TSTP Solution File: GRP368-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP368-1 : 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 : art06.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 298.4s
% Output : Assurance 298.4s
% 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/GRP368-1+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_c5,sk_c7),sk_c6) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(Z,sk_c5),sk_c7) | -equal(inverse(Z),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(U),sk_c7) | -equal(multiply(U,sk_c6),sk_c7).
% was split for some strategies as:
% -equal(inverse(U),sk_c7) | -equal(multiply(U,sk_c6),sk_c7).
% -equal(multiply(Z,sk_c5),sk_c7) | -equal(inverse(Z),sk_c5).
% -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7).
% -equal(multiply(sk_c5,sk_c7),sk_c6).
% -equal(multiply(sk_c6,sk_c7),sk_c5).
% -equal(inverse(sk_c6),sk_c5).
% -equal(multiply(sk_c7,sk_c5),sk_c6).
%
% 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(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(Z,sk_c5),sk_c7) | -equal(inverse(Z),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(U),sk_c7) | -equal(multiply(U,sk_c6),sk_c7).
% Split part used next: -equal(inverse(U),sk_c7) | -equal(multiply(U,sk_c6),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,74,0,0,2753,50,23,2792,0,23,6570,50,69,6609,0,69,11348,50,135,11387,0,135,16404,50,184,16443,0,184,21739,50,245,21778,0,245,27490,50,323,27529,0,323,33657,50,427,33696,0,427,40378,50,584,40417,0,584,47653,50,840,47653,40,840,47692,0,840,58218,3,1141,58963,4,1291,59632,5,1443,59632,1,1443,59632,50,1444,59632,40,1444,59671,0,1444,59934,3,1755,59943,4,1897,59952,5,2045,59952,1,2045,59952,50,2045,59952,40,2045,59991,0,2045,85305,3,3546,86473,4,4296,87479,1,5046,87479,50,5046,87479,40,5046,87518,0,5047,102710,3,5798,103636,4,6173,104426,5,6548,104427,1,6548,104427,50,6548,104427,40,6548,104466,0,6548,112577,3,7304,114327,4,7674,115798,1,8049,115798,50,8049,115798,40,8049,115837,0,8049,192888,3,11971,193811,4,13900,194702,5,15850,194703,1,15850,194703,50,15853,194703,40,15853,194742,0,15853,241443,3,18404,242209,4,19679,243038,1,20955,243038,50,20956,243038,40,20956,243077,0,20956,280341,3,22457,281410,4,23207,282552,5,23957,282553,1,23957,282553,50,23958,282553,40,23958,282592,0,23958,290603,3,24716,291803,4,25089,292419,5,25459,292419,1,25459,292419,50,25459,292419,40,25459,292458,0,25459,318344,3,26660,319271,4,27260,319915,1,27860,319915,50,27861,319915,40,27861,319954,0,27861,338748,3,28612,339576,4,28987,340145,5,29362,340146,1,29362,340146,50,29363,340146,40,29363,340146,40,29363,340181,0,29363)
%
%
% START OF PROOF
% 340148 [] equal(multiply(identity,X),X).
% 340149 [] equal(multiply(inverse(X),X),identity).
% 340150 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 340151 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 340152 [?] ?
% 340153 [] equal(inverse(sk_c3),sk_c5) | equal(inverse(sk_c4),sk_c7).
% 340157 [] equal(multiply(sk_c3,sk_c5),sk_c7) | equal(multiply(sk_c4,sk_c6),sk_c7).
% 340158 [] equal(multiply(sk_c3,sk_c5),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 340162 [?] ?
% 340163 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 340167 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c4,sk_c6),sk_c7).
% 340168 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c4),sk_c7).
% 340172 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(multiply(sk_c4,sk_c6),sk_c7).
% 340173 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 340177 [] equal(multiply(sk_c5,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c6),sk_c7).
% 340178 [] equal(multiply(sk_c5,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 340184 [hyper:340151,340153,binarycut:340152] equal(inverse(sk_c3),sk_c5).
% 340185 [para:340184.1.1,340149.1.1.1] equal(multiply(sk_c5,sk_c3),identity).
% 340193 [hyper:340151,340163,binarycut:340162] equal(inverse(sk_c1),sk_c7).
% 340196 [para:340193.1.1,340149.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 340200 [hyper:340151,340158,340157] equal(multiply(sk_c3,sk_c5),sk_c7).
% 340206 [hyper:340151,340168,340167] equal(multiply(sk_c1,sk_c7),sk_c2).
% 340212 [hyper:340151,340173,340172] equal(multiply(sk_c7,sk_c2),sk_c6).
% 340218 [hyper:340151,340178,340177] equal(multiply(sk_c5,sk_c7),sk_c6).
% 340219 [para:340149.1.1,340150.1.1.1,demod:340148] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 340220 [para:340185.1.1,340150.1.1.1,demod:340148] equal(X,multiply(sk_c5,multiply(sk_c3,X))).
