TSTP Solution File: GRP378-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP378-1 : 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 : art09.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 297.9s
% Output : Assurance 297.9s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP378-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 29)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 29)
% (binary-posweight-lex-big-order 30 #f 3 29)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -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_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11).
% -equal(inverse(sk_c11),sk_c10).
% -equal(multiply(sk_c11,sk_c9),sk_c10).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X2),W) | -equal(inverse(X1),X2) | -equal(multiply(X1,W),X2).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,149396,4,1284,153810,5,1501,153810,1,1501,153810,50,1501,153810,40,1501,153873,0,1501,163138,3,1860,163726,4,1952,164571,5,2104,164571,1,2104,164571,50,2104,164571,40,2104,164634,0,2104,166200,3,2410,166215,4,2570,166342,5,2705,166342,1,2705,166342,50,2705,166342,40,2705,166405,0,2705,186353,3,4206,188100,4,4956,189808,1,5706,189808,50,5706,189808,40,5706,189871,0,5706,202157,3,6457,203574,4,6832,205029,1,7207,205029,50,7207,205029,40,7207,205092,0,7207,218660,3,8021,219864,4,8333,221380,5,8708,221381,1,8708,221381,50,8708,221381,40,8708,221444,0,8708,265124,3,12609,266730,4,14560,268260,1,16509,268260,50,16510,268260,40,16510,268323,0,16510,305597,3,19061,306847,4,20336,307760,5,21611,307761,1,21611,307761,50,21612,307761,40,21612,307824,0,21613,338203,3,23114,339302,4,23864,340292,1,24614,340292,50,24615,340292,40,24615,340355,0,24615,353638,3,25373,355317,4,25741,357429,5,26116,357429,1,26116,357429,50,26116,357429,40,26116,357492,0,26116,378778,3,27317,379828,4,27917,380613,1,28517,380613,50,28517,380613,40,28517,380676,0,28517,396332,3,29268,397153,4,29643,397913,5,30018,397914,1,30018,397914,50,30018,397914,40,30018,397914,40,30018,398023,0,30018)
%
%
% START OF PROOF
% 397916 [] equal(multiply(identity,X),X).
% 397917 [] equal(multiply(inverse(X),X),identity).
% 397918 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 397969 [] -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).
% 397970 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst85,Y).
% 397971 [] -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | $spltprd1($spltcnst86,Y).
% 397972 [] -equal(multiply(X,sk_c10),sk_c11) | $spltprd1($spltcnst87,X).
% 397973 [] -$spltprd1($spltcnst86,X) | -$spltprd1($spltcnst85,X) | -$spltprd1($spltcnst87,X).
% 397974 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 397975 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 397976 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 397977 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 397978 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 397979 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 397984 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c2).
% 397985 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c6),sk_c8).
% 397986 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c7),sk_c6).
% 397987 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c2).
% 397988 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 397989 [?] ?
% 397994 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 397995 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 397996 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 397997 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 397998 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 397999 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 398004 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 398005 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 398006 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 398007 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 398008 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 398009 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 398014 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c11),sk_c10).
% 398015 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 398016 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 398017 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c11),sk_c10).
% 398018 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 398019 [?] ?
% 398138 [hyper:397971,397988,binarycut:397989] equal(inverse(sk_c1),sk_c2) | $spltprd1($spltcnst86,sk_c8).
% 398273 [hyper:397971,398018,binarycut:398019] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst86,sk_c8).
% 398515 [hyper:397970,397984,397985,397986] equal(inverse(sk_c1),sk_c2) | $spltprd1($spltcnst85,sk_c8).
% 398588 [hyper:397972,397987] equal(inverse(sk_c1),sk_c2) | $spltprd1($spltcnst87,sk_c8).
% 398612 [hyper:397973,398588,398515,398138] equal(inverse(sk_c1),sk_c2).
% 398629 [para:398612.1.1,397917.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 398982 [hyper:397970,398014,398015,398016] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst85,sk_c8).
% 399037 [hyper:397972,398017] equal(inverse(sk_c11),sk_c10) | $spltprd1($spltcnst87,sk_c8).
% 399123 [hyper:397973,399037,398982,398273] equal(inverse(sk_c11),sk_c10).
% 399165 [para:399123.1.1,397917.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 401623 [hyper:397969,397979,397977,397978,397975,397974,397976] equal(multiply(sk_c2,sk_c10),sk_c11).
