TSTP Solution File: GRP338-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP338-1 : 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 : art09.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 299.3s
% Output : Assurance 299.3s
% 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/GRP338-1+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 29)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 29)
% (binary-posweight-lex-big-order 30 #f 3 29)
% (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_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% was split for some strategies as:
% -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X2),W) | -equal(inverse(X1),X2) | -equal(multiply(X1,W),X2).
% -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10).
% -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11).
% -equal(multiply(Y,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10).
% -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11).
% -equal(multiply(sk_c10,sk_c11),sk_c9).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X2),W) | -equal(inverse(X1),X2) | -equal(multiply(X1,W),X2).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,119,0,1,69238,4,1437,71167,5,1502,71168,1,1502,71168,50,1502,71168,40,1502,71232,0,1502,71591,5,2104,71596,1,2105,71596,50,2105,71596,40,2105,71660,0,2105,72019,5,2707,72024,1,2709,72024,50,2709,72024,40,2709,72088,0,2709,91038,3,4210,92836,4,4960,94339,1,5710,94339,50,5710,94339,40,5710,94403,0,5710,107912,3,6461,109147,4,6836,110127,1,7211,110127,50,7211,110127,40,7211,110191,0,7211,110699,5,8721,110701,1,8721,110701,50,8721,110701,40,8721,110765,0,8721,145287,3,12623,147442,4,14572,149527,1,16522,149527,50,16523,149527,40,16523,149591,0,16523,179587,3,19080,181088,4,20349,182521,1,21624,182521,50,21625,182521,40,21625,182585,0,21625,208999,3,23126,210142,4,23876,211292,1,24626,211292,50,24627,211292,40,24627,211356,0,24627,211866,5,26138,211866,1,26138,211866,50,26138,211866,40,26138,211930,0,26138,231779,3,27339,232760,4,27939,233698,1,28539,233698,50,28539,233698,40,28539,233762,0,28539,248690,3,29293,249504,4,29665,250398,5,30040,250399,1,30040,250399,50,30040,250399,40,30040,250399,40,30040,250508,0,30041,254251,50,30055,254360,0,30055)
%
%
% START OF PROOF
% 254252 [] equal(X,X).
% 254253 [] equal(multiply(identity,X),X).
% 254254 [] equal(multiply(inverse(X),X),identity).
% 254255 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 254306 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,X),sk_c11) | -equal(multiply(Z,X),U) | -equal(inverse(Z),U) | -equal(inverse(U),X) | -equal(inverse(Y),X).
% 254307 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst97,Y).
% 254308 [] -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | $spltprd1($spltcnst98,Y).
% 254309 [] -equal(multiply(X,sk_c10),sk_c11) | $spltprd1($spltcnst99,X).
% 254310 [] -$spltprd1($spltcnst98,X) | -$spltprd1($spltcnst97,X) | -$spltprd1($spltcnst99,X).
% 254311 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c10).
% 254312 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 254313 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 254314 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c2),sk_c10).
% 254315 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 254316 [?] ?
% 254321 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 254322 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 254323 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 254324 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 254325 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 254326 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 254331 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 254332 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 254333 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 254334 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 254335 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 254336 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 254341 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c11).
% 254342 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 254343 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 254344 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 254345 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 254346 [?] ?
% 254351 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 254352 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c6),sk_c8).
% 254353 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 254354 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 254355 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 254356 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 254454 [hyper:254308,254315,binarycut:254316] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst98,sk_c8).
% 254563 [hyper:254308,254345,binarycut:254346] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst98,sk_c8).
% 254638 [hyper:254307,254311,254312,254313] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst97,sk_c8).
% 254686 [hyper:254309,254314] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst99,sk_c8).
% 254700 [hyper:254310,254686,254638,254454] equal(inverse(sk_c2),sk_c10).
% 254707 [para:254700.1.1,254254.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 255184 [hyper:254307,254341,254342,254343] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst97,sk_c8).
% 255381 [hyper:254309,254344] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst99,sk_c8).
% 255455 [hyper:254310,255381,255184,254563] equal(inverse(sk_c1),sk_c11).
% 255569 [para:255455.1.1,254254.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 255939 [hyper:254306,254326,254324,254325,254322,254321,254323] equal(multiply(sk_c2,sk_c10),sk_c11).
