TSTP Solution File: GRP286-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP286-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art07.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 297.5s
% Output : Assurance 297.5s
% 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/GRP286-1+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 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% was split for some strategies as:
% -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7).
% -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(multiply(sk_c8,sk_c7),sk_c6).
% -equal(multiply(sk_c7,sk_c8),sk_c6).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,758,50,6,798,0,6,1822,50,20,1862,0,20,3067,50,38,3107,0,38,4406,50,54,4446,0,54,5840,50,74,5880,0,74,7414,50,103,7454,0,103,9128,50,149,9168,0,149,11028,50,231,11068,0,231,13114,50,384,13154,0,384,15432,50,622,15472,0,622,17982,50,1042,17982,40,1042,18022,0,1042,28777,3,1344,29458,4,1493,30153,5,1643,30154,1,1643,30154,50,1643,30154,40,1643,30194,0,1643,30546,3,1945,30558,4,2105,30577,5,2244,30577,1,2244,30577,50,2244,30577,40,2244,30617,0,2244,54388,3,3746,55660,4,4495,56832,5,5245,56833,1,5245,56833,50,5245,56833,40,5245,56873,0,5246,73320,3,5998,74238,4,6372,75136,1,6747,75136,50,6747,75136,40,6747,75176,0,6747,86700,3,7505,87315,4,7873,88914,1,8248,88914,50,8248,88914,40,8248,88954,0,8248,156101,3,12149,157192,4,14099,158294,1,16049,158294,50,16051,158294,40,16051,158334,0,16051,213403,3,18604,214287,4,19877,215121,5,21152,215122,1,21152,215122,50,21154,215122,40,21154,215162,0,21154,263956,3,22656,264566,4,23405,265224,1,24155,265224,50,24157,265224,40,24157,265264,0,24157,275501,3,24914,276735,4,25283,277417,5,25658,277418,1,25658,277418,50,25658,277418,40,25658,277458,0,25658,316819,3,26860,317425,4,27459,317941,5,28059,317942,1,28059,317942,50,28060,317942,40,28060,317982,0,28060,345660,3,28811,346212,4,29186,346614,5,29561,346615,1,29561,346615,50,29562,346615,40,29562,346615,40,29562,346650,0,29562)
%
%
% START OF PROOF
% 346616 [] equal(X,X).
% 346617 [] equal(multiply(identity,X),X).
% 346618 [] equal(multiply(inverse(X),X),identity).
% 346619 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 346620 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 346621 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 346622 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c2),sk_c7).
% 346623 [?] ?
% 346627 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 346628 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 346629 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 346633 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 346634 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c8).
% 346635 [?] ?
% 346639 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 346640 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 346641 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 346645 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 346646 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 346647 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 346676 [hyper:346620,346622,346621,binarycut:346623] equal(inverse(sk_c2),sk_c7).
% 346677 [para:346676.1.1,346618.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 346687 [hyper:346620,346634,346633,binarycut:346635] equal(inverse(sk_c1),sk_c8).
% 346697 [para:346687.1.1,346618.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 346723 [hyper:346620,346629,346628,346627] equal(multiply(sk_c2,sk_c7),sk_c6).
% 346735 [hyper:346620,346641,346640,346639] equal(multiply(sk_c1,sk_c8),sk_c7).
% 346746 [hyper:346620,346647,346646,346645] equal(multiply(sk_c8,sk_c7),sk_c6).
% 346747 [para:346618.1.1,346619.1.1.1,demod:346617] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 346748 [para:346677.1.1,346619.1.1.1,demod:346617] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 346749 [para:346697.1.1,346619.1.1.1,demod:346617] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 346751 [para:346735.1.1,346619.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c1,multiply(sk_c8,X))).
% 346752 [para:346746.1.1,346619.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c8,multiply(sk_c7,X))).
% 346755 [para:346723.1.1,346748.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 346759 [para:346735.1.1,346749.1.2.2,demod:346746] equal(sk_c8,sk_c6).
