TSTP Solution File: GRP242-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP242-1 : 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 : art03.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 299.7s
% Output : Assurance 299.7s
% 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/GRP242-1+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 31)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 31)
% (binary-posweight-lex-big-order 30 #f 3 31)
% (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(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,U),sk_c11) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c10),sk_c11) | -equal(inverse(V),W) | -equal(inverse(W),U) | -equal(multiply(V,U),W) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(inverse(sk_c10),sk_c9) | -equal(multiply(X1,sk_c10),sk_c11) | -equal(inverse(X1),sk_c10) | -equal(multiply(X2,sk_c11),sk_c9) | -equal(inverse(X2),sk_c11).
% was split for some strategies as:
% -equal(multiply(X2,sk_c11),sk_c9) | -equal(inverse(X2),sk_c11).
% -equal(multiply(X1,sk_c10),sk_c11) | -equal(inverse(X1),sk_c10).
% -equal(multiply(Z,U),sk_c11) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c10),sk_c11) | -equal(inverse(W),U) | -equal(inverse(V),W) | -equal(multiply(V,U),W).
% -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10).
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% -equal(multiply(sk_c10,sk_c9),sk_c11).
% -equal(inverse(sk_c10),sk_c9).
%
% 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(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,U),sk_c11) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c10),sk_c11) | -equal(inverse(V),W) | -equal(inverse(W),U) | -equal(multiply(V,U),W) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(inverse(sk_c10),sk_c9) | -equal(multiply(X1,sk_c10),sk_c11) | -equal(inverse(X1),sk_c10) | -equal(multiply(X2,sk_c11),sk_c9) | -equal(inverse(X2),sk_c11).
% Split part used next: -equal(multiply(X2,sk_c11),sk_c9) | -equal(inverse(X2),sk_c11).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,1,153001,4,1488,153622,5,1502,153623,1,1502,153623,50,1502,153623,40,1502,153697,0,1502,154166,5,2105,154168,1,2105,154168,50,2105,154168,40,2105,154242,0,2105,154711,5,2709,154713,1,2710,154713,50,2710,154713,40,2710,154787,0,2710,174320,3,4211,175746,4,4961,177148,1,5711,177148,50,5711,177148,40,5711,177222,0,5711,187951,3,6462,189507,4,6837,191562,50,7203,191562,40,7203,191636,0,7203,192306,5,8706,192306,1,8706,192306,50,8706,192306,40,8706,192380,0,8706,233315,3,12607,234771,4,14557,236270,1,16507,236270,50,16521,236270,40,16521,236344,0,16521,271787,3,19083,273009,4,20347,274365,5,21622,274366,1,21622,274366,50,21623,274366,40,21623,274440,0,21623,298234,3,23124,299412,4,23874,300684,5,24624,300685,1,24624,300685,50,24624,300685,40,24624,300759,0,24625,301441,5,26129,301441,1,26129,301441,50,26129,301441,40,26129,301515,0,26129,322740,3,27330,323774,4,27930,324897,5,28530,324898,1,28530,324898,50,28531,324898,40,28531,324972,0,28531,341643,3,29282,342495,4,29657,343516,5,30032,343517,1,30032,343517,50,30032,343517,40,30032,343517,40,30032,343582,0,30032,343769,50,30034,343834,0,30034)
%
%
% START OF PROOF
% 343768 [?] ?
% 343771 [] equal(multiply(identity,X),X).
% 343772 [] equal(multiply(inverse(X),X),identity).
% 343773 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 343774 [] -equal(multiply(X,sk_c11),sk_c9) | -equal(inverse(X),sk_c11).
% 343781 [] equal(inverse(sk_c4),sk_c6) | equal(inverse(sk_c8),sk_c11).
% 343782 [?] ?
% 343787 [] equal(inverse(sk_c5),sk_c4) | equal(inverse(sk_c8),sk_c11).
% 343788 [?] ?
% 343799 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c8),sk_c11).
% 343800 [?] ?
% 343805 [] equal(multiply(sk_c3,sk_c6),sk_c11) | equal(inverse(sk_c8),sk_c11).
% 343806 [] equal(multiply(sk_c3,sk_c6),sk_c11) | equal(multiply(sk_c8,sk_c11),sk_c9).
% 343823 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c8),sk_c11).
% 343824 [?] ?
% 343837 [hyper:343774,343781,binarycut:343782] equal(inverse(sk_c4),sk_c6).
% 343838 [para:343837.1.1,343772.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 343842 [hyper:343774,343787,binarycut:343788] equal(inverse(sk_c5),sk_c4).
% 343843 [para:343842.1.1,343772.1.1.1] equal(multiply(sk_c4,sk_c5),identity).
% 343846 [hyper:343774,343799,binarycut:343800] equal(inverse(sk_c3),sk_c6).
% 343850 [para:343846.1.1,343772.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 343861 [hyper:343774,343823,binarycut:343824] equal(inverse(sk_c1),sk_c11).
% 343864 [para:343861.1.1,343772.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 343885 [hyper:343774,343806,343805] equal(multiply(sk_c3,sk_c6),sk_c11).
% 343898 [para:343772.1.1,343773.1.1.1,demod:343771] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 343899 [para:343838.1.1,343773.1.1.1,demod:343771] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 343900 [para:343843.1.1,343773.1.1.1,demod:343771] equal(X,multiply(sk_c4,multiply(sk_c5,X))).
% 343906 [para:343885.1.1,343773.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c3,multiply(sk_c6,X))).
% 343909 [para:343843.1.1,343899.1.2.2] equal(sk_c5,multiply(sk_c6,identity)).
% 343910 [para:343909.1.2,343773.1.1.1,demod:343771] equal(multiply(sk_c5,X),multiply(sk_c6,X)).
% 343915 [para:343838.1.1,343898.1.2.2] equal(sk_c4,multiply(inverse(sk_c6),identity)).
% 343917 [para:343850.1.1,343898.1.2.2,demod:343915] equal(sk_c3,sk_c4).
% 343928 [para:343917.1.2,343900.1.2.1,demod:343906,343910] equal(X,multiply(sk_c11,X)).
% 343929 [para:343928.1.2,343864.1.1] equal(sk_c1,identity).
