% 360510 [] equal(inverse(sk_c7),sk_c5) | equal(inverse(sk_c3),sk_c7).
% 360515 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 360516 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 360524 [hyper:360488,360492,binarycut:360491] equal(inverse(sk_c1),sk_c7).
% 360527 [para:360524.1.1,360486.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 360533 [hyper:360488,360510,binarycut:360509] equal(inverse(sk_c7),sk_c5).
% 360534 [para:360533.1.1,360486.1.1.1] equal(multiply(sk_c5,sk_c7),identity).
% 360549 [hyper:360488,360497,360498] equal(multiply(sk_c1,sk_c7),sk_c2).
% 360553 [hyper:360488,360503,360504] equal(multiply(sk_c7,sk_c2),sk_c6).
% 360557 [hyper:360488,360515,360516] equal(multiply(sk_c6,sk_c5),sk_c7).
% 360558 [para:360486.1.1,360487.1.1.1,demod:360485] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 360559 [para:360527.1.1,360487.1.1.1,demod:360485] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 360560 [para:360534.1.1,360487.1.1.1,demod:360485] equal(X,multiply(sk_c5,multiply(sk_c7,X))).
% 360561 [para:360549.1.1,360487.1.1.1] equal(multiply(sk_c2,X),multiply(sk_c1,multiply(sk_c7,X))).
% 360564 [para:360549.1.1,360559.1.2.2,demod:360553] equal(sk_c7,sk_c6).
% 360565 [para:360564.1.2,360557.1.1.1] equal(multiply(sk_c7,sk_c5),sk_c7).
% 360567 [para:360527.1.1,360560.1.2.2] equal(sk_c1,multiply(sk_c5,identity)).
% 360568 [para:360553.1.1,360560.1.2.2] equal(sk_c2,multiply(sk_c5,sk_c6)).
% 360569 [para:360559.1.2,360560.1.2.2] equal(multiply(sk_c1,X),multiply(sk_c5,X)).
% 360570 [para:360565.1.1,360560.1.2.2,demod:360534] equal(sk_c5,identity).
% 360571 [para:360570.1.1,360534.1.1.1,demod:360485] equal(sk_c7,identity).
% 360574 [para:360570.1.1,360560.1.2.1,demod:360485] equal(X,multiply(sk_c7,X)).
% 360576 [para:360486.1.1,360558.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 360577 [para:360533.1.1,360558.1.2.1,demod:360569,360574] equal(X,multiply(sk_c1,X)).
% 360580 [para:360487.1.1,360558.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 360582 [para:360558.1.2,360558.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 360585 [para:360571.1.1,360549.1.1.2,demod:360577] equal(identity,sk_c2).
% 360587 [para:360571.1.1,360565.1.1.1,demod:360485] equal(sk_c5,sk_c7).
% 360594 [para:360553.1.1,360561.1.2.2,demod:360577] equal(multiply(sk_c2,sk_c2),sk_c6).
% 360597 [para:360559.1.2,360561.1.2.2,demod:360577] equal(multiply(sk_c2,X),X).
% 360607 [para:360585.1.2,360594.1.1.2,demod:360597] equal(identity,sk_c6).
% 360608 [para:360607.1.2,360568.1.2.2,demod:360567] equal(sk_c2,sk_c1).
% 360609 [para:360608.1.2,360524.1.1.1] equal(inverse(sk_c2),sk_c7).
% 360613 [para:360582.1.2,360486.1.1] equal(multiply(X,inverse(X)),identity).
% 360615 [para:360582.1.2,360576.1.2] equal(X,multiply(X,identity)).
% 360619 [para:360615.1.2,360576.1.2] equal(X,inverse(inverse(X))).
% 360625 [para:360553.1.1,360580.1.2.2.2] equal(sk_c2,multiply(inverse(multiply(X,sk_c7)),multiply(X,sk_c6))).
% 360635 [para:360609.1.1,360619.1.2.1,demod:360533] equal(sk_c2,sk_c5).