% 346760 [para:346759.1.1,346697.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 346761 [para:346759.1.1,346735.1.1.2] equal(multiply(sk_c1,sk_c6),sk_c7).
% 346762 [para:346759.1.1,346746.1.1.1] equal(multiply(sk_c6,sk_c7),sk_c6).
% 346775 [para:346762.1.1,346747.1.2.2,demod:346618] equal(sk_c7,identity).
% 346776 [para:346775.1.1,346677.1.1.1,demod:346617] equal(sk_c2,identity).
% 346779 [para:346775.1.1,346748.1.2.1,demod:346617] equal(X,multiply(sk_c2,X)).
% 346780 [para:346775.1.1,346755.1.2.1,demod:346617] equal(sk_c7,sk_c6).
% 346784 [para:346776.1.1,346748.1.2.2.1,demod:346617] equal(X,multiply(sk_c7,X)).
% 346788 [para:346780.1.1,346775.1.1] equal(sk_c6,identity).
% 346792 [para:346788.1.1,346760.1.1.1,demod:346617] equal(sk_c1,identity).
% 346793 [para:346788.1.1,346761.1.1.2] equal(multiply(sk_c1,identity),sk_c7).
% 346795 [para:346792.1.1,346735.1.1.1,demod:346617] equal(sk_c8,sk_c7).
% 346796 [para:346792.1.1,346749.1.2.2.1,demod:346617] equal(X,multiply(sk_c8,X)).
% 346802 [para:346697.1.1,346751.1.2.2,demod:346793,346784] equal(sk_c1,sk_c7).
% 346803 [para:346802.1.2,346723.1.1.2,demod:346779] equal(sk_c1,sk_c6).
% 346805 [para:346803.1.1,346687.1.1.1] equal(inverse(sk_c6),sk_c8).
% 346806 [hyper:346620,346752,demod:346805,346796,346784,cut:346795,cut:346616] 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 21
% 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,758,50,6,798,0,6,1822,50,20,1862,0,20,3067,50,38,3107,0,38,4406,50,54,4446,0,54,5840,50,74,5880,0,74,7414,50,103,7454,0,103,9128,50,149,9168,0,149,11028,50,231,11068,0,231,13114,50,384,13154,0,384,15432,50,622,15472,0,622,17982,50,1042,17982,40,1042,18022,0,1042,28777,3,1344,29458,4,1493,30153,5,1643,30154,1,1643,30154,50,1643,30154,40,1643,30194,0,1643,30546,3,1945,30558,4,2105,30577,5,2244,30577,1,2244,30577,50,2244,30577,40,2244,30617,0,2244,54388,3,3746,55660,4,4495,56832,5,5245,56833,1,5245,56833,50,5245,56833,40,5245,56873,0,5246,73320,3,5998,74238,4,6372,75136,1,6747,75136,50,6747,75136,40,6747,75176,0,6747,86700,3,7505,87315,4,7873,88914,1,8248,88914,50,8248,88914,40,8248,88954,0,8248,156101,3,12149,157192,4,14099,158294,1,16049,158294,50,16051,158294,40,16051,158334,0,16051,213403,3,18604,214287,4,19877,215121,5,21152,215122,1,21152,215122,50,21154,215122,40,21154,215162,0,21154,263956,3,22656,264566,4,23405,265224,1,24155,265224,50,24157,265224,40,24157,265264,0,24157,275501,3,24914,276735,4,25283,277417,5,25658,277418,1,25658,277418,50,25658,277418,40,25658,277458,0,25658,316819,3,26860,317425,4,27459,317941,5,28059,317942,1,28059,317942,50,28060,317942,40,28060,317982,0,28060,345660,3,28811,346212,4,29186,346614,5,29561,346615,1,29561,346615,50,29562,346615,40,29562,346615,40,29562,346650,0,29562,346805,50,29562,346805,30,29562,346805,40,29562,346840,0,29562)
%
%
% START OF PROOF
% 346807 [] equal(multiply(identity,X),X).
