TSTP Solution File: GRP330-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP330-1 : 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 : art05.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 299.5s
% Output : Assurance 299.5s
% 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/GRP330-1+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(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c10) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(inverse(Y),sk_c9) | -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_c9),sk_c10) | -equal(inverse(Y),sk_c9).
% -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c10).
% -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(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c10) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(inverse(Y),sk_c9) | -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(55,40,0,119,0,0,69544,4,1317,73133,5,1502,73133,1,1502,73133,50,1502,73133,40,1502,73197,0,1502,75295,3,1947,75468,4,1953,75705,5,2103,75705,1,2103,75705,50,2103,75705,40,2103,75769,0,2103,77867,3,2549,78018,4,2554,78277,5,2704,78277,1,2704,78277,50,2704,78277,40,2704,78341,0,2704,99465,3,4206,100833,4,4955,101975,1,5705,101975,50,5705,101975,40,5705,102039,0,5705,115617,3,6456,116575,4,6831,117488,1,7206,117488,50,7206,117488,40,7206,117552,0,7206,128160,3,7981,129980,4,8332,132009,5,8707,132010,1,8707,132010,50,8707,132010,40,8707,132074,0,8707,171806,3,12610,173402,4,14558,175061,1,16508,175061,50,16509,175061,40,16509,175125,0,16510,209516,3,19074,210767,4,20336,211774,1,21611,211774,50,21612,211774,40,21612,211838,0,21612,240500,3,23114,241504,4,23863,242492,1,24613,242492,50,24614,242492,40,24614,242556,0,24614,250984,3,25418,254161,4,25740,255771,5,26115,255771,1,26115,255771,50,26115,255771,40,26115,255835,0,26115,278187,3,27316,279052,4,27916,279901,1,28516,279901,50,28516,279901,40,28516,279965,0,28517,296162,3,29268,296814,4,29643,297368,1,30018,297368,50,30018,297368,40,30018,297368,40,30018,297477,0,30019)
%
%
% START OF PROOF
% 297369 [] equal(X,X).
% 297370 [] equal(multiply(identity,X),X).
% 297371 [] equal(multiply(inverse(X),X),identity).
% 297372 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 297423 [] -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).
% 297424 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst97,Y).
% 297425 [] -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | $spltprd1($spltcnst98,Y).
% 297426 [] -equal(multiply(X,sk_c10),sk_c11) | $spltprd1($spltcnst99,X).
% 297427 [] -$spltprd1($spltcnst98,X) | -$spltprd1($spltcnst97,X) | -$spltprd1($spltcnst99,X).
% 297428 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c9).
% 297429 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c6),sk_c8).
% 297430 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 297431 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c2),sk_c9).
% 297432 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 297433 [?] ?
% 297438 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 297439 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 297440 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 297441 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 297442 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 297443 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 297448 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c10).
% 297449 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 297450 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 297451 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c10).
% 297452 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 297453 [?] ?
% 297458 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 297459 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 297460 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 297461 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 297462 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 297463 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 297468 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 297469 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c6),sk_c8).
% 297470 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 297471 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 297472 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 297473 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 297544 [hyper:297425,297432,binarycut:297433] equal(inverse(sk_c2),sk_c9) | $spltprd1($spltcnst98,sk_c8).
% 297654 [hyper:297425,297452,binarycut:297453] equal(inverse(sk_c1),sk_c10) | $spltprd1($spltcnst98,sk_c8).
% 297758 [hyper:297424,297428,297429,297430] equal(inverse(sk_c2),sk_c9) | $spltprd1($spltcnst97,sk_c8).
% 297787 [hyper:297426,297431] equal(inverse(sk_c2),sk_c9) | $spltprd1($spltcnst99,sk_c8).
% 297798 [hyper:297427,297787,297758,297544] equal(inverse(sk_c2),sk_c9).
% 297805 [para:297798.1.1,297371.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 297888 [hyper:297424,297448,297449,297450] equal(inverse(sk_c1),sk_c10) | $spltprd1($spltcnst97,sk_c8).
% 297932 [hyper:297426,297451] equal(inverse(sk_c1),sk_c10) | $spltprd1($spltcnst99,sk_c8).
% 297944 [hyper:297427,297932,297654,297888] equal(inverse(sk_c1),sk_c10).
% 297951 [para:297944.1.1,297371.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 298482 [hyper:297423,297443,297441,297442,297439,297438,297440] equal(multiply(sk_c2,sk_c9),sk_c10).
% 298688 [hyper:297423,297463,297461,297462,297459,297458,297460] equal(multiply(sk_c1,sk_c10),sk_c11).
% 298774 [hyper:297423,297473,297471,297472,297469,297468,297470] equal(multiply(sk_c10,sk_c11),sk_c9).
% 298782 [para:297371.1.1,297372.1.1.1,demod:297370] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 298783 [para:297805.1.1,297372.1.1.1,demod:297370] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 298784 [para:297951.1.1,297372.1.1.1,demod:297370] equal(X,multiply(sk_c10,multiply(sk_c1,X))).