% 360638 [para:360613.1.1,360580.1.2.2.2,demod:360615] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 360641 [para:360559.1.2,360638.1.2.1.1,demod:360577] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 360642 [para:360560.1.2,360638.1.2.1.1,demod:360574] equal(inverse(X),multiply(inverse(X),sk_c5)).
% 360653 [para:360641.1.2,360582.1.2,demod:360619] equal(multiply(X,sk_c7),X).
% 360654 [para:360642.1.2,360582.1.2,demod:360619] equal(multiply(X,sk_c5),X).
% 360657 [para:360635.1.2,360654.1.1.2] equal(multiply(X,sk_c2),X).
% 360658 [para:360625.1.2,360558.1.2.2,demod:360657,360619,360653] equal(multiply(X,sk_c6),X).
% 360659 [hyper:360488,360658,demod:360533,cut:360587] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c5),sk_c7) | -equal(inverse(U),sk_c5).
% Split part used next: -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,74,0,0,863,50,8,902,0,8,2405,50,32,2444,0,32,4304,50,64,4343,0,64,6385,50,91,6424,0,91,8649,50,125,8688,0,125,11185,50,172,11224,0,172,13994,50,240,14033,0,240,17165,50,353,17204,0,353,20698,50,547,20737,0,547,24683,50,836,24683,40,836,24722,0,836,35612,3,1137,36348,4,1287,37044,5,1437,37044,1,1437,37044,50,1437,37044,40,1437,37083,0,1437,37366,3,1751,37375,4,1895,37388,5,2038,37388,1,2038,37388,50,2038,37388,40,2038,37427,0,2038,64830,3,3539,65304,4,4289,65721,1,5039,65721,50,5040,65721,40,5040,65760,0,5040,84884,3,5791,85466,4,6166,86050,5,6541,86051,1,6541,86051,50,6542,86051,40,6542,86090,0,6542,100193,3,7601,100368,4,7668,101040,1,8043,101040,50,8043,101040,40,8043,101079,0,8043,158943,3,11946,159910,4,13894,161045,1,15844,161045,50,15846,161045,40,15846,161084,0,15846,210928,3,18399,211628,4,19672,212114,1,20947,212114,50,20949,212114,40,20949,212153,0,20949,263190,3,22450,263723,4,23201,264315,5,23950,264316,1,23950,264316,50,23951,264316,40,23951,264355,0,23952,273259,3,24712,274860,4,25078,275759,5,25453,275759,1,25453,275759,50,25453,275759,40,25453,275798,0,25453,324517,3,26654,324958,4,27254,325302,1,27854,325302,50,27856,325302,40,27856,325341,0,27856,359665,3,28607,360039,4,28982,360276,1,29357,360276,50,29358,360276,40,29358,360276,40,29358,360311,0,29358,360357,50,29358,360357,30,29358,360357,40,29358,360392,0,29358,360483,50,29358,360518,0,29363,360658,50,29364,360658,30,29364,360658,40,29364,360693,0,29364)
%
%
% START OF PROOF
% 360659 [] equal(X,X).
% 360660 [] equal(multiply(identity,X),X).
% 360661 [] equal(multiply(inverse(X),X),identity).
% 360662 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 360663 [] -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7).
% 360664 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c5).
% 360665 [] equal(multiply(sk_c4,sk_c5),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 360666 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 360667 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 360668 [] equal(multiply(sk_c5,sk_c7),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 360670 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c4),sk_c5).
% 360671 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c4,sk_c5),sk_c7).
% 360672 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 360673 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c3),sk_c7).
% 360674 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 360676 [?] ?
% 360677 [?] ?
% 360678 [?] ?
% 360679 [?] ?
% 360680 [?] ?
% 360738 [hyper:360663,360670,binarycut:360676,binarycut:360664] equal(inverse(sk_c4),sk_c5).
% 360739 [para:360738.1.1,360661.1.1.1] equal(multiply(sk_c5,sk_c4),identity).
% 360742 [hyper:360663,360673,binarycut:360679,binarycut:360667] equal(inverse(sk_c3),sk_c7).
