TSTP Solution File: GRP346-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP346-1 : 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 299.6s
% Output : Assurance 299.6s
% 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/GRP346-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 23)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 23)
% (binary-posweight-lex-big-order 30 #f 3 23)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% was split for some strategies as:
% -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6).
% -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6).
% -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7).
% -equal(multiply(sk_c6,sk_c7),sk_c5).
% -equal(multiply(sk_c6,sk_c5),sk_c7).
% -equal(multiply(sk_c7,sk_c5),sk_c6).
% -equal(inverse(sk_c7),sk_c5).
%
% Starting a split proof attempt with 8 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,1,85,0,1,949,50,7,994,0,7,1873,50,14,1918,0,14,2806,50,22,2851,0,22,3745,50,28,3790,0,28,4691,50,38,4736,0,38,5645,50,53,5690,0,53,6607,50,81,6652,0,81,7579,50,140,7624,0,140,8561,50,268,8606,0,268,9555,50,472,9600,0,472,10561,50,860,10561,40,860,10606,0,861,21061,3,1162,21807,4,1312,22543,5,1462,22544,1,1462,22544,50,1462,22544,40,1462,22589,0,1462,22866,3,1772,22875,4,1914,22887,5,2063,22887,1,2063,22887,50,2063,22887,40,2063,22932,0,2063,49014,3,3572,50277,4,4314,51458,5,5064,51459,1,5064,51459,50,5065,51459,40,5065,51504,0,5065,67610,3,5816,68511,4,6191,69392,1,6566,69392,50,6566,69392,40,6566,69437,0,6566,76895,3,7321,78252,4,7692,79443,5,8067,79444,1,8067,79444,50,8067,79444,40,8067,79489,0,8067,135469,3,11970,136919,4,13918,137998,1,15868,137998,50,15870,137998,40,15870,138043,0,15870,184890,3,18421,185950,4,19696,187001,1,20971,187001,50,20973,187001,40,20973,187046,0,20973,227247,3,22474,227867,4,23224,229978,5,23974,229979,1,23974,229979,50,23976,229979,40,23976,230024,0,23976,235851,3,24760,236663,4,25102,236893,5,25477,236893,1,25477,236893,50,25477,236893,40,25477,236938,0,25478,267203,3,26679,268076,4,27279,268621,1,27879,268621,50,27880,268621,40,27880,268666,0,27880,290594,3,28638,291287,4,29006,291745,1,29381,291745,50,29381,291745,40,29381,291745,40,29381,291785,0,29381)
%
%
% START OF PROOF
% 291747 [] equal(multiply(identity,X),X).
% 291748 [] equal(multiply(inverse(X),X),identity).
% 291749 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 291750 [] -equal(multiply(X,sk_c7),sk_c5) | -equal(inverse(X),sk_c7).
% 291751 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 291752 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(multiply(sk_c4,sk_c7),sk_c5).
% 291758 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 291759 [?] ?
% 291765 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 291766 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c5).
% 291772 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 291773 [?] ?
% 291779 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c4),sk_c7).
% 291780 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(multiply(sk_c4,sk_c7),sk_c5).
% 291788 [hyper:291750,291758,binarycut:291759] equal(inverse(sk_c2),sk_c6).
% 291794 [hyper:291750,291772,binarycut:291773] equal(inverse(sk_c1),sk_c7).
% 291797 [para:291794.1.1,291748.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 291804 [hyper:291750,291752,291751] equal(multiply(sk_c2,sk_c5),sk_c6).
% 291820 [hyper:291750,291766,291765] equal(multiply(sk_c1,sk_c6),sk_c7).
% 291824 [hyper:291750,291780,291779] equal(multiply(sk_c6,sk_c7),sk_c5).
% 291828 [para:291748.1.1,291749.1.1.1,demod:291747] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 291837 [para:291804.1.1,291828.1.2.2,demod:291788] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 291838 [para:291820.1.1,291828.1.2.2,demod:291794] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 291839 [para:291824.1.1,291828.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 291841 [para:291837.1.2,291828.1.2.2,demod:291839] equal(sk_c6,sk_c7).
% 291844 [para:291841.1.1,291824.1.1.1,demod:291838] equal(sk_c6,sk_c5).
% 291848 [para:291844.1.1,291824.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 291852 [para:291841.1.1,291844.1.1] equal(sk_c7,sk_c5).
% 291877 [para:291848.1.1,291828.1.2.2,demod:291748] equal(sk_c7,identity).
