TSTP Solution File: GRP375-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP375-1 : 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 297.8s
% Output : Assurance 297.8s
% 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/GRP375-1+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 27)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 27)
% (binary-posweight-lex-big-order 30 #f 3 27)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(inverse(sk_c10),sk_c9) | -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(sk_c8,sk_c10),sk_c9) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% was split for some strategies as:
% -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(X1),V) | -equal(inverse(W),X1) | -equal(multiply(W,V),X1).
% -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9).
% -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10).
% -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% -equal(inverse(sk_c10),sk_c9).
% -equal(multiply(sk_c8,sk_c10),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(inverse(sk_c10),sk_c9) | -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(sk_c8,sk_c10),sk_c9) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% Split part used next: -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(X1),V) | -equal(inverse(W),X1) | -equal(multiply(W,V),X1).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(45,40,1,98,0,1,74811,50,787,74811,40,787,74864,0,787,81855,3,1090,83186,4,1238,83856,5,1388,83857,1,1388,83857,50,1388,83857,40,1388,83910,0,1388,86112,3,1691,86267,4,1842,86299,5,1989,86299,1,1989,86299,50,1989,86299,40,1989,86352,0,1989,115414,3,3490,116309,4,4240,117111,5,4990,117112,1,4990,117112,50,4991,117112,40,4991,117165,0,4991,135066,3,5742,135799,4,6117,136446,1,6492,136446,50,6492,136446,40,6492,136499,0,6492,150344,3,7334,151492,4,7618,153115,5,7993,153116,5,7993,153117,1,7993,153117,50,7993,153117,40,7993,153170,0,7993,223318,3,11896,224419,4,13845,225408,5,15794,225409,1,15794,225409,50,15796,225409,40,15796,225462,0,15796,280469,3,18348,281344,4,19622,282157,5,20897,282158,1,20898,282158,50,20899,282158,40,20899,282211,0,20899,321560,3,22412,322289,4,23150,323211,1,23900,323211,50,23901,323211,40,23901,323264,0,23901,336099,3,24665,337782,4,25027,339857,5,25402,339858,1,25402,339858,50,25402,339858,40,25402,339911,0,25402,374756,3,26617,375331,4,27203,375858,5,27803,375859,1,27803,375859,50,27804,375859,40,27804,375912,0,27804,400657,3,28556,401100,4,28930,401586,1,29305,401586,50,29306,401586,40,29306,401586,40,29306,401675,0,29306)
%
%
% START OF PROOF
% 401587 [] equal(X,X).
% 401588 [] equal(multiply(identity,X),X).
% 401589 [] equal(multiply(inverse(X),X),identity).
% 401590 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 401631 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,X),sk_c10) | -equal(multiply(Z,X),U) | -equal(inverse(Z),U) | -equal(inverse(U),X) | -equal(inverse(Y),X).
% 401632 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst85,Y).
% 401633 [] -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | $spltprd1($spltcnst86,Y).
% 401634 [] -equal(multiply(X,sk_c9),sk_c10) | $spltprd1($spltcnst87,X).
% 401635 [] -$spltprd1($spltcnst86,X) | -$spltprd1($spltcnst85,X) | -$spltprd1($spltcnst87,X).
% 401646 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c10).
% 401647 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c5),sk_c7).
% 401648 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c6),sk_c5).
% 401649 [] equal(multiply(sk_c7,sk_c9),sk_c10) | equal(inverse(sk_c1),sk_c10).
% 401650 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c4),sk_c7).
% 401651 [?] ?
% 401656 [] equal(multiply(sk_c1,sk_c10),sk_c9) | equal(multiply(sk_c6,sk_c7),sk_c5).
% 401657 [] equal(multiply(sk_c1,sk_c10),sk_c9) | equal(inverse(sk_c5),sk_c7).
% 401658 [] equal(multiply(sk_c1,sk_c10),sk_c9) | equal(inverse(sk_c6),sk_c5).
% 401659 [] equal(multiply(sk_c1,sk_c10),sk_c9) | equal(multiply(sk_c7,sk_c9),sk_c10).
% 401660 [] equal(multiply(sk_c1,sk_c10),sk_c9) | equal(inverse(sk_c4),sk_c7).
% 401661 [] equal(multiply(sk_c1,sk_c10),sk_c9) | equal(multiply(sk_c4,sk_c7),sk_c10).
% 401666 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c10),sk_c9).
