TSTP Solution File: GRP384-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP384-1 : 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 309.0s
% Output : Assurance 309.0s
% 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/GRP384-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 31)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 31)
% (binary-posweight-lex-big-order 30 #f 3 31)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),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(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),sk_c10).
% -equal(inverse(sk_c11),sk_c10).
% -equal(multiply(sk_c10,sk_c9),sk_c11).
% -equal(multiply(sk_c11,sk_c9),sk_c10).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),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(65,40,0,138,0,0,78682,4,1221,82987,5,1501,82987,1,1501,82987,50,1501,82987,40,1501,83060,0,1501,91513,3,1818,92335,4,1952,93125,5,2102,93126,1,2102,93126,50,2102,93126,40,2102,93199,0,2102,94768,3,2414,94783,4,2557,94868,5,2703,94868,1,2703,94868,50,2703,94868,40,2703,94941,0,2703,118397,3,4205,119454,4,4954,120410,1,5704,120410,50,5704,120410,40,5704,120483,0,5705,135884,3,6457,136714,4,6831,137195,5,7206,137196,1,7206,137196,50,7206,137196,40,7206,137269,0,7206,148630,3,7982,150377,4,8332,151837,1,8707,151837,50,8707,151837,40,8707,151910,0,8707,203868,3,12609,205162,4,14559,206531,5,16508,206532,1,16508,206532,50,16510,206532,40,16510,206605,0,16510,250590,3,19063,251565,4,20336,252633,1,21611,252633,50,21612,252633,40,21612,252706,0,21612,292119,3,23120,292853,4,23863,293541,1,24613,293541,50,24615,293541,40,24615,293614,0,24615,304780,3,25383,306785,4,25749,308106,5,26116,308106,1,26116,308106,50,26116,308106,40,26116,308179,0,26116,334239,3,27317,334867,4,27917,335380,5,28517,335381,1,28517,335381,50,28518,335381,40,28518,335454,0,28518,354963,3,29269,355425,4,29644,355779,5,30019,355780,1,30019,355780,50,30019,355780,40,30019,355780,40,30019,355909,0,30019)
%
%
% START OF PROOF
% 355781 [] equal(X,X).
% 355782 [] equal(multiply(identity,X),X).
% 355783 [] equal(multiply(inverse(X),X),identity).
% 355784 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 355845 [] -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).
% 355846 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst85,Y).
% 355847 [] -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | $spltprd1($spltcnst86,Y).
% 355848 [] -equal(multiply(X,sk_c10),sk_c11) | $spltprd1($spltcnst87,X).
% 355849 [] -$spltprd1($spltcnst86,X) | -$spltprd1($spltcnst85,X) | -$spltprd1($spltcnst87,X).
% 355860 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c2).
% 355861 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c6),sk_c8).
% 355862 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c7),sk_c6).
% 355863 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c2).
% 355864 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 355865 [?] ?
% 355870 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 355871 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 355872 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 355873 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 355874 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 355875 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 355880 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 355881 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 355882 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 355883 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 355884 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 355885 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 355890 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 355891 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 355892 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 355893 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 355894 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 355895 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 355900 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c11),sk_c10).
% 355901 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 355902 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 355903 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c11),sk_c10).
% 355904 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 355905 [?] ?
% 355976 [hyper:355847,355864,binarycut:355865] equal(inverse(sk_c1),sk_c2) | $spltprd1($spltcnst86,sk_c8).
% 356064 [hyper:355847,355904,binarycut:355905] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst86,sk_c8).
% 356186 [hyper:355846,355860,355861,355862] equal(inverse(sk_c1),sk_c2) | $spltprd1($spltcnst85,sk_c8).
% 356215 [hyper:355848,355863] equal(inverse(sk_c1),sk_c2) | $spltprd1($spltcnst87,sk_c8).
% 356226 [hyper:355849,356215,356186,355976] equal(inverse(sk_c1),sk_c2).
% 356233 [para:356226.1.1,355783.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 356472 [hyper:355846,355900,355901,355902] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst85,sk_c8).
% 356515 [hyper:355848,355903] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst87,sk_c8).
% 356532 [hyper:355849,356515,356472,356064] equal(inverse(sk_c11),sk_c10).
% 356545 [para:356532.1.1,355783.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 356907 [hyper:355845,355875,355873,355874,355871,355870,355872] equal(multiply(sk_c1,sk_c2),sk_c10).
% 357008 [hyper:355845,355885,355883,355884,355881,355880,355882] equal(multiply(sk_c11,sk_c9),sk_c10).
% 357099 [hyper:355845,355895,355893,355894,355891,355890,355892] equal(multiply(sk_c10,sk_c9),sk_c11).