% 256082 [hyper:254306,254336,254334,254335,254332,254331,254333] equal(multiply(sk_c1,sk_c10),sk_c11).
% 256155 [hyper:254306,254356,254354,254355,254352,254351,254353] equal(multiply(sk_c10,sk_c11),sk_c9).
% 256165 [para:254254.1.1,254255.1.1.1,demod:254253] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 256166 [para:254707.1.1,254255.1.1.1,demod:254253] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 256169 [para:255569.1.1,254255.1.1.1,demod:254253] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 256211 [para:255939.1.1,256166.1.2.2,demod:256155] equal(sk_c10,sk_c9).
% 256216 [para:256211.1.1,256155.1.1.1] equal(multiply(sk_c9,sk_c11),sk_c9).
% 256285 [para:256082.1.1,256169.1.2.2] equal(sk_c10,multiply(sk_c11,sk_c11)).
% 256360 [para:254254.1.1,256165.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 256392 [para:256216.1.1,256165.1.2.2,demod:254254] equal(sk_c11,identity).
% 256395 [para:256165.1.2,256165.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 256397 [para:256392.1.1,255569.1.1.1,demod:254253] equal(sk_c1,identity).
% 256401 [para:256392.1.1,256285.1.2.1,demod:254253] equal(sk_c10,sk_c11).
% 256402 [para:256392.1.1,256285.1.2.2] equal(sk_c10,multiply(sk_c11,identity)).
% 256405 [para:256397.1.1,255455.1.1.1] equal(inverse(identity),sk_c11).
% 256406 [para:256397.1.1,255569.1.1.2,demod:256402] equal(sk_c10,identity).
% 256409 [para:256397.1.1,256169.1.2.2.1,demod:254253] equal(X,multiply(sk_c11,X)).
% 256412 [para:256401.1.1,256166.1.2.1,demod:256409] equal(X,multiply(sk_c2,X)).
% 256414 [para:256406.1.1,255939.1.1.2,demod:256412] equal(identity,sk_c11).
% 257737 [para:256395.1.2,256360.1.2] equal(X,multiply(X,identity)).
% 257821 [para:257737.1.2,256360.1.2] equal(X,inverse(inverse(X))).
% 257831 [hyper:254306,257821,254253,254253,demod:257821,demod:256409,256405,cut:256401,cut:256414,demod:256405,cut:254252] 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 29
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10).
% 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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,119,0,1,69238,4,1437,71167,5,1502,71168,1,1502,71168,50,1502,71168,40,1502,71232,0,1502,71591,5,2104,71596,1,2105,71596,50,2105,71596,40,2105,71660,0,2105,72019,5,2707,72024,1,2709,72024,50,2709,72024,40,2709,72088,0,2709,91038,3,4210,92836,4,4960,94339,1,5710,94339,50,5710,94339,40,5710,94403,0,5710,107912,3,6461,109147,4,6836,110127,1,7211,110127,50,7211,110127,40,7211,110191,0,7211,110699,5,8721,110701,1,8721,110701,50,8721,110701,40,8721,110765,0,8721,145287,3,12623,147442,4,14572,149527,1,16522,149527,50,16523,149527,40,16523,149591,0,16523,179587,3,19080,181088,4,20349,182521,1,21624,182521,50,21625,182521,40,21625,182585,0,21625,208999,3,23126,210142,4,23876,211292,1,24626,211292,50,24627,211292,40,24627,211356,0,24627,211866,5,26138,211866,1,26138,211866,50,26138,211866,40,26138,211930,0,26138,231779,3,27339,232760,4,27939,233698,1,28539,233698,50,28539,233698,40,28539,233762,0,28539,248690,3,29293,249504,4,29665,250398,5,30040,250399,1,30040,250399,50,30040,250399,40,30040,250399,40,30040,250508,0,30041,254251,50,30055,254360,0,30055,257830,50,30067,257830,30,30067,257830,40,30067,257885,0,30067)
%
%
% START OF PROOF
% 257832 [] equal(multiply(identity,X),X).
% 257833 [] equal(multiply(inverse(X),X),identity).
% 257834 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 257835 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 257842 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 257843 [?] ?