% 401667 [] equal(inverse(sk_c10),sk_c9) | equal(inverse(sk_c5),sk_c7).
% 401668 [] equal(inverse(sk_c10),sk_c9) | equal(inverse(sk_c6),sk_c5).
% 401669 [] equal(multiply(sk_c7,sk_c9),sk_c10) | equal(inverse(sk_c10),sk_c9).
% 401670 [] equal(inverse(sk_c10),sk_c9) | equal(inverse(sk_c4),sk_c7).
% 401671 [?] ?
% 401742 [hyper:401633,401650,binarycut:401651] equal(inverse(sk_c1),sk_c10) | $spltprd1($spltcnst86,sk_c7).
% 401830 [hyper:401633,401670,binarycut:401671] equal(inverse(sk_c10),sk_c9) | $spltprd1($spltcnst86,sk_c7).
% 401952 [hyper:401632,401646,401647,401648] equal(inverse(sk_c1),sk_c10) | $spltprd1($spltcnst85,sk_c7).
% 401981 [hyper:401634,401649] equal(inverse(sk_c1),sk_c10) | $spltprd1($spltcnst87,sk_c7).
% 401992 [hyper:401635,401981,401952,401742] equal(inverse(sk_c1),sk_c10).
% 401999 [para:401992.1.1,401589.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 402086 [hyper:401632,401666,401667,401668] equal(inverse(sk_c10),sk_c9) | $spltprd1($spltcnst85,sk_c7).
% 402100 [hyper:401634,401669] equal(inverse(sk_c10),sk_c9) | $spltprd1($spltcnst87,sk_c7).
% 402122 [hyper:401635,402100,402086,401830] equal(inverse(sk_c10),sk_c9).
% 402129 [para:402122.1.1,401589.1.1.1] equal(multiply(sk_c9,sk_c10),identity).
% 402353 [hyper:401631,401661,401659,401660,401657,401656,401658] equal(multiply(sk_c1,sk_c10),sk_c9).
% 402362 [para:401999.1.1,401590.1.1.1,demod:401588] equal(X,multiply(sk_c10,multiply(sk_c1,X))).
% 402363 [para:402129.1.1,401590.1.1.1,demod:401588] equal(X,multiply(sk_c9,multiply(sk_c10,X))).
% 402382 [para:402353.1.1,402362.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 402401 [para:402362.1.2,402363.1.2.2] equal(multiply(sk_c1,X),multiply(sk_c9,X)).
% 402402 [para:402382.1.2,402363.1.2.2,demod:402129] equal(sk_c9,identity).
% 402403 [para:402402.1.1,402129.1.1.1,demod:401588] equal(sk_c10,identity).
% 402406 [para:402403.1.1,401999.1.1.1,demod:401588] equal(sk_c1,identity).
% 402407 [para:402403.1.1,402122.1.1.1] equal(inverse(identity),sk_c9).
% 402410 [para:402403.1.1,402362.1.2.1,demod:401588] equal(X,multiply(sk_c1,X)).
% 402411 [para:402403.1.1,402382.1.2.1,demod:401588] equal(sk_c10,sk_c9).
% 402412 [para:402406.1.1,401992.1.1.1,demod:402407] equal(sk_c9,sk_c10).
% 402413 [para:402411.1.1,402122.1.1.1] equal(inverse(sk_c9),sk_c9).
% 402420 [hyper:401631,402407,401588,demod:402410,402401,401588,cut:402412,cut:402412,demod:402407,402413,cut:401587,cut:401587] 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 27
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c10),sk_c9) | -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(sk_c8,sk_c10),sk_c9) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% Split part used next: -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),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 27
% 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 27
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(45,40,1,98,0,1,74811,50,787,74811,40,787,74864,0,787,81855,3,1090,83186,4,1238,83856,5,1388,83857,1,1388,83857,50,1388,83857,40,1388,83910,0,1388,86112,3,1691,86267,4,1842,86299,5,1989,86299,1,1989,86299,50,1989,86299,40,1989,86352,0,1989,115414,3,3490,116309,4,4240,117111,5,4990,117112,1,4990,117112,50,4991,117112,40,4991,117165,0,4991,135066,3,5742,135799,4,6117,136446,1,6492,136446,50,6492,136446,40,6492,136499,0,6492,150344,3,7334,151492,4,7618,153115,5,7993,153116,5,7993,153117,1,7993,153117,50,7993,153117,40,7993,153170,0,7993,223318,3,11896,224419,4,13845,225408,5,15794,225409,1,15794,225409,50,15796,225409,40,15796,225462,0,15796,280469,3,18348,281344,4,19622,282157,5,20897,282158,1,20898,282158,50,20899,282158,40,20899,282211,0,20899,321560,3,22412,322289,4,23150,323211,1,23900,323211,50,23901,323211,40,23901,323264,0,23901,336099,3,24665,337782,4,25027,339857,5,25402,339858,1,25402,339858,50,25402,339858,40,25402,339911,0,25402,374756,3,26617,375331,4,27203,375858,5,27803,375859,1,27803,375859,50,27804,375859,40,27804,375912,0,27804,400657,3,28556,401100,4,28930,401586,1,29305,401586,50,29306,401586,40,29306,401586,40,29306,401675,0,29306,402419,50,29312,402419,30,29312,402419,40,29312,402464,0,29312,402554,50,29312,402599,0,29312)
%
%
% START OF PROOF
% 402556 [] equal(multiply(identity,X),X).