% 357106 [para:355783.1.1,355784.1.1.1,demod:355782] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 357107 [para:356233.1.1,355784.1.1.1,demod:355782] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 357108 [para:356545.1.1,355784.1.1.1,demod:355782] equal(X,multiply(sk_c10,multiply(sk_c11,X))).
% 357155 [para:357008.1.1,357108.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 357178 [para:357107.1.2,357106.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 357200 [para:357178.1.2,355783.1.1,demod:356907] equal(sk_c10,identity).
% 357206 [para:357200.1.1,356545.1.1.1,demod:355782] equal(sk_c11,identity).
% 357207 [para:357200.1.1,357099.1.1.1,demod:355782] equal(sk_c9,sk_c11).
% 357210 [para:357200.1.1,357155.1.2.1,demod:355782] equal(sk_c9,sk_c10).
% 357213 [para:357206.1.1,356532.1.1.1] equal(inverse(identity),sk_c10).
% 357215 [para:357207.1.2,357008.1.1.1] equal(multiply(sk_c9,sk_c9),sk_c10).
% 357217 [para:357210.1.2,357099.1.1.1,demod:357215] equal(sk_c10,sk_c11).
% 357225 [para:357217.1.2,356532.1.1.1] equal(inverse(sk_c10),sk_c10).
% 357249 [hyper:355845,357213,355782,demod:357155,355782,cut:357217,cut:357207,demod:357213,357225,cut:355781,cut:355781] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,138,0,0,78682,4,1221,82987,5,1501,82987,1,1501,82987,50,1501,82987,40,1501,83060,0,1501,91513,3,1818,92335,4,1952,93125,5,2102,93126,1,2102,93126,50,2102,93126,40,2102,93199,0,2102,94768,3,2414,94783,4,2557,94868,5,2703,94868,1,2703,94868,50,2703,94868,40,2703,94941,0,2703,118397,3,4205,119454,4,4954,120410,1,5704,120410,50,5704,120410,40,5704,120483,0,5705,135884,3,6457,136714,4,6831,137195,5,7206,137196,1,7206,137196,50,7206,137196,40,7206,137269,0,7206,148630,3,7982,150377,4,8332,151837,1,8707,151837,50,8707,151837,40,8707,151910,0,8707,203868,3,12609,205162,4,14559,206531,5,16508,206532,1,16508,206532,50,16510,206532,40,16510,206605,0,16510,250590,3,19063,251565,4,20336,252633,1,21611,252633,50,21612,252633,40,21612,252706,0,21612,292119,3,23120,292853,4,23863,293541,1,24613,293541,50,24615,293541,40,24615,293614,0,24615,304780,3,25383,306785,4,25749,308106,5,26116,308106,1,26116,308106,50,26116,308106,40,26116,308179,0,26116,334239,3,27317,334867,4,27917,335380,5,28517,335381,1,28517,335381,50,28518,335381,40,28518,335454,0,28518,354963,3,29269,355425,4,29644,355779,5,30019,355780,1,30019,355780,50,30019,355780,40,30019,355780,40,30019,355909,0,30019,357248,50,30025,357248,30,30025,357248,40,30025,357313,0,30025)
%
%
% START OF PROOF
% 357249 [] equal(X,X).
% 357250 [] equal(multiply(identity,X),X).
% 357251 [] equal(multiply(inverse(X),X),identity).
% 357252 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 357253 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 357270 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c4),sk_c10).
% 357271 [?] ?
% 357280 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 357281 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 357290 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 357291 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 357300 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 357301 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 357310 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 357311 [?] ?
% 357320 [hyper:357253,357270,binarycut:357271] equal(inverse(sk_c1),sk_c2).
% 357321 [para:357320.1.1,357251.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 357335 [hyper:357253,357310,binarycut:357311] equal(inverse(sk_c11),sk_c10).
% 357338 [para:357335.1.1,357251.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 357378 [hyper:357253,357281,357280] equal(multiply(sk_c1,sk_c2),sk_c10).
% 357384 [hyper:357253,357291,357290] equal(multiply(sk_c11,sk_c9),sk_c10).
% 357390 [hyper:357253,357301,357300] equal(multiply(sk_c10,sk_c9),sk_c11).
% 357392 [para:357321.1.1,357252.1.1.1,demod:357250] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 357393 [para:357338.1.1,357252.1.1.1,demod:357250] equal(X,multiply(sk_c10,multiply(sk_c11,X))).
% 357395 [para:357378.1.1,357252.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c1,multiply(sk_c2,X))).
% 357398 [para:357378.1.1,357392.1.2.2] equal(sk_c2,multiply(sk_c2,sk_c10)).
% 357400 [para:357384.1.1,357393.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 357413 [para:357398.1.2,357395.1.2.2,demod:357378,357400] equal(sk_c9,sk_c10).
% 357419 [para:357413.1.2,357400.1.2.1] equal(sk_c9,multiply(sk_c9,sk_c10)).
