TSTP Solution File: GRP373-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP373-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art03.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 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/GRP373-1+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 31)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 31)
% (binary-posweight-lex-big-order 30 #f 3 31)
% (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(inverse(sk_c11),sk_c10) | -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),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_c11),sk_c10) | -equal(inverse(X),sk_c11).
% -equal(inverse(sk_c11),sk_c10).
% -equal(multiply(sk_c11,sk_c9),sk_c10).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),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(65,40,0,139,0,1,101374,5,1502,101375,1,1502,101375,50,1502,101375,40,1502,101449,0,1502,103557,3,1829,103945,4,1953,104009,5,2103,104009,1,2103,104009,50,2103,104009,40,2103,104083,0,2103,106191,3,2411,106582,4,2555,106644,5,2704,106644,1,2704,106644,50,2704,106644,40,2704,106718,0,2704,129304,3,4205,130393,4,4955,131326,5,5705,131327,1,5705,131327,50,5706,131327,40,5706,131401,0,5706,147501,3,6457,148329,4,6832,149014,1,7207,149014,50,7207,149014,40,7207,149088,0,7207,161293,3,8035,162927,4,8333,165181,5,8708,165181,1,8708,165181,50,8708,165181,40,8708,165255,0,8708,241481,3,12628,242296,4,14560,243083,1,16509,243083,50,16512,243083,40,16512,243157,0,16512,303908,3,19063,304616,4,20339,305257,1,21613,305257,50,21616,305257,40,21616,305331,0,21616,349201,3,23118,349888,4,23867,350409,5,24617,350410,1,24617,350410,50,24618,350410,40,24618,350484,0,24618,361878,3,25374,364321,4,25744,365956,5,26119,365956,1,26119,365956,50,26119,365956,40,26119,366030,0,26119,391242,3,27320,391860,4,27920,392246,5,28520,392247,1,28520,392247,50,28521,392247,40,28521,392321,0,28521,413487,3,29272,414025,4,29647,414442,1,30022,414442,50,30022,414442,40,30022,414442,40,30022,414571,0,30023)
%
%
% START OF PROOF
% 414443 [] equal(X,X).
% 414444 [] equal(multiply(identity,X),X).
% 414445 [] equal(multiply(inverse(X),X),identity).
% 414446 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 414507 [] -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).
% 414508 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst97,Y).
% 414509 [] -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | $spltprd1($spltcnst98,Y).
% 414510 [] -equal(multiply(X,sk_c10),sk_c11) | $spltprd1($spltcnst99,X).
% 414511 [] -$spltprd1($spltcnst98,X) | -$spltprd1($spltcnst97,X) | -$spltprd1($spltcnst99,X).
% 414532 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 414533 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 414534 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 414535 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 414536 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 414537 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 414542 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c11).
% 414543 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 414544 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 414545 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 414546 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 414547 [?] ?
% 414552 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 414553 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 414554 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 414555 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 414556 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 414557 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 414562 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c11),sk_c10).
% 414563 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 414564 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 414565 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c11),sk_c10).
% 414566 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 414567 [?] ?
% 414726 [hyper:414509,414546,binarycut:414547] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst98,sk_c8).
% 414814 [hyper:414509,414566,binarycut:414567] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst98,sk_c8).
% 415102 [hyper:414508,414542,414543,414544] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst97,sk_c8).
% 415131 [hyper:414510,414545] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst99,sk_c8).
% 415142 [hyper:414511,415131,415102,414726] equal(inverse(sk_c1),sk_c11).
% 415149 [para:415142.1.1,414445.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 415255 [hyper:414508,414562,414563,414564] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst97,sk_c8).
% 415298 [hyper:414510,414565] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst99,sk_c8).
% 415322 [hyper:414511,415298,415255,414814] equal(inverse(sk_c11),sk_c10).
% 415338 [para:415322.1.1,414445.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 415629 [hyper:414507,414537,414535,414536,414533,414532,414534] equal(multiply(sk_c11,sk_c9),sk_c10).
% 415703 [hyper:414507,414557,414555,414556,414553,414552,414554] equal(multiply(sk_c1,sk_c11),sk_c10).
% 415713 [para:415149.1.1,414446.1.1.1,demod:414444] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 415714 [para:415338.1.1,414446.1.1.1,demod:414444] equal(X,multiply(sk_c10,multiply(sk_c11,X))).