% 343931 [para:343929.1.1,343861.1.1.1] equal(inverse(identity),sk_c11).
% 343936 [hyper:343774,343931,demod:343771,cut:343768] 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 31
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,U),sk_c11) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c10),sk_c11) | -equal(inverse(V),W) | -equal(inverse(W),U) | -equal(multiply(V,U),W) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(inverse(sk_c10),sk_c9) | -equal(multiply(X1,sk_c10),sk_c11) | -equal(inverse(X1),sk_c10) | -equal(multiply(X2,sk_c11),sk_c9) | -equal(inverse(X2),sk_c11).
% Split part used next: -equal(multiply(X1,sk_c10),sk_c11) | -equal(inverse(X1),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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,1,153001,4,1488,153622,5,1502,153623,1,1502,153623,50,1502,153623,40,1502,153697,0,1502,154166,5,2105,154168,1,2105,154168,50,2105,154168,40,2105,154242,0,2105,154711,5,2709,154713,1,2710,154713,50,2710,154713,40,2710,154787,0,2710,174320,3,4211,175746,4,4961,177148,1,5711,177148,50,5711,177148,40,5711,177222,0,5711,187951,3,6462,189507,4,6837,191562,50,7203,191562,40,7203,191636,0,7203,192306,5,8706,192306,1,8706,192306,50,8706,192306,40,8706,192380,0,8706,233315,3,12607,234771,4,14557,236270,1,16507,236270,50,16521,236270,40,16521,236344,0,16521,271787,3,19083,273009,4,20347,274365,5,21622,274366,1,21622,274366,50,21623,274366,40,21623,274440,0,21623,298234,3,23124,299412,4,23874,300684,5,24624,300685,1,24624,300685,50,24624,300685,40,24624,300759,0,24625,301441,5,26129,301441,1,26129,301441,50,26129,301441,40,26129,301515,0,26129,322740,3,27330,323774,4,27930,324897,5,28530,324898,1,28530,324898,50,28531,324898,40,28531,324972,0,28531,341643,3,29282,342495,4,29657,343516,5,30032,343517,1,30032,343517,50,30032,343517,40,30032,343517,40,30032,343582,0,30032,343769,50,30034,343834,0,30034,343935,50,30034,343935,30,30034,343935,40,30034,344000,0,30038)
%
%
% START OF PROOF
% 343937 [] equal(multiply(identity,X),X).
% 343938 [] equal(multiply(inverse(X),X),identity).
% 343939 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 343940 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(inverse(X),sk_c10).
% 343949 [] equal(inverse(sk_c4),sk_c6) | equal(inverse(sk_c7),sk_c10).
% 343950 [?] ?
% 343955 [] equal(inverse(sk_c5),sk_c4) | equal(inverse(sk_c7),sk_c10).
% 343956 [?] ?
% 343961 [] equal(multiply(sk_c6,sk_c10),sk_c11) | equal(inverse(sk_c7),sk_c10).
% 343962 [] equal(multiply(sk_c6,sk_c10),sk_c11) | equal(multiply(sk_c7,sk_c10),sk_c11).
% 343967 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c7),sk_c10).
% 343968 [?] ?
% 343973 [] equal(multiply(sk_c3,sk_c6),sk_c11) | equal(inverse(sk_c7),sk_c10).
% 343974 [] equal(multiply(sk_c3,sk_c6),sk_c11) | equal(multiply(sk_c7,sk_c10),sk_c11).
% 343991 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c10).
% 343992 [?] ?
% 343997 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(inverse(sk_c7),sk_c10).
% 343998 [] equal(multiply(sk_c1,sk_c11),sk_c10) | equal(multiply(sk_c7,sk_c10),sk_c11).
% 344004 [hyper:343940,343949,binarycut:343950] equal(inverse(sk_c4),sk_c6).
% 344006 [para:344004.1.1,343938.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 344010 [hyper:343940,343955,binarycut:343956] equal(inverse(sk_c5),sk_c4).
% 344011 [para:344010.1.1,343938.1.1.1] equal(multiply(sk_c4,sk_c5),identity).
% 344016 [hyper:343940,343967,binarycut:343968] equal(inverse(sk_c3),sk_c6).
% 344017 [para:344016.1.1,343938.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 344036 [hyper:343940,343991,binarycut:343992] equal(inverse(sk_c1),sk_c11).
% 344037 [para:344036.1.1,343938.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 344065 [hyper:343940,343962,343961] equal(multiply(sk_c6,sk_c10),sk_c11).
% 344080 [hyper:343940,343974,343973] equal(multiply(sk_c3,sk_c6),sk_c11).
% 344089 [hyper:343940,343998,343997] equal(multiply(sk_c1,sk_c11),sk_c10).
% 344090 [para:343938.1.1,343939.1.1.1,demod:343937] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 344091 [para:344006.1.1,343939.1.1.1,demod:343937] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 344092 [para:344011.1.1,343939.1.1.1,demod:343937] equal(X,multiply(sk_c4,multiply(sk_c5,X))).
% 344098 [para:344080.1.1,343939.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c3,multiply(sk_c6,X))).
% 344101 [para:344011.1.1,344091.1.2.2] equal(sk_c5,multiply(sk_c6,identity)).
% 344102 [para:344101.1.2,343939.1.1.1,demod:343937] equal(multiply(sk_c5,X),multiply(sk_c6,X)).
% 344105 [para:344006.1.1,344090.1.2.2] equal(sk_c4,multiply(inverse(sk_c6),identity)).
% 344107 [para:344017.1.1,344090.1.2.2,demod:344105] equal(sk_c3,sk_c4).
% 344111 [para:344080.1.1,344090.1.2.2,demod:344016] equal(sk_c6,multiply(sk_c6,sk_c11)).
% 344116 [para:344107.1.2,344092.1.2.1,demod:344098,344102] equal(X,multiply(sk_c11,X)).
% 344117 [para:344116.1.2,344037.1.1] equal(sk_c1,identity).
% 344120 [para:344117.1.1,344089.1.1.1,demod:343937] equal(sk_c11,sk_c10).
% 344132 [para:344120.1.1,344111.1.2.2,demod:344065] equal(sk_c6,sk_c11).
