TSTP Solution File: GRP260-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP260-1 : 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 : art02.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 297.9s
% Output : Assurance 297.9s
% 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/GRP260-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 29)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 29)
% (binary-posweight-lex-big-order 30 #f 3 29)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c11),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% was split for some strategies as:
% -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X2),W) | -equal(inverse(X1),X2) | -equal(multiply(X1,W),X2).
% -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10).
% -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11).
% -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10).
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% -equal(multiply(sk_c9,sk_c11),sk_c10).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c11),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X2),W) | -equal(inverse(X1),X2) | -equal(multiply(X1,W),X2).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,119,0,0,159601,5,1501,159601,1,1501,159601,50,1501,159601,40,1501,159665,0,1501,169843,3,1802,170638,4,1952,171399,5,2102,171400,1,2102,171400,50,2104,171400,40,2104,171464,0,2104,173234,3,2415,173248,4,2564,173460,5,2705,173460,1,2705,173460,50,2705,173460,40,2705,173524,0,2705,206033,3,4234,206828,4,4956,207688,1,5706,207688,50,5707,207688,40,5707,207752,0,5707,231082,3,6458,231668,4,6833,232253,1,7208,232253,50,7209,232253,40,7209,232317,0,7209,250977,3,8009,251659,4,8335,252765,5,8710,252766,1,8710,252766,50,8710,252766,40,8710,252830,0,8710,314626,3,12611,315898,4,14561,317046,5,16511,317047,1,16511,317047,50,16513,317047,40,16513,317111,0,16513,360296,3,19065,361521,4,20339,362292,5,21614,362293,1,21614,362293,50,21616,362293,40,21616,362357,0,21616,394309,3,23117,395473,4,23867,396184,1,24617,396184,50,24618,396184,40,24618,396248,0,24618,412743,3,25379,413810,4,25744,415849,5,26119,415850,1,26119,415850,50,26119,415850,40,26119,415914,0,26119,443671,3,27320,444517,4,27920,444938,1,28520,444938,50,28520,444938,40,28520,445002,0,28521,462861,3,29272,463671,4,29647,464152,1,30022,464152,50,30022,464152,40,30022,464152,40,30022,464261,0,30022)
%
%
% START OF PROOF
% 464153 [] equal(X,X).
% 464154 [] equal(multiply(identity,X),X).
% 464155 [] equal(multiply(inverse(X),X),identity).
% 464156 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 464207 [] -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).
% 464208 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst97,Y).
% 464209 [] -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | $spltprd1($spltcnst98,Y).
% 464210 [] -equal(multiply(X,sk_c10),sk_c11) | $spltprd1($spltcnst99,X).
% 464211 [] -$spltprd1($spltcnst98,X) | -$spltprd1($spltcnst97,X) | -$spltprd1($spltcnst99,X).
% 464212 [] equal(multiply(sk_c9,sk_c11),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 464213 [] equal(multiply(sk_c9,sk_c11),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 464214 [] equal(multiply(sk_c9,sk_c11),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 464215 [] equal(multiply(sk_c9,sk_c11),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 464216 [] equal(multiply(sk_c9,sk_c11),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 464217 [] equal(multiply(sk_c9,sk_c11),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 464222 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c10).
% 464223 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 464224 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 464225 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c2),sk_c10).
% 464226 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 464227 [?] ?
% 464232 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 464233 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(inverse(sk_c6),sk_c8).
% 464234 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 464235 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 464236 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 464237 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 464242 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c11).
% 464243 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 464244 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 464245 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 464246 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 464247 [?] ?
% 464252 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 464253 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 464254 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 464255 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 464256 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 464257 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 464328 [hyper:464209,464226,binarycut:464227] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst98,sk_c8).
% 464416 [hyper:464209,464246,binarycut:464247] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst98,sk_c8).
% 464538 [hyper:464208,464222,464223,464224] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst97,sk_c8).