% 402557 [] equal(multiply(inverse(X),X),identity).
% 402558 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 402559 [] -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% 402566 [] equal(multiply(sk_c8,sk_c10),sk_c9) | equal(inverse(sk_c3),sk_c9).
% 402567 [] equal(multiply(sk_c8,sk_c10),sk_c9) | equal(multiply(sk_c3,sk_c9),sk_c8).
% 402576 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c3),sk_c9).
% 402577 [?] ?
% 402586 [] equal(multiply(sk_c1,sk_c10),sk_c9) | equal(inverse(sk_c3),sk_c9).
% 402587 [] equal(multiply(sk_c1,sk_c10),sk_c9) | equal(multiply(sk_c3,sk_c9),sk_c8).
% 402596 [] equal(inverse(sk_c10),sk_c9) | equal(inverse(sk_c3),sk_c9).
% 402597 [?] ?
% 402606 [hyper:402559,402576,binarycut:402577] equal(inverse(sk_c1),sk_c10).
% 402607 [para:402606.1.1,402557.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 402621 [hyper:402559,402596,binarycut:402597] equal(inverse(sk_c10),sk_c9).
% 402624 [para:402621.1.1,402557.1.1.1] equal(multiply(sk_c9,sk_c10),identity).
% 402644 [hyper:402559,402567,402566] equal(multiply(sk_c8,sk_c10),sk_c9).
% 402650 [hyper:402559,402587,402586] equal(multiply(sk_c1,sk_c10),sk_c9).
% 402651 [para:402557.1.1,402558.1.1.1,demod:402556] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 402652 [para:402607.1.1,402558.1.1.1,demod:402556] equal(X,multiply(sk_c10,multiply(sk_c1,X))).
% 402654 [para:402644.1.1,402558.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c8,multiply(sk_c10,X))).
% 402656 [para:402650.1.1,402652.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 402659 [para:402557.1.1,402651.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 402660 [para:402607.1.1,402651.1.2.2,demod:402621] equal(sk_c1,multiply(sk_c9,identity)).
% 402663 [para:402558.1.1,402651.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 402664 [para:402652.1.2,402651.1.2.2,demod:402621] equal(multiply(sk_c1,X),multiply(sk_c9,X)).
% 402665 [para:402656.1.2,402651.1.2.2,demod:402624,402621] equal(sk_c9,identity).
% 402666 [para:402651.1.2,402651.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 402667 [para:402665.1.1,402624.1.1.1,demod:402556] equal(sk_c10,identity).
% 402668 [para:402665.1.1,402656.1.2.2] equal(sk_c10,multiply(sk_c10,identity)).
% 402669 [para:402667.1.1,402607.1.1.1,demod:402556] equal(sk_c1,identity).
% 402671 [para:402667.1.1,402644.1.1.2] equal(multiply(sk_c8,identity),sk_c9).
% 402673 [para:402667.1.1,402652.1.2.1,demod:402556] equal(X,multiply(sk_c1,X)).
% 402674 [para:402667.1.1,402656.1.2.1,demod:402556] equal(sk_c10,sk_c9).
% 402676 [para:402669.1.1,402652.1.2.2.1,demod:402556] equal(X,multiply(sk_c10,X)).
% 402679 [para:402667.1.1,402674.1.1] equal(identity,sk_c9).
% 402684 [para:402607.1.1,402654.1.2.2,demod:402671,402673,402664] equal(sk_c1,sk_c9).