% 298785 [para:298482.1.1,297372.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c2,multiply(sk_c9,X))).
% 298804 [para:298482.1.1,298783.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c10)).
% 298822 [para:298688.1.1,298784.1.2.2,demod:298774] equal(sk_c10,sk_c9).
% 298827 [para:298822.1.1,298804.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c9)).
% 298828 [para:298822.1.1,298784.1.2.1] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 298873 [para:297805.1.1,298782.1.2.2] equal(sk_c2,multiply(inverse(sk_c9),identity)).
% 298884 [para:298783.1.2,298782.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c9),X)).
% 298888 [para:298827.1.2,298782.1.2.2,demod:298482,298884] equal(sk_c9,sk_c10).
% 298889 [para:298828.1.2,298782.1.2.2,demod:298884] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 298968 [para:298884.1.2,297371.1.1,demod:298482] equal(sk_c10,identity).
% 298971 [para:298884.1.2,298782.1.2,demod:298785] equal(X,multiply(sk_c10,X)).
% 298972 [para:298884.1.2,298873.1.2,demod:298889] equal(sk_c2,multiply(sk_c1,identity)).
% 298973 [para:298968.1.1,297951.1.1.1,demod:297370] equal(sk_c1,identity).
% 298974 [para:298968.1.1,298688.1.1.2,demod:298972] equal(sk_c2,sk_c11).
% 298981 [para:298973.1.1,297944.1.1.1] equal(inverse(identity),sk_c10).
% 298982 [para:298973.1.1,298688.1.1.1,demod:297370] equal(sk_c10,sk_c11).
% 298987 [para:298974.1.2,298774.1.1.2,demod:298971] equal(sk_c2,sk_c9).
% 298999 [para:298987.1.1,297798.1.1.1] equal(inverse(sk_c9),sk_c9).
% 299091 [hyper:297423,298981,298884,demod:298971,297370,cut:298982,cut:298982,demod:297798,298804,298999,cut:298888,cut:297369] 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(sk_c10,sk_c11),sk_c9) | -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c10) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(inverse(Y),sk_c9) | -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(55,40,0,119,0,0,69544,4,1317,73133,5,1502,73133,1,1502,73133,50,1502,73133,40,1502,73197,0,1502,75295,3,1947,75468,4,1953,75705,5,2103,75705,1,2103,75705,50,2103,75705,40,2103,75769,0,2103,77867,3,2549,78018,4,2554,78277,5,2704,78277,1,2704,78277,50,2704,78277,40,2704,78341,0,2704,99465,3,4206,100833,4,4955,101975,1,5705,101975,50,5705,101975,40,5705,102039,0,5705,115617,3,6456,116575,4,6831,117488,1,7206,117488,50,7206,117488,40,7206,117552,0,7206,128160,3,7981,129980,4,8332,132009,5,8707,132010,1,8707,132010,50,8707,132010,40,8707,132074,0,8707,171806,3,12610,173402,4,14558,175061,1,16508,175061,50,16509,175061,40,16509,175125,0,16510,209516,3,19074,210767,4,20336,211774,1,21611,211774,50,21612,211774,40,21612,211838,0,21612,240500,3,23114,241504,4,23863,242492,1,24613,242492,50,24614,242492,40,24614,242556,0,24614,250984,3,25418,254161,4,25740,255771,5,26115,255771,1,26115,255771,50,26115,255771,40,26115,255835,0,26115,278187,3,27316,279052,4,27916,279901,1,28516,279901,50,28516,279901,40,28516,279965,0,28517,296162,3,29268,296814,4,29643,297368,1,30018,297368,50,30018,297368,40,30018,297368,40,30018,297477,0,30019,299090,50,30025,299090,30,30025,299090,40,30025,299145,0,30025)
%
%
% START OF PROOF
% 299091 [] equal(X,X).
% 299092 [] equal(multiply(identity,X),X).
% 299093 [] equal(multiply(inverse(X),X),identity).
% 299094 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 299095 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 299102 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c4),sk_c10).
% 299103 [?] ?
% 299112 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 299113 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 299122 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 299123 [?] ?
% 299132 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 299133 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 299142 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c4),sk_c10).
% 299143 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 299152 [hyper:299095,299102,binarycut:299103] equal(inverse(sk_c2),sk_c9).
% 299153 [para:299152.1.1,299093.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 299167 [hyper:299095,299122,binarycut:299123] equal(inverse(sk_c1),sk_c10).
% 299170 [para:299167.1.1,299093.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 299196 [hyper:299095,299113,299112] equal(multiply(sk_c2,sk_c9),sk_c10).
% 299203 [hyper:299095,299133,299132] equal(multiply(sk_c1,sk_c10),sk_c11).
% 299209 [hyper:299095,299143,299142] equal(multiply(sk_c10,sk_c11),sk_c9).
% 299210 [para:299093.1.1,299094.1.1.1,demod:299092] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 299211 [para:299153.1.1,299094.1.1.1,demod:299092] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 299212 [para:299170.1.1,299094.1.1.1,demod:299092] equal(X,multiply(sk_c10,multiply(sk_c1,X))).
