TSTP Solution File: GRP213-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP213-1 : 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 299.0s
% Output : Assurance 299.0s
% 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/GRP213-1+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 19)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 19)
% (binary-posweight-lex-big-order 30 #f 3 19)
% (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_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(inverse(sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% was split for some strategies as:
% -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8).
% -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(inverse(sk_c8),sk_c7).
%
% Starting a split proof attempt with 5 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(inverse(sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(29,40,0,63,0,0,42564,50,566,42598,0,566,85362,50,1198,85362,40,1198,85396,0,1198,94971,3,1499,95731,4,1649,96419,1,1799,96419,50,1799,96419,40,1799,96453,0,1799,97260,3,2116,97272,4,2269,97309,5,2400,97309,1,2400,97309,50,2400,97309,40,2400,97343,0,2400,119128,3,3901,120443,4,4651,121737,1,5401,121737,50,5401,121737,40,5401,121771,0,5401,137909,3,6152,138605,4,6527,139403,1,6902,139403,50,6902,139403,40,6902,139437,0,6902,156048,3,7659,156739,4,8028,157644,5,8403,157645,5,8403,157646,1,8403,157646,50,8403,157646,40,8403,157680,0,8403,187550,3,12308,189200,4,14254,189972,5,16204,189973,1,16204,189973,50,16205,189973,40,16205,190007,0,16205,215924,3,18759,217377,4,20031,217989,1,21306,217989,50,21306,217989,40,21306,218023,0,21306,250167,3,22809,251252,4,23557,251988,5,24307,251989,1,24307,251989,50,24308,251989,40,24308,252023,0,24308,267921,3,25094,268826,4,25434,269764,5,25809,269764,1,25809,269764,50,25809,269764,40,25809,269798,0,25809,294415,3,27011,295305,4,27610,295960,5,28210,295961,1,28210,295961,50,28211,295961,40,28211,295995,0,28211,316831,3,28962,317465,4,29337,317888,5,29712,317889,1,29712,317889,50,29713,317889,40,29713,317889,40,29713,317918,0,29713)
%
%
% START OF PROOF
% 317890 [] equal(X,X).
% 317891 [] equal(multiply(identity,X),X).
% 317892 [] equal(multiply(inverse(X),X),identity).
% 317893 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 317894 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 317895 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 317896 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c3).
% 317897 [?] ?
% 317901 [] equal(multiply(sk_c2,sk_c3),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 317902 [] equal(multiply(sk_c2,sk_c3),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 317903 [] equal(multiply(sk_c2,sk_c3),sk_c8) | equal(multiply(sk_c8,sk_c6),sk_c7).
% 317907 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 317908 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 317909 [?] ?
% 317913 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c5),sk_c8).
% 317914 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 317915 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c8,sk_c6),sk_c7).
% 317956 [hyper:317894,317896,317895,binarycut:317897] equal(inverse(sk_c2),sk_c3).
% 317975 [hyper:317894,317908,317907,binarycut:317909] equal(inverse(sk_c1),sk_c8).
% 317982 [para:317975.1.1,317892.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 317998 [hyper:317894,317903,317902,317901] equal(multiply(sk_c2,sk_c3),sk_c8).
% 318019 [hyper:317894,317915,317914,317913] equal(multiply(sk_c1,sk_c8),sk_c7).
% 318023 [para:317892.1.1,317893.1.1.1,demod:317891] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 318025 [para:317982.1.1,317893.1.1.1,demod:317891] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 318033 [para:317998.1.1,318023.1.2.2,demod:317956] equal(sk_c3,multiply(sk_c3,sk_c8)).
% 318036 [para:318033.1.2,318023.1.2.2,demod:317892] equal(sk_c8,identity).
% 318037 [para:318036.1.1,317982.1.1.1,demod:317891] equal(sk_c1,identity).
% 318040 [para:318037.1.1,317975.1.1.1] equal(inverse(identity),sk_c8).
% 318042 [para:318037.1.1,318019.1.1.1,demod:317891] equal(sk_c8,sk_c7).
% 318055 [para:318037.1.1,318025.1.2.2.1,demod:317891] equal(X,multiply(sk_c8,X)).