% 344137 [para:344132.1.2,344120.1.1] equal(sk_c6,sk_c10).
% 344143 [para:344137.1.1,344080.1.1.2] equal(multiply(sk_c3,sk_c10),sk_c11).
% 344211 [hyper:343940,344143,demod:344016,cut:344137] 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 31
% 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(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,U),sk_c11) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c10),sk_c11) | -equal(inverse(V),W) | -equal(inverse(W),U) | -equal(multiply(V,U),W) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(inverse(sk_c10),sk_c9) | -equal(multiply(X1,sk_c10),sk_c11) | -equal(inverse(X1),sk_c10) | -equal(multiply(X2,sk_c11),sk_c9) | -equal(inverse(X2),sk_c11).
% Split part used next: -equal(multiply(Z,U),sk_c11) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c10),sk_c11) | -equal(inverse(W),U) | -equal(inverse(V),W) | -equal(multiply(V,U),W).
% END OF PROOFPART
% Orig sos clause for pseudosplit:
% -equal(multiply(Z,U),sk_c11) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c10),sk_c11) | -equal(inverse(W),U) | -equal(inverse(V),W) | -equal(multiply(V,U),W).
% Pseudo-split-input-clause results in:
% -$spltprd1($spltcnst99,U) | -$spltprd1($spltcnst98,U) | -$spltprd1($spltcnst97,U).
% $spltprd1($spltcnst99,U) | -equal(multiply(U,sk_c10),sk_c11).
% $spltprd1($spltcnst98,U) | -equal(multiply(Z,U),sk_c11) | -equal(inverse(Z),U).
% $spltprd1($spltcnst97,U) | -equal(inverse(W),U) | -equal(inverse(V),W) | -equal(multiply(V,U),W).
%
% 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,1,153001,4,1488,153622,5,1502,153623,1,1502,153623,50,1502,153623,40,1502,153697,0,1502,154166,5,2105,154168,1,2105,154168,50,2105,154168,40,2105,154242,0,2105,154711,5,2709,154713,1,2710,154713,50,2710,154713,40,2710,154787,0,2710,174320,3,4211,175746,4,4961,177148,1,5711,177148,50,5711,177148,40,5711,177222,0,5711,187951,3,6462,189507,4,6837,191562,50,7203,191562,40,7203,191636,0,7203,192306,5,8706,192306,1,8706,192306,50,8706,192306,40,8706,192380,0,8706,233315,3,12607,234771,4,14557,236270,1,16507,236270,50,16521,236270,40,16521,236344,0,16521,271787,3,19083,273009,4,20347,274365,5,21622,274366,1,21622,274366,50,21623,274366,40,21623,274440,0,21623,298234,3,23124,299412,4,23874,300684,5,24624,300685,1,24624,300685,50,24624,300685,40,24624,300759,0,24625,301441,5,26129,301441,1,26129,301441,50,26129,301441,40,26129,301515,0,26129,322740,3,27330,323774,4,27930,324897,5,28530,324898,1,28530,324898,50,28531,324898,40,28531,324972,0,28531,341643,3,29282,342495,4,29657,343516,5,30032,343517,1,30032,343517,50,30032,343517,40,30032,343517,40,30032,343582,0,30032,343769,50,30034,343834,0,30034,343935,50,30034,343935,30,30034,343935,40,30034,344000,0,30038,344210,50,30039,344210,30,30039,344210,40,30039,344339,0,30039)
%
%
% START OF PROOF
% 344211 [] equal(X,X).
% 344212 [] equal(multiply(identity,X),X).
% 344213 [] equal(multiply(inverse(X),X),identity).
% 344214 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 344275 [] -equal(multiply(X,sk_c10),sk_c11) | -equal(multiply(Y,X),sk_c11) | -equal(multiply(Z,X),U) | -equal(inverse(Z),U) | -equal(inverse(U),X) | -equal(inverse(Y),X).
% 344276 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst97,Y).
% 344277 [] -equal(multiply(X,Y),sk_c11) | -equal(inverse(X),Y) | $spltprd1($spltcnst98,Y).
% 344278 [] -equal(multiply(X,sk_c10),sk_c11) | $spltprd1($spltcnst99,X).
% 344279 [] -$spltprd1($spltcnst98,X) | -$spltprd1($spltcnst97,X) | -$spltprd1($spltcnst99,X).
% 344280 [] equal(multiply(sk_c5,sk_c6),sk_c4) | equal(inverse(sk_c8),sk_c11).
% 344281 [] equal(multiply(sk_c5,sk_c6),sk_c4) | equal(multiply(sk_c8,sk_c11),sk_c9).
% 344282 [] equal(multiply(sk_c5,sk_c6),sk_c4) | equal(inverse(sk_c7),sk_c10).
% 344283 [] equal(multiply(sk_c5,sk_c6),sk_c4) | equal(multiply(sk_c7,sk_c10),sk_c11).
% 344284 [] equal(multiply(sk_c5,sk_c6),sk_c4) | equal(inverse(sk_c10),sk_c9).
% 344285 [] equal(multiply(sk_c5,sk_c6),sk_c4) | equal(multiply(sk_c10,sk_c9),sk_c11).
% 344286 [] equal(inverse(sk_c4),sk_c6) | equal(inverse(sk_c8),sk_c11).
% 344287 [] equal(multiply(sk_c8,sk_c11),sk_c9) | equal(inverse(sk_c4),sk_c6).
% 344288 [] equal(inverse(sk_c4),sk_c6) | equal(inverse(sk_c7),sk_c10).
% 344289 [] equal(multiply(sk_c7,sk_c10),sk_c11) | equal(inverse(sk_c4),sk_c6).
% 344290 [] equal(inverse(sk_c4),sk_c6) | equal(inverse(sk_c10),sk_c9).
% 344291 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c4),sk_c6).
% 344292 [] equal(inverse(sk_c5),sk_c4) | equal(inverse(sk_c8),sk_c11).
% 344293 [] equal(multiply(sk_c8,sk_c11),sk_c9) | equal(inverse(sk_c5),sk_c4).
% 344294 [] equal(inverse(sk_c5),sk_c4) | equal(inverse(sk_c7),sk_c10).