% 257852 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 257853 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 257862 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 257863 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 257872 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 257873 [?] ?
% 257882 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c4),sk_c10).
% 257883 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 257897 [hyper:257835,257842,binarycut:257843] equal(inverse(sk_c2),sk_c10).
% 257900 [para:257897.1.1,257833.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 257908 [hyper:257835,257872,binarycut:257873] equal(inverse(sk_c1),sk_c11).
% 257909 [para:257908.1.1,257833.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 257934 [hyper:257835,257853,257852] equal(multiply(sk_c2,sk_c10),sk_c11).
% 257941 [hyper:257835,257863,257862] equal(multiply(sk_c1,sk_c10),sk_c11).
% 257947 [hyper:257835,257883,257882] equal(multiply(sk_c10,sk_c11),sk_c9).
% 257948 [para:257833.1.1,257834.1.1.1,demod:257832] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 257949 [para:257900.1.1,257834.1.1.1,demod:257832] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 257950 [para:257909.1.1,257834.1.1.1,demod:257832] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 257954 [para:257934.1.1,257949.1.2.2,demod:257947] equal(sk_c10,sk_c9).
% 257957 [para:257954.1.1,257941.1.1.2] equal(multiply(sk_c1,sk_c9),sk_c11).
% 257958 [para:257954.1.1,257947.1.1.1] equal(multiply(sk_c9,sk_c11),sk_c9).
% 257961 [para:257900.1.1,257948.1.2.2] equal(sk_c2,multiply(inverse(sk_c10),identity)).
% 257964 [para:257947.1.1,257948.1.2.2] equal(sk_c11,multiply(inverse(sk_c10),sk_c9)).
% 257971 [para:257958.1.1,257948.1.2.2,demod:257833] equal(sk_c11,identity).
% 257972 [para:257971.1.1,257909.1.1.1,demod:257832] equal(sk_c1,identity).
% 257976 [para:257971.1.1,257950.1.2.1,demod:257832] equal(X,multiply(sk_c1,X)).
% 257980 [para:257972.1.1,257957.1.1.1,demod:257832] equal(sk_c9,sk_c11).
% 257989 [para:257980.1.2,257971.1.1] equal(sk_c9,identity).
% 257990 [para:257980.1.2,257950.1.2.1,demod:257976] equal(X,multiply(sk_c9,X)).
% 258000 [para:257989.1.1,257964.1.2.2,demod:257961] equal(sk_c11,sk_c2).
% 258002 [para:258000.1.1,257980.1.2] equal(sk_c9,sk_c2).
% 258007 [para:258002.1.2,257897.1.1.1] equal(inverse(sk_c9),sk_c10).
% 258009 [hyper:257835,258007,demod:257990,cut:257954] 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 29
% 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(sk_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,119,0,1,69238,4,1437,71167,5,1502,71168,1,1502,71168,50,1502,71168,40,1502,71232,0,1502,71591,5,2104,71596,1,2105,71596,50,2105,71596,40,2105,71660,0,2105,72019,5,2707,72024,1,2709,72024,50,2709,72024,40,2709,72088,0,2709,91038,3,4210,92836,4,4960,94339,1,5710,94339,50,5710,94339,40,5710,94403,0,5710,107912,3,6461,109147,4,6836,110127,1,7211,110127,50,7211,110127,40,7211,110191,0,7211,110699,5,8721,110701,1,8721,110701,50,8721,110701,40,8721,110765,0,8721,145287,3,12623,147442,4,14572,149527,1,16522,149527,50,16523,149527,40,16523,149591,0,16523,179587,3,19080,181088,4,20349,182521,1,21624,182521,50,21625,182521,40,21625,182585,0,21625,208999,3,23126,210142,4,23876,211292,1,24626,211292,50,24627,211292,40,24627,211356,0,24627,211866,5,26138,211866,1,26138,211866,50,26138,211866,40,26138,211930,0,26138,231779,3,27339,232760,4,27939,233698,1,28539,233698,50,28539,233698,40,28539,233762,0,28539,248690,3,29293,249504,4,29665,250398,5,30040,250399,1,30040,250399,50,30040,250399,40,30040,250399,40,30040,250508,0,30041,254251,50,30055,254360,0,30055,257830,50,30067,257830,30,30067,257830,40,30067,257885,0,30067,258008,50,30068,258008,30,30068,258008,40,30068,258063,0,30069)
%
%
% START OF PROOF
% 258010 [] equal(multiply(identity,X),X).
