TSTP Solution File: GRP312-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP312-1 : 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 298.2s
% Output : Assurance 298.2s
% 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/GRP312-1+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 33)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 33)
% (binary-posweight-lex-big-order 30 #f 3 33)
% (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_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(Z,sk_c11),sk_c12) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% was split for some strategies as:
% -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X3),X1) | -equal(inverse(X2),X3) | -equal(multiply(X2,X1),X3).
% -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11).
% -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12).
% -equal(multiply(Z,sk_c11),sk_c12) | -equal(inverse(Z),sk_c11).
% -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11).
% -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12).
% -equal(multiply(sk_c11,sk_c12),sk_c10).
%
% 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_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(Z,sk_c11),sk_c12) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X3),X1) | -equal(inverse(X2),X3) | -equal(multiply(X2,X1),X3).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,1,160,0,2,83149,5,1503,83149,1,1503,83149,50,1503,83149,40,1503,83234,0,1503,89442,3,1807,91056,4,1958,91590,5,2104,91590,1,2104,91590,50,2104,91590,40,2104,91675,0,2104,93617,3,2406,93719,4,2575,93774,5,2705,93774,1,2705,93774,50,2705,93774,40,2705,93859,0,2705,113525,3,4206,115389,4,4956,117137,1,5706,117137,50,5706,117137,40,5706,117222,0,5706,129974,3,6460,131429,4,6832,132893,1,7207,132893,50,7207,132893,40,7207,132978,0,7207,147401,3,8079,148136,4,8333,149950,5,8708,149951,1,8708,149951,50,8708,149951,40,8708,150036,0,8708,186625,3,12611,188610,4,14559,190293,5,16509,190294,1,16509,190294,50,16510,190294,40,16510,190379,0,16510,218094,3,19061,219918,4,20336,221908,5,21611,221909,1,21611,221909,50,21612,221909,40,21612,221994,0,21612,246920,3,23113,248343,4,23863,249522,5,24613,249523,1,24613,249523,50,24614,249523,40,24614,249608,0,24614,263015,3,25389,265054,4,25740,267099,5,26115,267100,1,26115,267100,50,26115,267100,40,26115,267185,0,26115,287566,3,27316,288817,4,27916,289847,5,28516,289848,1,28516,289848,50,28516,289848,40,28516,289933,0,28517,304161,3,29268,305248,4,29643,306295,5,30018,306296,1,30018,306296,50,30018,306296,40,30018,306296,40,30018,306445,0,30018)
%
%
% START OF PROOF
% 306297 [] equal(X,X).
% 306298 [] equal(multiply(identity,X),X).
% 306299 [] equal(multiply(inverse(X),X),identity).
% 306300 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 306371 [] -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,X),sk_c12) | -equal(multiply(Z,X),U) | -equal(inverse(Z),U) | -equal(inverse(U),X) | -equal(inverse(Y),X).
% 306372 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst109,Y).
% 306373 [] -equal(multiply(X,Y),sk_c12) | -equal(inverse(X),Y) | $spltprd1($spltcnst110,Y).
% 306374 [] -equal(multiply(X,sk_c11),sk_c12) | $spltprd1($spltcnst111,X).
% 306375 [] -$spltprd1($spltcnst110,X) | -$spltprd1($spltcnst109,X) | -$spltprd1($spltcnst111,X).
% 306376 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c3),sk_c11).
% 306377 [] equal(inverse(sk_c3),sk_c11) | equal(inverse(sk_c7),sk_c9).
% 306378 [] equal(inverse(sk_c3),sk_c11) | equal(inverse(sk_c8),sk_c7).
% 306379 [] equal(multiply(sk_c9,sk_c11),sk_c12) | equal(inverse(sk_c3),sk_c11).
% 306380 [] equal(inverse(sk_c3),sk_c11) | equal(inverse(sk_c6),sk_c9).
% 306381 [?] ?
% 306386 [] equal(multiply(sk_c3,sk_c11),sk_c12) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 306387 [] equal(multiply(sk_c3,sk_c11),sk_c12) | equal(inverse(sk_c7),sk_c9).
% 306388 [] equal(multiply(sk_c3,sk_c11),sk_c12) | equal(inverse(sk_c8),sk_c7).
% 306389 [] equal(multiply(sk_c3,sk_c11),sk_c12) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 306390 [] equal(multiply(sk_c3,sk_c11),sk_c12) | equal(inverse(sk_c6),sk_c9).
% 306391 [] equal(multiply(sk_c3,sk_c11),sk_c12) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 306396 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c2),sk_c11).
% 306397 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c7),sk_c9).
% 306398 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c8),sk_c7).
% 306399 [] equal(multiply(sk_c9,sk_c11),sk_c12) | equal(inverse(sk_c2),sk_c11).
% 306400 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c6),sk_c9).
