TSTP Solution File: GRP340-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP340-1 : 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 : art01.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 299.2s
% Output : Assurance 299.2s
% 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/GRP340-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 29)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 29)
% (binary-posweight-lex-big-order 30 #f 3 29)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -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(inverse(Y),sk_c10) | -equal(multiply(Y,sk_c9),sk_c10).
% -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11).
% -equal(multiply(sk_c10,sk_c11),sk_c9).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -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(55,40,1,119,0,1,80394,5,1502,80394,1,1502,80394,50,1502,80394,40,1502,80458,0,1502,80850,5,2112,80854,1,2113,80854,50,2113,80854,40,2113,80918,0,2113,81359,5,2714,81360,1,2714,81360,50,2714,81360,40,2714,81424,0,2714,101118,3,4215,102776,4,4965,104445,1,5715,104445,50,5715,104445,40,5715,104509,0,5715,118180,3,6466,119332,4,6841,120553,1,7216,120553,50,7216,120553,40,7216,120617,0,7216,121282,5,8722,121284,1,8722,121284,50,8722,121284,40,8722,121348,0,8722,155836,3,12623,157861,4,14573,160120,1,16523,160120,50,16524,160120,40,16524,160184,0,16524,187609,3,19075,188973,4,20350,190716,5,21625,190717,1,21625,190717,50,21626,190717,40,21626,190781,0,21626,217627,3,23127,218899,4,23877,219861,1,24627,219861,50,24628,219861,40,24628,219925,0,24628,220593,5,26129,220593,1,26129,220593,50,26129,220593,40,26129,220657,0,26129,242908,3,27336,243693,4,27930,244390,1,28530,244390,50,28530,244390,40,28530,244454,0,28531,260629,3,29282,261169,4,29657,261683,1,30032,261683,50,30032,261683,40,30032,261683,40,30032,261792,0,30033)
%
%
% START OF PROOF
% 261684 [] equal(X,X).
% 261685 [] equal(multiply(identity,X),X).
% 261686 [] equal(multiply(inverse(X),X),identity).
% 261687 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 261738 [] -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).
% 261739 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst97,Y).
% 261740 [] -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | $spltprd1($spltcnst98,Y).
% 261741 [] -equal(multiply(X,sk_c10),sk_c11) | $spltprd1($spltcnst99,X).
% 261742 [] -$spltprd1($spltcnst98,X) | -$spltprd1($spltcnst97,X) | -$spltprd1($spltcnst99,X).
% 261743 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 261744 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 261745 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 261746 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 261747 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 261748 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 261753 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c10).
% 261754 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 261755 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 261756 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c2),sk_c10).
% 261757 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 261758 [?] ?
% 261763 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 261764 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 261765 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 261766 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 261767 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 261768 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 261773 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c11).
% 261774 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 261775 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 261776 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 261777 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 261778 [?] ?
% 261783 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 261784 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c6),sk_c8).
% 261785 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 261786 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 261787 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 261788 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 261859 [hyper:261740,261757,binarycut:261758] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst98,sk_c8).
% 261947 [hyper:261740,261777,binarycut:261778] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst98,sk_c8).
% 262079 [hyper:261739,261753,261754,261755] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst97,sk_c8).
% 262126 [hyper:261741,261756] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst99,sk_c8).
% 262143 [hyper:261742,262126,262079,261859] equal(inverse(sk_c2),sk_c10).
% 262156 [para:262143.1.1,261686.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 262351 [hyper:261739,261773,261774,261775] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst97,sk_c8).
% 262438 [hyper:261741,261776] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst99,sk_c8).
% 262476 [hyper:261742,262438,262351,261947] equal(inverse(sk_c1),sk_c11).
% 262510 [para:262476.1.1,261686.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 262805 [hyper:261738,261748,261746,261747,261744,261743,261745] equal(multiply(sk_c2,sk_c9),sk_c10).
% 262995 [hyper:261738,261768,261766,261767,261764,261763,261765] equal(multiply(sk_c1,sk_c10),sk_c11).
% 263083 [hyper:261738,261788,261786,261787,261784,261783,261785] equal(multiply(sk_c10,sk_c11),sk_c9).
% 263091 [para:261686.1.1,261687.1.1.1,demod:261685] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 263092 [para:262156.1.1,261687.1.1.1,demod:261685] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 263093 [para:262510.1.1,261687.1.1.1,demod:261685] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 263096 [para:263083.1.1,261687.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c10,multiply(sk_c11,X))).
% 263112 [para:262805.1.1,263092.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 263131 [para:262995.1.1,263093.1.2.2] equal(sk_c10,multiply(sk_c11,sk_c11)).
% 263142 [para:262156.1.1,263091.1.2.2] equal(sk_c2,multiply(inverse(sk_c10),identity)).
% 263152 [para:263083.1.1,263091.1.2.2] equal(sk_c11,multiply(inverse(sk_c10),sk_c9)).
