TSTP Solution File: GRP208-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP208-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art08.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 298.3s
% Output : Assurance 298.3s
% 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/GRP208-1+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 31)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 31)
% (binary-posweight-lex-big-order 30 #f 3 31)
% (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(X,Y),sk_c12) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c11),sk_c12) | -equal(multiply(sk_c12,Z),sk_c11) | -equal(multiply(U,sk_c12),Z) | -equal(inverse(U),sk_c12) | -equal(multiply(V,W),sk_c12) | -equal(inverse(V),W) | -equal(multiply(W,sk_c11),sk_c12) | -equal(inverse(X1),sk_c12) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(multiply(X2,X3),sk_c11) | -equal(inverse(X2),X3) | -equal(multiply(X3,sk_c12),sk_c11) | -equal(inverse(X4),sk_c11) | -equal(multiply(X4,sk_c12),sk_c11).
% was split for some strategies as:
% -equal(inverse(X4),sk_c11) | -equal(multiply(X4,sk_c12),sk_c11).
% -equal(multiply(X2,X3),sk_c11) | -equal(inverse(X2),X3) | -equal(multiply(X3,sk_c12),sk_c11).
% -equal(inverse(X1),sk_c12) | -equal(multiply(X1,sk_c11),sk_c12).
% -equal(multiply(V,W),sk_c12) | -equal(inverse(V),W) | -equal(multiply(W,sk_c11),sk_c12).
% -equal(multiply(sk_c12,Z),sk_c11) | -equal(multiply(U,sk_c12),Z) | -equal(inverse(U),sk_c12).
% -equal(multiply(X,Y),sk_c12) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c11),sk_c12).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,Y),sk_c12) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c11),sk_c12) | -equal(multiply(sk_c12,Z),sk_c11) | -equal(multiply(U,sk_c12),Z) | -equal(inverse(U),sk_c12) | -equal(multiply(V,W),sk_c12) | -equal(inverse(V),W) | -equal(multiply(W,sk_c11),sk_c12) | -equal(inverse(X1),sk_c12) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(multiply(X2,X3),sk_c11) | -equal(inverse(X2),X3) | -equal(multiply(X3,sk_c12),sk_c11) | -equal(inverse(X4),sk_c11) | -equal(multiply(X4,sk_c12),sk_c11).
% Split part used next: -equal(inverse(X4),sk_c11) | -equal(multiply(X4,sk_c12),sk_c11).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,137,0,0,317219,5,1501,317220,1,1501,317220,50,1501,317220,40,1501,317292,0,1501,317783,5,2103,317784,1,2103,317784,50,2103,317784,40,2103,317856,0,2103,318346,5,2705,318347,1,2705,318347,50,2705,318347,40,2705,318419,0,2705,337590,3,4206,338289,4,4956,339079,5,5706,339080,1,5706,339080,50,5706,339080,40,5706,339152,0,5706,352133,3,6457,353035,4,6832,353673,1,7207,353673,50,7207,353673,40,7207,353745,0,7207,357525,5,8708,357527,1,8708,357527,50,8708,357527,40,8708,357599,0,8708,407596,3,12612,408911,4,14559,409953,1,16509,409953,50,16511,409953,40,16511,410025,0,16511,449078,3,19066,450161,4,20337,451247,5,21612,451248,1,21612,451248,50,21613,451248,40,21613,451320,0,21613,486950,3,23114,487636,4,23864,488492,5,24614,488493,1,24614,488493,50,24615,488493,40,24615,488565,0,24615,493248,3,26094,493248,4,26094,493412,5,26119,493412,1,26119,493412,50,26119,493412,40,26119,493484,0,26119,515021,3,27320,515714,4,27920,516243,1,28520,516243,50,28520,516243,40,28520,516315,0,28521,533623,3,29272,534277,4,29647,534645,1,30022,534645,50,30022,534645,40,30022,534645,40,30022,534710,0,30022,534815,50,30023,534880,0,30023,535045,50,30026,535110,0,30030,535286,50,30033,535351,0,30034)
%
%
% START OF PROOF
% 535288 [] equal(multiply(identity,X),X).
% 535289 [] equal(multiply(inverse(X),X),identity).
% 535290 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 535291 [] -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c11).
% 535292 [?] ?
% 535293 [] equal(inverse(sk_c3),sk_c12) | equal(inverse(sk_c10),sk_c11).
% 535302 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(multiply(sk_c10,sk_c12),sk_c11).
% 535303 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(inverse(sk_c10),sk_c11).
% 535312 [] equal(multiply(sk_c12,sk_c4),sk_c11) | equal(multiply(sk_c10,sk_c12),sk_c11).
% 535313 [] equal(multiply(sk_c12,sk_c4),sk_c11) | equal(inverse(sk_c10),sk_c11).
% 535322 [] equal(multiply(sk_c2,sk_c11),sk_c12) | equal(multiply(sk_c10,sk_c12),sk_c11).
% 535323 [] equal(multiply(sk_c2,sk_c11),sk_c12) | equal(inverse(sk_c10),sk_c11).
% 535332 [?] ?
% 535333 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c10),sk_c11).
% 535342 [] equal(multiply(sk_c1,sk_c2),sk_c12) | equal(multiply(sk_c10,sk_c12),sk_c11).
% 535343 [] equal(multiply(sk_c1,sk_c2),sk_c12) | equal(inverse(sk_c10),sk_c11).