% 306401 [?] ?
% 306406 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 306407 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(inverse(sk_c7),sk_c9).
% 306408 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(inverse(sk_c8),sk_c7).
% 306409 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 306410 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(inverse(sk_c6),sk_c9).
% 306411 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 306416 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c1),sk_c12).
% 306417 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c7),sk_c9).
% 306418 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c8),sk_c7).
% 306419 [] equal(multiply(sk_c9,sk_c11),sk_c12) | equal(inverse(sk_c1),sk_c12).
% 306420 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c6),sk_c9).
% 306421 [?] ?
% 306426 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 306427 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(inverse(sk_c7),sk_c9).
% 306428 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(inverse(sk_c8),sk_c7).
% 306429 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 306430 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(inverse(sk_c6),sk_c9).
% 306431 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 306436 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 306437 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(inverse(sk_c7),sk_c9).
% 306438 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(inverse(sk_c8),sk_c7).
% 306439 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 306440 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(inverse(sk_c6),sk_c9).
% 306441 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 306536 [hyper:306373,306380,binarycut:306381] equal(inverse(sk_c3),sk_c11) | $spltprd1($spltcnst110,sk_c9).
% 306647 [hyper:306373,306400,binarycut:306401] equal(inverse(sk_c2),sk_c11) | $spltprd1($spltcnst110,sk_c9).
% 306732 [hyper:306373,306420,binarycut:306421] equal(inverse(sk_c1),sk_c12) | $spltprd1($spltcnst110,sk_c9).
% 306828 [hyper:306372,306376,306377,306378] equal(inverse(sk_c3),sk_c11) | $spltprd1($spltcnst109,sk_c9).
% 306880 [hyper:306374,306379] equal(inverse(sk_c3),sk_c11) | $spltprd1($spltcnst111,sk_c9).
% 306894 [hyper:306375,306880,306828,306536] equal(inverse(sk_c3),sk_c11).
% 306910 [para:306894.1.1,306299.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 307128 [hyper:306372,306396,306397,306398] equal(inverse(sk_c2),sk_c11) | $spltprd1($spltcnst109,sk_c9).
% 307163 [hyper:306374,306399] equal(inverse(sk_c2),sk_c11) | $spltprd1($spltcnst111,sk_c9).
% 307178 [hyper:306375,307163,307128,306647] equal(inverse(sk_c2),sk_c11).
% 307191 [para:307178.1.1,306299.1.1.1] equal(multiply(sk_c11,sk_c2),identity).
% 307308 [hyper:306372,306416,306417,306418] equal(inverse(sk_c1),sk_c12) | $spltprd1($spltcnst109,sk_c9).
% 307344 [hyper:306374,306419] equal(inverse(sk_c1),sk_c12) | $spltprd1($spltcnst111,sk_c9).
% 307360 [hyper:306375,307344,307308,306732] equal(inverse(sk_c1),sk_c12).
% 307373 [para:307360.1.1,306299.1.1.1] equal(multiply(sk_c12,sk_c1),identity).
% 307928 [hyper:306371,306391,306389,306390,306387,306386,306388] equal(multiply(sk_c3,sk_c11),sk_c12).
% 308091 [hyper:306371,306411,306409,306410,306407,306406,306408] equal(multiply(sk_c2,sk_c11),sk_c10).
% 308186 [hyper:306371,306431,306429,306430,306427,306426,306428] equal(multiply(sk_c1,sk_c12),sk_c11).
% 308249 [hyper:306371,306441,306439,306440,306437,306436,306438] equal(multiply(sk_c11,sk_c12),sk_c10).
% 308257 [para:306299.1.1,306300.1.1.1,demod:306298] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 308258 [para:306910.1.1,306300.1.1.1,demod:306298] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 308259 [para:307191.1.1,306300.1.1.1,demod:306298] equal(X,multiply(sk_c11,multiply(sk_c2,X))).
% 308260 [para:307373.1.1,306300.1.1.1,demod:306298] equal(X,multiply(sk_c12,multiply(sk_c1,X))).
% 308281 [para:307928.1.1,308258.1.2.2,demod:308249] equal(sk_c11,sk_c10).
% 308287 [para:308281.1.1,308249.1.1.1] equal(multiply(sk_c10,sk_c12),sk_c10).
% 308333 [para:308091.1.1,308259.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 308354 [para:308186.1.1,308260.1.2.2] equal(sk_c12,multiply(sk_c12,sk_c11)).
% 308356 [para:308281.1.1,308354.1.2.2] equal(sk_c12,multiply(sk_c12,sk_c10)).
% 308399 [para:306910.1.1,308257.1.2.2] equal(sk_c3,multiply(inverse(sk_c11),identity)).
% 308410 [para:308249.1.1,308257.1.2.2] equal(sk_c12,multiply(inverse(sk_c11),sk_c10)).