% 340226 [para:340200.1.1,340220.1.2.2,demod:340218] equal(sk_c5,sk_c6).
% 340227 [para:340226.1.1,340185.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 340228 [para:340226.1.1,340200.1.1.2] equal(multiply(sk_c3,sk_c6),sk_c7).
% 340229 [para:340226.1.1,340218.1.1.1] equal(multiply(sk_c6,sk_c7),sk_c6).
% 340237 [para:340206.1.1,340219.1.2.2,demod:340212,340193] equal(sk_c7,sk_c6).
% 340247 [para:340229.1.1,340219.1.2.2,demod:340149] equal(sk_c7,identity).
% 340249 [para:340247.1.1,340196.1.1.1,demod:340148] equal(sk_c1,identity).
% 340253 [para:340247.1.1,340237.1.1] equal(identity,sk_c6).
% 340256 [para:340249.1.1,340193.1.1.1] equal(inverse(identity),sk_c7).
% 340264 [para:340253.1.2,340227.1.1.1,demod:340148] equal(sk_c3,identity).
% 340276 [para:340264.1.1,340228.1.1.1,demod:340148] equal(sk_c6,sk_c7).
% 340287 [hyper:340151,340256,demod:340148,cut:340276] 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 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(Z,sk_c5),sk_c7) | -equal(inverse(Z),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(U),sk_c7) | -equal(multiply(U,sk_c6),sk_c7).
% Split part used next: -equal(multiply(Z,sk_c5),sk_c7) | -equal(inverse(Z),sk_c5).
% 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(35,40,0,74,0,0,2753,50,23,2792,0,23,6570,50,69,6609,0,69,11348,50,135,11387,0,135,16404,50,184,16443,0,184,21739,50,245,21778,0,245,27490,50,323,27529,0,323,33657,50,427,33696,0,427,40378,50,584,40417,0,584,47653,50,840,47653,40,840,47692,0,840,58218,3,1141,58963,4,1291,59632,5,1443,59632,1,1443,59632,50,1444,59632,40,1444,59671,0,1444,59934,3,1755,59943,4,1897,59952,5,2045,59952,1,2045,59952,50,2045,59952,40,2045,59991,0,2045,85305,3,3546,86473,4,4296,87479,1,5046,87479,50,5046,87479,40,5046,87518,0,5047,102710,3,5798,103636,4,6173,104426,5,6548,104427,1,6548,104427,50,6548,104427,40,6548,104466,0,6548,112577,3,7304,114327,4,7674,115798,1,8049,115798,50,8049,115798,40,8049,115837,0,8049,192888,3,11971,193811,4,13900,194702,5,15850,194703,1,15850,194703,50,15853,194703,40,15853,194742,0,15853,241443,3,18404,242209,4,19679,243038,1,20955,243038,50,20956,243038,40,20956,243077,0,20956,280341,3,22457,281410,4,23207,282552,5,23957,282553,1,23957,282553,50,23958,282553,40,23958,282592,0,23958,290603,3,24716,291803,4,25089,292419,5,25459,292419,1,25459,292419,50,25459,292419,40,25459,292458,0,25459,318344,3,26660,319271,4,27260,319915,1,27860,319915,50,27861,319915,40,27861,319954,0,27861,338748,3,28612,339576,4,28987,340145,5,29362,340146,1,29362,340146,50,29363,340146,40,29363,340146,40,29363,340181,0,29363,340286,50,29363,340286,30,29363,340286,40,29363,340321,0,29363)
%
%
% START OF PROOF
% 340288 [] equal(multiply(identity,X),X).
% 340289 [] equal(multiply(inverse(X),X),identity).
% 340290 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 340291 [] -equal(multiply(X,sk_c5),sk_c7) | -equal(inverse(X),sk_c5).
% 340292 [] equal(multiply(sk_c4,sk_c6),sk_c7) | equal(inverse(sk_c3),sk_c5).
% 340293 [] equal(inverse(sk_c3),sk_c5) | equal(inverse(sk_c4),sk_c7).
% 340294 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c3),sk_c5).
% 340295 [] equal(inverse(sk_c3),sk_c5) | equal(inverse(sk_c6),sk_c5).
% 340296 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c3),sk_c5).
% 340297 [?] ?
% 340298 [?] ?
% 340299 [?] ?
% 340300 [?] ?
% 340301 [?] ?
% 340324 [hyper:340291,340293,binarycut:340298] equal(inverse(sk_c4),sk_c7).
% 340325 [para:340324.1.1,340289.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 340329 [hyper:340291,340295,binarycut:340300] equal(inverse(sk_c6),sk_c5).
% 340333 [para:340329.1.1,340289.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 340337 [hyper:340291,340292,binarycut:340297] equal(multiply(sk_c4,sk_c6),sk_c7).