% 415752 [para:415703.1.1,415713.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 415771 [para:415629.1.1,415714.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 415773 [para:415752.1.2,415714.1.2.2,demod:415338] equal(sk_c10,identity).
% 415774 [para:415773.1.1,415338.1.1.1,demod:414444] equal(sk_c11,identity).
% 415778 [para:415774.1.1,415149.1.1.1,demod:414444] equal(sk_c1,identity).
% 415779 [para:415774.1.1,415322.1.1.1] equal(inverse(identity),sk_c10).
% 415780 [para:415774.1.1,415629.1.1.1,demod:414444] equal(sk_c9,sk_c10).
% 415783 [para:415774.1.1,415752.1.2.1,demod:414444] equal(sk_c11,sk_c10).
% 415784 [para:415778.1.1,415142.1.1.1,demod:415779] equal(sk_c10,sk_c11).
% 415785 [para:415780.1.2,415338.1.1.1] equal(multiply(sk_c9,sk_c11),identity).
% 415790 [para:415783.1.1,415752.1.2.1,demod:415771] equal(sk_c11,sk_c9).
% 415795 [para:415790.1.1,415322.1.1.1] equal(inverse(sk_c9),sk_c10).
% 415923 [hyper:414507,415785,414444,demod:415779,415795,415752,cut:414443,cut:415773,cut:415784,demod:415779,cut:415784] 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 31
% 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(inverse(sk_c11),sk_c10) | -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,1,101374,5,1502,101375,1,1502,101375,50,1502,101375,40,1502,101449,0,1502,103557,3,1829,103945,4,1953,104009,5,2103,104009,1,2103,104009,50,2103,104009,40,2103,104083,0,2103,106191,3,2411,106582,4,2555,106644,5,2704,106644,1,2704,106644,50,2704,106644,40,2704,106718,0,2704,129304,3,4205,130393,4,4955,131326,5,5705,131327,1,5705,131327,50,5706,131327,40,5706,131401,0,5706,147501,3,6457,148329,4,6832,149014,1,7207,149014,50,7207,149014,40,7207,149088,0,7207,161293,3,8035,162927,4,8333,165181,5,8708,165181,1,8708,165181,50,8708,165181,40,8708,165255,0,8708,241481,3,12628,242296,4,14560,243083,1,16509,243083,50,16512,243083,40,16512,243157,0,16512,303908,3,19063,304616,4,20339,305257,1,21613,305257,50,21616,305257,40,21616,305331,0,21616,349201,3,23118,349888,4,23867,350409,5,24617,350410,1,24617,350410,50,24618,350410,40,24618,350484,0,24618,361878,3,25374,364321,4,25744,365956,5,26119,365956,1,26119,365956,50,26119,365956,40,26119,366030,0,26119,391242,3,27320,391860,4,27920,392246,5,28520,392247,1,28520,392247,50,28521,392247,40,28521,392321,0,28521,413487,3,29272,414025,4,29647,414442,1,30022,414442,50,30022,414442,40,30022,414442,40,30022,414571,0,30023,415922,50,30027,415922,30,30027,415922,40,30027,415987,0,30027)
%
%
% START OF PROOF
% 415924 [] equal(multiply(identity,X),X).
% 415925 [] equal(multiply(inverse(X),X),identity).
% 415926 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 415927 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 415954 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 415955 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 415964 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 415965 [?] ?
% 415974 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 415975 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 415984 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 415985 [?] ?
% 416002 [hyper:415927,415964,binarycut:415965] equal(inverse(sk_c1),sk_c11).
% 416003 [para:416002.1.1,415925.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 416017 [hyper:415927,415984,binarycut:415985] equal(inverse(sk_c11),sk_c10).
% 416020 [para:416017.1.1,415925.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 416052 [hyper:415927,415955,415954] equal(multiply(sk_c11,sk_c9),sk_c10).
% 416058 [hyper:415927,415975,415974] equal(multiply(sk_c1,sk_c11),sk_c10).
% 416059 [para:415925.1.1,415926.1.1.1,demod:415924] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 416061 [para:416003.1.1,415926.1.1.1,demod:415924] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 416068 [para:416058.1.1,416061.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 416073 [para:416052.1.1,416059.1.2.2,demod:416017] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 416077 [para:416068.1.2,416059.1.2.2,demod:416020,416017] equal(sk_c10,identity).
% 416080 [para:416077.1.1,416020.1.1.1,demod:415924] equal(sk_c11,identity).
% 416083 [para:416080.1.1,416017.1.1.1] equal(inverse(identity),sk_c10).