% 258011 [] equal(multiply(inverse(X),X),identity).
% 258012 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 258013 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 258022 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 258023 [?] ?
% 258032 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 258033 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 258042 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 258043 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 258052 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 258053 [?] ?
% 258062 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c3),sk_c11).
% 258063 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 258071 [hyper:258013,258022,binarycut:258023] equal(inverse(sk_c2),sk_c10).
% 258072 [para:258071.1.1,258011.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 258089 [hyper:258013,258052,binarycut:258053] equal(inverse(sk_c1),sk_c11).
% 258092 [para:258089.1.1,258011.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 258117 [hyper:258013,258033,258032] equal(multiply(sk_c2,sk_c10),sk_c11).
% 258127 [hyper:258013,258043,258042] equal(multiply(sk_c1,sk_c10),sk_c11).
% 258134 [hyper:258013,258063,258062] equal(multiply(sk_c10,sk_c11),sk_c9).
% 258135 [para:258011.1.1,258012.1.1.1,demod:258010] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 258136 [para:258072.1.1,258012.1.1.1,demod:258010] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 258137 [para:258092.1.1,258012.1.1.1,demod:258010] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 258141 [para:258117.1.1,258136.1.2.2,demod:258134] equal(sk_c10,sk_c9).
% 258145 [para:258141.1.1,258134.1.1.1] equal(multiply(sk_c9,sk_c11),sk_c9).
% 258158 [para:258145.1.1,258135.1.2.2,demod:258011] equal(sk_c11,identity).
% 258159 [para:258158.1.1,258092.1.1.1,demod:258010] equal(sk_c1,identity).
% 258164 [para:258159.1.1,258089.1.1.1] equal(inverse(identity),sk_c11).
% 258166 [para:258159.1.1,258127.1.1.1,demod:258010] equal(sk_c10,sk_c11).
% 258168 [para:258159.1.1,258137.1.2.2.1,demod:258010] equal(X,multiply(sk_c11,X)).
% 258169 [para:258166.1.1,258072.1.1.1,demod:258168] equal(sk_c2,identity).
% 258178 [para:258169.1.1,258071.1.1.1,demod:258164] equal(sk_c11,sk_c10).
% 258182 [hyper:258013,258164,demod:258010,cut:258178] 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 29
% 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_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(Y,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10).
% 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 29
% 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 29
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,119,0,1,69238,4,1437,71167,5,1502,71168,1,1502,71168,50,1502,71168,40,1502,71232,0,1502,71591,5,2104,71596,1,2105,71596,50,2105,71596,40,2105,71660,0,2105,72019,5,2707,72024,1,2709,72024,50,2709,72024,40,2709,72088,0,2709,91038,3,4210,92836,4,4960,94339,1,5710,94339,50,5710,94339,40,5710,94403,0,5710,107912,3,6461,109147,4,6836,110127,1,7211,110127,50,7211,110127,40,7211,110191,0,7211,110699,5,8721,110701,1,8721,110701,50,8721,110701,40,8721,110765,0,8721,145287,3,12623,147442,4,14572,149527,1,16522,149527,50,16523,149527,40,16523,149591,0,16523,179587,3,19080,181088,4,20349,182521,1,21624,182521,50,21625,182521,40,21625,182585,0,21625,208999,3,23126,210142,4,23876,211292,1,24626,211292,50,24627,211292,40,24627,211356,0,24627,211866,5,26138,211866,1,26138,211866,50,26138,211866,40,26138,211930,0,26138,231779,3,27339,232760,4,27939,233698,1,28539,233698,50,28539,233698,40,28539,233762,0,28539,248690,3,29293,249504,4,29665,250398,5,30040,250399,1,30040,250399,50,30040,250399,40,30040,250399,40,30040,250508,0,30041,254251,50,30055,254360,0,30055,257830,50,30067,257830,30,30067,257830,40,30067,257885,0,30067,258008,50,30068,258008,30,30068,258008,40,30068,258063,0,30069,258181,50,30070,258181,30,30070,258181,40,30070,258236,0,30070,258432,50,30072,258487,0,30073)
%
%
% START OF PROOF
% 258434 [] equal(multiply(identity,X),X).