% 340340 [hyper:340291,340294,binarycut:340299] equal(multiply(sk_c7,sk_c5),sk_c6).
% 340343 [hyper:340291,340296,binarycut:340301] equal(multiply(sk_c6,sk_c7),sk_c5).
% 340344 [para:340289.1.1,340290.1.1.1,demod:340288] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 340345 [para:340325.1.1,340290.1.1.1,demod:340288] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 340346 [para:340333.1.1,340290.1.1.1,demod:340288] equal(X,multiply(sk_c5,multiply(sk_c6,X))).
% 340347 [para:340337.1.1,340290.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c4,multiply(sk_c6,X))).
% 340348 [para:340340.1.1,340290.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c5,X))).
% 340350 [para:340337.1.1,340345.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 340352 [para:340343.1.1,340346.1.2.2] equal(sk_c7,multiply(sk_c5,sk_c5)).
% 340357 [para:340340.1.1,340344.1.2.2] equal(sk_c5,multiply(inverse(sk_c7),sk_c6)).
% 340359 [para:340350.1.2,340344.1.2.2,demod:340357] equal(sk_c7,sk_c5).
% 340362 [para:340359.1.2,340333.1.1.1] equal(multiply(sk_c7,sk_c6),identity).
% 340364 [para:340359.1.2,340352.1.2.1,demod:340340] equal(sk_c7,sk_c6).
% 340368 [para:340364.1.1,340343.1.1.2] equal(multiply(sk_c6,sk_c6),sk_c5).
% 340371 [para:340364.1.1,340350.1.2.2,demod:340362] equal(sk_c6,identity).
% 340377 [para:340371.1.1,340329.1.1.1] equal(inverse(identity),sk_c5).
% 340379 [para:340371.1.1,340337.1.1.2] equal(multiply(sk_c4,identity),sk_c7).
% 340381 [para:340371.1.1,340347.1.2.2.1,demod:340288] equal(multiply(sk_c7,X),multiply(sk_c4,X)).
% 340383 [para:340333.1.1,340348.1.2.2,demod:340379,340381,340368] equal(sk_c5,sk_c7).
% 340390 [hyper:340291,340377,demod:340288,cut:340383] 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_c5,sk_c7),sk_c6) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(Z,sk_c5),sk_c7) | -equal(inverse(Z),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(U),sk_c7) | -equal(multiply(U,sk_c6),sk_c7).
% Split part used next: -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),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
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,74,0,0,2753,50,23,2792,0,23,6570,50,69,6609,0,69,11348,50,135,11387,0,135,16404,50,184,16443,0,184,21739,50,245,21778,0,245,27490,50,323,27529,0,323,33657,50,427,33696,0,427,40378,50,584,40417,0,584,47653,50,840,47653,40,840,47692,0,840,58218,3,1141,58963,4,1291,59632,5,1443,59632,1,1443,59632,50,1444,59632,40,1444,59671,0,1444,59934,3,1755,59943,4,1897,59952,5,2045,59952,1,2045,59952,50,2045,59952,40,2045,59991,0,2045,85305,3,3546,86473,4,4296,87479,1,5046,87479,50,5046,87479,40,5046,87518,0,5047,102710,3,5798,103636,4,6173,104426,5,6548,104427,1,6548,104427,50,6548,104427,40,6548,104466,0,6548,112577,3,7304,114327,4,7674,115798,1,8049,115798,50,8049,115798,40,8049,115837,0,8049,192888,3,11971,193811,4,13900,194702,5,15850,194703,1,15850,194703,50,15853,194703,40,15853,194742,0,15853,241443,3,18404,242209,4,19679,243038,1,20955,243038,50,20956,243038,40,20956,243077,0,20956,280341,3,22457,281410,4,23207,282552,5,23957,282553,1,23957,282553,50,23958,282553,40,23958,282592,0,23958,290603,3,24716,291803,4,25089,292419,5,25459,292419,1,25459,292419,50,25459,292419,40,25459,292458,0,25459,318344,3,26660,319271,4,27260,319915,1,27860,319915,50,27861,319915,40,27861,319954,0,27861,338748,3,28612,339576,4,28987,340145,5,29362,340146,1,29362,340146,50,29363,340146,40,29363,340146,40,29363,340181,0,29363,340286,50,29363,340286,30,29363,340286,40,29363,340321,0,29363,340389,50,29363,340389,30,29363,340389,40,29363,340424,0,29369)
%
%
% START OF PROOF
% 340391 [] equal(multiply(identity,X),X).
% 340392 [] equal(multiply(inverse(X),X),identity).
% 340393 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 340394 [] -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7).
% 340405 [] equal(multiply(sk_c4,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 340406 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 340407 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 340408 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c6),sk_c5).
% 340409 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 340410 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c4,sk_c6),sk_c7).
% 340411 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c4),sk_c7).