% 416087 [para:416080.1.1,416068.1.2.1,demod:415924] equal(sk_c11,sk_c10).
% 416095 [para:416087.1.1,416068.1.2.1,demod:416073] equal(sk_c11,sk_c9).
% 416102 [para:416087.1.1,416095.1.1] equal(sk_c10,sk_c9).
% 416114 [hyper:415927,416083,demod:415924,cut:416102] 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 31
% 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(inverse(sk_c11),sk_c10) | -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,1,101374,5,1502,101375,1,1502,101375,50,1502,101375,40,1502,101449,0,1502,103557,3,1829,103945,4,1953,104009,5,2103,104009,1,2103,104009,50,2103,104009,40,2103,104083,0,2103,106191,3,2411,106582,4,2555,106644,5,2704,106644,1,2704,106644,50,2704,106644,40,2704,106718,0,2704,129304,3,4205,130393,4,4955,131326,5,5705,131327,1,5705,131327,50,5706,131327,40,5706,131401,0,5706,147501,3,6457,148329,4,6832,149014,1,7207,149014,50,7207,149014,40,7207,149088,0,7207,161293,3,8035,162927,4,8333,165181,5,8708,165181,1,8708,165181,50,8708,165181,40,8708,165255,0,8708,241481,3,12628,242296,4,14560,243083,1,16509,243083,50,16512,243083,40,16512,243157,0,16512,303908,3,19063,304616,4,20339,305257,1,21613,305257,50,21616,305257,40,21616,305331,0,21616,349201,3,23118,349888,4,23867,350409,5,24617,350410,1,24617,350410,50,24618,350410,40,24618,350484,0,24618,361878,3,25374,364321,4,25744,365956,5,26119,365956,1,26119,365956,50,26119,365956,40,26119,366030,0,26119,391242,3,27320,391860,4,27920,392246,5,28520,392247,1,28520,392247,50,28521,392247,40,28521,392321,0,28521,413487,3,29272,414025,4,29647,414442,1,30022,414442,50,30022,414442,40,30022,414442,40,30022,414571,0,30023,415922,50,30027,415922,30,30027,415922,40,30027,415987,0,30027,416113,50,30027,416113,30,30027,416113,40,30027,416178,0,30032)
%
%
% START OF PROOF
% 416114 [] equal(X,X).
% 416118 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 416157 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 416158 [?] ?
% 416167 [?] ?
% 416168 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 416210 [hyper:416118,416157,binarycut:416167] equal(inverse(sk_c3),sk_c11).
% 416212 [hyper:416118,416157,binarycut:416158] equal(inverse(sk_c1),sk_c11).
% 416243 [hyper:416118,416168,demod:416212,cut:416114] equal(multiply(sk_c3,sk_c11),sk_c10).
% 416245 [hyper:416118,416243,demod:416210,cut:416114] 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),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 31
% 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 31
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,1,101374,5,1502,101375,1,1502,101375,50,1502,101375,40,1502,101449,0,1502,103557,3,1829,103945,4,1953,104009,5,2103,104009,1,2103,104009,50,2103,104009,40,2103,104083,0,2103,106191,3,2411,106582,4,2555,106644,5,2704,106644,1,2704,106644,50,2704,106644,40,2704,106718,0,2704,129304,3,4205,130393,4,4955,131326,5,5705,131327,1,5705,131327,50,5706,131327,40,5706,131401,0,5706,147501,3,6457,148329,4,6832,149014,1,7207,149014,50,7207,149014,40,7207,149088,0,7207,161293,3,8035,162927,4,8333,165181,5,8708,165181,1,8708,165181,50,8708,165181,40,8708,165255,0,8708,241481,3,12628,242296,4,14560,243083,1,16509,243083,50,16512,243083,40,16512,243157,0,16512,303908,3,19063,304616,4,20339,305257,1,21613,305257,50,21616,305257,40,21616,305331,0,21616,349201,3,23118,349888,4,23867,350409,5,24617,350410,1,24617,350410,50,24618,350410,40,24618,350484,0,24618,361878,3,25374,364321,4,25744,365956,5,26119,365956,1,26119,365956,50,26119,365956,40,26119,366030,0,26119,391242,3,27320,391860,4,27920,392246,5,28520,392247,1,28520,392247,50,28521,392247,40,28521,392321,0,28521,413487,3,29272,414025,4,29647,414442,1,30022,414442,50,30022,414442,40,30022,414442,40,30022,414571,0,30023,415922,50,30027,415922,30,30027,415922,40,30027,415987,0,30027,416113,50,30027,416113,30,30027,416113,40,30027,416178,0,30032,416244,50,30032,416244,30,30032,416244,40,30032,416309,0,30032,416494,50,30034,416559,0,30038)
%
%
% START OF PROOF
% 416496 [] equal(multiply(identity,X),X).
