TSTP Solution File: GRP324-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP324-1 : 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 : art08.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 297.0s
% Output : Assurance 297.0s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP324-1+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 23)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 23)
% (binary-posweight-lex-big-order 30 #f 3 23)
% (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_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% was split for some strategies as:
% -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% -equal(multiply(sk_c7,sk_c8),sk_c6).
% -equal(multiply(sk_c8,sk_c7),sk_c6).
% -equal(inverse(sk_c8),sk_c6).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,897,50,8,943,0,8,2085,50,25,2131,0,25,3564,50,46,3610,0,46,5171,50,68,5217,0,68,6945,50,97,6991,0,97,8847,50,139,8893,0,139,10918,50,203,10964,0,203,13159,50,313,13205,0,313,15611,50,488,15657,0,488,18275,50,756,18275,40,756,18321,0,756,28798,3,1060,29530,4,1207,30263,5,1357,30264,1,1357,30264,50,1357,30264,40,1357,30310,0,1357,30649,3,1659,30660,4,1816,30684,5,1958,30684,1,1958,30684,50,1958,30684,40,1958,30730,0,1958,63113,3,3460,63915,4,4209,64862,5,4959,64863,1,4959,64863,50,4960,64863,40,4960,64909,0,4960,85548,3,5711,86205,4,6086,86874,1,6461,86874,50,6461,86874,40,6461,86920,0,6461,96859,3,7217,98446,4,7587,100065,5,7962,100066,1,7962,100066,50,7962,100066,40,7962,100112,0,7962,166678,3,11876,167581,4,13813,168301,1,15763,168301,50,15766,168301,40,15766,168347,0,15766,220054,3,18318,220820,4,19592,221466,5,20867,221467,1,20868,221467,50,20869,221467,40,20869,221513,0,20869,261976,3,22370,262842,4,23120,263620,1,23870,263620,50,23871,263620,40,23871,263666,0,23871,272529,3,24635,273475,4,24997,273664,5,25372,273664,1,25372,273664,50,25372,273664,40,25372,273710,0,25372,304230,3,26573,305001,4,27173,305659,1,27773,305659,50,27774,305659,40,27774,305705,0,27774,327307,3,28527,328024,4,28900,328651,5,29275,328652,1,29275,328652,50,29275,328652,40,29275,328652,40,29275,328693,0,29275)
%
%
% START OF PROOF
% 328654 [] equal(multiply(identity,X),X).
% 328655 [] equal(multiply(inverse(X),X),identity).
% 328656 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 328657 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 328658 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 328659 [?] ?
% 328664 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c7).
% 328665 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 328670 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 328671 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 328676 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 328677 [?] ?
% 328682 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 328683 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 328688 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c5),sk_c7).
% 328689 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 328696 [hyper:328657,328658,binarycut:328659] equal(inverse(sk_c2),sk_c8).
% 328697 [para:328696.1.1,328655.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 328705 [hyper:328657,328676,binarycut:328677] equal(inverse(sk_c1),sk_c7).
% 328708 [para:328705.1.1,328655.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 328713 [hyper:328657,328665,328664] equal(multiply(sk_c2,sk_c8),sk_c3).
% 328719 [hyper:328657,328671,328670] equal(multiply(sk_c8,sk_c3),sk_c7).
% 328725 [hyper:328657,328683,328682] equal(multiply(sk_c1,sk_c7),sk_c8).
% 328733 [hyper:328657,328689,328688] equal(multiply(sk_c7,sk_c8),sk_c6).
% 328734 [para:328655.1.1,328656.1.1.1,demod:328654] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 328735 [para:328697.1.1,328656.1.1.1,demod:328654] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 328737 [para:328713.1.1,328656.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c8,X))).
% 328741 [para:328713.1.1,328735.1.2.2,demod:328719] equal(sk_c8,sk_c7).
% 328742 [para:328741.1.2,328708.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 328743 [para:328741.1.2,328725.1.1.2] equal(multiply(sk_c1,sk_c8),sk_c8).
% 328746 [para:328743.1.1,328656.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c8,X))).
% 328748 [para:328697.1.1,328734.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 328751 [para:328725.1.1,328734.1.2.2,demod:328733,328705] equal(sk_c7,sk_c6).
% 328754 [para:328742.1.1,328734.1.2.2,demod:328748] equal(sk_c1,sk_c2).
% 328755 [para:328743.1.1,328734.1.2.2,demod:328733,328705] equal(sk_c8,sk_c6).
% 328757 [para:328754.1.2,328713.1.1.1,demod:328743] equal(sk_c8,sk_c3).
% 328758 [para:328751.1.1,328708.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 328771 [para:328757.1.1,328735.1.2.1] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 328785 [para:328735.1.2,328737.1.2.2,demod:328771] equal(X,multiply(sk_c2,X)).