% 318058 [hyper:317894,318040,317890,demod:318055,317891,cut:318042] 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 19
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(inverse(sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(29,40,0,63,0,0,42564,50,566,42598,0,566,85362,50,1198,85362,40,1198,85396,0,1198,94971,3,1499,95731,4,1649,96419,1,1799,96419,50,1799,96419,40,1799,96453,0,1799,97260,3,2116,97272,4,2269,97309,5,2400,97309,1,2400,97309,50,2400,97309,40,2400,97343,0,2400,119128,3,3901,120443,4,4651,121737,1,5401,121737,50,5401,121737,40,5401,121771,0,5401,137909,3,6152,138605,4,6527,139403,1,6902,139403,50,6902,139403,40,6902,139437,0,6902,156048,3,7659,156739,4,8028,157644,5,8403,157645,5,8403,157646,1,8403,157646,50,8403,157646,40,8403,157680,0,8403,187550,3,12308,189200,4,14254,189972,5,16204,189973,1,16204,189973,50,16205,189973,40,16205,190007,0,16205,215924,3,18759,217377,4,20031,217989,1,21306,217989,50,21306,217989,40,21306,218023,0,21306,250167,3,22809,251252,4,23557,251988,5,24307,251989,1,24307,251989,50,24308,251989,40,24308,252023,0,24308,267921,3,25094,268826,4,25434,269764,5,25809,269764,1,25809,269764,50,25809,269764,40,25809,269798,0,25809,294415,3,27011,295305,4,27610,295960,5,28210,295961,1,28210,295961,50,28211,295961,40,28211,295995,0,28211,316831,3,28962,317465,4,29337,317888,5,29712,317889,1,29712,317889,50,29713,317889,40,29713,317889,40,29713,317918,0,29713,318057,50,29713,318057,30,29713,318057,40,29713,318086,0,29713)
%
%
% START OF PROOF
% 318058 [] equal(X,X).
% 318059 [] equal(multiply(identity,X),X).
% 318060 [] equal(multiply(inverse(X),X),identity).
% 318061 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 318062 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c8).
% 318066 [?] ?
% 318067 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 318072 [] equal(multiply(sk_c2,sk_c3),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 318073 [] equal(multiply(sk_c2,sk_c3),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 318078 [?] ?
% 318079 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 318084 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 318085 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 318091 [hyper:318062,318067,binarycut:318066] equal(inverse(sk_c2),sk_c3).
% 318093 [para:318091.1.1,318060.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 318105 [hyper:318062,318079,binarycut:318078] equal(inverse(sk_c1),sk_c8).
% 318108 [para:318105.1.1,318060.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 318125 [hyper:318062,318072,318073] equal(multiply(sk_c2,sk_c3),sk_c8).
% 318130 [hyper:318062,318084,318085] equal(multiply(sk_c1,sk_c8),sk_c7).
% 318131 [para:318060.1.1,318061.1.1.1,demod:318059] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 318132 [para:318093.1.1,318061.1.1.1,demod:318059] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 318139 [para:318125.1.1,318131.1.2.2,demod:318091] equal(sk_c3,multiply(sk_c3,sk_c8)).
% 318140 [para:318130.1.1,318131.1.2.2,demod:318105] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 318141 [para:318139.1.2,318061.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c3,multiply(sk_c8,X))).
% 318142 [para:318139.1.2,318131.1.2.2,demod:318060] equal(sk_c8,identity).
% 318145 [para:318142.1.1,318139.1.2.2] equal(sk_c3,multiply(sk_c3,identity)).
% 318149 [para:318132.1.2,318131.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c3),X)).
% 318166 [para:318108.1.1,318141.1.2.2,demod:318145] equal(multiply(sk_c3,sk_c1),sk_c3).
% 318167 [para:318166.1.1,318131.1.2.2,demod:318125,318149] equal(sk_c1,sk_c8).
% 318168 [para:318167.1.1,318105.1.1.1] equal(inverse(sk_c8),sk_c8).
% 318169 [hyper:318062,318168,demod:318140,cut:318058] 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 19
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(inverse(sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z).