% 402507 [hyper:397969,397999,397997,397998,397995,397994,397996] equal(multiply(sk_c1,sk_c2),sk_c11).
% 402675 [hyper:397969,398009,398007,398008,398005,398004,398006] equal(multiply(sk_c11,sk_c9),sk_c10).
% 402683 [para:397917.1.1,397918.1.1.1,demod:397916] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 402684 [para:398629.1.1,397918.1.1.1,demod:397916] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 402685 [para:399165.1.1,397918.1.1.1,demod:397916] equal(X,multiply(sk_c10,multiply(sk_c11,X))).
% 402687 [para:402507.1.1,397918.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c1,multiply(sk_c2,X))).
% 402705 [para:402507.1.1,402684.1.2.2] equal(sk_c2,multiply(sk_c2,sk_c11)).
% 402734 [para:398629.1.1,402683.1.2.2] equal(sk_c1,multiply(inverse(sk_c2),identity)).
% 402735 [para:399165.1.1,402683.1.2.2] equal(sk_c11,multiply(inverse(sk_c10),identity)).
% 402744 [para:401623.1.1,402683.1.2.2] equal(sk_c10,multiply(inverse(sk_c2),sk_c11)).
% 402745 [para:402684.1.2,402683.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 402766 [para:402745.1.2,397917.1.1,demod:402507] equal(sk_c11,identity).
% 402769 [para:402745.1.2,402683.1.2,demod:402687] equal(X,multiply(sk_c11,X)).
% 402772 [para:402766.1.1,399123.1.1.1] equal(inverse(identity),sk_c10).
% 402774 [para:402766.1.1,402675.1.1.1,demod:397916] equal(sk_c9,sk_c10).
% 402775 [para:402766.1.1,402705.1.2.2] equal(sk_c2,multiply(sk_c2,identity)).
% 402776 [para:402766.1.1,402685.1.2.2.1,demod:397916] equal(X,multiply(sk_c10,X)).
% 402777 [para:402766.1.1,402744.1.2.2,demod:402734] equal(sk_c10,sk_c1).
% 402779 [para:402774.1.2,401623.1.1.2] equal(multiply(sk_c2,sk_c9),sk_c11).
% 402786 [para:402777.1.1,402735.1.2.1.1,demod:402775,398612] equal(sk_c11,sk_c2).
% 402794 [para:402786.1.1,399165.1.1.2,demod:402776] equal(sk_c2,identity).
% 402795 [para:402786.1.1,402675.1.1.1,demod:402779] equal(sk_c11,sk_c10).
% 402800 [para:402794.1.1,401623.1.1.1,demod:397916] equal(sk_c10,sk_c11).
% 402806 [para:402795.1.1,399123.1.1.1] equal(inverse(sk_c10),sk_c10).
% 402839 [hyper:397969,402772,397916,demod:402806,397916,demod:402772,402769,cut:402800,cut:402800,cut:402800,cut:402795] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,149396,4,1284,153810,5,1501,153810,1,1501,153810,50,1501,153810,40,1501,153873,0,1501,163138,3,1860,163726,4,1952,164571,5,2104,164571,1,2104,164571,50,2104,164571,40,2104,164634,0,2104,166200,3,2410,166215,4,2570,166342,5,2705,166342,1,2705,166342,50,2705,166342,40,2705,166405,0,2705,186353,3,4206,188100,4,4956,189808,1,5706,189808,50,5706,189808,40,5706,189871,0,5706,202157,3,6457,203574,4,6832,205029,1,7207,205029,50,7207,205029,40,7207,205092,0,7207,218660,3,8021,219864,4,8333,221380,5,8708,221381,1,8708,221381,50,8708,221381,40,8708,221444,0,8708,265124,3,12609,266730,4,14560,268260,1,16509,268260,50,16510,268260,40,16510,268323,0,16510,305597,3,19061,306847,4,20336,307760,5,21611,307761,1,21611,307761,50,21612,307761,40,21612,307824,0,21613,338203,3,23114,339302,4,23864,340292,1,24614,340292,50,24615,340292,40,24615,340355,0,24615,353638,3,25373,355317,4,25741,357429,5,26116,357429,1,26116,357429,50,26116,357429,40,26116,357492,0,26116,378778,3,27317,379828,4,27917,380613,1,28517,380613,50,28517,380613,40,28517,380676,0,28517,396332,3,29268,397153,4,29643,397913,5,30018,397914,1,30018,397914,50,30018,397914,40,30018,397914,40,30018,398023,0,30018,402838,50,30035,402838,30,30035,402838,40,30035,402893,0,30035)
%
%
% START OF PROOF
% 402840 [] equal(multiply(identity,X),X).