% 328786 [para:328754.1.2,328737.1.2.1,demod:328746] equal(multiply(sk_c3,X),multiply(sk_c8,X)).
% 328787 [para:328755.1.1,328737.1.2.2.1,demod:328785] equal(multiply(sk_c3,X),multiply(sk_c6,X)).
% 328788 [para:328785.1.2,328735.1.2.2,demod:328787,328786] equal(X,multiply(sk_c6,X)).
% 328791 [para:328788.1.2,328758.1.1] equal(sk_c1,identity).
% 328792 [para:328791.1.1,328705.1.1.1] equal(inverse(identity),sk_c7).
% 328793 [hyper:328657,328792,demod:328654,cut:328751] 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 23
% 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_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% 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 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,897,50,8,943,0,8,2085,50,25,2131,0,25,3564,50,46,3610,0,46,5171,50,68,5217,0,68,6945,50,97,6991,0,97,8847,50,139,8893,0,139,10918,50,203,10964,0,203,13159,50,313,13205,0,313,15611,50,488,15657,0,488,18275,50,756,18275,40,756,18321,0,756,28798,3,1060,29530,4,1207,30263,5,1357,30264,1,1357,30264,50,1357,30264,40,1357,30310,0,1357,30649,3,1659,30660,4,1816,30684,5,1958,30684,1,1958,30684,50,1958,30684,40,1958,30730,0,1958,63113,3,3460,63915,4,4209,64862,5,4959,64863,1,4959,64863,50,4960,64863,40,4960,64909,0,4960,85548,3,5711,86205,4,6086,86874,1,6461,86874,50,6461,86874,40,6461,86920,0,6461,96859,3,7217,98446,4,7587,100065,5,7962,100066,1,7962,100066,50,7962,100066,40,7962,100112,0,7962,166678,3,11876,167581,4,13813,168301,1,15763,168301,50,15766,168301,40,15766,168347,0,15766,220054,3,18318,220820,4,19592,221466,5,20867,221467,1,20868,221467,50,20869,221467,40,20869,221513,0,20869,261976,3,22370,262842,4,23120,263620,1,23870,263620,50,23871,263620,40,23871,263666,0,23871,272529,3,24635,273475,4,24997,273664,5,25372,273664,1,25372,273664,50,25372,273664,40,25372,273710,0,25372,304230,3,26573,305001,4,27173,305659,1,27773,305659,50,27774,305659,40,27774,305705,0,27774,327307,3,28527,328024,4,28900,328651,5,29275,328652,1,29275,328652,50,29275,328652,40,29275,328652,40,29275,328693,0,29275,328792,50,29275,328792,30,29275,328792,40,29275,328833,0,29275)
%
%
% START OF PROOF
% 328794 [] equal(multiply(identity,X),X).
% 328795 [] equal(multiply(inverse(X),X),identity).
% 328796 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 328797 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 328801 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 328802 [?] ?
% 328807 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 328808 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 328813 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 328814 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 328819 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 328820 [?] ?
% 328825 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 328826 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 328831 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 328832 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 328842 [hyper:328797,328801,binarycut:328802] equal(inverse(sk_c2),sk_c8).
% 328845 [para:328842.1.1,328795.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 328852 [hyper:328797,328819,binarycut:328820] equal(inverse(sk_c1),sk_c7).
% 328853 [para:328852.1.1,328795.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 328863 [hyper:328797,328808,328807] equal(multiply(sk_c2,sk_c8),sk_c3).
% 328880 [hyper:328797,328814,328813] equal(multiply(sk_c8,sk_c3),sk_c7).
% 328884 [hyper:328797,328826,328825] equal(multiply(sk_c1,sk_c7),sk_c8).
% 328888 [hyper:328797,328832,328831] equal(multiply(sk_c7,sk_c8),sk_c6).
% 328889 [para:328795.1.1,328796.1.1.1,demod:328794] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 328890 [para:328845.1.1,328796.1.1.1,demod:328794] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 328892 [para:328863.1.1,328796.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c8,X))).
% 328896 [para:328863.1.1,328890.1.2.2,demod:328880] equal(sk_c8,sk_c7).
% 328897 [para:328896.1.2,328853.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 328898 [para:328896.1.2,328884.1.1.2] equal(multiply(sk_c1,sk_c8),sk_c8).
% 328899 [para:328896.1.2,328888.1.1.1] equal(multiply(sk_c8,sk_c8),sk_c6).
% 328901 [?] ?
% 328903 [para:328845.1.1,328889.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 328905 [para:328880.1.1,328889.1.2.2] equal(sk_c3,multiply(inverse(sk_c8),sk_c7)).
% 328909 [para:328897.1.1,328889.1.2.2,demod:328903] equal(sk_c1,sk_c2).