% 346808 [] equal(multiply(inverse(X),X),identity).
% 346809 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 346810 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% 346814 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 346815 [?] ?
% 346820 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 346821 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c7),sk_c8).
% 346826 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c7).
% 346827 [?] ?
% 346832 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 346833 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c3,sk_c7),sk_c8).
% 346838 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 346839 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c7),sk_c8).
% 346846 [hyper:346810,346814,binarycut:346815] equal(inverse(sk_c2),sk_c7).
% 346849 [para:346846.1.1,346808.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 346855 [hyper:346810,346826,binarycut:346827] equal(inverse(sk_c1),sk_c8).
% 346856 [para:346855.1.1,346808.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 346872 [hyper:346810,346821,346820] equal(multiply(sk_c2,sk_c7),sk_c6).
% 346877 [hyper:346810,346833,346832] equal(multiply(sk_c1,sk_c8),sk_c7).
% 346882 [hyper:346810,346839,346838] equal(multiply(sk_c8,sk_c7),sk_c6).
% 346883 [para:346808.1.1,346809.1.1.1,demod:346807] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 346884 [para:346849.1.1,346809.1.1.1,demod:346807] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 346885 [para:346856.1.1,346809.1.1.1,demod:346807] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 346889 [para:346872.1.1,346884.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 346891 [para:346877.1.1,346885.1.2.2,demod:346882] equal(sk_c8,sk_c6).
% 346892 [para:346891.1.1,346856.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 346894 [para:346891.1.1,346882.1.1.1] equal(multiply(sk_c6,sk_c7),sk_c6).
% 346905 [para:346894.1.1,346883.1.2.2,demod:346808] equal(sk_c7,identity).
% 346906 [para:346905.1.1,346849.1.1.1,demod:346807] equal(sk_c2,identity).
% 346910 [para:346905.1.1,346889.1.2.1,demod:346807] equal(sk_c7,sk_c6).
% 346912 [para:346906.1.1,346846.1.1.1] equal(inverse(identity),sk_c7).
% 346918 [para:346910.1.1,346905.1.1] equal(sk_c6,identity).
% 346920 [para:346918.1.1,346892.1.1.1,demod:346807] equal(sk_c1,identity).
% 346922 [para:346920.1.1,346855.1.1.1,demod:346912] equal(sk_c7,sk_c8).
% 346932 [hyper:346810,346912,demod:346807,cut:346922] 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 21
% 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,758,50,6,798,0,6,1822,50,20,1862,0,20,3067,50,38,3107,0,38,4406,50,54,4446,0,54,5840,50,74,5880,0,74,7414,50,103,7454,0,103,9128,50,149,9168,0,149,11028,50,231,11068,0,231,13114,50,384,13154,0,384,15432,50,622,15472,0,622,17982,50,1042,17982,40,1042,18022,0,1042,28777,3,1344,29458,4,1493,30153,5,1643,30154,1,1643,30154,50,1643,30154,40,1643,30194,0,1643,30546,3,1945,30558,4,2105,30577,5,2244,30577,1,2244,30577,50,2244,30577,40,2244,30617,0,2244,54388,3,3746,55660,4,4495,56832,5,5245,56833,1,5245,56833,50,5245,56833,40,5245,56873,0,5246,73320,3,5998,74238,4,6372,75136,1,6747,75136,50,6747,75136,40,6747,75176,0,6747,86700,3,7505,87315,4,7873,88914,1,8248,88914,50,8248,88914,40,8248,88954,0,8248,156101,3,12149,157192,4,14099,158294,1,16049,158294,50,16051,158294,40,16051,158334,0,16051,213403,3,18604,214287,4,19877,215121,5,21152,215122,1,21152,215122,50,21154,215122,40,21154,215162,0,21154,263956,3,22656,264566,4,23405,265224,1,24155,265224,50,24157,265224,40,24157,265264,0,24157,275501,3,24914,276735,4,25283,277417,5,25658,277418,1,25658,277418,50,25658,277418,40,25658,277458,0,25658,316819,3,26860,317425,4,27459,317941,5,28059,317942,1,28059,317942,50,28060,317942,40,28060,317982,0,28060,345660,3,28811,346212,4,29186,346614,5,29561,346615,1,29561,346615,50,29562,346615,40,29562,346615,40,29562,346650,0,29562,346805,50,29562,346805,30,29562,346805,40,29562,346840,0,29562,346931,50,29563,346931,30,29563,346931,40,29563,346966,0,29568)
%
%
% START OF PROOF
% 346933 [] equal(multiply(identity,X),X).
