TSTP Solution File: GRP220-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP220-1 : 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 : art07.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 298.1s
% Output : Assurance 298.1s
% 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/GRP220-1+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 33)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 33)
% (binary-posweight-lex-big-order 30 #f 3 33)
% (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(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(sk_c12,U),sk_c11) | -equal(multiply(V,sk_c12),U) | -equal(inverse(V),sk_c12) | -equal(inverse(sk_c12),sk_c11) | -equal(inverse(W),sk_c12) | -equal(multiply(W,sk_c11),sk_c12) | -equal(multiply(X1,X2),sk_c12) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c12) | -equal(inverse(X3),X4) | -equal(inverse(X4),X2) | -equal(multiply(X3,X2),X4).
% was split for some strategies as:
% -equal(multiply(X1,X2),sk_c12) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c12) | -equal(inverse(X4),X2) | -equal(inverse(X3),X4) | -equal(multiply(X3,X2),X4).
% -equal(inverse(W),sk_c12) | -equal(multiply(W,sk_c11),sk_c12).
% -equal(multiply(sk_c12,U),sk_c11) | -equal(multiply(V,sk_c12),U) | -equal(inverse(V),sk_c12).
% -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11).
% -equal(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12).
% -equal(inverse(sk_c12),sk_c11).
%
% 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(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(sk_c12,U),sk_c11) | -equal(multiply(V,sk_c12),U) | -equal(inverse(V),sk_c12) | -equal(inverse(sk_c12),sk_c11) | -equal(inverse(W),sk_c12) | -equal(multiply(W,sk_c11),sk_c12) | -equal(multiply(X1,X2),sk_c12) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c12) | -equal(inverse(X3),X4) | -equal(inverse(X4),X2) | -equal(multiply(X3,X2),X4).
% Split part used next: -equal(multiply(X1,X2),sk_c12) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c12) | -equal(inverse(X4),X2) | -equal(inverse(X3),X4) | -equal(multiply(X3,X2),X4).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(77,40,1,163,0,2,200699,5,1503,200700,1,1503,200700,50,1503,200700,40,1503,200786,0,1503,201260,5,2110,201269,1,2111,201269,50,2111,201269,40,2111,201355,0,2111,201883,5,2712,201896,1,2713,201896,50,2713,201896,40,2713,201982,0,2713,222028,3,4214,223699,4,4964,225209,1,5714,225209,50,5714,225209,40,5714,225295,0,5714,236243,3,6465,237787,4,6840,239661,1,7215,239661,50,7215,239661,40,7215,239747,0,7215,240551,5,8739,240555,1,8740,240555,50,8740,240555,40,8740,240641,0,8740,277283,3,12641,279334,4,14591,280968,1,16541,280968,50,16542,280968,40,16542,281054,0,16542,314787,3,19093,316208,4,20368,317255,5,21643,317256,1,21643,317256,50,21644,317256,40,21644,317342,0,21644,339105,3,23145,340797,4,23895,341911,1,24645,341911,50,24645,341911,40,24645,341997,0,24646,342814,5,26155,342815,1,26155,342815,50,26155,342815,40,26155,342901,0,26155,362028,3,27356,362761,4,27956,363643,1,28556,363643,50,28556,363643,40,28556,363729,0,28556,376415,3,29315,377531,4,29682,378719,5,30057,378720,1,30057,378720,50,30057,378720,40,30057,378720,40,30057,378873,0,30057)
%
%
% START OF PROOF
% 378721 [] equal(X,X).
% 378722 [] equal(multiply(identity,X),X).
% 378723 [] equal(multiply(inverse(X),X),identity).
% 378724 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 378797 [] -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,X),sk_c12) | -equal(multiply(Z,X),U) | -equal(inverse(Z),U) | -equal(inverse(U),X) | -equal(inverse(Y),X).
% 378798 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst97,Y).
% 378799 [] -equal(multiply(X,Y),sk_c12) | -equal(inverse(X),Y) | $spltprd1($spltcnst98,Y).
% 378800 [] -equal(multiply(X,sk_c11),sk_c12) | $spltprd1($spltcnst99,X).
% 378801 [] -$spltprd1($spltcnst98,X) | -$spltprd1($spltcnst97,X) | -$spltprd1($spltcnst99,X).
% 378802 [] equal(multiply(sk_c9,sk_c10),sk_c8) | equal(inverse(sk_c4),sk_c12).
% 378803 [] equal(inverse(sk_c4),sk_c12) | equal(inverse(sk_c8),sk_c10).
% 378804 [] equal(inverse(sk_c4),sk_c12) | equal(inverse(sk_c9),sk_c8).
% 378805 [] equal(multiply(sk_c10,sk_c11),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 378806 [] equal(inverse(sk_c4),sk_c12) | equal(inverse(sk_c7),sk_c10).
% 378807 [?] ?
% 378811 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(multiply(sk_c9,sk_c10),sk_c8).
% 378812 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(inverse(sk_c8),sk_c10).
% 378813 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(inverse(sk_c9),sk_c8).
% 378814 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(multiply(sk_c10,sk_c11),sk_c12).
% 378815 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(inverse(sk_c7),sk_c10).
% 378816 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(multiply(sk_c7,sk_c10),sk_c12).