% 308411 [para:308258.1.2,308257.1.2.2] equal(multiply(sk_c3,X),multiply(inverse(sk_c11),X)).
% 308413 [para:308287.1.1,308257.1.2.2,demod:306299] equal(sk_c12,identity).
% 308415 [para:308333.1.2,308257.1.2.2,demod:307928,308411] equal(sk_c10,sk_c12).
% 308422 [para:308413.1.1,307373.1.1.1,demod:306298] equal(sk_c1,identity).
% 308427 [para:308413.1.1,308354.1.2.1,demod:306298] equal(sk_c12,sk_c11).
% 308431 [para:308415.1.2,308413.1.1] equal(sk_c10,identity).
% 308434 [para:308422.1.1,308260.1.2.2.1,demod:306298] equal(X,multiply(sk_c12,X)).
% 308435 [para:308427.1.2,306910.1.1.1,demod:308434] equal(sk_c3,identity).
% 308440 [para:308427.1.2,308333.1.2.1,demod:308356] equal(sk_c11,sk_c12).
% 308445 [para:308435.1.1,308258.1.2.2.1,demod:306298] equal(X,multiply(sk_c11,X)).
% 308943 [para:308431.1.1,308410.1.2.2,demod:308399] equal(sk_c12,sk_c3).
% 308946 [para:308943.1.1,308415.1.2] equal(sk_c10,sk_c3).
% 308952 [para:308946.1.2,306894.1.1.1] equal(inverse(sk_c10),sk_c11).
% 309049 [hyper:306371,308952,308091,307928,demod:308445,cut:308440,demod:307178,cut:308281,demod:306894,cut:306297] 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 33
% 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_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(Z,sk_c11),sk_c12) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),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 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,1,160,0,2,83149,5,1503,83149,1,1503,83149,50,1503,83149,40,1503,83234,0,1503,89442,3,1807,91056,4,1958,91590,5,2104,91590,1,2104,91590,50,2104,91590,40,2104,91675,0,2104,93617,3,2406,93719,4,2575,93774,5,2705,93774,1,2705,93774,50,2705,93774,40,2705,93859,0,2705,113525,3,4206,115389,4,4956,117137,1,5706,117137,50,5706,117137,40,5706,117222,0,5706,129974,3,6460,131429,4,6832,132893,1,7207,132893,50,7207,132893,40,7207,132978,0,7207,147401,3,8079,148136,4,8333,149950,5,8708,149951,1,8708,149951,50,8708,149951,40,8708,150036,0,8708,186625,3,12611,188610,4,14559,190293,5,16509,190294,1,16509,190294,50,16510,190294,40,16510,190379,0,16510,218094,3,19061,219918,4,20336,221908,5,21611,221909,1,21611,221909,50,21612,221909,40,21612,221994,0,21612,246920,3,23113,248343,4,23863,249522,5,24613,249523,1,24613,249523,50,24614,249523,40,24614,249608,0,24614,263015,3,25389,265054,4,25740,267099,5,26115,267100,1,26115,267100,50,26115,267100,40,26115,267185,0,26115,287566,3,27316,288817,4,27916,289847,5,28516,289848,1,28516,289848,50,28516,289848,40,28516,289933,0,28517,304161,3,29268,305248,4,29643,306295,5,30018,306296,1,30018,306296,50,30018,306296,40,30018,306296,40,30018,306445,0,30018,309048,50,30030,309048,30,30030,309048,40,30030,309123,0,30030)
%
%
% START OF PROOF
% 309049 [] equal(X,X).
% 309053 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 309080 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c5),sk_c11).
% 309081 [?] ?
% 309090 [?] ?
% 309091 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(multiply(sk_c5,sk_c11),sk_c10).
% 309157 [hyper:309053,309080,binarycut:309090] equal(inverse(sk_c5),sk_c11).
% 309159 [hyper:309053,309080,binarycut:309081] equal(inverse(sk_c2),sk_c11).
% 309183 [hyper:309053,309091,demod:309159,cut:309049] equal(multiply(sk_c5,sk_c11),sk_c10).