% 357420 [para:357413.1.2,357400.1.2.2,demod:357390] equal(sk_c9,sk_c11).
% 357430 [para:357420.1.2,357335.1.1.1] equal(inverse(sk_c9),sk_c10).
% 357458 [hyper:357253,357430,demod:357419,cut:357249] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),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 31
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,138,0,0,78682,4,1221,82987,5,1501,82987,1,1501,82987,50,1501,82987,40,1501,83060,0,1501,91513,3,1818,92335,4,1952,93125,5,2102,93126,1,2102,93126,50,2102,93126,40,2102,93199,0,2102,94768,3,2414,94783,4,2557,94868,5,2703,94868,1,2703,94868,50,2703,94868,40,2703,94941,0,2703,118397,3,4205,119454,4,4954,120410,1,5704,120410,50,5704,120410,40,5704,120483,0,5705,135884,3,6457,136714,4,6831,137195,5,7206,137196,1,7206,137196,50,7206,137196,40,7206,137269,0,7206,148630,3,7982,150377,4,8332,151837,1,8707,151837,50,8707,151837,40,8707,151910,0,8707,203868,3,12609,205162,4,14559,206531,5,16508,206532,1,16508,206532,50,16510,206532,40,16510,206605,0,16510,250590,3,19063,251565,4,20336,252633,1,21611,252633,50,21612,252633,40,21612,252706,0,21612,292119,3,23120,292853,4,23863,293541,1,24613,293541,50,24615,293541,40,24615,293614,0,24615,304780,3,25383,306785,4,25749,308106,5,26116,308106,1,26116,308106,50,26116,308106,40,26116,308179,0,26116,334239,3,27317,334867,4,27917,335380,5,28517,335381,1,28517,335381,50,28518,335381,40,28518,335454,0,28518,354963,3,29269,355425,4,29644,355779,5,30019,355780,1,30019,355780,50,30019,355780,40,30019,355780,40,30019,355909,0,30019,357248,50,30025,357248,30,30025,357248,40,30025,357313,0,30025,357457,50,30025,357457,30,30025,357457,40,30025,357522,0,30031,357663,50,30032,357728,0,30032)
%
%
% START OF PROOF
% 357665 [] equal(multiply(identity,X),X).
% 357666 [] equal(multiply(inverse(X),X),identity).
% 357667 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 357668 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 357677 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 357678 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 357687 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c3),sk_c11).
% 357688 [?] ?
% 357697 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 357698 [] equal(multiply(sk_c1,sk_c2),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 357707 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 357708 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 357717 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 357718 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 357727 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 357728 [?] ?
% 357736 [hyper:357668,357687,binarycut:357688] equal(inverse(sk_c1),sk_c2).
% 357737 [para:357736.1.1,357666.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 357745 [hyper:357668,357727,binarycut:357728] equal(inverse(sk_c11),sk_c10).
% 357747 [para:357745.1.1,357666.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 357775 [hyper:357668,357678,357677] equal(multiply(sk_c2,sk_c9),sk_c10).
% 357787 [hyper:357668,357698,357697] equal(multiply(sk_c1,sk_c2),sk_c10).
% 357794 [hyper:357668,357708,357707] equal(multiply(sk_c11,sk_c9),sk_c10).
% 357801 [hyper:357668,357718,357717] equal(multiply(sk_c10,sk_c9),sk_c11).
% 357802 [para:357666.1.1,357667.1.1.1,demod:357665] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 357803 [para:357737.1.1,357667.1.1.1,demod:357665] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 357804 [para:357747.1.1,357667.1.1.1,demod:357665] equal(X,multiply(sk_c10,multiply(sk_c11,X))).
% 357805 [para:357775.1.1,357667.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c2,multiply(sk_c9,X))).
% 357806 [para:357787.1.1,357667.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c1,multiply(sk_c2,X))).
% 357807 [para:357794.1.1,357667.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c11,multiply(sk_c9,X))).
% 357808 [para:357801.1.1,357667.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c10,multiply(sk_c9,X))).
% 357809 [para:357787.1.1,357803.1.2.2] equal(sk_c2,multiply(sk_c2,sk_c10)).
% 357811 [para:357794.1.1,357804.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 357814 [para:357666.1.1,357802.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 357818 [para:357667.1.1,357802.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 357820 [para:357803.1.2,357802.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 357822 [para:357802.1.2,357802.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 357823 [para:357805.1.2,357802.1.2.2,demod:357820] equal(multiply(sk_c9,X),multiply(sk_c1,multiply(sk_c10,X))).
% 357827 [para:357809.1.2,357806.1.2.2,demod:357787,357811] equal(sk_c9,sk_c10).