% 402687 [para:402654.1.2,402651.1.2.2,demod:402673,402664,402676] equal(X,multiply(inverse(sk_c8),X)).
% 402689 [para:402674.1.1,402668.1.2.1,demod:402660] equal(sk_c10,sk_c1).
% 402695 [para:402666.1.2,402659.1.2] equal(X,multiply(X,identity)).
% 402697 [para:402695.1.2,402671.1.1] equal(sk_c8,sk_c9).
% 402698 [para:402695.1.2,402687.1.2] equal(identity,inverse(sk_c8)).
% 402699 [para:402695.1.2,402659.1.2] equal(X,inverse(inverse(X))).
% 402700 [para:402607.1.1,402663.1.2.2.2,demod:402695] equal(sk_c1,multiply(inverse(multiply(X,sk_c10)),X)).
% 402702 [para:402644.1.1,402663.1.2.2.2] equal(sk_c10,multiply(inverse(multiply(X,sk_c8)),multiply(X,sk_c9))).
% 402709 [para:402697.1.2,402684.1.2] equal(sk_c1,sk_c8).
% 402713 [para:402689.1.1,402700.1.2.1.1.2] equal(sk_c1,multiply(inverse(multiply(X,sk_c1)),X)).
% 402717 [para:402713.1.2,402651.1.2.2,demod:402673,402558,402699] equal(X,multiply(X,sk_c1)).
% 402718 [para:402709.1.1,402717.1.2.2] equal(X,multiply(X,sk_c8)).
% 402720 [para:402702.1.2,402651.1.2.2,demod:402699,402718] equal(multiply(X,sk_c9),multiply(X,sk_c10)).
% 402721 [para:402667.1.1,402720.1.2.2,demod:402695] equal(multiply(X,sk_c9),X).
% 402722 [hyper:402559,402721,demod:402698,cut:402679] 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 27
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c10),sk_c9) | -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(sk_c8,sk_c10),sk_c9) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% Split part used next: -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),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 27
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(45,40,1,98,0,1,74811,50,787,74811,40,787,74864,0,787,81855,3,1090,83186,4,1238,83856,5,1388,83857,1,1388,83857,50,1388,83857,40,1388,83910,0,1388,86112,3,1691,86267,4,1842,86299,5,1989,86299,1,1989,86299,50,1989,86299,40,1989,86352,0,1989,115414,3,3490,116309,4,4240,117111,5,4990,117112,1,4990,117112,50,4991,117112,40,4991,117165,0,4991,135066,3,5742,135799,4,6117,136446,1,6492,136446,50,6492,136446,40,6492,136499,0,6492,150344,3,7334,151492,4,7618,153115,5,7993,153116,5,7993,153117,1,7993,153117,50,7993,153117,40,7993,153170,0,7993,223318,3,11896,224419,4,13845,225408,5,15794,225409,1,15794,225409,50,15796,225409,40,15796,225462,0,15796,280469,3,18348,281344,4,19622,282157,5,20897,282158,1,20898,282158,50,20899,282158,40,20899,282211,0,20899,321560,3,22412,322289,4,23150,323211,1,23900,323211,50,23901,323211,40,23901,323264,0,23901,336099,3,24665,337782,4,25027,339857,5,25402,339858,1,25402,339858,50,25402,339858,40,25402,339911,0,25402,374756,3,26617,375331,4,27203,375858,5,27803,375859,1,27803,375859,50,27804,375859,40,27804,375912,0,27804,400657,3,28556,401100,4,28930,401586,1,29305,401586,50,29306,401586,40,29306,401586,40,29306,401675,0,29306,402419,50,29312,402419,30,29312,402419,40,29312,402464,0,29312,402554,50,29312,402599,0,29312,402721,50,29313,402721,30,29313,402721,40,29313,402766,0,29317)
%
%
% START OF PROOF
% 402722 [] equal(X,X).
% 402726 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 402745 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c2),sk_c10).
% 402746 [?] ?
% 402755 [?] ?
% 402756 [] equal(multiply(sk_c1,sk_c10),sk_c9) | equal(multiply(sk_c2,sk_c10),sk_c9).
% 402792 [hyper:402726,402745,binarycut:402755] equal(inverse(sk_c2),sk_c10).
% 402794 [hyper:402726,402745,binarycut:402746] equal(inverse(sk_c1),sk_c10).
% 402829 [hyper:402726,402756,demod:402794,cut:402722] equal(multiply(sk_c2,sk_c10),sk_c9).