% 535354 [hyper:535291,535293,binarycut:535292] equal(inverse(sk_c3),sk_c12).
% 535355 [para:535354.1.1,535289.1.1.1] equal(multiply(sk_c12,sk_c3),identity).
% 535359 [hyper:535291,535333,binarycut:535332] equal(inverse(sk_c1),sk_c2).
% 535363 [para:535359.1.1,535289.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 535366 [hyper:535291,535303,535302] equal(multiply(sk_c3,sk_c12),sk_c4).
% 535372 [hyper:535291,535313,535312] equal(multiply(sk_c12,sk_c4),sk_c11).
% 535378 [hyper:535291,535323,535322] equal(multiply(sk_c2,sk_c11),sk_c12).
% 535387 [hyper:535291,535342,535343] equal(multiply(sk_c1,sk_c2),sk_c12).
% 535388 [para:535289.1.1,535290.1.1.1,demod:535288] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 535389 [para:535355.1.1,535290.1.1.1,demod:535288] equal(X,multiply(sk_c12,multiply(sk_c3,X))).
% 535390 [para:535363.1.1,535290.1.1.1,demod:535288] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 535391 [para:535366.1.1,535290.1.1.1] equal(multiply(sk_c4,X),multiply(sk_c3,multiply(sk_c12,X))).
% 535394 [para:535387.1.1,535290.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c1,multiply(sk_c2,X))).
% 535395 [para:535366.1.1,535389.1.2.2,demod:535372] equal(sk_c12,sk_c11).
% 535396 [para:535395.1.2,535378.1.1.2] equal(multiply(sk_c2,sk_c12),sk_c12).
% 535397 [para:535396.1.1,535290.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c2,multiply(sk_c12,X))).
% 535398 [para:535387.1.1,535390.1.2.2,demod:535396] equal(sk_c2,sk_c12).
% 535400 [para:535289.1.1,535388.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 535401 [para:535355.1.1,535388.1.2.2] equal(sk_c3,multiply(inverse(sk_c12),identity)).
% 535402 [para:535363.1.1,535388.1.2.2] equal(sk_c1,multiply(inverse(sk_c2),identity)).
% 535403 [para:535372.1.1,535388.1.2.2] equal(sk_c4,multiply(inverse(sk_c12),sk_c11)).
% 535404 [para:535378.1.1,535388.1.2.2] equal(sk_c11,multiply(inverse(sk_c2),sk_c12)).
% 535405 [para:535290.1.1,535388.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 535408 [para:535388.1.2,535388.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 535409 [para:535398.1.1,535363.1.1.1] equal(multiply(sk_c12,sk_c1),identity).
% 535410 [para:535398.1.1,535378.1.1.1] equal(multiply(sk_c12,sk_c11),sk_c12).
% 535413 [para:535398.1.1,535390.1.2.1] equal(X,multiply(sk_c12,multiply(sk_c1,X))).
% 535418 [para:535409.1.1,535388.1.2.2,demod:535401] equal(sk_c1,sk_c3).
% 535427 [para:535410.1.1,535391.1.2.2,demod:535366] equal(multiply(sk_c4,sk_c11),sk_c4).
% 535436 [para:535394.1.2,535390.1.2.2,demod:535397] equal(multiply(sk_c2,X),multiply(sk_c12,X)).
% 535437 [para:535390.1.2,535394.1.2.2,demod:535413] equal(X,multiply(sk_c1,X)).
% 535439 [para:535437.1.2,535390.1.2.2,demod:535436] equal(X,multiply(sk_c12,X)).
% 535440 [para:535418.1.1,535437.1.2.1] equal(X,multiply(sk_c3,X)).
% 535446 [para:535427.1.1,535388.1.2.2,demod:535289] equal(sk_c11,identity).
% 535447 [para:535446.1.1,535378.1.1.2,demod:535439,535436] equal(identity,sk_c12).
% 535451 [para:535446.1.1,535403.1.2.2,demod:535401] equal(sk_c4,sk_c3).
% 535452 [para:535451.1.2,535354.1.1.1] equal(inverse(sk_c4),sk_c12).
% 535454 [para:535447.1.2,535404.1.2.2,demod:535402] equal(sk_c11,sk_c1).
% 535455 [para:535454.1.2,535359.1.1.1] equal(inverse(sk_c11),sk_c2).
% 535487 [para:535408.1.2,535289.1.1] equal(multiply(X,inverse(X)),identity).
% 535489 [para:535408.1.2,535400.1.2] equal(X,multiply(X,identity)).
% 535491 [para:535489.1.2,535400.1.2] equal(X,inverse(inverse(X))).
% 535498 [para:535487.1.1,535405.1.2.2.2,demod:535489] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 535501 [para:535389.1.2,535498.1.2.1.1,demod:535440] equal(inverse(X),multiply(inverse(X),sk_c12)).
% 535506 [para:535427.1.1,535498.1.2.1.1,demod:535372,535452,535455] equal(sk_c2,sk_c11).
% 535518 [para:535501.1.2,535408.1.2,demod:535491] equal(multiply(X,sk_c12),X).
% 535519 [hyper:535291,535518,demod:535455,cut:535506] 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 31
% clause depth limited to 6
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,Y),sk_c12) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c11),sk_c12) | -equal(multiply(sk_c12,Z),sk_c11) | -equal(multiply(U,sk_c12),Z) | -equal(inverse(U),sk_c12) | -equal(multiply(V,W),sk_c12) | -equal(inverse(V),W) | -equal(multiply(W,sk_c11),sk_c12) | -equal(inverse(X1),sk_c12) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(multiply(X2,X3),sk_c11) | -equal(inverse(X2),X3) | -equal(multiply(X3,sk_c12),sk_c11) | -equal(inverse(X4),sk_c11) | -equal(multiply(X4,sk_c12),sk_c11).