% 464567 [hyper:464210,464225] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst99,sk_c8).
% 464578 [hyper:464211,464567,464538,464328] equal(inverse(sk_c2),sk_c10).
% 464585 [para:464578.1.1,464155.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 464672 [hyper:464208,464242,464243,464244] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst97,sk_c8).
% 464699 [hyper:464210,464245] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst99,sk_c8).
% 464710 [hyper:464211,464699,464672,464416] equal(inverse(sk_c1),sk_c11).
% 464717 [para:464710.1.1,464155.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 464876 [hyper:464207,464217,464215,464216,464213,464212,464214] equal(multiply(sk_c9,sk_c11),sk_c10).
% 465041 [hyper:464207,464237,464235,464236,464233,464232,464234] equal(multiply(sk_c2,sk_c10),sk_c9).
% 465118 [hyper:464207,464257,464255,464256,464253,464252,464254] equal(multiply(sk_c1,sk_c11),sk_c10).
% 465126 [para:464155.1.1,464156.1.1.1,demod:464154] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 465127 [para:464585.1.1,464156.1.1.1,demod:464154] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 465128 [para:464717.1.1,464156.1.1.1,demod:464154] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 465130 [para:465041.1.1,464156.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c2,multiply(sk_c10,X))).
% 465166 [para:465118.1.1,465128.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 465177 [para:464585.1.1,465126.1.2.2] equal(sk_c2,multiply(inverse(sk_c10),identity)).
% 465178 [para:464717.1.1,465126.1.2.2] equal(sk_c1,multiply(inverse(sk_c11),identity)).
% 465183 [para:464876.1.1,465126.1.2.2] equal(sk_c11,multiply(inverse(sk_c9),sk_c10)).
% 465188 [para:465127.1.2,465126.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c10),X)).
% 465209 [para:465188.1.2,464155.1.1,demod:465041] equal(sk_c9,identity).
% 465212 [para:465188.1.2,465126.1.2,demod:465130] equal(X,multiply(sk_c9,X)).
% 465214 [para:465209.1.1,464876.1.1.1,demod:464154] equal(sk_c11,sk_c10).
% 465217 [para:465214.1.1,465118.1.1.2] equal(multiply(sk_c1,sk_c10),sk_c10).
% 465220 [para:465214.1.1,465178.1.2.1.1,demod:465177] equal(sk_c1,sk_c2).
% 465241 [para:465212.1.2,465126.1.2.2] equal(X,multiply(inverse(sk_c9),X)).
% 465252 [para:465220.1.1,465217.1.1.1,demod:465041] equal(sk_c9,sk_c10).
% 465254 [para:465252.1.1,465183.1.2.1.1,demod:465041,465188] equal(sk_c11,sk_c9).
% 465255 [para:465252.1.1,465209.1.1] equal(sk_c10,identity).
% 465258 [para:465254.1.1,464717.1.1.1,demod:465212] equal(sk_c1,identity).
% 465265 [para:465255.1.1,465166.1.2.2] equal(sk_c11,multiply(sk_c11,identity)).
% 465266 [para:465255.1.1,465183.1.2.2,demod:465241] equal(sk_c11,identity).
% 465267 [para:465258.1.1,464710.1.1.1] equal(inverse(identity),sk_c11).
% 465271 [para:465266.1.1,465178.1.2.1.1,demod:465265,465267] equal(sk_c1,sk_c11).
% 465288 [para:465271.1.1,464710.1.1.1] equal(inverse(sk_c11),sk_c11).