% 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 19
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(29,40,0,63,0,0,42564,50,566,42598,0,566,85362,50,1198,85362,40,1198,85396,0,1198,94971,3,1499,95731,4,1649,96419,1,1799,96419,50,1799,96419,40,1799,96453,0,1799,97260,3,2116,97272,4,2269,97309,5,2400,97309,1,2400,97309,50,2400,97309,40,2400,97343,0,2400,119128,3,3901,120443,4,4651,121737,1,5401,121737,50,5401,121737,40,5401,121771,0,5401,137909,3,6152,138605,4,6527,139403,1,6902,139403,50,6902,139403,40,6902,139437,0,6902,156048,3,7659,156739,4,8028,157644,5,8403,157645,5,8403,157646,1,8403,157646,50,8403,157646,40,8403,157680,0,8403,187550,3,12308,189200,4,14254,189972,5,16204,189973,1,16204,189973,50,16205,189973,40,16205,190007,0,16205,215924,3,18759,217377,4,20031,217989,1,21306,217989,50,21306,217989,40,21306,218023,0,21306,250167,3,22809,251252,4,23557,251988,5,24307,251989,1,24307,251989,50,24308,251989,40,24308,252023,0,24308,267921,3,25094,268826,4,25434,269764,5,25809,269764,1,25809,269764,50,25809,269764,40,25809,269798,0,25809,294415,3,27011,295305,4,27610,295960,5,28210,295961,1,28210,295961,50,28211,295961,40,28211,295995,0,28211,316831,3,28962,317465,4,29337,317888,5,29712,317889,1,29712,317889,50,29713,317889,40,29713,317889,40,29713,317918,0,29713,318057,50,29713,318057,30,29713,318057,40,29713,318086,0,29713,318168,50,29714,318168,30,29714,318168,40,29714,318197,0,29715)
%
%
% START OF PROOF
% 318170 [] equal(multiply(identity,X),X).
% 318171 [] equal(multiply(inverse(X),X),identity).
% 318172 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 318173 [] -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y).
% 318174 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 318175 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c3).
% 318176 [] equal(multiply(sk_c8,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c3).
% 318177 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c2),sk_c3).
% 318178 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 318179 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c8),sk_c7).
% 318180 [?] ?
% 318181 [?] ?
% 318182 [?] ?
% 318183 [?] ?
% 318184 [?] ?
% 318185 [?] ?
% 318202 [hyper:318173,318174,binarycut:318180] equal(inverse(sk_c5),sk_c8).
% 318205 [para:318202.1.1,318171.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 318211 [hyper:318173,318178,binarycut:318184] equal(inverse(sk_c4),sk_c8).
% 318215 [para:318211.1.1,318171.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 318219 [hyper:318173,318179,binarycut:318185] equal(inverse(sk_c8),sk_c7).
% 318224 [hyper:318173,318175,binarycut:318181] equal(multiply(sk_c5,sk_c8),sk_c6).
% 318226 [para:318219.1.1,318171.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 318230 [hyper:318173,318176,binarycut:318182] equal(multiply(sk_c8,sk_c6),sk_c7).
% 318234 [hyper:318173,318177,binarycut:318183] equal(multiply(sk_c4,sk_c7),sk_c8).
% 318238 [para:318171.1.1,318172.1.1.1,demod:318170] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 318239 [para:318205.1.1,318172.1.1.1,demod:318170] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 318241 [para:318224.1.1,318172.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c5,multiply(sk_c8,X))).
% 318243 [para:318230.1.1,318172.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c6,X))).
% 318244 [para:318234.1.1,318172.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c4,multiply(sk_c7,X))).
% 318247 [para:318224.1.1,318239.1.2.2,demod:318230] equal(sk_c8,sk_c7).
% 318251 [para:318205.1.1,318238.1.2.2,demod:318219] equal(sk_c5,multiply(sk_c7,identity)).
% 318252 [para:318215.1.1,318238.1.2.2,demod:318251,318219] equal(sk_c4,sk_c5).