% 291879 [para:291877.1.1,291797.1.1.1,demod:291747] equal(sk_c1,identity).
% 291887 [para:291879.1.1,291794.1.1.1] equal(inverse(identity),sk_c7).
% 291894 [hyper:291750,291887,demod:291747,cut:291852] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,1,85,0,1,949,50,7,994,0,7,1873,50,14,1918,0,14,2806,50,22,2851,0,22,3745,50,28,3790,0,28,4691,50,38,4736,0,38,5645,50,53,5690,0,53,6607,50,81,6652,0,81,7579,50,140,7624,0,140,8561,50,268,8606,0,268,9555,50,472,9600,0,472,10561,50,860,10561,40,860,10606,0,861,21061,3,1162,21807,4,1312,22543,5,1462,22544,1,1462,22544,50,1462,22544,40,1462,22589,0,1462,22866,3,1772,22875,4,1914,22887,5,2063,22887,1,2063,22887,50,2063,22887,40,2063,22932,0,2063,49014,3,3572,50277,4,4314,51458,5,5064,51459,1,5064,51459,50,5065,51459,40,5065,51504,0,5065,67610,3,5816,68511,4,6191,69392,1,6566,69392,50,6566,69392,40,6566,69437,0,6566,76895,3,7321,78252,4,7692,79443,5,8067,79444,1,8067,79444,50,8067,79444,40,8067,79489,0,8067,135469,3,11970,136919,4,13918,137998,1,15868,137998,50,15870,137998,40,15870,138043,0,15870,184890,3,18421,185950,4,19696,187001,1,20971,187001,50,20973,187001,40,20973,187046,0,20973,227247,3,22474,227867,4,23224,229978,5,23974,229979,1,23974,229979,50,23976,229979,40,23976,230024,0,23976,235851,3,24760,236663,4,25102,236893,5,25477,236893,1,25477,236893,50,25477,236893,40,25477,236938,0,25478,267203,3,26679,268076,4,27279,268621,1,27879,268621,50,27880,268621,40,27880,268666,0,27880,290594,3,28638,291287,4,29006,291745,1,29381,291745,50,29381,291745,40,29381,291745,40,29381,291785,0,29381,291893,50,29381,291893,30,29381,291893,40,29381,291933,0,29381)
%
%
% START OF PROOF
% 291895 [] equal(multiply(identity,X),X).
% 291896 [] equal(multiply(inverse(X),X),identity).
% 291897 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 291898 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6).
% 291901 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 291902 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 291908 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 291909 [?] ?
% 291915 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 291916 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 291922 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 291923 [?] ?
% 291929 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c3),sk_c6).
% 291930 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 291939 [hyper:291898,291908,binarycut:291909] equal(inverse(sk_c2),sk_c6).
% 291942 [para:291939.1.1,291896.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 291947 [hyper:291898,291922,binarycut:291923] equal(inverse(sk_c1),sk_c7).
% 291948 [para:291947.1.1,291896.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 291973 [hyper:291898,291902,291901] equal(multiply(sk_c2,sk_c5),sk_c6).
% 291980 [hyper:291898,291916,291915] equal(multiply(sk_c1,sk_c6),sk_c7).
% 291987 [hyper:291898,291930,291929] equal(multiply(sk_c6,sk_c7),sk_c5).
% 291988 [para:291896.1.1,291897.1.1.1,demod:291895] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 291991 [para:291973.1.1,291897.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c2,multiply(sk_c5,X))).
% 291995 [para:291942.1.1,291988.1.2.2] equal(sk_c2,multiply(inverse(sk_c6),identity)).
% 291996 [para:291948.1.1,291988.1.2.2] equal(sk_c1,multiply(inverse(sk_c7),identity)).
% 291997 [para:291973.1.1,291988.1.2.2,demod:291939] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 291998 [para:291980.1.1,291988.1.2.2,demod:291947] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 291999 [para:291987.1.1,291988.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 292001 [para:291997.1.2,291988.1.2.2,demod:291999] equal(sk_c6,sk_c7).
% 292002 [para:292001.1.1,291942.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 292004 [para:292001.1.1,291987.1.1.1,demod:291998] equal(sk_c6,sk_c5).
% 292006 [para:292004.1.1,291942.1.1.1] equal(multiply(sk_c5,sk_c2),identity).
% 292007 [para:292004.1.1,291980.1.1.2] equal(multiply(sk_c1,sk_c5),sk_c7).