% 360749 [para:360742.1.1,360661.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 360755 [hyper:360663,360671,360665,binarycut:360677] equal(multiply(sk_c4,sk_c5),sk_c7).
% 360766 [hyper:360663,360672,360666,binarycut:360678] equal(multiply(sk_c3,sk_c6),sk_c7).
% 360770 [hyper:360663,360674,360668,binarycut:360680] equal(multiply(sk_c5,sk_c7),sk_c6).
% 360781 [para:360661.1.1,360662.1.1.1,demod:360660] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 360782 [para:360739.1.1,360662.1.1.1,demod:360660] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 360784 [para:360755.1.1,360662.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c4,multiply(sk_c5,X))).
% 360792 [para:360755.1.1,360782.1.2.2,demod:360770] equal(sk_c5,sk_c6).
% 360793 [para:360792.1.2,360766.1.1.2] equal(multiply(sk_c3,sk_c5),sk_c7).
% 360795 [para:360793.1.1,360662.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c5,X))).
% 360799 [para:360739.1.1,360781.1.2.2] equal(sk_c4,multiply(inverse(sk_c5),identity)).
% 360801 [para:360766.1.1,360781.1.2.2,demod:360742] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 360802 [para:360770.1.1,360781.1.2.2] equal(sk_c7,multiply(inverse(sk_c5),sk_c6)).
% 360804 [para:360782.1.2,360781.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c5),X)).
% 360814 [para:360804.1.2,360661.1.1,demod:360755] equal(sk_c7,identity).
% 360816 [para:360804.1.2,360781.1.2,demod:360784] equal(X,multiply(sk_c7,X)).
% 360819 [para:360814.1.1,360749.1.1.1,demod:360660] equal(sk_c3,identity).
% 360823 [para:360814.1.1,360801.1.2.2,demod:360816] equal(sk_c6,identity).
% 360826 [para:360819.1.1,360793.1.1.1,demod:360660] equal(sk_c5,sk_c7).
% 360832 [para:360823.1.1,360802.1.2.2,demod:360799] equal(sk_c7,sk_c4).
% 360843 [para:360832.1.2,360738.1.1.1] equal(inverse(sk_c7),sk_c5).
% 360856 [hyper:360663,360795,demod:360843,360801,360766,360770,cut:360659,cut:360826] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c5),sk_c7) | -equal(inverse(U),sk_c5).
% Split part used next: -equal(multiply(sk_c6,sk_c5),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 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,74,0,0,863,50,8,902,0,8,2405,50,32,2444,0,32,4304,50,64,4343,0,64,6385,50,91,6424,0,91,8649,50,125,8688,0,125,11185,50,172,11224,0,172,13994,50,240,14033,0,240,17165,50,353,17204,0,353,20698,50,547,20737,0,547,24683,50,836,24683,40,836,24722,0,836,35612,3,1137,36348,4,1287,37044,5,1437,37044,1,1437,37044,50,1437,37044,40,1437,37083,0,1437,37366,3,1751,37375,4,1895,37388,5,2038,37388,1,2038,37388,50,2038,37388,40,2038,37427,0,2038,64830,3,3539,65304,4,4289,65721,1,5039,65721,50,5040,65721,40,5040,65760,0,5040,84884,3,5791,85466,4,6166,86050,5,6541,86051,1,6541,86051,50,6542,86051,40,6542,86090,0,6542,100193,3,7601,100368,4,7668,101040,1,8043,101040,50,8043,101040,40,8043,101079,0,8043,158943,3,11946,159910,4,13894,161045,1,15844,161045,50,15846,161045,40,15846,161084,0,15846,210928,3,18399,211628,4,19672,212114,1,20947,212114,50,20949,212114,40,20949,212153,0,20949,263190,3,22450,263723,4,23201,264315,5,23950,264316,1,23950,264316,50,23951,264316,40,23951,264355,0,23952,273259,3,24712,274860,4,25078,275759,5,25453,275759,1,25453,275759,50,25453,275759,40,25453,275798,0,25453,324517,3,26654,324958,4,27254,325302,1,27854,325302,50,27856,325302,40,27856,325341,0,27856,359665,3,28607,360039,4,28982,360276,1,29357,360276,50,29358,360276,40,29358,360276,40,29358,360311,0,29358,360357,50,29358,360357,30,29358,360357,40,29358,360392,0,29358,360483,50,29358,360518,0,29363,360658,50,29364,360658,30,29364,360658,40,29364,360693,0,29364,360855,50,29365,360855,30,29365,360855,40,29365,360890,0,29365,360983,50,29365,361018,0,29370,361161,50,29372,361196,0,29372,361347,50,29375,361382,0,29380,361541,50,29385,361576,0,29385,361741,50,29394,361776,0,29394,361949,50,29409,361984,0,29413,362165,50,29442,362200,0,29442,362391,50,29503,362426,0,29503,362627,50,29618,362627,40,29618,362662,0,29618)
%
%
% START OF PROOF
% 362629 [] equal(multiply(identity,X),X).