% 258435 [] equal(multiply(inverse(X),X),identity).
% 258436 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 258437 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c10).
% 258438 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c10).
% 258439 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 258440 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 258442 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 258443 [] equal(multiply(sk_c5,sk_c8),sk_c11) | equal(inverse(sk_c2),sk_c10).
% 258444 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 258446 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 258447 [] equal(multiply(sk_c3,sk_c11),sk_c10) | equal(inverse(sk_c2),sk_c10).
% 258448 [?] ?
% 258449 [?] ?
% 258450 [?] ?
% 258452 [?] ?
% 258453 [?] ?
% 258454 [?] ?
% 258456 [?] ?
% 258457 [?] ?
% 258490 [hyper:258437,258439,binarycut:258449] equal(inverse(sk_c6),sk_c8).
% 258491 [para:258490.1.1,258435.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 258495 [hyper:258437,258440,binarycut:258450] equal(inverse(sk_c7),sk_c6).
% 258496 [para:258495.1.1,258435.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 258499 [hyper:258437,258442,binarycut:258452] equal(inverse(sk_c5),sk_c8).
% 258502 [hyper:258437,258438,binarycut:258448] equal(multiply(sk_c7,sk_c8),sk_c6).
% 258503 [para:258499.1.1,258435.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 258506 [hyper:258437,258444,binarycut:258454] equal(inverse(sk_c4),sk_c10).
% 258510 [para:258506.1.1,258435.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 258521 [hyper:258437,258446,binarycut:258456] equal(inverse(sk_c3),sk_c11).
% 258522 [para:258521.1.1,258435.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 258525 [hyper:258437,258443,binarycut:258453] equal(multiply(sk_c5,sk_c8),sk_c11).
% 258531 [hyper:258437,258447,binarycut:258457] equal(multiply(sk_c3,sk_c11),sk_c10).
% 258532 [para:258435.1.1,258436.1.1.1,demod:258434] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 258533 [para:258491.1.1,258436.1.1.1,demod:258434] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 258534 [para:258496.1.1,258436.1.1.1,demod:258434] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 258535 [para:258502.1.1,258436.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c8,X))).
% 258537 [para:258510.1.1,258436.1.1.1,demod:258434] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 258540 [para:258525.1.1,258436.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 258542 [para:258531.1.1,258436.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c3,multiply(sk_c11,X))).
% 258543 [para:258496.1.1,258533.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 258545 [para:258435.1.1,258532.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 258546 [para:258491.1.1,258532.1.2.2] equal(sk_c6,multiply(inverse(sk_c8),identity)).
% 258547 [para:258502.1.1,258532.1.2.2,demod:258495] equal(sk_c8,multiply(sk_c6,sk_c6)).
% 258548 [para:258503.1.1,258532.1.2.2,demod:258546] equal(sk_c5,sk_c6).
% 258551 [para:258522.1.1,258532.1.2.2] equal(sk_c3,multiply(inverse(sk_c11),identity)).
% 258552 [para:258525.1.1,258532.1.2.2,demod:258499] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 258555 [para:258436.1.1,258532.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 258556 [para:258533.1.2,258532.1.2.2] equal(multiply(sk_c6,X),multiply(inverse(sk_c8),X)).
% 258557 [para:258532.1.2,258532.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 258559 [para:258543.1.2,258436.1.1.1,demod:258434] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 258565 [para:258552.1.2,258532.1.2.2,demod:258556] equal(sk_c11,multiply(sk_c6,sk_c8)).
% 258569 [para:258548.1.2,258534.1.2.1,demod:258540,258559] equal(X,multiply(sk_c11,X)).
% 258571 [para:258491.1.1,258535.1.2.2,demod:258543,258559,258547] equal(sk_c8,sk_c7).
% 258576 [para:258571.1.2,258496.1.1.2,demod:258565] equal(sk_c11,identity).
% 258579 [para:258576.1.1,258522.1.1.1,demod:258434] equal(sk_c3,identity).