% 416497 [] equal(multiply(inverse(X),X),identity).
% 416498 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 416499 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c9).
% 416500 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c9).
% 416501 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c6),sk_c8).
% 416502 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 416503 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c2),sk_c9).
% 416504 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 416505 [] equal(multiply(sk_c5,sk_c8),sk_c11) | equal(inverse(sk_c2),sk_c9).
% 416506 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c4),sk_c10).
% 416507 [] equal(multiply(sk_c4,sk_c10),sk_c9) | equal(inverse(sk_c2),sk_c9).
% 416508 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c3),sk_c11).
% 416509 [] equal(multiply(sk_c3,sk_c11),sk_c10) | equal(inverse(sk_c2),sk_c9).
% 416510 [?] ?
% 416511 [?] ?
% 416512 [?] ?
% 416513 [?] ?
% 416514 [?] ?
% 416515 [?] ?
% 416516 [?] ?
% 416517 [?] ?
% 416518 [?] ?
% 416519 [?] ?
% 416562 [hyper:416499,416501,binarycut:416511] equal(inverse(sk_c6),sk_c8).
% 416563 [para:416562.1.1,416497.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 416567 [hyper:416499,416502,binarycut:416512] equal(inverse(sk_c7),sk_c6).
% 416568 [para:416567.1.1,416497.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 416571 [hyper:416499,416504,binarycut:416514] equal(inverse(sk_c5),sk_c8).
% 416574 [hyper:416499,416500,binarycut:416510] equal(multiply(sk_c7,sk_c8),sk_c6).
% 416575 [para:416571.1.1,416497.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 416578 [hyper:416499,416506,binarycut:416516] equal(inverse(sk_c4),sk_c10).
% 416579 [para:416578.1.1,416497.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 416582 [hyper:416499,416503,binarycut:416513] equal(multiply(sk_c8,sk_c10),sk_c11).
% 416585 [hyper:416499,416508,binarycut:416518] equal(inverse(sk_c3),sk_c11).
% 416586 [para:416585.1.1,416497.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 416589 [hyper:416499,416505,binarycut:416515] equal(multiply(sk_c5,sk_c8),sk_c11).
% 416592 [hyper:416499,416507,binarycut:416517] equal(multiply(sk_c4,sk_c10),sk_c9).
% 416595 [hyper:416499,416509,binarycut:416519] equal(multiply(sk_c3,sk_c11),sk_c10).
% 416596 [para:416497.1.1,416498.1.1.1,demod:416496] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 416597 [para:416563.1.1,416498.1.1.1,demod:416496] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 416598 [para:416568.1.1,416498.1.1.1,demod:416496] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 416599 [para:416574.1.1,416498.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c8,X))).
% 416600 [para:416575.1.1,416498.1.1.1,demod:416496] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 416601 [para:416579.1.1,416498.1.1.1,demod:416496] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 416602 [para:416582.1.1,416498.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c8,multiply(sk_c10,X))).
% 416604 [para:416589.1.1,416498.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 416607 [para:416568.1.1,416597.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 416608 [para:416607.1.2,416498.1.1.1,demod:416496] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 416609 [para:416574.1.1,416598.1.2.2] equal(sk_c8,multiply(sk_c6,sk_c6)).
% 416612 [para:416497.1.1,416596.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 416613 [para:416563.1.1,416596.1.2.2] equal(sk_c6,multiply(inverse(sk_c8),identity)).
% 416615 [para:416575.1.1,416596.1.2.2,demod:416613] equal(sk_c5,sk_c6).
% 416616 [para:416579.1.1,416596.1.2.2] equal(sk_c4,multiply(inverse(sk_c10),identity)).
% 416619 [para:416589.1.1,416596.1.2.2,demod:416571] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 416622 [para:416498.1.1,416596.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 416624 [para:416596.1.2,416596.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 416626 [para:416615.1.2,416598.1.2.1,demod:416604,416608] equal(X,multiply(sk_c11,X)).
% 416627 [para:416626.1.2,416586.1.1] equal(sk_c3,identity).