% 328910 [para:328898.1.1,328889.1.2.2,demod:328888,328852] equal(sk_c8,sk_c6).
% 328912 [para:328909.1.2,328863.1.1.1,demod:328898] equal(sk_c8,sk_c3).
% 328917 [para:328910.1.1,328863.1.1.2] equal(multiply(sk_c2,sk_c6),sk_c3).
% 328926 [para:328912.1.1,328890.1.2.1] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 328929 [para:328912.1.1,328910.1.1] equal(sk_c3,sk_c6).
% 328933 [para:328929.1.1,328880.1.1.2] equal(multiply(sk_c8,sk_c6),sk_c7).
% 328935 [para:328912.1.1,328899.1.1.1] equal(multiply(sk_c3,sk_c8),sk_c6).
% 328940 [para:328890.1.2,328892.1.2.2,demod:328926] equal(X,multiply(sk_c2,X)).
% 328941 [para:328909.1.2,328892.1.2.1,demod:328901] equal(multiply(sk_c3,X),multiply(sk_c8,X)).
% 328942 [para:328910.1.1,328892.1.2.2.1,demod:328940] equal(multiply(sk_c3,X),multiply(sk_c6,X)).
% 328943 [para:328940.1.2,328890.1.2.2,demod:328942,328941] equal(X,multiply(sk_c6,X)).
% 328945 [para:328943.1.2,328889.1.2.2] equal(X,multiply(inverse(sk_c6),X)).
% 328951 [para:328917.1.1,328890.1.2.2,demod:328880] equal(sk_c6,sk_c7).
% 328957 [para:328945.1.2,328795.1.1] equal(sk_c6,identity).
% 328961 [para:328957.1.1,328933.1.1.2,demod:328943,328942,328941] equal(identity,sk_c7).
% 328964 [para:328961.1.2,328905.1.2.2,demod:328903] equal(sk_c3,sk_c2).
% 328965 [para:328964.1.2,328842.1.1.1] equal(inverse(sk_c3),sk_c8).
% 328976 [hyper:328797,328965,demod:328935,cut:328951] 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 23
% 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_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% 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 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,897,50,8,943,0,8,2085,50,25,2131,0,25,3564,50,46,3610,0,46,5171,50,68,5217,0,68,6945,50,97,6991,0,97,8847,50,139,8893,0,139,10918,50,203,10964,0,203,13159,50,313,13205,0,313,15611,50,488,15657,0,488,18275,50,756,18275,40,756,18321,0,756,28798,3,1060,29530,4,1207,30263,5,1357,30264,1,1357,30264,50,1357,30264,40,1357,30310,0,1357,30649,3,1659,30660,4,1816,30684,5,1958,30684,1,1958,30684,50,1958,30684,40,1958,30730,0,1958,63113,3,3460,63915,4,4209,64862,5,4959,64863,1,4959,64863,50,4960,64863,40,4960,64909,0,4960,85548,3,5711,86205,4,6086,86874,1,6461,86874,50,6461,86874,40,6461,86920,0,6461,96859,3,7217,98446,4,7587,100065,5,7962,100066,1,7962,100066,50,7962,100066,40,7962,100112,0,7962,166678,3,11876,167581,4,13813,168301,1,15763,168301,50,15766,168301,40,15766,168347,0,15766,220054,3,18318,220820,4,19592,221466,5,20867,221467,1,20868,221467,50,20869,221467,40,20869,221513,0,20869,261976,3,22370,262842,4,23120,263620,1,23870,263620,50,23871,263620,40,23871,263666,0,23871,272529,3,24635,273475,4,24997,273664,5,25372,273664,1,25372,273664,50,25372,273664,40,25372,273710,0,25372,304230,3,26573,305001,4,27173,305659,1,27773,305659,50,27774,305659,40,27774,305705,0,27774,327307,3,28527,328024,4,28900,328651,5,29275,328652,1,29275,328652,50,29275,328652,40,29275,328652,40,29275,328693,0,29275,328792,50,29275,328792,30,29275,328792,40,29275,328833,0,29275,328975,50,29275,328975,30,29275,328975,40,29275,329016,0,29279)
%
%
% START OF PROOF
% 328976 [] equal(X,X).
% 328977 [] equal(multiply(identity,X),X).
% 328978 [] equal(multiply(inverse(X),X),identity).
% 328979 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 328980 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 328981 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 328982 [] equal(multiply(sk_c5,sk_c7),sk_c6) | equal(inverse(sk_c2),sk_c8).
% 328983 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c8),sk_c6).
% 328984 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 328985 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c8).
% 328986 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c2),sk_c8).
% 328987 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c7).
% 328988 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 328989 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c8),sk_c6).
% 328990 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 328991 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 328992 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c8,sk_c7),sk_c6).