% 346934 [] equal(multiply(inverse(X),X),identity).
% 346935 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 346936 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 346937 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 346938 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c2),sk_c7).
% 346939 [] equal(multiply(sk_c8,sk_c5),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 346940 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 346941 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(inverse(sk_c2),sk_c7).
% 346942 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c7).
% 346943 [?] ?
% 346944 [?] ?
% 346945 [?] ?
% 346946 [?] ?
% 346947 [?] ?
% 346948 [?] ?
% 346969 [hyper:346936,346937,binarycut:346943] equal(inverse(sk_c4),sk_c8).
% 346970 [para:346969.1.1,346934.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 346974 [hyper:346936,346940,binarycut:346946] equal(inverse(sk_c3),sk_c7).
% 346978 [para:346974.1.1,346934.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 346982 [hyper:346936,346938,binarycut:346944] equal(multiply(sk_c4,sk_c8),sk_c5).
% 346985 [hyper:346936,346939,binarycut:346945] equal(multiply(sk_c8,sk_c5),sk_c7).
% 346988 [hyper:346936,346941,binarycut:346947] equal(multiply(sk_c3,sk_c7),sk_c8).
% 346991 [hyper:346936,346942,binarycut:346948] equal(multiply(sk_c7,sk_c8),sk_c6).
% 346992 [para:346934.1.1,346935.1.1.1,demod:346933] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 346993 [para:346970.1.1,346935.1.1.1,demod:346933] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 346995 [para:346982.1.1,346935.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c4,multiply(sk_c8,X))).
% 346996 [para:346985.1.1,346935.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c5,X))).
% 346997 [para:346988.1.1,346935.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c3,multiply(sk_c7,X))).
% 346999 [para:346982.1.1,346993.1.2.2,demod:346985] equal(sk_c8,sk_c7).
% 347000 [para:346999.1.1,346970.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 347001 [para:346999.1.1,346982.1.1.2] equal(multiply(sk_c4,sk_c7),sk_c5).
% 347008 [para:346978.1.1,346992.1.2.2] equal(sk_c3,multiply(inverse(sk_c7),identity)).
% 347010 [para:346988.1.1,346992.1.2.2,demod:346991,346974] equal(sk_c7,sk_c6).
% 347013 [para:347000.1.1,346992.1.2.2,demod:347008] equal(sk_c4,sk_c3).
% 347014 [para:347010.1.1,346978.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 347023 [para:347013.1.1,347001.1.1.1,demod:346988] equal(sk_c8,sk_c5).
% 347027 [para:347023.1.1,346993.1.2.1] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 347028 [para:347023.1.1,346999.1.1] equal(sk_c5,sk_c7).
% 347033 [para:347028.1.2,347010.1.1] equal(sk_c5,sk_c6).
% 347044 [para:346995.1.2,346993.1.2.2,demod:346996] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 347045 [para:346993.1.2,346995.1.2.2,demod:347027] equal(X,multiply(sk_c4,X)).
% 347046 [para:347013.1.1,346995.1.2.1,demod:346997,347044] equal(multiply(sk_c5,X),multiply(sk_c7,X)).
% 347047 [para:347045.1.2,346993.1.2.2,demod:347046,347044] equal(X,multiply(sk_c5,X)).
% 347050 [para:347033.1.1,347047.1.2.1] equal(X,multiply(sk_c6,X)).
% 347051 [para:347050.1.2,346992.1.2.2] equal(X,multiply(inverse(sk_c6),X)).