% 344295 [] equal(multiply(sk_c7,sk_c10),sk_c11) | equal(inverse(sk_c5),sk_c4).
% 344296 [] equal(inverse(sk_c5),sk_c4) | equal(inverse(sk_c10),sk_c9).
% 344297 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c5),sk_c4).
% 344298 [] equal(multiply(sk_c6,sk_c10),sk_c11) | equal(inverse(sk_c8),sk_c11).
% 344299 [] equal(multiply(sk_c6,sk_c10),sk_c11) | equal(multiply(sk_c8,sk_c11),sk_c9).
% 344300 [] equal(multiply(sk_c6,sk_c10),sk_c11) | equal(inverse(sk_c7),sk_c10).
% 344301 [] equal(multiply(sk_c6,sk_c10),sk_c11) | equal(multiply(sk_c7,sk_c10),sk_c11).
% 344302 [] equal(multiply(sk_c6,sk_c10),sk_c11) | equal(inverse(sk_c10),sk_c9).
% 344303 [] equal(multiply(sk_c6,sk_c10),sk_c11) | equal(multiply(sk_c10,sk_c9),sk_c11).
% 344304 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c8),sk_c11).
% 344305 [] equal(multiply(sk_c8,sk_c11),sk_c9) | equal(inverse(sk_c3),sk_c6).
% 344306 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c7),sk_c10).
% 344307 [] equal(multiply(sk_c7,sk_c10),sk_c11) | equal(inverse(sk_c3),sk_c6).
% 344308 [] equal(inverse(sk_c3),sk_c6) | equal(inverse(sk_c10),sk_c9).
% 344309 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c3),sk_c6).
% 344310 [?] ?
% 344311 [?] ?
% 344312 [?] ?
% 344313 [] equal(multiply(sk_c3,sk_c6),sk_c11) | equal(multiply(sk_c7,sk_c10),sk_c11).
% 344314 [?] ?
% 344315 [] equal(multiply(sk_c3,sk_c6),sk_c11) | equal(multiply(sk_c10,sk_c9),sk_c11).
% 344503 [hyper:344277,344304,binarycut:344310] equal(inverse(sk_c8),sk_c11) | $spltprd1($spltcnst98,sk_c6).
% 344537 [hyper:344277,344306,binarycut:344312] equal(inverse(sk_c7),sk_c10) | $spltprd1($spltcnst98,sk_c6).
% 344580 [hyper:344277,344308,binarycut:344314] equal(inverse(sk_c10),sk_c9) | $spltprd1($spltcnst98,sk_c6).
% 344737 [hyper:344276,344280,binarycut:344286,binarycut:344292] equal(inverse(sk_c8),sk_c11) | $spltprd1($spltcnst97,sk_c6).
% 344763 [hyper:344276,344282,binarycut:344288,binarycut:344294] equal(inverse(sk_c7),sk_c10) | $spltprd1($spltcnst97,sk_c6).
% 344789 [hyper:344276,344284,binarycut:344290,binarycut:344296] equal(inverse(sk_c10),sk_c9) | $spltprd1($spltcnst97,sk_c6).
% 344908 [hyper:344278,344298] equal(inverse(sk_c8),sk_c11) | $spltprd1($spltcnst99,sk_c6).
% 344927 [hyper:344279,344908,344737,344503] equal(inverse(sk_c8),sk_c11).
% 344944 [hyper:344278,344300] equal(inverse(sk_c7),sk_c10) | $spltprd1($spltcnst99,sk_c6).
% 344954 [para:344927.1.1,344213.1.1.1] equal(multiply(sk_c11,sk_c8),identity).
% 344974 [hyper:344279,344944,344763,344537] equal(inverse(sk_c7),sk_c10).
% 344985 [para:344974.1.1,344213.1.1.1] equal(multiply(sk_c10,sk_c7),identity).
% 345006 [hyper:344278,344302] equal(inverse(sk_c10),sk_c9) | $spltprd1($spltcnst99,sk_c6).
% 345041 [hyper:344279,345006,344789,344580] equal(inverse(sk_c10),sk_c9).
% 345059 [para:345041.1.1,344213.1.1.1] equal(multiply(sk_c9,sk_c10),identity).
% 345090 [hyper:344277,344305,binarycut:344311] equal(multiply(sk_c8,sk_c11),sk_c9) | $spltprd1($spltcnst98,sk_c6).
% 345370 [hyper:344276,344281,344287,344293] equal(multiply(sk_c8,sk_c11),sk_c9) | $spltprd1($spltcnst97,sk_c6).
% 345881 [hyper:344278,344299] equal(multiply(sk_c8,sk_c11),sk_c9) | $spltprd1($spltcnst99,sk_c6).
% 345907 [hyper:344279,345881,345370,345090] equal(multiply(sk_c8,sk_c11),sk_c9).
% 346037 [hyper:344275,344313,344307,344289,344295,binarycut:344301,binarycut:344283] equal(multiply(sk_c7,sk_c10),sk_c11).
% 346097 [hyper:344275,344315,344309,344291,344297,binarycut:344303,binarycut:344285] equal(multiply(sk_c10,sk_c9),sk_c11).
% 346115 [para:344954.1.1,344214.1.1.1,demod:344212] equal(X,multiply(sk_c11,multiply(sk_c8,X))).
% 346116 [para:344985.1.1,344214.1.1.1,demod:344212] equal(X,multiply(sk_c10,multiply(sk_c7,X))).
% 346117 [para:345059.1.1,344214.1.1.1,demod:344212] equal(X,multiply(sk_c9,multiply(sk_c10,X))).
% 346137 [para:345907.1.1,346115.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c9)).
% 346155 [para:346037.1.1,346116.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c11)).
% 346165 [para:344985.1.1,346117.1.2.2] equal(sk_c7,multiply(sk_c9,identity)).
% 346175 [para:346116.1.2,346117.1.2.2] equal(multiply(sk_c7,X),multiply(sk_c9,X)).
% 346176 [para:346155.1.2,346117.1.2.2,demod:345059] equal(sk_c11,identity).
% 346177 [para:346176.1.1,344954.1.1.1,demod:344212] equal(sk_c8,identity).