% 340412 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c7,sk_c5),sk_c6).
% 340413 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c6),sk_c5).
% 340414 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c6,sk_c7),sk_c5).
% 340415 [?] ?
% 340416 [?] ?
% 340417 [?] ?
% 340418 [?] ?
% 340419 [?] ?
% 340503 [hyper:340394,340411,binarycut:340416,binarycut:340406] equal(inverse(sk_c4),sk_c7).
% 340513 [para:340503.1.1,340392.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 340519 [hyper:340394,340413,binarycut:340418,binarycut:340408] equal(inverse(sk_c6),sk_c5).
% 340520 [para:340519.1.1,340392.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 340533 [hyper:340394,340410,340405,binarycut:340415] equal(multiply(sk_c4,sk_c6),sk_c7).
% 340537 [hyper:340394,340412,340407,binarycut:340417] equal(multiply(sk_c7,sk_c5),sk_c6).
% 340563 [hyper:340394,340414,340409,binarycut:340419] equal(multiply(sk_c6,sk_c7),sk_c5).
% 340568 [para:340392.1.1,340393.1.1.1,demod:340391] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 340569 [para:340513.1.1,340393.1.1.1,demod:340391] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 340570 [para:340520.1.1,340393.1.1.1,demod:340391] equal(X,multiply(sk_c5,multiply(sk_c6,X))).
% 340571 [para:340533.1.1,340393.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c4,multiply(sk_c6,X))).
% 340572 [para:340537.1.1,340393.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c5,X))).
% 340576 [para:340533.1.1,340569.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 340577 [para:340576.1.2,340393.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c7,X))).
% 340580 [para:340563.1.1,340570.1.2.2] equal(sk_c7,multiply(sk_c5,sk_c5)).
% 340587 [para:340537.1.1,340568.1.2.2] equal(sk_c5,multiply(inverse(sk_c7),sk_c6)).
% 340589 [para:340576.1.2,340568.1.2.2,demod:340587] equal(sk_c7,sk_c5).
% 340594 [para:340589.1.2,340520.1.1.1] equal(multiply(sk_c7,sk_c6),identity).
% 340596 [para:340589.1.2,340580.1.2.1,demod:340537] equal(sk_c7,sk_c6).
% 340600 [para:340596.1.1,340563.1.1.2] equal(multiply(sk_c6,sk_c6),sk_c5).
% 340603 [para:340596.1.1,340576.1.2.2,demod:340594] equal(sk_c6,identity).
% 340611 [para:340603.1.1,340533.1.1.2] equal(multiply(sk_c4,identity),sk_c7).
% 340613 [para:340603.1.1,340571.1.2.2.1,demod:340391] equal(multiply(sk_c7,X),multiply(sk_c4,X)).
% 340617 [para:340520.1.1,340572.1.2.2,demod:340611,340613,340600] equal(sk_c5,sk_c7).
% 340628 [hyper:340394,340577,demod:340519,340611,340613,340594,340576,cut:340596,cut:340617] 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 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(Z,sk_c5),sk_c7) | -equal(inverse(Z),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(U),sk_c7) | -equal(multiply(U,sk_c6),sk_c7).
% Split part used next: -equal(multiply(sk_c5,sk_c7),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(35,40,0,74,0,0,2753,50,23,2792,0,23,6570,50,69,6609,0,69,11348,50,135,11387,0,135,16404,50,184,16443,0,184,21739,50,245,21778,0,245,27490,50,323,27529,0,323,33657,50,427,33696,0,427,40378,50,584,40417,0,584,47653,50,840,47653,40,840,47692,0,840,58218,3,1141,58963,4,1291,59632,5,1443,59632,1,1443,59632,50,1444,59632,40,1444,59671,0,1444,59934,3,1755,59943,4,1897,59952,5,2045,59952,1,2045,59952,50,2045,59952,40,2045,59991,0,2045,85305,3,3546,86473,4,4296,87479,1,5046,87479,50,5046,87479,40,5046,87518,0,5047,102710,3,5798,103636,4,6173,104426,5,6548,104427,1,6548,104427,50,6548,104427,40,6548,104466,0,6548,112577,3,7304,114327,4,7674,115798,1,8049,115798,50,8049,115798,40,8049,115837,0,8049,192888,3,11971,193811,4,13900,194702,5,15850,194703,1,15850,194703,50,15853,194703,40,15853,194742,0,15853,241443,3,18404,242209,4,19679,243038,1,20955,243038,50,20956,243038,40,20956,243077,0,20956,280341,3,22457,281410,4,23207,282552,5,23957,282553,1,23957,282553,50,23958,282553,40,23958,282592,0,23958,290603,3,24716,291803,4,25089,292419,5,25459,292419,1,25459,292419,50,25459,292419,40,25459,292458,0,25459,318344,3,26660,319271,4,27260,319915,1,27860,319915,50,27861,319915,40,27861,319954,0,27861,338748,3,28612,339576,4,28987,340145,5,29362,340146,1,29362,340146,50,29363,340146,40,29363,340146,40,29363,340181,0,29363,340286,50,29363,340286,30,29363,340286,40,29363,340321,0,29363,340389,50,29363,340389,30,29363,340389,40,29363,340424,0,29369,340627,50,29369,340627,30,29369,340627,40,29369,340662,0,29369,340755,50,29370,340790,0,29370,340920,50,29372,340955,0,29377,341093,50,29380,341128,0,29380,341274,50,29385,341309,0,29389,341461,50,29397,341496,0,29397,341656,50,29411,341691,0,29411,341859,50,29438,341894,0,29442,342072,50,29496,342107,0,29496,342295,50,29607,342295,40,29607,342330,0,29607)
%
%
% START OF PROOF
% 342296 [] equal(X,X).