% 402831 [hyper:402726,402829,demod:402792,cut:402722] 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 27
% 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(sk_c10),sk_c9) | -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(sk_c8,sk_c10),sk_c9) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% Split part used next: -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),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 27
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(45,40,1,98,0,1,74811,50,787,74811,40,787,74864,0,787,81855,3,1090,83186,4,1238,83856,5,1388,83857,1,1388,83857,50,1388,83857,40,1388,83910,0,1388,86112,3,1691,86267,4,1842,86299,5,1989,86299,1,1989,86299,50,1989,86299,40,1989,86352,0,1989,115414,3,3490,116309,4,4240,117111,5,4990,117112,1,4990,117112,50,4991,117112,40,4991,117165,0,4991,135066,3,5742,135799,4,6117,136446,1,6492,136446,50,6492,136446,40,6492,136499,0,6492,150344,3,7334,151492,4,7618,153115,5,7993,153116,5,7993,153117,1,7993,153117,50,7993,153117,40,7993,153170,0,7993,223318,3,11896,224419,4,13845,225408,5,15794,225409,1,15794,225409,50,15796,225409,40,15796,225462,0,15796,280469,3,18348,281344,4,19622,282157,5,20897,282158,1,20898,282158,50,20899,282158,40,20899,282211,0,20899,321560,3,22412,322289,4,23150,323211,1,23900,323211,50,23901,323211,40,23901,323264,0,23901,336099,3,24665,337782,4,25027,339857,5,25402,339858,1,25402,339858,50,25402,339858,40,25402,339911,0,25402,374756,3,26617,375331,4,27203,375858,5,27803,375859,1,27803,375859,50,27804,375859,40,27804,375912,0,27804,400657,3,28556,401100,4,28930,401586,1,29305,401586,50,29306,401586,40,29306,401586,40,29306,401675,0,29306,402419,50,29312,402419,30,29312,402419,40,29312,402464,0,29312,402554,50,29312,402599,0,29312,402721,50,29313,402721,30,29313,402721,40,29313,402766,0,29317,402830,50,29318,402830,30,29318,402830,40,29318,402875,0,29318)
%
%
% START OF PROOF
% 402831 [] equal(X,X).
% 402835 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 402854 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c2),sk_c10).
% 402855 [?] ?
% 402864 [?] ?
% 402865 [] equal(multiply(sk_c1,sk_c10),sk_c9) | equal(multiply(sk_c2,sk_c10),sk_c9).
% 402901 [hyper:402835,402854,binarycut:402864] equal(inverse(sk_c2),sk_c10).
% 402903 [hyper:402835,402854,binarycut:402855] equal(inverse(sk_c1),sk_c10).
% 402938 [hyper:402835,402865,demod:402903,cut:402831] equal(multiply(sk_c2,sk_c10),sk_c9).
% 402940 [hyper:402835,402938,demod:402901,cut:402831] 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 27
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c10),sk_c9) | -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(sk_c8,sk_c10),sk_c9) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% Split part used next: -equal(inverse(sk_c10),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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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(45,40,1,98,0,1,74811,50,787,74811,40,787,74864,0,787,81855,3,1090,83186,4,1238,83856,5,1388,83857,1,1388,83857,50,1388,83857,40,1388,83910,0,1388,86112,3,1691,86267,4,1842,86299,5,1989,86299,1,1989,86299,50,1989,86299,40,1989,86352,0,1989,115414,3,3490,116309,4,4240,117111,5,4990,117112,1,4990,117112,50,4991,117112,40,4991,117165,0,4991,135066,3,5742,135799,4,6117,136446,1,6492,136446,50,6492,136446,40,6492,136499,0,6492,150344,3,7334,151492,4,7618,153115,5,7993,153116,5,7993,153117,1,7993,153117,50,7993,153117,40,7993,153170,0,7993,223318,3,11896,224419,4,13845,225408,5,15794,225409,1,15794,225409,50,15796,225409,40,15796,225462,0,15796,280469,3,18348,281344,4,19622,282157,5,20897,282158,1,20898,282158,50,20899,282158,40,20899,282211,0,20899,321560,3,22412,322289,4,23150,323211,1,23900,323211,50,23901,323211,40,23901,323264,0,23901,336099,3,24665,337782,4,25027,339857,5,25402,339858,1,25402,339858,50,25402,339858,40,25402,339911,0,25402,374756,3,26617,375331,4,27203,375858,5,27803,375859,1,27803,375859,50,27804,375859,40,27804,375912,0,27804,400657,3,28556,401100,4,28930,401586,1,29305,401586,50,29306,401586,40,29306,401586,40,29306,401675,0,29306,402419,50,29312,402419,30,29312,402419,40,29312,402464,0,29312,402554,50,29312,402599,0,29312,402721,50,29313,402721,30,29313,402721,40,29313,402766,0,29317,402830,50,29318,402830,30,29318,402830,40,29318,402875,0,29318,402939,50,29318,402939,30,29318,402939,40,29318,402984,0,29318,403176,50,29320,403221,0,29325,403476,50,29330,403521,0,29330,403784,50,29336,403829,0,29341,404100,50,29350,404145,0,29350,404422,50,29362,404467,0,29362,404752,50,29383,404797,0,29387,405090,50,29454,405135,0,29454,405438,50,29527,405438,40,29527,405483,0,29527)
%
%
% START OF PROOF
% 405440 [] equal(multiply(identity,X),X).