% 346179 [para:346176.1.1,346115.1.2.1,demod:344212] equal(X,multiply(sk_c8,X)).
% 346180 [para:346176.1.1,346137.1.2.1,demod:344212] equal(sk_c11,sk_c9).
% 346182 [para:346177.1.1,344927.1.1.1] equal(inverse(identity),sk_c11).
% 346184 [para:346177.1.1,346115.1.2.2.1,demod:344212] equal(X,multiply(sk_c11,X)).
% 346187 [para:346180.1.1,346155.1.2.2,demod:346097] equal(sk_c10,sk_c11).
% 346193 [para:346187.1.2,346176.1.1] equal(sk_c10,identity).
% 346198 [para:346193.1.1,346037.1.1.2,demod:346165,346175] equal(sk_c7,sk_c11).
% 346204 [para:346198.1.2,345907.1.1.2,demod:346179] equal(sk_c7,sk_c9).
% 346210 [para:346204.1.1,344974.1.1.1] equal(inverse(sk_c9),sk_c10).
% 346263 [hyper:344275,346182,345907,demod:346184,344212,cut:344211,cut:346187,demod:344927,346210,cut:346187,cut:346180] 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 31
% 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(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,U),sk_c11) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c10),sk_c11) | -equal(inverse(V),W) | -equal(inverse(W),U) | -equal(multiply(V,U),W) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(inverse(sk_c10),sk_c9) | -equal(multiply(X1,sk_c10),sk_c11) | -equal(inverse(X1),sk_c10) | -equal(multiply(X2,sk_c11),sk_c9) | -equal(inverse(X2),sk_c11).
% 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,1,153001,4,1488,153622,5,1502,153623,1,1502,153623,50,1502,153623,40,1502,153697,0,1502,154166,5,2105,154168,1,2105,154168,50,2105,154168,40,2105,154242,0,2105,154711,5,2709,154713,1,2710,154713,50,2710,154713,40,2710,154787,0,2710,174320,3,4211,175746,4,4961,177148,1,5711,177148,50,5711,177148,40,5711,177222,0,5711,187951,3,6462,189507,4,6837,191562,50,7203,191562,40,7203,191636,0,7203,192306,5,8706,192306,1,8706,192306,50,8706,192306,40,8706,192380,0,8706,233315,3,12607,234771,4,14557,236270,1,16507,236270,50,16521,236270,40,16521,236344,0,16521,271787,3,19083,273009,4,20347,274365,5,21622,274366,1,21622,274366,50,21623,274366,40,21623,274440,0,21623,298234,3,23124,299412,4,23874,300684,5,24624,300685,1,24624,300685,50,24624,300685,40,24624,300759,0,24625,301441,5,26129,301441,1,26129,301441,50,26129,301441,40,26129,301515,0,26129,322740,3,27330,323774,4,27930,324897,5,28530,324898,1,28530,324898,50,28531,324898,40,28531,324972,0,28531,341643,3,29282,342495,4,29657,343516,5,30032,343517,1,30032,343517,50,30032,343517,40,30032,343517,40,30032,343582,0,30032,343769,50,30034,343834,0,30034,343935,50,30034,343935,30,30034,343935,40,30034,344000,0,30038,344210,50,30039,344210,30,30039,344210,40,30039,344339,0,30039,346262,50,30046,346262,30,30046,346262,40,30046,346327,0,30050)
%
%
% START OF PROOF
% 346264 [] equal(multiply(identity,X),X).
% 346265 [] equal(multiply(inverse(X),X),identity).
% 346266 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 346267 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 346304 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c8),sk_c11).
% 346305 [] equal(multiply(sk_c8,sk_c11),sk_c9) | equal(inverse(sk_c2),sk_c10).
% 346306 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c10).
% 346307 [] equal(multiply(sk_c7,sk_c10),sk_c11) | equal(inverse(sk_c2),sk_c10).
% 346308 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c10),sk_c9).
% 346309 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c2),sk_c10).
% 346310 [?] ?
% 346311 [?] ?
% 346312 [?] ?
% 346313 [?] ?
% 346314 [?] ?
% 346315 [?] ?
% 346346 [hyper:346267,346304,binarycut:346310] equal(inverse(sk_c8),sk_c11).
% 346347 [para:346346.1.1,346265.1.1.1] equal(multiply(sk_c11,sk_c8),identity).
% 346351 [hyper:346267,346306,binarycut:346312] equal(inverse(sk_c7),sk_c10).
% 346355 [para:346351.1.1,346265.1.1.1] equal(multiply(sk_c10,sk_c7),identity).
% 346359 [hyper:346267,346308,binarycut:346314] equal(inverse(sk_c10),sk_c9).
% 346361 [para:346359.1.1,346265.1.1.1] equal(multiply(sk_c9,sk_c10),identity).
% 346377 [hyper:346267,346305,binarycut:346311] equal(multiply(sk_c8,sk_c11),sk_c9).
% 346381 [hyper:346267,346307,binarycut:346313] equal(multiply(sk_c7,sk_c10),sk_c11).
% 346384 [hyper:346267,346309,binarycut:346315] equal(multiply(sk_c10,sk_c9),sk_c11).
% 346385 [para:346265.1.1,346266.1.1.1,demod:346264] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 346386 [para:346347.1.1,346266.1.1.1,demod:346264] equal(X,multiply(sk_c11,multiply(sk_c8,X))).
% 346387 [para:346355.1.1,346266.1.1.1,demod:346264] equal(X,multiply(sk_c10,multiply(sk_c7,X))).
% 346392 [para:346377.1.1,346386.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c9)).
% 346394 [para:346381.1.1,346387.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c11)).
% 346397 [para:346355.1.1,346385.1.2.2,demod:346359] equal(sk_c7,multiply(sk_c9,identity)).
% 346401 [para:346387.1.2,346385.1.2.2,demod:346359] equal(multiply(sk_c7,X),multiply(sk_c9,X)).
% 346403 [para:346394.1.2,346385.1.2.2,demod:346361,346359] equal(sk_c11,identity).
% 346407 [para:346403.1.1,346386.1.2.1,demod:346264] equal(X,multiply(sk_c8,X)).