% 347054 [para:347014.1.1,346992.1.2.2,demod:347051] equal(sk_c3,identity).
% 347055 [para:347054.1.1,346974.1.1.1] equal(inverse(identity),sk_c7).
% 347056 [hyper:346936,347055,demod:346933,cut:347010] 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 21
% 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,758,50,6,798,0,6,1822,50,20,1862,0,20,3067,50,38,3107,0,38,4406,50,54,4446,0,54,5840,50,74,5880,0,74,7414,50,103,7454,0,103,9128,50,149,9168,0,149,11028,50,231,11068,0,231,13114,50,384,13154,0,384,15432,50,622,15472,0,622,17982,50,1042,17982,40,1042,18022,0,1042,28777,3,1344,29458,4,1493,30153,5,1643,30154,1,1643,30154,50,1643,30154,40,1643,30194,0,1643,30546,3,1945,30558,4,2105,30577,5,2244,30577,1,2244,30577,50,2244,30577,40,2244,30617,0,2244,54388,3,3746,55660,4,4495,56832,5,5245,56833,1,5245,56833,50,5245,56833,40,5245,56873,0,5246,73320,3,5998,74238,4,6372,75136,1,6747,75136,50,6747,75136,40,6747,75176,0,6747,86700,3,7505,87315,4,7873,88914,1,8248,88914,50,8248,88914,40,8248,88954,0,8248,156101,3,12149,157192,4,14099,158294,1,16049,158294,50,16051,158294,40,16051,158334,0,16051,213403,3,18604,214287,4,19877,215121,5,21152,215122,1,21152,215122,50,21154,215122,40,21154,215162,0,21154,263956,3,22656,264566,4,23405,265224,1,24155,265224,50,24157,265224,40,24157,265264,0,24157,275501,3,24914,276735,4,25283,277417,5,25658,277418,1,25658,277418,50,25658,277418,40,25658,277458,0,25658,316819,3,26860,317425,4,27459,317941,5,28059,317942,1,28059,317942,50,28060,317942,40,28060,317982,0,28060,345660,3,28811,346212,4,29186,346614,5,29561,346615,1,29561,346615,50,29562,346615,40,29562,346615,40,29562,346650,0,29562,346805,50,29562,346805,30,29562,346805,40,29562,346840,0,29562,346931,50,29563,346931,30,29563,346931,40,29563,346966,0,29568,347055,50,29568,347055,30,29568,347055,40,29568,347090,0,29568)
%
%
% START OF PROOF
% 347057 [] equal(multiply(identity,X),X).
% 347058 [] equal(multiply(inverse(X),X),identity).
% 347059 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 347060 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 347073 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 347074 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c8).
% 347075 [] equal(multiply(sk_c8,sk_c5),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 347076 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c7).
% 347077 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 347078 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 347079 [?] ?
% 347080 [?] ?
% 347081 [?] ?
% 347082 [?] ?
% 347083 [?] ?
% 347084 [?] ?
% 347097 [hyper:347060,347073,binarycut:347079] equal(inverse(sk_c4),sk_c8).
% 347101 [para:347097.1.1,347058.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 347105 [hyper:347060,347076,binarycut:347082] equal(inverse(sk_c3),sk_c7).
% 347106 [para:347105.1.1,347058.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 347114 [hyper:347060,347074,binarycut:347080] equal(multiply(sk_c4,sk_c8),sk_c5).
% 347117 [hyper:347060,347075,binarycut:347081] equal(multiply(sk_c8,sk_c5),sk_c7).
% 347121 [hyper:347060,347077,binarycut:347083] equal(multiply(sk_c3,sk_c7),sk_c8).
% 347124 [hyper:347060,347078,binarycut:347084] equal(multiply(sk_c7,sk_c8),sk_c6).
% 347125 [para:347058.1.1,347059.1.1.1,demod:347057] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 347126 [para:347101.1.1,347059.1.1.1,demod:347057] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 347128 [para:347114.1.1,347059.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c4,multiply(sk_c8,X))).