% 402841 [] equal(multiply(inverse(X),X),identity).
% 402842 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 402843 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 402850 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 402851 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 402860 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c4),sk_c10).
% 402861 [?] ?
% 402870 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 402871 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 402880 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 402881 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 402890 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 402891 [?] ?
% 402900 [hyper:402843,402860,binarycut:402861] equal(inverse(sk_c1),sk_c2).
% 402901 [para:402900.1.1,402841.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 402915 [hyper:402843,402890,binarycut:402891] equal(inverse(sk_c11),sk_c10).
% 402918 [para:402915.1.1,402841.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 402945 [hyper:402843,402851,402850] equal(multiply(sk_c2,sk_c10),sk_c11).
% 402951 [hyper:402843,402871,402870] equal(multiply(sk_c1,sk_c2),sk_c11).
% 402957 [hyper:402843,402881,402880] equal(multiply(sk_c11,sk_c9),sk_c10).
% 402958 [para:402841.1.1,402842.1.1.1,demod:402840] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 402959 [para:402901.1.1,402842.1.1.1,demod:402840] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 402960 [para:402918.1.1,402842.1.1.1,demod:402840] equal(X,multiply(sk_c10,multiply(sk_c11,X))).
% 402961 [para:402945.1.1,402842.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c2,multiply(sk_c10,X))).
% 402962 [para:402951.1.1,402842.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c1,multiply(sk_c2,X))).
% 402964 [para:402951.1.1,402959.1.2.2] equal(sk_c2,multiply(sk_c2,sk_c11)).
% 402966 [para:402957.1.1,402960.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 402970 [para:402945.1.1,402958.1.2.2] equal(sk_c10,multiply(inverse(sk_c2),sk_c11)).
% 402975 [para:402918.1.1,402961.1.2.2] equal(multiply(sk_c11,sk_c11),multiply(sk_c2,identity)).
% 402977 [para:402966.1.2,402961.1.2.2] equal(multiply(sk_c11,sk_c10),multiply(sk_c2,sk_c9)).
% 402978 [para:402975.1.1,402960.1.2.2] equal(sk_c11,multiply(sk_c10,multiply(sk_c2,identity))).
% 402980 [para:402977.1.1,402960.1.2.2] equal(sk_c10,multiply(sk_c10,multiply(sk_c2,sk_c9))).
% 402982 [para:402978.1.2,402961.1.2.2,demod:402964] equal(multiply(sk_c11,multiply(sk_c2,identity)),sk_c2).
% 402987 [para:402945.1.1,402962.1.2.2,demod:402977] equal(multiply(sk_c2,sk_c9),multiply(sk_c1,sk_c11)).
% 402989 [para:402964.1.2,402962.1.2.2,demod:402951,402975] equal(multiply(sk_c2,identity),sk_c11).
% 402991 [para:402989.1.1,402842.1.1.1,demod:402840] equal(multiply(sk_c11,X),multiply(sk_c2,X)).
% 402992 [para:402989.1.1,402958.1.2.2,demod:402970] equal(identity,sk_c10).
% 402993 [para:402989.1.1,402978.1.2.2,demod:402918] equal(sk_c11,identity).
% 402994 [para:402989.1.1,402982.1.1.2,demod:402989,402975] equal(sk_c11,sk_c2).
% 402995 [para:402989.1.1,402962.1.2.2,demod:402989,402991] equal(sk_c11,multiply(sk_c1,sk_c11)).
% 402999 [para:402992.1.2,402980.1.2.1,demod:402840,402995,402987] equal(sk_c10,sk_c11).
% 403000 [para:402993.1.1,402915.1.1.1] equal(inverse(identity),sk_c10).
% 403006 [para:402994.1.1,402915.1.1.1] equal(inverse(sk_c2),sk_c10).
% 403014 [para:402999.1.2,402970.1.2.2,demod:402966,403006] equal(sk_c10,sk_c9).
