TSTP Solution File: GRP367-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP367-1 : 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 298.1s
% Output : Assurance 298.1s
% 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/GRP367-1+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 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (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_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% was split for some strategies as:
% -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8).
% -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6).
% -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% -equal(multiply(sk_c6,sk_c8),sk_c7).
% -equal(multiply(sk_c7,sk_c8),sk_c6).
%
% 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_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,665,50,6,705,0,6,1495,50,16,1535,0,16,2427,50,31,2467,0,31,3413,50,43,3453,0,43,4454,50,59,4494,0,59,5575,50,83,5615,0,83,6776,50,122,6816,0,122,8083,50,193,8123,0,193,9496,50,333,9536,0,333,11041,50,557,11081,0,557,12718,50,960,12718,40,960,12758,0,960,23342,3,1261,24092,4,1411,24786,1,1561,24786,50,1561,24786,40,1561,24826,0,1561,25043,3,1873,25051,4,2017,25059,5,2162,25059,1,2162,25059,50,2162,25059,40,2162,25099,0,2162,50671,3,3667,51915,4,4413,53033,1,5163,53033,50,5163,53033,40,5163,53073,0,5163,65291,3,5914,66540,4,6289,67835,5,6664,67836,1,6664,67836,50,6664,67836,40,6664,67876,0,6664,78526,3,7427,79841,4,7790,81482,1,8165,81482,50,8165,81482,40,8165,81522,0,8165,141763,3,12067,143007,4,14016,144235,1,15966,144235,50,15968,144235,40,15968,144275,0,15968,189537,3,18521,190627,4,19794,191590,1,21069,191590,50,21071,191590,40,21071,191630,0,21071,231367,3,22572,232080,4,23322,232846,5,24072,232847,1,24072,232847,50,24074,232847,40,24074,232887,0,24074,242326,3,24825,243353,4,25209,243500,5,25575,243500,1,25575,243500,50,25575,243500,40,25575,243540,0,25575,271139,3,26776,271971,4,27376,272551,1,27976,272551,50,27977,272551,40,27977,272591,0,27977,290788,3,28728,291572,4,29103,292146,1,29478,292146,50,29478,292146,40,29478,292146,40,29478,292181,0,29478,292291,50,29479,292326,0,29479)
%
%
% START OF PROOF
% 292293 [] equal(multiply(identity,X),X).
% 292294 [] equal(multiply(inverse(X),X),identity).
% 292295 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 292296 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 292297 [?] ?
% 292298 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c5),sk_c7).
% 292302 [] equal(multiply(sk_c3,sk_c6),sk_c8) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 292303 [] equal(multiply(sk_c3,sk_c6),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 292307 [?] ?
% 292308 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 292312 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 292313 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c5),sk_c7).
% 292317 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 292318 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 292322 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 292323 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 292329 [hyper:292296,292298,binarycut:292297] equal(inverse(sk_c3),sk_c6).
% 292330 [para:292329.1.1,292294.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 292337 [hyper:292296,292308,binarycut:292307] equal(inverse(sk_c1),sk_c8).
% 292338 [para:292337.1.1,292294.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 292341 [hyper:292296,292303,292302] equal(multiply(sk_c3,sk_c6),sk_c8).
% 292347 [hyper:292296,292313,292312] equal(multiply(sk_c1,sk_c8),sk_c2).
% 292353 [hyper:292296,292318,292317] equal(multiply(sk_c8,sk_c2),sk_c7).
% 292359 [hyper:292296,292323,292322] equal(multiply(sk_c6,sk_c8),sk_c7).
% 292360 [para:292294.1.1,292295.1.1.1,demod:292293] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 292361 [para:292330.1.1,292295.1.1.1,demod:292293] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 292362 [para:292338.1.1,292295.1.1.1,demod:292293] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 292363 [para:292341.1.1,292295.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c3,multiply(sk_c6,X))).
% 292367 [para:292341.1.1,292361.1.2.2,demod:292359] equal(sk_c6,sk_c7).
% 292368 [para:292367.1.1,292330.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 292369 [para:292367.1.1,292341.1.1.2] equal(multiply(sk_c3,sk_c7),sk_c8).