% 378820 [] equal(multiply(sk_c12,sk_c5),sk_c11) | equal(multiply(sk_c9,sk_c10),sk_c8).
% 378821 [] equal(multiply(sk_c12,sk_c5),sk_c11) | equal(inverse(sk_c8),sk_c10).
% 378822 [] equal(multiply(sk_c12,sk_c5),sk_c11) | equal(inverse(sk_c9),sk_c8).
% 378823 [] equal(multiply(sk_c12,sk_c5),sk_c11) | equal(multiply(sk_c10,sk_c11),sk_c12).
% 378824 [] equal(multiply(sk_c12,sk_c5),sk_c11) | equal(inverse(sk_c7),sk_c10).
% 378825 [] equal(multiply(sk_c12,sk_c5),sk_c11) | equal(multiply(sk_c7,sk_c10),sk_c12).
% 378829 [] equal(multiply(sk_c3,sk_c12),sk_c11) | equal(multiply(sk_c9,sk_c10),sk_c8).
% 378830 [] equal(multiply(sk_c3,sk_c12),sk_c11) | equal(inverse(sk_c8),sk_c10).
% 378831 [] equal(multiply(sk_c3,sk_c12),sk_c11) | equal(inverse(sk_c9),sk_c8).
% 378832 [] equal(multiply(sk_c3,sk_c12),sk_c11) | equal(multiply(sk_c10,sk_c11),sk_c12).
% 378833 [] equal(multiply(sk_c3,sk_c12),sk_c11) | equal(inverse(sk_c7),sk_c10).
% 378834 [] equal(multiply(sk_c3,sk_c12),sk_c11) | equal(multiply(sk_c7,sk_c10),sk_c12).
% 378838 [] equal(multiply(sk_c9,sk_c10),sk_c8) | equal(inverse(sk_c2),sk_c3).
% 378839 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c8),sk_c10).
% 378840 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c9),sk_c8).
% 378841 [] equal(multiply(sk_c10,sk_c11),sk_c12) | equal(inverse(sk_c2),sk_c3).
% 378842 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c7),sk_c10).
% 378843 [?] ?
% 378847 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(multiply(sk_c9,sk_c10),sk_c8).
% 378848 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(inverse(sk_c8),sk_c10).
% 378849 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(inverse(sk_c9),sk_c8).
% 378850 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(multiply(sk_c10,sk_c11),sk_c12).
% 378851 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(inverse(sk_c7),sk_c10).
% 378852 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(multiply(sk_c7,sk_c10),sk_c12).
% 378856 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c9,sk_c10),sk_c8).
% 378857 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(inverse(sk_c8),sk_c10).
% 378858 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(inverse(sk_c9),sk_c8).
% 378859 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c10,sk_c11),sk_c12).
% 378860 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(inverse(sk_c7),sk_c10).
% 378861 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c7,sk_c10),sk_c12).
% 378865 [] equal(multiply(sk_c9,sk_c10),sk_c8) | equal(inverse(sk_c1),sk_c12).
% 378866 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c8),sk_c10).
% 378867 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c9),sk_c8).
% 378868 [] equal(multiply(sk_c10,sk_c11),sk_c12) | equal(inverse(sk_c1),sk_c12).
% 378869 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c7),sk_c10).
% 378870 [?] ?
% 378940 [hyper:378799,378806,binarycut:378807] equal(inverse(sk_c4),sk_c12) | $spltprd1($spltcnst98,sk_c10).
% 379028 [hyper:378799,378842,binarycut:378843] equal(inverse(sk_c2),sk_c3) | $spltprd1($spltcnst98,sk_c10).
% 379116 [hyper:378799,378869,binarycut:378870] equal(inverse(sk_c1),sk_c12) | $spltprd1($spltcnst98,sk_c10).
% 379194 [hyper:378798,378802,378803,378804] equal(inverse(sk_c4),sk_c12) | $spltprd1($spltcnst97,sk_c10).
% 379228 [hyper:378800,378805] equal(inverse(sk_c4),sk_c12) | $spltprd1($spltcnst99,sk_c10).
% 379239 [hyper:378801,379228,379194,378940] equal(inverse(sk_c4),sk_c12).
% 379246 [para:379239.1.1,378723.1.1.1] equal(multiply(sk_c12,sk_c4),identity).
% 379463 [hyper:378798,378838,378839,378840] equal(inverse(sk_c2),sk_c3) | $spltprd1($spltcnst97,sk_c10).
% 379497 [hyper:378800,378841] equal(inverse(sk_c2),sk_c3) | $spltprd1($spltcnst99,sk_c10).
% 379508 [hyper:378801,379497,379463,379028] equal(inverse(sk_c2),sk_c3).
% 379515 [para:379508.1.1,378723.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 379823 [hyper:378798,378865,378866,378867] equal(inverse(sk_c1),sk_c12) | $spltprd1($spltcnst97,sk_c10).
% 379874 [hyper:378800,378868] equal(inverse(sk_c1),sk_c12) | $spltprd1($spltcnst99,sk_c10).
% 379960 [hyper:378801,379874,379823,379116] equal(inverse(sk_c1),sk_c12).
% 379999 [para:379960.1.1,378723.1.1.1] equal(multiply(sk_c12,sk_c1),identity).