% 403033 [hyper:402843,403000,demod:402840,cut:403014] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(V,W),sk_c11) | -equal(inverse(V),W) | -equal(multiply(W,sk_c10),sk_c11) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(Z,sk_c11),sk_c10) | -equal(inverse(Z),sk_c11).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,149396,4,1284,153810,5,1501,153810,1,1501,153810,50,1501,153810,40,1501,153873,0,1501,163138,3,1860,163726,4,1952,164571,5,2104,164571,1,2104,164571,50,2104,164571,40,2104,164634,0,2104,166200,3,2410,166215,4,2570,166342,5,2705,166342,1,2705,166342,50,2705,166342,40,2705,166405,0,2705,186353,3,4206,188100,4,4956,189808,1,5706,189808,50,5706,189808,40,5706,189871,0,5706,202157,3,6457,203574,4,6832,205029,1,7207,205029,50,7207,205029,40,7207,205092,0,7207,218660,3,8021,219864,4,8333,221380,5,8708,221381,1,8708,221381,50,8708,221381,40,8708,221444,0,8708,265124,3,12609,266730,4,14560,268260,1,16509,268260,50,16510,268260,40,16510,268323,0,16510,305597,3,19061,306847,4,20336,307760,5,21611,307761,1,21611,307761,50,21612,307761,40,21612,307824,0,21613,338203,3,23114,339302,4,23864,340292,1,24614,340292,50,24615,340292,40,24615,340355,0,24615,353638,3,25373,355317,4,25741,357429,5,26116,357429,1,26116,357429,50,26116,357429,40,26116,357492,0,26116,378778,3,27317,379828,4,27917,380613,1,28517,380613,50,28517,380613,40,28517,380676,0,28517,396332,3,29268,397153,4,29643,397913,5,30018,397914,1,30018,397914,50,30018,397914,40,30018,397914,40,30018,398023,0,30018,402838,50,30035,402838,30,30035,402838,40,30035,402893,0,30035,403032,50,30035,403032,30,30035,403032,40,30035,403087,0,30035,403222,50,30035,403277,0,30040)
%
%
% START OF PROOF
% 403224 [] equal(multiply(identity,X),X).
% 403225 [] equal(multiply(inverse(X),X),identity).
% 403226 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 403227 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 403236 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 403237 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 403246 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c3),sk_c11).
% 403247 [?] ?
% 403256 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 403257 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 403266 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 403267 [] equal(multiply(sk_c11,sk_c9),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 403276 [] equal(inverse(sk_c11),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 403277 [?] ?
% 403285 [hyper:403227,403246,binarycut:403247] equal(inverse(sk_c1),sk_c2).
% 403286 [para:403285.1.1,403225.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 403294 [hyper:403227,403276,binarycut:403277] equal(inverse(sk_c11),sk_c10).
% 403296 [para:403294.1.1,403225.1.1.1] equal(multiply(sk_c10,sk_c11),identity).
% 403322 [hyper:403227,403237,403236] equal(multiply(sk_c2,sk_c10),sk_c11).
% 403329 [hyper:403227,403257,403256] equal(multiply(sk_c1,sk_c2),sk_c11).
% 403336 [hyper:403227,403267,403266] equal(multiply(sk_c11,sk_c9),sk_c10).
% 403337 [para:403225.1.1,403226.1.1.1,demod:403224] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 403338 [para:403286.1.1,403226.1.1.1,demod:403224] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 403339 [para:403296.1.1,403226.1.1.1,demod:403224] equal(X,multiply(sk_c10,multiply(sk_c11,X))).
% 403340 [para:403322.1.1,403226.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c2,multiply(sk_c10,X))).
% 403341 [para:403329.1.1,403226.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c1,multiply(sk_c2,X))).
% 403342 [para:403336.1.1,403226.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c11,multiply(sk_c9,X))).
% 403343 [para:403329.1.1,403338.1.2.2] equal(sk_c2,multiply(sk_c2,sk_c11)).
% 403345 [para:403336.1.1,403339.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 403347 [para:403225.1.1,403337.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 403350 [para:403322.1.1,403337.1.2.2] equal(sk_c10,multiply(inverse(sk_c2),sk_c11)).
% 403351 [para:403226.1.1,403337.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 403354 [para:403337.1.2,403337.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 403357 [para:403296.1.1,403340.1.2.2] equal(multiply(sk_c11,sk_c11),multiply(sk_c2,identity)).
% 403359 [para:403345.1.2,403340.1.2.2] equal(multiply(sk_c11,sk_c10),multiply(sk_c2,sk_c9)).