% 405441 [] equal(multiply(inverse(X),X),identity).
% 405442 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 405443 [] -equal(inverse(sk_c10),sk_c9).
% 405474 [?] ?
% 405475 [?] ?
% 405476 [?] ?
% 405477 [?] ?
% 405478 [?] ?
% 405479 [?] ?
% 405480 [?] ?
% 405481 [?] ?
% 405482 [?] ?
% 405483 [?] ?
% 405500 [input:405475,cut:405443] equal(inverse(sk_c5),sk_c7).
% 405501 [para:405500.1.1,405441.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 405503 [input:405476,cut:405443] equal(inverse(sk_c6),sk_c5).
% 405504 [para:405503.1.1,405441.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 405505 [input:405478,cut:405443] equal(inverse(sk_c4),sk_c7).
% 405506 [para:405505.1.1,405441.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 405508 [input:405480,cut:405443] equal(inverse(sk_c3),sk_c9).
% 405509 [para:405508.1.1,405441.1.1.1] equal(multiply(sk_c9,sk_c3),identity).
% 405510 [input:405482,cut:405443] equal(inverse(sk_c2),sk_c10).
% 405511 [para:405510.1.1,405441.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 405533 [input:405474,cut:405443] equal(multiply(sk_c6,sk_c7),sk_c5).
% 405535 [input:405477,cut:405443] equal(multiply(sk_c7,sk_c9),sk_c10).
% 405537 [input:405479,cut:405443] equal(multiply(sk_c4,sk_c7),sk_c10).
% 405538 [input:405481,cut:405443] equal(multiply(sk_c3,sk_c9),sk_c8).
% 405539 [input:405483,cut:405443] equal(multiply(sk_c2,sk_c10),sk_c9).
% 405553 [para:405501.1.1,405442.1.1.1,demod:405440] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 405554 [para:405504.1.1,405442.1.1.1,demod:405440] equal(X,multiply(sk_c5,multiply(sk_c6,X))).
% 405555 [para:405506.1.1,405442.1.1.1,demod:405440] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 405557 [para:405509.1.1,405442.1.1.1,demod:405440] equal(X,multiply(sk_c9,multiply(sk_c3,X))).
% 405558 [para:405511.1.1,405442.1.1.1,demod:405440] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 405583 [para:405537.1.1,405442.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c4,multiply(sk_c7,X))).
% 405595 [para:405504.1.1,405553.1.2.2] equal(sk_c6,multiply(sk_c7,identity)).
% 405596 [para:405595.1.2,405442.1.1.1,demod:405440] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 405599 [para:405533.1.1,405554.1.2.2] equal(sk_c7,multiply(sk_c5,sk_c5)).
% 405602 [para:405599.1.2,405553.1.2.2] equal(sk_c5,multiply(sk_c7,sk_c7)).
% 405607 [para:405537.1.1,405555.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c10)).
% 405611 [para:405538.1.1,405557.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c8)).
% 405615 [para:405539.1.1,405558.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 405619 [para:405596.1.1,405554.1.2.2] equal(X,multiply(sk_c5,multiply(sk_c7,X))).
% 405620 [para:405501.1.1,405619.1.2.2] equal(sk_c5,multiply(sk_c5,identity)).
% 405621 [para:405506.1.1,405619.1.2.2,demod:405620] equal(sk_c4,sk_c5).
% 405629 [para:405621.1.2,405554.1.2.1,demod:405583,405596] equal(X,multiply(sk_c10,X)).