% 318256 [para:318239.1.2,318238.1.2.2,demod:318219] equal(multiply(sk_c5,X),multiply(sk_c7,X)).
% 318262 [para:318247.1.1,318239.1.2.1,demod:318256] equal(X,multiply(sk_c7,multiply(sk_c7,X))).
% 318274 [para:318241.1.2,318239.1.2.2,demod:318243] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 318276 [para:318247.1.1,318241.1.2.2.1,demod:318262,318256] equal(multiply(sk_c6,X),X).
% 318277 [para:318252.1.2,318241.1.2.1,demod:318244,318274,318276] equal(X,multiply(sk_c7,X)).
% 318283 [para:318277.1.2,318226.1.1] equal(sk_c8,identity).
% 318284 [para:318277.1.2,318251.1.2] equal(sk_c5,identity).
% 318287 [para:318283.1.1,318219.1.1.1] equal(inverse(identity),sk_c7).
% 318292 [para:318284.1.1,318202.1.1.1,demod:318287] equal(sk_c7,sk_c8).
% 318310 [hyper:318173,318287,demod:318170,cut:318292] 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 19
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(inverse(sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 6
%
%
% 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 19
% clause depth limited to 4
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(29,40,0,63,0,0,42564,50,566,42598,0,566,85362,50,1198,85362,40,1198,85396,0,1198,94971,3,1499,95731,4,1649,96419,1,1799,96419,50,1799,96419,40,1799,96453,0,1799,97260,3,2116,97272,4,2269,97309,5,2400,97309,1,2400,97309,50,2400,97309,40,2400,97343,0,2400,119128,3,3901,120443,4,4651,121737,1,5401,121737,50,5401,121737,40,5401,121771,0,5401,137909,3,6152,138605,4,6527,139403,1,6902,139403,50,6902,139403,40,6902,139437,0,6902,156048,3,7659,156739,4,8028,157644,5,8403,157645,5,8403,157646,1,8403,157646,50,8403,157646,40,8403,157680,0,8403,187550,3,12308,189200,4,14254,189972,5,16204,189973,1,16204,189973,50,16205,189973,40,16205,190007,0,16205,215924,3,18759,217377,4,20031,217989,1,21306,217989,50,21306,217989,40,21306,218023,0,21306,250167,3,22809,251252,4,23557,251988,5,24307,251989,1,24307,251989,50,24308,251989,40,24308,252023,0,24308,267921,3,25094,268826,4,25434,269764,5,25809,269764,1,25809,269764,50,25809,269764,40,25809,269798,0,25809,294415,3,27011,295305,4,27610,295960,5,28210,295961,1,28210,295961,50,28211,295961,40,28211,295995,0,28211,316831,3,28962,317465,4,29337,317888,5,29712,317889,1,29712,317889,50,29713,317889,40,29713,317889,40,29713,317918,0,29713,318057,50,29713,318057,30,29713,318057,40,29713,318086,0,29713,318168,50,29714,318168,30,29714,318168,40,29714,318197,0,29715,318309,50,29716,318309,30,29716,318309,40,29716,318338,0,29716,318431,50,29716,318460,0,29716)
%
%
% START OF PROOF
% 318433 [] equal(multiply(identity,X),X).
% 318434 [] equal(multiply(inverse(X),X),identity).
% 318435 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 318436 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 318449 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 318450 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 318451 [] equal(multiply(sk_c8,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 318452 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 318453 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 318454 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c8),sk_c7).
% 318455 [?] ?
% 318456 [?] ?
% 318457 [?] ?
% 318458 [?] ?
% 318459 [?] ?
% 318460 [?] ?
% 318469 [hyper:318436,318449,binarycut:318455] equal(inverse(sk_c5),sk_c8).
% 318473 [para:318469.1.1,318434.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 318477 [hyper:318436,318453,binarycut:318459] equal(inverse(sk_c4),sk_c8).
% 318482 [para:318477.1.1,318434.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 318486 [hyper:318436,318454,binarycut:318460] equal(inverse(sk_c8),sk_c7).
% 318487 [para:318486.1.1,318434.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 318492 [hyper:318436,318450,binarycut:318456] equal(multiply(sk_c5,sk_c8),sk_c6).