% 347129 [para:347117.1.1,347059.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c5,X))).
% 347130 [para:347121.1.1,347059.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c3,multiply(sk_c7,X))).
% 347132 [para:347114.1.1,347126.1.2.2,demod:347117] equal(sk_c8,sk_c7).
% 347133 [para:347132.1.1,347101.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 347134 [para:347132.1.1,347114.1.1.2] equal(multiply(sk_c4,sk_c7),sk_c5).
% 347140 [para:347101.1.1,347125.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 347141 [para:347106.1.1,347125.1.2.2] equal(sk_c3,multiply(inverse(sk_c7),identity)).
% 347142 [para:347117.1.1,347125.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),sk_c7)).
% 347143 [para:347121.1.1,347125.1.2.2,demod:347124,347105] equal(sk_c7,sk_c6).
% 347146 [para:347133.1.1,347125.1.2.2,demod:347141] equal(sk_c4,sk_c3).
% 347148 [para:347143.1.1,347121.1.1.2] equal(multiply(sk_c3,sk_c6),sk_c8).
% 347156 [para:347146.1.1,347134.1.1.1,demod:347121] equal(sk_c8,sk_c5).
% 347160 [para:347156.1.1,347126.1.2.1] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 347161 [para:347156.1.1,347132.1.1] equal(sk_c5,sk_c7).
% 347165 [para:347161.1.2,347124.1.1.1] equal(multiply(sk_c5,sk_c8),sk_c6).
% 347177 [para:347128.1.2,347126.1.2.2,demod:347129] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 347178 [para:347126.1.2,347128.1.2.2,demod:347160] equal(X,multiply(sk_c4,X)).
% 347179 [para:347146.1.1,347128.1.2.1,demod:347130,347177] equal(multiply(sk_c5,X),multiply(sk_c7,X)).
% 347180 [para:347178.1.2,347126.1.2.2,demod:347179,347177] equal(X,multiply(sk_c5,X)).
% 347181 [para:347146.1.1,347178.1.2.1] equal(X,multiply(sk_c3,X)).
% 347182 [para:347180.1.2,347125.1.2.2] equal(X,multiply(inverse(sk_c5),X)).
% 347187 [para:347148.1.1,347181.1.2] equal(sk_c6,sk_c8).
% 347188 [para:347187.1.2,347132.1.1] equal(sk_c6,sk_c7).
% 347193 [para:347182.1.2,347058.1.1] equal(sk_c5,identity).
% 347194 [para:347193.1.1,347117.1.1.2,demod:347180,347179,347177] equal(identity,sk_c7).
% 347200 [para:347194.1.2,347142.1.2.2,demod:347140] equal(sk_c5,sk_c4).
% 347201 [para:347200.1.2,347097.1.1.1] equal(inverse(sk_c5),sk_c8).