% 309186 [hyper:309053,309183,demod:309157,cut:309049] 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 33
% 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_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(Z,sk_c11),sk_c12) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(U,sk_c12),sk_c11) | -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 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,1,160,0,2,83149,5,1503,83149,1,1503,83149,50,1503,83149,40,1503,83234,0,1503,89442,3,1807,91056,4,1958,91590,5,2104,91590,1,2104,91590,50,2104,91590,40,2104,91675,0,2104,93617,3,2406,93719,4,2575,93774,5,2705,93774,1,2705,93774,50,2705,93774,40,2705,93859,0,2705,113525,3,4206,115389,4,4956,117137,1,5706,117137,50,5706,117137,40,5706,117222,0,5706,129974,3,6460,131429,4,6832,132893,1,7207,132893,50,7207,132893,40,7207,132978,0,7207,147401,3,8079,148136,4,8333,149950,5,8708,149951,1,8708,149951,50,8708,149951,40,8708,150036,0,8708,186625,3,12611,188610,4,14559,190293,5,16509,190294,1,16509,190294,50,16510,190294,40,16510,190379,0,16510,218094,3,19061,219918,4,20336,221908,5,21611,221909,1,21611,221909,50,21612,221909,40,21612,221994,0,21612,246920,3,23113,248343,4,23863,249522,5,24613,249523,1,24613,249523,50,24614,249523,40,24614,249608,0,24614,263015,3,25389,265054,4,25740,267099,5,26115,267100,1,26115,267100,50,26115,267100,40,26115,267185,0,26115,287566,3,27316,288817,4,27916,289847,5,28516,289848,1,28516,289848,50,28516,289848,40,28516,289933,0,28517,304161,3,29268,305248,4,29643,306295,5,30018,306296,1,30018,306296,50,30018,306296,40,30018,306296,40,30018,306445,0,30018,309048,50,30030,309048,30,30030,309048,40,30030,309123,0,30030,309185,50,30030,309185,30,30030,309185,40,30030,309260,0,30030)
%
%
% START OF PROOF
% 309186 [] equal(X,X).
% 309190 [] -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12).
% 309239 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 309240 [?] ?
% 309249 [?] ?
% 309250 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 309301 [hyper:309190,309239,binarycut:309249] equal(inverse(sk_c4),sk_c12).
% 309303 [hyper:309190,309239,binarycut:309240] equal(inverse(sk_c1),sk_c12).
% 309327 [hyper:309190,309250,demod:309303,cut:309186] equal(multiply(sk_c4,sk_c12),sk_c11).
% 309329 [hyper:309190,309327,demod:309301,cut:309186] 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 33
% 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_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(Z,sk_c11),sk_c12) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(Z,sk_c11),sk_c12) | -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 33
% 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 33
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,1,160,0,2,83149,5,1503,83149,1,1503,83149,50,1503,83149,40,1503,83234,0,1503,89442,3,1807,91056,4,1958,91590,5,2104,91590,1,2104,91590,50,2104,91590,40,2104,91675,0,2104,93617,3,2406,93719,4,2575,93774,5,2705,93774,1,2705,93774,50,2705,93774,40,2705,93859,0,2705,113525,3,4206,115389,4,4956,117137,1,5706,117137,50,5706,117137,40,5706,117222,0,5706,129974,3,6460,131429,4,6832,132893,1,7207,132893,50,7207,132893,40,7207,132978,0,7207,147401,3,8079,148136,4,8333,149950,5,8708,149951,1,8708,149951,50,8708,149951,40,8708,150036,0,8708,186625,3,12611,188610,4,14559,190293,5,16509,190294,1,16509,190294,50,16510,190294,40,16510,190379,0,16510,218094,3,19061,219918,4,20336,221908,5,21611,221909,1,21611,221909,50,21612,221909,40,21612,221994,0,21612,246920,3,23113,248343,4,23863,249522,5,24613,249523,1,24613,249523,50,24614,249523,40,24614,249608,0,24614,263015,3,25389,265054,4,25740,267099,5,26115,267100,1,26115,267100,50,26115,267100,40,26115,267185,0,26115,287566,3,27316,288817,4,27916,289847,5,28516,289848,1,28516,289848,50,28516,289848,40,28516,289933,0,28517,304161,3,29268,305248,4,29643,306295,5,30018,306296,1,30018,306296,50,30018,306296,40,30018,306296,40,30018,306445,0,30018,309048,50,30030,309048,30,30030,309048,40,30030,309123,0,30030,309185,50,30030,309185,30,30030,309185,40,30030,309260,0,30030,309328,50,30030,309328,30,30030,309328,40,30030,309403,0,30032,309591,50,30033,309666,0,30033)
%
%
% START OF PROOF
% 309593 [] equal(multiply(identity,X),X).
% 309594 [] equal(multiply(inverse(X),X),identity).
% 309595 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 309596 [] -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c11).
% 309597 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c3),sk_c11).
% 309598 [] equal(inverse(sk_c3),sk_c11) | equal(inverse(sk_c7),sk_c9).
% 309599 [] equal(inverse(sk_c3),sk_c11) | equal(inverse(sk_c8),sk_c7).
% 309600 [] equal(multiply(sk_c9,sk_c11),sk_c12) | equal(inverse(sk_c3),sk_c11).
% 309601 [] equal(inverse(sk_c3),sk_c11) | equal(inverse(sk_c6),sk_c9).
% 309602 [] equal(multiply(sk_c6,sk_c9),sk_c12) | equal(inverse(sk_c3),sk_c11).