% 465307 [hyper:464207,465267,464155,464154,demod:465166,cut:464153,demod:465288,cut:465266,demod:465267,cut:464153] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c11),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,119,0,0,159601,5,1501,159601,1,1501,159601,50,1501,159601,40,1501,159665,0,1501,169843,3,1802,170638,4,1952,171399,5,2102,171400,1,2102,171400,50,2104,171400,40,2104,171464,0,2104,173234,3,2415,173248,4,2564,173460,5,2705,173460,1,2705,173460,50,2705,173460,40,2705,173524,0,2705,206033,3,4234,206828,4,4956,207688,1,5706,207688,50,5707,207688,40,5707,207752,0,5707,231082,3,6458,231668,4,6833,232253,1,7208,232253,50,7209,232253,40,7209,232317,0,7209,250977,3,8009,251659,4,8335,252765,5,8710,252766,1,8710,252766,50,8710,252766,40,8710,252830,0,8710,314626,3,12611,315898,4,14561,317046,5,16511,317047,1,16511,317047,50,16513,317047,40,16513,317111,0,16513,360296,3,19065,361521,4,20339,362292,5,21614,362293,1,21614,362293,50,21616,362293,40,21616,362357,0,21616,394309,3,23117,395473,4,23867,396184,1,24617,396184,50,24618,396184,40,24618,396248,0,24618,412743,3,25379,413810,4,25744,415849,5,26119,415850,1,26119,415850,50,26119,415850,40,26119,415914,0,26119,443671,3,27320,444517,4,27920,444938,1,28520,444938,50,28520,444938,40,28520,445002,0,28521,462861,3,29272,463671,4,29647,464152,1,30022,464152,50,30022,464152,40,30022,464152,40,30022,464261,0,30022,465306,50,30025,465306,30,30025,465306,40,30025,465361,0,30025)
%
%
% START OF PROOF
% 465307 [] equal(X,X).
% 465311 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 465328 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 465329 [?] ?
% 465338 [?] ?
% 465339 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 465378 [hyper:465311,465328,binarycut:465338] equal(inverse(sk_c4),sk_c10).
% 465380 [hyper:465311,465328,binarycut:465329] equal(inverse(sk_c2),sk_c10).
% 465408 [hyper:465311,465339,demod:465380,cut:465307] equal(multiply(sk_c4,sk_c10),sk_c9).
% 465411 [hyper:465311,465408,demod:465378,cut:465307] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c11),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,119,0,0,159601,5,1501,159601,1,1501,159601,50,1501,159601,40,1501,159665,0,1501,169843,3,1802,170638,4,1952,171399,5,2102,171400,1,2102,171400,50,2104,171400,40,2104,171464,0,2104,173234,3,2415,173248,4,2564,173460,5,2705,173460,1,2705,173460,50,2705,173460,40,2705,173524,0,2705,206033,3,4234,206828,4,4956,207688,1,5706,207688,50,5707,207688,40,5707,207752,0,5707,231082,3,6458,231668,4,6833,232253,1,7208,232253,50,7209,232253,40,7209,232317,0,7209,250977,3,8009,251659,4,8335,252765,5,8710,252766,1,8710,252766,50,8710,252766,40,8710,252830,0,8710,314626,3,12611,315898,4,14561,317046,5,16511,317047,1,16511,317047,50,16513,317047,40,16513,317111,0,16513,360296,3,19065,361521,4,20339,362292,5,21614,362293,1,21614,362293,50,21616,362293,40,21616,362357,0,21616,394309,3,23117,395473,4,23867,396184,1,24617,396184,50,24618,396184,40,24618,396248,0,24618,412743,3,25379,413810,4,25744,415849,5,26119,415850,1,26119,415850,50,26119,415850,40,26119,415914,0,26119,443671,3,27320,444517,4,27920,444938,1,28520,444938,50,28520,444938,40,28520,445002,0,28521,462861,3,29272,463671,4,29647,464152,1,30022,464152,50,30022,464152,40,30022,464152,40,30022,464261,0,30022,465306,50,30025,465306,30,30025,465306,40,30025,465361,0,30025,465410,50,30025,465410,30,30025,465410,40,30025,465465,0,30031)
%
%
% START OF PROOF
% 465411 [] equal(X,X).
% 465415 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 465454 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 465455 [?] ?