% 405638 [para:405629.1.2,405558.1.2] equal(X,multiply(sk_c2,X)).
% 405640 [para:405629.1.2,405615.1.2] equal(sk_c10,sk_c9).
% 405665 [para:405640.1.1,405607.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c9)).
% 405666 [para:405640.1.1,405558.1.2.1,demod:405638] equal(X,multiply(sk_c9,X)).
% 405673 [para:405666.1.2,405611.1.2] equal(sk_c9,sk_c8).
% 405724 [para:405673.1.1,405535.1.1.2] equal(multiply(sk_c7,sk_c8),sk_c10).
% 405726 [para:405673.1.1,405615.1.2.2,demod:405629] equal(sk_c10,sk_c8).
% 405734 [para:405726.1.1,405607.1.2.2,demod:405724] equal(sk_c7,sk_c10).
% 405746 [para:405734.1.2,405539.1.1.2,demod:405638] equal(sk_c7,sk_c9).
% 405751 [para:405734.1.2,405607.1.2.2,demod:405602] equal(sk_c7,sk_c5).
% 405753 [para:405734.1.2,405615.1.2.1,demod:405665] equal(sk_c10,sk_c7).
% 405763 [para:405751.1.2,405500.1.1.1] equal(inverse(sk_c7),sk_c7).
% 405769 [para:405753.1.1,405443.1.1.1,demod:405763,cut:405746] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c10),sk_c9) | -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10) | -equal(multiply(sk_c8,sk_c10),sk_c9) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(U,V),sk_c10) | -equal(inverse(U),V) | -equal(multiply(V,sk_c9),sk_c10) | -equal(inverse(W),X1) | -equal(inverse(X1),V) | -equal(multiply(W,V),X1).
% Split part used next: -equal(multiply(sk_c8,sk_c10),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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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(45,40,1,98,0,1,74811,50,787,74811,40,787,74864,0,787,81855,3,1090,83186,4,1238,83856,5,1388,83857,1,1388,83857,50,1388,83857,40,1388,83910,0,1388,86112,3,1691,86267,4,1842,86299,5,1989,86299,1,1989,86299,50,1989,86299,40,1989,86352,0,1989,115414,3,3490,116309,4,4240,117111,5,4990,117112,1,4990,117112,50,4991,117112,40,4991,117165,0,4991,135066,3,5742,135799,4,6117,136446,1,6492,136446,50,6492,136446,40,6492,136499,0,6492,150344,3,7334,151492,4,7618,153115,5,7993,153116,5,7993,153117,1,7993,153117,50,7993,153117,40,7993,153170,0,7993,223318,3,11896,224419,4,13845,225408,5,15794,225409,1,15794,225409,50,15796,225409,40,15796,225462,0,15796,280469,3,18348,281344,4,19622,282157,5,20897,282158,1,20898,282158,50,20899,282158,40,20899,282211,0,20899,321560,3,22412,322289,4,23150,323211,1,23900,323211,50,23901,323211,40,23901,323264,0,23901,336099,3,24665,337782,4,25027,339857,5,25402,339858,1,25402,339858,50,25402,339858,40,25402,339911,0,25402,374756,3,26617,375331,4,27203,375858,5,27803,375859,1,27803,375859,50,27804,375859,40,27804,375912,0,27804,400657,3,28556,401100,4,28930,401586,1,29305,401586,50,29306,401586,40,29306,401586,40,29306,401675,0,29306,402419,50,29312,402419,30,29312,402419,40,29312,402464,0,29312,402554,50,29312,402599,0,29312,402721,50,29313,402721,30,29313,402721,40,29313,402766,0,29317,402830,50,29318,402830,30,29318,402830,40,29318,402875,0,29318,402939,50,29318,402939,30,29318,402939,40,29318,402984,0,29318,403176,50,29320,403221,0,29325,403476,50,29330,403521,0,29330,403784,50,29336,403829,0,29341,404100,50,29350,404145,0,29350,404422,50,29362,404467,0,29362,404752,50,29383,404797,0,29387,405090,50,29454,405135,0,29454,405438,50,29527,405438,40,29527,405483,0,29527,405768,50,29528,405768,30,29528,405768,40,29528,405813,0,29528,406012,50,29531,406057,0,29536,406314,50,29541,406359,0,29541,406624,50,29547,406669,0,29547,406942,50,29556,406987,0,29560,407266,50,29573,407311,0,29573,407598,50,29594,407643,0,29599,407938,50,29635,407983,0,29635,408288,50,29707,408333,0,29707,408648,50,29846,408648,40,29846,408693,0,29846)
%
%
% START OF PROOF
% 408594 [?] ?