% 299213 [para:299196.1.1,299094.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c2,multiply(sk_c9,X))).
% 299214 [para:299203.1.1,299094.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c1,multiply(sk_c10,X))).
% 299215 [para:299209.1.1,299094.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c10,multiply(sk_c11,X))).
% 299216 [para:299196.1.1,299211.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c10)).
% 299218 [para:299203.1.1,299212.1.2.2,demod:299209] equal(sk_c10,sk_c9).
% 299220 [para:299153.1.1,299210.1.2.2] equal(sk_c2,multiply(inverse(sk_c9),identity)).
% 299221 [para:299170.1.1,299210.1.2.2] equal(sk_c1,multiply(inverse(sk_c10),identity)).
% 299222 [para:299209.1.1,299210.1.2.2] equal(sk_c11,multiply(inverse(sk_c10),sk_c9)).
% 299225 [para:299218.1.1,299170.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 299226 [para:299218.1.1,299203.1.1.2] equal(multiply(sk_c1,sk_c9),sk_c11).
% 299230 [para:299225.1.1,299210.1.2.2,demod:299220] equal(sk_c1,sk_c2).
% 299231 [para:299230.1.2,299196.1.1.1,demod:299226] equal(sk_c11,sk_c10).
% 299232 [para:299231.1.2,299170.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 299235 [para:299231.1.2,299212.1.2.1] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 299236 [para:299231.1.2,299218.1.1] equal(sk_c11,sk_c9).
% 299242 [para:299230.1.2,299213.1.2.1] equal(multiply(sk_c10,X),multiply(sk_c1,multiply(sk_c9,X))).
% 299243 [para:299226.1.1,299094.1.1.1,demod:299242] equal(multiply(sk_c11,X),multiply(sk_c10,X)).
% 299249 [para:299214.1.2,299212.1.2.2,demod:299215,299243] equal(multiply(sk_c11,X),multiply(sk_c9,X)).
% 299250 [para:299212.1.2,299214.1.2.2,demod:299235] equal(X,multiply(sk_c1,X)).
% 299252 [para:299250.1.2,299212.1.2.2,demod:299249,299243] equal(X,multiply(sk_c9,X)).
% 299257 [para:299232.1.1,299210.1.2.2] equal(sk_c1,multiply(inverse(sk_c11),identity)).
% 299259 [para:299257.1.2,299094.1.1.1,demod:299092,299250] equal(X,multiply(inverse(sk_c11),X)).
% 299260 [para:299259.1.2,299093.1.1] equal(sk_c11,identity).
% 299262 [para:299260.1.1,299209.1.1.2,demod:299252,299249,299243] equal(identity,sk_c9).
% 299266 [para:299262.1.2,299222.1.2.2,demod:299221] equal(sk_c11,sk_c1).
% 299267 [para:299266.1.1,299236.1.1] equal(sk_c1,sk_c9).
% 299272 [para:299267.1.1,299167.1.1.1] equal(inverse(sk_c9),sk_c10).
% 299273 [hyper:299095,299272,demod:299216,cut:299091] 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(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c10) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(inverse(Y),sk_c9) | -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
%
%
% 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(55,40,0,119,0,0,69544,4,1317,73133,5,1502,73133,1,1502,73133,50,1502,73133,40,1502,73197,0,1502,75295,3,1947,75468,4,1953,75705,5,2103,75705,1,2103,75705,50,2103,75705,40,2103,75769,0,2103,77867,3,2549,78018,4,2554,78277,5,2704,78277,1,2704,78277,50,2704,78277,40,2704,78341,0,2704,99465,3,4206,100833,4,4955,101975,1,5705,101975,50,5705,101975,40,5705,102039,0,5705,115617,3,6456,116575,4,6831,117488,1,7206,117488,50,7206,117488,40,7206,117552,0,7206,128160,3,7981,129980,4,8332,132009,5,8707,132010,1,8707,132010,50,8707,132010,40,8707,132074,0,8707,171806,3,12610,173402,4,14558,175061,1,16508,175061,50,16509,175061,40,16509,175125,0,16510,209516,3,19074,210767,4,20336,211774,1,21611,211774,50,21612,211774,40,21612,211838,0,21612,240500,3,23114,241504,4,23863,242492,1,24613,242492,50,24614,242492,40,24614,242556,0,24614,250984,3,25418,254161,4,25740,255771,5,26115,255771,1,26115,255771,50,26115,255771,40,26115,255835,0,26115,278187,3,27316,279052,4,27916,279901,1,28516,279901,50,28516,279901,40,28516,279965,0,28517,296162,3,29268,296814,4,29643,297368,1,30018,297368,50,30018,297368,40,30018,297368,40,30018,297477,0,30019,299090,50,30025,299090,30,30025,299090,40,30025,299145,0,30025,299272,50,30025,299272,30,30025,299272,40,30025,299327,0,30031,299450,50,30031,299505,0,30031)
%
%
% START OF PROOF
% 299452 [] equal(multiply(identity,X),X).
% 299453 [] equal(multiply(inverse(X),X),identity).