% 357828 [para:357805.1.2,357806.1.2.2,demod:357823,357808] equal(multiply(sk_c11,X),multiply(sk_c9,X)).
% 357831 [para:357827.1.2,357809.1.2.2,demod:357775] equal(sk_c2,sk_c10).
% 357834 [para:357827.1.2,357811.1.2.2,demod:357801] equal(sk_c9,sk_c11).
% 357838 [para:357831.1.2,357801.1.1.1,demod:357775] equal(sk_c10,sk_c11).
% 357840 [para:357831.1.2,357804.1.2.1,demod:357805,357828] equal(X,multiply(sk_c10,X)).
% 357847 [para:357834.1.2,357804.1.2.2.1,demod:357828,357808] equal(X,multiply(sk_c9,X)).
% 357848 [para:357838.1.2,357745.1.1.1] equal(inverse(sk_c10),sk_c10).
% 357886 [para:357822.1.2,357666.1.1] equal(multiply(X,inverse(X)),identity).
% 357888 [para:357822.1.2,357814.1.2] equal(X,multiply(X,identity)).
% 357889 [para:357888.1.2,357814.1.2] equal(X,inverse(inverse(X))).
% 357890 [para:357886.1.1,357818.1.2.2.2,demod:357888] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 357896 [para:357807.1.2,357890.1.2.1.1,demod:357840,357847] equal(inverse(X),multiply(inverse(X),sk_c11)).
% 357905 [para:357896.1.2,357822.1.2,demod:357889] equal(multiply(X,sk_c11),X).
% 357906 [hyper:357668,357905,demod:357848,cut:357838] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),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,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),sk_c10).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,138,0,0,78682,4,1221,82987,5,1501,82987,1,1501,82987,50,1501,82987,40,1501,83060,0,1501,91513,3,1818,92335,4,1952,93125,5,2102,93126,1,2102,93126,50,2102,93126,40,2102,93199,0,2102,94768,3,2414,94783,4,2557,94868,5,2703,94868,1,2703,94868,50,2703,94868,40,2703,94941,0,2703,118397,3,4205,119454,4,4954,120410,1,5704,120410,50,5704,120410,40,5704,120483,0,5705,135884,3,6457,136714,4,6831,137195,5,7206,137196,1,7206,137196,50,7206,137196,40,7206,137269,0,7206,148630,3,7982,150377,4,8332,151837,1,8707,151837,50,8707,151837,40,8707,151910,0,8707,203868,3,12609,205162,4,14559,206531,5,16508,206532,1,16508,206532,50,16510,206532,40,16510,206605,0,16510,250590,3,19063,251565,4,20336,252633,1,21611,252633,50,21612,252633,40,21612,252706,0,21612,292119,3,23120,292853,4,23863,293541,1,24613,293541,50,24615,293541,40,24615,293614,0,24615,304780,3,25383,306785,4,25749,308106,5,26116,308106,1,26116,308106,50,26116,308106,40,26116,308179,0,26116,334239,3,27317,334867,4,27917,335380,5,28517,335381,1,28517,335381,50,28518,335381,40,28518,335454,0,28518,354963,3,29269,355425,4,29644,355779,5,30019,355780,1,30019,355780,50,30019,355780,40,30019,355780,40,30019,355909,0,30019,357248,50,30025,357248,30,30025,357248,40,30025,357313,0,30025,357457,50,30025,357457,30,30025,357457,40,30025,357522,0,30031,357663,50,30032,357728,0,30032,357905,50,30033,357905,30,30033,357905,40,30033,357970,0,30038)
%
%
% START OF PROOF
% 357906 [] equal(X,X).
% 357907 [] equal(multiply(identity,X),X).
% 357908 [] equal(multiply(inverse(X),X),identity).
% 357909 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 357910 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,X),sk_c10) | -equal(inverse(Y),X).
% 357912 [?] ?
% 357913 [?] ?
% 357915 [?] ?
% 357916 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 357917 [?] ?
% 357918 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 357919 [?] ?
% 357920 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 357922 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c6),sk_c8).
% 357923 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c7),sk_c6).
% 357925 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 357926 [] equal(multiply(sk_c5,sk_c8),sk_c11) | equal(inverse(sk_c1),sk_c2).
% 357927 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c4),sk_c10).
% 357928 [] equal(multiply(sk_c4,sk_c10),sk_c9) | equal(inverse(sk_c1),sk_c2).
% 357929 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c3),sk_c11).
% 357930 [] equal(multiply(sk_c3,sk_c11),sk_c10) | equal(inverse(sk_c1),sk_c2).
% 357932 [?] ?
% 357933 [?] ?
% 357935 [?] ?
% 357936 [?] ?
% 357937 [?] ?
% 357938 [?] ?
% 357939 [?] ?
% 357940 [?] ?