% 328993 [?] ?
% 328994 [?] ?
% 328995 [?] ?
% 328996 [?] ?
% 328997 [?] ?
% 328998 [?] ?
% 329062 [hyper:328980,328987,binarycut:328993,binarycut:328981] equal(inverse(sk_c5),sk_c7).
% 329063 [para:329062.1.1,328978.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 329066 [hyper:328980,328989,binarycut:328995,binarycut:328983] equal(inverse(sk_c8),sk_c6).
% 329071 [hyper:328980,328988,328982,binarycut:328994] equal(multiply(sk_c5,sk_c7),sk_c6).
% 329072 [para:329066.1.1,328978.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 329077 [hyper:328980,328990,binarycut:328996,binarycut:328984] equal(inverse(sk_c4),sk_c8).
% 329087 [para:329077.1.1,328978.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 329094 [hyper:328980,328991,328985,binarycut:328997] equal(multiply(sk_c4,sk_c8),sk_c7).
% 329103 [hyper:328980,328992,328986,binarycut:328998] equal(multiply(sk_c8,sk_c7),sk_c6).
% 329104 [para:328978.1.1,328979.1.1.1,demod:328977] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 329105 [para:329063.1.1,328979.1.1.1,demod:328977] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 329107 [para:329072.1.1,328979.1.1.1,demod:328977] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 329108 [para:329087.1.1,328979.1.1.1,demod:328977] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 329113 [para:329071.1.1,329105.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 329120 [para:329087.1.1,329104.1.2.2,demod:329066] equal(sk_c4,multiply(sk_c6,identity)).
% 329121 [para:329094.1.1,329104.1.2.2,demod:329103,329077] equal(sk_c8,sk_c6).
% 329122 [para:329103.1.1,329104.1.2.2,demod:329066] equal(sk_c7,multiply(sk_c6,sk_c6)).
% 329124 [para:329120.1.2,328979.1.1.1,demod:328977] equal(multiply(sk_c4,X),multiply(sk_c6,X)).
% 329126 [para:329121.1.1,329066.1.1.1] equal(inverse(sk_c6),sk_c6).
% 329127 [para:329121.1.1,329072.1.1.2,demod:329122] equal(sk_c7,identity).
% 329133 [para:329127.1.1,329105.1.2.1,demod:328977] equal(X,multiply(sk_c5,X)).
% 329134 [para:329127.1.1,329113.1.2.1,demod:328977] equal(sk_c7,sk_c6).
% 329140 [para:329134.1.1,329105.1.2.1,demod:329133] equal(X,multiply(sk_c6,X)).
% 329153 [para:329107.1.2,329104.1.2.2,demod:329140,329126] equal(multiply(sk_c8,X),X).
% 329160 [hyper:328980,329108,329094,demod:329153,329140,329124,demod:329077,cut:328976] 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 23
% 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(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% 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 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,897,50,8,943,0,8,2085,50,25,2131,0,25,3564,50,46,3610,0,46,5171,50,68,5217,0,68,6945,50,97,6991,0,97,8847,50,139,8893,0,139,10918,50,203,10964,0,203,13159,50,313,13205,0,313,15611,50,488,15657,0,488,18275,50,756,18275,40,756,18321,0,756,28798,3,1060,29530,4,1207,30263,5,1357,30264,1,1357,30264,50,1357,30264,40,1357,30310,0,1357,30649,3,1659,30660,4,1816,30684,5,1958,30684,1,1958,30684,50,1958,30684,40,1958,30730,0,1958,63113,3,3460,63915,4,4209,64862,5,4959,64863,1,4959,64863,50,4960,64863,40,4960,64909,0,4960,85548,3,5711,86205,4,6086,86874,1,6461,86874,50,6461,86874,40,6461,86920,0,6461,96859,3,7217,98446,4,7587,100065,5,7962,100066,1,7962,100066,50,7962,100066,40,7962,100112,0,7962,166678,3,11876,167581,4,13813,168301,1,15763,168301,50,15766,168301,40,15766,168347,0,15766,220054,3,18318,220820,4,19592,221466,5,20867,221467,1,20868,221467,50,20869,221467,40,20869,221513,0,20869,261976,3,22370,262842,4,23120,263620,1,23870,263620,50,23871,263620,40,23871,263666,0,23871,272529,3,24635,273475,4,24997,273664,5,25372,273664,1,25372,273664,50,25372,273664,40,25372,273710,0,25372,304230,3,26573,305001,4,27173,305659,1,27773,305659,50,27774,305659,40,27774,305705,0,27774,327307,3,28527,328024,4,28900,328651,5,29275,328652,1,29275,328652,50,29275,328652,40,29275,328652,40,29275,328693,0,29275,328792,50,29275,328792,30,29275,328792,40,29275,328833,0,29275,328975,50,29275,328975,30,29275,328975,40,29275,329016,0,29279,329159,50,29280,329159,30,29280,329159,40,29280,329200,0,29280)
%
%
% START OF PROOF
% 329161 [] equal(multiply(identity,X),X).