% Split part used next: -equal(multiply(X2,X3),sk_c11) | -equal(inverse(X2),X3) | -equal(multiply(X3,sk_c12),sk_c11).
% 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,137,0,0,317219,5,1501,317220,1,1501,317220,50,1501,317220,40,1501,317292,0,1501,317783,5,2103,317784,1,2103,317784,50,2103,317784,40,2103,317856,0,2103,318346,5,2705,318347,1,2705,318347,50,2705,318347,40,2705,318419,0,2705,337590,3,4206,338289,4,4956,339079,5,5706,339080,1,5706,339080,50,5706,339080,40,5706,339152,0,5706,352133,3,6457,353035,4,6832,353673,1,7207,353673,50,7207,353673,40,7207,353745,0,7207,357525,5,8708,357527,1,8708,357527,50,8708,357527,40,8708,357599,0,8708,407596,3,12612,408911,4,14559,409953,1,16509,409953,50,16511,409953,40,16511,410025,0,16511,449078,3,19066,450161,4,20337,451247,5,21612,451248,1,21612,451248,50,21613,451248,40,21613,451320,0,21613,486950,3,23114,487636,4,23864,488492,5,24614,488493,1,24614,488493,50,24615,488493,40,24615,488565,0,24615,493248,3,26094,493248,4,26094,493412,5,26119,493412,1,26119,493412,50,26119,493412,40,26119,493484,0,26119,515021,3,27320,515714,4,27920,516243,1,28520,516243,50,28520,516243,40,28520,516315,0,28521,533623,3,29272,534277,4,29647,534645,1,30022,534645,50,30022,534645,40,30022,534645,40,30022,534710,0,30022,534815,50,30023,534880,0,30023,535045,50,30026,535110,0,30030,535286,50,30033,535351,0,30034,535518,50,30035,535518,30,30035,535518,40,30035,535583,0,30040)
%
%
% START OF PROOF
% 535520 [] equal(multiply(identity,X),X).
% 535521 [] equal(multiply(inverse(X),X),identity).
% 535522 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 535523 [] -equal(multiply(X,sk_c12),sk_c11) | -equal(multiply(Y,X),sk_c11) | -equal(inverse(Y),X).
% 535526 [?] ?
% 535527 [] equal(inverse(sk_c3),sk_c12) | equal(inverse(sk_c8),sk_c9).
% 535528 [?] ?
% 535536 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(multiply(sk_c9,sk_c12),sk_c11).
% 535537 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(inverse(sk_c8),sk_c9).
% 535538 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(multiply(sk_c8,sk_c9),sk_c11).
% 535546 [] equal(multiply(sk_c12,sk_c4),sk_c11) | equal(multiply(sk_c9,sk_c12),sk_c11).
% 535547 [] equal(multiply(sk_c12,sk_c4),sk_c11) | equal(inverse(sk_c8),sk_c9).
% 535548 [] equal(multiply(sk_c12,sk_c4),sk_c11) | equal(multiply(sk_c8,sk_c9),sk_c11).
% 535556 [] equal(multiply(sk_c2,sk_c11),sk_c12) | equal(multiply(sk_c9,sk_c12),sk_c11).
% 535557 [] equal(multiply(sk_c2,sk_c11),sk_c12) | equal(inverse(sk_c8),sk_c9).
% 535558 [] equal(multiply(sk_c2,sk_c11),sk_c12) | equal(multiply(sk_c8,sk_c9),sk_c11).
% 535566 [?] ?
% 535567 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c8),sk_c9).
% 535568 [?] ?
% 535576 [] equal(multiply(sk_c1,sk_c2),sk_c12) | equal(multiply(sk_c9,sk_c12),sk_c11).
% 535577 [] equal(multiply(sk_c1,sk_c2),sk_c12) | equal(inverse(sk_c8),sk_c9).
% 535578 [] equal(multiply(sk_c1,sk_c2),sk_c12) | equal(multiply(sk_c8,sk_c9),sk_c11).
% 535592 [hyper:535523,535527,binarycut:535528,binarycut:535526] equal(inverse(sk_c3),sk_c12).
% 535595 [para:535592.1.1,535521.1.1.1] equal(multiply(sk_c12,sk_c3),identity).
% 535610 [hyper:535523,535567,binarycut:535568,binarycut:535566] equal(inverse(sk_c1),sk_c2).
% 535613 [para:535610.1.1,535521.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 535651 [hyper:535523,535538,535536,535537] equal(multiply(sk_c3,sk_c12),sk_c4).
% 535688 [hyper:535523,535548,535546,535547] equal(multiply(sk_c12,sk_c4),sk_c11).
% 535718 [hyper:535523,535558,535556,535557] equal(multiply(sk_c2,sk_c11),sk_c12).
% 535733 [hyper:535523,535578,535576,535577] equal(multiply(sk_c1,sk_c2),sk_c12).
% 535735 [para:535595.1.1,535522.1.1.1,demod:535520] equal(X,multiply(sk_c12,multiply(sk_c3,X))).