% 347211 [hyper:347060,347201,demod:347165,cut:347188] 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 21
% 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,0,75,0,0,758,50,6,798,0,6,1822,50,20,1862,0,20,3067,50,38,3107,0,38,4406,50,54,4446,0,54,5840,50,74,5880,0,74,7414,50,103,7454,0,103,9128,50,149,9168,0,149,11028,50,231,11068,0,231,13114,50,384,13154,0,384,15432,50,622,15472,0,622,17982,50,1042,17982,40,1042,18022,0,1042,28777,3,1344,29458,4,1493,30153,5,1643,30154,1,1643,30154,50,1643,30154,40,1643,30194,0,1643,30546,3,1945,30558,4,2105,30577,5,2244,30577,1,2244,30577,50,2244,30577,40,2244,30617,0,2244,54388,3,3746,55660,4,4495,56832,5,5245,56833,1,5245,56833,50,5245,56833,40,5245,56873,0,5246,73320,3,5998,74238,4,6372,75136,1,6747,75136,50,6747,75136,40,6747,75176,0,6747,86700,3,7505,87315,4,7873,88914,1,8248,88914,50,8248,88914,40,8248,88954,0,8248,156101,3,12149,157192,4,14099,158294,1,16049,158294,50,16051,158294,40,16051,158334,0,16051,213403,3,18604,214287,4,19877,215121,5,21152,215122,1,21152,215122,50,21154,215122,40,21154,215162,0,21154,263956,3,22656,264566,4,23405,265224,1,24155,265224,50,24157,265224,40,24157,265264,0,24157,275501,3,24914,276735,4,25283,277417,5,25658,277418,1,25658,277418,50,25658,277418,40,25658,277458,0,25658,316819,3,26860,317425,4,27459,317941,5,28059,317942,1,28059,317942,50,28060,317942,40,28060,317982,0,28060,345660,3,28811,346212,4,29186,346614,5,29561,346615,1,29561,346615,50,29562,346615,40,29562,346615,40,29562,346650,0,29562,346805,50,29562,346805,30,29562,346805,40,29562,346840,0,29562,346931,50,29563,346931,30,29563,346931,40,29563,346966,0,29568,347055,50,29568,347055,30,29568,347055,40,29568,347090,0,29568,347210,50,29569,347210,30,29569,347210,40,29569,347245,0,29569,347373,50,29570,347408,0,29574,347586,50,29578,347621,0,29578,347807,50,29582,347842,0,29587,348036,50,29594,348071,0,29594,348271,50,29603,348306,0,29603,348514,50,29620,348549,0,29624,348765,50,29656,348800,0,29656,349026,50,29721,349061,0,29721,349297,50,29843,349297,40,29843,349332,0,29843)
%
%
% START OF PROOF
% 349119 [?] ?
% 349299 [] equal(multiply(identity,X),X).
% 349300 [] equal(multiply(inverse(X),X),identity).
% 349301 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 349302 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 349327 [?] ?
% 349328 [?] ?
% 349329 [?] ?
% 349370 [input:349327,cut:349302] equal(inverse(sk_c4),sk_c8).
% 349371 [para:349370.1.1,349300.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 349385 [input:349328,cut:349302] equal(multiply(sk_c4,sk_c8),sk_c5).
% 349386 [input:349329,cut:349302] equal(multiply(sk_c8,sk_c5),sk_c7).
% 349407 [para:349371.1.1,349301.1.1.1,demod:349299] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 349438 [para:349385.1.1,349407.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 349443 [para:349438.1.2,349386.1.1] equal(sk_c8,sk_c7).
% 349445 [para:349443.1.1,349302.1.1.1,cut:349119] 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(Z),sk_c7) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,0,75,0,0,758,50,6,798,0,6,1822,50,20,1862,0,20,3067,50,38,3107,0,38,4406,50,54,4446,0,54,5840,50,74,5880,0,74,7414,50,103,7454,0,103,9128,50,149,9168,0,149,11028,50,231,11068,0,231,13114,50,384,13154,0,384,15432,50,622,15472,0,622,17982,50,1042,17982,40,1042,18022,0,1042,28777,3,1344,29458,4,1493,30153,5,1643,30154,1,1643,30154,50,1643,30154,40,1643,30194,0,1643,30546,3,1945,30558,4,2105,30577,5,2244,30577,1,2244,30577,50,2244,30577,40,2244,30617,0,2244,54388,3,3746,55660,4,4495,56832,5,5245,56833,1,5245,56833,50,5245,56833,40,5245,56873,0,5246,73320,3,5998,74238,4,6372,75136,1,6747,75136,50,6747,75136,40,6747,75176,0,6747,86700,3,7505,87315,4,7873,88914,1,8248