% 309603 [] equal(inverse(sk_c3),sk_c11) | equal(inverse(sk_c5),sk_c11).
% 309605 [] equal(inverse(sk_c3),sk_c11) | equal(inverse(sk_c4),sk_c12).
% 309606 [] equal(multiply(sk_c4,sk_c12),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 309607 [?] ?
% 309608 [?] ?
% 309609 [?] ?
% 309610 [?] ?
% 309611 [?] ?
% 309612 [?] ?
% 309613 [?] ?
% 309615 [?] ?
% 309616 [?] ?
% 309669 [hyper:309596,309598,binarycut:309608] equal(inverse(sk_c7),sk_c9).
% 309670 [para:309669.1.1,309594.1.1.1] equal(multiply(sk_c9,sk_c7),identity).
% 309674 [hyper:309596,309599,binarycut:309609] equal(inverse(sk_c8),sk_c7).
% 309675 [para:309674.1.1,309594.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 309678 [hyper:309596,309601,binarycut:309611] equal(inverse(sk_c6),sk_c9).
% 309681 [hyper:309596,309597,binarycut:309607] equal(multiply(sk_c8,sk_c9),sk_c7).
% 309682 [para:309678.1.1,309594.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 309685 [hyper:309596,309603,binarycut:309613] equal(inverse(sk_c5),sk_c11).
% 309689 [para:309685.1.1,309594.1.1.1] equal(multiply(sk_c11,sk_c5),identity).
% 309694 [hyper:309596,309600,binarycut:309610] equal(multiply(sk_c9,sk_c11),sk_c12).
% 309700 [hyper:309596,309605,binarycut:309615] equal(inverse(sk_c4),sk_c12).
% 309701 [para:309700.1.1,309594.1.1.1] equal(multiply(sk_c12,sk_c4),identity).
% 309704 [hyper:309596,309602,binarycut:309612] equal(multiply(sk_c6,sk_c9),sk_c12).
% 309710 [hyper:309596,309606,binarycut:309616] equal(multiply(sk_c4,sk_c12),sk_c11).
% 309711 [para:309594.1.1,309595.1.1.1,demod:309593] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 309712 [para:309670.1.1,309595.1.1.1,demod:309593] equal(X,multiply(sk_c9,multiply(sk_c7,X))).
% 309713 [para:309675.1.1,309595.1.1.1,demod:309593] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 309714 [para:309681.1.1,309595.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c9,X))).
% 309715 [para:309682.1.1,309595.1.1.1,demod:309593] equal(X,multiply(sk_c9,multiply(sk_c6,X))).
% 309716 [para:309689.1.1,309595.1.1.1,demod:309593] equal(X,multiply(sk_c11,multiply(sk_c5,X))).
% 309718 [para:309701.1.1,309595.1.1.1,demod:309593] equal(X,multiply(sk_c12,multiply(sk_c4,X))).
% 309719 [para:309704.1.1,309595.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c6,multiply(sk_c9,X))).
% 309722 [para:309675.1.1,309712.1.2.2] equal(sk_c8,multiply(sk_c9,identity)).
% 309723 [para:309722.1.2,309595.1.1.1,demod:309593] equal(multiply(sk_c8,X),multiply(sk_c9,X)).
% 309724 [para:309681.1.1,309713.1.2.2] equal(sk_c9,multiply(sk_c7,sk_c7)).
% 309730 [para:309594.1.1,309711.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 309731 [para:309670.1.1,309711.1.2.2] equal(sk_c7,multiply(inverse(sk_c9),identity)).
% 309733 [para:309682.1.1,309711.1.2.2,demod:309731] equal(sk_c6,sk_c7).
% 309736 [para:309701.1.1,309711.1.2.2] equal(sk_c4,multiply(inverse(sk_c12),identity)).
% 309737 [para:309704.1.1,309711.1.2.2,demod:309678] equal(sk_c9,multiply(sk_c9,sk_c12)).
% 309740 [para:309595.1.1,309711.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 309742 [para:309711.1.2,309711.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 309744 [para:309733.1.2,309713.1.2.1,demod:309719,309723] equal(X,multiply(sk_c12,X)).
% 309747 [para:309744.1.2,309701.1.1] equal(sk_c4,identity).
% 309748 [para:309744.1.2,309711.1.2.2] equal(X,multiply(inverse(sk_c12),X)).
% 309750 [para:309747.1.1,309710.1.1.1,demod:309593] equal(sk_c12,sk_c11).
% 309752 [para:309750.1.2,309694.1.1.2,demod:309737] equal(sk_c9,sk_c12).
% 309756 [para:309670.1.1,309714.1.2.2,demod:309722,309723,309724] equal(sk_c9,sk_c8).