% 292370 [para:292367.1.1,292359.1.1.1] equal(multiply(sk_c7,sk_c8),sk_c7).
% 292374 [para:292294.1.1,292360.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 292377 [para:292347.1.1,292360.1.2.2,demod:292353,292337] equal(sk_c8,sk_c7).
% 292379 [para:292295.1.1,292360.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 292383 [para:292360.1.2,292360.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 292389 [para:292370.1.1,292360.1.2.2,demod:292294] equal(sk_c8,identity).
% 292391 [para:292389.1.1,292338.1.1.1,demod:292293] equal(sk_c1,identity).
% 292395 [para:292389.1.1,292377.1.1] equal(identity,sk_c7).
% 292398 [para:292391.1.1,292337.1.1.1] equal(inverse(identity),sk_c8).
% 292405 [para:292391.1.1,292362.1.2.2.1,demod:292293] equal(X,multiply(sk_c8,X)).
% 292406 [para:292395.1.2,292368.1.1.1,demod:292293] equal(sk_c3,identity).
% 292407 [para:292395.1.2,292369.1.1.2] equal(multiply(sk_c3,identity),sk_c8).
% 292415 [para:292406.1.1,292329.1.1.1,demod:292398] equal(sk_c8,sk_c6).
% 292419 [para:292330.1.1,292363.1.2.2,demod:292407,292405] equal(sk_c3,sk_c8).
% 292422 [para:292415.1.2,292361.1.2.1,demod:292405] equal(X,multiply(sk_c3,X)).
% 292425 [para:292419.1.2,292377.1.1] equal(sk_c3,sk_c7).
% 292428 [para:292425.1.1,292329.1.1.1] equal(inverse(sk_c7),sk_c6).
% 292446 [para:292361.1.2,292379.1.2.2.2,demod:292422] equal(X,multiply(inverse(multiply(Y,sk_c6)),multiply(Y,X))).
% 292457 [para:292383.1.2,292294.1.1] equal(multiply(X,inverse(X)),identity).
% 292459 [para:292383.1.2,292374.1.2] equal(X,multiply(X,identity)).
% 292461 [para:292459.1.2,292374.1.2] equal(X,inverse(inverse(X))).
% 292473 [para:292457.1.1,292446.1.2.2,demod:292459] equal(inverse(X),inverse(multiply(X,sk_c6))).
% 292488 [para:292473.1.2,292374.1.2.1.1,demod:292459,292461] equal(multiply(X,sk_c6),X).
% 292489 [hyper:292296,292488,demod:292428,cut:292367] 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 21
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8).
% 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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,665,50,6,705,0,6,1495,50,16,1535,0,16,2427,50,31,2467,0,31,3413,50,43,3453,0,43,4454,50,59,4494,0,59,5575,50,83,5615,0,83,6776,50,122,6816,0,122,8083,50,193,8123,0,193,9496,50,333,9536,0,333,11041,50,557,11081,0,557,12718,50,960,12718,40,960,12758,0,960,23342,3,1261,24092,4,1411,24786,1,1561,24786,50,1561,24786,40,1561,24826,0,1561,25043,3,1873,25051,4,2017,25059,5,2162,25059,1,2162,25059,50,2162,25059,40,2162,25099,0,2162,50671,3,3667,51915,4,4413,53033,1,5163,53033,50,5163,53033,40,5163,53073,0,5163,65291,3,5914,66540,4,6289,67835,5,6664,67836,1,6664,67836,50,6664,67836,40,6664,67876,0,6664,78526,3,7427,79841,4,7790,81482,1,8165,81482,50,8165,81482,40,8165,81522,0,8165,141763,3,12067,143007,4,14016,144235,1,15966,144235,50,15968,144235,40,15968,144275,0,15968,189537,3,18521,190627,4,19794,191590,1,21069,191590,50,21071,191590,40,21071,191630,0,21071,231367,3,22572,232080,4,23322,232846,5,24072,232847,1,24072,232847,50,24074,232847,40,24074,232887,0,24074,242326,3,24825,243353,4,25209,243500,5,25575,243500,1,25575,243500,50,25575,243500,40,25575,243540,0,25575,271139,3,26776,271971,4,27376,272551,1,27976,272551,50,27977,272551,40,27977,272591,0,27977,290788,3,28728,291572,4,29103,292146,1,29478,292146,50,29478,292146,40,29478,292146,40,29478,292181,0,29478,292291,50,29479,292326,0,29479,292488,50,29480,292488,30,29480,292488,40,29480,292523,0,29485)
%
%
% START OF PROOF
% 292490 [] equal(multiply(identity,X),X).