% 362630 [] equal(multiply(inverse(X),X),identity).
% 362631 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 362632 [] -equal(multiply(sk_c6,sk_c5),sk_c7).
% 362657 [?] ?
% 362658 [?] ?
% 362659 [?] ?
% 362660 [?] ?
% 362661 [?] ?
% 362662 [?] ?
% 362700 [input:362657,cut:362632] equal(inverse(sk_c4),sk_c5).
% 362701 [para:362700.1.1,362630.1.1.1] equal(multiply(sk_c5,sk_c4),identity).
% 362703 [input:362660,cut:362632] equal(inverse(sk_c3),sk_c7).
% 362704 [para:362703.1.1,362630.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 362715 [input:362658,cut:362632] equal(multiply(sk_c4,sk_c5),sk_c7).
% 362716 [input:362659,cut:362632] equal(multiply(sk_c3,sk_c6),sk_c7).
% 362717 [input:362661,cut:362632] equal(multiply(sk_c5,sk_c7),sk_c6).
% 362726 [input:362662,cut:362632] equal(multiply(sk_c6,sk_c7),sk_c5).
% 362730 [para:362630.1.1,362631.1.1.1,demod:362629] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 362741 [para:362701.1.1,362631.1.1.1,demod:362629] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 362744 [para:362704.1.1,362631.1.1.1,demod:362629] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 362759 [para:362717.1.1,362631.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c5,multiply(sk_c7,X))).
% 362768 [para:362715.1.1,362741.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c7)).
% 362773 [para:362768.1.2,362717.1.1] equal(sk_c5,sk_c6).
% 362774 [para:362768.1.2,362631.1.1.1,demod:362759] equal(multiply(sk_c5,X),multiply(sk_c6,X)).
% 362780 [para:362773.1.2,362716.1.1.2] equal(multiply(sk_c3,sk_c5),sk_c7).
% 362787 [para:362716.1.1,362744.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 362808 [para:362726.1.1,362730.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 362816 [para:362774.1.2,362730.1.2.2] equal(X,multiply(inverse(sk_c6),multiply(sk_c5,X))).
% 362819 [para:362808.1.2,362631.1.1.1,demod:362816] equal(multiply(sk_c7,X),X).
% 362820 [para:362819.1.1,362704.1.1] equal(sk_c3,identity).
% 362823 [para:362819.1.1,362787.1.2] equal(sk_c6,sk_c7).
% 362825 [para:362820.1.1,362780.1.1.1,demod:362629] equal(sk_c5,sk_c7).
% 362827 [para:362823.1.1,362632.1.1.1,demod:362819,cut:362825] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c5),sk_c7) | -equal(inverse(U),sk_c5).