% 357975 [hyper:357910,357922,binarycut:357932,binarycut:357912] equal(inverse(sk_c6),sk_c8).
% 357978 [para:357975.1.1,357908.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 357982 [hyper:357910,357923,binarycut:357933,binarycut:357913] equal(inverse(sk_c7),sk_c6).
% 357986 [para:357982.1.1,357908.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 357990 [hyper:357910,357925,binarycut:357935,binarycut:357915] equal(inverse(sk_c5),sk_c8).
% 357999 [para:357990.1.1,357908.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 358003 [hyper:357910,357927,binarycut:357937,binarycut:357917] equal(inverse(sk_c4),sk_c10).
% 358012 [para:358003.1.1,357908.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 358016 [hyper:357910,357929,binarycut:357939,binarycut:357919] equal(inverse(sk_c3),sk_c11).
% 358022 [para:358016.1.1,357908.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 358042 [hyper:357910,357926,binarycut:357936,binarycut:357916] equal(multiply(sk_c5,sk_c8),sk_c11).
% 358045 [hyper:357910,357928,binarycut:357938,binarycut:357918] equal(multiply(sk_c4,sk_c10),sk_c9).
% 358056 [hyper:357910,357930,binarycut:357940,binarycut:357920] equal(multiply(sk_c3,sk_c11),sk_c10).
% 358060 [para:357908.1.1,357909.1.1.1,demod:357907] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 358061 [para:357978.1.1,357909.1.1.1,demod:357907] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 358062 [para:357986.1.1,357909.1.1.1,demod:357907] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 358064 [para:358012.1.1,357909.1.1.1,demod:357907] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 358068 [para:358042.1.1,357909.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 358073 [para:357986.1.1,358061.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 358074 [para:358073.1.2,357909.1.1.1,demod:357907] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 358079 [para:357978.1.1,358060.1.2.2] equal(sk_c6,multiply(inverse(sk_c8),identity)).
% 358081 [para:357999.1.1,358060.1.2.2,demod:358079] equal(sk_c5,sk_c6).
% 358086 [para:358045.1.1,358060.1.2.2,demod:358003] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 358090 [para:358081.1.2,358062.1.2.1,demod:358068,358074] equal(X,multiply(sk_c11,X)).
% 358093 [para:358090.1.2,358022.1.1] equal(sk_c3,identity).
% 358096 [para:358093.1.1,358056.1.1.1,demod:357907] equal(sk_c11,sk_c10).
% 358099 [para:358096.1.1,358090.1.2.1] equal(X,multiply(sk_c10,X)).
% 358108 [para:358099.1.2,358060.1.2.2] equal(X,multiply(inverse(sk_c10),X)).
% 358123 [para:358064.1.2,358060.1.2.2,demod:358108] equal(multiply(sk_c4,X),X).
% 358124 [hyper:357910,358123,demod:358003,358086,cut:357906,cut:357906] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),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(inverse(sk_c11),sk_c10).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,138,0,0,78682,4,1221,82987,5,1501,82987,1,1501,82987,50,1501,82987,40,1501,83060,0,1501,91513,3,1818,92335,4,1952,93125,5,2102,93126,1,2102,93126,50,2102,93126,40,2102,93199,0,2102,94768,3,2414,94783,4,2557,94868,5,2703,94868,1,2703,94868,50,2703,94868,40,2703,94941,0,2703,118397,3,4205,119454,4,4954,120410,1,5704,120410,50,5704,120410,40,5704,120483,0,5705,135884,3,6457,136714,4,6831,137195,5,7206,137196,1,7206,137196,50,7206,137196,40,7206,137269,0,7206,148630,3,7982,150377,4,8332,151837,1,8707,151837,50,8707,151837,40,8707,151910,0,8707,203868,3,12609,205162,4,14559,206531,5,16508,206532,1,16508,206532,50,16510,206532,40,16510,206605,0,16510,250590,3,19063,251565,4,20336,252633,1,21611,252633,50,21612,252633,40,21612,252706,0,21612,292119,3,23120,292853,4,23863,293541,1,24613,293541,50,24615,293541,40,24615,293614,0,24615,304780,3,25383,306785,4,25749,308106,5,26116,308106,1,26116,308106,50,26116,308106,40,26116,308179,0,26116,334239,3,27317,334867,4,27917,335380,5,28517,335381,1,28517,335381,50,28518,335381,40,28518,335454,0,28518,354963,3,29269,355425,4,29644,355779,5,30019,355780,1,30019,355780,50,30019,355780,40,30019,355780,40,30019,355909,0,30019,357248,50,30025,357248,30,30025,357248,40,30025,357313,0,30025,357457,50,30025,357457,30,30025,357457,40,30025,357522,0,30031,357663,50,30032,357728,0,30032,357905,50,30033,357905,30,30033,357905,40,30033,357970,0,30038,358123,50,30039,358123,30,30039,358123,40,30039,358188,0,30039,358402,50,30040,358467,0,30046,358744,50,30051,358809,0,30051,359094,50,30059,359159,0,30063,359452,50,30073,359517,0,30073,359816,50,30086,359881,0,30090,360188,50,30111,360253,0,30111,360568,50,30148,360633,0,30153,360958,50,30223,361023,0,30223,361358,50,30360,361358,40,30360,361423,0,30360)
%
%
% START OF PROOF
% 361360 [] equal(multiply(identity,X),X).