% 403360 [para:403357.1.1,403339.1.2.2] equal(sk_c11,multiply(sk_c10,multiply(sk_c2,identity))).
% 403362 [para:403359.1.1,403339.1.2.2] equal(sk_c10,multiply(sk_c10,multiply(sk_c2,sk_c9))).
% 403367 [para:403322.1.1,403341.1.2.2,demod:403359] equal(multiply(sk_c2,sk_c9),multiply(sk_c1,sk_c11)).
% 403369 [para:403343.1.2,403341.1.2.2,demod:403329,403357] equal(multiply(sk_c2,identity),sk_c11).
% 403372 [para:403369.1.1,403337.1.2.2,demod:403350] equal(identity,sk_c10).
% 403373 [para:403369.1.1,403360.1.2.2,demod:403296] equal(sk_c11,identity).
% 403374 [?] ?
% 403378 [para:403372.1.2,403362.1.2.1,demod:403224,403374,403367] equal(sk_c10,sk_c11).
% 403382 [para:403373.1.1,403339.1.2.2.1,demod:403224] equal(X,multiply(sk_c10,X)).
% 403384 [para:403373.1.1,403342.1.2.1,demod:403224,403382] equal(X,multiply(sk_c9,X)).
% 403389 [para:403378.1.2,403294.1.1.1] equal(inverse(sk_c10),sk_c10).
% 403421 [para:403354.1.2,403225.1.1] equal(multiply(X,inverse(X)),identity).
% 403423 [para:403354.1.2,403347.1.2] equal(X,multiply(X,identity)).
% 403427 [para:403423.1.2,403347.1.2] equal(X,inverse(inverse(X))).
% 403428 [para:403421.1.1,403351.1.2.2.2,demod:403423] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 403434 [para:403342.1.2,403428.1.2.1.1,demod:403382,403384] equal(inverse(X),multiply(inverse(X),sk_c11)).
% 403443 [para:403434.1.2,403354.1.2,demod:403427] equal(multiply(X,sk_c11),X).
% 403444 [hyper:403227,403443,demod:403389,cut:403378] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 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_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -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_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,149396,4,1284,153810,5,1501,153810,1,1501,153810,50,1501,153810,40,1501,153873,0,1501,163138,3,1860,163726,4,1952,164571,5,2104,164571,1,2104,164571,50,2104,164571,40,2104,164634,0,2104,166200,3,2410,166215,4,2570,166342,5,2705,166342,1,2705,166342,50,2705,166342,40,2705,166405,0,2705,186353,3,4206,188100,4,4956,189808,1,5706,189808,50,5706,189808,40,5706,189871,0,5706,202157,3,6457,203574,4,6832,205029,1,7207,205029,50,7207,205029,40,7207,205092,0,7207,218660,3,8021,219864,4,8333,221380,5,8708,221381,1,8708,221381,50,8708,221381,40,8708,221444,0,8708,265124,3,12609,266730,4,14560,268260,1,16509,268260,50,16510,268260,40,16510,268323,0,16510,305597,3,19061,306847,4,20336,307760,5,21611,307761,1,21611,307761,50,21612,307761,40,21612,307824,0,21613,338203,3,23114,339302,4,23864,340292,1,24614,340292,50,24615,340292,40,24615,340355,0,24615,353638,3,25373,355317,4,25741,357429,5,26116,357429,1,26116,357429,50,26116,357429,40,26116,357492,0,26116,378778,3,27317,379828,4,27917,380613,1,28517,380613,50,28517,380613,40,28517,380676,0,28517,396332,3,29268,397153,4,29643,397913,5,30018,397914,1,30018,397914,50,30018,397914,40,30018,397914,40,30018,398023,0,30018,402838,50,30035,402838,30,30035,402838,40,30035,402893,0,30035,403032,50,30035,403032,30,30035,403032,40,30035,403087,0,30035,403222,50,30035,403277,0,30040,403443,50,30041,403443,30,30041,403443,40,30041,403498,0,30041)
%
%
% START OF PROOF
% 403444 [] equal(X,X).
% 403448 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,X),sk_c11) | -equal(inverse(Y),X).
% 403452 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 403453 [?] ?
% 403454 [] equal(multiply(sk_c2,sk_c10),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 403462 [?] ?
% 403463 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 403464 [?] ?