% 465464 [?] ?
% 465465 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 465499 [hyper:465415,465454,binarycut:465464] equal(inverse(sk_c3),sk_c11).
% 465501 [hyper:465415,465454,binarycut:465455] equal(inverse(sk_c1),sk_c11).
% 465535 [hyper:465415,465465,demod:465501,cut:465411] equal(multiply(sk_c3,sk_c11),sk_c10).
% 465537 [hyper:465415,465535,demod:465499,cut:465411] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c11),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,119,0,0,159601,5,1501,159601,1,1501,159601,50,1501,159601,40,1501,159665,0,1501,169843,3,1802,170638,4,1952,171399,5,2102,171400,1,2102,171400,50,2104,171400,40,2104,171464,0,2104,173234,3,2415,173248,4,2564,173460,5,2705,173460,1,2705,173460,50,2705,173460,40,2705,173524,0,2705,206033,3,4234,206828,4,4956,207688,1,5706,207688,50,5707,207688,40,5707,207752,0,5707,231082,3,6458,231668,4,6833,232253,1,7208,232253,50,7209,232253,40,7209,232317,0,7209,250977,3,8009,251659,4,8335,252765,5,8710,252766,1,8710,252766,50,8710,252766,40,8710,252830,0,8710,314626,3,12611,315898,4,14561,317046,5,16511,317047,1,16511,317047,50,16513,317047,40,16513,317111,0,16513,360296,3,19065,361521,4,20339,362292,5,21614,362293,1,21614,362293,50,21616,362293,40,21616,362357,0,21616,394309,3,23117,395473,4,23867,396184,1,24617,396184,50,24618,396184,40,24618,396248,0,24618,412743,3,25379,413810,4,25744,415849,5,26119,415850,1,26119,415850,50,26119,415850,40,26119,415914,0,26119,443671,3,27320,444517,4,27920,444938,1,28520,444938,50,28520,444938,40,28520,445002,0,28521,462861,3,29272,463671,4,29647,464152,1,30022,464152,50,30022,464152,40,30022,464152,40,30022,464261,0,30022,465306,50,30025,465306,30,30025,465306,40,30025,465361,0,30025,465410,50,30025,465410,30,30025,465410,40,30025,465465,0,30031,465536,50,30031,465536,30,30031,465536,40,30031,465591,0,30031)
%
%
% START OF PROOF
% 465537 [] equal(X,X).
% 465541 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 465558 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 465559 [?] ?
% 465568 [?] ?
% 465569 [] equal(multiply(sk_c2,sk_c10),sk_c9) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 465608 [hyper:465541,465558,binarycut:465568] equal(inverse(sk_c4),sk_c10).
% 465610 [hyper:465541,465558,binarycut:465559] equal(inverse(sk_c2),sk_c10).
% 465638 [hyper:465541,465569,demod:465610,cut:465537] equal(multiply(sk_c4,sk_c10),sk_c9).