% 535736 [para:535613.1.1,535522.1.1.1,demod:535520] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 535740 [para:535733.1.1,535522.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c1,multiply(sk_c2,X))).
% 535743 [para:535651.1.1,535735.1.2.2,demod:535688] equal(sk_c12,sk_c11).
% 535744 [para:535743.1.2,535718.1.1.2] equal(multiply(sk_c2,sk_c12),sk_c12).
% 535745 [para:535744.1.1,535522.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c2,multiply(sk_c12,X))).
% 535748 [para:535733.1.1,535736.1.2.2,demod:535744] equal(sk_c2,sk_c12).
% 535761 [para:535748.1.1,535744.1.1.1] equal(multiply(sk_c12,sk_c12),sk_c12).
% 535762 [para:535748.1.1,535736.1.2.1] equal(X,multiply(sk_c12,multiply(sk_c1,X))).
% 535785 [para:535740.1.2,535736.1.2.2,demod:535745] equal(multiply(sk_c2,X),multiply(sk_c12,X)).
% 535786 [para:535736.1.2,535740.1.2.2,demod:535762] equal(X,multiply(sk_c1,X)).
% 535790 [para:535786.1.2,535736.1.2.2,demod:535785] equal(X,multiply(sk_c12,X)).
% 535794 [para:535790.1.2,535595.1.1] equal(sk_c3,identity).
% 535797 [para:535794.1.1,535592.1.1.1] equal(inverse(identity),sk_c12).
% 535799 [hyper:535523,535797,demod:535761,535520,cut:535743,cut:535743] 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,Y),sk_c12) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c11),sk_c12) | -equal(multiply(sk_c12,Z),sk_c11) | -equal(multiply(U,sk_c12),Z) | -equal(inverse(U),sk_c12) | -equal(multiply(V,W),sk_c12) | -equal(inverse(V),W) | -equal(multiply(W,sk_c11),sk_c12) | -equal(inverse(X1),sk_c12) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(multiply(X2,X3),sk_c11) | -equal(inverse(X2),X3) | -equal(multiply(X3,sk_c12),sk_c11) | -equal(inverse(X4),sk_c11) | -equal(multiply(X4,sk_c12),sk_c11).
% Split part used next: -equal(inverse(X1),sk_c12) | -equal(multiply(X1,sk_c11),sk_c12).
% 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,137,0,0,317219,5,1501,317220,1,1501,317220,50,1501,317220,40,1501,317292,0,1501,317783,5,2103,317784,1,2103,317784,50,2103,317784,40,2103,317856,0,2103,318346,5,2705,318347,1,2705,318347,50,2705,318347,40,2705,318419,0,2705,337590,3,4206,338289,4,4956,339079,5,5706,339080,1,5706,339080,50,5706,339080,40,5706,339152,0,5706,352133,3,6457,353035,4,6832,353673,1,7207,353673,50,7207,353673,40,7207,353745,0,7207,357525,5,8708,357527,1,8708,357527,50,8708,357527,40,8708,357599,0,8708,407596,3,12612,408911,4,14559,409953,1,16509,409953,50,16511,409953,40,16511,410025,0,16511,449078,3,19066,450161,4,20337,451247,5,21612,451248,1,21612,451248,50,21613,451248,40,21613,451320,0,21613,486950,3,23114,487636,4,23864,488492,5,24614,488493,1,24614,488493,50,24615,488493,40,24615,488565,0,24615,493248,3,26094,493248,4,26094,493412,5,26119,493412,1,26119,493412,50,26119,493412,40,26119,493484,0,26119,515021,3,27320,515714,4,27920,516243,1,28520,516243,50,28520,516243,40,28520,516315,0,28521,533623,3,29272,534277,4,29647,534645,1,30022,534645,50,30022,534645,40,30022,534645,40,30022,534710,0,30022,534815,50,30023,534880,0,30023,535045,50,30026,535110,0,30030,535286,50,30033,535351,0,30034,535518,50,30035,535518,30,30035,535518,40,30035,535583,0,30040,535798,50,30040,535798,30,30040,535798,40,30040,535863,0,30040)
%
%
% START OF PROOF
% 535800 [] equal(multiply(identity,X),X).
% 535801 [] equal(multiply(inverse(X),X),identity).
% 535802 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 535803 [] -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c12).
% 535809 [?] ?
% 535810 [] equal(inverse(sk_c3),sk_c12) | equal(inverse(sk_c7),sk_c12).
% 535819 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(multiply(sk_c7,sk_c11),sk_c12).
% 535820 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(inverse(sk_c7),sk_c12).
% 535829 [] equal(multiply(sk_c12,sk_c4),sk_c11) | equal(multiply(sk_c7,sk_c11),sk_c12).
% 535830 [] equal(multiply(sk_c12,sk_c4),sk_c11) | equal(inverse(sk_c7),sk_c12).
% 535839 [] equal(multiply(sk_c2,sk_c11),sk_c12) | equal(multiply(sk_c7,sk_c11),sk_c12).
% 535840 [] equal(multiply(sk_c2,sk_c11),sk_c12) | equal(inverse(sk_c7),sk_c12).
% 535849 [?] ?
% 535850 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c7),sk_c12).
% 535859 [] equal(multiply(sk_c1,sk_c2),sk_c12) | equal(multiply(sk_c7,sk_c11),sk_c12).
% 535860 [] equal(multiply(sk_c1,sk_c2),sk_c12) | equal(inverse(sk_c7),sk_c12).