% Split part used next: -equal(inverse(sk_c7),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,74,0,0,863,50,8,902,0,8,2405,50,32,2444,0,32,4304,50,64,4343,0,64,6385,50,91,6424,0,91,8649,50,125,8688,0,125,11185,50,172,11224,0,172,13994,50,240,14033,0,240,17165,50,353,17204,0,353,20698,50,547,20737,0,547,24683,50,836,24683,40,836,24722,0,836,35612,3,1137,36348,4,1287,37044,5,1437,37044,1,1437,37044,50,1437,37044,40,1437,37083,0,1437,37366,3,1751,37375,4,1895,37388,5,2038,37388,1,2038,37388,50,2038,37388,40,2038,37427,0,2038,64830,3,3539,65304,4,4289,65721,1,5039,65721,50,5040,65721,40,5040,65760,0,5040,84884,3,5791,85466,4,6166,86050,5,6541,86051,1,6541,86051,50,6542,86051,40,6542,86090,0,6542,100193,3,7601,100368,4,7668,101040,1,8043,101040,50,8043,101040,40,8043,101079,0,8043,158943,3,11946,159910,4,13894,161045,1,15844,161045,50,15846,161045,40,15846,161084,0,15846,210928,3,18399,211628,4,19672,212114,1,20947,212114,50,20949,212114,40,20949,212153,0,20949,263190,3,22450,263723,4,23201,264315,5,23950,264316,1,23950,264316,50,23951,264316,40,23951,264355,0,23952,273259,3,24712,274860,4,25078,275759,5,25453,275759,1,25453,275759,50,25453,275759,40,25453,275798,0,25453,324517,3,26654,324958,4,27254,325302,1,27854,325302,50,27856,325302,40,27856,325341,0,27856,359665,3,28607,360039,4,28982,360276,1,29357,360276,50,29358,360276,40,29358,360276,40,29358,360311,0,29358,360357,50,29358,360357,30,29358,360357,40,29358,360392,0,29358,360483,50,29358,360518,0,29363,360658,50,29364,360658,30,29364,360658,40,29364,360693,0,29364,360855,50,29365,360855,30,29365,360855,40,29365,360890,0,29365,360983,50,29365,361018,0,29370,361161,50,29372,361196,0,29372,361347,50,29375,361382,0,29380,361541,50,29385,361576,0,29385,361741,50,29394,361776,0,29394,361949,50,29409,361984,0,29413,362165,50,29442,362200,0,29442,362391,50,29503,362426,0,29503,362627,50,29618,362627,40,29618,362662,0,29618,362826,50,29618,362826,30,29618,362826,40,29618,362861,0,29619)
%
%
% START OF PROOF
% 362828 [] equal(multiply(identity,X),X).
% 362829 [] equal(multiply(inverse(X),X),identity).
% 362830 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 362831 [] -equal(inverse(sk_c7),sk_c5).
% 362850 [?] ?
% 362851 [?] ?
% 362852 [?] ?
% 362853 [?] ?
% 362854 [?] ?
% 362855 [?] ?
% 362865 [input:362850,cut:362831] equal(inverse(sk_c4),sk_c5).
% 362866 [para:362865.1.1,362829.1.1.1] equal(multiply(sk_c5,sk_c4),identity).
% 362867 [input:362853,cut:362831] equal(inverse(sk_c3),sk_c7).
% 362868 [para:362867.1.1,362829.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 362877 [input:362851,cut:362831] equal(multiply(sk_c4,sk_c5),sk_c7).
% 362878 [input:362852,cut:362831] equal(multiply(sk_c3,sk_c6),sk_c7).
% 362879 [input:362854,cut:362831] equal(multiply(sk_c5,sk_c7),sk_c6).
% 362880 [input:362855,cut:362831] equal(multiply(sk_c6,sk_c7),sk_c5).
% 362894 [para:362829.1.1,362830.1.1.1,demod:362828] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 362895 [para:362866.1.1,362830.1.1.1,demod:362828] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 362896 [para:362868.1.1,362830.1.1.1,demod:362828] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 362897 [para:362877.1.1,362830.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c4,multiply(sk_c5,X))).
% 362900 [para:362880.1.1,362830.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c6,multiply(sk_c7,X))).
% 362901 [para:362877.1.1,362895.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c7)).
% 362902 [para:362901.1.2,362879.1.1] equal(sk_c5,sk_c6).
% 362905 [para:362866.1.1,362894.1.2.2] equal(sk_c4,multiply(inverse(sk_c5),identity)).