% 292491 [] equal(multiply(inverse(X),X),identity).
% 292492 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 292493 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c8).
% 292496 [?] ?
% 292497 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 292501 [] equal(multiply(sk_c3,sk_c6),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 292502 [] equal(multiply(sk_c3,sk_c6),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 292506 [?] ?
% 292507 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 292511 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 292512 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c4),sk_c8).
% 292516 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 292517 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 292521 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 292522 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 292527 [hyper:292493,292497,binarycut:292496] equal(inverse(sk_c3),sk_c6).
% 292529 [para:292527.1.1,292491.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 292537 [hyper:292493,292507,binarycut:292506] equal(inverse(sk_c1),sk_c8).
% 292540 [para:292537.1.1,292491.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 292548 [hyper:292493,292502,292501] equal(multiply(sk_c3,sk_c6),sk_c8).
% 292560 [hyper:292493,292511,292512] equal(multiply(sk_c1,sk_c8),sk_c2).
% 292568 [hyper:292493,292516,292517] equal(multiply(sk_c8,sk_c2),sk_c7).
% 292572 [hyper:292493,292521,292522] equal(multiply(sk_c6,sk_c8),sk_c7).
% 292573 [para:292491.1.1,292492.1.1.1,demod:292490] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 292574 [para:292529.1.1,292492.1.1.1,demod:292490] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 292580 [para:292548.1.1,292574.1.2.2,demod:292572] equal(sk_c6,sk_c7).
% 292581 [para:292580.1.1,292529.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 292582 [para:292580.1.1,292548.1.1.2] equal(multiply(sk_c3,sk_c7),sk_c8).
% 292583 [para:292580.1.1,292572.1.1.1] equal(multiply(sk_c7,sk_c8),sk_c7).
% 292591 [para:292560.1.1,292573.1.2.2,demod:292568,292537] equal(sk_c8,sk_c7).
% 292601 [para:292583.1.1,292573.1.2.2,demod:292491] equal(sk_c8,identity).
% 292603 [para:292601.1.1,292540.1.1.1,demod:292490] equal(sk_c1,identity).
% 292607 [para:292601.1.1,292591.1.1] equal(identity,sk_c7).
% 292610 [para:292603.1.1,292537.1.1.1] equal(inverse(identity),sk_c8).
% 292618 [para:292607.1.2,292581.1.1.1,demod:292490] equal(sk_c3,identity).
% 292630 [para:292618.1.1,292582.1.1.1,demod:292490] equal(sk_c7,sk_c8).
% 292641 [hyper:292493,292610,demod:292490,cut:292630] 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 21
% 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_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6).