% 309758 [para:309722.1.2,309714.1.2.2,demod:309723] equal(multiply(sk_c7,identity),multiply(sk_c9,sk_c8)).
% 309762 [para:309752.1.2,309744.1.2.1] equal(X,multiply(sk_c9,X)).
% 309767 [para:309756.1.2,309674.1.1.1] equal(inverse(sk_c9),sk_c7).
% 309768 [para:309756.1.2,309713.1.2.2.1,demod:309762] equal(X,multiply(sk_c7,X)).
% 309774 [para:309715.1.2,309711.1.2.2,demod:309768,309767] equal(multiply(sk_c6,X),X).
% 309789 [para:309750.1.2,309716.1.2.1,demod:309744] equal(X,multiply(sk_c5,X)).
% 309799 [para:309718.1.2,309711.1.2.2,demod:309748] equal(multiply(sk_c4,X),X).
% 309844 [para:309752.1.2,309736.1.2.1.1,demod:309762,309758,309767] equal(sk_c4,sk_c8).
% 309845 [para:309844.1.2,309756.1.2] equal(sk_c9,sk_c4).
% 309850 [para:309845.1.1,309704.1.1.2,demod:309774] equal(sk_c4,sk_c12).
% 309853 [para:309850.1.2,309710.1.1.2,demod:309799] equal(sk_c4,sk_c11).
% 309902 [para:309742.1.2,309594.1.1] equal(multiply(X,inverse(X)),identity).
% 309904 [para:309742.1.2,309730.1.2] equal(X,multiply(X,identity)).
% 309905 [para:309904.1.2,309730.1.2] equal(X,inverse(inverse(X))).
% 309907 [para:309904.1.2,309736.1.2] equal(sk_c4,inverse(sk_c12)).
% 309911 [para:309902.1.1,309740.1.2.2.2,demod:309904] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 309918 [para:309716.1.2,309911.1.2.1.1,demod:309789] equal(inverse(X),multiply(inverse(X),sk_c11)).
% 309936 [para:309918.1.2,309742.1.2,demod:309905] equal(multiply(X,sk_c11),X).
% 309937 [hyper:309596,309936,demod:309907,cut:309853] 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 33
% 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_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(Z,sk_c11),sk_c12) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),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 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,1,160,0,2,83149,5,1503,83149,1,1503,83149,50,1503,83149,40,1503,83234,0,1503,89442,3,1807,91056,4,1958,91590,5,2104,91590,1,2104,91590,50,2104,91590,40,2104,91675,0,2104,93617,3,2406,93719,4,2575,93774,5,2705,93774,1,2705,93774,50,2705,93774,40,2705,93859,0,2705,113525,3,4206,115389,4,4956,117137,1,5706,117137,50,5706,117137,40,5706,117222,0,5706,129974,3,6460,131429,4,6832,132893,1,7207,132893,50,7207,132893,40,7207,132978,0,7207,147401,3,8079,148136,4,8333,149950,5,8708,149951,1,8708,149951,50,8708,149951,40,8708,150036,0,8708,186625,3,12611,188610,4,14559,190293,5,16509,190294,1,16509,190294,50,16510,190294,40,16510,190379,0,16510,218094,3,19061,219918,4,20336,221908,5,21611,221909,1,21611,221909,50,21612,221909,40,21612,221994,0,21612,246920,3,23113,248343,4,23863,249522,5,24613,249523,1,24613,249523,50,24614,249523,40,24614,249608,0,24614,263015,3,25389,265054,4,25740,267099,5,26115,267100,1,26115,267100,50,26115,267100,40,26115,267185,0,26115,287566,3,27316,288817,4,27916,289847,5,28516,289848,1,28516,289848,50,28516,289848,40,28516,289933,0,28517,304161,3,29268,305248,4,29643,306295,5,30018,306296,1,30018,306296,50,30018,306296,40,30018,306296,40,30018,306445,0,30018,309048,50,30030,309048,30,30030,309048,40,30030,309123,0,30030,309185,50,30030,309185,30,30030,309185,40,30030,309260,0,30030,309328,50,30030,309328,30,30030,309328,40,30030,309403,0,30032,309591,50,30033,309666,0,30033,309936,50,30037,309936,30,30037,309936,40,30037,310011,0,30038)
%
%
% START OF PROOF
% 309937 [] equal(X,X).
% 309941 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 309968 [] equal(inverse(sk_c2),sk_c11) | equal(inverse(sk_c5),sk_c11).
% 309969 [?] ?
% 309978 [?] ?
% 309979 [] equal(multiply(sk_c2,sk_c11),sk_c10) | equal(multiply(sk_c5,sk_c11),sk_c10).
% 310045 [hyper:309941,309968,binarycut:309978] equal(inverse(sk_c5),sk_c11).
% 310047 [hyper:309941,309968,binarycut:309969] equal(inverse(sk_c2),sk_c11).