% 258580 [para:258576.1.1,258531.1.1.2] equal(multiply(sk_c3,identity),sk_c10).
% 258582 [para:258579.1.1,258531.1.1.1,demod:258434] equal(sk_c11,sk_c10).
% 258585 [para:258582.1.2,258510.1.1.1,demod:258569] equal(sk_c4,identity).
% 258603 [para:258582.1.2,258537.1.2.1,demod:258569] equal(X,multiply(sk_c4,X)).
% 258604 [para:258585.1.1,258537.1.2.2.1,demod:258434] equal(X,multiply(sk_c10,X)).
% 258648 [para:258522.1.1,258542.1.2.2,demod:258580,258604] equal(sk_c3,sk_c10).
% 258710 [para:258557.1.2,258435.1.1] equal(multiply(X,inverse(X)),identity).
% 258712 [para:258557.1.2,258545.1.2] equal(X,multiply(X,identity)).
% 258725 [para:258712.1.2,258545.1.2] equal(X,inverse(inverse(X))).
% 258727 [para:258712.1.2,258551.1.2] equal(sk_c3,inverse(sk_c11)).
% 258732 [para:258710.1.1,258555.1.2.2.2,demod:258712] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 258749 [para:258537.1.2,258732.1.2.1.1,demod:258603] equal(inverse(X),multiply(inverse(X),sk_c10)).
% 258752 [para:258749.1.2,258557.1.2,demod:258725] equal(multiply(X,sk_c10),X).
% 258753 [hyper:258437,258752,demod:258727,cut:258648] 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 29
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,119,0,1,69238,4,1437,71167,5,1502,71168,1,1502,71168,50,1502,71168,40,1502,71232,0,1502,71591,5,2104,71596,1,2105,71596,50,2105,71596,40,2105,71660,0,2105,72019,5,2707,72024,1,2709,72024,50,2709,72024,40,2709,72088,0,2709,91038,3,4210,92836,4,4960,94339,1,5710,94339,50,5710,94339,40,5710,94403,0,5710,107912,3,6461,109147,4,6836,110127,1,7211,110127,50,7211,110127,40,7211,110191,0,7211,110699,5,8721,110701,1,8721,110701,50,8721,110701,40,8721,110765,0,8721,145287,3,12623,147442,4,14572,149527,1,16522,149527,50,16523,149527,40,16523,149591,0,16523,179587,3,19080,181088,4,20349,182521,1,21624,182521,50,21625,182521,40,21625,182585,0,21625,208999,3,23126,210142,4,23876,211292,1,24626,211292,50,24627,211292,40,24627,211356,0,24627,211866,5,26138,211866,1,26138,211866,50,26138,211866,40,26138,211930,0,26138,231779,3,27339,232760,4,27939,233698,1,28539,233698,50,28539,233698,40,28539,233762,0,28539,248690,3,29293,249504,4,29665,250398,5,30040,250399,1,30040,250399,50,30040,250399,40,30040,250399,40,30040,250508,0,30041,254251,50,30055,254360,0,30055,257830,50,30067,257830,30,30067,257830,40,30067,257885,0,30067,258008,50,30068,258008,30,30068,258008,40,30068,258063,0,30069,258181,50,30070,258181,30,30070,258181,40,30070,258236,0,30070,258432,50,30072,258487,0,30073,258752,50,30077,258752,30,30077,258752,40,30077,258807,0,30077)
%
%
% START OF PROOF
% 258754 [] equal(multiply(identity,X),X).
% 258755 [] equal(multiply(inverse(X),X),identity).
% 258756 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 258757 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c11).
% 258778 [?] ?
% 258779 [?] ?
% 258780 [?] ?
% 258781 [?] ?
% 258782 [?] ?
% 258783 [?] ?
% 258786 [?] ?
% 258787 [?] ?
% 258788 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c11).
% 258789 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 258790 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 258791 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 258792 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 258793 [] equal(multiply(sk_c5,sk_c8),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 258796 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 258797 [] equal(multiply(sk_c3,sk_c11),sk_c10) | equal(inverse(sk_c1),sk_c11).
% 258818 [hyper:258757,258789,binarycut:258779] equal(inverse(sk_c6),sk_c8).