% 342297 [] equal(multiply(identity,X),X).
% 342298 [] equal(multiply(inverse(X),X),identity).
% 342299 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 342300 [] -equal(multiply(sk_c5,sk_c7),sk_c6).
% 342326 [?] ?
% 342327 [?] ?
% 342328 [?] ?
% 342369 [input:342327,cut:342300] equal(inverse(sk_c4),sk_c7).
% 342370 [para:342369.1.1,342298.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 342384 [input:342326,cut:342300] equal(multiply(sk_c4,sk_c6),sk_c7).
% 342385 [input:342328,cut:342300] equal(multiply(sk_c7,sk_c5),sk_c6).
% 342390 [para:342298.1.1,342299.1.1.1,demod:342297] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 342409 [para:342370.1.1,342299.1.1.1,demod:342297] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 342438 [para:342384.1.1,342409.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 342489 [para:342385.1.1,342390.1.2.2] equal(sk_c5,multiply(inverse(sk_c7),sk_c6)).
% 342496 [para:342438.1.2,342390.1.2.2,demod:342489] equal(sk_c7,sk_c5).
% 342500 [para:342496.1.2,342300.1.1.1,demod:342438,cut:342296] 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 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(Z,sk_c5),sk_c7) | -equal(inverse(Z),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(U),sk_c7) | -equal(multiply(U,sk_c6),sk_c7).
% Split part used next: -equal(multiply(sk_c6,sk_c7),sk_c5).
% 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(35,40,0,74,0,0,2753,50,23,2792,0,23,6570,50,69,6609,0,69,11348,50,135,11387,0,135,16404,50,184,16443,0,184,21739,50,245,21778,0,245,27490,50,323,27529,0,323,33657,50,427,33696,0,427,40378,50,584,40417,0,584,47653,50,840,47653,40,840,47692,0,840,58218,3,1141,58963,4,1291,59632,5,1443,59632,1,1443,59632,50,1444,59632,40,1444,59671,0,1444,59934,3,1755,59943,4,1897,59952,5,2045,59952,1,2045,59952,50,2045,59952,40,2045,59991,0,2045,85305,3,3546,86473,4,4296,87479,1,5046,87479,50,5046,87479,40,5046,87518,0,5047,102710,3,5798,103636,4,6173,104426,5,6548,104427,1,6548,104427,50,6548,104427,40,6548,104466,0,6548,112577,3,7304,114327,4,7674,115798,1,8049,115798,50,8049,115798,40,8049,115837,0,8049,192888,3,11971,193811,4,13900,194702,5,15850,194703,1,15850,194703,50,15853,194703,40,15853,194742,0,15853,241443,3,18404,242209,4,19679,243038,1,20955,243038,50,20956,243038,40,20956,243077,0,20956,280341,3,22457,281410,4,23207,282552,5,23957,282553,1,23957,282553,50,23958,282553,40,23958,282592,0,23958,290603,3,24716,291803,4,25089,292419,5,25459,292419,1,25459,292419,50,25459,292419,40,25459,292458,0,25459,318344,3,26660,319271,4,27260,319915,1,27860,319915,50,27861,319915,40,27861,319954,0,27861,338748,3,28612,339576,4,28987,340145,5,29362,340146,1,29362,340146,50,29363,340146,40,29363,340146,40,29363,340181,0,29363,340286,50,29363,340286,30,29363,340286,40,29363,340321,0,29363,340389,50,29363,340389,30,29363,340389,40,29363,340424,0,29369,340627,50,29369,340627,30,29369,340627,40,29369,340662,0,29369,340755,50,29370,340790,0,29370,340920,50,29372,340955,0,29377,341093,50,29380,341128,0,29380,341274,50,29385,341309,0,29389,341461,50,29397,341496,0,29397,341656,50,29411,341691,0,29411,341859,50,29438,341894,0,29442,342072,50,29496,342107,0,29496,342295,50,29607,342295,40,29607,342330,0,29607,342499,50,29608,342499,30,29608,342499,40,29608,342534,0,29608,342652,50,29609,342687,0,29613,342855,50,29616,342890,0,29616,343066,50,29620,343101,0,29620,343285,50,29626,343320,0,29630,343510,50,29639,343545,0,29639,343743,50,29656,343778,0,29660,343984,50,29690,344019,0,29690,344235,50,29753,344270,0,29753,344496,50,29873,344496,40,29873,344531,0,29873)
%
%
% START OF PROOF
% 344327 [?] ?