% 403472 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 403473 [?] ?
% 403474 [] equal(multiply(sk_c1,sk_c2),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 403519 [hyper:403448,403463,binarycut:403473,binarycut:403453] equal(inverse(sk_c5),sk_c8).
% 403521 [hyper:403448,403463,binarycut:403464,binarycut:403462] equal(inverse(sk_c1),sk_c2).
% 403563 [hyper:403448,403454,403452,demod:403519,cut:403444] equal(multiply(sk_c2,sk_c10),sk_c11).
% 403573 [hyper:403448,403472,demod:403521,403563,cut:403444,cut:403444] equal(multiply(sk_c8,sk_c10),sk_c11).
% 403579 [hyper:403448,403474,demod:403521,403563,cut:403444,cut:403444] equal(multiply(sk_c5,sk_c8),sk_c11).
% 403588 [hyper:403448,403579,demod:403519,403573,cut:403444,cut:403444] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c11),sk_c10) | -equal(multiply(sk_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -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 29
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,149396,4,1284,153810,5,1501,153810,1,1501,153810,50,1501,153810,40,1501,153873,0,1501,163138,3,1860,163726,4,1952,164571,5,2104,164571,1,2104,164571,50,2104,164571,40,2104,164634,0,2104,166200,3,2410,166215,4,2570,166342,5,2705,166342,1,2705,166342,50,2705,166342,40,2705,166405,0,2705,186353,3,4206,188100,4,4956,189808,1,5706,189808,50,5706,189808,40,5706,189871,0,5706,202157,3,6457,203574,4,6832,205029,1,7207,205029,50,7207,205029,40,7207,205092,0,7207,218660,3,8021,219864,4,8333,221380,5,8708,221381,1,8708,221381,50,8708,221381,40,8708,221444,0,8708,265124,3,12609,266730,4,14560,268260,1,16509,268260,50,16510,268260,40,16510,268323,0,16510,305597,3,19061,306847,4,20336,307760,5,21611,307761,1,21611,307761,50,21612,307761,40,21612,307824,0,21613,338203,3,23114,339302,4,23864,340292,1,24614,340292,50,24615,340292,40,24615,340355,0,24615,353638,3,25373,355317,4,25741,357429,5,26116,357429,1,26116,357429,50,26116,357429,40,26116,357492,0,26116,378778,3,27317,379828,4,27917,380613,1,28517,380613,50,28517,380613,40,28517,380676,0,28517,396332,3,29268,397153,4,29643,397913,5,30018,397914,1,30018,397914,50,30018,397914,40,30018,397914,40,30018,398023,0,30018,402838,50,30035,402838,30,30035,402838,40,30035,402893,0,30035,403032,50,30035,403032,30,30035,403032,40,30035,403087,0,30035,403222,50,30035,403277,0,30040,403443,50,30041,403443,30,30041,403443,40,30041,403498,0,30041,403587,50,30041,403587,30,30041,403587,40,30041,403642,0,30046,403846,50,30048,403901,0,30048,404169,50,30053,404224,0,30058,404500,50,30065,404555,0,30065,404839,50,30074,404894,0,30078,405184,50,30092,405239,0,30092,405537,50,30113,405592,0,30118,405898,50,30155,405953,0,30155,406269,50,30228,406324,0,30228,406650,50,30375,406650,40,30375,406705,0,30375)
%
%
% START OF PROOF
% 406652 [] equal(multiply(identity,X),X).
% 406653 [] equal(multiply(inverse(X),X),identity).
% 406654 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 406655 [] -equal(inverse(sk_c11),sk_c10).
% 406696 [?] ?
% 406697 [?] ?
% 406698 [?] ?
% 406699 [?] ?
% 406700 [?] ?
% 406701 [?] ?
% 406702 [?] ?
% 406703 [?] ?
% 406704 [?] ?
% 406705 [?] ?
% 406722 [input:406697,cut:406655] equal(inverse(sk_c6),sk_c8).
% 406723 [para:406722.1.1,406653.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 406725 [input:406698,cut:406655] equal(inverse(sk_c7),sk_c6).
% 406726 [para:406725.1.1,406653.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 406727 [input:406700,cut:406655] equal(inverse(sk_c5),sk_c8).
% 406728 [para:406727.1.1,406653.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 406730 [input:406702,cut:406655] equal(inverse(sk_c4),sk_c10).