% 263154 [para:263112.1.2,263091.1.2.2,demod:263152] equal(sk_c10,sk_c11).
% 263158 [para:263154.1.1,263083.1.1.1,demod:263131] equal(sk_c10,sk_c9).
% 263160 [para:263154.1.1,263112.1.2.1] equal(sk_c9,multiply(sk_c11,sk_c10)).
% 263163 [para:263158.1.1,263083.1.1.1] equal(multiply(sk_c9,sk_c11),sk_c9).
% 263165 [para:263158.1.1,263112.1.2.1] equal(sk_c9,multiply(sk_c9,sk_c10)).
% 263166 [?] ?
% 263167 [para:263158.1.1,263154.1.1] equal(sk_c9,sk_c11).
% 263316 [para:263163.1.1,263091.1.2.2,demod:261686] equal(sk_c11,identity).
% 263318 [para:263316.1.1,262510.1.1.1,demod:261685] equal(sk_c1,identity).
% 263321 [para:263316.1.1,263131.1.2.2] equal(sk_c10,multiply(sk_c11,identity)).
% 263328 [para:263318.1.1,262476.1.1.1] equal(inverse(identity),sk_c11).
% 263329 [para:263318.1.1,262510.1.1.2,demod:263321] equal(sk_c10,identity).
% 263758 [para:263329.1.1,263142.1.2.1.1,demod:263321,263328] equal(sk_c2,sk_c10).
% 263760 [para:263758.1.2,263158.1.1] equal(sk_c2,sk_c9).
% 263839 [para:263760.1.1,262143.1.1.1] equal(inverse(sk_c9),sk_c10).
% 263960 [hyper:261738,263839,263096,demod:263112,263165,cut:263167,cut:263167,demod:263839,263166,263160,cut:261684,cut:263158] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -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 29
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(55,40,1,119,0,1,80394,5,1502,80394,1,1502,80394,50,1502,80394,40,1502,80458,0,1502,80850,5,2112,80854,1,2113,80854,50,2113,80854,40,2113,80918,0,2113,81359,5,2714,81360,1,2714,81360,50,2714,81360,40,2714,81424,0,2714,101118,3,4215,102776,4,4965,104445,1,5715,104445,50,5715,104445,40,5715,104509,0,5715,118180,3,6466,119332,4,6841,120553,1,7216,120553,50,7216,120553,40,7216,120617,0,7216,121282,5,8722,121284,1,8722,121284,50,8722,121284,40,8722,121348,0,8722,155836,3,12623,157861,4,14573,160120,1,16523,160120,50,16524,160120,40,16524,160184,0,16524,187609,3,19075,188973,4,20350,190716,5,21625,190717,1,21625,190717,50,21626,190717,40,21626,190781,0,21626,217627,3,23127,218899,4,23877,219861,1,24627,219861,50,24628,219861,40,24628,219925,0,24628,220593,5,26129,220593,1,26129,220593,50,26129,220593,40,26129,220657,0,26129,242908,3,27336,243693,4,27930,244390,1,28530,244390,50,28530,244390,40,28530,244454,0,28531,260629,3,29282,261169,4,29657,261683,1,30032,261683,50,30032,261683,40,30032,261683,40,30032,261792,0,30033,263959,50,30041,263959,30,30041,263959,40,30041,264014,0,30041)
%
%
% START OF PROOF
% 263961 [] equal(multiply(identity,X),X).
% 263962 [] equal(multiply(inverse(X),X),identity).
% 263963 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 263964 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 263971 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 263972 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 263981 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 263982 [?] ?
% 263991 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 263992 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 264001 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c4),sk_c10).
% 264002 [?] ?
% 264011 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c4),sk_c10).
% 264012 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 264026 [hyper:263964,263981,binarycut:263982] equal(inverse(sk_c2),sk_c10).
% 264029 [para:264026.1.1,263962.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 264037 [hyper:263964,264001,binarycut:264002] equal(inverse(sk_c1),sk_c11).
% 264038 [para:264037.1.1,263962.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 264064 [hyper:263964,263972,263971] equal(multiply(sk_c2,sk_c9),sk_c10).
% 264070 [hyper:263964,263992,263991] equal(multiply(sk_c1,sk_c10),sk_c11).
% 264076 [hyper:263964,264012,264011] equal(multiply(sk_c10,sk_c11),sk_c9).
% 264077 [para:263962.1.1,263963.1.1.1,demod:263961] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 264078 [para:264029.1.1,263963.1.1.1,demod:263961] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 264079 [para:264038.1.1,263963.1.1.1,demod:263961] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 264080 [para:264064.1.1,263963.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c2,multiply(sk_c9,X))).
% 264081 [para:264070.1.1,263963.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c1,multiply(sk_c10,X))).
% 264082 [para:264076.1.1,263963.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c10,multiply(sk_c11,X))).
% 264083 [para:264064.1.1,264078.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 264085 [para:264070.1.1,264079.1.2.2] equal(sk_c10,multiply(sk_c11,sk_c11)).