% 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 21
% 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 21
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,665,50,6,705,0,6,1495,50,16,1535,0,16,2427,50,31,2467,0,31,3413,50,43,3453,0,43,4454,50,59,4494,0,59,5575,50,83,5615,0,83,6776,50,122,6816,0,122,8083,50,193,8123,0,193,9496,50,333,9536,0,333,11041,50,557,11081,0,557,12718,50,960,12718,40,960,12758,0,960,23342,3,1261,24092,4,1411,24786,1,1561,24786,50,1561,24786,40,1561,24826,0,1561,25043,3,1873,25051,4,2017,25059,5,2162,25059,1,2162,25059,50,2162,25059,40,2162,25099,0,2162,50671,3,3667,51915,4,4413,53033,1,5163,53033,50,5163,53033,40,5163,53073,0,5163,65291,3,5914,66540,4,6289,67835,5,6664,67836,1,6664,67836,50,6664,67836,40,6664,67876,0,6664,78526,3,7427,79841,4,7790,81482,1,8165,81482,50,8165,81482,40,8165,81522,0,8165,141763,3,12067,143007,4,14016,144235,1,15966,144235,50,15968,144235,40,15968,144275,0,15968,189537,3,18521,190627,4,19794,191590,1,21069,191590,50,21071,191590,40,21071,191630,0,21071,231367,3,22572,232080,4,23322,232846,5,24072,232847,1,24072,232847,50,24074,232847,40,24074,232887,0,24074,242326,3,24825,243353,4,25209,243500,5,25575,243500,1,25575,243500,50,25575,243500,40,25575,243540,0,25575,271139,3,26776,271971,4,27376,272551,1,27976,272551,50,27977,272551,40,27977,272591,0,27977,290788,3,28728,291572,4,29103,292146,1,29478,292146,50,29478,292146,40,29478,292146,40,29478,292181,0,29478,292291,50,29479,292326,0,29479,292488,50,29480,292488,30,29480,292488,40,29480,292523,0,29485,292640,50,29485,292640,30,29485,292640,40,29485,292675,0,29485,292753,50,29486,292788,0,29486)
%
%
% START OF PROOF
% 292755 [] equal(multiply(identity,X),X).
% 292756 [] equal(multiply(inverse(X),X),identity).
% 292757 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 292758 [] -equal(multiply(X,sk_c6),sk_c8) | -equal(inverse(X),sk_c6).
% 292759 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 292760 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c5),sk_c7).
% 292761 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c3),sk_c6).
% 292762 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 292763 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 292764 [?] ?
% 292765 [?] ?
% 292766 [?] ?
% 292767 [?] ?
% 292768 [?] ?
% 292791 [hyper:292758,292760,binarycut:292765] equal(inverse(sk_c5),sk_c7).
% 292792 [para:292791.1.1,292756.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 292796 [hyper:292758,292762,binarycut:292767] equal(inverse(sk_c4),sk_c8).
% 292797 [para:292796.1.1,292756.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 292800 [hyper:292758,292759,binarycut:292764] equal(multiply(sk_c5,sk_c6),sk_c7).
% 292803 [hyper:292758,292761,binarycut:292766] equal(multiply(sk_c4,sk_c7),sk_c8).
% 292806 [hyper:292758,292763,binarycut:292768] equal(multiply(sk_c7,sk_c8),sk_c6).
% 292807 [para:292756.1.1,292757.1.1.1,demod:292755] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 292808 [para:292792.1.1,292757.1.1.1,demod:292755] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 292809 [para:292797.1.1,292757.1.1.1,demod:292755] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 292811 [para:292803.1.1,292757.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c4,multiply(sk_c7,X))).
% 292812 [para:292806.1.1,292757.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c8,X))).
% 292813 [para:292800.1.1,292808.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 292815 [para:292803.1.1,292809.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 292818 [para:292756.1.1,292807.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 292819 [para:292792.1.1,292807.1.2.2] equal(sk_c5,multiply(inverse(sk_c7),identity)).
% 292820 [para:292797.1.1,292807.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 292821 [para:292806.1.1,292807.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 292822 [para:292757.1.1,292807.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 292823 [para:292808.1.2,292807.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c7),X)).
% 292824 [para:292813.1.2,292807.1.2.2,demod:292821] equal(sk_c7,sk_c8).
% 292826 [para:292807.1.2,292807.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 292827 [para:292824.1.2,292797.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 292829 [para:292824.1.2,292815.1.2.1,demod:292806] equal(sk_c7,sk_c6).
% 292831 [para:292829.1.2,292800.1.1.2] equal(multiply(sk_c5,sk_c7),sk_c7).
% 292832 [?] ?
% 292839 [para:292827.1.1,292811.1.2.2,demod:292797] equal(identity,multiply(sk_c4,identity)).
% 292842 [para:292839.1.2,292757.1.1.1,demod:292755] equal(X,multiply(sk_c4,X)).
% 292845 [para:292809.1.2,292812.1.2.2,demod:292842] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 292846 [para:292812.1.2,292807.1.2.2,demod:292832,292823,292845] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 292847 [para:292842.1.2,292809.1.2.2,demod:292846] equal(X,multiply(sk_c7,X)).