% 535872 [hyper:535803,535810,binarycut:535809] equal(inverse(sk_c3),sk_c12).
% 535875 [para:535872.1.1,535801.1.1.1] equal(multiply(sk_c12,sk_c3),identity).
% 535882 [hyper:535803,535850,binarycut:535849] equal(inverse(sk_c1),sk_c2).
% 535883 [para:535882.1.1,535801.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 535911 [hyper:535803,535819,535820] equal(multiply(sk_c3,sk_c12),sk_c4).
% 535926 [hyper:535803,535829,535830] equal(multiply(sk_c12,sk_c4),sk_c11).
% 535939 [hyper:535803,535839,535840] equal(multiply(sk_c2,sk_c11),sk_c12).
% 535948 [hyper:535803,535859,535860] equal(multiply(sk_c1,sk_c2),sk_c12).
% 535949 [para:535801.1.1,535802.1.1.1,demod:535800] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 535950 [para:535875.1.1,535802.1.1.1,demod:535800] equal(X,multiply(sk_c12,multiply(sk_c3,X))).
% 535951 [para:535883.1.1,535802.1.1.1,demod:535800] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 535955 [para:535948.1.1,535802.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c1,multiply(sk_c2,X))).
% 535956 [para:535911.1.1,535950.1.2.2,demod:535926] equal(sk_c12,sk_c11).
% 535957 [para:535956.1.2,535939.1.1.2] equal(multiply(sk_c2,sk_c12),sk_c12).
% 535958 [para:535957.1.1,535802.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c2,multiply(sk_c12,X))).
% 535959 [para:535948.1.1,535951.1.2.2,demod:535957] equal(sk_c2,sk_c12).
% 535961 [para:535875.1.1,535949.1.2.2] equal(sk_c3,multiply(inverse(sk_c12),identity)).
% 535965 [para:535950.1.2,535949.1.2.2] equal(multiply(sk_c3,X),multiply(inverse(sk_c12),X)).
% 535967 [para:535959.1.1,535883.1.1.1] equal(multiply(sk_c12,sk_c1),identity).
% 535968 [para:535959.1.1,535939.1.1.1] equal(multiply(sk_c12,sk_c11),sk_c12).
% 535969 [para:535959.1.1,535948.1.1.2] equal(multiply(sk_c1,sk_c12),sk_c12).
% 535971 [para:535959.1.1,535951.1.2.1] equal(X,multiply(sk_c12,multiply(sk_c1,X))).
% 535976 [para:535967.1.1,535949.1.2.2,demod:535961] equal(sk_c1,sk_c3).
% 535986 [para:535968.1.1,535949.1.2.2,demod:535911,535965] equal(sk_c11,sk_c4).
% 535989 [para:535976.1.1,535969.1.1.1,demod:535911] equal(sk_c4,sk_c12).
% 535990 [para:535989.1.1,535986.1.2] equal(sk_c11,sk_c12).
% 535996 [para:535955.1.2,535951.1.2.2,demod:535958] equal(multiply(sk_c2,X),multiply(sk_c12,X)).
% 535997 [para:535951.1.2,535955.1.2.2,demod:535971] equal(X,multiply(sk_c1,X)).
% 535999 [para:535997.1.2,535951.1.2.2,demod:535996] equal(X,multiply(sk_c12,X)).
% 536001 [para:535999.1.2,535875.1.1] equal(sk_c3,identity).
% 536004 [para:536001.1.1,535872.1.1.1] equal(inverse(identity),sk_c12).
% 536006 [hyper:535803,536004,demod:535800,cut:535990] 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 31
% 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(X,Y),sk_c12) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c11),sk_c12) | -equal(multiply(sk_c12,Z),sk_c11) | -equal(multiply(U,sk_c12),Z) | -equal(inverse(U),sk_c12) | -equal(multiply(V,W),sk_c12) | -equal(inverse(V),W) | -equal(multiply(W,sk_c11),sk_c12) | -equal(inverse(X1),sk_c12) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(multiply(X2,X3),sk_c11) | -equal(inverse(X2),X3) | -equal(multiply(X3,sk_c12),sk_c11) | -equal(inverse(X4),sk_c11) | -equal(multiply(X4,sk_c12),sk_c11).
% Split part used next: -equal(multiply(V,W),sk_c12) | -equal(inverse(V),W) | -equal(multiply(W,sk_c11),sk_c12).
% 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,137,0,0,317219,5,1501,317220,1,1501,317220,50,1501,317220,40,1501,317292,0,1501,317783,5,2103,317784,1,2103,317784,50,2103,317784,40,2103,317856,0,2103,318346,5,2705,318347,1,2705,318347,50,2705,318347,40,2705,318419,0,2705,337590,3,4206,338289,4,4956,339079,5,5706,339080,1,5706,339080,50,5706,339080,40,5706,339152,0,5706,352133,3,6457,353035,4,6832,353673,1,7207,353673,50,7207,353673,40,7207,353745,0,7207,357525,5,8708,357527,1,8708,357527,50,8708,357527,40,8708,357599,0,8708,407596,3,12612,408911,4,14559,409953,1,16509,409953,50,16511,409953,40,16511,410025,0,16511,449078,3,19066,450161,4,20337,451247,5,21612,451248,1,21612,451248,50,21613,451248,40,21613,451320,0,21613,486950,3,23114,487636,4,23864,488492,5,24614,488493,1,24614,488493,50,24615,488493,40,24615,488565,0,24615,493248,3,26094,493248,4,26094,493412,5,26119,493412,1,26119,493412,50,26119,493412,40,26119,493484,0,26119,515021,3,27320,515714,4,27920,516243,1,28520,516243,50,28520,516243,40,28520,516315,0,28521,533623,3,29272,534277,4,29647,534645,1,30022,534645,50,30022,534645,40,30022,534645,40,30022,534710,0,30022,534815,50,30023,534880,0,30023,535045,50,30026,535110,0,30030,535286,50,30033,535351,0,30034,535518,50,30035,535518,30,30035,535518,40,30035,535583,0,30040,535798,50,30040,535798,30,30040,535798,40,30040,535863,0,30040,536005,50,30040,536005,30,30040,536005,40,30040,536070,0,30045)
%
%
% START OF PROOF
% 536006 [] equal(X,X).