% 258819 [para:258818.1.1,258755.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 258823 [hyper:258757,258790,binarycut:258780] equal(inverse(sk_c7),sk_c6).
% 258824 [para:258823.1.1,258755.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 258827 [hyper:258757,258792,binarycut:258782] equal(inverse(sk_c5),sk_c8).
% 258831 [para:258827.1.1,258755.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 258839 [hyper:258757,258796,binarycut:258786] equal(inverse(sk_c3),sk_c11).
% 258843 [para:258839.1.1,258755.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 258852 [hyper:258757,258788,binarycut:258778] equal(multiply(sk_c7,sk_c8),sk_c6).
% 258856 [hyper:258757,258791,binarycut:258781] equal(multiply(sk_c8,sk_c10),sk_c11).
% 258862 [hyper:258757,258793,binarycut:258783] equal(multiply(sk_c5,sk_c8),sk_c11).
% 258871 [hyper:258757,258797,binarycut:258787] equal(multiply(sk_c3,sk_c11),sk_c10).
% 258872 [para:258755.1.1,258756.1.1.1,demod:258754] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 258873 [para:258819.1.1,258756.1.1.1,demod:258754] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 258874 [para:258824.1.1,258756.1.1.1,demod:258754] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 258880 [para:258862.1.1,258756.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 258883 [para:258824.1.1,258873.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 258885 [para:258819.1.1,258872.1.2.2] equal(sk_c6,multiply(inverse(sk_c8),identity)).
% 258886 [para:258831.1.1,258872.1.2.2,demod:258885] equal(sk_c5,sk_c6).
% 258889 [para:258852.1.1,258872.1.2.2,demod:258823] equal(sk_c8,multiply(sk_c6,sk_c6)).
% 258891 [para:258862.1.1,258872.1.2.2,demod:258827] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 258896 [para:258883.1.2,258756.1.1.1,demod:258754] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 258898 [para:258889.1.2,258873.1.2.2] equal(sk_c6,multiply(sk_c8,sk_c8)).
% 258905 [para:258886.1.2,258874.1.2.1,demod:258880,258896] equal(X,multiply(sk_c11,X)).
% 258908 [para:258905.1.2,258843.1.1] equal(sk_c3,identity).
% 258910 [para:258908.1.1,258839.1.1.1] equal(inverse(identity),sk_c11).
% 258911 [para:258908.1.1,258871.1.1.1,demod:258754] equal(sk_c11,sk_c10).
% 258913 [para:258911.1.2,258856.1.1.2,demod:258891] equal(sk_c8,sk_c11).
% 258922 [para:258913.1.2,258891.1.2.2,demod:258898] equal(sk_c8,sk_c6).
% 258937 [para:258922.1.2,258889.1.2.1,demod:258819] equal(sk_c8,identity).
% 258958 [para:258937.1.1,258856.1.1.1,demod:258754] equal(sk_c10,sk_c11).
% 259012 [hyper:258757,258910,demod:258754,cut:258958] 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 29
% 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_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(sk_c10,sk_c11),sk_c9).