% 380175 [hyper:378797,378816,378814,378811,378813,378812,378815] equal(multiply(sk_c4,sk_c12),sk_c5).
% 380458 [hyper:378797,378825,378823,378824,378821,378820,378822] equal(multiply(sk_c12,sk_c5),sk_c11).
% 380603 [hyper:378797,378834,378832,378833,378830,378829,378831] equal(multiply(sk_c3,sk_c12),sk_c11).
% 380708 [hyper:378797,378852,378850,378851,378848,378847,378849] equal(multiply(sk_c2,sk_c3),sk_c11).
% 380855 [hyper:378797,378861,378859,378860,378857,378856,378858] equal(multiply(sk_c1,sk_c11),sk_c12).
% 380879 [para:378723.1.1,378724.1.1.1,demod:378722] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 380880 [para:379246.1.1,378724.1.1.1,demod:378722] equal(X,multiply(sk_c12,multiply(sk_c4,X))).
% 380881 [para:379515.1.1,378724.1.1.1,demod:378722] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 380882 [para:379999.1.1,378724.1.1.1,demod:378722] equal(X,multiply(sk_c12,multiply(sk_c1,X))).
% 380903 [para:380175.1.1,380880.1.2.2,demod:380458] equal(sk_c12,sk_c11).
% 380908 [para:380903.1.1,380458.1.1.1] equal(multiply(sk_c11,sk_c5),sk_c11).
% 380909 [para:380903.1.1,380603.1.1.2] equal(multiply(sk_c3,sk_c11),sk_c11).
% 380951 [para:380708.1.1,380881.1.2.2,demod:380909] equal(sk_c3,sk_c11).
% 380953 [para:380951.1.1,380603.1.1.1] equal(multiply(sk_c11,sk_c12),sk_c11).
% 380992 [para:380855.1.1,380882.1.2.2] equal(sk_c11,multiply(sk_c12,sk_c12)).
% 380994 [para:380903.1.1,380992.1.2.2] equal(sk_c11,multiply(sk_c12,sk_c11)).
% 381053 [para:379246.1.1,380879.1.2.2] equal(sk_c4,multiply(inverse(sk_c12),identity)).
% 381065 [para:380603.1.1,380879.1.2.2] equal(sk_c12,multiply(inverse(sk_c3),sk_c11)).
% 381068 [para:380908.1.1,380879.1.2.2,demod:378723] equal(sk_c5,identity).
% 381069 [para:380909.1.1,380879.1.2.2,demod:381065] equal(sk_c11,sk_c12).
% 381072 [para:380953.1.1,380879.1.2.2,demod:378723] equal(sk_c12,identity).
% 381082 [para:381068.1.1,380458.1.1.2] equal(multiply(sk_c12,identity),sk_c11).
% 381090 [para:381072.1.1,379246.1.1.1,demod:378722] equal(sk_c4,identity).
% 381116 [para:381090.1.1,379239.1.1.1] equal(inverse(identity),sk_c12).
% 381613 [para:381072.1.1,381053.1.2.1.1,demod:381082,381116] equal(sk_c4,sk_c11).
% 381614 [para:381613.1.1,379239.1.1.1] equal(inverse(sk_c11),sk_c12).
% 381676 [hyper:378797,381614,378722,380953,demod:380994,cut:381069,demod:381116,cut:378721,demod:381614,cut:380903] 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 33
% 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(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(sk_c12,U),sk_c11) | -equal(multiply(V,sk_c12),U) | -equal(inverse(V),sk_c12) | -equal(inverse(sk_c12),sk_c11) | -equal(inverse(W),sk_c12) | -equal(multiply(W,sk_c11),sk_c12) | -equal(multiply(X1,X2),sk_c12) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c12) | -equal(inverse(X3),X4) | -equal(inverse(X4),X2) | -equal(multiply(X3,X2),X4).
% Split part used next: -equal(inverse(W),sk_c12) | -equal(multiply(W,sk_c11),sk_c12).
% 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 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(77,40,1,163,0,2,200699,5,1503,200700,1,1503,200700,50,1503,200700,40,1503,200786,0,1503,201260,5,2110,201269,1,2111,201269,50,2111,201269,40,2111,201355,0,2111,201883,5,2712,201896,1,2713,201896,50,2713,201896,40,2713,201982,0,2713,222028,3,4214,223699,4,4964,225209,1,5714,225209,50,5714,225209,40,5714,225295,0,5714,236243,3,6465,237787,4,6840,239661,1,7215,239661,50,7215,239661,40,7215,239747,0,7215,240551,5,8739,240555,1,8740,240555,50,8740,240555,40,8740,240641,0,8740,277283,3,12641,279334,4,14591,280968,1,16541,280968,50,16542,280968,40,16542,281054,0,16542,314787,3,19093,316208,4,20368,317255,5,21643,317256,1,21643,317256,50,21644,317256,40,21644,317342,0,21644,339105,3,23145,340797,4,23895,341911,1,24645,341911,50,24645,341911,40,24645,341997,0,24646,342814,5,26155,342815,1,26155,342815,50,26155,342815,40,26155,342901,0,26155,362028,3,27356,362761,4,27956,363643,1,28556,363643,50,28556,363643,40,28556,363729,0,28556,376415,3,29315,377531,4,29682,378719,5,30057,378720,1,30057,378720,50,30057,378720,40,30057,378720,40,30057,378873,0,30057,381675,50,30068,381675,30,30068,381675,40,30068,381752,0,30069)
%
%
% START OF PROOF
% 381676 [] equal(X,X).