% 292866 [para:292823.1.2,292756.1.1,demod:292831] equal(sk_c7,identity).
% 292868 [para:292866.1.1,292813.1.2.2,demod:292847] equal(sk_c6,identity).
% 292872 [para:292868.1.1,292821.1.2.2,demod:292819] equal(sk_c8,sk_c5).
% 292873 [para:292872.1.1,292824.1.2] equal(sk_c7,sk_c5).
% 292875 [para:292873.1.2,292791.1.1.1] equal(inverse(sk_c7),sk_c7).
% 292878 [para:292826.1.2,292756.1.1] equal(multiply(X,inverse(X)),identity).
% 292880 [para:292826.1.2,292818.1.2] equal(X,multiply(X,identity)).
% 292882 [para:292880.1.2,292820.1.2] equal(sk_c4,inverse(sk_c8)).
% 292883 [para:292880.1.2,292818.1.2] equal(X,inverse(inverse(X))).
% 292885 [para:292878.1.1,292822.1.2.2.2,demod:292880] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 292891 [para:292815.1.2,292885.1.2.1.1,demod:292806,292875,292882] equal(sk_c4,sk_c6).
% 292895 [para:292845.1.1,292885.1.2.1.1,demod:292847] equal(inverse(X),multiply(inverse(X),sk_c6)).
% 292904 [para:292895.1.2,292826.1.2,demod:292883] equal(multiply(X,sk_c6),X).
% 292905 [hyper:292758,292904,demod:292882,cut:292891] 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 21
% 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_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,665,50,6,705,0,6,1495,50,16,1535,0,16,2427,50,31,2467,0,31,3413,50,43,3453,0,43,4454,50,59,4494,0,59,5575,50,83,5615,0,83,6776,50,122,6816,0,122,8083,50,193,8123,0,193,9496,50,333,9536,0,333,11041,50,557,11081,0,557,12718,50,960,12718,40,960,12758,0,960,23342,3,1261,24092,4,1411,24786,1,1561,24786,50,1561,24786,40,1561,24826,0,1561,25043,3,1873,25051,4,2017,25059,5,2162,25059,1,2162,25059,50,2162,25059,40,2162,25099,0,2162,50671,3,3667,51915,4,4413,53033,1,5163,53033,50,5163,53033,40,5163,53073,0,5163,65291,3,5914,66540,4,6289,67835,5,6664,67836,1,6664,67836,50,6664,67836,40,6664,67876,0,6664,78526,3,7427,79841,4,7790,81482,1,8165,81482,50,8165,81482,40,8165,81522,0,8165,141763,3,12067,143007,4,14016,144235,1,15966,144235,50,15968,144235,40,15968,144275,0,15968,189537,3,18521,190627,4,19794,191590,1,21069,191590,50,21071,191590,40,21071,191630,0,21071,231367,3,22572,232080,4,23322,232846,5,24072,232847,1,24072,232847,50,24074,232847,40,24074,232887,0,24074,242326,3,24825,243353,4,25209,243500,5,25575,243500,1,25575,243500,50,25575,243500,40,25575,243540,0,25575,271139,3,26776,271971,4,27376,272551,1,27976,272551,50,27977,272551,40,27977,272591,0,27977,290788,3,28728,291572,4,29103,292146,1,29478,292146,50,29478,292146,40,29478,292146,40,29478,292181,0,29478,292291,50,29479,292326,0,29479,292488,50,29480,292488,30,29480,292488,40,29480,292523,0,29485,292640,50,29485,292640,30,29485,292640,40,29485,292675,0,29485,292753,50,29486,292788,0,29486,292904,50,29487,292904,30,29487,292904,40,29487,292939,0,29492)
%
%
% START OF PROOF
% 292905 [] equal(X,X).
% 292906 [] equal(multiply(identity,X),X).
% 292907 [] equal(multiply(inverse(X),X),identity).
% 292908 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 292909 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 292920 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 292921 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 292922 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 292923 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 292924 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 292925 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 292926 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c5),sk_c7).