% 318496 [hyper:318436,318451,binarycut:318457] equal(multiply(sk_c8,sk_c6),sk_c7).
% 318499 [hyper:318436,318452,binarycut:318458] equal(multiply(sk_c4,sk_c7),sk_c8).
% 318500 [para:318434.1.1,318435.1.1.1,demod:318433] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 318501 [para:318473.1.1,318435.1.1.1,demod:318433] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 318502 [para:318482.1.1,318435.1.1.1,demod:318433] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 318503 [para:318487.1.1,318435.1.1.1,demod:318433] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 318507 [para:318492.1.1,318501.1.2.2,demod:318496] equal(sk_c8,sk_c7).
% 318509 [para:318434.1.1,318500.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 318510 [para:318473.1.1,318500.1.2.2,demod:318486] equal(sk_c5,multiply(sk_c7,identity)).
% 318511 [para:318482.1.1,318500.1.2.2,demod:318510,318486] equal(sk_c4,sk_c5).
% 318513 [para:318496.1.1,318500.1.2.2,demod:318486] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 318514 [para:318499.1.1,318500.1.2.2,demod:318477] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 318515 [para:318435.1.1,318500.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 318516 [para:318501.1.2,318500.1.2.2,demod:318486] equal(multiply(sk_c5,X),multiply(sk_c7,X)).
% 318517 [para:318500.1.2,318500.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 318520 [para:318507.1.1,318486.1.1.1] equal(inverse(sk_c7),sk_c7).
% 318523 [para:318507.1.1,318501.1.2.1,demod:318516] equal(X,multiply(sk_c7,multiply(sk_c7,X))).
% 318524 [para:318502.1.2,318500.1.2.2,demod:318486] equal(multiply(sk_c4,X),multiply(sk_c7,X)).
% 318526 [para:318511.1.2,318501.1.2.2.1,demod:318524] equal(X,multiply(sk_c8,multiply(sk_c7,X))).
% 318528 [para:318503.1.2,318500.1.2.2,demod:318520] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 318529 [para:318513.1.2,318435.1.1.1,demod:318523] equal(multiply(sk_c6,X),X).
% 318531 [para:318514.1.2,318435.1.1.1,demod:318526,318528] equal(multiply(sk_c7,X),X).
% 318532 [para:318514.1.2,318500.1.2.2,demod:318513,318486] equal(sk_c8,sk_c6).
% 318539 [para:318532.1.1,318514.1.2.1,demod:318529] equal(sk_c7,sk_c8).
% 318571 [para:318517.1.2,318434.1.1] equal(multiply(X,inverse(X)),identity).
% 318573 [para:318517.1.2,318509.1.2] equal(X,multiply(X,identity)).
% 318574 [para:318573.1.2,318509.1.2] equal(X,inverse(inverse(X))).
% 318575 [para:318571.1.1,318515.1.2.2.2,demod:318573] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 318577 [para:318501.1.2,318575.1.2.1.1,demod:318531,318516] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 318585 [para:318577.1.2,318517.1.2,demod:318574] equal(multiply(X,sk_c8),X).