% 362909 [para:362879.1.1,362894.1.2.2] equal(sk_c7,multiply(inverse(sk_c5),sk_c6)).
% 362911 [para:362895.1.2,362894.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c5),X)).
% 362912 [para:362901.1.2,362894.1.2.2,demod:362911] equal(sk_c7,multiply(sk_c4,sk_c5)).
% 362914 [para:362878.1.1,362896.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 362921 [para:362895.1.2,362897.1.2.2] equal(multiply(sk_c7,multiply(sk_c4,X)),multiply(sk_c4,X)).
% 362922 [para:362901.1.2,362897.1.2.2,demod:362912,362914] equal(sk_c6,sk_c7).
% 362925 [para:362922.1.1,362880.1.1.1,demod:362914] equal(sk_c6,sk_c5).
% 362926 [para:362922.1.1,362902.1.2] equal(sk_c5,sk_c7).
% 362927 [para:362922.1.1,362925.1.1] equal(sk_c7,sk_c5).
% 362930 [para:362926.1.1,362895.1.2.1,demod:362921] equal(X,multiply(sk_c4,X)).
% 362931 [para:362927.1.2,362895.1.2.1,demod:362930] equal(X,multiply(sk_c7,X)).
% 362932 [para:362930.1.2,362895.1.2.2] equal(X,multiply(sk_c5,X)).
% 362942 [para:362900.1.2,362894.1.2.2,demod:362932,362931] equal(X,multiply(inverse(sk_c6),X)).
% 362945 [para:362942.1.2,362829.1.1] equal(sk_c6,identity).
% 362951 [para:362945.1.1,362909.1.2.2,demod:362905] equal(sk_c7,sk_c4).
% 362952 [para:362951.1.2,362865.1.1.1,cut:362831] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c5),sk_c7) | -equal(inverse(U),sk_c5).
% Split part used next: -equal(multiply(sk_c6,sk_c7),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,74,0,0,863,50,8,902,0,8,2405,50,32,2444,0,32,4304,50,64,4343,0,64,6385,50,91,6424,0,91,8649,50,125,8688,0,125,11185,50,172,11224,0,172,13994,50,240,14033,0,240,17165,50,353,17204,0,353,20698,50,547,20737,0,547,24683,50,836,24683,40,836,24722,0,836,35612,3,1137,36348,4,1287,37044,5,1437,37044,1,1437,37044,50,1437,37044,40,1437,37083,0,1437,37366,3,1751,37375,4,1895,37388,5,2038,37388,1,2038,37388,50,2038,37388,40,2038,37427,0,2038,64830,3,3539,65304,4,4289,65721,1,5039,65721,50,5040,65721,40,5040,65760,0,5040,84884,3,5791,85466,4,6166,86050,5,6541,86051,1,6541,86051,50,6542,86051,40,6542,86090,0,6542,100193,3,7601,100368,4,7668,101040,1,8043,101040,50,8043,101040,40,8043,101079,0,8043,158943,3,11946,159910,4,13894,161045,1,15844,161045,50,15846,161045,40,15846,161084,0,15846,210928,3,18399,211628,4,19672,212114,1,20947,212114,50,20949,212114,40,20949,212153,0,20949,263190,3,22450,263723,4,23201,264315,5,23950,264316,1,23950,264316,50,23951,264316,40,23951,264355,0,23952,273259,3,24712,274860,4,25078,275759,5,25453,275759,1,25453,275759,50,25453,275759,40,25453,275798,0,25453,324517,3,26654,324958,4,27254,325302,1,27854,325302,50,27856,325302,40,27856,325341,0,27856,359665,3,28607,360039,4,28982,360276,1,29357,360276,50,29358,360276,40,29358,360276,40,29358,360311,0,29358,360357,50,29358,360357,30,29358,360357,40,29358,360392,0,29358,360483,50,29358,360518,0,29363,360658,50,29364,360658,30,29364,360658,40,29364,360693,0,29364,360855,50,29365,360855,30,29365,360855,40,29365,360890,0,29365,360983,50,29365,361018,0,29370,361161,50,29372,361196,0,29372,361347,50,29375,361382,0,29380,361541,50,29385,361576,0,29385,361741,50,29394,361776,0,29394,361949,50,29409,361984,0,29413,362165,50,29442,362200,0,29442,362391,50,29503,362426,0,29503,362627,50,29618,362627,40,29618,362662,0,29618,362826,50,29618,362826,30,29618,362826,40,29618,362861,0,29619,362951,50,29619,362951,30,29619,362951,40,29619,362986,0,29624,363075,50,29624,363110,0,29624,363248,50,29626,363283,0,29626,363429,50,29629,363464,0,29634,363617,50,29639,363652,0,29639,363812,50,29648,363847,0,29652,364015,50,29668,364050,0,29668,364227,50,29698,364262,0,29698,364449,50,29762,364484,0,29762,364682,50,29885,364682,40,29885,364717,0,29885)
%
%
% START OF PROOF
% 364570 [?] ?