% 344498 [] equal(multiply(identity,X),X).
% 344499 [] equal(multiply(inverse(X),X),identity).
% 344500 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 344501 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 344506 [?] ?
% 344511 [?] ?
% 344531 [?] ?
% 344548 [input:344506,cut:344501] equal(inverse(sk_c3),sk_c5).
% 344549 [para:344548.1.1,344499.1.1.1] equal(multiply(sk_c5,sk_c3),identity).
% 344568 [input:344511,cut:344501] equal(multiply(sk_c3,sk_c5),sk_c7).
% 344587 [input:344531,cut:344501] equal(multiply(sk_c5,sk_c7),sk_c6).
% 344594 [para:344549.1.1,344500.1.1.1,demod:344498] equal(X,multiply(sk_c5,multiply(sk_c3,X))).
% 344633 [para:344568.1.1,344594.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c7)).
% 344638 [para:344633.1.2,344587.1.1] equal(sk_c5,sk_c6).
% 344640 [para:344638.1.1,344501.1.2,cut:344327] 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_c5,sk_c7),sk_c6) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(Z,sk_c5),sk_c7) | -equal(inverse(Z),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(U),sk_c7) | -equal(multiply(U,sk_c6),sk_c7).
% Split part used next: -equal(inverse(sk_c6),sk_c5).
% 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(35,40,0,74,0,0,2753,50,23,2792,0,23,6570,50,69,6609,0,69,11348,50,135,11387,0,135,16404,50,184,16443,0,184,21739,50,245,21778,0,245,27490,50,323,27529,0,323,33657,50,427,33696,0,427,40378,50,584,40417,0,584,47653,50,840,47653,40,840,47692,0,840,58218,3,1141,58963,4,1291,59632,5,1443,59632,1,1443,59632,50,1444,59632,40,1444,59671,0,1444,59934,3,1755,59943,4,1897,59952,5,2045,59952,1,2045,59952,50,2045,59952,40,2045,59991,0,2045,85305,3,3546,86473,4,4296,87479,1,5046,87479,50,5046,87479,40,5046,87518,0,5047,102710,3,5798,103636,4,6173,104426,5,6548,104427,1,6548,104427,50,6548,104427,40,6548,104466,0,6548,112577,3,7304,114327,4,7674,115798,1,8049,115798,50,8049,115798,40,8049,115837,0,8049,192888,3,11971,193811,4,13900,194702,5,15850,194703,1,15850,194703,50,15853,194703,40,15853,194742,0,15853,241443,3,18404,242209,4,19679,243038,1,20955,243038,50,20956,243038,40,20956,243077,0,20956,280341,3,22457,281410,4,23207,282552,5,23957,282553,1,23957,282553,50,23958,282553,40,23958,282592,0,23958,290603,3,24716,291803,4,25089,292419,5,25459,292419,1,25459,292419,50,25459,292419,40,25459,292458,0,25459,318344,3,26660,319271,4,27260,319915,1,27860,319915,50,27861,319915,40,27861,319954,0,27861,338748,3,28612,339576,4,28987,340145,5,29362,340146,1,29362,340146,50,29363,340146,40,29363,340146,40,29363,340181,0,29363,340286,50,29363,340286,30,29363,340286,40,29363,340321,0,29363,340389,50,29363,340389,30,29363,340389,40,29363,340424,0,29369,340627,50,29369,340627,30,29369,340627,40,29369,340662,0,29369,340755,50,29370,340790,0,29370,340920,50,29372,340955,0,29377,341093,50,29380,341128,0,29380,341274,50,29385,341309,0,29389,341461,50,29397,341496,0,29397,341656,50,29411,341691,0,29411,341859,50,29438,341894,0,29442,342072,50,29496,342107,0,29496,342295,50,29607,342295,40,29607,342330,0,29607,342499,50,29608,342499,30,29608,342499,40,29608,342534,0,29608,342652,50,29609,342687,0,29613,342855,50,29616,342890,0,29616,343066,50,29620,343101,0,29620,343285,50,29626,343320,0,29630,343510,50,29639,343545,0,29639,343743,50,29656,343778,0,29660,343984,50,29690,344019,0,29690,344235,50,29753,344270,0,29753,344496,50,29873,344496,40,29873,344531,0,29873,344639,50,29873,344639,30,29873,344639,40,29873,344674,0,29873,344792,50,29874,344827,0,29878,344995,50,29881,345030,0,29881,345206,50,29886,345241,0,29886,345425,50,29892,345460,0,29896,345650,50,29906,345685,0,29906,345883,50,29922,345918,0,29927,346124,50,29957,346159,0,29957,346375,50,30021,346410,0,30021,346636,50,30139,346636,40,30139,346671,0,30139)
%
%
% START OF PROOF
% 346638 [] equal(multiply(identity,X),X).