% 264088 [para:264038.1.1,264077.1.2.2] equal(sk_c1,multiply(inverse(sk_c11),identity)).
% 264089 [para:264076.1.1,264077.1.2.2] equal(sk_c11,multiply(inverse(sk_c10),sk_c9)).
% 264091 [para:264083.1.2,264077.1.2.2,demod:264089] equal(sk_c10,sk_c11).
% 264093 [para:264091.1.1,264029.1.1.1] equal(multiply(sk_c11,sk_c2),identity).
% 264095 [para:264091.1.1,264076.1.1.1,demod:264085] equal(sk_c10,sk_c9).
% 264096 [para:264091.1.1,264078.1.2.1] equal(X,multiply(sk_c11,multiply(sk_c2,X))).
% 264098 [para:264095.1.1,264029.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 264110 [para:264093.1.1,264077.1.2.2,demod:264088] equal(sk_c2,sk_c1).
% 264114 [para:264110.1.1,264080.1.2.1] equal(multiply(sk_c10,X),multiply(sk_c1,multiply(sk_c9,X))).
% 264119 [para:264078.1.2,264081.1.2.2,demod:264096] equal(X,multiply(sk_c1,X)).
% 264120 [para:264095.1.1,264081.1.2.2.1,demod:264114] equal(multiply(sk_c11,X),multiply(sk_c10,X)).
% 264122 [para:264079.1.2,264082.1.2.2,demod:264120,264119] equal(multiply(sk_c9,X),multiply(sk_c11,X)).
% 264124 [para:264119.1.2,264079.1.2.2,demod:264122] equal(X,multiply(sk_c9,X)).
% 264125 [para:264124.1.2,264077.1.2.2] equal(X,multiply(inverse(sk_c9),X)).
% 264127 [para:264098.1.1,264077.1.2.2,demod:264125] equal(sk_c2,identity).
% 264128 [para:264127.1.1,264026.1.1.1] equal(inverse(identity),sk_c10).
% 264131 [hyper:263964,264128,demod:263961,cut:264095] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -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 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(55,40,1,119,0,1,80394,5,1502,80394,1,1502,80394,50,1502,80394,40,1502,80458,0,1502,80850,5,2112,80854,1,2113,80854,50,2113,80854,40,2113,80918,0,2113,81359,5,2714,81360,1,2714,81360,50,2714,81360,40,2714,81424,0,2714,101118,3,4215,102776,4,4965,104445,1,5715,104445,50,5715,104445,40,5715,104509,0,5715,118180,3,6466,119332,4,6841,120553,1,7216,120553,50,7216,120553,40,7216,120617,0,7216,121282,5,8722,121284,1,8722,121284,50,8722,121284,40,8722,121348,0,8722,155836,3,12623,157861,4,14573,160120,1,16523,160120,50,16524,160120,40,16524,160184,0,16524,187609,3,19075,188973,4,20350,190716,5,21625,190717,1,21625,190717,50,21626,190717,40,21626,190781,0,21626,217627,3,23127,218899,4,23877,219861,1,24627,219861,50,24628,219861,40,24628,219925,0,24628,220593,5,26129,220593,1,26129,220593,50,26129,220593,40,26129,220657,0,26129,242908,3,27336,243693,4,27930,244390,1,28530,244390,50,28530,244390,40,28530,244454,0,28531,260629,3,29282,261169,4,29657,261683,1,30032,261683,50,30032,261683,40,30032,261683,40,30032,261792,0,30033,263959,50,30041,263959,30,30041,263959,40,30041,264014,0,30041,264130,50,30041,264130,30,30041,264130,40,30041,264185,0,30041,264325,50,30042,264380,0,30044)
%
%
% START OF PROOF
% 264327 [] equal(multiply(identity,X),X).
% 264328 [] equal(multiply(inverse(X),X),identity).
% 264329 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 264330 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 264339 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 264340 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 264349 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 264350 [?] ?
% 264359 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 264360 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 264369 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 264370 [?] ?
% 264379 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(inverse(sk_c3),sk_c11).
% 264380 [] equal(multiply(sk_c10,sk_c11),sk_c9) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 264388 [hyper:264330,264349,binarycut:264350] equal(inverse(sk_c2),sk_c10).
% 264389 [para:264388.1.1,264328.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 264406 [hyper:264330,264369,binarycut:264370] equal(inverse(sk_c1),sk_c11).
% 264410 [para:264406.1.1,264328.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 264437 [hyper:264330,264340,264339] equal(multiply(sk_c2,sk_c9),sk_c10).
% 264444 [hyper:264330,264360,264359] equal(multiply(sk_c1,sk_c10),sk_c11).
% 264451 [hyper:264330,264380,264379] equal(multiply(sk_c10,sk_c11),sk_c9).
% 264452 [para:264328.1.1,264329.1.1.1,demod:264327] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 264453 [para:264389.1.1,264329.1.1.1,demod:264327] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 264454 [para:264410.1.1,264329.1.1.1,demod:264327] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 264455 [para:264437.1.1,264329.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c2,multiply(sk_c9,X))).