% 364684 [] equal(multiply(identity,X),X).
% 364685 [] equal(multiply(inverse(X),X),identity).
% 364686 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 364687 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 364693 [?] ?
% 364698 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 364704 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 364711 [?] ?
% 364716 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 364736 [input:364693,cut:364687] equal(inverse(sk_c1),sk_c7).
% 364737 [para:364736.1.1,364685.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 364753 [input:364711,cut:364687] equal(inverse(sk_c7),sk_c5).
% 364754 [para:364753.1.1,364685.1.1.1] equal(multiply(sk_c5,sk_c7),identity).
% 364765 [para:364698.2.1,364754.1.1] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(sk_c6,identity).
% 364768 [para:364765.2.1,364687.1.1.1,demod:364684,cut:364570] equal(multiply(sk_c1,sk_c7),sk_c2).
% 364776 [para:364704.2.1,364754.1.1] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(sk_c6,identity).
% 364779 [para:364776.2.1,364687.1.1.1,demod:364684,cut:364570] equal(multiply(sk_c7,sk_c2),sk_c6).
% 364783 [para:364716.2.1,364754.1.1] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(sk_c6,identity).
% 364786 [para:364783.2.1,364687.1.1.1,demod:364684,cut:364570] equal(multiply(sk_c6,sk_c5),sk_c7).
% 364788 [para:364737.1.1,364686.1.1.1,demod:364684] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 364789 [para:364754.1.1,364686.1.1.1,demod:364684] equal(X,multiply(sk_c5,multiply(sk_c7,X))).
% 364793 [para:364768.1.1,364788.1.2.2,demod:364779] equal(sk_c7,sk_c6).
% 364795 [para:364793.1.2,364786.1.1.1] equal(multiply(sk_c7,sk_c5),sk_c7).
% 364800 [para:364795.1.1,364789.1.2.2,demod:364754] equal(sk_c5,identity).
% 364802 [para:364800.1.1,364754.1.1.1,demod:364684] equal(sk_c7,identity).
% 364803 [para:364800.1.1,364786.1.1.2] equal(multiply(sk_c6,identity),sk_c7).
% 364807 [para:364802.1.1,364687.1.1.2,demod:364803,cut:364570] 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_c6,sk_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(multiply(U,sk_c5),sk_c7) | -equal(inverse(U),sk_c5).