% 465641 [hyper:465541,465638,demod:465608,cut:465537] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c11),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,119,0,0,159601,5,1501,159601,1,1501,159601,50,1501,159601,40,1501,159665,0,1501,169843,3,1802,170638,4,1952,171399,5,2102,171400,1,2102,171400,50,2104,171400,40,2104,171464,0,2104,173234,3,2415,173248,4,2564,173460,5,2705,173460,1,2705,173460,50,2705,173460,40,2705,173524,0,2705,206033,3,4234,206828,4,4956,207688,1,5706,207688,50,5707,207688,40,5707,207752,0,5707,231082,3,6458,231668,4,6833,232253,1,7208,232253,50,7209,232253,40,7209,232317,0,7209,250977,3,8009,251659,4,8335,252765,5,8710,252766,1,8710,252766,50,8710,252766,40,8710,252830,0,8710,314626,3,12611,315898,4,14561,317046,5,16511,317047,1,16511,317047,50,16513,317047,40,16513,317111,0,16513,360296,3,19065,361521,4,20339,362292,5,21614,362293,1,21614,362293,50,21616,362293,40,21616,362357,0,21616,394309,3,23117,395473,4,23867,396184,1,24617,396184,50,24618,396184,40,24618,396248,0,24618,412743,3,25379,413810,4,25744,415849,5,26119,415850,1,26119,415850,50,26119,415850,40,26119,415914,0,26119,443671,3,27320,444517,4,27920,444938,1,28520,444938,50,28520,444938,40,28520,445002,0,28521,462861,3,29272,463671,4,29647,464152,1,30022,464152,50,30022,464152,40,30022,464152,40,30022,464261,0,30022,465306,50,30025,465306,30,30025,465306,40,30025,465361,0,30025,465410,50,30025,465410,30,30025,465410,40,30025,465465,0,30031,465536,50,30031,465536,30,30031,465536,40,30031,465591,0,30031,465640,50,30031,465640,30,30031,465640,40,30031,465695,0,30036)
%
%
% START OF PROOF
% 465641 [] equal(X,X).
% 465645 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 465684 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 465685 [?] ?
% 465694 [?] ?
% 465695 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 465729 [hyper:465645,465684,binarycut:465694] equal(inverse(sk_c3),sk_c11).
% 465731 [hyper:465645,465684,binarycut:465685] equal(inverse(sk_c1),sk_c11).
% 465765 [hyper:465645,465695,demod:465731,cut:465641] equal(multiply(sk_c3,sk_c11),sk_c10).
% 465767 [hyper:465645,465765,demod:465729,cut:465641] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(sk_c9,sk_c11),sk_c10) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(sk_c9,sk_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 29
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,119,0,0,159601,5,1501,159601,1,1501,159601,50,1501,159601,40,1501,159665,0,1501,169843,3,1802,170638,4,1952,171399,5,2102,171400,1,2102,171400,50,2104,171400,40,2104,171464,0,2104,173234,3,2415,173248,4,2564,173460,5,2705,173460,1,2705,173460,50,2705,173460,40,2705,173524,0,2705,206033,3,4234,206828,4,4956,207688,1,5706,207688,50,5707,207688,40,5707,207752,0,5707,231082,3,6458,231668,4,6833,232253,1,7208,232253,50,7209,232253,40,7209,232317,0,7209,250977,3,8009,251659,4,8335,252765,5,8710,252766,1,8710,252766,50,8710,252766,40,8710,252830,0,8710,314626,3,12611,315898,4,14561,317046,5,16511,317047,1,16511,317047,50,16513,317047,40,16513,317111,0,16513,360296,3,19065,361521,4,20339,362292,5,21614,362293,1,21614,362293,50,21616,362293,40,21616,362357,0,21616,394309,3,23117,395473,4,23867,396184,1,24617,396184,50,24618,396184,40,24618,396248,0,24618,412743,3,25379,413810,4,25744,415849,5,26119,415850,1,26119,415850,50,26119,415850,40,26119,415914,0,26119,443671,3,27320,444517,4,27920,444938,1,28520,444938,50,28520,444938,40,28520,445002,0,28521,462861,3,29272,463671,4,29647,464152,1,30022,464152,50,30022,464152,40,30022,464152,40,30022,464261,0,30022,465306,50,30025,465306,30,30025,465306,40,30025,465361,0,30025,465410,50,30025,465410,30,30025,465410,40,30025,465465,0,30031,465536,50,30031,465536,30,30031,465536,40,30031,465591,0,30031,465640,50,30031,465640,30,30031,465640,40,30031,465695,0,30036,465766,50,30036,465766,30,30036,465766,40,30036,465821,0,30036,466014,50,30038,466069,0,30042,466335,50,30048,466390,0,30048,466664,50,30055,466719,0,30059,467001,50,30068,467056,0,30068,467344,50,30080,467399,0,30085,467695,50,30106,467750,0,30106,468054,50,30143,468109,0,30147,468423,50,30217,468478,0,30217,468802,50,30355,468802,40,30355,468857,0,30355)
%
%
% START OF PROOF
% 468804 [] equal(multiply(identity,X),X).