% 536010 [] -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,X),sk_c12) | -equal(inverse(Y),X).
% 536048 [] equal(multiply(sk_c2,sk_c11),sk_c12) | equal(multiply(sk_c6,sk_c11),sk_c12).
% 536049 [?] ?
% 536050 [] equal(multiply(sk_c2,sk_c11),sk_c12) | equal(multiply(sk_c5,sk_c6),sk_c12).
% 536058 [?] ?
% 536059 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c6).
% 536060 [?] ?
% 536068 [] equal(multiply(sk_c1,sk_c2),sk_c12) | equal(multiply(sk_c6,sk_c11),sk_c12).
% 536069 [?] ?
% 536070 [] equal(multiply(sk_c1,sk_c2),sk_c12) | equal(multiply(sk_c5,sk_c6),sk_c12).
% 536122 [hyper:536010,536059,binarycut:536069,binarycut:536049] equal(inverse(sk_c5),sk_c6).
% 536124 [hyper:536010,536059,binarycut:536060,binarycut:536058] equal(inverse(sk_c1),sk_c2).
% 536197 [hyper:536010,536050,536048,demod:536122,cut:536006] equal(multiply(sk_c2,sk_c11),sk_c12).
% 536217 [hyper:536010,536068,demod:536124,536197,cut:536006,cut:536006] equal(multiply(sk_c6,sk_c11),sk_c12).
% 536231 [hyper:536010,536070,demod:536124,536197,cut:536006,cut:536006] equal(multiply(sk_c5,sk_c6),sk_c12).
% 536233 [hyper:536010,536231,demod:536122,536217,cut:536006,cut:536006] 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,Y),sk_c12) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c11),sk_c12) | -equal(multiply(sk_c12,Z),sk_c11) | -equal(multiply(U,sk_c12),Z) | -equal(inverse(U),sk_c12) | -equal(multiply(V,W),sk_c12) | -equal(inverse(V),W) | -equal(multiply(W,sk_c11),sk_c12) | -equal(inverse(X1),sk_c12) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(multiply(X2,X3),sk_c11) | -equal(inverse(X2),X3) | -equal(multiply(X3,sk_c12),sk_c11) | -equal(inverse(X4),sk_c11) | -equal(multiply(X4,sk_c12),sk_c11).
% Split part used next: -equal(multiply(sk_c12,Z),sk_c11) | -equal(multiply(U,sk_c12),Z) | -equal(inverse(U),sk_c12).
% 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,137,0,0,317219,5,1501,317220,1,1501,317220,50,1501,317220,40,1501,317292,0,1501,317783,5,2103,317784,1,2103,317784,50,2103,317784,40,2103,317856,0,2103,318346,5,2705,318347,1,2705,318347,50,2705,318347,40,2705,318419,0,2705,337590,3,4206,338289,4,4956,339079,5,5706,339080,1,5706,339080,50,5706,339080,40,5706,339152,0,5706,352133,3,6457,353035,4,6832,353673,1,7207,353673,50,7207,353673,40,7207,353745,0,7207,357525,5,8708,357527,1,8708,357527,50,8708,357527,40,8708,357599,0,8708,407596,3,12612,408911,4,14559,409953,1,16509,409953,50,16511,409953,40,16511,410025,0,16511,449078,3,19066,450161,4,20337,451247,5,21612,451248,1,21612,451248,50,21613,451248,40,21613,451320,0,21613,486950,3,23114,487636,4,23864,488492,5,24614,488493,1,24614,488493,50,24615,488493,40,24615,488565,0,24615,493248,3,26094,493248,4,26094,493412,5,26119,493412,1,26119,493412,50,26119,493412,40,26119,493484,0,26119,515021,3,27320,515714,4,27920,516243,1,28520,516243,50,28520,516243,40,28520,516315,0,28521,533623,3,29272,534277,4,29647,534645,1,30022,534645,50,30022,534645,40,30022,534645,40,30022,534710,0,30022,534815,50,30023,534880,0,30023,535045,50,30026,535110,0,30030,535286,50,30033,535351,0,30034,535518,50,30035,535518,30,30035,535518,40,30035,535583,0,30040,535798,50,30040,535798,30,30040,535798,40,30040,535863,0,30040,536005,50,30040,536005,30,30040,536005,40,30040,536070,0,30045,536232,50,30045,536232,30,30045,536232,40,30045,536297,0,30045)
%
%
% START OF PROOF
% 536234 [] equal(multiply(identity,X),X).
% 536235 [] equal(multiply(inverse(X),X),identity).
% 536236 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 536237 [] -equal(multiply(sk_c12,X),sk_c11) | -equal(multiply(Y,sk_c12),X) | -equal(inverse(Y),sk_c12).