% 329162 [] equal(multiply(inverse(X),X),identity).
% 329163 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 329164 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% 329183 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 329184 [] equal(multiply(sk_c5,sk_c7),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 329185 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c8),sk_c6).
% 329186 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 329187 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 329188 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 329189 [?] ?
% 329190 [?] ?
% 329191 [?] ?
% 329192 [?] ?
% 329193 [?] ?
% 329194 [?] ?
% 329208 [hyper:329164,329183,binarycut:329189] equal(inverse(sk_c5),sk_c7).
% 329212 [para:329208.1.1,329162.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 329216 [hyper:329164,329185,binarycut:329191] equal(inverse(sk_c8),sk_c6).
% 329218 [para:329216.1.1,329162.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 329221 [hyper:329164,329186,binarycut:329192] equal(inverse(sk_c4),sk_c8).
% 329222 [para:329221.1.1,329162.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 329227 [hyper:329164,329184,binarycut:329190] equal(multiply(sk_c5,sk_c7),sk_c6).
% 329230 [hyper:329164,329187,binarycut:329193] equal(multiply(sk_c4,sk_c8),sk_c7).
% 329233 [hyper:329164,329188,binarycut:329194] equal(multiply(sk_c8,sk_c7),sk_c6).
% 329234 [para:329162.1.1,329163.1.1.1,demod:329161] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 329235 [para:329212.1.1,329163.1.1.1,demod:329161] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 329236 [para:329218.1.1,329163.1.1.1,demod:329161] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 329241 [para:329227.1.1,329235.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 329243 [para:329222.1.1,329236.1.2.2] equal(sk_c4,multiply(sk_c6,identity)).
% 329244 [para:329233.1.1,329236.1.2.2] equal(sk_c7,multiply(sk_c6,sk_c6)).
% 329248 [para:329230.1.1,329234.1.2.2,demod:329233,329221] equal(sk_c8,sk_c6).
% 329252 [para:329248.1.1,329218.1.1.2,demod:329244] equal(sk_c7,identity).
% 329257 [para:329252.1.1,329212.1.1.1,demod:329161] equal(sk_c5,identity).
% 329261 [para:329252.1.1,329241.1.2.1,demod:329161] equal(sk_c7,sk_c6).
% 329262 [para:329257.1.1,329208.1.1.1] equal(inverse(identity),sk_c7).
% 329268 [para:329261.1.1,329252.1.1] equal(sk_c6,identity).
% 329270 [para:329268.1.1,329218.1.1.1,demod:329161] equal(sk_c8,identity).
% 329273 [para:329270.1.1,329218.1.1.2,demod:329243] equal(sk_c4,identity).
% 329275 [para:329273.1.1,329221.1.1.1,demod:329262] equal(sk_c7,sk_c8).
% 329279 [hyper:329164,329262,demod:329161,cut:329275] 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 23
% 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(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(multiply(sk_c7,sk_c8),sk_c6).
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,0,87,0,0,897,50,8,943,0,8,2085,50,25,2131,0,25,3564,50,46,3610,0,46,5171,50,68,5217,0,68,6945,50,97,6991,0,97,8847,50,139,8893,0,139,10918,50,203,10964,0,203,13159,50,313,13205,0,313,15611,50,488,15657,0,488,18275,50,756,18275,40,756,18321,0,756,28798,3,1060,29530,4,1207,30263,5,1357,30264,1,1357,30264,50,1357,30264,40,1357,30310,0,1357,30649,3,1659,30660,4,1816,30684,5,1958,30684,1,1958,30684,50,1958,30684,40,1958,30730,0,1958,63113,3,3460,63915,4,4209,64862,5,4959,64863,1,4959,64863,50,4960,64863,40,4960,64909,0,4960,85548,3,5711,86205,4,6086,86874,1,6461,86874,50,6461,86874,40,6461,86920,0,6461,96859,3,7217,98446,4,7587,100065,5,7962,100066,1,7962,100066,50,7962,100066,40,7962,100112,0,7962,166678,3,11876,167581,4,13813,168301,1,15763,168301,50,15766,168301,40,15766,168347,0,15766,220054,3,18318,220820,4,19592,221466,5,20867,221467,1,20868,221467,50,20869,221467,40,20869,221513,0,20869,261976,3,22370,262842,4,23120,263620,1,23870,263620,50,23871,263620,40,23871,263666,0,23871,272529,3,24635,273475,4,24997,273664,5,25372,273664,1,25372,273664,50,25372,273664,40,25372,273710,0,25372,304230,3,26573,305001,4,27173,305659,1,27773,305659,50,27774,305659,40,27774,305705,0,27774,327307,3,28527,328024,4,28900,328651,5,29275,328652,1,29275,328652,50,29275,328652,40,29275,328652,40,29275,328693,0,29275,328792,50,29275,328792,30,29275,328792,40,29275,328833,0,29275,328975,50,29275,328975,30,29275,328975,40,29275,329016,0,29279,329159,50,29280,329159,30,29280,329159,40,29280,329200,0,29280,329278,50,29280,329278,30,29280,329278,40,29280,329319,0,29284,329422,50,29285,329463,0,29285,329612,50,29287,329653,0,29292,329810,50,29296,329851,0,29296,330016,50,29301,330057,0,29306,330228,50,29314,330269,0,29314,330448,50,29329,330489,0,29334,330676,50,29362,330717,0,29362,330914,50,29423,330955,0,29423,331162,50,29537,331162,40,29537,331203,0,29537)
%
%
% START OF PROOF
% 331034 [?] ?