% 292927 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 292928 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c4),sk_c8).
% 292929 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 292930 [?] ?
% 292931 [?] ?
% 292932 [?] ?
% 292933 [?] ?
% 292934 [?] ?
% 292994 [hyper:292909,292926,binarycut:292931,binarycut:292921] equal(inverse(sk_c5),sk_c7).
% 292995 [para:292994.1.1,292907.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 292998 [hyper:292909,292928,binarycut:292933,binarycut:292923] equal(inverse(sk_c4),sk_c8).
% 293005 [para:292998.1.1,292907.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 293014 [hyper:292909,292925,292920,binarycut:292930] equal(multiply(sk_c5,sk_c6),sk_c7).
% 293018 [hyper:292909,292927,292922,binarycut:292932] equal(multiply(sk_c4,sk_c7),sk_c8).
% 293022 [hyper:292909,292929,292924,binarycut:292934] equal(multiply(sk_c7,sk_c8),sk_c6).
% 293027 [para:292907.1.1,292908.1.1.1,demod:292906] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 293028 [para:292995.1.1,292908.1.1.1,demod:292906] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 293029 [para:293005.1.1,292908.1.1.1,demod:292906] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 293030 [para:293014.1.1,292908.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c5,multiply(sk_c6,X))).
% 293031 [para:293018.1.1,292908.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c4,multiply(sk_c7,X))).
% 293032 [para:293022.1.1,292908.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c8,X))).
% 293035 [para:293014.1.1,293028.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 293039 [para:293018.1.1,293029.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 293046 [para:293022.1.1,293027.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 293047 [para:293028.1.2,293027.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c7),X)).
% 293048 [para:293035.1.2,293027.1.2.2,demod:293046] equal(sk_c7,sk_c8).
% 293052 [para:293048.1.2,293005.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 293054 [para:293048.1.2,293039.1.2.1,demod:293022] equal(sk_c7,sk_c6).
% 293057 [para:293054.1.2,293030.1.2.2.1] equal(multiply(sk_c7,X),multiply(sk_c5,multiply(sk_c7,X))).
% 293066 [para:293052.1.1,293031.1.2.2,demod:293005] equal(identity,multiply(sk_c4,identity)).
% 293069 [para:293066.1.2,292908.1.1.1,demod:292906] equal(X,multiply(sk_c4,X)).
% 293074 [para:293029.1.2,293032.1.2.2,demod:293069] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 293075 [para:293032.1.2,293027.1.2.2,demod:293057,293047,293074] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 293078 [para:293069.1.2,293029.1.2.2,demod:293075] equal(X,multiply(sk_c7,X)).
% 293083 [para:293078.1.2,293028.1.2] equal(X,multiply(sk_c5,X)).
% 293100 [hyper:292909,293047,demod:292994,293039,293083,293047,cut:292905,cut:293048] 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 21
% 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_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(multiply(sk_c6,sk_c8),sk_c7).