% 536238 [] equal(multiply(sk_c10,sk_c12),sk_c11) | equal(inverse(sk_c3),sk_c12).
% 536239 [] equal(inverse(sk_c3),sk_c12) | equal(inverse(sk_c10),sk_c11).
% 536241 [] equal(inverse(sk_c3),sk_c12) | equal(inverse(sk_c8),sk_c9).
% 536242 [] equal(multiply(sk_c8,sk_c9),sk_c11) | equal(inverse(sk_c3),sk_c12).
% 536244 [] equal(inverse(sk_c3),sk_c12) | equal(inverse(sk_c7),sk_c12).
% 536245 [] equal(multiply(sk_c6,sk_c11),sk_c12) | equal(inverse(sk_c3),sk_c12).
% 536246 [] equal(inverse(sk_c3),sk_c12) | equal(inverse(sk_c5),sk_c6).
% 536247 [] equal(multiply(sk_c5,sk_c6),sk_c12) | equal(inverse(sk_c3),sk_c12).
% 536248 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(multiply(sk_c10,sk_c12),sk_c11).
% 536249 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(inverse(sk_c10),sk_c11).
% 536251 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(inverse(sk_c8),sk_c9).
% 536252 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(multiply(sk_c8,sk_c9),sk_c11).
% 536254 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(inverse(sk_c7),sk_c12).
% 536255 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(multiply(sk_c6,sk_c11),sk_c12).
% 536256 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(inverse(sk_c5),sk_c6).
% 536257 [] equal(multiply(sk_c3,sk_c12),sk_c4) | equal(multiply(sk_c5,sk_c6),sk_c12).
% 536258 [?] ?
% 536259 [?] ?
% 536261 [?] ?
% 536262 [?] ?
% 536264 [?] ?
% 536265 [?] ?
% 536266 [?] ?
% 536267 [?] ?
% 536366 [hyper:536237,536249,binarycut:536259,binarycut:536239] equal(inverse(sk_c10),sk_c11).
% 536367 [para:536366.1.1,536235.1.1.1] equal(multiply(sk_c11,sk_c10),identity).
% 536370 [hyper:536237,536251,binarycut:536261,binarycut:536241] equal(inverse(sk_c8),sk_c9).
% 536377 [hyper:536237,536248,536238,binarycut:536258] equal(multiply(sk_c10,sk_c12),sk_c11).
% 536384 [hyper:536237,536254,binarycut:536264,binarycut:536244] equal(inverse(sk_c7),sk_c12).
% 536391 [para:536384.1.1,536235.1.1.1] equal(multiply(sk_c12,sk_c7),identity).
% 536405 [hyper:536237,536256,binarycut:536266,binarycut:536246] equal(inverse(sk_c5),sk_c6).
% 536411 [hyper:536237,536252,536242,binarycut:536262] equal(multiply(sk_c8,sk_c9),sk_c11).
% 536421 [hyper:536237,536255,536245,binarycut:536265] equal(multiply(sk_c6,sk_c11),sk_c12).
% 536426 [hyper:536237,536257,536247,binarycut:536267] equal(multiply(sk_c5,sk_c6),sk_c12).
% 536427 [para:536235.1.1,536236.1.1.1,demod:536234] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 536428 [para:536367.1.1,536236.1.1.1,demod:536234] equal(X,multiply(sk_c11,multiply(sk_c10,X))).
% 536431 [para:536391.1.1,536236.1.1.1,demod:536234] equal(X,multiply(sk_c12,multiply(sk_c7,X))).
% 536440 [para:536377.1.1,536428.1.2.2] equal(sk_c12,multiply(sk_c11,sk_c11)).
% 536444 [para:536367.1.1,536427.1.2.2] equal(sk_c10,multiply(inverse(sk_c11),identity)).
% 536446 [para:536391.1.1,536427.1.2.2] equal(sk_c7,multiply(inverse(sk_c12),identity)).
% 536449 [para:536411.1.1,536427.1.2.2,demod:536370] equal(sk_c9,multiply(sk_c9,sk_c11)).
% 536452 [para:536426.1.1,536427.1.2.2,demod:536405] equal(sk_c6,multiply(sk_c6,sk_c12)).
% 536456 [para:536449.1.2,536427.1.2.2,demod:536235] equal(sk_c11,identity).
% 536457 [para:536456.1.1,536367.1.1.1,demod:536234] equal(sk_c10,identity).
% 536460 [para:536456.1.1,536428.1.2.1,demod:536234] equal(X,multiply(sk_c10,X)).
% 536461 [para:536456.1.1,536440.1.2.1,demod:536234] equal(sk_c12,sk_c11).
% 536466 [para:536457.1.1,536428.1.2.2.1,demod:536234] equal(X,multiply(sk_c11,X)).
% 536472 [para:536461.1.2,536421.1.1.2,demod:536452] equal(sk_c6,sk_c12).
% 536473 [para:536461.1.2,536428.1.2.1,demod:536460] equal(X,multiply(sk_c12,X)).
% 536475 [para:536461.1.2,536444.1.2.1.1,demod:536446] equal(sk_c10,sk_c7).
% 536479 [para:536472.1.1,536421.1.1.1,demod:536473] equal(sk_c11,sk_c12).
% 536485 [para:536475.1.1,536428.1.2.2.1,demod:536466] equal(X,multiply(sk_c7,X)).