% 346639 [] equal(multiply(inverse(X),X),identity).
% 346640 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 346641 [] -equal(inverse(sk_c6),sk_c5).
% 346645 [?] ?
% 346650 [?] ?
% 346655 [?] ?
% 346660 [?] ?
% 346665 [?] ?
% 346670 [?] ?
% 346677 [input:346645,cut:346641] equal(inverse(sk_c3),sk_c5).
% 346678 [para:346677.1.1,346639.1.1.1] equal(multiply(sk_c5,sk_c3),identity).
% 346682 [input:346655,cut:346641] equal(inverse(sk_c1),sk_c7).
% 346683 [para:346682.1.1,346639.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 346688 [input:346650,cut:346641] equal(multiply(sk_c3,sk_c5),sk_c7).
% 346695 [input:346660,cut:346641] equal(multiply(sk_c1,sk_c7),sk_c2).
% 346698 [input:346665,cut:346641] equal(multiply(sk_c7,sk_c2),sk_c6).
% 346702 [input:346670,cut:346641] equal(multiply(sk_c5,sk_c7),sk_c6).
% 346715 [para:346639.1.1,346640.1.1.1,demod:346638] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 346717 [para:346678.1.1,346640.1.1.1,demod:346638] equal(X,multiply(sk_c5,multiply(sk_c3,X))).
% 346718 [para:346683.1.1,346640.1.1.1,demod:346638] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 346730 [para:346698.1.1,346640.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c2,X))).
% 346733 [para:346702.1.1,346640.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c5,multiply(sk_c7,X))).
% 346747 [para:346688.1.1,346717.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c7)).
% 346749 [para:346747.1.2,346702.1.1] equal(sk_c5,sk_c6).
% 346750 [para:346747.1.2,346640.1.1.1,demod:346733] equal(multiply(sk_c5,X),multiply(sk_c6,X)).
% 346751 [para:346749.1.1,346641.1.2] -equal(inverse(sk_c6),sk_c6).
% 346755 [para:346749.1.1,346688.1.1.2] equal(multiply(sk_c3,sk_c6),sk_c7).
% 346759 [para:346749.1.1,346702.1.1.1] equal(multiply(sk_c6,sk_c7),sk_c6).
% 346766 [para:346755.1.1,346640.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c6,X))).
% 346770 [para:346695.1.1,346718.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c2)).
% 346772 [para:346770.1.2,346698.1.1] equal(sk_c7,sk_c6).
% 346773 [para:346770.1.2,346640.1.1.1,demod:346730] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 346839 [para:346717.1.2,346715.1.2.2] equal(multiply(sk_c3,X),multiply(inverse(sk_c5),X)).
% 346842 [para:346759.1.1,346715.1.2.2,demod:346639] equal(sk_c7,identity).
% 346848 [para:346750.1.1,346715.1.2.2,demod:346773,346766,346839] equal(X,multiply(sk_c6,X)).
% 346853 [para:346842.1.1,346683.1.1.1,demod:346638] equal(sk_c1,identity).
% 346861 [para:346842.1.1,346702.1.1.2,demod:346848,346750] equal(identity,sk_c6).
% 346887 [para:346853.1.1,346682.1.1.1] equal(inverse(identity),sk_c7).
% 346892 [para:346861.1.2,346751.1.1.1,demod:346887,cut:346772] 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(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(Z,sk_c5),sk_c7) | -equal(inverse(Z),sk_c5) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(U),sk_c7) | -equal(multiply(U,sk_c6),sk_c7).