% 318586 [hyper:318436,318585,demod:318520,cut:318539] 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 19
% clause depth limited to 4
% seconds given: 6
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,Z),sk_c8) | -equal(inverse(Y),Z) | -equal(inverse(sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(inverse(sk_c8),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 3
% seconds given: 6
%
%
% 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 19
% clause depth limited to 4
% seconds given: 6
%
%
% 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 19
% clause depth limited to 5
% seconds given: 6
%
%
% 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 19
% clause depth limited to 6
% seconds given: 6
%
%
% 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 19
% clause depth limited to 7
% seconds given: 6
%
%
% 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 19
% clause depth limited to 8
% seconds given: 6
%
%
% 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 19
% clause depth limited to 9
% seconds given: 6
%
%
% 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 19
% clause depth limited to 10
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(29,40,0,63,0,0,42564,50,566,42598,0,566,85362,50,1198,85362,40,1198,85396,0,1198,94971,3,1499,95731,4,1649,96419,1,1799,96419,50,1799,96419,40,1799,96453,0,1799,97260,3,2116,97272,4,2269,97309,5,2400,97309,1,2400,97309,50,2400,97309,40,2400,97343,0,2400,119128,3,3901,120443,4,4651,121737,1,5401,121737,50,5401,121737,40,5401,121771,0,5401,137909,3,6152,138605,4,6527,139403,1,6902,139403,50,6902,139403,40,6902,139437,0,6902,156048,3,7659,156739,4,8028,157644,5,8403,157645,5,8403,157646,1,8403,157646,50,8403,157646,40,8403,157680,0,8403,187550,3,12308,189200,4,14254,189972,5,16204,189973,1,16204,189973,50,16205,189973,40,16205,190007,0,16205,215924,3,18759,217377,4,20031,217989,1,21306,217989,50,21306,217989,40,21306,218023,0,21306,250167,3,22809,251252,4,23557,251988,5,24307,251989,1,24307,251989,50,24308,251989,40,24308,252023,0,24308,267921,3,25094,268826,4,25434,269764,5,25809,269764,1,25809,269764,50,25809,269764,40,25809,269798,0,25809,294415,3,27011,295305,4,27610,295960,5,28210,295961,1,28210,295961,50,28211,295961,40,28211,295995,0,28211,316831,3,28962,317465,4,29337,317888,5,29712,317889,1,29712,317889,50,29713,317889,40,29713,317889,40,29713,317918,0,29713,318057,50,29713,318057,30,29713,318057,40,29713,318086,0,29713,318168,50,29714,318168,30,29714,318168,40,29714,318197,0,29715,318309,50,29716,318309,30,29716,318309,40,29716,318338,0,29716,318431,50,29716,318460,0,29716,318585,50,29717,318585,30,29717,318585,40,29717,318614,0,29719,318692,50,29719,318721,0,29719,318845,50,29722,318874,0,29724,319012,50,29729,319041,0,29729,319199,50,29740,319228,0,29740,319408,50,29762,319437,0,29762,319653,50,29811,319682,0,29811,319942,50,29943,319971,0,29943,320292,4,30171)
%
%
% START OF PROOF
% 319944 [] equal(multiply(identity,X),X).
% 319945 [] equal(multiply(inverse(X),X),identity).
% 319946 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 319947 [] -equal(inverse(sk_c8),sk_c7).
% 319953 [?] ?
% 319959 [?] ?
% 319965 [?] ?
% 319971 [?] ?
% 319975 [input:319953,cut:319947] equal(inverse(sk_c2),sk_c3).
% 319976 [para:319975.1.1,319945.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 319980 [input:319965,cut:319947] equal(inverse(sk_c1),sk_c8).
% 319981 [para:319980.1.1,319945.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 319986 [input:319959,cut:319947] equal(multiply(sk_c2,sk_c3),sk_c8).
% 319993 [input:319971,cut:319947] equal(multiply(sk_c1,sk_c8),sk_c7).
% 319998 [para:319945.1.1,319946.1.1.1,demod:319944] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 319999 [para:319976.1.1,319946.1.1.1,demod:319944] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 320000 [para:319981.1.1,319946.1.1.1,demod:319944] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 320001 [para:319986.1.1,319946.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c2,multiply(sk_c3,X))).
% 320002 [para:319993.1.1,319946.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c1,multiply(sk_c8,X))).
% 320003 [para:319986.1.1,319999.1.2.2] equal(sk_c3,multiply(sk_c3,sk_c8)).
% 320005 [para:319993.1.1,320000.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 320008 [para:319945.1.1,319998.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 320013 [para:319946.1.1,319998.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 320014 [para:319999.1.2,319998.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c3),X)).
% 320015 [para:320003.1.2,319998.1.2.2,demod:320014] equal(sk_c8,multiply(sk_c2,sk_c3)).
% 320016 [para:320000.1.2,319998.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c8),X)).
% 320017 [para:320005.1.2,319998.1.2.2,demod:320016] equal(sk_c7,multiply(sk_c1,sk_c8)).