% 416630 [para:416627.1.1,416595.1.1.1,demod:416496] equal(sk_c11,sk_c10).
% 416633 [para:416630.1.1,416626.1.2.1] equal(X,multiply(sk_c10,X)).
% 416634 [para:416563.1.1,416599.1.2.2,demod:416607,416608,416609] equal(sk_c8,sk_c7).
% 416639 [para:416634.1.2,416567.1.1.1] equal(inverse(sk_c8),sk_c6).
% 416640 [para:416634.1.2,416568.1.1.2] equal(multiply(sk_c6,sk_c8),identity).
% 416644 [para:416633.1.2,416596.1.2.2] equal(X,multiply(inverse(sk_c10),X)).
% 416650 [para:416600.1.2,416596.1.2.2,demod:416639] equal(multiply(sk_c5,X),multiply(sk_c6,X)).
% 416654 [para:416619.1.2,416596.1.2.2,demod:416640,416639] equal(sk_c11,identity).
% 416655 [para:416630.1.1,416619.1.2.2,demod:416582] equal(sk_c8,sk_c11).
% 416663 [para:416655.1.2,416630.1.1] equal(sk_c8,sk_c10).
% 416665 [para:416655.1.2,416654.1.1] equal(sk_c8,identity).
% 416666 [para:416601.1.2,416596.1.2.2,demod:416644] equal(multiply(sk_c4,X),X).
% 416671 [para:416663.1.2,416592.1.1.2,demod:416666] equal(sk_c8,sk_c9).
% 416682 [para:416665.1.1,416597.1.2.1,demod:416496,416650] equal(X,multiply(sk_c5,X)).
% 416684 [para:416579.1.1,416602.1.2.2,demod:416607,416626] equal(sk_c4,sk_c7).
% 416705 [para:416684.1.2,416634.1.2] equal(sk_c8,sk_c4).
% 416723 [para:416705.1.1,416671.1.1] equal(sk_c4,sk_c9).
% 416768 [para:416624.1.2,416497.1.1] equal(multiply(X,inverse(X)),identity).
% 416770 [para:416624.1.2,416612.1.2] equal(X,multiply(X,identity)).
% 416771 [para:416770.1.2,416612.1.2] equal(X,inverse(inverse(X))).
% 416772 [para:416770.1.2,416616.1.2] equal(sk_c4,inverse(sk_c10)).
% 416779 [para:416768.1.1,416622.1.2.2.2,demod:416770] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 416781 [para:416597.1.2,416779.1.2.1.1,demod:416682,416650] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 416799 [para:416781.1.2,416624.1.2,demod:416771] equal(multiply(X,sk_c8),X).
% 416800 [para:416671.1.1,416799.1.1.2] equal(multiply(X,sk_c9),X).
% 416804 [hyper:416499,416800,demod:416772,cut:416723] 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 31
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),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_c11),sk_c10) | -equal(inverse(X),sk_c11).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,1,101374,5,1502,101375,1,1502,101375,50,1502,101375,40,1502,101449,0,1502,103557,3,1829,103945,4,1953,104009,5,2103,104009,1,2103,104009,50,2103,104009,40,2103,104083,0,2103,106191,3,2411,106582,4,2555,106644,5,2704,106644,1,2704,106644,50,2704,106644,40,2704,106718,0,2704,129304,3,4205,130393,4,4955,131326,5,5705,131327,1,5705,131327,50,5706,131327,40,5706,131401,0,5706,147501,3,6457,148329,4,6832,149014,1,7207,149014,50,7207,149014,40,7207,149088,0,7207,161293,3,8035,162927,4,8333,165181,5,8708,165181,1,8708,165181,50,8708,165181,40,8708,165255,0,8708,241481,3,12628,242296,4,14560,243083,1,16509,243083,50,16512,243083,40,16512,243157,0,16512,303908,3,19063,304616,4,20339,305257,1,21613,305257,50,21616,305257,40,21616,305331,0,21616,349201,3,23118,349888,4,23867,350409,5,24617,350410,1,24617,350410,50,24618,350410,40,24618,350484,0,24618,361878,3,25374,364321,4,25744,365956,5,26119,365956,1,26119,365956,50,26119,365956,40,26119,366030,0,26119,391242,3,27320,391860,4,27920,392246,5,28520,392247,1,28520,392247,50,28521,392247,40,28521,392321,0,28521,413487,3,29272,414025,4,29647,414442,1,30022,414442,50,30022,414442,40,30022,414442,40,30022,414571,0,30023,415922,50,30027,415922,30,30027,415922,40,30027,415987,0,30027,416113,50,30027,416113,30,30027,416113,40,30027,416178,0,30032,416244,50,30032,416244,30,30032,416244,40,30032,416309,0,30032,416494,50,30034,416559,0,30038,416803,50,30041,416803,30,30041,416803,40,30041,416868,0,30041)
%
%
% START OF PROOF
% 416804 [] equal(X,X).