% 264456 [para:264444.1.1,264329.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c1,multiply(sk_c10,X))).
% 264457 [para:264451.1.1,264329.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c10,multiply(sk_c11,X))).
% 264458 [para:264437.1.1,264453.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 264460 [para:264444.1.1,264454.1.2.2] equal(sk_c10,multiply(sk_c11,sk_c11)).
% 264462 [para:264328.1.1,264452.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 264463 [para:264389.1.1,264452.1.2.2] equal(sk_c2,multiply(inverse(sk_c10),identity)).
% 264464 [para:264410.1.1,264452.1.2.2] equal(sk_c1,multiply(inverse(sk_c11),identity)).
% 264465 [para:264451.1.1,264452.1.2.2] equal(sk_c11,multiply(inverse(sk_c10),sk_c9)).
% 264466 [para:264329.1.1,264452.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 264468 [para:264458.1.2,264452.1.2.2,demod:264465] equal(sk_c10,sk_c11).
% 264470 [para:264452.1.2,264452.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 264471 [para:264468.1.1,264389.1.1.1] equal(multiply(sk_c11,sk_c2),identity).
% 264472 [para:264468.1.1,264444.1.1.2] equal(multiply(sk_c1,sk_c11),sk_c11).
% 264473 [para:264468.1.1,264451.1.1.1,demod:264460] equal(sk_c10,sk_c9).
% 264474 [para:264468.1.1,264453.1.2.1] equal(X,multiply(sk_c11,multiply(sk_c2,X))).
% 264488 [para:264471.1.1,264452.1.2.2,demod:264464] equal(sk_c2,sk_c1).
% 264492 [para:264488.1.1,264455.1.2.1] equal(multiply(sk_c10,X),multiply(sk_c1,multiply(sk_c9,X))).
% 264497 [para:264453.1.2,264456.1.2.2,demod:264474] equal(X,multiply(sk_c1,X)).
% 264498 [para:264473.1.1,264456.1.2.2.1,demod:264492] equal(multiply(sk_c11,X),multiply(sk_c10,X)).
% 264500 [para:264454.1.2,264457.1.2.2,demod:264498,264497] equal(multiply(sk_c9,X),multiply(sk_c11,X)).
% 264502 [para:264497.1.2,264454.1.2.2,demod:264500] equal(X,multiply(sk_c9,X)).
% 264503 [para:264502.1.2,264452.1.2.2] equal(X,multiply(inverse(sk_c9),X)).
% 264504 [para:264502.1.2,264455.1.2.2,demod:264502,264500,264498] equal(X,multiply(sk_c2,X)).
% 264511 [para:264503.1.2,264328.1.1] equal(sk_c9,identity).
% 264517 [para:264511.1.1,264465.1.2.2,demod:264463] equal(sk_c11,sk_c2).
% 264520 [para:264517.1.1,264472.1.1.2,demod:264497] equal(sk_c2,sk_c11).
% 264555 [para:264470.1.2,264328.1.1] equal(multiply(X,inverse(X)),identity).
% 264557 [para:264470.1.2,264462.1.2] equal(X,multiply(X,identity)).
% 264558 [para:264557.1.2,264462.1.2] equal(X,inverse(inverse(X))).
% 264559 [para:264557.1.2,264463.1.2] equal(sk_c2,inverse(sk_c10)).
% 264566 [para:264555.1.1,264466.1.2.2.2,demod:264557] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 264569 [para:264453.1.2,264566.1.2.1.1,demod:264504] equal(inverse(X),multiply(inverse(X),sk_c10)).
% 264578 [para:264569.1.2,264470.1.2,demod:264558] equal(multiply(X,sk_c10),X).
% 264579 [para:264468.1.1,264578.1.1.2] equal(multiply(X,sk_c11),X).
% 264583 [hyper:264330,264579,demod:264559,cut:264520] 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(multiply(sk_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -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(Y),sk_c10) | -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 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(55,40,1,119,0,1,80394,5,1502,80394,1,1502,80394,50,1502,80394,40,1502,80458,0,1502,80850,5,2112,80854,1,2113,80854,50,2113,80854,40,2113,80918,0,2113,81359,5,2714,81360,1,2714,81360,50,2714,81360,40,2714,81424,0,2714,101118,3,4215,102776,4,4965,104445,1,5715,104445,50,5715,104445,40,5715,104509,0,5715,118180,3,6466,119332,4,6841,120553,1,7216,120553,50,7216,120553,40,7216,120617,0,7216,121282,5,8722,121284,1,8722,121284,50,8722,121284,40,8722,121348,0,8722,155836,3,12623,157861,4,14573,160120,1,16523,160120,50,16524,160120,40,16524,160184,0,16524,187609,3,19075,188973,4,20350,190716,5,21625,190717,1,21625,190717,50,21626,190717,40,21626,190781,0,21626,217627,3,23127,218899,4,23877,219861,1,24627,219861,50,24628,219861,40,24628,219925,0,24628,220593,5,26129,220593,1,26129,220593,50,26129,220593,40,26129,220657,0,26129,242908,3,27336,243693,4,27930,244390,1,28530,244390,50,28530,244390,40,28530,244454,0,28531,260629,3,29282,261169,4,29657,261683,1,30032,261683,50,30032,261683,40,30032,261683,40,30032,261792,0,30033,263959,50,30041,263959,30,30041,263959,40,30041,264014,0,30041,264130,50,30041,264130,30,30041,264130,40,30041,264185,0,30041,264325,50,30042,264380,0,30044,264582,50,30045,264582,30,30045,264582,40,30045,264637,0,30045,264832,50,30047,264887,0,30049)
%
%
% START OF PROOF
% 264834 [] equal(multiply(identity,X),X).