% Split part used next: -equal(multiply(sk_c5,sk_c7),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,74,0,0,863,50,8,902,0,8,2405,50,32,2444,0,32,4304,50,64,4343,0,64,6385,50,91,6424,0,91,8649,50,125,8688,0,125,11185,50,172,11224,0,172,13994,50,240,14033,0,240,17165,50,353,17204,0,353,20698,50,547,20737,0,547,24683,50,836,24683,40,836,24722,0,836,35612,3,1137,36348,4,1287,37044,5,1437,37044,1,1437,37044,50,1437,37044,40,1437,37083,0,1437,37366,3,1751,37375,4,1895,37388,5,2038,37388,1,2038,37388,50,2038,37388,40,2038,37427,0,2038,64830,3,3539,65304,4,4289,65721,1,5039,65721,50,5040,65721,40,5040,65760,0,5040,84884,3,5791,85466,4,6166,86050,5,6541,86051,1,6541,86051,50,6542,86051,40,6542,86090,0,6542,100193,3,7601,100368,4,7668,101040,1,8043,101040,50,8043,101040,40,8043,101079,0,8043,158943,3,11946,159910,4,13894,161045,1,15844,161045,50,15846,161045,40,15846,161084,0,15846,210928,3,18399,211628,4,19672,212114,1,20947,212114,50,20949,212114,40,20949,212153,0,20949,263190,3,22450,263723,4,23201,264315,5,23950,264316,1,23950,264316,50,23951,264316,40,23951,264355,0,23952,273259,3,24712,274860,4,25078,275759,5,25453,275759,1,25453,275759,50,25453,275759,40,25453,275798,0,25453,324517,3,26654,324958,4,27254,325302,1,27854,325302,50,27856,325302,40,27856,325341,0,27856,359665,3,28607,360039,4,28982,360276,1,29357,360276,50,29358,360276,40,29358,360276,40,29358,360311,0,29358,360357,50,29358,360357,30,29358,360357,40,29358,360392,0,29358,360483,50,29358,360518,0,29363,360658,50,29364,360658,30,29364,360658,40,29364,360693,0,29364,360855,50,29365,360855,30,29365,360855,40,29365,360890,0,29365,360983,50,29365,361018,0,29370,361161,50,29372,361196,0,29372,361347,50,29375,361382,0,29380,361541,50,29385,361576,0,29385,361741,50,29394,361776,0,29394,361949,50,29409,361984,0,29413,362165,50,29442,362200,0,29442,362391,50,29503,362426,0,29503,362627,50,29618,362627,40,29618,362662,0,29618,362826,50,29618,362826,30,29618,362826,40,29618,362861,0,29619,362951,50,29619,362951,30,29619,362951,40,29619,362986,0,29624,363075,50,29624,363110,0,29624,363248,50,29626,363283,0,29626,363429,50,29629,363464,0,29634,363617,50,29639,363652,0,29639,363812,50,29648,363847,0,29652,364015,50,29668,364050,0,29668,364227,50,29698,364262,0,29698,364449,50,29762,364484,0,29762,364682,50,29885,364682,40,29885,364717,0,29885,364806,50,29885,364806,30,29885,364806,40,29885,364841,0,29885,364930,50,29886,364965,0,29890,365103,50,29892,365138,0,29892,365284,50,29895,365319,0,29895,365472,50,29900,365507,0,29905,365667,50,29913,365702,0,29914,365870,50,29929,365905,0,29934,366082,50,29964,366117,0,29964,366304,50,30027,366339,0,30028,366537,50,30149,366537,40,30149,366572,0,30150)
%
%
% START OF PROOF
% 366431 [?] ?
% 366540 [] equal(multiply(inverse(X),X),identity).
% 366542 [] -equal(multiply(sk_c5,sk_c7),sk_c6).
% 366565 [?] ?
% 366605 [input:366565,cut:366542] equal(inverse(sk_c7),sk_c5).
% 366606 [para:366605.1.1,366540.1.1.1] equal(multiply(sk_c5,sk_c7),identity).
% 366607 [para:366606.1.1,366542.1.1,cut:366431] 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: 29181
% derived clauses: 5583642
% kept clauses: 311081
% kept size sum: 33180
% kept mid-nuclei: 18244
% kept new demods: 4958
% forw unit-subs: 2231821
% forw double-subs: 2608529
% forw overdouble-subs: 371461
% backward subs: 11337
% fast unit cutoff: 24895
% full unit cutoff: 0
% dbl unit cutoff: 10481
% real runtime : 304.13
% process. runtime: 301.50
% specific non-discr-tree subsumption statistics:
% tried: 41178639
% length fails: 4179835
% strength fails: 9336221
% predlist fails: 1486664
% aux str. fails: 6409250
% by-lit fails: 9682987
% full subs tried: 2280549
% full subs fail: 2127777
%
% ; 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/GRP361-1+eq_r.in")
%
%------------------------------------------------------------------------------