TSTP Solution File: GRP263-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP263-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art03.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 297.8s
% Output : Assurance 297.8s
% 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/GRP263-1+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(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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_c9) | -equal(inverse(Y),sk_c10).
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% -equal(multiply(sk_c9,sk_c10),sk_c11).
%
% 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,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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(55,40,1,119,0,1,113497,5,1502,113497,1,1502,113497,50,1502,113497,40,1502,113561,0,1502,125057,3,1803,125765,4,1953,126460,5,2103,126461,1,2103,126461,50,2103,126461,40,2103,126525,0,2103,127885,3,2410,127944,4,2575,128097,5,2704,128097,1,2704,128097,50,2704,128097,40,2704,128161,0,2704,155712,3,4206,156769,4,4955,157539,1,5705,157539,50,5705,157539,40,5705,157603,0,5706,176306,3,6457,177066,4,6832,177630,5,7207,177631,5,7207,177631,1,7207,177631,50,7207,177631,40,7207,177695,0,7207,194811,3,7958,195709,4,8333,197027,5,8708,197028,1,8708,197028,50,8708,197028,40,8708,197092,0,8708,244490,3,12611,246257,4,14559,247519,5,16509,247520,1,16509,247520,50,16511,247520,40,16511,247584,0,16511,288917,3,19063,290133,4,20337,291000,5,21612,291001,1,21612,291001,50,21613,291001,40,21613,291065,0,21613,328263,3,23114,328827,4,23864,330205,1,24614,330205,50,24615,330205,40,24615,330269,0,24615,347149,3,25376,348135,4,25741,350059,5,26116,350060,1,26116,350060,50,26116,350060,40,26116,350124,0,26116,374590,3,27318,375521,4,27917,376137,1,28517,376137,50,28518,376137,40,28518,376201,0,28518,393930,3,29269,394741,4,29644,395181,5,30019,395182,1,30019,395182,50,30019,395182,40,30019,395182,40,30019,395291,0,30019)
%
%
% START OF PROOF
% 395183 [] equal(X,X).
% 395184 [] equal(multiply(identity,X),X).
% 395185 [] equal(multiply(inverse(X),X),identity).
% 395186 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 395237 [] -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).
% 395238 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst97,Y).
% 395239 [] -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | $spltprd1($spltcnst98,Y).
% 395240 [] -equal(multiply(X,sk_c10),sk_c11) | $spltprd1($spltcnst99,X).
% 395241 [] -$spltprd1($spltcnst98,X) | -$spltprd1($spltcnst97,X) | -$spltprd1($spltcnst99,X).
% 395242 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 395243 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 395244 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 395245 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 395246 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 395247 [] equal(multiply(sk_c9,sk_c10),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 395252 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c10).
% 395253 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 395254 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 395255 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c2),sk_c10).
% 395256 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 395257 [?] ?
% 395262 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 395263 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(inverse(sk_c6),sk_c8).
% 395264 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 395265 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 395266 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 395267 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 395272 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c11).
% 395273 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 395274 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 395275 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 395276 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 395277 [?] ?
% 395282 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 395283 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 395284 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 395285 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 395286 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 395287 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 395358 [hyper:395239,395256,binarycut:395257] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst98,sk_c8).
% 395446 [hyper:395239,395276,binarycut:395277] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst98,sk_c8).
% 395650 [hyper:395238,395252,395253,395254] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst97,sk_c8).
% 395689 [hyper:395240,395255] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst99,sk_c8).
% 395705 [hyper:395241,395689,395650,395358] equal(inverse(sk_c2),sk_c10).
% 395717 [para:395705.1.1,395185.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 395821 [hyper:395238,395272,395273,395274] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst97,sk_c8).
% 395858 [hyper:395240,395275] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst99,sk_c8).
% 395874 [hyper:395241,395858,395821,395446] equal(inverse(sk_c1),sk_c11).
% 395886 [para:395874.1.1,395185.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 396261 [hyper:395237,395247,395245,395246,395243,395242,395244] equal(multiply(sk_c9,sk_c10),sk_c11).
% 396384 [hyper:395237,395267,395265,395266,395263,395262,395264] equal(multiply(sk_c2,sk_c10),sk_c9).
% 396458 [hyper:395237,395287,395285,395286,395283,395282,395284] equal(multiply(sk_c1,sk_c11),sk_c10).
% 396466 [para:395185.1.1,395186.1.1.1,demod:395184] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 396467 [para:395717.1.1,395186.1.1.1,demod:395184] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 396468 [para:395886.1.1,395186.1.1.1,demod:395184] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 396470 [para:396384.1.1,395186.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c2,multiply(sk_c10,X))).