% 264835 [] equal(multiply(inverse(X),X),identity).
% 264836 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 264837 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c10).
% 264838 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 264839 [?] ?
% 264840 [?] ?
% 264841 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c8,sk_c10),sk_c11).
% 264842 [?] ?
% 264843 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 264844 [?] ?
% 264845 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c10),sk_c9).
% 264846 [?] ?
% 264847 [] equal(multiply(sk_c2,sk_c9),sk_c10) | equal(multiply(sk_c3,sk_c11),sk_c10).
% 264848 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c10).
% 264849 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 264850 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 264851 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c2),sk_c10).
% 264852 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 264853 [] equal(multiply(sk_c5,sk_c8),sk_c11) | equal(inverse(sk_c2),sk_c10).
% 264854 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 264855 [] equal(multiply(sk_c4,sk_c10),sk_c9) | equal(inverse(sk_c2),sk_c10).
% 264856 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c3),sk_c11).
% 264857 [] equal(multiply(sk_c3,sk_c11),sk_c10) | equal(inverse(sk_c2),sk_c10).
% 264890 [hyper:264837,264849,binarycut:264839] equal(inverse(sk_c6),sk_c8).
% 264891 [para:264890.1.1,264835.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 264895 [hyper:264837,264850,binarycut:264840] equal(inverse(sk_c7),sk_c6).
% 264896 [para:264895.1.1,264835.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 264899 [hyper:264837,264852,binarycut:264842] equal(inverse(sk_c5),sk_c8).
% 264903 [para:264899.1.1,264835.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 264906 [hyper:264837,264854,binarycut:264844] equal(inverse(sk_c4),sk_c10).
% 264913 [para:264906.1.1,264835.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 264917 [hyper:264837,264856,binarycut:264846] equal(inverse(sk_c3),sk_c11).
% 264918 [para:264917.1.1,264835.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 264924 [hyper:264837,264848,binarycut:264838] equal(multiply(sk_c7,sk_c8),sk_c6).
% 264927 [hyper:264837,264851,binarycut:264841] equal(multiply(sk_c8,sk_c10),sk_c11).
% 264933 [hyper:264837,264853,binarycut:264843] equal(multiply(sk_c5,sk_c8),sk_c11).
% 264936 [hyper:264837,264855,binarycut:264845] equal(multiply(sk_c4,sk_c10),sk_c9).
% 264942 [hyper:264837,264857,binarycut:264847] equal(multiply(sk_c3,sk_c11),sk_c10).
% 264943 [para:264835.1.1,264836.1.1.1,demod:264834] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 264944 [para:264891.1.1,264836.1.1.1,demod:264834] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 264945 [para:264896.1.1,264836.1.1.1,demod:264834] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 264946 [para:264903.1.1,264836.1.1.1,demod:264834] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 264948 [para:264918.1.1,264836.1.1.1,demod:264834] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 264949 [para:264924.1.1,264836.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c8,X))).
% 264950 [para:264927.1.1,264836.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c8,multiply(sk_c10,X))).
% 264951 [para:264933.1.1,264836.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 264954 [para:264896.1.1,264944.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 264956 [para:264835.1.1,264943.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 264957 [para:264891.1.1,264943.1.2.2] equal(sk_c6,multiply(inverse(sk_c8),identity)).
% 264958 [para:264903.1.1,264943.1.2.2,demod:264957] equal(sk_c5,sk_c6).
% 264959 [para:264913.1.1,264943.1.2.2] equal(sk_c4,multiply(inverse(sk_c10),identity)).
% 264963 [para:264933.1.1,264943.1.2.2,demod:264899] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 264964 [para:264936.1.1,264943.1.2.2,demod:264906] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 264966 [para:264836.1.1,264943.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 264967 [para:264944.1.2,264943.1.2.2] equal(multiply(sk_c6,X),multiply(inverse(sk_c8),X)).
% 264968 [para:264943.1.2,264943.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 264970 [para:264954.1.2,264836.1.1.1,demod:264834] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 264980 [para:264958.1.2,264945.1.2.1,demod:264951,264970] equal(X,multiply(sk_c11,X)).