% Split part used next: -equal(multiply(sk_c7,sk_c5),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(35,40,0,74,0,0,2753,50,23,2792,0,23,6570,50,69,6609,0,69,11348,50,135,11387,0,135,16404,50,184,16443,0,184,21739,50,245,21778,0,245,27490,50,323,27529,0,323,33657,50,427,33696,0,427,40378,50,584,40417,0,584,47653,50,840,47653,40,840,47692,0,840,58218,3,1141,58963,4,1291,59632,5,1443,59632,1,1443,59632,50,1444,59632,40,1444,59671,0,1444,59934,3,1755,59943,4,1897,59952,5,2045,59952,1,2045,59952,50,2045,59952,40,2045,59991,0,2045,85305,3,3546,86473,4,4296,87479,1,5046,87479,50,5046,87479,40,5046,87518,0,5047,102710,3,5798,103636,4,6173,104426,5,6548,104427,1,6548,104427,50,6548,104427,40,6548,104466,0,6548,112577,3,7304,114327,4,7674,115798,1,8049,115798,50,8049,115798,40,8049,115837,0,8049,192888,3,11971,193811,4,13900,194702,5,15850,194703,1,15850,194703,50,15853,194703,40,15853,194742,0,15853,241443,3,18404,242209,4,19679,243038,1,20955,243038,50,20956,243038,40,20956,243077,0,20956,280341,3,22457,281410,4,23207,282552,5,23957,282553,1,23957,282553,50,23958,282553,40,23958,282592,0,23958,290603,3,24716,291803,4,25089,292419,5,25459,292419,1,25459,292419,50,25459,292419,40,25459,292458,0,25459,318344,3,26660,319271,4,27260,319915,1,27860,319915,50,27861,319915,40,27861,319954,0,27861,338748,3,28612,339576,4,28987,340145,5,29362,340146,1,29362,340146,50,29363,340146,40,29363,340146,40,29363,340181,0,29363,340286,50,29363,340286,30,29363,340286,40,29363,340321,0,29363,340389,50,29363,340389,30,29363,340389,40,29363,340424,0,29369,340627,50,29369,340627,30,29369,340627,40,29369,340662,0,29369,340755,50,29370,340790,0,29370,340920,50,29372,340955,0,29377,341093,50,29380,341128,0,29380,341274,50,29385,341309,0,29389,341461,50,29397,341496,0,29397,341656,50,29411,341691,0,29411,341859,50,29438,341894,0,29442,342072,50,29496,342107,0,29496,342295,50,29607,342295,40,29607,342330,0,29607,342499,50,29608,342499,30,29608,342499,40,29608,342534,0,29608,342652,50,29609,342687,0,29613,342855,50,29616,342890,0,29616,343066,50,29620,343101,0,29620,343285,50,29626,343320,0,29630,343510,50,29639,343545,0,29639,343743,50,29656,343778,0,29660,343984,50,29690,344019,0,29690,344235,50,29753,344270,0,29753,344496,50,29873,344496,40,29873,344531,0,29873,344639,50,29873,344639,30,29873,344639,40,29873,344674,0,29873,344792,50,29874,344827,0,29878,344995,50,29881,345030,0,29881,345206,50,29886,345241,0,29886,345425,50,29892,345460,0,29896,345650,50,29906,345685,0,29906,345883,50,29922,345918,0,29927,346124,50,29957,346159,0,29957,346375,50,30021,346410,0,30021,346636,50,30139,346636,40,30139,346671,0,30139,346891,50,30140,346891,30,30140,346891,40,30140,346926,0,30140,347044,50,30140,347079,0,30145,347247,50,30148,347282,0,30148,347458,50,30152,347493,0,30152,347677,50,30158,347712,0,30163,347902,50,30172,347937,0,30172,348135,50,30189,348170,0,30193,348376,50,30223,348411,0,30223,348627,50,30287,348662,0,30287,348888,50,30405,348888,40,30405,348923,0,30405)
%
%
% START OF PROOF
% 348829 [?] ?
% 348890 [] equal(multiply(identity,X),X).
% 348891 [] equal(multiply(inverse(X),X),identity).
% 348892 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 348893 [] -equal(multiply(sk_c7,sk_c5),sk_c6).
% 348906 [?] ?
% 348911 [?] ?
% 348916 [?] ?
% 348947 [input:348906,cut:348893] equal(inverse(sk_c1),sk_c7).
% 348948 [para:348947.1.1,348891.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 348970 [input:348911,cut:348893] equal(multiply(sk_c1,sk_c7),sk_c2).
% 348973 [input:348916,cut:348893] equal(multiply(sk_c7,sk_c2),sk_c6).
% 348987 [para:348948.1.1,348892.1.1.1,demod:348890] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 349046 [para:348970.1.1,348987.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c2)).
% 349050 [para:349046.1.2,348973.1.1] equal(sk_c7,sk_c6).
% 349055 [para:349050.1.1,348893.1.1.1,cut:348829] 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: 37194
% derived clauses: 6528275
% kept clauses: 263763
% kept size sum: 279317
% kept mid-nuclei: 36510
% kept new demods: 6999
% forw unit-subs: 2553944
% forw double-subs: 3364099
% forw overdouble-subs: 234569
% backward subs: 8709
% fast unit cutoff: 25017
% full unit cutoff: 0
% dbl unit cutoff: 15354
% real runtime : 305.98
% process. runtime: 304.5
% specific non-discr-tree subsumption statistics:
% tried: 43478090
% length fails: 4308429
% strength fails: 11880479
% predlist fails: 4288939
% aux str. fails: 6027909
% by-lit fails: 10615373
% full subs tried: 1378089
% full subs fail: 1286434
%
% ; 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/GRP368-1+eq_r.in")
%
%------------------------------------------------------------------------------