% 299454 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 299455 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 299464 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c3),sk_c11).
% 299465 [?] ?
% 299474 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 299475 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 299484 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 299485 [?] ?
% 299494 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 299495 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 299504 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c3),sk_c11).
% 299505 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 299513 [hyper:299455,299464,binarycut:299465] equal(inverse(sk_c2),sk_c9).
% 299514 [para:299513.1.1,299453.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 299522 [hyper:299455,299484,binarycut:299485] equal(inverse(sk_c1),sk_c10).
% 299523 [para:299522.1.1,299453.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 299547 [hyper:299455,299475,299474] equal(multiply(sk_c2,sk_c9),sk_c10).
% 299557 [hyper:299455,299495,299494] equal(multiply(sk_c1,sk_c10),sk_c11).
% 299564 [hyper:299455,299505,299504] equal(multiply(sk_c10,sk_c11),sk_c9).
% 299565 [para:299453.1.1,299454.1.1.1,demod:299452] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 299567 [para:299523.1.1,299454.1.1.1,demod:299452] equal(X,multiply(sk_c10,multiply(sk_c1,X))).
% 299568 [para:299547.1.1,299454.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c2,multiply(sk_c9,X))).
% 299569 [para:299557.1.1,299454.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c1,multiply(sk_c10,X))).
% 299570 [para:299564.1.1,299454.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c10,multiply(sk_c11,X))).
% 299573 [para:299557.1.1,299567.1.2.2,demod:299564] equal(sk_c10,sk_c9).
% 299575 [para:299453.1.1,299565.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 299576 [para:299514.1.1,299565.1.2.2] equal(sk_c2,multiply(inverse(sk_c9),identity)).
% 299577 [para:299523.1.1,299565.1.2.2] equal(sk_c1,multiply(inverse(sk_c10),identity)).
% 299578 [para:299564.1.1,299565.1.2.2] equal(sk_c11,multiply(inverse(sk_c10),sk_c9)).
% 299579 [para:299454.1.1,299565.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 299582 [para:299565.1.2,299565.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 299583 [para:299573.1.1,299523.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 299584 [para:299573.1.1,299557.1.1.2] equal(multiply(sk_c1,sk_c9),sk_c11).
% 299588 [para:299583.1.1,299565.1.2.2,demod:299576] equal(sk_c1,sk_c2).
% 299589 [para:299588.1.2,299547.1.1.1,demod:299584] equal(sk_c11,sk_c10).
% 299591 [para:299589.1.2,299557.1.1.2] equal(multiply(sk_c1,sk_c11),sk_c11).
% 299593 [para:299589.1.2,299567.1.2.1] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 299600 [para:299588.1.2,299568.1.2.1] equal(multiply(sk_c10,X),multiply(sk_c1,multiply(sk_c9,X))).
% 299601 [para:299584.1.1,299454.1.1.1,demod:299600] equal(multiply(sk_c11,X),multiply(sk_c10,X)).
% 299608 [para:299569.1.2,299567.1.2.2,demod:299570,299601] equal(multiply(sk_c11,X),multiply(sk_c9,X)).
% 299609 [para:299567.1.2,299569.1.2.2,demod:299593] equal(X,multiply(sk_c1,X)).
% 299611 [para:299609.1.2,299567.1.2.2,demod:299608,299601] equal(X,multiply(sk_c9,X)).
% 299624 [para:299557.1.1,299579.1.2.1.1,demod:299609,299611,299608,299601] equal(X,multiply(inverse(sk_c11),X)).
% 299633 [para:299624.1.2,299453.1.1] equal(sk_c11,identity).
% 299634 [para:299633.1.1,299564.1.1.2,demod:299611,299608,299601] equal(identity,sk_c9).
% 299638 [para:299634.1.2,299578.1.2.2,demod:299577] equal(sk_c11,sk_c1).
% 299642 [para:299638.1.1,299591.1.1.2,demod:299609] equal(sk_c1,sk_c11).
% 299644 [para:299582.1.2,299453.1.1] equal(multiply(X,inverse(X)),identity).
% 299646 [para:299582.1.2,299575.1.2] equal(X,multiply(X,identity)).
% 299647 [para:299646.1.2,299575.1.2] equal(X,inverse(inverse(X))).
% 299650 [para:299646.1.2,299577.1.2] equal(sk_c1,inverse(sk_c10)).
% 299659 [para:299644.1.1,299579.1.2.2.2,demod:299646] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 299663 [para:299567.1.2,299659.1.2.1.1,demod:299609] equal(inverse(X),multiply(inverse(X),sk_c10)).
% 299672 [para:299663.1.2,299582.1.2,demod:299647] equal(multiply(X,sk_c10),X).
% 299673 [para:299589.1.2,299672.1.1.2] equal(multiply(X,sk_c11),X).