% 331164 [] equal(multiply(identity,X),X).
% 331165 [] equal(multiply(inverse(X),X),identity).
% 331166 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 331167 [] -equal(multiply(sk_c7,sk_c8),sk_c6).
% 331198 [?] ?
% 331199 [?] ?
% 331201 [?] ?
% 331202 [?] ?
% 331203 [?] ?
% 331254 [input:331198,cut:331167] equal(inverse(sk_c5),sk_c7).
% 331255 [para:331254.1.1,331165.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 331259 [input:331201,cut:331167] equal(inverse(sk_c4),sk_c8).
% 331260 [para:331259.1.1,331165.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 331273 [input:331199,cut:331167] equal(multiply(sk_c5,sk_c7),sk_c6).
% 331274 [input:331202,cut:331167] equal(multiply(sk_c4,sk_c8),sk_c7).
% 331275 [input:331203,cut:331167] equal(multiply(sk_c8,sk_c7),sk_c6).
% 331299 [para:331255.1.1,331166.1.1.1,demod:331164] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 331303 [para:331260.1.1,331166.1.1.1,demod:331164] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 331333 [para:331273.1.1,331299.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 331361 [para:331274.1.1,331303.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 331368 [para:331361.1.2,331275.1.1] equal(sk_c8,sk_c6).
% 331371 [para:331368.1.1,331167.1.1.2,demod:331333,cut:331034] 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(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(multiply(sk_c8,sk_c7),sk_c6).
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,0,87,0,0,897,50,8,943,0,8,2085,50,25,2131,0,25,3564,50,46,3610,0,46,5171,50,68,5217,0,68,6945,50,97,6991,0,97,8847,50,139,8893,0,139,10918,50,203,10964,0,203,13159,50,313,13205,0,313,15611,50,488,15657,0,488,18275,50,756,18275,40,756,18321,0,756,28798,3,1060,29530,4,1207,30263,5,1357,30264,1,1357,30264,50,1357,30264,40,1357,30310,0,1357,30649,3,1659,30660,4,1816,30684,5,1958,30684,1,1958,30684,50,1958,30684,40,1958,30730,0,1958,63113,3,3460,63915,4,4209,64862,5,4959,64863,1,4959,64863,50,4960,64863,40,4960,64909,0,4960,85548,3,5711,86205,4,6086,86874,1,6461,86874,50,6461,86874,40,6461,86920,0,6461,96859,3,7217,98446,4,7587,100065,5,7962,100066,1,7962,100066,50,7962,100066,40,7962,100112,0,7962,166678,3,11876,167581,4,13813,168301,1,15763,168301,50,15766,168301,40,15766,168347,0,15766,220054,3,18318,220820,4,19592,221466,5,20867,221467,1,20868,221467,50,20869,221467,40,20869,221513,0,20869,261976,3,22370,262842,4,23120,263620,1,23870,263620,50,23871,263620,40,23871,263666,0,23871,272529,3,24635,273475,4,24997,273664,5,25372,273664,1,25372,273664,50,25372,273664,40,25372,273710,0,25372,304230,3,26573,305001,4,27173,305659,1,27773,305659,50,27774,305659,40,27774,305705,0,27774,327307,3,28527,328024,4,28900,328651,5,29275,328652,1,29275,328652,50,29275,328652,40,29275,328652,40,29275,328693,0,29275,328792,50,29275,328792,30,29275,328792,40,29275,328833,0,29275,328975,50,29275,328975,30,29275,328975,40,29275,329016,0,29279,329159,50,29280,329159,30,29280,329159,40,29280,329200,0,29280,329278,50,29280,329278,30,29280,329278,40,29280,329319,0,29284,329422,50,29285,329463,0,29285,329612,50,29287,329653,0,29292,329810,50,29296,329851,0,29296,330016,50,29301,330057,0,29306,330228,50,29314,330269,0,29314,330448,50,29329,330489,0,29334,330676,50,29362,330717,0,29362,330914,50,29423,330955,0,29423,331162,50,29537,331162,40,29537,331203,0,29537,331370,50,29538,331370,30,29538,331370,40,29538,331411,0,29538,331536,50,29539,331577,0,29543,331757,50,29545,331798,0,29546,331979,50,29550,332020,0,29554,332224,50,29561,332265,0,29561,332476,50,29571,332517,0,29576,332736,50,29594,332777,0,29594,333005,50,29628,333046,0,29633,333284,50,29698,333325,0,29698,333574,50,29831,333574,40,29831,333615,0,29831)
%
%
% START OF PROOF
% 333376 [?] ?