% 381680 [] -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c12).
% 381741 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c6,sk_c11),sk_c12).
% 381742 [?] ?
% 381750 [?] ?
% 381751 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c6),sk_c12).
% 381795 [hyper:381680,381751,binarycut:381742] equal(inverse(sk_c6),sk_c12).
% 381797 [hyper:381680,381751,binarycut:381750] equal(inverse(sk_c1),sk_c12).
% 381844 [hyper:381680,381741,demod:381797,cut:381676] equal(multiply(sk_c6,sk_c11),sk_c12).
% 381846 [hyper:381680,381844,demod:381795,cut:381676] 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 33
% 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(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(sk_c12,U),sk_c11) | -equal(multiply(V,sk_c12),U) | -equal(inverse(V),sk_c12) | -equal(inverse(sk_c12),sk_c11) | -equal(inverse(W),sk_c12) | -equal(multiply(W,sk_c11),sk_c12) | -equal(multiply(X1,X2),sk_c12) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c12) | -equal(inverse(X3),X4) | -equal(inverse(X4),X2) | -equal(multiply(X3,X2),X4).
% Split part used next: -equal(multiply(sk_c12,U),sk_c11) | -equal(multiply(V,sk_c12),U) | -equal(inverse(V),sk_c12).
% 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 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(77,40,1,163,0,2,200699,5,1503,200700,1,1503,200700,50,1503,200700,40,1503,200786,0,1503,201260,5,2110,201269,1,2111,201269,50,2111,201269,40,2111,201355,0,2111,201883,5,2712,201896,1,2713,201896,50,2713,201896,40,2713,201982,0,2713,222028,3,4214,223699,4,4964,225209,1,5714,225209,50,5714,225209,40,5714,225295,0,5714,236243,3,6465,237787,4,6840,239661,1,7215,239661,50,7215,239661,40,7215,239747,0,7215,240551,5,8739,240555,1,8740,240555,50,8740,240555,40,8740,240641,0,8740,277283,3,12641,279334,4,14591,280968,1,16541,280968,50,16542,280968,40,16542,281054,0,16542,314787,3,19093,316208,4,20368,317255,5,21643,317256,1,21643,317256,50,21644,317256,40,21644,317342,0,21644,339105,3,23145,340797,4,23895,341911,1,24645,341911,50,24645,341911,40,24645,341997,0,24646,342814,5,26155,342815,1,26155,342815,50,26155,342815,40,26155,342901,0,26155,362028,3,27356,362761,4,27956,363643,1,28556,363643,50,28556,363643,40,28556,363729,0,28556,376415,3,29315,377531,4,29682,378719,5,30057,378720,1,30057,378720,50,30057,378720,40,30057,378720,40,30057,378873,0,30057,381675,50,30068,381675,30,30068,381675,40,30068,381752,0,30069,381845,50,30069,381845,30,30069,381845,40,30069,381922,0,30074)
%
%
% START OF PROOF
% 381847 [] equal(multiply(identity,X),X).
% 381848 [] equal(multiply(inverse(X),X),identity).
% 381849 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 381850 [] -equal(multiply(sk_c12,X),sk_c11) | -equal(multiply(Y,sk_c12),X) | -equal(inverse(Y),sk_c12).
% 381851 [] equal(multiply(sk_c9,sk_c10),sk_c8) | equal(inverse(sk_c4),sk_c12).
% 381852 [] equal(inverse(sk_c4),sk_c12) | equal(inverse(sk_c8),sk_c10).
% 381853 [] equal(inverse(sk_c4),sk_c12) | equal(inverse(sk_c9),sk_c8).
% 381854 [] equal(multiply(sk_c10,sk_c11),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 381855 [] equal(inverse(sk_c4),sk_c12) | equal(inverse(sk_c7),sk_c10).
% 381856 [] equal(multiply(sk_c7,sk_c10),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 381857 [] equal(multiply(sk_c6,sk_c11),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 381858 [] equal(inverse(sk_c4),sk_c12) | equal(inverse(sk_c6),sk_c12).
% 381859 [] equal(inverse(sk_c4),sk_c12) | equal(inverse(sk_c12),sk_c11).
% 381860 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(multiply(sk_c9,sk_c10),sk_c8).
% 381861 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(inverse(sk_c8),sk_c10).
% 381862 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(inverse(sk_c9),sk_c8).
% 381863 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(multiply(sk_c10,sk_c11),sk_c12).
% 381864 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(inverse(sk_c7),sk_c10).
% 381865 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(multiply(sk_c7,sk_c10),sk_c12).
% 381866 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(multiply(sk_c6,sk_c11),sk_c12).
% 381867 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(inverse(sk_c6),sk_c12).
% 381868 [] equal(multiply(sk_c4,sk_c12),sk_c5) | equal(inverse(sk_c12),sk_c11).
% 381869 [?] ?
% 381870 [?] ?
% 381871 [?] ?
% 381872 [?] ?