% 396488 [para:396384.1.1,396467.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 396506 [para:396458.1.1,396468.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 396517 [para:395717.1.1,396466.1.2.2] equal(sk_c2,multiply(inverse(sk_c10),identity)).
% 396518 [para:395886.1.1,396466.1.2.2] equal(sk_c1,multiply(inverse(sk_c11),identity)).
% 396528 [para:396467.1.2,396466.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c10),X)).
% 396549 [para:396528.1.2,395185.1.1,demod:396384] equal(sk_c9,identity).
% 396552 [para:396528.1.2,396466.1.2,demod:396470] equal(X,multiply(sk_c9,X)).
% 396554 [para:396549.1.1,396261.1.1.1,demod:395184] equal(sk_c10,sk_c11).
% 396556 [para:396549.1.1,396488.1.2.2] equal(sk_c10,multiply(sk_c10,identity)).
% 396558 [para:396554.1.2,396458.1.1.2] equal(multiply(sk_c1,sk_c10),sk_c10).
% 396561 [para:396554.1.2,396518.1.2.1.1,demod:396517] equal(sk_c1,sk_c2).
% 396595 [para:396561.1.1,396558.1.1.1,demod:396384] equal(sk_c9,sk_c10).
% 396597 [para:396595.1.1,396549.1.1] equal(sk_c10,identity).
% 396602 [para:396597.1.1,395717.1.1.1,demod:395184] equal(sk_c2,identity).
% 396603 [para:396597.1.1,396261.1.1.2,demod:396552] equal(identity,sk_c11).
% 396610 [para:396602.1.1,395705.1.1.1] equal(inverse(identity),sk_c10).
% 396612 [para:396603.1.2,396506.1.2.1,demod:395184] equal(sk_c11,sk_c10).
% 396613 [para:396603.1.2,396518.1.2.1.1,demod:396556,396610] equal(sk_c1,sk_c10).
% 396619 [para:396613.1.1,395874.1.1.1] equal(inverse(sk_c10),sk_c11).
% 396631 [hyper:395237,396610,395184,demod:396619,395184,demod:396610,396506,cut:395183,cut:396554,cut:395183,cut:396612] 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 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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(55,40,1,119,0,1,113497,5,1502,113497,1,1502,113497,50,1502,113497,40,1502,113561,0,1502,125057,3,1803,125765,4,1953,126460,5,2103,126461,1,2103,126461,50,2103,126461,40,2103,126525,0,2103,127885,3,2410,127944,4,2575,128097,5,2704,128097,1,2704,128097,50,2704,128097,40,2704,128161,0,2704,155712,3,4206,156769,4,4955,157539,1,5705,157539,50,5705,157539,40,5705,157603,0,5706,176306,3,6457,177066,4,6832,177630,5,7207,177631,5,7207,177631,1,7207,177631,50,7207,177631,40,7207,177695,0,7207,194811,3,7958,195709,4,8333,197027,5,8708,197028,1,8708,197028,50,8708,197028,40,8708,197092,0,8708,244490,3,12611,246257,4,14559,247519,5,16509,247520,1,16509,247520,50,16511,247520,40,16511,247584,0,16511,288917,3,19063,290133,4,20337,291000,5,21612,291001,1,21612,291001,50,21613,291001,40,21613,291065,0,21613,328263,3,23114,328827,4,23864,330205,1,24614,330205,50,24615,330205,40,24615,330269,0,24615,347149,3,25376,348135,4,25741,350059,5,26116,350060,1,26116,350060,50,26116,350060,40,26116,350124,0,26116,374590,3,27318,375521,4,27917,376137,1,28517,376137,50,28518,376137,40,28518,376201,0,28518,393930,3,29269,394741,4,29644,395181,5,30019,395182,1,30019,395182,50,30019,395182,40,30019,395182,40,30019,395291,0,30019,396630,50,30027,396630,30,30027,396630,40,30027,396685,0,30027)
%
%
% START OF PROOF
% 396631 [] equal(X,X).
% 396635 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 396652 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 396653 [?] ?
% 396662 [?] ?
% 396663 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 396702 [hyper:396635,396652,binarycut:396662] equal(inverse(sk_c4),sk_c10).
% 396704 [hyper:396635,396652,binarycut:396653] equal(inverse(sk_c2),sk_c10).
% 396732 [hyper:396635,396663,demod:396704,cut:396631] equal(multiply(sk_c4,sk_c10),sk_c9).