% 406731 [para:406730.1.1,406653.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 406732 [input:406704,cut:406655] equal(inverse(sk_c3),sk_c11).
% 406733 [para:406732.1.1,406653.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 406762 [input:406696,cut:406655] equal(multiply(sk_c7,sk_c8),sk_c6).
% 406763 [input:406699,cut:406655] equal(multiply(sk_c8,sk_c10),sk_c11).
% 406765 [input:406701,cut:406655] equal(multiply(sk_c5,sk_c8),sk_c11).
% 406766 [input:406703,cut:406655] equal(multiply(sk_c4,sk_c10),sk_c9).
% 406767 [input:406705,cut:406655] equal(multiply(sk_c3,sk_c11),sk_c10).
% 406787 [para:406723.1.1,406654.1.1.1,demod:406652] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 406788 [para:406726.1.1,406654.1.1.1,demod:406652] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 406789 [para:406728.1.1,406654.1.1.1,demod:406652] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 406791 [para:406731.1.1,406654.1.1.1,demod:406652] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 406792 [para:406733.1.1,406654.1.1.1,demod:406652] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 406824 [para:406765.1.1,406654.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 406842 [para:406726.1.1,406787.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 406843 [para:406842.1.2,406654.1.1.1,demod:406652] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 406847 [para:406762.1.1,406788.1.2.2] equal(sk_c8,multiply(sk_c6,sk_c6)).
% 406850 [para:406847.1.2,406787.1.2.2] equal(sk_c6,multiply(sk_c8,sk_c8)).
% 406856 [para:406765.1.1,406789.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 406862 [para:406766.1.1,406791.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 406868 [para:406767.1.1,406792.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 406870 [para:406843.1.1,406788.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 406871 [para:406723.1.1,406870.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 406872 [para:406728.1.1,406870.1.2.2,demod:406871] equal(sk_c5,sk_c6).
% 406880 [para:406872.1.2,406788.1.2.1,demod:406824,406843] equal(X,multiply(sk_c11,X)).
% 406945 [para:406880.1.2,406792.1.2] equal(X,multiply(sk_c3,X)).
% 406946 [para:406880.1.2,406868.1.2] equal(sk_c11,sk_c10).
% 406952 [para:406946.1.1,406856.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c10)).
% 406953 [para:406946.1.1,406792.1.2.1,demod:406945] equal(X,multiply(sk_c10,X)).
% 406958 [para:406953.1.2,406862.1.2] equal(sk_c10,sk_c9).
% 406969 [para:406958.1.1,406763.1.1.2] equal(multiply(sk_c8,sk_c9),sk_c11).
% 406971 [para:406958.1.1,406868.1.2.2,demod:406880] equal(sk_c11,sk_c9).
% 406974 [para:406971.1.1,406856.1.2.2,demod:406969] equal(sk_c8,sk_c11).
% 406979 [para:406974.1.2,406767.1.1.2,demod:406945] equal(sk_c8,sk_c10).
% 406980 [para:406974.1.2,406856.1.2.2,demod:406850] equal(sk_c8,sk_c6).
% 406982 [para:406974.1.2,406868.1.2.1,demod:406952] equal(sk_c11,sk_c8).
% 407002 [para:406980.1.2,406722.1.1.1] equal(inverse(sk_c8),sk_c8).