% 333576 [] equal(multiply(identity,X),X).
% 333577 [] equal(multiply(inverse(X),X),identity).
% 333578 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 333579 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 333585 [?] ?
% 333591 [?] ?
% 333597 [?] ?
% 333638 [input:333585,cut:333579] equal(inverse(sk_c2),sk_c8).
% 333639 [para:333638.1.1,333577.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 333666 [input:333591,cut:333579] equal(multiply(sk_c2,sk_c8),sk_c3).
% 333678 [input:333597,cut:333579] equal(multiply(sk_c8,sk_c3),sk_c7).
% 333694 [para:333639.1.1,333578.1.1.1,demod:333576] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 333744 [para:333666.1.1,333694.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c3)).
% 333750 [para:333744.1.2,333678.1.1] equal(sk_c8,sk_c7).
% 333752 [para:333750.1.2,333579.1.1.2,cut:333376] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% Split part used next: -equal(inverse(sk_c8),sk_c6).
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,0,87,0,0,897,50,8,943,0,8,2085,50,25,2131,0,25,3564,50,46,3610,0,46,5171,50,68,5217,0,68,6945,50,97,6991,0,97,8847,50,139,8893,0,139,10918,50,203,10964,0,203,13159,50,313,13205,0,313,15611,50,488,15657,0,488,18275,50,756,18275,40,756,18321,0,756,28798,3,1060,29530,4,1207,30263,5,1357,30264,1,1357,30264,50,1357,30264,40,1357,30310,0,1357,30649,3,1659,30660,4,1816,30684,5,1958,30684,1,1958,30684,50,1958,30684,40,1958,30730,0,1958,63113,3,3460,63915,4,4209,64862,5,4959,64863,1,4959,64863,50,4960,64863,40,4960,64909,0,4960,85548,3,5711,86205,4,6086,86874,1,6461,86874,50,6461,86874,40,6461,86920,0,6461,96859,3,7217,98446,4,7587,100065,5,7962,100066,1,7962,100066,50,7962,100066,40,7962,100112,0,7962,166678,3,11876,167581,4,13813,168301,1,15763,168301,50,15766,168301,40,15766,168347,0,15766,220054,3,18318,220820,4,19592,221466,5,20867,221467,1,20868,221467,50,20869,221467,40,20869,221513,0,20869,261976,3,22370,262842,4,23120,263620,1,23870,263620,50,23871,263620,40,23871,263666,0,23871,272529,3,24635,273475,4,24997,273664,5,25372,273664,1,25372,273664,50,25372,273664,40,25372,273710,0,25372,304230,3,26573,305001,4,27173,305659,1,27773,305659,50,27774,305659,40,27774,305705,0,27774,327307,3,28527,328024,4,28900,328651,5,29275,328652,1,29275,328652,50,29275,328652,40,29275,328652,40,29275,328693,0,29275,328792,50,29275,328792,30,29275,328792,40,29275,328833,0,29275,328975,50,29275,328975,30,29275,328975,40,29275,329016,0,29279,329159,50,29280,329159,30,29280,329159,40,29280,329200,0,29280,329278,50,29280,329278,30,29280,329278,40,29280,329319,0,29284,329422,50,29285,329463,0,29285,329612,50,29287,329653,0,29292,329810,50,29296,329851,0,29296,330016,50,29301,330057,0,29306,330228,50,29314,330269,0,29314,330448,50,29329,330489,0,29334,330676,50,29362,330717,0,29362,330914,50,29423,330955,0,29423,331162,50,29537,331162,40,29537,331203,0,29537,331370,50,29538,331370,30,29538,331370,40,29538,331411,0,29538,331536,50,29539,331577,0,29543,331757,50,29545,331798,0,29546,331979,50,29550,332020,0,29554,332224,50,29561,332265,0,29561,332476,50,29571,332517,0,29576,332736,50,29594,332777,0,29594,333005,50,29628,333046,0,29633,333284,50,29698,333325,0,29698,333574,50,29831,333574,40,29831,333615,0,29831,333751,50,29831,333751,30,29831,333751,40,29831,333792,0,29831,333917,50,29832,333958,0,29837,334138,50,29840,334179,0,29840,334360,50,29844,334401,0,29848,334605,50,29856,334646,0,29856,334857,50,29867,334898,0,29871,335117,50,29890,335158,0,29890,335386,50,29924,335427,0,29928,335665,50,29994,335706,0,29994,335955,50,30130,335955,40,30130,335996,0,30130)
%
%
% START OF PROOF
% 335957 [] equal(multiply(identity,X),X).