% 536496 [hyper:536237,536431,536377,demod:536473,536485,demod:536366,cut:536479] 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 31
% 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(X,Y),sk_c12) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c11),sk_c12) | -equal(multiply(sk_c12,Z),sk_c11) | -equal(multiply(U,sk_c12),Z) | -equal(inverse(U),sk_c12) | -equal(multiply(V,W),sk_c12) | -equal(inverse(V),W) | -equal(multiply(W,sk_c11),sk_c12) | -equal(inverse(X1),sk_c12) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(multiply(X2,X3),sk_c11) | -equal(inverse(X2),X3) | -equal(multiply(X3,sk_c12),sk_c11) | -equal(inverse(X4),sk_c11) | -equal(multiply(X4,sk_c12),sk_c11).
% Split part used next: -equal(multiply(X,Y),sk_c12) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c11),sk_c12).
% 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,137,0,0,317219,5,1501,317220,1,1501,317220,50,1501,317220,40,1501,317292,0,1501,317783,5,2103,317784,1,2103,317784,50,2103,317784,40,2103,317856,0,2103,318346,5,2705,318347,1,2705,318347,50,2705,318347,40,2705,318419,0,2705,337590,3,4206,338289,4,4956,339079,5,5706,339080,1,5706,339080,50,5706,339080,40,5706,339152,0,5706,352133,3,6457,353035,4,6832,353673,1,7207,353673,50,7207,353673,40,7207,353745,0,7207,357525,5,8708,357527,1,8708,357527,50,8708,357527,40,8708,357599,0,8708,407596,3,12612,408911,4,14559,409953,1,16509,409953,50,16511,409953,40,16511,410025,0,16511,449078,3,19066,450161,4,20337,451247,5,21612,451248,1,21612,451248,50,21613,451248,40,21613,451320,0,21613,486950,3,23114,487636,4,23864,488492,5,24614,488493,1,24614,488493,50,24615,488493,40,24615,488565,0,24615,493248,3,26094,493248,4,26094,493412,5,26119,493412,1,26119,493412,50,26119,493412,40,26119,493484,0,26119,515021,3,27320,515714,4,27920,516243,1,28520,516243,50,28520,516243,40,28520,516315,0,28521,533623,3,29272,534277,4,29647,534645,1,30022,534645,50,30022,534645,40,30022,534645,40,30022,534710,0,30022,534815,50,30023,534880,0,30023,535045,50,30026,535110,0,30030,535286,50,30033,535351,0,30034,535518,50,30035,535518,30,30035,535518,40,30035,535583,0,30040,535798,50,30040,535798,30,30040,535798,40,30040,535863,0,30040,536005,50,30040,536005,30,30040,536005,40,30040,536070,0,30045,536232,50,30045,536232,30,30045,536232,40,30045,536297,0,30045,536495,50,30046,536495,30,30046,536495,40,30046,536560,0,30051)
%
%
% START OF PROOF
% 536496 [] equal(X,X).
% 536500 [] -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,X),sk_c12) | -equal(inverse(Y),X).
% 536538 [] equal(multiply(sk_c2,sk_c11),sk_c12) | equal(multiply(sk_c6,sk_c11),sk_c12).
% 536539 [?] ?
% 536540 [] equal(multiply(sk_c2,sk_c11),sk_c12) | equal(multiply(sk_c5,sk_c6),sk_c12).
% 536548 [?] ?
% 536549 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c6).
% 536550 [?] ?
% 536558 [] equal(multiply(sk_c1,sk_c2),sk_c12) | equal(multiply(sk_c6,sk_c11),sk_c12).
% 536559 [?] ?
% 536560 [] equal(multiply(sk_c1,sk_c2),sk_c12) | equal(multiply(sk_c5,sk_c6),sk_c12).
% 536612 [hyper:536500,536549,binarycut:536559,binarycut:536539] equal(inverse(sk_c5),sk_c6).
% 536614 [hyper:536500,536549,binarycut:536550,binarycut:536548] equal(inverse(sk_c1),sk_c2).
% 536687 [hyper:536500,536540,536538,demod:536612,cut:536496] equal(multiply(sk_c2,sk_c11),sk_c12).
% 536707 [hyper:536500,536558,demod:536614,536687,cut:536496,cut:536496] equal(multiply(sk_c6,sk_c11),sk_c12).
% 536721 [hyper:536500,536560,demod:536614,536687,cut:536496,cut:536496] equal(multiply(sk_c5,sk_c6),sk_c12).
% 536723 [hyper:536500,536721,demod:536612,536707,cut:536496,cut:536496] 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% Split attempt finished with SUCCESS.
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 23615
% derived clauses: 3403233
% kept clauses: 178058
% kept size sum: 964435
% kept mid-nuclei: 317480
% kept new demods: 976
% forw unit-subs: 1141456
% forw double-subs: 1519489
% forw overdouble-subs: 197025
% backward subs: 21793
% fast unit cutoff: 17102
% full unit cutoff: 0
% dbl unit cutoff: 3329
% real runtime : 302.60
% process. runtime: 300.52
% specific non-discr-tree subsumption statistics:
% tried: 97430153
% length fails: 19019695
% strength fails: 28284298
% predlist fails: 405945
% aux str. fails: 14158698
% by-lit fails: 13925175
% full subs tried: 7044000
% full subs fail: 6907884
%
% ; 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/GRP208-1+eq_r.in")
%
%------------------------------------------------------------------------------