% 292008 [para:292004.1.1,291987.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 292009 [para:292004.1.1,291997.1.2.1] equal(sk_c5,multiply(sk_c5,sk_c6)).
% 292011 [para:292004.1.1,292001.1.1] equal(sk_c5,sk_c7).
% 292017 [para:292002.1.1,291988.1.2.2,demod:291996] equal(sk_c2,sk_c1).
% 292030 [para:292007.1.1,291897.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c1,multiply(sk_c5,X))).
% 292032 [para:292017.1.1,291991.1.2.1,demod:292030] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 292033 [para:292006.1.1,291991.1.2.2,demod:291942] equal(identity,multiply(sk_c2,identity)).
% 292035 [para:292008.1.1,291988.1.2.2,demod:291896] equal(sk_c7,identity).
% 292037 [para:292035.1.1,291948.1.1.1,demod:291895] equal(sk_c1,identity).
% 292038 [para:292035.1.1,291987.1.1.2,demod:292032] equal(multiply(sk_c7,identity),sk_c5).
% 292039 [para:292035.1.1,292011.1.2] equal(sk_c5,identity).
% 292045 [para:292037.1.1,291947.1.1.1] equal(inverse(identity),sk_c7).
% 292047 [para:292039.1.1,291973.1.1.2,demod:292033] equal(identity,sk_c6).
% 292052 [para:292047.1.2,291995.1.2.1.1,demod:292038,292045] equal(sk_c2,sk_c5).
% 292053 [para:292052.1.1,291939.1.1.1] equal(inverse(sk_c5),sk_c6).
% 292057 [hyper:291898,292053,demod:292009,cut:292011] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,1,85,0,1,949,50,7,994,0,7,1873,50,14,1918,0,14,2806,50,22,2851,0,22,3745,50,28,3790,0,28,4691,50,38,4736,0,38,5645,50,53,5690,0,53,6607,50,81,6652,0,81,7579,50,140,7624,0,140,8561,50,268,8606,0,268,9555,50,472,9600,0,472,10561,50,860,10561,40,860,10606,0,861,21061,3,1162,21807,4,1312,22543,5,1462,22544,1,1462,22544,50,1462,22544,40,1462,22589,0,1462,22866,3,1772,22875,4,1914,22887,5,2063,22887,1,2063,22887,50,2063,22887,40,2063,22932,0,2063,49014,3,3572,50277,4,4314,51458,5,5064,51459,1,5064,51459,50,5065,51459,40,5065,51504,0,5065,67610,3,5816,68511,4,6191,69392,1,6566,69392,50,6566,69392,40,6566,69437,0,6566,76895,3,7321,78252,4,7692,79443,5,8067,79444,1,8067,79444,50,8067,79444,40,8067,79489,0,8067,135469,3,11970,136919,4,13918,137998,1,15868,137998,50,15870,137998,40,15870,138043,0,15870,184890,3,18421,185950,4,19696,187001,1,20971,187001,50,20973,187001,40,20973,187046,0,20973,227247,3,22474,227867,4,23224,229978,5,23974,229979,1,23974,229979,50,23976,229979,40,23976,230024,0,23976,235851,3,24760,236663,4,25102,236893,5,25477,236893,1,25477,236893,50,25477,236893,40,25477,236938,0,25478,267203,3,26679,268076,4,27279,268621,1,27879,268621,50,27880,268621,40,27880,268666,0,27880,290594,3,28638,291287,4,29006,291745,1,29381,291745,50,29381,291745,40,29381,291745,40,29381,291785,0,29381,291893,50,29381,291893,30,29381,291893,40,29381,291933,0,29381,292056,50,29381,292056,30,29381,292056,40,29381,292096,0,29387,292197,50,29388,292237,0,29388)
%
%
% START OF PROOF
% 292178 [?] ?
% 292202 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 292207 [?] ?
% 292208 [?] ?
% 292214 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c7),sk_c5).
% 292215 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c2),sk_c6).
% 292256 [hyper:292202,292214,binarycut:292207] equal(inverse(sk_c7),sk_c5).
% 292270 [hyper:292202,292215,binarycut:292208] equal(multiply(sk_c7,sk_c5),sk_c6).