% 310071 [hyper:309941,309979,demod:310047,cut:309937] equal(multiply(sk_c5,sk_c11),sk_c10).
% 310074 [hyper:309941,310071,demod:310045,cut:309937] 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 33
% 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_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(Z,sk_c11),sk_c12) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),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 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,1,160,0,2,83149,5,1503,83149,1,1503,83149,50,1503,83149,40,1503,83234,0,1503,89442,3,1807,91056,4,1958,91590,5,2104,91590,1,2104,91590,50,2104,91590,40,2104,91675,0,2104,93617,3,2406,93719,4,2575,93774,5,2705,93774,1,2705,93774,50,2705,93774,40,2705,93859,0,2705,113525,3,4206,115389,4,4956,117137,1,5706,117137,50,5706,117137,40,5706,117222,0,5706,129974,3,6460,131429,4,6832,132893,1,7207,132893,50,7207,132893,40,7207,132978,0,7207,147401,3,8079,148136,4,8333,149950,5,8708,149951,1,8708,149951,50,8708,149951,40,8708,150036,0,8708,186625,3,12611,188610,4,14559,190293,5,16509,190294,1,16509,190294,50,16510,190294,40,16510,190379,0,16510,218094,3,19061,219918,4,20336,221908,5,21611,221909,1,21611,221909,50,21612,221909,40,21612,221994,0,21612,246920,3,23113,248343,4,23863,249522,5,24613,249523,1,24613,249523,50,24614,249523,40,24614,249608,0,24614,263015,3,25389,265054,4,25740,267099,5,26115,267100,1,26115,267100,50,26115,267100,40,26115,267185,0,26115,287566,3,27316,288817,4,27916,289847,5,28516,289848,1,28516,289848,50,28516,289848,40,28516,289933,0,28517,304161,3,29268,305248,4,29643,306295,5,30018,306296,1,30018,306296,50,30018,306296,40,30018,306296,40,30018,306445,0,30018,309048,50,30030,309048,30,30030,309048,40,30030,309123,0,30030,309185,50,30030,309185,30,30030,309185,40,30030,309260,0,30030,309328,50,30030,309328,30,30030,309328,40,30030,309403,0,30032,309591,50,30033,309666,0,30033,309936,50,30037,309936,30,30037,309936,40,30037,310011,0,30038,310073,50,30038,310073,30,30038,310073,40,30039,310148,0,30039)
%
%
% START OF PROOF
% 310074 [] equal(X,X).
% 310078 [] -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12).
% 310127 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 310128 [?] ?
% 310137 [?] ?
% 310138 [] equal(multiply(sk_c1,sk_c12),sk_c11) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 310189 [hyper:310078,310127,binarycut:310137] equal(inverse(sk_c4),sk_c12).
% 310191 [hyper:310078,310127,binarycut:310128] equal(inverse(sk_c1),sk_c12).
% 310215 [hyper:310078,310138,demod:310191,cut:310074] equal(multiply(sk_c4,sk_c12),sk_c11).
% 310217 [hyper:310078,310215,demod:310189,cut:310074] 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 33
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12) | -equal(multiply(Y,sk_c11),sk_c10) | -equal(inverse(Y),sk_c11) | -equal(multiply(Z,sk_c11),sk_c12) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(sk_c11,sk_c12),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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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(75,40,1,160,0,2,83149,5,1503,83149,1,1503,83149,50,1503,83149,40,1503,83234,0,1503,89442,3,1807,91056,4,1958,91590,5,2104,91590,1,2104,91590,50,2104,91590,40,2104,91675,0,2104,93617,3,2406,93719,4,2575,93774,5,2705,93774,1,2705,93774,50,2705,93774,40,2705,93859,0,2705,113525,3,4206,115389,4,4956,117137,1,5706,117137,50,5706,117137,40,5706,117222,0,5706,129974,3,6460,131429,4,6832,132893,1,7207,132893,50,7207,132893,40,7207,132978,0,7207,147401,3,8079,148136,4,8333,149950,5,8708,149951,1,8708,149951,50,8708,149951,40,8708,150036,0,8708,186625,3,12611,188610,4,14559,190293,5,16509,190294,1,16509,190294,50,16510,190294,40,16510,190379,0,16510,218094,3,19061,219918,4,20336,221908,5,21611,221909,1,21611,221909,50,21612,221909,40,21612,221994,0,21612,246920,3,23113,248343,4,23863,249522,5,24613,249523,1,24613,249523,50,24614,249523,40,24614,249608,0,24614,263015,3,25389,265054,4,25740,267099,5,26115,267100,1,26115,267100,50,26115,267100,40,26115,267185,0,26115,287566,3,27316,288817,4,27916,289847,5,28516,289848,1,28516,289848,50,28516,289848,40,28516,289933,0,28517,304161,3,29268,305248,4,29643,306295,5,30018,306296,1,30018,306296,50,30018,306296,40,30018,306296,40,30018,306445,0,30018,309048,50,30030,309048,30,30030,309048,40,30030,309123,0,30030,309185,50,30030,309185,30,30030,309185,40,30030,309260,0,30030,309328,50,30030,309328,30,30030,309328,40,30030,309403,0,30032,309591,50,30033,309666,0,30033,309936,50,30037,309936,30,30037,309936,40,30037,310011,0,30038,310073,50,30038,310073,30,30038,310073,40,30039,310148,0,30039,310216,50,30039,310216,30,30039,310216,40,30039,310291,0,30040,310512,50,30042,310587,0,30042,310863,50,30046,310938,0,30048,311227,50,30055,311302,0,30055,311616,50,30065,311691,0,30067,312011,50,30082,312086,0,30082,312414,50,30106,312489,0,30106,312826,50,30149,312901,0,30149,313248,50,30229,313323,0,30229,313681,50,30378,313681,40,30378,313756,0,30378)
%
%
% START OF PROOF
% 313451 [?] ?