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,0,75,0,0,665,50,6,705,0,6,1495,50,16,1535,0,16,2427,50,31,2467,0,31,3413,50,43,3453,0,43,4454,50,59,4494,0,59,5575,50,83,5615,0,83,6776,50,122,6816,0,122,8083,50,193,8123,0,193,9496,50,333,9536,0,333,11041,50,557,11081,0,557,12718,50,960,12718,40,960,12758,0,960,23342,3,1261,24092,4,1411,24786,1,1561,24786,50,1561,24786,40,1561,24826,0,1561,25043,3,1873,25051,4,2017,25059,5,2162,25059,1,2162,25059,50,2162,25059,40,2162,25099,0,2162,50671,3,3667,51915,4,4413,53033,1,5163,53033,50,5163,53033,40,5163,53073,0,5163,65291,3,5914,66540,4,6289,67835,5,6664,67836,1,6664,67836,50,6664,67836,40,6664,67876,0,6664,78526,3,7427,79841,4,7790,81482,1,8165,81482,50,8165,81482,40,8165,81522,0,8165,141763,3,12067,143007,4,14016,144235,1,15966,144235,50,15968,144235,40,15968,144275,0,15968,189537,3,18521,190627,4,19794,191590,1,21069,191590,50,21071,191590,40,21071,191630,0,21071,231367,3,22572,232080,4,23322,232846,5,24072,232847,1,24072,232847,50,24074,232847,40,24074,232887,0,24074,242326,3,24825,243353,4,25209,243500,5,25575,243500,1,25575,243500,50,25575,243500,40,25575,243540,0,25575,271139,3,26776,271971,4,27376,272551,1,27976,272551,50,27977,272551,40,27977,272591,0,27977,290788,3,28728,291572,4,29103,292146,1,29478,292146,50,29478,292146,40,29478,292146,40,29478,292181,0,29478,292291,50,29479,292326,0,29479,292488,50,29480,292488,30,29480,292488,40,29480,292523,0,29485,292640,50,29485,292640,30,29485,292640,40,29485,292675,0,29485,292753,50,29486,292788,0,29486,292904,50,29487,292904,30,29487,292904,40,29487,292939,0,29492,293099,50,29493,293099,30,29493,293099,40,29493,293134,0,29493,293233,50,29493,293268,0,29498,293412,50,29500,293447,0,29500,293599,50,29503,293634,0,29503,293794,50,29509,293829,0,29513,293995,50,29522,294030,0,29522,294204,50,29537,294239,0,29542,294421,50,29570,294456,0,29570,294648,50,29631,294683,0,29631,294885,50,29744,294885,40,29744,294920,0,29744)
%
%
% START OF PROOF
% 294886 [] equal(X,X).
% 294887 [] equal(multiply(identity,X),X).
% 294888 [] equal(multiply(inverse(X),X),identity).
% 294889 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 294890 [] -equal(multiply(sk_c6,sk_c8),sk_c7).
% 294916 [?] ?
% 294917 [?] ?
% 294918 [?] ?
% 294919 [?] ?
% 294920 [?] ?
% 294959 [input:294917,cut:294890] equal(inverse(sk_c5),sk_c7).
% 294960 [para:294959.1.1,294888.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 294962 [input:294919,cut:294890] equal(inverse(sk_c4),sk_c8).
% 294963 [para:294962.1.1,294888.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 294974 [input:294916,cut:294890] equal(multiply(sk_c5,sk_c6),sk_c7).
% 294975 [input:294918,cut:294890] equal(multiply(sk_c4,sk_c7),sk_c8).
% 294976 [input:294920,cut:294890] equal(multiply(sk_c7,sk_c8),sk_c6).
% 294980 [para:294888.1.1,294889.1.1.1,demod:294887] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 294999 [para:294960.1.1,294889.1.1.1,demod:294887] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 295000 [para:294963.1.1,294889.1.1.1,demod:294887] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 295028 [para:294974.1.1,294999.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 295035 [para:294975.1.1,295000.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 295080 [para:294976.1.1,294980.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 295086 [para:295028.1.2,294980.1.2.2,demod:295080] equal(sk_c7,sk_c8).
% 295103 [para:295086.1.2,295035.1.2.1] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 295131 [para:295103.1.2,294976.1.1] equal(sk_c7,sk_c6).
% 295134 [para:295131.1.2,294890.1.1.1,demod:295103,cut:294886] 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 component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c8) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(multiply(sk_c7,sk_c8),sk_c6).