% 335958 [] equal(multiply(inverse(X),X),identity).
% 335959 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 335960 [] -equal(inverse(sk_c8),sk_c6).
% 335963 [?] ?
% 335969 [?] ?
% 335975 [?] ?
% 335981 [?] ?
% 335987 [?] ?
% 335993 [?] ?
% 336002 [input:335963,cut:335960] equal(inverse(sk_c2),sk_c8).
% 336003 [para:336002.1.1,335958.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 336009 [input:335981,cut:335960] equal(inverse(sk_c1),sk_c7).
% 336010 [para:336009.1.1,335958.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 336017 [input:335969,cut:335960] equal(multiply(sk_c2,sk_c8),sk_c3).
% 336023 [input:335975,cut:335960] equal(multiply(sk_c8,sk_c3),sk_c7).
% 336032 [input:335987,cut:335960] equal(multiply(sk_c1,sk_c7),sk_c8).
% 336038 [input:335993,cut:335960] equal(multiply(sk_c7,sk_c8),sk_c6).
% 336058 [para:335958.1.1,335959.1.1.1,demod:335957] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 336060 [para:336003.1.1,335959.1.1.1,demod:335957] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 336062 [para:336010.1.1,335959.1.1.1,demod:335957] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 336068 [para:336023.1.1,335959.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c3,X))).
% 336096 [para:336017.1.1,336060.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c3)).
% 336098 [para:336096.1.2,336023.1.1] equal(sk_c8,sk_c7).
% 336099 [para:336096.1.2,335959.1.1.1,demod:336068] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 336107 [para:336098.1.2,336032.1.1.2] equal(multiply(sk_c1,sk_c8),sk_c8).
% 336110 [para:336098.1.2,336038.1.1.1] equal(multiply(sk_c8,sk_c8),sk_c6).
% 336122 [para:336032.1.1,336062.1.2.2,demod:336110,336099] equal(sk_c7,sk_c6).
% 336123 [para:336107.1.1,336062.1.2.2,demod:336110,336099] equal(sk_c8,sk_c6).
% 336131 [para:336122.1.1,336032.1.1.2] equal(multiply(sk_c1,sk_c6),sk_c8).
% 336134 [para:336122.1.1,336038.1.1.1] equal(multiply(sk_c6,sk_c8),sk_c6).
% 336142 [para:336123.1.1,335960.1.1.1] -equal(inverse(sk_c6),sk_c6).
% 336165 [para:336131.1.1,335959.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c6,X))).
% 336174 [para:336122.1.1,336099.1.2.1] equal(multiply(sk_c8,X),multiply(sk_c6,X)).
% 336220 [para:336062.1.2,336058.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c7),X)).
% 336224 [para:336134.1.1,336058.1.2.2,demod:335958] equal(sk_c8,identity).
% 336229 [para:336099.1.2,336058.1.2.2,demod:336165,336220,336174] equal(X,multiply(sk_c6,X)).
% 336262 [para:336224.1.1,336003.1.1.1,demod:335957] equal(sk_c2,identity).
% 336269 [para:336224.1.1,336038.1.1.2,demod:336229,336174,336099] equal(identity,sk_c6).
% 336290 [para:336262.1.1,336002.1.1.1] equal(inverse(identity),sk_c8).
% 336295 [para:336269.1.2,336142.1.1.1,demod:336290,cut:336123] 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: 35814
% derived clauses: 5479074
% kept clauses: 279315
% kept size sum: 365079
% kept mid-nuclei: 12818
% kept new demods: 5733
% forw unit-subs: 2006645
% forw double-subs: 2674489
% forw overdouble-subs: 459418
% backward subs: 9885
% fast unit cutoff: 17414
% full unit cutoff: 0
% dbl unit cutoff: 10706
% real runtime : 304.61
% process. runtime: 301.32
% specific non-discr-tree subsumption statistics:
% tried: 49261638
% length fails: 4525786
% strength fails: 16512973
% predlist fails: 3967079
% aux str. fails: 5448148
% by-lit fails: 10446063
% full subs tried: 2645405
% full subs fail: 2518362
%
% ; 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/GRP324-1+eq_r.in")
%
%------------------------------------------------------------------------------