% 313683 [] equal(multiply(identity,X),X).
% 313684 [] equal(multiply(inverse(X),X),identity).
% 313685 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 313686 [] -equal(multiply(sk_c11,sk_c12),sk_c10).
% 313748 [?] ?
% 313749 [?] ?
% 313751 [?] ?
% 313752 [?] ?
% 313755 [?] ?
% 313756 [?] ?
% 313868 [input:313748,cut:313686] equal(inverse(sk_c7),sk_c9).
% 313869 [para:313868.1.1,313684.1.1.1] equal(multiply(sk_c9,sk_c7),identity).
% 313870 [input:313749,cut:313686] equal(inverse(sk_c8),sk_c7).
% 313871 [para:313870.1.1,313684.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 313873 [input:313751,cut:313686] equal(inverse(sk_c6),sk_c9).
% 313874 [para:313873.1.1,313684.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 313877 [input:313755,cut:313686] equal(inverse(sk_c4),sk_c12).
% 313878 [para:313877.1.1,313684.1.1.1] equal(multiply(sk_c12,sk_c4),identity).
% 313904 [input:313752,cut:313686] equal(multiply(sk_c6,sk_c9),sk_c12).
% 313906 [input:313756,cut:313686] equal(multiply(sk_c4,sk_c12),sk_c11).
% 313954 [para:313869.1.1,313685.1.1.1,demod:313683] equal(X,multiply(sk_c9,multiply(sk_c7,X))).
% 313955 [para:313871.1.1,313685.1.1.1,demod:313683] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 313962 [para:313878.1.1,313685.1.1.1,demod:313683] equal(X,multiply(sk_c12,multiply(sk_c4,X))).
% 313994 [para:313904.1.1,313685.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c6,multiply(sk_c9,X))).
% 314001 [para:313871.1.1,313954.1.2.2] equal(sk_c8,multiply(sk_c9,identity)).
% 314002 [para:314001.1.2,313685.1.1.1,demod:313683] equal(multiply(sk_c8,X),multiply(sk_c9,X)).
% 314038 [para:313906.1.1,313962.1.2.2] equal(sk_c12,multiply(sk_c12,sk_c11)).
% 314040 [para:314002.1.1,313955.1.2.2] equal(X,multiply(sk_c7,multiply(sk_c9,X))).
% 314045 [para:313869.1.1,314040.1.2.2] equal(sk_c7,multiply(sk_c7,identity)).
% 314047 [para:313874.1.1,314040.1.2.2,demod:314045] equal(sk_c6,sk_c7).
% 314054 [para:314047.1.2,313955.1.2.1,demod:313994,314002] equal(X,multiply(sk_c12,X)).
% 314063 [para:314054.1.2,314038.1.2] equal(sk_c12,sk_c11).
% 314072 [para:314063.1.2,313686.1.1.1,demod:314054,cut:313451] 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: 49039
% derived clauses: 3484040
% kept clauses: 161802
% kept size sum: 932986
% kept mid-nuclei: 81269
% kept new demods: 3261
% forw unit-subs: 610944
% forw double-subs: 2399936
% forw overdouble-subs: 137143
% backward subs: 18139
% fast unit cutoff: 29059
% full unit cutoff: 0
% dbl unit cutoff: 17960
% real runtime : 306.3
% process. runtime: 303.78
% specific non-discr-tree subsumption statistics:
% tried: 17070509
% length fails: 2115012
% strength fails: 4472650
% predlist fails: 779903
% aux str. fails: 1972582
% by-lit fails: 2763486
% full subs tried: 3067640
% full subs fail: 2979056
%
% ; 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/GRP312-1+eq_r.in")
%
%------------------------------------------------------------------------------