% 264981 [?] ?
% 264982 [para:264946.1.2,264943.1.2.2,demod:264967] equal(multiply(sk_c5,X),multiply(sk_c6,X)).
% 264983 [para:264980.1.2,264918.1.1] equal(sk_c3,identity).
% 264984 [para:264980.1.2,264943.1.2.2] equal(X,multiply(inverse(sk_c11),X)).
% 264986 [para:264983.1.1,264942.1.1.1,demod:264834] equal(sk_c11,sk_c10).
% 264987 [para:264986.1.2,264913.1.1.1,demod:264980] equal(sk_c4,identity).
% 264988 [para:264986.1.2,264927.1.1.2,demod:264963] equal(sk_c8,sk_c11).
% 264990 [para:264986.1.2,264964.1.2.1,demod:264980] equal(sk_c10,sk_c9).
% 264993 [para:264987.1.1,264913.1.1.2,demod:264981] equal(sk_c10,identity).
% 264998 [para:264988.1.2,264980.1.2.1] equal(X,multiply(sk_c8,X)).
% 265000 [para:264990.1.1,264927.1.1.2,demod:264998] equal(sk_c9,sk_c11).
% 265004 [para:264993.1.1,264927.1.1.2,demod:264954] equal(sk_c7,sk_c11).
% 265013 [para:264948.1.2,264943.1.2.2,demod:264984] equal(multiply(sk_c3,X),X).
% 265015 [para:265000.1.2,264963.1.2.2,demod:264998] equal(sk_c8,sk_c9).
% 265018 [para:265004.1.2,264963.1.2.2,demod:264998] equal(sk_c8,sk_c7).
% 265024 [?] ?
% 265025 [para:264944.1.2,264949.1.2.2,demod:264998,264970,265024,264982] equal(multiply(sk_c5,X),X).
% 265036 [para:264913.1.1,264950.1.2.2,demod:264954,264980] equal(sk_c4,sk_c7).
% 265050 [para:265036.1.2,265018.1.2] equal(sk_c8,sk_c4).
% 265062 [para:265050.1.1,264933.1.1.2,demod:265025] equal(sk_c4,sk_c11).
% 265067 [para:265062.1.2,264942.1.1.2,demod:265013] equal(sk_c4,sk_c10).
% 265115 [para:264968.1.2,264835.1.1] equal(multiply(X,inverse(X)),identity).
% 265117 [para:264968.1.2,264956.1.2] equal(X,multiply(X,identity)).
% 265127 [para:265117.1.2,264956.1.2] equal(X,inverse(inverse(X))).
% 265128 [para:265117.1.2,264959.1.2] equal(sk_c4,inverse(sk_c10)).
% 265132 [para:265115.1.1,264966.1.2.2.2,demod:265117] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 265134 [para:264944.1.2,265132.1.2.1.1,demod:265025,264982] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 265149 [para:265134.1.2,264968.1.2,demod:265127] equal(multiply(X,sk_c8),X).
% 265151 [para:265015.1.1,265149.1.1.2] equal(multiply(X,sk_c9),X).
% 265156 [hyper:264837,265151,demod:265128,cut:265067] 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 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -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(X),sk_c11) | -equal(multiply(X,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(55,40,1,119,0,1,80394,5,1502,80394,1,1502,80394,50,1502,80394,40,1502,80458,0,1502,80850,5,2112,80854,1,2113,80854,50,2113,80854,40,2113,80918,0,2113,81359,5,2714,81360,1,2714,81360,50,2714,81360,40,2714,81424,0,2714,101118,3,4215,102776,4,4965,104445,1,5715,104445,50,5715,104445,40,5715,104509,0,5715,118180,3,6466,119332,4,6841,120553,1,7216,120553,50,7216,120553,40,7216,120617,0,7216,121282,5,8722,121284,1,8722,121284,50,8722,121284,40,8722,121348,0,8722,155836,3,12623,157861,4,14573,160120,1,16523,160120,50,16524,160120,40,16524,160184,0,16524,187609,3,19075,188973,4,20350,190716,5,21625,190717,1,21625,190717,50,21626,190717,40,21626,190781,0,21626,217627,3,23127,218899,4,23877,219861,1,24627,219861,50,24628,219861,40,24628,219925,0,24628,220593,5,26129,220593,1,26129,220593,50,26129,220593,40,26129,220657,0,26129,242908,3,27336,243693,4,27930,244390,1,28530,244390,50,28530,244390,40,28530,244454,0,28531,260629,3,29282,261169,4,29657,261683,1,30032,261683,50,30032,261683,40,30032,261683,40,30032,261792,0,30033,263959,50,30041,263959,30,30041,263959,40,30041,264014,0,30041,264130,50,30041,264130,30,30041,264130,40,30041,264185,0,30041,264325,50,30042,264380,0,30044,264582,50,30045,264582,30,30045,264582,40,30045,264637,0,30045,264832,50,30047,264887,0,30049,265155,50,30052,265155,30,30052,265155,40,30052,265210,0,30052)
%
%
% START OF PROOF
% 265157 [] equal(multiply(identity,X),X).