% 346408 [para:346403.1.1,346392.1.2.1,demod:346264] equal(sk_c11,sk_c9).
% 346415 [para:346408.1.1,346394.1.2.2,demod:346384] equal(sk_c10,sk_c11).
% 346417 [para:346403.1.1,346408.1.1] equal(identity,sk_c9).
% 346421 [para:346415.1.2,346403.1.1] equal(sk_c10,identity).
% 346425 [para:346421.1.1,346381.1.1.2,demod:346397,346401] equal(sk_c7,sk_c11).
% 346428 [para:346425.1.2,346377.1.1.2,demod:346407] equal(sk_c7,sk_c9).
% 346432 [para:346428.1.1,346351.1.1.1] equal(inverse(sk_c9),sk_c10).
% 346435 [hyper:346267,346432,demod:346361,cut:346417] 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 31
% 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(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,U),sk_c11) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c10),sk_c11) | -equal(inverse(V),W) | -equal(inverse(W),U) | -equal(multiply(V,U),W) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(inverse(sk_c10),sk_c9) | -equal(multiply(X1,sk_c10),sk_c11) | -equal(inverse(X1),sk_c10) | -equal(multiply(X2,sk_c11),sk_c9) | -equal(inverse(X2),sk_c11).
% Split part used next: -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,1,153001,4,1488,153622,5,1502,153623,1,1502,153623,50,1502,153623,40,1502,153697,0,1502,154166,5,2105,154168,1,2105,154168,50,2105,154168,40,2105,154242,0,2105,154711,5,2709,154713,1,2710,154713,50,2710,154713,40,2710,154787,0,2710,174320,3,4211,175746,4,4961,177148,1,5711,177148,50,5711,177148,40,5711,177222,0,5711,187951,3,6462,189507,4,6837,191562,50,7203,191562,40,7203,191636,0,7203,192306,5,8706,192306,1,8706,192306,50,8706,192306,40,8706,192380,0,8706,233315,3,12607,234771,4,14557,236270,1,16507,236270,50,16521,236270,40,16521,236344,0,16521,271787,3,19083,273009,4,20347,274365,5,21622,274366,1,21622,274366,50,21623,274366,40,21623,274440,0,21623,298234,3,23124,299412,4,23874,300684,5,24624,300685,1,24624,300685,50,24624,300685,40,24624,300759,0,24625,301441,5,26129,301441,1,26129,301441,50,26129,301441,40,26129,301515,0,26129,322740,3,27330,323774,4,27930,324897,5,28530,324898,1,28530,324898,50,28531,324898,40,28531,324972,0,28531,341643,3,29282,342495,4,29657,343516,5,30032,343517,1,30032,343517,50,30032,343517,40,30032,343517,40,30032,343582,0,30032,343769,50,30034,343834,0,30034,343935,50,30034,343935,30,30034,343935,40,30034,344000,0,30038,344210,50,30039,344210,30,30039,344210,40,30039,344339,0,30039,346262,50,30046,346262,30,30046,346262,40,30046,346327,0,30050,346434,50,30051,346434,30,30051,346434,40,30051,346499,0,30051)
%
%
% START OF PROOF
% 346436 [] equal(multiply(identity,X),X).
% 346437 [] equal(multiply(inverse(X),X),identity).
% 346438 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 346439 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 346488 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c8),sk_c11).
% 346489 [] equal(multiply(sk_c8,sk_c11),sk_c9) | equal(inverse(sk_c1),sk_c11).
% 346490 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c10).
% 346491 [] equal(multiply(sk_c7,sk_c10),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 346492 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c10),sk_c9).
% 346493 [] equal(multiply(sk_c10,sk_c9),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 346494 [?] ?
% 346495 [?] ?
% 346496 [?] ?
% 346497 [?] ?
% 346498 [?] ?
% 346499 [?] ?
% 346526 [hyper:346439,346488,binarycut:346494] equal(inverse(sk_c8),sk_c11).
% 346530 [para:346526.1.1,346437.1.1.1] equal(multiply(sk_c11,sk_c8),identity).
% 346534 [hyper:346439,346490,binarycut:346496] equal(inverse(sk_c7),sk_c10).
% 346536 [para:346534.1.1,346437.1.1.1] equal(multiply(sk_c10,sk_c7),identity).
% 346539 [hyper:346439,346492,binarycut:346498] equal(inverse(sk_c10),sk_c9).
% 346540 [para:346539.1.1,346437.1.1.1] equal(multiply(sk_c9,sk_c10),identity).
% 346559 [hyper:346439,346489,binarycut:346495] equal(multiply(sk_c8,sk_c11),sk_c9).
% 346563 [hyper:346439,346491,binarycut:346497] equal(multiply(sk_c7,sk_c10),sk_c11).
% 346566 [hyper:346439,346493,binarycut:346499] equal(multiply(sk_c10,sk_c9),sk_c11).
% 346567 [para:346437.1.1,346438.1.1.1,demod:346436] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 346568 [para:346530.1.1,346438.1.1.1,demod:346436] equal(X,multiply(sk_c11,multiply(sk_c8,X))).
% 346569 [para:346536.1.1,346438.1.1.1,demod:346436] equal(X,multiply(sk_c10,multiply(sk_c7,X))).
% 346574 [para:346559.1.1,346568.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c9)).
% 346576 [para:346563.1.1,346569.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c11)).
% 346585 [para:346576.1.2,346567.1.2.2,demod:346540,346539] equal(sk_c11,identity).
% 346587 [para:346585.1.1,346530.1.1.1,demod:346436] equal(sk_c8,identity).
% 346589 [para:346585.1.1,346568.1.2.1,demod:346436] equal(X,multiply(sk_c8,X)).
% 346590 [para:346585.1.1,346574.1.2.1,demod:346436] equal(sk_c11,sk_c9).
% 346592 [para:346587.1.1,346526.1.1.1] equal(inverse(identity),sk_c11).
% 346594 [para:346587.1.1,346568.1.2.2.1,demod:346436] equal(X,multiply(sk_c11,X)).
% 346597 [para:346590.1.1,346576.1.2.2,demod:346566] equal(sk_c10,sk_c11).
% 346601 [para:346597.1.2,346559.1.1.2,demod:346589] equal(sk_c10,sk_c9).