% 407008 [para:406982.1.1,406655.1.1.1,demod:407002,cut:406979] 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_c11,sk_c9),sk_c10) | -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c10),sk_c11) | -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 29
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,0,118,0,0,149396,4,1284,153810,5,1501,153810,1,1501,153810,50,1501,153810,40,1501,153873,0,1501,163138,3,1860,163726,4,1952,164571,5,2104,164571,1,2104,164571,50,2104,164571,40,2104,164634,0,2104,166200,3,2410,166215,4,2570,166342,5,2705,166342,1,2705,166342,50,2705,166342,40,2705,166405,0,2705,186353,3,4206,188100,4,4956,189808,1,5706,189808,50,5706,189808,40,5706,189871,0,5706,202157,3,6457,203574,4,6832,205029,1,7207,205029,50,7207,205029,40,7207,205092,0,7207,218660,3,8021,219864,4,8333,221380,5,8708,221381,1,8708,221381,50,8708,221381,40,8708,221444,0,8708,265124,3,12609,266730,4,14560,268260,1,16509,268260,50,16510,268260,40,16510,268323,0,16510,305597,3,19061,306847,4,20336,307760,5,21611,307761,1,21611,307761,50,21612,307761,40,21612,307824,0,21613,338203,3,23114,339302,4,23864,340292,1,24614,340292,50,24615,340292,40,24615,340355,0,24615,353638,3,25373,355317,4,25741,357429,5,26116,357429,1,26116,357429,50,26116,357429,40,26116,357492,0,26116,378778,3,27317,379828,4,27917,380613,1,28517,380613,50,28517,380613,40,28517,380676,0,28517,396332,3,29268,397153,4,29643,397913,5,30018,397914,1,30018,397914,50,30018,397914,40,30018,397914,40,30018,398023,0,30018,402838,50,30035,402838,30,30035,402838,40,30035,402893,0,30035,403032,50,30035,403032,30,30035,403032,40,30035,403087,0,30035,403222,50,30035,403277,0,30040,403443,50,30041,403443,30,30041,403443,40,30041,403498,0,30041,403587,50,30041,403587,30,30041,403587,40,30041,403642,0,30046,403846,50,30048,403901,0,30048,404169,50,30053,404224,0,30058,404500,50,30065,404555,0,30065,404839,50,30074,404894,0,30078,405184,50,30092,405239,0,30092,405537,50,30113,405592,0,30118,405898,50,30155,405953,0,30155,406269,50,30228,406324,0,30228,406650,50,30375,406650,40,30375,406705,0,30375,407007,50,30376,407007,30,30376,407007,40,30376,407062,0,30376,407266,50,30379,407321,0,30383,407589,50,30388,407644,0,30388,407920,50,30395,407975,0,30400,408259,50,30409,408314,0,30409,408604,50,30422,408659,0,30427,408957,50,30448,409012,0,30448,409318,50,30485,409373,0,30490,409689,50,30559,409744,0,30559,410070,50,30697,410070,40,30697,410125,0,30697)
%
%
% START OF PROOF
% 409858 [?] ?
% 410072 [] equal(multiply(identity,X),X).
% 410073 [] equal(multiply(inverse(X),X),identity).
% 410074 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 410075 [] -equal(multiply(sk_c11,sk_c9),sk_c10).
% 410107 [?] ?
% 410108 [?] ?
% 410110 [?] ?
% 410111 [?] ?
% 410190 [input:410107,cut:410075] equal(inverse(sk_c6),sk_c8).
% 410191 [para:410190.1.1,410073.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 410193 [input:410108,cut:410075] equal(inverse(sk_c7),sk_c6).
% 410194 [para:410193.1.1,410073.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 410195 [input:410110,cut:410075] equal(inverse(sk_c5),sk_c8).
% 410196 [para:410195.1.1,410073.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 410228 [input:410111,cut:410075] equal(multiply(sk_c5,sk_c8),sk_c11).
% 410255 [para:410191.1.1,410074.1.1.1,demod:410072] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 410258 [para:410194.1.1,410074.1.1.1,demod:410072] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 410289 [para:410228.1.1,410074.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 410292 [para:410194.1.1,410255.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 410293 [para:410292.1.2,410074.1.1.1,demod:410072] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 410321 [para:410293.1.1,410258.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 410324 [para:410191.1.1,410321.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 410325 [para:410196.1.1,410321.1.2.2,demod:410324] equal(sk_c5,sk_c6).
% 410333 [para:410325.1.2,410258.1.2.1,demod:410289,410293] equal(X,multiply(sk_c11,X)).
% 410336 [para:410333.1.2,410075.1.1,cut:409858] 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: 47292
% derived clauses: 3767383
% kept clauses: 192559
% kept size sum: 227638
% kept mid-nuclei: 85469
% kept new demods: 5292
% forw unit-subs: 959736
% forw double-subs: 2245252
% forw overdouble-subs: 131308
% backward subs: 15987
% fast unit cutoff: 33689
% full unit cutoff: 0
% dbl unit cutoff: 83086
% real runtime : 309.51
% process. runtime: 306.97
% specific non-discr-tree subsumption statistics:
% tried: 32685122
% length fails: 3593613
% strength fails: 11999766
% predlist fails: 2771496
% aux str. fails: 3149610
% by-lit fails: 6442864
% full subs tried: 2477034
% full subs fail: 2392959
%
% ; 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/GRP378-1+eq_r.in")
%
%------------------------------------------------------------------------------