% 265158 [] equal(multiply(inverse(X),X),identity).
% 265159 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 265160 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c11).
% 265181 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 265182 [?] ?
% 265183 [?] ?
% 265184 [?] ?
% 265185 [?] ?
% 265186 [] equal(multiply(sk_c1,sk_c10),sk_c11) | equal(multiply(sk_c5,sk_c8),sk_c11).
% 265189 [?] ?
% 265190 [?] ?
% 265191 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c11).
% 265192 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c8).
% 265193 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c6).
% 265194 [] equal(multiply(sk_c8,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 265195 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c5),sk_c8).
% 265196 [] equal(multiply(sk_c5,sk_c8),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 265199 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c3),sk_c11).
% 265200 [] equal(multiply(sk_c3,sk_c11),sk_c10) | equal(inverse(sk_c1),sk_c11).
% 265221 [hyper:265160,265192,binarycut:265182] equal(inverse(sk_c6),sk_c8).
% 265222 [para:265221.1.1,265158.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 265226 [hyper:265160,265193,binarycut:265183] equal(inverse(sk_c7),sk_c6).
% 265227 [para:265226.1.1,265158.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 265233 [hyper:265160,265195,binarycut:265185] equal(inverse(sk_c5),sk_c8).
% 265234 [para:265233.1.1,265158.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 265242 [hyper:265160,265199,binarycut:265189] equal(inverse(sk_c3),sk_c11).
% 265247 [para:265242.1.1,265158.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 265262 [hyper:265160,265191,binarycut:265181] equal(multiply(sk_c7,sk_c8),sk_c6).
% 265266 [hyper:265160,265194,binarycut:265184] equal(multiply(sk_c8,sk_c10),sk_c11).
% 265275 [hyper:265160,265196,binarycut:265186] equal(multiply(sk_c5,sk_c8),sk_c11).
% 265281 [hyper:265160,265200,binarycut:265190] equal(multiply(sk_c3,sk_c11),sk_c10).
% 265282 [para:265158.1.1,265159.1.1.1,demod:265157] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 265283 [para:265222.1.1,265159.1.1.1,demod:265157] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 265284 [para:265227.1.1,265159.1.1.1,demod:265157] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 265290 [para:265275.1.1,265159.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 265293 [para:265227.1.1,265283.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 265295 [para:265222.1.1,265282.1.2.2] equal(sk_c6,multiply(inverse(sk_c8),identity)).
% 265296 [para:265234.1.1,265282.1.2.2,demod:265295] equal(sk_c5,sk_c6).
% 265299 [para:265262.1.1,265282.1.2.2,demod:265226] equal(sk_c8,multiply(sk_c6,sk_c6)).
% 265301 [para:265275.1.1,265282.1.2.2,demod:265233] equal(sk_c8,multiply(sk_c8,sk_c11)).
% 265306 [para:265293.1.2,265159.1.1.1,demod:265157] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 265308 [para:265299.1.2,265283.1.2.2] equal(sk_c6,multiply(sk_c8,sk_c8)).
% 265315 [para:265296.1.2,265284.1.2.1,demod:265290,265306] equal(X,multiply(sk_c11,X)).
% 265318 [para:265315.1.2,265247.1.1] equal(sk_c3,identity).
% 265320 [para:265318.1.1,265242.1.1.1] equal(inverse(identity),sk_c11).
% 265321 [para:265318.1.1,265281.1.1.1,demod:265157] equal(sk_c11,sk_c10).
% 265323 [para:265321.1.2,265266.1.1.2,demod:265301] equal(sk_c8,sk_c11).
% 265332 [para:265323.1.2,265301.1.2.2,demod:265308] equal(sk_c8,sk_c6).
% 265347 [para:265332.1.2,265299.1.2.1,demod:265222] equal(sk_c8,identity).
% 265368 [para:265347.1.1,265266.1.1.1,demod:265157] equal(sk_c10,sk_c11).
% 265422 [hyper:265160,265320,demod:265157,cut:265368] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 29
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c10,sk_c11),sk_c9) | -equal(inverse(X),sk_c11) | -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(Y),sk_c10) | -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_c11),sk_c9).