% 299676 [hyper:299455,299673,demod:299650,cut:299642] 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 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c10,sk_c11),sk_c9) | -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c10) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(inverse(Y),sk_c9) | -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_c9),sk_c10) | -equal(inverse(Y),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
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,119,0,0,69544,4,1317,73133,5,1502,73133,1,1502,73133,50,1502,73133,40,1502,73197,0,1502,75295,3,1947,75468,4,1953,75705,5,2103,75705,1,2103,75705,50,2103,75705,40,2103,75769,0,2103,77867,3,2549,78018,4,2554,78277,5,2704,78277,1,2704,78277,50,2704,78277,40,2704,78341,0,2704,99465,3,4206,100833,4,4955,101975,1,5705,101975,50,5705,101975,40,5705,102039,0,5705,115617,3,6456,116575,4,6831,117488,1,7206,117488,50,7206,117488,40,7206,117552,0,7206,128160,3,7981,129980,4,8332,132009,5,8707,132010,1,8707,132010,50,8707,132010,40,8707,132074,0,8707,171806,3,12610,173402,4,14558,175061,1,16508,175061,50,16509,175061,40,16509,175125,0,16510,209516,3,19074,210767,4,20336,211774,1,21611,211774,50,21612,211774,40,21612,211838,0,21612,240500,3,23114,241504,4,23863,242492,1,24613,242492,50,24614,242492,40,24614,242556,0,24614,250984,3,25418,254161,4,25740,255771,5,26115,255771,1,26115,255771,50,26115,255771,40,26115,255835,0,26115,278187,3,27316,279052,4,27916,279901,1,28516,279901,50,28516,279901,40,28516,279965,0,28517,296162,3,29268,296814,4,29643,297368,1,30018,297368,50,30018,297368,40,30018,297368,40,30018,297477,0,30019,299090,50,30025,299090,30,30025,299090,40,30025,299145,0,30025,299272,50,30025,299272,30,30025,299272,40,30025,299327,0,30031,299450,50,30031,299505,0,30031,299675,50,30032,299675,30,30032,299675,40,30032,299730,0,30037)
%
%
% START OF PROOF
% 299677 [] equal(multiply(identity,X),X).
% 299678 [] equal(multiply(inverse(X),X),identity).
% 299679 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 299680 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9).
% 299681 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c9).
% 299682 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c6),sk_c8).
% 299683 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 299685 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 299686 [] equal(multiply(sk_c5,sk_c8),sk_c11) | equal(inverse(sk_c2),sk_c9).
% 299687 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c4),sk_c10).
% 299688 [] equal(multiply(sk_c4,sk_c10),sk_c9) | equal(inverse(sk_c2),sk_c9).
% 299689 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c3),sk_c11).
% 299690 [] equal(multiply(sk_c3,sk_c11),sk_c10) | equal(inverse(sk_c2),sk_c9).
% 299691 [?] ?
% 299692 [?] ?
% 299693 [?] ?
% 299695 [?] ?
% 299696 [?] ?
% 299697 [?] ?
% 299698 [?] ?
% 299699 [?] ?
% 299700 [?] ?
% 299733 [hyper:299680,299682,binarycut:299692] equal(inverse(sk_c6),sk_c8).
% 299734 [para:299733.1.1,299678.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 299738 [hyper:299680,299683,binarycut:299693] equal(inverse(sk_c7),sk_c6).
% 299739 [para:299738.1.1,299678.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 299742 [hyper:299680,299685,binarycut:299695] equal(inverse(sk_c5),sk_c8).
% 299745 [hyper:299680,299681,binarycut:299691] equal(multiply(sk_c7,sk_c8),sk_c6).
% 299746 [para:299742.1.1,299678.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 299749 [hyper:299680,299687,binarycut:299697] equal(inverse(sk_c4),sk_c10).
% 299756 [hyper:299680,299689,binarycut:299699] equal(inverse(sk_c3),sk_c11).
% 299757 [para:299756.1.1,299678.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 299760 [hyper:299680,299686,binarycut:299696] equal(multiply(sk_c5,sk_c8),sk_c11).
% 299763 [hyper:299680,299688,binarycut:299698] equal(multiply(sk_c4,sk_c10),sk_c9).
% 299766 [hyper:299680,299690,binarycut:299700] equal(multiply(sk_c3,sk_c11),sk_c10).
% 299767 [para:299678.1.1,299679.1.1.1,demod:299677] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 299768 [para:299734.1.1,299679.1.1.1,demod:299677] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 299769 [para:299739.1.1,299679.1.1.1,demod:299677] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 299770 [para:299745.1.1,299679.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c8,X))).
% 299775 [para:299760.1.1,299679.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 299778 [para:299739.1.1,299768.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 299780 [para:299734.1.1,299767.1.2.2] equal(sk_c6,multiply(inverse(sk_c8),identity)).
% 299781 [para:299745.1.1,299767.1.2.2,demod:299738] equal(sk_c8,multiply(sk_c6,sk_c6)).
% 299782 [para:299746.1.1,299767.1.2.2,demod:299780] equal(sk_c5,sk_c6).
% 299786 [para:299760.1.1,299767.1.2.2,demod:299742] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 299787 [para:299763.1.1,299767.1.2.2,demod:299749] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 299789 [para:299768.1.2,299767.1.2.2] equal(multiply(sk_c6,X),multiply(inverse(sk_c8),X)).