% 381873 [?] ?
% 381874 [?] ?
% 381875 [?] ?
% 381876 [?] ?
% 381877 [?] ?
% 382018 [hyper:381850,381860,381851,binarycut:381869] equal(multiply(sk_c9,sk_c10),sk_c8).
% 382021 [hyper:381850,381861,binarycut:381870,binarycut:381852] equal(inverse(sk_c8),sk_c10).
% 382022 [para:382021.1.1,381848.1.1.1] equal(multiply(sk_c10,sk_c8),identity).
% 382025 [hyper:381850,381862,binarycut:381871,binarycut:381853] equal(inverse(sk_c9),sk_c8).
% 382032 [hyper:381850,381863,381854,binarycut:381872] equal(multiply(sk_c10,sk_c11),sk_c12).
% 382033 [para:382025.1.1,381848.1.1.1] equal(multiply(sk_c8,sk_c9),identity).
% 382036 [hyper:381850,381864,binarycut:381873,binarycut:381855] equal(inverse(sk_c7),sk_c10).
% 382037 [para:382036.1.1,381848.1.1.1] equal(multiply(sk_c10,sk_c7),identity).
% 382043 [hyper:381850,381865,381856,binarycut:381874] equal(multiply(sk_c7,sk_c10),sk_c12).
% 382046 [hyper:381850,381867,binarycut:381876,binarycut:381858] equal(inverse(sk_c6),sk_c12).
% 382055 [hyper:381850,381866,381857,binarycut:381875] equal(multiply(sk_c6,sk_c11),sk_c12).
% 382058 [para:382046.1.1,381848.1.1.1] equal(multiply(sk_c12,sk_c6),identity).
% 382063 [hyper:381850,381868,binarycut:381877,binarycut:381859] equal(inverse(sk_c12),sk_c11).
% 382064 [para:382063.1.1,381848.1.1.1] equal(multiply(sk_c11,sk_c12),identity).
% 382066 [para:382018.1.1,381849.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c9,multiply(sk_c10,X))).
% 382067 [para:382022.1.1,381849.1.1.1,demod:381847] equal(X,multiply(sk_c10,multiply(sk_c8,X))).
% 382069 [para:382033.1.1,381849.1.1.1,demod:381847] equal(X,multiply(sk_c8,multiply(sk_c9,X))).
% 382070 [para:382037.1.1,381849.1.1.1,demod:381847] equal(X,multiply(sk_c10,multiply(sk_c7,X))).
% 382071 [para:382043.1.1,381849.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c7,multiply(sk_c10,X))).
% 382073 [para:382058.1.1,381849.1.1.1,demod:381847] equal(X,multiply(sk_c12,multiply(sk_c6,X))).
% 382079 [para:382033.1.1,382067.1.2.2] equal(sk_c9,multiply(sk_c10,identity)).
% 382080 [para:382079.1.2,381849.1.1.1,demod:381847] equal(multiply(sk_c9,X),multiply(sk_c10,X)).
% 382087 [para:382043.1.1,382070.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c12)).
% 382091 [para:382055.1.1,382073.1.2.2] equal(sk_c11,multiply(sk_c12,sk_c12)).
% 382101 [para:382080.1.1,382069.1.2.2] equal(X,multiply(sk_c8,multiply(sk_c10,X))).
% 382107 [para:382022.1.1,382101.1.2.2] equal(sk_c8,multiply(sk_c8,identity)).
% 382109 [para:382037.1.1,382101.1.2.2,demod:382107] equal(sk_c7,sk_c8).
% 382112 [para:382109.1.2,382069.1.2.1,demod:382071,382080] equal(X,multiply(sk_c12,X)).
% 382119 [para:382112.1.2,382091.1.2] equal(sk_c11,sk_c12).
% 382124 [para:382119.1.2,382087.1.2.2,demod:382032] equal(sk_c10,sk_c12).
% 382125 [para:382119.1.2,382091.1.2.1,demod:382064] equal(sk_c11,identity).
% 382135 [para:382125.1.1,382032.1.1.2,demod:382079] equal(sk_c9,sk_c12).
% 382152 [para:382135.1.2,382063.1.1.1,demod:382025] equal(sk_c8,sk_c11).
% 382177 [hyper:381850,382066,demod:382021,382112,382018,382087,cut:382152,cut:382124] 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 33
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(sk_c12,U),sk_c11) | -equal(multiply(V,sk_c12),U) | -equal(inverse(V),sk_c12) | -equal(inverse(sk_c12),sk_c11) | -equal(inverse(W),sk_c12) | -equal(multiply(W,sk_c11),sk_c12) | -equal(multiply(X1,X2),sk_c12) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c12) | -equal(inverse(X3),X4) | -equal(inverse(X4),X2) | -equal(multiply(X3,X2),X4).