% 416808 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 416847 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 416848 [?] ?
% 416857 [?] ?
% 416858 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 416900 [hyper:416808,416847,binarycut:416857] equal(inverse(sk_c3),sk_c11).
% 416902 [hyper:416808,416847,binarycut:416848] equal(inverse(sk_c1),sk_c11).
% 416933 [hyper:416808,416858,demod:416902,cut:416804] equal(multiply(sk_c3,sk_c11),sk_c10).
% 416935 [hyper:416808,416933,demod:416900,cut:416804] 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),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(inverse(sk_c11),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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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(65,40,0,139,0,1,101374,5,1502,101375,1,1502,101375,50,1502,101375,40,1502,101449,0,1502,103557,3,1829,103945,4,1953,104009,5,2103,104009,1,2103,104009,50,2103,104009,40,2103,104083,0,2103,106191,3,2411,106582,4,2555,106644,5,2704,106644,1,2704,106644,50,2704,106644,40,2704,106718,0,2704,129304,3,4205,130393,4,4955,131326,5,5705,131327,1,5705,131327,50,5706,131327,40,5706,131401,0,5706,147501,3,6457,148329,4,6832,149014,1,7207,149014,50,7207,149014,40,7207,149088,0,7207,161293,3,8035,162927,4,8333,165181,5,8708,165181,1,8708,165181,50,8708,165181,40,8708,165255,0,8708,241481,3,12628,242296,4,14560,243083,1,16509,243083,50,16512,243083,40,16512,243157,0,16512,303908,3,19063,304616,4,20339,305257,1,21613,305257,50,21616,305257,40,21616,305331,0,21616,349201,3,23118,349888,4,23867,350409,5,24617,350410,1,24617,350410,50,24618,350410,40,24618,350484,0,24618,361878,3,25374,364321,4,25744,365956,5,26119,365956,1,26119,365956,50,26119,365956,40,26119,366030,0,26119,391242,3,27320,391860,4,27920,392246,5,28520,392247,1,28520,392247,50,28521,392247,40,28521,392321,0,28521,413487,3,29272,414025,4,29647,414442,1,30022,414442,50,30022,414442,40,30022,414442,40,30022,414571,0,30023,415922,50,30027,415922,30,30027,415922,40,30027,415987,0,30027,416113,50,30027,416113,30,30027,416113,40,30027,416178,0,30032,416244,50,30032,416244,30,30032,416244,40,30032,416309,0,30032,416494,50,30034,416559,0,30038,416803,50,30041,416803,30,30041,416803,40,30041,416868,0,30041,416934,50,30041,416934,30,30041,416934,40,30041,416999,0,30045,417213,50,30046,417278,0,30046,417555,50,30052,417620,0,30056,417905,50,30064,417970,0,30064,418263,50,30073,418328,0,30078,418627,50,30091,418692,0,30091,418999,50,30112,419064,0,30116,419379,50,30153,419444,0,30153,419769,50,30226,419834,0,30226,420169,50,30360,420169,40,30360,420234,0,30360)
%
%
% START OF PROOF
% 420171 [] equal(multiply(identity,X),X).
% 420172 [] equal(multiply(inverse(X),X),identity).
% 420173 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 420174 [] -equal(inverse(sk_c11),sk_c10).
% 420225 [?] ?
% 420226 [?] ?
% 420227 [?] ?
% 420228 [?] ?
% 420229 [?] ?
% 420230 [?] ?
% 420231 [?] ?
% 420232 [?] ?
% 420233 [?] ?
% 420234 [?] ?
% 420269 [input:420226,cut:420174] equal(inverse(sk_c6),sk_c8).
% 420270 [para:420269.1.1,420172.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 420273 [input:420227,cut:420174] equal(inverse(sk_c7),sk_c6).
% 420274 [para:420273.1.1,420172.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 420275 [input:420229,cut:420174] equal(inverse(sk_c5),sk_c8).
% 420276 [para:420275.1.1,420172.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 420279 [input:420231,cut:420174] equal(inverse(sk_c4),sk_c10).