% 299791 [para:299778.1.2,299679.1.1.1,demod:299677] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 299797 [para:299786.1.2,299767.1.2.2,demod:299789] equal(sk_c11,multiply(sk_c6,sk_c8)).
% 299800 [para:299782.1.2,299769.1.2.1,demod:299775,299791] equal(X,multiply(sk_c11,X)).
% 299802 [para:299734.1.1,299770.1.2.2,demod:299778,299791,299781] equal(sk_c8,sk_c7).
% 299807 [para:299802.1.2,299739.1.1.2,demod:299797] equal(sk_c11,identity).
% 299810 [para:299807.1.1,299757.1.1.1,demod:299677] equal(sk_c3,identity).
% 299813 [para:299810.1.1,299766.1.1.1,demod:299677] equal(sk_c11,sk_c10).
% 299819 [para:299813.1.2,299787.1.2.1,demod:299800] equal(sk_c10,sk_c9).
% 299829 [para:299819.1.1,299813.1.2] equal(sk_c11,sk_c9).
% 299849 [para:299829.1.1,299766.1.1.2] equal(multiply(sk_c3,sk_c9),sk_c10).
% 299919 [hyper:299680,299849,demod:299756,cut:299829] 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(sk_c10,sk_c11),sk_c9) | -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c10) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(inverse(Y),sk_c9) | -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_c10),sk_c11) | -equal(inverse(X),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(55,40,0,119,0,0,69544,4,1317,73133,5,1502,73133,1,1502,73133,50,1502,73133,40,1502,73197,0,1502,75295,3,1947,75468,4,1953,75705,5,2103,75705,1,2103,75705,50,2103,75705,40,2103,75769,0,2103,77867,3,2549,78018,4,2554,78277,5,2704,78277,1,2704,78277,50,2704,78277,40,2704,78341,0,2704,99465,3,4206,100833,4,4955,101975,1,5705,101975,50,5705,101975,40,5705,102039,0,5705,115617,3,6456,116575,4,6831,117488,1,7206,117488,50,7206,117488,40,7206,117552,0,7206,128160,3,7981,129980,4,8332,132009,5,8707,132010,1,8707,132010,50,8707,132010,40,8707,132074,0,8707,171806,3,12610,173402,4,14558,175061,1,16508,175061,50,16509,175061,40,16509,175125,0,16510,209516,3,19074,210767,4,20336,211774,1,21611,211774,50,21612,211774,40,21612,211838,0,21612,240500,3,23114,241504,4,23863,242492,1,24613,242492,50,24614,242492,40,24614,242556,0,24614,250984,3,25418,254161,4,25740,255771,5,26115,255771,1,26115,255771,50,26115,255771,40,26115,255835,0,26115,278187,3,27316,279052,4,27916,279901,1,28516,279901,50,28516,279901,40,28516,279965,0,28517,296162,3,29268,296814,4,29643,297368,1,30018,297368,50,30018,297368,40,30018,297368,40,30018,297477,0,30019,299090,50,30025,299090,30,30025,299090,40,30025,299145,0,30025,299272,50,30025,299272,30,30025,299272,40,30025,299327,0,30031,299450,50,30031,299505,0,30031,299675,50,30032,299675,30,30032,299675,40,30032,299730,0,30037,299918,50,30039,299918,30,30039,299918,40,30039,299973,0,30039,300173,50,30041,300228,0,30046)
%
%
% START OF PROOF
% 300175 [] equal(multiply(identity,X),X).
% 300176 [] equal(multiply(inverse(X),X),identity).
% 300177 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 300178 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c10).
% 300199 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c10).
% 300200 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 300201 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 300202 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c10).
% 300203 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 300204 [] equal(multiply(sk_c5,sk_c8),sk_c11) | equal(inverse(sk_c1),sk_c10).
% 300205 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 300207 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 300208 [] equal(multiply(sk_c3,sk_c11),sk_c10) | equal(inverse(sk_c1),sk_c10).
% 300209 [?] ?
% 300210 [?] ?
% 300211 [?] ?
% 300212 [?] ?
% 300213 [?] ?
% 300214 [?] ?
% 300215 [?] ?
% 300217 [?] ?
% 300218 [?] ?
% 300239 [hyper:300178,300200,binarycut:300210] equal(inverse(sk_c6),sk_c8).
% 300240 [para:300239.1.1,300176.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 300244 [hyper:300178,300201,binarycut:300211] equal(inverse(sk_c7),sk_c6).
% 300245 [para:300244.1.1,300176.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 300248 [hyper:300178,300203,binarycut:300213] equal(inverse(sk_c5),sk_c8).
% 300252 [para:300248.1.1,300176.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 300255 [hyper:300178,300205,binarycut:300215] equal(inverse(sk_c4),sk_c10).
% 300259 [para:300255.1.1,300176.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 300264 [hyper:300178,300207,binarycut:300217] equal(inverse(sk_c3),sk_c11).
% 300265 [para:300264.1.1,300176.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 300271 [hyper:300178,300199,binarycut:300209] equal(multiply(sk_c7,sk_c8),sk_c6).