% Split part used next: -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),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 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(77,40,1,163,0,2,200699,5,1503,200700,1,1503,200700,50,1503,200700,40,1503,200786,0,1503,201260,5,2110,201269,1,2111,201269,50,2111,201269,40,2111,201355,0,2111,201883,5,2712,201896,1,2713,201896,50,2713,201896,40,2713,201982,0,2713,222028,3,4214,223699,4,4964,225209,1,5714,225209,50,5714,225209,40,5714,225295,0,5714,236243,3,6465,237787,4,6840,239661,1,7215,239661,50,7215,239661,40,7215,239747,0,7215,240551,5,8739,240555,1,8740,240555,50,8740,240555,40,8740,240641,0,8740,277283,3,12641,279334,4,14591,280968,1,16541,280968,50,16542,280968,40,16542,281054,0,16542,314787,3,19093,316208,4,20368,317255,5,21643,317256,1,21643,317256,50,21644,317256,40,21644,317342,0,21644,339105,3,23145,340797,4,23895,341911,1,24645,341911,50,24645,341911,40,24645,341997,0,24646,342814,5,26155,342815,1,26155,342815,50,26155,342815,40,26155,342901,0,26155,362028,3,27356,362761,4,27956,363643,1,28556,363643,50,28556,363643,40,28556,363729,0,28556,376415,3,29315,377531,4,29682,378719,5,30057,378720,1,30057,378720,50,30057,378720,40,30057,378720,40,30057,378873,0,30057,381675,50,30068,381675,30,30068,381675,40,30068,381752,0,30069,381845,50,30069,381845,30,30069,381845,40,30069,381922,0,30074,382176,50,30075,382176,30,30075,382176,40,30075,382253,0,30075)
%
%
% START OF PROOF
% 382177 [] equal(X,X).
% 382178 [] equal(multiply(identity,X),X).
% 382179 [] equal(multiply(inverse(X),X),identity).
% 382180 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 382181 [] -equal(multiply(X,sk_c12),sk_c11) | -equal(multiply(Y,X),sk_c11) | -equal(inverse(Y),X).
% 382210 [?] ?
% 382211 [?] ?
% 382213 [?] ?
% 382214 [?] ?
% 382215 [?] ?
% 382216 [?] ?
% 382217 [?] ?
% 382219 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c8),sk_c10).
% 382220 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c9),sk_c8).
% 382222 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c7),sk_c10).
% 382223 [] equal(multiply(sk_c7,sk_c10),sk_c12) | equal(inverse(sk_c2),sk_c3).
% 382224 [] equal(multiply(sk_c6,sk_c11),sk_c12) | equal(inverse(sk_c2),sk_c3).
% 382225 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c6),sk_c12).
% 382226 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c12),sk_c11).
% 382228 [?] ?
% 382229 [?] ?
% 382231 [?] ?
% 382232 [?] ?
% 382233 [?] ?
% 382234 [?] ?
% 382235 [?] ?
% 382280 [hyper:382181,382219,binarycut:382228,binarycut:382210] equal(inverse(sk_c8),sk_c10).
% 382284 [para:382280.1.1,382179.1.1.1] equal(multiply(sk_c10,sk_c8),identity).
% 382291 [hyper:382181,382220,binarycut:382229,binarycut:382211] equal(inverse(sk_c9),sk_c8).
% 382295 [para:382291.1.1,382179.1.1.1] equal(multiply(sk_c8,sk_c9),identity).
% 382299 [hyper:382181,382222,binarycut:382231,binarycut:382213] equal(inverse(sk_c7),sk_c10).
% 382306 [para:382299.1.1,382179.1.1.1] equal(multiply(sk_c10,sk_c7),identity).
% 382310 [hyper:382181,382225,binarycut:382234,binarycut:382216] equal(inverse(sk_c6),sk_c12).
% 382314 [para:382310.1.1,382179.1.1.1] equal(multiply(sk_c12,sk_c6),identity).
% 382321 [hyper:382181,382226,binarycut:382235,binarycut:382217] equal(inverse(sk_c12),sk_c11).
% 382325 [para:382321.1.1,382179.1.1.1] equal(multiply(sk_c11,sk_c12),identity).
% 382338 [hyper:382181,382223,binarycut:382232,binarycut:382214] equal(multiply(sk_c7,sk_c10),sk_c12).
% 382342 [hyper:382181,382224,binarycut:382233,binarycut:382215] equal(multiply(sk_c6,sk_c11),sk_c12).
% 382343 [para:382179.1.1,382180.1.1.1,demod:382178] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 382344 [para:382284.1.1,382180.1.1.1,demod:382178] equal(X,multiply(sk_c10,multiply(sk_c8,X))).
% 382345 [para:382295.1.1,382180.1.1.1,demod:382178] equal(X,multiply(sk_c8,multiply(sk_c9,X))).
% 382351 [para:382338.1.1,382180.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c7,multiply(sk_c10,X))).
% 382355 [para:382295.1.1,382344.1.2.2] equal(sk_c9,multiply(sk_c10,identity)).
% 382356 [para:382355.1.2,382180.1.1.1,demod:382178] equal(multiply(sk_c9,X),multiply(sk_c10,X)).
% 382363 [para:382284.1.1,382343.1.2.2] equal(sk_c8,multiply(inverse(sk_c10),identity)).
% 382365 [para:382306.1.1,382343.1.2.2,demod:382363] equal(sk_c7,sk_c8).
% 382370 [para:382342.1.1,382343.1.2.2,demod:382310] equal(sk_c11,multiply(sk_c12,sk_c12)).
% 382373 [para:382365.1.2,382345.1.2.1,demod:382351,382356] equal(X,multiply(sk_c12,X)).