% 396735 [hyper:396635,396732,demod:396702,cut:396631] 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(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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(55,40,1,119,0,1,113497,5,1502,113497,1,1502,113497,50,1502,113497,40,1502,113561,0,1502,125057,3,1803,125765,4,1953,126460,5,2103,126461,1,2103,126461,50,2103,126461,40,2103,126525,0,2103,127885,3,2410,127944,4,2575,128097,5,2704,128097,1,2704,128097,50,2704,128097,40,2704,128161,0,2704,155712,3,4206,156769,4,4955,157539,1,5705,157539,50,5705,157539,40,5705,157603,0,5706,176306,3,6457,177066,4,6832,177630,5,7207,177631,5,7207,177631,1,7207,177631,50,7207,177631,40,7207,177695,0,7207,194811,3,7958,195709,4,8333,197027,5,8708,197028,1,8708,197028,50,8708,197028,40,8708,197092,0,8708,244490,3,12611,246257,4,14559,247519,5,16509,247520,1,16509,247520,50,16511,247520,40,16511,247584,0,16511,288917,3,19063,290133,4,20337,291000,5,21612,291001,1,21612,291001,50,21613,291001,40,21613,291065,0,21613,328263,3,23114,328827,4,23864,330205,1,24614,330205,50,24615,330205,40,24615,330269,0,24615,347149,3,25376,348135,4,25741,350059,5,26116,350060,1,26116,350060,50,26116,350060,40,26116,350124,0,26116,374590,3,27318,375521,4,27917,376137,1,28517,376137,50,28518,376137,40,28518,376201,0,28518,393930,3,29269,394741,4,29644,395181,5,30019,395182,1,30019,395182,50,30019,395182,40,30019,395182,40,30019,395291,0,30019,396630,50,30027,396630,30,30027,396630,40,30027,396685,0,30027,396734,50,30027,396734,30,30027,396734,40,30027,396789,0,30027)
%
%
% START OF PROOF
% 396735 [] equal(X,X).
% 396739 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 396778 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 396779 [?] ?
% 396788 [?] ?
% 396789 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 396819 [hyper:396739,396778,binarycut:396788] equal(inverse(sk_c3),sk_c11).
% 396821 [hyper:396739,396778,binarycut:396779] equal(inverse(sk_c1),sk_c11).
% 396847 [hyper:396739,396789,demod:396821,cut:396735] equal(multiply(sk_c3,sk_c11),sk_c10).
% 396849 [hyper:396739,396847,demod:396819,cut:396735] 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(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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_c9) | -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
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,119,0,1,113497,5,1502,113497,1,1502,113497,50,1502,113497,40,1502,113561,0,1502,125057,3,1803,125765,4,1953,126460,5,2103,126461,1,2103,126461,50,2103,126461,40,2103,126525,0,2103,127885,3,2410,127944,4,2575,128097,5,2704,128097,1,2704,128097,50,2704,128097,40,2704,128161,0,2704,155712,3,4206,156769,4,4955,157539,1,5705,157539,50,5705,157539,40,5705,157603,0,5706,176306,3,6457,177066,4,6832,177630,5,7207,177631,5,7207,177631,1,7207,177631,50,7207,177631,40,7207,177695,0,7207,194811,3,7958,195709,4,8333,197027,5,8708,197028,1,8708,197028,50,8708,197028,40,8708,197092,0,8708,244490,3,12611,246257,4,14559,247519,5,16509,247520,1,16509,247520,50,16511,247520,40,16511,247584,0,16511,288917,3,19063,290133,4,20337,291000,5,21612,291001,1,21612,291001,50,21613,291001,40,21613,291065,0,21613,328263,3,23114,328827,4,23864,330205,1,24614,330205,50,24615,330205,40,24615,330269,0,24615,347149,3,25376,348135,4,25741,350059,5,26116,350060,1,26116,350060,50,26116,350060,40,26116,350124,0,26116,374590,3,27318,375521,4,27917,376137,1,28517,376137,50,28518,376137,40,28518,376201,0,28518,393930,3,29269,394741,4,29644,395181,5,30019,395182,1,30019,395182,50,30019,395182,40,30019,395182,40,30019,395291,0,30019,396630,50,30027,396630,30,30027,396630,40,30027,396685,0,30027,396734,50,30027,396734,30,30027,396734,40,30027,396789,0,30027,396848,50,30027,396848,30,30027,396848,40,30027,396903,0,30032)
%
%
% START OF PROOF
% 396849 [] equal(X,X).
% 396853 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 396870 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 396871 [?] ?
% 396880 [?] ?
% 396881 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 396920 [hyper:396853,396870,binarycut:396880] equal(inverse(sk_c4),sk_c10).
% 396922 [hyper:396853,396870,binarycut:396871] equal(inverse(sk_c2),sk_c10).