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,0,75,0,0,665,50,6,705,0,6,1495,50,16,1535,0,16,2427,50,31,2467,0,31,3413,50,43,3453,0,43,4454,50,59,4494,0,59,5575,50,83,5615,0,83,6776,50,122,6816,0,122,8083,50,193,8123,0,193,9496,50,333,9536,0,333,11041,50,557,11081,0,557,12718,50,960,12718,40,960,12758,0,960,23342,3,1261,24092,4,1411,24786,1,1561,24786,50,1561,24786,40,1561,24826,0,1561,25043,3,1873,25051,4,2017,25059,5,2162,25059,1,2162,25059,50,2162,25059,40,2162,25099,0,2162,50671,3,3667,51915,4,4413,53033,1,5163,53033,50,5163,53033,40,5163,53073,0,5163,65291,3,5914,66540,4,6289,67835,5,6664,67836,1,6664,67836,50,6664,67836,40,6664,67876,0,6664,78526,3,7427,79841,4,7790,81482,1,8165,81482,50,8165,81482,40,8165,81522,0,8165,141763,3,12067,143007,4,14016,144235,1,15966,144235,50,15968,144235,40,15968,144275,0,15968,189537,3,18521,190627,4,19794,191590,1,21069,191590,50,21071,191590,40,21071,191630,0,21071,231367,3,22572,232080,4,23322,232846,5,24072,232847,1,24072,232847,50,24074,232847,40,24074,232887,0,24074,242326,3,24825,243353,4,25209,243500,5,25575,243500,1,25575,243500,50,25575,243500,40,25575,243540,0,25575,271139,3,26776,271971,4,27376,272551,1,27976,272551,50,27977,272551,40,27977,272591,0,27977,290788,3,28728,291572,4,29103,292146,1,29478,292146,50,29478,292146,40,29478,292146,40,29478,292181,0,29478,292291,50,29479,292326,0,29479,292488,50,29480,292488,30,29480,292488,40,29480,292523,0,29485,292640,50,29485,292640,30,29485,292640,40,29485,292675,0,29485,292753,50,29486,292788,0,29486,292904,50,29487,292904,30,29487,292904,40,29487,292939,0,29492,293099,50,29493,293099,30,29493,293099,40,29493,293134,0,29493,293233,50,29493,293268,0,29498,293412,50,29500,293447,0,29500,293599,50,29503,293634,0,29503,293794,50,29509,293829,0,29513,293995,50,29522,294030,0,29522,294204,50,29537,294239,0,29542,294421,50,29570,294456,0,29570,294648,50,29631,294683,0,29631,294885,50,29744,294885,40,29744,294920,0,29744,295133,50,29744,295133,30,29744,295133,40,29744,295168,0,29744,295286,50,29745,295321,0,29750,295489,50,29752,295524,0,29752,295700,50,29756,295735,0,29756,295919,50,29762,295954,0,29767,296144,50,29776,296179,0,29776,296377,50,29792,296412,0,29797,296618,50,29827,296653,0,29827,296869,50,29891,296904,0,29891,297130,50,30010,297130,40,30010,297165,0,30010)
%
%
% START OF PROOF
% 296961 [?] ?
% 297132 [] equal(multiply(identity,X),X).
% 297133 [] equal(multiply(inverse(X),X),identity).
% 297134 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 297135 [] -equal(multiply(sk_c7,sk_c8),sk_c6).
% 297140 [?] ?
% 297145 [?] ?
% 297165 [?] ?
% 297182 [input:297140,cut:297135] equal(inverse(sk_c3),sk_c6).
% 297183 [para:297182.1.1,297133.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 297202 [input:297145,cut:297135] equal(multiply(sk_c3,sk_c6),sk_c8).
% 297221 [input:297165,cut:297135] equal(multiply(sk_c6,sk_c8),sk_c7).
% 297228 [para:297183.1.1,297134.1.1.1,demod:297132] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 297267 [para:297202.1.1,297228.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c8)).
% 297272 [para:297267.1.2,297221.1.1] equal(sk_c6,sk_c7).
% 297274 [para:297272.1.1,297135.1.2,cut:296961] 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: 37684
% derived clauses: 6406499
% kept clauses: 246009
% kept size sum: 259049
% kept mid-nuclei: 9653
% kept new demods: 4314
% forw unit-subs: 2830649
% forw double-subs: 3037745
% forw overdouble-subs: 238789
% backward subs: 8476
% fast unit cutoff: 16829
% full unit cutoff: 0
% dbl unit cutoff: 5886
% real runtime : 302.28
% process. runtime: 300.10
% specific non-discr-tree subsumption statistics:
% tried: 38622888
% length fails: 4298229
% strength fails: 9738737
% predlist fails: 3581981
% aux str. fails: 6591439
% by-lit fails: 7007097
% full subs tried: 1589634
% full subs fail: 1487702
%
% ; 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/GRP367-1+eq_r.in")
%
%------------------------------------------------------------------------------