% 382378 [para:382373.1.2,382314.1.1] equal(sk_c6,identity).
% 382379 [para:382373.1.2,382343.1.2.2,demod:382321] equal(X,multiply(sk_c11,X)).
% 382380 [para:382378.1.1,382310.1.1.1] equal(inverse(identity),sk_c12).
% 382381 [para:382378.1.1,382342.1.1.1,demod:382178] equal(sk_c11,sk_c12).
% 382383 [para:382381.1.2,382325.1.1.2,demod:382379] equal(sk_c11,identity).
% 382384 [para:382383.1.1,382325.1.1.1,demod:382178] equal(sk_c12,identity).
% 382390 [para:382384.1.1,382321.1.1.1,demod:382380] equal(sk_c12,sk_c11).
% 382450 [hyper:382181,382380,demod:382370,382178,cut:382390,cut:382177] 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 33
% 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(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(sk_c12,U),sk_c11) | -equal(multiply(V,sk_c12),U) | -equal(inverse(V),sk_c12) | -equal(inverse(sk_c12),sk_c11) | -equal(inverse(W),sk_c12) | -equal(multiply(W,sk_c11),sk_c12) | -equal(multiply(X1,X2),sk_c12) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c12) | -equal(inverse(X3),X4) | -equal(inverse(X4),X2) | -equal(multiply(X3,X2),X4).
% Split part used next: -equal(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12).
% 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 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(77,40,1,163,0,2,200699,5,1503,200700,1,1503,200700,50,1503,200700,40,1503,200786,0,1503,201260,5,2110,201269,1,2111,201269,50,2111,201269,40,2111,201355,0,2111,201883,5,2712,201896,1,2713,201896,50,2713,201896,40,2713,201982,0,2713,222028,3,4214,223699,4,4964,225209,1,5714,225209,50,5714,225209,40,5714,225295,0,5714,236243,3,6465,237787,4,6840,239661,1,7215,239661,50,7215,239661,40,7215,239747,0,7215,240551,5,8739,240555,1,8740,240555,50,8740,240555,40,8740,240641,0,8740,277283,3,12641,279334,4,14591,280968,1,16541,280968,50,16542,280968,40,16542,281054,0,16542,314787,3,19093,316208,4,20368,317255,5,21643,317256,1,21643,317256,50,21644,317256,40,21644,317342,0,21644,339105,3,23145,340797,4,23895,341911,1,24645,341911,50,24645,341911,40,24645,341997,0,24646,342814,5,26155,342815,1,26155,342815,50,26155,342815,40,26155,342901,0,26155,362028,3,27356,362761,4,27956,363643,1,28556,363643,50,28556,363643,40,28556,363729,0,28556,376415,3,29315,377531,4,29682,378719,5,30057,378720,1,30057,378720,50,30057,378720,40,30057,378720,40,30057,378873,0,30057,381675,50,30068,381675,30,30068,381675,40,30068,381752,0,30069,381845,50,30069,381845,30,30069,381845,40,30069,381922,0,30074,382176,50,30075,382176,30,30075,382176,40,30075,382253,0,30075,382449,50,30075,382449,30,30075,382449,40,30075,382526,0,30079)
%
%
% START OF PROOF
% 382450 [] equal(X,X).
% 382454 [] -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c12).
% 382515 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c6,sk_c11),sk_c12).
% 382516 [?] ?
% 382524 [?] ?
% 382525 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c6),sk_c12).
% 382569 [hyper:382454,382525,binarycut:382516] equal(inverse(sk_c6),sk_c12).
% 382571 [hyper:382454,382525,binarycut:382524] equal(inverse(sk_c1),sk_c12).
% 382618 [hyper:382454,382515,demod:382571,cut:382450] equal(multiply(sk_c6,sk_c11),sk_c12).
% 382620 [hyper:382454,382618,demod:382569,cut:382450] 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 33
% 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(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(sk_c12,U),sk_c11) | -equal(multiply(V,sk_c12),U) | -equal(inverse(V),sk_c12) | -equal(inverse(sk_c12),sk_c11) | -equal(inverse(W),sk_c12) | -equal(multiply(W,sk_c11),sk_c12) | -equal(multiply(X1,X2),sk_c12) | -equal(inverse(X1),X2) | -equal(multiply(X2,sk_c11),sk_c12) | -equal(inverse(X3),X4) | -equal(inverse(X4),X2) | -equal(multiply(X3,X2),X4).