% 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 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(55,40,1,119,0,1,80394,5,1502,80394,1,1502,80394,50,1502,80394,40,1502,80458,0,1502,80850,5,2112,80854,1,2113,80854,50,2113,80854,40,2113,80918,0,2113,81359,5,2714,81360,1,2714,81360,50,2714,81360,40,2714,81424,0,2714,101118,3,4215,102776,4,4965,104445,1,5715,104445,50,5715,104445,40,5715,104509,0,5715,118180,3,6466,119332,4,6841,120553,1,7216,120553,50,7216,120553,40,7216,120617,0,7216,121282,5,8722,121284,1,8722,121284,50,8722,121284,40,8722,121348,0,8722,155836,3,12623,157861,4,14573,160120,1,16523,160120,50,16524,160120,40,16524,160184,0,16524,187609,3,19075,188973,4,20350,190716,5,21625,190717,1,21625,190717,50,21626,190717,40,21626,190781,0,21626,217627,3,23127,218899,4,23877,219861,1,24627,219861,50,24628,219861,40,24628,219925,0,24628,220593,5,26129,220593,1,26129,220593,50,26129,220593,40,26129,220657,0,26129,242908,3,27336,243693,4,27930,244390,1,28530,244390,50,28530,244390,40,28530,244454,0,28531,260629,3,29282,261169,4,29657,261683,1,30032,261683,50,30032,261683,40,30032,261683,40,30032,261792,0,30033,263959,50,30041,263959,30,30041,263959,40,30041,264014,0,30041,264130,50,30041,264130,30,30041,264130,40,30041,264185,0,30041,264325,50,30042,264380,0,30044,264582,50,30045,264582,30,30045,264582,40,30045,264637,0,30045,264832,50,30047,264887,0,30049,265155,50,30052,265155,30,30052,265155,40,30052,265210,0,30052,265421,50,30053,265421,30,30053,265421,40,30053,265476,0,30055,265683,50,30057,265738,0,30057,266006,50,30063,266061,0,30064,266340,50,30072,266395,0,30072,266694,50,30085,266749,0,30085,267054,50,30101,267109,0,30101,267422,50,30129,267477,0,30129,267799,50,30175,267854,0,30175,268186,50,30258,268186,40,30258,268241,0,30258)
%
%
% START OF PROOF
% 267967 [?] ?
% 268188 [] equal(multiply(identity,X),X).
% 268189 [] equal(multiply(inverse(X),X),identity).
% 268190 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 268191 [] -equal(multiply(sk_c10,sk_c11),sk_c9).
% 268233 [?] ?
% 268234 [?] ?
% 268236 [?] ?
% 268237 [?] ?
% 268240 [?] ?
% 268241 [?] ?
% 268318 [input:268233,cut:268191] equal(inverse(sk_c6),sk_c8).
% 268319 [para:268318.1.1,268189.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 268321 [input:268234,cut:268191] equal(inverse(sk_c7),sk_c6).
% 268322 [para:268321.1.1,268189.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 268323 [input:268236,cut:268191] equal(inverse(sk_c5),sk_c8).
% 268324 [para:268323.1.1,268189.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 268328 [input:268240,cut:268191] equal(inverse(sk_c3),sk_c11).
% 268329 [para:268328.1.1,268189.1.1.1] equal(multiply(sk_c11,sk_c3),identity).
% 268344 [input:268237,cut:268191] equal(multiply(sk_c5,sk_c8),sk_c11).
% 268346 [input:268241,cut:268191] equal(multiply(sk_c3,sk_c11),sk_c10).
% 268382 [para:268319.1.1,268190.1.1.1,demod:268188] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 268383 [para:268322.1.1,268190.1.1.1,demod:268188] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 268388 [para:268329.1.1,268190.1.1.1,demod:268188] equal(X,multiply(sk_c11,multiply(sk_c3,X))).
% 268405 [para:268344.1.1,268190.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c5,multiply(sk_c8,X))).
% 268408 [para:268322.1.1,268382.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 268409 [para:268408.1.2,268190.1.1.1,demod:268188] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 268435 [para:268346.1.1,268388.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 268437 [para:268409.1.1,268383.1.2.2] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 268442 [para:268319.1.1,268437.1.2.2] equal(sk_c6,multiply(sk_c6,identity)).
% 268443 [para:268324.1.1,268437.1.2.2,demod:268442] equal(sk_c5,sk_c6).
% 268449 [para:268443.1.2,268383.1.2.1,demod:268405,268409] equal(X,multiply(sk_c11,X)).
% 268458 [para:268449.1.2,268435.1.2] equal(sk_c11,sk_c10).
% 268465 [para:268458.1.2,268191.1.1.1,demod:268449,cut:267967] 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: 38724
% derived clauses: 2844953
% kept clauses: 140953
% kept size sum: 846871
% kept mid-nuclei: 72251
% kept new demods: 3095
% forw unit-subs: 473354
% forw double-subs: 1931867
% forw overdouble-subs: 126214
% backward subs: 17682
% fast unit cutoff: 22090
% full unit cutoff: 0
% dbl unit cutoff: 16180
% real runtime : 303.71
% process. runtime: 302.58
% specific non-discr-tree subsumption statistics:
% tried: 54845874
% length fails: 10803321
% strength fails: 14882167
% predlist fails: 216784
% aux str. fails: 9415575
% by-lit fails: 7166584
% full subs tried: 5971373
% full subs fail: 5906715
%
% ; 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/GRP340-1+eq_r.in")
%
%------------------------------------------------------------------------------