% 408650 [] equal(multiply(identity,X),X).
% 408651 [] equal(multiply(inverse(X),X),identity).
% 408652 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 408653 [] -equal(multiply(sk_c8,sk_c10),sk_c9).
% 408655 [?] ?
% 408656 [?] ?
% 408658 [?] ?
% 408659 [?] ?
% 408660 [?] ?
% 408661 [?] ?
% 408662 [?] ?
% 408663 [?] ?
% 408713 [input:408655,cut:408653] equal(inverse(sk_c5),sk_c7).
% 408714 [para:408713.1.1,408651.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 408727 [input:408656,cut:408653] equal(inverse(sk_c6),sk_c5).
% 408728 [para:408727.1.1,408651.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 408729 [input:408658,cut:408653] equal(inverse(sk_c4),sk_c7).
% 408730 [para:408729.1.1,408651.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 408731 [input:408660,cut:408653] equal(inverse(sk_c3),sk_c9).
% 408732 [para:408731.1.1,408651.1.1.1] equal(multiply(sk_c9,sk_c3),identity).
% 408734 [input:408662,cut:408653] equal(inverse(sk_c2),sk_c10).
% 408735 [para:408734.1.1,408651.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 408742 [input:408659,cut:408653] equal(multiply(sk_c4,sk_c7),sk_c10).
% 408750 [input:408661,cut:408653] equal(multiply(sk_c3,sk_c9),sk_c8).
% 408755 [input:408663,cut:408653] equal(multiply(sk_c2,sk_c10),sk_c9).
% 408783 [para:408714.1.1,408652.1.1.1,demod:408650] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 408784 [para:408728.1.1,408652.1.1.1,demod:408650] equal(X,multiply(sk_c5,multiply(sk_c6,X))).
% 408786 [para:408732.1.1,408652.1.1.1,demod:408650] equal(X,multiply(sk_c9,multiply(sk_c3,X))).
% 408788 [para:408735.1.1,408652.1.1.1,demod:408650] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 408790 [para:408742.1.1,408652.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c4,multiply(sk_c7,X))).
% 408817 [para:408728.1.1,408783.1.2.2] equal(sk_c6,multiply(sk_c7,identity)).
% 408818 [para:408817.1.2,408652.1.1.1,demod:408650] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 408832 [para:408750.1.1,408786.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c8)).
% 408837 [para:408755.1.1,408788.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 408839 [para:408818.1.1,408784.1.2.2] equal(X,multiply(sk_c5,multiply(sk_c7,X))).
% 408840 [para:408714.1.1,408839.1.2.2] equal(sk_c5,multiply(sk_c5,identity)).
% 408841 [para:408730.1.1,408839.1.2.2,demod:408840] equal(sk_c4,sk_c5).
% 408847 [para:408841.1.2,408784.1.2.1,demod:408790,408818] equal(X,multiply(sk_c10,X)).
% 408859 [para:408847.1.2,408788.1.2] equal(X,multiply(sk_c2,X)).
% 408860 [para:408847.1.2,408837.1.2] equal(sk_c10,sk_c9).
% 408890 [para:408860.1.1,408788.1.2.1,demod:408859] equal(X,multiply(sk_c9,X)).
% 408907 [para:408890.1.2,408832.1.2] equal(sk_c9,sk_c8).
% 408910 [para:408907.1.1,408653.1.2,cut:408594] 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: 33022
% derived clauses: 4966627
% kept clauses: 287943
% kept size sum: 449234
% kept mid-nuclei: 63208
% kept new demods: 4791
% forw unit-subs: 2063419
% forw double-subs: 2267925
% forw overdouble-subs: 230321
% backward subs: 10641
% fast unit cutoff: 31943
% full unit cutoff: 0
% dbl unit cutoff: 21817
% real runtime : 301.15
% process. runtime: 298.46
% specific non-discr-tree subsumption statistics:
% tried: 60880296
% length fails: 7031329
% strength fails: 18004622
% predlist fails: 3382663
% aux str. fails: 5319306
% by-lit fails: 10317876
% full subs tried: 2978820
% full subs fail: 2865980
%
% ; 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/GRP375-1+eq_r.in")
%
%------------------------------------------------------------------------------