% 300275 [hyper:300178,300202,binarycut:300212] equal(multiply(sk_c8,sk_c10),sk_c11).
% 300281 [hyper:300178,300204,binarycut:300214] equal(multiply(sk_c5,sk_c8),sk_c11).
% 300288 [hyper:300178,300208,binarycut:300218] equal(multiply(sk_c3,sk_c11),sk_c10).
% 300289 [para:300176.1.1,300177.1.1.1,demod:300175] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 300290 [para:300240.1.1,300177.1.1.1,demod:300175] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 300291 [para:300245.1.1,300177.1.1.1,demod:300175] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 300292 [para:300252.1.1,300177.1.1.1,demod:300175] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 300293 [para:300259.1.1,300177.1.1.1,demod:300175] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 300295 [para:300271.1.1,300177.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c8,X))).
% 300296 [para:300275.1.1,300177.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c8,multiply(sk_c10,X))).
% 300297 [para:300281.1.1,300177.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 300300 [para:300245.1.1,300290.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 300302 [para:300176.1.1,300289.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 300303 [para:300240.1.1,300289.1.2.2] equal(sk_c6,multiply(inverse(sk_c8),identity)).
% 300304 [para:300252.1.1,300289.1.2.2,demod:300303] equal(sk_c5,sk_c6).
% 300306 [para:300265.1.1,300289.1.2.2] equal(sk_c3,multiply(inverse(sk_c11),identity)).
% 300309 [para:300281.1.1,300289.1.2.2,demod:300248] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 300312 [para:300177.1.1,300289.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 300313 [para:300290.1.2,300289.1.2.2] equal(multiply(sk_c6,X),multiply(inverse(sk_c8),X)).
% 300314 [para:300289.1.2,300289.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 300316 [para:300300.1.2,300177.1.1.1,demod:300175] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 300326 [para:300304.1.2,300291.1.2.1,demod:300297,300316] equal(X,multiply(sk_c11,X)).
% 300327 [?] ?
% 300328 [para:300292.1.2,300289.1.2.2,demod:300313] equal(multiply(sk_c5,X),multiply(sk_c6,X)).
% 300329 [para:300326.1.2,300265.1.1] equal(sk_c3,identity).
% 300332 [para:300329.1.1,300288.1.1.1,demod:300175] equal(sk_c11,sk_c10).
% 300333 [para:300332.1.2,300259.1.1.1,demod:300326] equal(sk_c4,identity).
% 300334 [para:300332.1.2,300275.1.1.2,demod:300309] equal(sk_c8,sk_c11).
% 300338 [para:300332.1.2,300293.1.2.1,demod:300326] equal(X,multiply(sk_c4,X)).
% 300339 [para:300333.1.1,300259.1.1.2,demod:300327] equal(sk_c10,identity).
% 300344 [para:300334.1.2,300326.1.2.1] equal(X,multiply(sk_c8,X)).
% 300350 [para:300339.1.1,300275.1.1.2,demod:300300] equal(sk_c7,sk_c11).
% 300364 [para:300350.1.2,300309.1.2.2,demod:300344] equal(sk_c8,sk_c7).
% 300370 [?] ?
% 300371 [para:300290.1.2,300295.1.2.2,demod:300344,300316,300370,300328] equal(multiply(sk_c5,X),X).
% 300382 [para:300259.1.1,300296.1.2.2,demod:300300,300326] equal(sk_c4,sk_c7).
% 300396 [para:300382.1.2,300364.1.2] equal(sk_c8,sk_c4).
% 300408 [para:300396.1.1,300281.1.1.2,demod:300371] equal(sk_c4,sk_c11).
% 300415 [para:300408.1.2,300306.1.2.1.1,demod:300327,300255] equal(sk_c3,sk_c10).
% 300461 [para:300314.1.2,300176.1.1] equal(multiply(X,inverse(X)),identity).
% 300463 [para:300314.1.2,300302.1.2] equal(X,multiply(X,identity)).
% 300473 [para:300463.1.2,300302.1.2] equal(X,inverse(inverse(X))).
% 300475 [para:300463.1.2,300306.1.2] equal(sk_c3,inverse(sk_c11)).
% 300478 [para:300461.1.1,300312.1.2.2.2,demod:300463] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 300484 [para:300293.1.2,300478.1.2.1.1,demod:300338] equal(inverse(X),multiply(inverse(X),sk_c10)).
% 300505 [para:300484.1.2,300314.1.2,demod:300473] equal(multiply(X,sk_c10),X).