% 361361 [] equal(multiply(inverse(X),X),identity).
% 361362 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 361363 [] -equal(inverse(sk_c11),sk_c10).
% 361414 [?] ?
% 361415 [?] ?
% 361416 [?] ?
% 361417 [?] ?
% 361418 [?] ?
% 361419 [?] ?
% 361420 [?] ?
% 361421 [?] ?
% 361422 [?] ?
% 361423 [?] ?
% 361440 [input:361415,cut:361363] equal(inverse(sk_c6),sk_c8).
% 361441 [para:361440.1.1,361361.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 361443 [input:361416,cut:361363] equal(inverse(sk_c7),sk_c6).
% 361444 [para:361443.1.1,361361.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 361445 [input:361418,cut:361363] equal(inverse(sk_c5),sk_c8).
% 361446 [para:361445.1.1,361361.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 361448 [input:361420,cut:361363] equal(inverse(sk_c4),sk_c10).
% 361449 [para:361448.1.1,361361.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 361450 [input:361422,cut:361363] equal(inverse(sk_c3),sk_c11).
% 361451 [para:361450.1.1,361361.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 361486 [input:361414,cut:361363] equal(multiply(sk_c7,sk_c8),sk_c6).
% 361487 [input:361417,cut:361363] equal(multiply(sk_c8,sk_c10),sk_c11).
% 361489 [input:361419,cut:361363] equal(multiply(sk_c5,sk_c8),sk_c11).
% 361490 [input:361421,cut:361363] equal(multiply(sk_c4,sk_c10),sk_c9).
% 361491 [input:361423,cut:361363] equal(multiply(sk_c3,sk_c11),sk_c10).
% 361513 [para:361441.1.1,361362.1.1.1,demod:361360] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 361514 [para:361444.1.1,361362.1.1.1,demod:361360] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 361515 [para:361446.1.1,361362.1.1.1,demod:361360] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 361517 [para:361449.1.1,361362.1.1.1,demod:361360] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 361518 [para:361451.1.1,361362.1.1.1,demod:361360] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 361558 [para:361489.1.1,361362.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 361578 [para:361444.1.1,361513.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 361579 [para:361578.1.2,361362.1.1.1,demod:361360] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 361583 [para:361486.1.1,361514.1.2.2] equal(sk_c8,multiply(sk_c6,sk_c6)).
% 361588 [para:361583.1.2,361513.1.2.2] equal(sk_c6,multiply(sk_c8,sk_c8)).
% 361593 [para:361489.1.1,361515.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 361597 [para:361490.1.1,361517.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 361612 [para:361491.1.1,361518.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 361614 [para:361579.1.1,361514.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 361615 [para:361441.1.1,361614.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 361616 [para:361446.1.1,361614.1.2.2,demod:361615] equal(sk_c5,sk_c6).
% 361626 [para:361616.1.2,361514.1.2.1,demod:361558,361579] equal(X,multiply(sk_c11,X)).
% 361637 [para:361626.1.2,361518.1.2] equal(X,multiply(sk_c3,X)).
% 361638 [para:361626.1.2,361612.1.2] equal(sk_c11,sk_c10).
% 361644 [para:361638.1.1,361593.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c10)).
% 361645 [para:361638.1.1,361518.1.2.1,demod:361637] equal(X,multiply(sk_c10,X)).
% 361657 [para:361645.1.2,361597.1.2] equal(sk_c10,sk_c9).
% 361669 [para:361657.1.1,361487.1.1.2] equal(multiply(sk_c8,sk_c9),sk_c11).
% 361672 [para:361657.1.1,361612.1.2.2,demod:361626] equal(sk_c11,sk_c9).
% 361675 [para:361672.1.1,361593.1.2.2,demod:361669] equal(sk_c8,sk_c11).
% 361680 [para:361675.1.2,361491.1.1.2,demod:361637] equal(sk_c8,sk_c10).
% 361681 [para:361675.1.2,361593.1.2.2,demod:361588] equal(sk_c8,sk_c6).
% 361683 [para:361675.1.2,361612.1.2.1,demod:361644] equal(sk_c11,sk_c8).
% 361745 [para:361681.1.2,361440.1.1.1] equal(inverse(sk_c8),sk_c8).