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% 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 29
% clause depth limited to 10
% 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(55,40,1,119,0,1,69238,4,1437,71167,5,1502,71168,1,1502,71168,50,1502,71168,40,1502,71232,0,1502,71591,5,2104,71596,1,2105,71596,50,2105,71596,40,2105,71660,0,2105,72019,5,2707,72024,1,2709,72024,50,2709,72024,40,2709,72088,0,2709,91038,3,4210,92836,4,4960,94339,1,5710,94339,50,5710,94339,40,5710,94403,0,5710,107912,3,6461,109147,4,6836,110127,1,7211,110127,50,7211,110127,40,7211,110191,0,7211,110699,5,8721,110701,1,8721,110701,50,8721,110701,40,8721,110765,0,8721,145287,3,12623,147442,4,14572,149527,1,16522,149527,50,16523,149527,40,16523,149591,0,16523,179587,3,19080,181088,4,20349,182521,1,21624,182521,50,21625,182521,40,21625,182585,0,21625,208999,3,23126,210142,4,23876,211292,1,24626,211292,50,24627,211292,40,24627,211356,0,24627,211866,5,26138,211866,1,26138,211866,50,26138,211866,40,26138,211930,0,26138,231779,3,27339,232760,4,27939,233698,1,28539,233698,50,28539,233698,40,28539,233762,0,28539,248690,3,29293,249504,4,29665,250398,5,30040,250399,1,30040,250399,50,30040,250399,40,30040,250399,40,30040,250508,0,30041,254251,50,30055,254360,0,30055,257830,50,30067,257830,30,30067,257830,40,30067,257885,0,30067,258008,50,30068,258008,30,30068,258008,40,30068,258063,0,30069,258181,50,30070,258181,30,30070,258181,40,30070,258236,0,30070,258432,50,30072,258487,0,30073,258752,50,30077,258752,30,30077,258752,40,30077,258807,0,30077,259011,50,30078,259011,30,30078,259011,40,30078,259066,0,30080,259273,50,30082,259328,0,30082,259596,50,30087,259651,0,30089,259930,50,30096,259985,0,30097,260284,50,30110,260339,0,30110,260644,50,30125,260699,0,30125,261012,50,30153,261067,0,30153,261389,50,30199,261444,0,30199,261776,50,30282,261776,40,30282,261831,0,30282)
%
%
% START OF PROOF
% 261557 [?] ?
% 261778 [] equal(multiply(identity,X),X).
% 261779 [] equal(multiply(inverse(X),X),identity).
% 261780 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 261781 [] -equal(multiply(sk_c10,sk_c11),sk_c9).
% 261823 [?] ?
% 261824 [?] ?
% 261826 [?] ?
% 261827 [?] ?
% 261830 [?] ?
% 261831 [?] ?
% 261905 [input:261823,cut:261781] equal(inverse(sk_c6),sk_c8).
% 261906 [para:261905.1.1,261779.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 261908 [input:261824,cut:261781] equal(inverse(sk_c7),sk_c6).
% 261909 [para:261908.1.1,261779.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 261911 [input:261826,cut:261781] equal(inverse(sk_c5),sk_c8).
% 261912 [para:261911.1.1,261779.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 261916 [input:261830,cut:261781] equal(inverse(sk_c3),sk_c11).
% 261917 [para:261916.1.1,261779.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 261934 [input:261827,cut:261781] equal(multiply(sk_c5,sk_c8),sk_c11).
% 261936 [input:261831,cut:261781] equal(multiply(sk_c3,sk_c11),sk_c10).
% 261964 [para:261906.1.1,261780.1.1.1,demod:261778] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 261969 [para:261909.1.1,261780.1.1.1,demod:261778] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 261974 [para:261917.1.1,261780.1.1.1,demod:261778] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 261995 [para:261934.1.1,261780.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 261998 [para:261909.1.1,261964.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 261999 [para:261998.1.2,261780.1.1.1,demod:261778] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 262029 [para:261936.1.1,261974.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 262031 [para:261999.1.1,261969.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 262035 [para:261906.1.1,262031.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 262036 [para:261912.1.1,262031.1.2.2,demod:262035] equal(sk_c5,sk_c6).
% 262044 [para:262036.1.2,261969.1.2.1,demod:261995,261999] equal(X,multiply(sk_c11,X)).
% 262053 [para:262044.1.2,262029.1.2] equal(sk_c11,sk_c10).
% 262060 [para:262053.1.2,261781.1.1.1,demod:262044,cut:261557] 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: 40563
% derived clauses: 3250817
% kept clauses: 138397
% kept size sum: 774807
% kept mid-nuclei: 68330
% kept new demods: 3046
% forw unit-subs: 495084
% forw double-subs: 2325909
% forw overdouble-subs: 114079
% backward subs: 19352
% fast unit cutoff: 30745
% full unit cutoff: 0
% dbl unit cutoff: 14383
% real runtime : 303.93
% process. runtime: 302.82
% specific non-discr-tree subsumption statistics:
% tried: 22523126
% length fails: 4484535
% strength fails: 5640116
% predlist fails: 185867
% aux str. fails: 3798562
% by-lit fails: 2495146
% full subs tried: 4296273
% full subs fail: 4232357
%
% ; 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/GRP338-1+eq_r.in")
%
%------------------------------------------------------------------------------