% 346604 [para:346601.1.2,346574.1.2.2,demod:346594] equal(sk_c11,sk_c10).
% 346617 [hyper:346439,346592,demod:346436,cut:346604] 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,U),sk_c11) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c10),sk_c11) | -equal(inverse(V),W) | -equal(inverse(W),U) | -equal(multiply(V,U),W) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(inverse(sk_c10),sk_c9) | -equal(multiply(X1,sk_c10),sk_c11) | -equal(inverse(X1),sk_c10) | -equal(multiply(X2,sk_c11),sk_c9) | -equal(inverse(X2),sk_c11).
% Split part used next: -equal(multiply(sk_c10,sk_c9),sk_c11).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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(65,40,0,139,0,1,153001,4,1488,153622,5,1502,153623,1,1502,153623,50,1502,153623,40,1502,153697,0,1502,154166,5,2105,154168,1,2105,154168,50,2105,154168,40,2105,154242,0,2105,154711,5,2709,154713,1,2710,154713,50,2710,154713,40,2710,154787,0,2710,174320,3,4211,175746,4,4961,177148,1,5711,177148,50,5711,177148,40,5711,177222,0,5711,187951,3,6462,189507,4,6837,191562,50,7203,191562,40,7203,191636,0,7203,192306,5,8706,192306,1,8706,192306,50,8706,192306,40,8706,192380,0,8706,233315,3,12607,234771,4,14557,236270,1,16507,236270,50,16521,236270,40,16521,236344,0,16521,271787,3,19083,273009,4,20347,274365,5,21622,274366,1,21622,274366,50,21623,274366,40,21623,274440,0,21623,298234,3,23124,299412,4,23874,300684,5,24624,300685,1,24624,300685,50,24624,300685,40,24624,300759,0,24625,301441,5,26129,301441,1,26129,301441,50,26129,301441,40,26129,301515,0,26129,322740,3,27330,323774,4,27930,324897,5,28530,324898,1,28530,324898,50,28531,324898,40,28531,324972,0,28531,341643,3,29282,342495,4,29657,343516,5,30032,343517,1,30032,343517,50,30032,343517,40,30032,343517,40,30032,343582,0,30032,343769,50,30034,343834,0,30034,343935,50,30034,343935,30,30034,343935,40,30034,344000,0,30038,344210,50,30039,344210,30,30039,344210,40,30039,344339,0,30039,346262,50,30046,346262,30,30046,346262,40,30046,346327,0,30050,346434,50,30051,346434,30,30051,346434,40,30051,346499,0,30051,346616,50,30051,346616,30,30051,346616,40,30051,346681,0,30056,346869,50,30057,346934,0,30058,347210,50,30063,347275,0,30067,347559,50,30074,347624,0,30074,347916,50,30083,347981,0,30087,348279,50,30100,348344,0,30100,348650,50,30120,348715,0,30125,349029,50,30160,349094,0,30160,349418,50,30232,349483,0,30232,349817,50,30362,349817,40,30362,349882,0,30362)
%
%
% START OF PROOF
% 349616 [?] ?
% 349819 [] equal(multiply(identity,X),X).
% 349820 [] equal(multiply(inverse(X),X),identity).
% 349821 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 349822 [] -equal(multiply(sk_c10,sk_c9),sk_c11).
% 349864 [?] ?
% 349870 [?] ?
% 349975 [input:349864,cut:349822] equal(inverse(sk_c2),sk_c10).
% 349976 [para:349975.1.1,349820.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 350005 [input:349870,cut:349822] equal(multiply(sk_c2,sk_c10),sk_c9).
% 350049 [para:349976.1.1,349821.1.1.1,demod:349819] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 350110 [para:350005.1.1,350049.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c9)).
% 350111 [para:350110.1.2,349822.1.1,cut:349616] 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(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11) | -equal(multiply(Y,sk_c10),sk_c9) | -equal(inverse(Y),sk_c10) | -equal(multiply(Z,U),sk_c11) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c10),sk_c11) | -equal(inverse(V),W) | -equal(inverse(W),U) | -equal(multiply(V,U),W) | -equal(multiply(sk_c10,sk_c9),sk_c11) | -equal(inverse(sk_c10),sk_c9) | -equal(multiply(X1,sk_c10),sk_c11) | -equal(inverse(X1),sk_c10) | -equal(multiply(X2,sk_c11),sk_c9) | -equal(inverse(X2),sk_c11).
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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(65,40,0,139,0,1,153001,4,1488,153622,5,1502,153623,1,1502,153623,50,1502,153623,40,1502,153697,0,1502,154166,5,2105,154168,1,2105,154168,50,2105,154168,40,2105,154242,0,2105,154711,5,2709,154713,1,2710,154713,50,2710,154713,40,2710,154787,0,2710,174320,3,4211,175746,4,4961,177148,1,5711,177148,50,5711,177148,40,5711,177222,0,5711,187951,3,6462,189507,4,6837,191562,50,7203,191562,40,7203,191636,0,7203,192306,5,8706,192306,1,8706,192306,50,8706,192306,40,8706,192380,0,8706,233315,3,12607,234771,4,14557,236270,1,16507,236270,50,16521,236270,40,16521,236344,0,16521,271787,3,19083,273009,4,20347,274365,5,21622,274366,1,21622,274366,50,21623,274366,40,21623,274440,0,21623,298234,3,23124,299412,4,23874,300684,5,24624,300685,1,24624,300685,50,24624,300685,40,24624,300759,0,24625,301441,5,26129,301441,1,26129,301441,50,26129,301441,40,26129,301515,0,26129,322740,3,27330,323774,4,27930,324897,5,28530,324898,1,28530,324898,50,28531,324898,40,28531,324972,0,28531,341643,3,29282,342495,4,29657,343516,5,30032,343517,1,30032,343517,50,30032,343517,40,30032,343517,40,30032,343582,0,30032,343769,50,30034,343834,0,30034,343935,50,30034,343935,30,30034,343935,40,30034,344000,0,30038,344210,50,30039,344210,30,30039,344210,40,30039,344339,0,30039,346262,50,30046,346262,30,30046,346262,40,30046,346327,0,30050,346434,50,30051,346434,30,30051,346434,40,30051,346499,0,30051,346616,50,30051,346616,30,30051,346616,40,30051,346681,0,30056,346869,50,30057,346934,0,30058,347210,50,30063,347275,0,30067,347559,50,30074,347624,0,30074,347916,50,30083,347981,0,30087,348279,50,30100,348344,0,30100,348650,50,30120,348715,0,30125,349029,50,30160,349094,0,30160,349418,50,30232,349483,0,30232,349817,50,30362,349817,40,30362,349882,0,30362,350110,50,30363,350110,30,30363,350110,40,30363,350175,0,30363,350363,50,30364,350428,0,30369,350747,50,30374,350812,0,30374,351155,50,30380,351220,0,30384,351569,50,30391,351634,0,30391,351993,50,30401,352058,0,30406,352428,50,30422,352493,0,30422,352871,50,30450,352936,0,30455,353323,50,30507,353388,0,30508,353785,50,30611,353785,40,30611,353850,0,30612)
%
%
% START OF PROOF
% 353673 [?] ?