% 420280 [para:420279.1.1,420172.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 420281 [input:420233,cut:420174] equal(inverse(sk_c3),sk_c11).
% 420282 [para:420281.1.1,420172.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 420316 [input:420225,cut:420174] equal(multiply(sk_c7,sk_c8),sk_c6).
% 420317 [input:420228,cut:420174] equal(multiply(sk_c8,sk_c10),sk_c11).
% 420318 [input:420230,cut:420174] equal(multiply(sk_c5,sk_c8),sk_c11).
% 420319 [input:420232,cut:420174] equal(multiply(sk_c4,sk_c10),sk_c9).
% 420321 [input:420234,cut:420174] equal(multiply(sk_c3,sk_c11),sk_c10).
% 420344 [para:420270.1.1,420173.1.1.1,demod:420171] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 420345 [para:420274.1.1,420173.1.1.1,demod:420171] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 420346 [para:420276.1.1,420173.1.1.1,demod:420171] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 420348 [para:420280.1.1,420173.1.1.1,demod:420171] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 420349 [para:420282.1.1,420173.1.1.1,demod:420171] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 420385 [para:420318.1.1,420173.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 420407 [para:420274.1.1,420344.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 420408 [para:420407.1.2,420173.1.1.1,demod:420171] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 420413 [para:420316.1.1,420345.1.2.2] equal(sk_c8,multiply(sk_c6,sk_c6)).
% 420416 [para:420413.1.2,420344.1.2.2] equal(sk_c6,multiply(sk_c8,sk_c8)).
% 420422 [para:420318.1.1,420346.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 420427 [para:420319.1.1,420348.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 420432 [para:420321.1.1,420349.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 420436 [para:420408.1.1,420345.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 420438 [para:420270.1.1,420436.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 420439 [para:420276.1.1,420436.1.2.2,demod:420438] equal(sk_c5,sk_c6).
% 420447 [para:420439.1.2,420345.1.2.1,demod:420385,420408] equal(X,multiply(sk_c11,X)).
% 420463 [para:420447.1.2,420349.1.2] equal(X,multiply(sk_c3,X)).
% 420464 [para:420447.1.2,420432.1.2] equal(sk_c11,sk_c10).
% 420481 [para:420464.1.1,420422.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c10)).
% 420482 [para:420464.1.1,420349.1.2.1,demod:420463] equal(X,multiply(sk_c10,X)).
% 420489 [para:420482.1.2,420427.1.2] equal(sk_c10,sk_c9).
% 420496 [para:420489.1.1,420317.1.1.2] equal(multiply(sk_c8,sk_c9),sk_c11).
% 420498 [para:420489.1.1,420432.1.2.2,demod:420447] equal(sk_c11,sk_c9).
% 420507 [para:420498.1.1,420422.1.2.2,demod:420496] equal(sk_c8,sk_c11).
% 420517 [para:420507.1.2,420321.1.1.2,demod:420463] equal(sk_c8,sk_c10).
% 420522 [para:420507.1.2,420422.1.2.2,demod:420416] equal(sk_c8,sk_c6).
% 420524 [para:420507.1.2,420432.1.2.1,demod:420481] equal(sk_c11,sk_c8).
% 420536 [para:420522.1.2,420269.1.1.1] equal(inverse(sk_c8),sk_c8).