% 300506 [hyper:300178,300505,demod:300475,cut:300415] 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 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c10,sk_c11),sk_c9) | -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c10) | -equal(multiply(Y,sk_c9),sk_c10) | -equal(inverse(Y),sk_c9) | -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(55,40,0,119,0,0,69544,4,1317,73133,5,1502,73133,1,1502,73133,50,1502,73133,40,1502,73197,0,1502,75295,3,1947,75468,4,1953,75705,5,2103,75705,1,2103,75705,50,2103,75705,40,2103,75769,0,2103,77867,3,2549,78018,4,2554,78277,5,2704,78277,1,2704,78277,50,2704,78277,40,2704,78341,0,2704,99465,3,4206,100833,4,4955,101975,1,5705,101975,50,5705,101975,40,5705,102039,0,5705,115617,3,6456,116575,4,6831,117488,1,7206,117488,50,7206,117488,40,7206,117552,0,7206,128160,3,7981,129980,4,8332,132009,5,8707,132010,1,8707,132010,50,8707,132010,40,8707,132074,0,8707,171806,3,12610,173402,4,14558,175061,1,16508,175061,50,16509,175061,40,16509,175125,0,16510,209516,3,19074,210767,4,20336,211774,1,21611,211774,50,21612,211774,40,21612,211838,0,21612,240500,3,23114,241504,4,23863,242492,1,24613,242492,50,24614,242492,40,24614,242556,0,24614,250984,3,25418,254161,4,25740,255771,5,26115,255771,1,26115,255771,50,26115,255771,40,26115,255835,0,26115,278187,3,27316,279052,4,27916,279901,1,28516,279901,50,28516,279901,40,28516,279965,0,28517,296162,3,29268,296814,4,29643,297368,1,30018,297368,50,30018,297368,40,30018,297368,40,30018,297477,0,30019,299090,50,30025,299090,30,30025,299090,40,30025,299145,0,30025,299272,50,30025,299272,30,30025,299272,40,30025,299327,0,30031,299450,50,30031,299505,0,30031,299675,50,30032,299675,30,30032,299675,40,30032,299730,0,30037,299918,50,30039,299918,30,30039,299918,40,30039,299973,0,30039,300173,50,30041,300228,0,30046,300505,50,30049,300505,30,30049,300505,40,30049,300560,0,30049,300767,50,30051,300822,0,30055,301090,50,30061,301145,0,30061,301424,50,30068,301479,0,30073,301778,50,30084,301833,0,30084,302138,50,30100,302193,0,30104,302506,50,30129,302561,0,30129,302883,50,30171,302938,0,30176,303270,50,30253,303270,40,30253,303325,0,30253)
%
%
% START OF PROOF
% 303051 [?] ?
% 303272 [] equal(multiply(identity,X),X).
% 303273 [] equal(multiply(inverse(X),X),identity).
% 303274 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 303275 [] -equal(multiply(sk_c10,sk_c11),sk_c9).
% 303317 [?] ?
% 303318 [?] ?
% 303320 [?] ?
% 303321 [?] ?
% 303324 [?] ?
% 303325 [?] ?
% 303399 [input:303317,cut:303275] equal(inverse(sk_c6),sk_c8).
% 303400 [para:303399.1.1,303273.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 303402 [input:303318,cut:303275] equal(inverse(sk_c7),sk_c6).
% 303403 [para:303402.1.1,303273.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 303405 [input:303320,cut:303275] equal(inverse(sk_c5),sk_c8).
% 303406 [para:303405.1.1,303273.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 303410 [input:303324,cut:303275] equal(inverse(sk_c3),sk_c11).
% 303411 [para:303410.1.1,303273.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 303428 [input:303321,cut:303275] equal(multiply(sk_c5,sk_c8),sk_c11).
% 303430 [input:303325,cut:303275] equal(multiply(sk_c3,sk_c11),sk_c10).
% 303458 [para:303400.1.1,303274.1.1.1,demod:303272] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 303463 [para:303403.1.1,303274.1.1.1,demod:303272] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 303468 [para:303411.1.1,303274.1.1.1,demod:303272] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 303489 [para:303428.1.1,303274.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 303492 [para:303403.1.1,303458.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 303493 [para:303492.1.2,303274.1.1.1,demod:303272] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 303523 [para:303430.1.1,303468.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 303525 [para:303493.1.1,303463.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 303529 [para:303400.1.1,303525.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 303530 [para:303406.1.1,303525.1.2.2,demod:303529] equal(sk_c5,sk_c6).
% 303538 [para:303530.1.2,303463.1.2.1,demod:303489,303493] equal(X,multiply(sk_c11,X)).
% 303543 [para:303538.1.2,303523.1.2] equal(sk_c11,sk_c10).
% 303550 [para:303543.1.2,303275.1.1.1,demod:303538,cut:303051] 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: 41619
% derived clauses: 3312791
% kept clauses: 176632
% kept size sum: 865091
% kept mid-nuclei: 62233
% kept new demods: 3407
% forw unit-subs: 636261
% forw double-subs: 2189836
% forw overdouble-subs: 152307
% backward subs: 21673
% fast unit cutoff: 31714
% full unit cutoff: 0
% dbl unit cutoff: 18568
% real runtime : 303.42
% process. runtime: 302.54
% specific non-discr-tree subsumption statistics:
% tried: 40247602
% length fails: 7555989
% strength fails: 10178221
% predlist fails: 360736
% aux str. fails: 5028624
% by-lit fails: 7008737
% full subs tried: 3196096
% full subs fail: 3102128
%
% ; 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/GRP330-1+eq_r.in")
%
%------------------------------------------------------------------------------