% 361751 [para:361683.1.1,361363.1.1.1,demod:361745,cut:361680] 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(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),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_c10,sk_c9),sk_c11).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,138,0,0,78682,4,1221,82987,5,1501,82987,1,1501,82987,50,1501,82987,40,1501,83060,0,1501,91513,3,1818,92335,4,1952,93125,5,2102,93126,1,2102,93126,50,2102,93126,40,2102,93199,0,2102,94768,3,2414,94783,4,2557,94868,5,2703,94868,1,2703,94868,50,2703,94868,40,2703,94941,0,2703,118397,3,4205,119454,4,4954,120410,1,5704,120410,50,5704,120410,40,5704,120483,0,5705,135884,3,6457,136714,4,6831,137195,5,7206,137196,1,7206,137196,50,7206,137196,40,7206,137269,0,7206,148630,3,7982,150377,4,8332,151837,1,8707,151837,50,8707,151837,40,8707,151910,0,8707,203868,3,12609,205162,4,14559,206531,5,16508,206532,1,16508,206532,50,16510,206532,40,16510,206605,0,16510,250590,3,19063,251565,4,20336,252633,1,21611,252633,50,21612,252633,40,21612,252706,0,21612,292119,3,23120,292853,4,23863,293541,1,24613,293541,50,24615,293541,40,24615,293614,0,24615,304780,3,25383,306785,4,25749,308106,5,26116,308106,1,26116,308106,50,26116,308106,40,26116,308179,0,26116,334239,3,27317,334867,4,27917,335380,5,28517,335381,1,28517,335381,50,28518,335381,40,28518,335454,0,28518,354963,3,29269,355425,4,29644,355779,5,30019,355780,1,30019,355780,50,30019,355780,40,30019,355780,40,30019,355909,0,30019,357248,50,30025,357248,30,30025,357248,40,30025,357313,0,30025,357457,50,30025,357457,30,30025,357457,40,30025,357522,0,30031,357663,50,30032,357728,0,30032,357905,50,30033,357905,30,30033,357905,40,30033,357970,0,30038,358123,50,30039,358123,30,30039,358123,40,30039,358188,0,30039,358402,50,30040,358467,0,30046,358744,50,30051,358809,0,30051,359094,50,30059,359159,0,30063,359452,50,30073,359517,0,30073,359816,50,30086,359881,0,30090,360188,50,30111,360253,0,30111,360568,50,30148,360633,0,30153,360958,50,30223,361023,0,30223,361358,50,30360,361358,40,30360,361423,0,30360,361750,50,30362,361750,30,30362,361750,40,30362,361815,0,30362,362029,50,30363,362094,0,30368,362371,50,30373,362436,0,30373,362721,50,30381,362786,0,30385,363079,50,30395,363144,0,30395,363443,50,30408,363508,0,30413,363815,50,30434,363880,0,30434,364195,50,30471,364260,0,30476,364585,50,30545,364650,0,30545,364985,50,30683,364985,40,30683,365050,0,30683)
%
%
% START OF PROOF
% 364770 [?] ?
% 364987 [] equal(multiply(identity,X),X).
% 364988 [] equal(multiply(inverse(X),X),identity).
% 364989 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 364990 [] -equal(multiply(sk_c10,sk_c9),sk_c11).
% 365037 [?] ?
% 365038 [?] ?
% 365135 [input:365037,cut:364990] equal(inverse(sk_c4),sk_c10).
% 365136 [para:365135.1.1,364988.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 365169 [input:365038,cut:364990] equal(multiply(sk_c4,sk_c10),sk_c9).