% 420544 [para:420524.1.1,420174.1.1.1,demod:420536,cut:420517] 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 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c11,sk_c9),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_c11,sk_c9),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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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(65,40,0,139,0,1,101374,5,1502,101375,1,1502,101375,50,1502,101375,40,1502,101449,0,1502,103557,3,1829,103945,4,1953,104009,5,2103,104009,1,2103,104009,50,2103,104009,40,2103,104083,0,2103,106191,3,2411,106582,4,2555,106644,5,2704,106644,1,2704,106644,50,2704,106644,40,2704,106718,0,2704,129304,3,4205,130393,4,4955,131326,5,5705,131327,1,5705,131327,50,5706,131327,40,5706,131401,0,5706,147501,3,6457,148329,4,6832,149014,1,7207,149014,50,7207,149014,40,7207,149088,0,7207,161293,3,8035,162927,4,8333,165181,5,8708,165181,1,8708,165181,50,8708,165181,40,8708,165255,0,8708,241481,3,12628,242296,4,14560,243083,1,16509,243083,50,16512,243083,40,16512,243157,0,16512,303908,3,19063,304616,4,20339,305257,1,21613,305257,50,21616,305257,40,21616,305331,0,21616,349201,3,23118,349888,4,23867,350409,5,24617,350410,1,24617,350410,50,24618,350410,40,24618,350484,0,24618,361878,3,25374,364321,4,25744,365956,5,26119,365956,1,26119,365956,50,26119,365956,40,26119,366030,0,26119,391242,3,27320,391860,4,27920,392246,5,28520,392247,1,28520,392247,50,28521,392247,40,28521,392321,0,28521,413487,3,29272,414025,4,29647,414442,1,30022,414442,50,30022,414442,40,30022,414442,40,30022,414571,0,30023,415922,50,30027,415922,30,30027,415922,40,30027,415987,0,30027,416113,50,30027,416113,30,30027,416113,40,30027,416178,0,30032,416244,50,30032,416244,30,30032,416244,40,30032,416309,0,30032,416494,50,30034,416559,0,30038,416803,50,30041,416803,30,30041,416803,40,30041,416868,0,30041,416934,50,30041,416934,30,30041,416934,40,30041,416999,0,30045,417213,50,30046,417278,0,30046,417555,50,30052,417620,0,30056,417905,50,30064,417970,0,30064,418263,50,30073,418328,0,30078,418627,50,30091,418692,0,30091,418999,50,30112,419064,0,30116,419379,50,30153,419444,0,30153,419769,50,30226,419834,0,30226,420169,50,30360,420169,40,30360,420234,0,30360,420543,50,30362,420543,30,30362,420543,40,30362,420608,0,30362,420822,50,30364,420887,0,30369,421164,50,30374,421229,0,30374,421514,50,30381,421579,0,30386,421872,50,30395,421937,0,30395,422236,50,30408,422301,0,30413,422608,50,30434,422673,0,30434,422988,50,30471,423053,0,30476,423378,50,30545,423443,0,30545,423778,50,30683,423778,40,30683,423843,0,30683)
%
%
% START OF PROOF
% 423559 [?] ?
% 423780 [] equal(multiply(identity,X),X).
% 423781 [] equal(multiply(inverse(X),X),identity).
% 423782 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 423783 [] -equal(multiply(sk_c11,sk_c9),sk_c10).
% 423805 [?] ?
% 423806 [?] ?
% 423808 [?] ?
% 423809 [?] ?
% 423910 [input:423805,cut:423783] equal(inverse(sk_c6),sk_c8).
% 423911 [para:423910.1.1,423781.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 423912 [input:423806,cut:423783] equal(inverse(sk_c7),sk_c6).
% 423913 [para:423912.1.1,423781.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 423914 [input:423808,cut:423783] equal(inverse(sk_c5),sk_c8).
% 423915 [para:423914.1.1,423781.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 423953 [input:423809,cut:423783] equal(multiply(sk_c5,sk_c8),sk_c11).
% 423989 [para:423911.1.1,423782.1.1.1,demod:423780] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 423990 [para:423913.1.1,423782.1.1.1,demod:423780] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 424020 [para:423953.1.1,423782.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 424043 [para:423913.1.1,423989.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 424044 [para:424043.1.2,423782.1.1.1,demod:423780] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 424075 [para:424044.1.1,423990.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 424077 [para:423911.1.1,424075.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 424079 [para:423915.1.1,424075.1.2.2,demod:424077] equal(sk_c5,sk_c6).
% 424087 [para:424079.1.2,423990.1.2.1,demod:424020,424044] equal(X,multiply(sk_c11,X)).
% 424093 [para:424087.1.2,423783.1.1,cut:423559] 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: 34415
% derived clauses: 4539530
% kept clauses: 272547
% kept size sum: 35106
% kept mid-nuclei: 73690
% kept new demods: 5427
% forw unit-subs: 1728666
% forw double-subs: 2170592
% forw overdouble-subs: 219386
% backward subs: 17482
% fast unit cutoff: 31922
% full unit cutoff: 0
% dbl unit cutoff: 38621
% real runtime : 307.70
% process. runtime: 306.84
% specific non-discr-tree subsumption statistics:
% tried: 61298950
% length fails: 8762111
% strength fails: 15793733
% predlist fails: 2372725
% aux str. fails: 5874238
% by-lit fails: 11572904
% full subs tried: 2806820
% full subs fail: 2682196
%
% ; 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/GRP373-1+eq_r.in")
%
%------------------------------------------------------------------------------