% 396950 [hyper:396853,396881,demod:396922,cut:396849] equal(multiply(sk_c4,sk_c10),sk_c9).
% 396953 [hyper:396853,396950,demod:396920,cut:396849] 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 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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(X,sk_c11),sk_c10) | -equal(inverse(X),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(55,40,1,119,0,1,113497,5,1502,113497,1,1502,113497,50,1502,113497,40,1502,113561,0,1502,125057,3,1803,125765,4,1953,126460,5,2103,126461,1,2103,126461,50,2103,126461,40,2103,126525,0,2103,127885,3,2410,127944,4,2575,128097,5,2704,128097,1,2704,128097,50,2704,128097,40,2704,128161,0,2704,155712,3,4206,156769,4,4955,157539,1,5705,157539,50,5705,157539,40,5705,157603,0,5706,176306,3,6457,177066,4,6832,177630,5,7207,177631,5,7207,177631,1,7207,177631,50,7207,177631,40,7207,177695,0,7207,194811,3,7958,195709,4,8333,197027,5,8708,197028,1,8708,197028,50,8708,197028,40,8708,197092,0,8708,244490,3,12611,246257,4,14559,247519,5,16509,247520,1,16509,247520,50,16511,247520,40,16511,247584,0,16511,288917,3,19063,290133,4,20337,291000,5,21612,291001,1,21612,291001,50,21613,291001,40,21613,291065,0,21613,328263,3,23114,328827,4,23864,330205,1,24614,330205,50,24615,330205,40,24615,330269,0,24615,347149,3,25376,348135,4,25741,350059,5,26116,350060,1,26116,350060,50,26116,350060,40,26116,350124,0,26116,374590,3,27318,375521,4,27917,376137,1,28517,376137,50,28518,376137,40,28518,376201,0,28518,393930,3,29269,394741,4,29644,395181,5,30019,395182,1,30019,395182,50,30019,395182,40,30019,395182,40,30019,395291,0,30019,396630,50,30027,396630,30,30027,396630,40,30027,396685,0,30027,396734,50,30027,396734,30,30027,396734,40,30027,396789,0,30027,396848,50,30027,396848,30,30027,396848,40,30027,396903,0,30032,396952,50,30032,396952,30,30032,396952,40,30032,397007,0,30032)
%
%
% START OF PROOF
% 396953 [] equal(X,X).
% 396957 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 396996 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 396997 [?] ?
% 397006 [?] ?
% 397007 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 397037 [hyper:396957,396996,binarycut:397006] equal(inverse(sk_c3),sk_c11).
% 397039 [hyper:396957,396996,binarycut:396997] equal(inverse(sk_c1),sk_c11).
% 397065 [hyper:396957,397007,demod:397039,cut:396953] equal(multiply(sk_c3,sk_c11),sk_c10).
% 397067 [hyper:396957,397065,demod:397037,cut:396953] 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(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c10),sk_c11) | -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_c9,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
%
%
% 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 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 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(55,40,1,119,0,1,113497,5,1502,113497,1,1502,113497,50,1502,113497,40,1502,113561,0,1502,125057,3,1803,125765,4,1953,126460,5,2103,126461,1,2103,126461,50,2103,126461,40,2103,126525,0,2103,127885,3,2410,127944,4,2575,128097,5,2704,128097,1,2704,128097,50,2704,128097,40,2704,128161,0,2704,155712,3,4206,156769,4,4955,157539,1,5705,157539,50,5705,157539,40,5705,157603,0,5706,176306,3,6457,177066,4,6832,177630,5,7207,177631,5,7207,177631,1,7207,177631,50,7207,177631,40,7207,177695,0,7207,194811,3,7958,195709,4,8333,197027,5,8708,197028,1,8708,197028,50,8708,197028,40,8708,197092,0,8708,244490,3,12611,246257,4,14559,247519,5,16509,247520,1,16509,247520,50,16511,247520,40,16511,247584,0,16511,288917,3,19063,290133,4,20337,291000,5,21612,291001,1,21612,291001,50,21613,291001,40,21613,291065,0,21613,328263,3,23114,328827,4,23864,330205,1,24614,330205,50,24615,330205,40,24615,330269,0,24615,347149,3,25376,348135,4,25741,350059,5,26116,350060,1,26116,350060,50,26116,350060,40,26116,350124,0,26116,374590,3,27318,375521,4,27917,376137,1,28517,376137,50,28518,376137,40,28518,376201,0,28518,393930,3,29269,394741,4,29644,395181,5,30019,395182,1,30019,395182,50,30019,395182,40,30019,395182,40,30019,395291,0,30019,396630,50,30027,396630,30,30027,396630,40,30027,396685,0,30027,396734,50,30027,396734,30,30027,396734,40,30027,396789,0,30027,396848,50,30027,396848,30,30027,396848,40,30027,396903,0,30032,396952,50,30032,396952,30,30032,396952,40,30032,397007,0,30032,397066,50,30032,397066,30,30032,397066,40,30032,397121,0,30037,397314,50,30038,397369,0,30038,397635,50,30044,397690,0,30048,397964,50,30055,398019,0,30055,398301,50,30064,398356,0,30069,398644,50,30082,398699,0,30082,398995,50,30103,399050,0,30107,399354,50,30144,399409,0,30144,399723,50,30217,399778,0,30218,400102,50,30350,400102,40,30350,400157,0,30350)
%
%
% START OF PROOF
% 400104 [] equal(multiply(identity,X),X).