,88914,50,8248,88914,40,8248,88954,0,8248,156101,3,12149,157192,4,14099,158294,1,16049,158294,50,16051,158294,40,16051,158334,0,16051,213403,3,18604,214287,4,19877,215121,5,21152,215122,1,21152,215122,50,21154,215122,40,21154,215162,0,21154,263956,3,22656,264566,4,23405,265224,1,24155,265224,50,24157,265224,40,24157,265264,0,24157,275501,3,24914,276735,4,25283,277417,5,25658,277418,1,25658,277418,50,25658,277418,40,25658,277458,0,25658,316819,3,26860,317425,4,27459,317941,5,28059,317942,1,28059,317942,50,28060,317942,40,28060,317982,0,28060,345660,3,28811,346212,4,29186,346614,5,29561,346615,1,29561,346615,50,29562,346615,40,29562,346615,40,29562,346650,0,29562,346805,50,29562,346805,30,29562,346805,40,29562,346840,0,29562,346931,50,29563,346931,30,29563,346931,40,29563,346966,0,29568,347055,50,29568,347055,30,29568,347055,40,29568,347090,0,29568,347210,50,29569,347210,30,29569,347210,40,29569,347245,0,29569,347373,50,29570,347408,0,29574,347586,50,29578,347621,0,29578,347807,50,29582,347842,0,29587,348036,50,29594,348071,0,29594,348271,50,29603,348306,0,29603,348514,50,29620,348549,0,29624,348765,50,29656,348800,0,29656,349026,50,29721,349061,0,29721,349297,50,29843,349297,40,29843,349332,0,29843,349444,50,29843,349444,30,29843,349444,40,29843,349479,0,29843,349579,50,29844,349614,0,29848,349760,50,29851,349795,0,29851,349949,50,29855,349984,0,29856,350146,50,29861,350181,0,29865,350349,50,29873,350384,0,29873,350560,50,29887,350595,0,29893,350779,50,29921,350814,0,29921,351008,50,29981,351043,0,29981,351247,50,30102,351247,40,30102,351282,0,30102)
%
%
% START OF PROOF
% 351117 [?] ?
% 351249 [] equal(multiply(identity,X),X).
% 351250 [] equal(multiply(inverse(X),X),identity).
% 351251 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 351252 [] -equal(multiply(sk_c7,sk_c8),sk_c6).
% 351258 [?] ?
% 351264 [?] ?
% 351270 [?] ?
% 351276 [?] ?
% 351282 [?] ?
% 351301 [input:351258,cut:351252] equal(inverse(sk_c2),sk_c7).
% 351302 [para:351301.1.1,351250.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 351314 [input:351270,cut:351252] equal(inverse(sk_c1),sk_c8).
% 351315 [para:351314.1.1,351250.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 351330 [input:351264,cut:351252] equal(multiply(sk_c2,sk_c7),sk_c6).
% 351334 [input:351276,cut:351252] equal(multiply(sk_c1,sk_c8),sk_c7).
% 351338 [input:351282,cut:351252] equal(multiply(sk_c8,sk_c7),sk_c6).
% 351343 [para:351302.1.1,351251.1.1.1,demod:351249] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 351351 [para:351315.1.1,351251.1.1.1,demod:351249] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 351384 [para:351330.1.1,351343.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 351391 [para:351334.1.1,351351.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 351397 [para:351391.1.2,351338.1.1] equal(sk_c8,sk_c6).
% 351399 [para:351397.1.1,351252.1.1.2,demod:351384,cut:351117] 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: 34565
% derived clauses: 5652872
% kept clauses: 295747
% kept size sum: 377524
% kept mid-nuclei: 14396
% kept new demods: 4099
% forw unit-subs: 1736797
% forw double-subs: 3213972
% forw overdouble-subs: 352564
% backward subs: 12473
% fast unit cutoff: 31745
% full unit cutoff: 0
% dbl unit cutoff: 7678
% real runtime : 304.10
% process. runtime: 301.4
% specific non-discr-tree subsumption statistics:
% tried: 40522243
% length fails: 3910856
% strength fails: 12990213
% predlist fails: 4349293
% aux str. fails: 6862379
% by-lit fails: 6831622
% full subs tried: 1267102
% full subs fail: 1155644
%
% ; 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/GRP286-1+eq_r.in")
%
%------------------------------------------------------------------------------