% 320018 [para:319998.1.2,319998.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 320021 [para:320003.1.2,320001.1.2.2,demod:320015] equal(multiply(sk_c8,sk_c8),sk_c8).
% 320024 [para:320021.1.1,319998.1.2.2,demod:320017,320016] equal(sk_c8,sk_c7).
% 320026 [para:320000.1.2,320002.1.2.2] equal(multiply(sk_c7,multiply(sk_c1,X)),multiply(sk_c1,X)).
% 320027 [para:320005.1.2,320002.1.2.2,demod:320017] equal(multiply(sk_c7,sk_c7),sk_c7).
% 320029 [para:320021.1.1,320002.1.2.2,demod:320017] equal(multiply(sk_c7,sk_c8),sk_c7).
% 320033 [para:320024.1.1,320000.1.2.1,demod:320026] equal(X,multiply(sk_c1,X)).
% 320034 [para:320024.1.1,320021.1.1.1,demod:320029] equal(sk_c7,sk_c8).
% 320035 [para:320034.1.2,320000.1.2.1,demod:320033] equal(X,multiply(sk_c7,X)).
% 320036 [para:320033.1.2,320000.1.2.2] equal(X,multiply(sk_c8,X)).
% 320038 [para:320035.1.2,319998.1.2.2] equal(X,multiply(inverse(sk_c7),X)).
% 320042 [para:320038.1.2,319945.1.1] equal(sk_c7,identity).
% 320044 [para:320042.1.1,320027.1.1.2,demod:320035] equal(identity,sk_c7).
% 320068 [para:320018.1.2,319945.1.1] equal(multiply(X,inverse(X)),identity).
% 320070 [para:320018.1.2,320008.1.2] equal(X,multiply(X,identity)).
% 320072 [para:320070.1.2,320008.1.2] equal(X,inverse(inverse(X))).
% 320077 [para:320068.1.1,320013.1.2.2.2,demod:320070] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 320087 [para:320077.1.2,320077.1.2.1.1,demod:320072] equal(inverse(X),multiply(Y,inverse(multiply(X,Y)))).
% 320095 [para:320087.1.2,319946.1.1] equal(inverse(X),multiply(Y,multiply(Z,inverse(multiply(X,multiply(Y,Z)))))).
% 320097 [para:319946.1.1,320087.1.2.2.1] equal(inverse(multiply(X,Y)),multiply(Z,inverse(multiply(X,multiply(Y,Z))))).
% 320110 [para:320095.1.2,319946.1.1,demod:319946] equal(inverse(X),multiply(Y,multiply(Z,multiply(U,inverse(multiply(X,multiply(Y,multiply(Z,U)))))))).
% 320114 [para:319946.1.1,320097.1.2.2.1,demod:319946] equal(inverse(multiply(X,multiply(Y,Z))),multiply(U,inverse(multiply(X,multiply(Y,multiply(Z,U)))))).
% 320139 [para:320110.1.2,319946.1.1,demod:319946] equal(inverse(X),multiply(Y,multiply(Z,multiply(U,multiply(V,inverse(multiply(X,multiply(Y,multiply(Z,multiply(U,V)))))))))).
% 320293 [para:320139.1.1,319947.1.1,demod:320068,320087,320097,320114,320036,cut:320044] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 10
% seconds given: 6
%
%
% Split attempt finished with SUCCESS.
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 31549
% derived clauses: 7177841
% kept clauses: 199784
% kept size sum: 19404
% kept mid-nuclei: 84342
% kept new demods: 2286
% forw unit-subs: 3376517
% forw double-subs: 2963928
% forw overdouble-subs: 294508
% backward subs: 19367
% fast unit cutoff: 30927
% full unit cutoff: 0
% dbl unit cutoff: 2832
% real runtime : 303.23
% process. runtime: 301.72
% specific non-discr-tree subsumption statistics:
% tried: 20483613
% length fails: 2159527
% strength fails: 7302685
% predlist fails: 654212
% aux str. fails: 2813225
% by-lit fails: 2399097
% full subs tried: 2961632
% full subs fail: 2808913
%
% ; 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/GRP213-1+eq_r.in")
%
%------------------------------------------------------------------------------