% 468805 [] equal(multiply(inverse(X),X),identity).
% 468806 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 468807 [] -equal(multiply(sk_c9,sk_c11),sk_c10).
% 468809 [?] ?
% 468810 [?] ?
% 468812 [?] ?
% 468813 [?] ?
% 468814 [?] ?
% 468815 [?] ?
% 468816 [?] ?
% 468817 [?] ?
% 468877 [input:468809,cut:468807] equal(inverse(sk_c6),sk_c8).
% 468878 [para:468877.1.1,468805.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 468891 [input:468810,cut:468807] equal(inverse(sk_c7),sk_c6).
% 468892 [para:468891.1.1,468805.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 468893 [input:468812,cut:468807] equal(inverse(sk_c5),sk_c8).
% 468894 [para:468893.1.1,468805.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 468895 [input:468814,cut:468807] equal(inverse(sk_c4),sk_c10).
% 468896 [para:468895.1.1,468805.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 468898 [input:468816,cut:468807] equal(inverse(sk_c3),sk_c11).
% 468899 [para:468898.1.1,468805.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 468906 [input:468813,cut:468807] equal(multiply(sk_c5,sk_c8),sk_c11).
% 468914 [input:468815,cut:468807] equal(multiply(sk_c4,sk_c10),sk_c9).
% 468919 [input:468817,cut:468807] equal(multiply(sk_c3,sk_c11),sk_c10).
% 468955 [para:468878.1.1,468806.1.1.1,demod:468804] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 468956 [para:468892.1.1,468806.1.1.1,demod:468804] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 468958 [para:468896.1.1,468806.1.1.1,demod:468804] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 468960 [para:468899.1.1,468806.1.1.1,demod:468804] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 468962 [para:468906.1.1,468806.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 468997 [para:468892.1.1,468955.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 468998 [para:468997.1.2,468806.1.1.1,demod:468804] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 469010 [para:468914.1.1,468958.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 469015 [para:468919.1.1,468960.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 469017 [para:468998.1.1,468956.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 469018 [para:468878.1.1,469017.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 469019 [para:468894.1.1,469017.1.2.2,demod:469018] equal(sk_c5,sk_c6).
% 469026 [para:469019.1.2,468956.1.2.1,demod:468962,468998] equal(X,multiply(sk_c11,X)).
% 469034 [para:469026.1.2,468960.1.2] equal(X,multiply(sk_c3,X)).
% 469035 [para:469026.1.2,469015.1.2] equal(sk_c11,sk_c10).
% 469053 [para:469035.1.1,468960.1.2.1,demod:469034] equal(X,multiply(sk_c10,X)).
% 469065 [para:469053.1.2,469010.1.2] equal(sk_c10,sk_c9).
% 469068 [para:469065.1.2,468807.1.1.1,demod:469053,cut:469035] 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: 34688
% derived clauses: 4379204
% kept clauses: 256163
% kept size sum: 258983
% kept mid-nuclei: 149638
% kept new demods: 2767
% forw unit-subs: 1375918
% forw double-subs: 2343292
% forw overdouble-subs: 196799
% backward subs: 13160
% fast unit cutoff: 34457
% full unit cutoff: 0
% dbl unit cutoff: 22751
% real runtime : 306.0
% process. runtime: 303.56
% specific non-discr-tree subsumption statistics:
% tried: 37065980
% length fails: 4659323
% strength fails: 14935572
% predlist fails: 2630492
% aux str. fails: 2395655
% by-lit fails: 5235737
% full subs tried: 2394536
% full subs fail: 2261632
%
% ; 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/GRP260-1+eq_r.in")
%
%------------------------------------------------------------------------------