% Split part used next: -equal(inverse(sk_c12),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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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 33
% 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(77,40,1,163,0,2,200699,5,1503,200700,1,1503,200700,50,1503,200700,40,1503,200786,0,1503,201260,5,2110,201269,1,2111,201269,50,2111,201269,40,2111,201355,0,2111,201883,5,2712,201896,1,2713,201896,50,2713,201896,40,2713,201982,0,2713,222028,3,4214,223699,4,4964,225209,1,5714,225209,50,5714,225209,40,5714,225295,0,5714,236243,3,6465,237787,4,6840,239661,1,7215,239661,50,7215,239661,40,7215,239747,0,7215,240551,5,8739,240555,1,8740,240555,50,8740,240555,40,8740,240641,0,8740,277283,3,12641,279334,4,14591,280968,1,16541,280968,50,16542,280968,40,16542,281054,0,16542,314787,3,19093,316208,4,20368,317255,5,21643,317256,1,21643,317256,50,21644,317256,40,21644,317342,0,21644,339105,3,23145,340797,4,23895,341911,1,24645,341911,50,24645,341911,40,24645,341997,0,24646,342814,5,26155,342815,1,26155,342815,50,26155,342815,40,26155,342901,0,26155,362028,3,27356,362761,4,27956,363643,1,28556,363643,50,28556,363643,40,28556,363729,0,28556,376415,3,29315,377531,4,29682,378719,5,30057,378720,1,30057,378720,50,30057,378720,40,30057,378720,40,30057,378873,0,30057,381675,50,30068,381675,30,30068,381675,40,30068,381752,0,30069,381845,50,30069,381845,30,30069,381845,40,30069,381922,0,30074,382176,50,30075,382176,30,30075,382176,40,30075,382253,0,30075,382449,50,30075,382449,30,30075,382449,40,30075,382526,0,30079,382619,50,30080,382619,30,30080,382619,40,30080,382696,0,30080,382879,50,30081,382956,0,30086,383150,50,30088,383227,0,30088,383462,50,30092,383539,0,30096,383795,50,30102,383872,0,30102,384147,50,30112,384224,0,30116,384507,50,30132,384584,0,30132,384881,50,30159,384958,0,30164,385265,50,30217,385342,0,30217,385659,50,30322,385659,40,30322,385736,0,30322)
%
%
% START OF PROOF
% 385661 [] equal(multiply(identity,X),X).
% 385662 [] equal(multiply(inverse(X),X),identity).
% 385663 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 385664 [] -equal(inverse(sk_c12),sk_c11).
% 385673 [?] ?
% 385682 [?] ?
% 385691 [?] ?
% 385700 [?] ?
% 385709 [?] ?
% 385718 [?] ?
% 385736 [?] ?
% 385751 [input:385673,cut:385664] equal(inverse(sk_c4),sk_c12).
% 385752 [para:385751.1.1,385662.1.1.1] equal(multiply(sk_c12,sk_c4),identity).
% 385766 [input:385709,cut:385664] equal(inverse(sk_c2),sk_c3).
% 385767 [para:385766.1.1,385662.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 385782 [input:385736,cut:385664] equal(inverse(sk_c1),sk_c12).
% 385783 [para:385782.1.1,385662.1.1.1] equal(multiply(sk_c12,sk_c1),identity).
% 385793 [input:385682,cut:385664] equal(multiply(sk_c4,sk_c12),sk_c5).
% 385803 [input:385691,cut:385664] equal(multiply(sk_c12,sk_c5),sk_c11).
% 385814 [input:385700,cut:385664] equal(multiply(sk_c3,sk_c12),sk_c11).
% 385829 [input:385718,cut:385664] equal(multiply(sk_c2,sk_c3),sk_c11).
% 385872 [para:385662.1.1,385663.1.1.1,demod:385661] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 385874 [para:385752.1.1,385663.1.1.1,demod:385661] equal(X,multiply(sk_c12,multiply(sk_c4,X))).
% 385877 [para:385767.1.1,385663.1.1.1,demod:385661] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 385954 [para:385793.1.1,385874.1.2.2] equal(sk_c12,multiply(sk_c12,sk_c5)).
% 385959 [para:385954.1.2,385803.1.1] equal(sk_c12,sk_c11).
% 385961 [para:385959.1.1,385664.1.1.1] -equal(inverse(sk_c11),sk_c11).
% 385979 [para:385959.1.1,385814.1.1.2] equal(multiply(sk_c3,sk_c11),sk_c11).
% 385998 [para:385829.1.1,385877.1.2.2,demod:385979] equal(sk_c3,sk_c11).
% 386004 [para:385998.1.1,385814.1.1.1] equal(multiply(sk_c11,sk_c12),sk_c11).
% 386117 [para:386004.1.1,385872.1.2.2,demod:385662] equal(sk_c12,identity).
% 386147 [para:386117.1.1,385783.1.1.1,demod:385661] equal(sk_c1,identity).
% 386168 [para:386117.1.1,385959.1.1] equal(identity,sk_c11).
% 386192 [para:386147.1.1,385782.1.1.1] equal(inverse(identity),sk_c12).
% 386204 [para:386168.1.2,385961.1.1.1,demod:386192,cut:385959] 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: 36137
% derived clauses: 2730268
% kept clauses: 134878
% kept size sum: 717987
% kept mid-nuclei: 203113
% kept new demods: 2257
% forw unit-subs: 469833
% forw double-subs: 1697610
% forw overdouble-subs: 186533
% backward subs: 15249
% fast unit cutoff: 21674
% full unit cutoff: 0
% dbl unit cutoff: 8260
% real runtime : 305.46
% process. runtime: 303.23
% specific non-discr-tree subsumption statistics:
% tried: 43519119
% length fails: 7130397
% strength fails: 13590482
% predlist fails: 456035
% aux str. fails: 7318805
% by-lit fails: 5298309
% full subs tried: 5928920
% full subs fail: 5788737
%
% ; 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/GRP220-1+eq_r.in")
%
%------------------------------------------------------------------------------