% 400105 [] equal(multiply(inverse(X),X),identity).
% 400106 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 400107 [] -equal(multiply(sk_c9,sk_c10),sk_c11).
% 400109 [?] ?
% 400110 [?] ?
% 400112 [?] ?
% 400113 [?] ?
% 400114 [?] ?
% 400115 [?] ?
% 400116 [?] ?
% 400117 [?] ?
% 400177 [input:400109,cut:400107] equal(inverse(sk_c6),sk_c8).
% 400178 [para:400177.1.1,400105.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 400191 [input:400110,cut:400107] equal(inverse(sk_c7),sk_c6).
% 400192 [para:400191.1.1,400105.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 400193 [input:400112,cut:400107] equal(inverse(sk_c5),sk_c8).
% 400194 [para:400193.1.1,400105.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 400195 [input:400114,cut:400107] equal(inverse(sk_c4),sk_c10).
% 400196 [para:400195.1.1,400105.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 400198 [input:400116,cut:400107] equal(inverse(sk_c3),sk_c11).
% 400199 [para:400198.1.1,400105.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 400206 [input:400113,cut:400107] equal(multiply(sk_c5,sk_c8),sk_c11).
% 400214 [input:400115,cut:400107] equal(multiply(sk_c4,sk_c10),sk_c9).
% 400219 [input:400117,cut:400107] equal(multiply(sk_c3,sk_c11),sk_c10).
% 400255 [para:400178.1.1,400106.1.1.1,demod:400104] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 400256 [para:400192.1.1,400106.1.1.1,demod:400104] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 400258 [para:400196.1.1,400106.1.1.1,demod:400104] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 400260 [para:400199.1.1,400106.1.1.1,demod:400104] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 400262 [para:400206.1.1,400106.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 400297 [para:400192.1.1,400255.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 400298 [para:400297.1.2,400106.1.1.1,demod:400104] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 400310 [para:400214.1.1,400258.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 400315 [para:400219.1.1,400260.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 400317 [para:400298.1.1,400256.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 400318 [para:400178.1.1,400317.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 400319 [para:400194.1.1,400317.1.2.2,demod:400318] equal(sk_c5,sk_c6).
% 400326 [para:400319.1.2,400256.1.2.1,demod:400262,400298] equal(X,multiply(sk_c11,X)).
% 400334 [para:400326.1.2,400260.1.2] equal(X,multiply(sk_c3,X)).
% 400335 [para:400326.1.2,400315.1.2] equal(sk_c11,sk_c10).
% 400336 [para:400315.1.2,400326.1.2] equal(sk_c10,sk_c11).
% 400353 [para:400335.1.1,400260.1.2.1,demod:400334] equal(X,multiply(sk_c10,X)).
% 400365 [para:400353.1.2,400310.1.2] equal(sk_c10,sk_c9).
% 400368 [para:400365.1.2,400107.1.1.1,demod:400353,cut:400336] 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: 36466
% derived clauses: 4330569
% kept clauses: 234596
% kept size sum: 16544
% kept mid-nuclei: 108623
% kept new demods: 2868
% forw unit-subs: 1425023
% forw double-subs: 2267610
% forw overdouble-subs: 212873
% backward subs: 14636
% fast unit cutoff: 38408
% full unit cutoff: 5
% dbl unit cutoff: 18738
% real runtime : 306.2
% process. runtime: 303.51
% specific non-discr-tree subsumption statistics:
% tried: 30044880
% length fails: 3460738
% strength fails: 11645013
% predlist fails: 2325898
% aux str. fails: 1704368
% by-lit fails: 4834852
% full subs tried: 2289636
% full subs fail: 2147856
%
% ; 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/GRP263-1+eq_r.in")
%
%------------------------------------------------------------------------------