% 353787 [] equal(multiply(identity,X),X).
% 353788 [] equal(multiply(inverse(X),X),identity).
% 353789 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 353790 [] -equal(inverse(sk_c10),sk_c9).
% 353795 [?] ?
% 353801 [?] ?
% 353807 [?] ?
% 353813 [?] ?
% 353819 [?] ?
% 353825 [?] ?
% 353843 [?] ?
% 353849 [?] ?
% 353859 [input:353801,cut:353790] equal(inverse(sk_c4),sk_c6).
% 353860 [para:353859.1.1,353788.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 353868 [input:353807,cut:353790] equal(inverse(sk_c5),sk_c4).
% 353869 [para:353868.1.1,353788.1.1.1] equal(multiply(sk_c4,sk_c5),identity).
% 353876 [input:353819,cut:353790] equal(inverse(sk_c3),sk_c6).
% 353877 [para:353876.1.1,353788.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 353895 [input:353843,cut:353790] equal(inverse(sk_c1),sk_c11).
% 353896 [para:353895.1.1,353788.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 353897 [input:353795,cut:353790] equal(multiply(sk_c5,sk_c6),sk_c4).
% 353909 [input:353813,cut:353790] equal(multiply(sk_c6,sk_c10),sk_c11).
% 353919 [input:353825,cut:353790] equal(multiply(sk_c3,sk_c6),sk_c11).
% 353938 [input:353849,cut:353790] equal(multiply(sk_c1,sk_c11),sk_c10).
% 353958 [para:353860.1.1,353789.1.1.1,demod:353787] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 353961 [para:353869.1.1,353789.1.1.1,demod:353787] equal(X,multiply(sk_c4,multiply(sk_c5,X))).
% 353963 [para:353877.1.1,353789.1.1.1,demod:353787] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 353967 [para:353896.1.1,353789.1.1.1,demod:353787] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 353986 [para:353919.1.1,353789.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c3,multiply(sk_c6,X))).
% 354019 [para:353869.1.1,353958.1.2.2] equal(sk_c5,multiply(sk_c6,identity)).
% 354020 [para:354019.1.2,353789.1.1.1,demod:353787] equal(multiply(sk_c5,X),multiply(sk_c6,X)).
% 354025 [para:353897.1.1,353961.1.2.2] equal(sk_c6,multiply(sk_c4,sk_c4)).
% 354028 [para:354025.1.2,353958.1.2.2] equal(sk_c4,multiply(sk_c6,sk_c6)).
% 354033 [para:353919.1.1,353963.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c11)).
% 354050 [para:353938.1.1,353967.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 354053 [para:354020.1.1,353961.1.2.2] equal(X,multiply(sk_c4,multiply(sk_c6,X))).
% 354054 [para:353860.1.1,354053.1.2.2] equal(sk_c4,multiply(sk_c4,identity)).
% 354055 [para:353877.1.1,354053.1.2.2,demod:354054] equal(sk_c3,sk_c4).
% 354058 [para:353909.1.1,354053.1.2.2] equal(sk_c10,multiply(sk_c4,sk_c11)).
% 354063 [para:354055.1.2,353961.1.2.1,demod:353986,354020] equal(X,multiply(sk_c11,X)).
% 354068 [para:354063.1.2,353896.1.1] equal(sk_c1,identity).
% 354073 [para:354063.1.2,353967.1.2] equal(X,multiply(sk_c1,X)).
% 354074 [para:354063.1.2,354050.1.2] equal(sk_c11,sk_c10).
% 354079 [para:354068.1.1,353895.1.1.1] equal(inverse(identity),sk_c11).
% 354091 [para:354074.1.1,354033.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c10)).
% 354117 [para:354058.1.2,353958.1.2.2,demod:354091] equal(sk_c11,sk_c6).
% 354126 [para:354117.1.1,353938.1.1.2,demod:354073] equal(sk_c6,sk_c10).
% 354131 [para:354117.1.1,354033.1.2.2,demod:354028] equal(sk_c6,sk_c4).
% 354143 [para:354131.1.2,354025.1.2.1,demod:353860] equal(sk_c6,identity).
% 354161 [para:354143.1.1,354126.1.1] equal(identity,sk_c10).
% 354189 [para:354161.1.2,353790.1.1.1,demod:354079,cut:353673] 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: 40710
% derived clauses: 3348054
% kept clauses: 150884
% kept size sum: 930930
% kept mid-nuclei: 151044
% kept new demods: 4962
% forw unit-subs: 802058
% forw double-subs: 1920466
% forw overdouble-subs: 280265
% backward subs: 16761
% fast unit cutoff: 95479
% full unit cutoff: 0
% dbl unit cutoff: 11331
% real runtime : 306.82
% process. runtime: 306.13
% specific non-discr-tree subsumption statistics:
% tried: 63052242
% length fails: 10645583
% strength fails: 18218242
% predlist fails: 188574
% aux str. fails: 8289804
% by-lit fails: 12388848
% full subs tried: 5799073
% full subs fail: 5732953
%
% ; 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/GRP242-1+eq_r.in")
%
%------------------------------------------------------------------------------