% 365211 [para:365136.1.1,364989.1.1.1,demod:364987] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 365271 [para:365169.1.1,365211.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 365272 [para:365271.1.2,364990.1.1,cut:364770] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c9),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_c11,sk_c9),sk_c10).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,138,0,0,78682,4,1221,82987,5,1501,82987,1,1501,82987,50,1501,82987,40,1501,83060,0,1501,91513,3,1818,92335,4,1952,93125,5,2102,93126,1,2102,93126,50,2102,93126,40,2102,93199,0,2102,94768,3,2414,94783,4,2557,94868,5,2703,94868,1,2703,94868,50,2703,94868,40,2703,94941,0,2703,118397,3,4205,119454,4,4954,120410,1,5704,120410,50,5704,120410,40,5704,120483,0,5705,135884,3,6457,136714,4,6831,137195,5,7206,137196,1,7206,137196,50,7206,137196,40,7206,137269,0,7206,148630,3,7982,150377,4,8332,151837,1,8707,151837,50,8707,151837,40,8707,151910,0,8707,203868,3,12609,205162,4,14559,206531,5,16508,206532,1,16508,206532,50,16510,206532,40,16510,206605,0,16510,250590,3,19063,251565,4,20336,252633,1,21611,252633,50,21612,252633,40,21612,252706,0,21612,292119,3,23120,292853,4,23863,293541,1,24613,293541,50,24615,293541,40,24615,293614,0,24615,304780,3,25383,306785,4,25749,308106,5,26116,308106,1,26116,308106,50,26116,308106,40,26116,308179,0,26116,334239,3,27317,334867,4,27917,335380,5,28517,335381,1,28517,335381,50,28518,335381,40,28518,335454,0,28518,354963,3,29269,355425,4,29644,355779,5,30019,355780,1,30019,355780,50,30019,355780,40,30019,355780,40,30019,355909,0,30019,357248,50,30025,357248,30,30025,357248,40,30025,357313,0,30025,357457,50,30025,357457,30,30025,357457,40,30025,357522,0,30031,357663,50,30032,357728,0,30032,357905,50,30033,357905,30,30033,357905,40,30033,357970,0,30038,358123,50,30039,358123,30,30039,358123,40,30039,358188,0,30039,358402,50,30040,358467,0,30046,358744,50,30051,358809,0,30051,359094,50,30059,359159,0,30063,359452,50,30073,359517,0,30073,359816,50,30086,359881,0,30090,360188,50,30111,360253,0,30111,360568,50,30148,360633,0,30153,360958,50,30223,361023,0,30223,361358,50,30360,361358,40,30360,361423,0,30360,361750,50,30362,361750,30,30362,361750,40,30362,361815,0,30362,362029,50,30363,362094,0,30368,362371,50,30373,362436,0,30373,362721,50,30381,362786,0,30385,363079,50,30395,363144,0,30395,363443,50,30408,363508,0,30413,363815,50,30434,363880,0,30434,364195,50,30471,364260,0,30476,364585,50,30545,364650,0,30545,364985,50,30683,364985,40,30683,365050,0,30683,365271,50,30683,365271,30,30683,365271,40,30683,365336,0,30683,365550,50,30685,365615,0,30690,365892,50,30695,365957,0,30695,366242,50,30702,366307,0,30706,366600,50,30716,366665,0,30716,366964,50,30729,367029,0,30734,367336,50,30755,367401,0,30755,367716,50,30792,367781,0,30797,368106,50,30866,368171,0,30866,368506,50,31005,368506,40,31005,368571,0,31005)
%
%
% START OF PROOF
% 368287 [?] ?
% 368508 [] equal(multiply(identity,X),X).
% 368509 [] equal(multiply(inverse(X),X),identity).
% 368510 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 368511 [] -equal(multiply(sk_c11,sk_c9),sk_c10).
% 368543 [?] ?
% 368544 [?] ?
% 368546 [?] ?
% 368547 [?] ?
% 368636 [input:368543,cut:368511] equal(inverse(sk_c6),sk_c8).
% 368637 [para:368636.1.1,368509.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 368639 [input:368544,cut:368511] equal(inverse(sk_c7),sk_c6).
% 368640 [para:368639.1.1,368509.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 368641 [input:368546,cut:368511] equal(inverse(sk_c5),sk_c8).
% 368642 [para:368641.1.1,368509.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 368677 [input:368547,cut:368511] equal(multiply(sk_c5,sk_c8),sk_c11).
% 368711 [para:368637.1.1,368510.1.1.1,demod:368508] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 368714 [para:368640.1.1,368510.1.1.1,demod:368508] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 368748 [para:368677.1.1,368510.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 368758 [para:368640.1.1,368711.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 368759 [para:368758.1.2,368510.1.1.1,demod:368508] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 368796 [para:368759.1.1,368714.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 368799 [para:368637.1.1,368796.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 368800 [para:368642.1.1,368796.1.2.2,demod:368799] equal(sk_c5,sk_c6).
% 368808 [para:368800.1.2,368714.1.2.1,demod:368748,368759] equal(X,multiply(sk_c11,X)).
% 368811 [para:368808.1.2,368511.1.1,cut:368287] 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: 41759
% derived clauses: 4701406
% kept clauses: 236463
% kept size sum: 50635
% kept mid-nuclei: 68585
% kept new demods: 7393
% forw unit-subs: 1684857
% forw double-subs: 2426551
% forw overdouble-subs: 213533
% backward subs: 15616
% fast unit cutoff: 40749
% full unit cutoff: 0
% dbl unit cutoff: 21918
% real runtime : 311.32
% process. runtime: 310.7
% specific non-discr-tree subsumption statistics:
% tried: 48868919
% length fails: 6233152
% strength fails: 15480292
% predlist fails: 5637585
% aux str. fails: 5107047
% by-lit fails: 9428618
% full subs tried: 2471254
% full subs fail: 2351862
%
% ; 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/GRP384-1+eq_r.in")
%
%------------------------------------------------------------------------------