% 292274 [hyper:292202,292270,demod:292256,cut:292178] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 2
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,1,85,0,1,949,50,7,994,0,7,1873,50,14,1918,0,14,2806,50,22,2851,0,22,3745,50,28,3790,0,28,4691,50,38,4736,0,38,5645,50,53,5690,0,53,6607,50,81,6652,0,81,7579,50,140,7624,0,140,8561,50,268,8606,0,268,9555,50,472,9600,0,472,10561,50,860,10561,40,860,10606,0,861,21061,3,1162,21807,4,1312,22543,5,1462,22544,1,1462,22544,50,1462,22544,40,1462,22589,0,1462,22866,3,1772,22875,4,1914,22887,5,2063,22887,1,2063,22887,50,2063,22887,40,2063,22932,0,2063,49014,3,3572,50277,4,4314,51458,5,5064,51459,1,5064,51459,50,5065,51459,40,5065,51504,0,5065,67610,3,5816,68511,4,6191,69392,1,6566,69392,50,6566,69392,40,6566,69437,0,6566,76895,3,7321,78252,4,7692,79443,5,8067,79444,1,8067,79444,50,8067,79444,40,8067,79489,0,8067,135469,3,11970,136919,4,13918,137998,1,15868,137998,50,15870,137998,40,15870,138043,0,15870,184890,3,18421,185950,4,19696,187001,1,20971,187001,50,20973,187001,40,20973,187046,0,20973,227247,3,22474,227867,4,23224,229978,5,23974,229979,1,23974,229979,50,23976,229979,40,23976,230024,0,23976,235851,3,24760,236663,4,25102,236893,5,25477,236893,1,25477,236893,50,25477,236893,40,25477,236938,0,25478,267203,3,26679,268076,4,27279,268621,1,27879,268621,50,27880,268621,40,27880,268666,0,27880,290594,3,28638,291287,4,29006,291745,1,29381,291745,50,29381,291745,40,29381,291745,40,29381,291785,0,29381,291893,50,29381,291893,30,29381,291893,40,29381,291933,0,29381,292056,50,29381,292056,30,29381,292056,40,29381,292096,0,29387,292197,50,29388,292237,0,29388,292273,50,29388,292273,30,29388,292273,40,29388,292313,0,29388,292430,50,29389,292470,0,29393)
%
%
% START OF PROOF
% 292380 [?] ?
% 292431 [] equal(X,X).
% 292435 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 292452 [?] ?
% 292453 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 292459 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 292460 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 292487 [hyper:292435,292459,binarycut:292452] equal(inverse(sk_c3),sk_c6).
% 292507 [hyper:292435,292453,demod:292487,cut:292380] equal(multiply(sk_c1,sk_c6),sk_c7).
% 292510 [hyper:292435,292460,demod:292487,cut:292380] equal(inverse(sk_c1),sk_c7).
% 292513 [hyper:292435,292510,demod:292507,cut:292431] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 2
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(multiply(sk_c6,sk_c7),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 2
%
%
% 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(40,40,1,85,0,1,949,50,7,994,0,7,1873,50,14,1918,0,14,2806,50,22,2851,0,22,3745,50,28,3790,0,28,4691,50,38,4736,0,38,5645,50,53,5690,0,53,6607,50,81,6652,0,81,7579,50,140,7624,0,140,8561,50,268,8606,0,268,9555,50,472,9600,0,472,10561,50,860,10561,40,860,10606,0,861,21061,3,1162,21807,4,1312,22543,5,1462,22544,1,1462,22544,50,1462,22544,40,1462,22589,0,1462,22866,3,1772,22875,4,1914,22887,5,2063,22887,1,2063,22887,50,2063,22887,40,2063,22932,0,2063,49014,3,3572,50277,4,4314,51458,5,5064,51459,1,5064,51459,50,5065,51459,40,5065,51504,0,5065,67610,3,5816,68511,4,6191,69392,1,6566,69392,50,6566,69392,40,6566,69437,0,6566,76895,3,7321,78252,4,7692,79443,5,8067,79444,1,8067,79444,50,8067,79444,40,8067,79489,0,8067,135469,3,11970,136919,4,13918,137998,1,15868,137998,50,15870,137998,40,15870,138043,0,15870,184890,3,18421,185950,4,19696,187001,1,20971,187001,50,20973,187001,40,20973,187046,0,20973,227247,3,22474,227867,4,23224,229978,5,23974,229979,1,23974,229979,50,23976,229979,40,23976,230024,0,23976,235851,3,24760,236663,4,25102,236893,5,25477,236893,1,25477,236893,50,25477,236893,40,25477,236938,0,25478,267203,3,26679,268076,4,27279,268621,1,27879,268621,50,27880,268621,40,27880,268666,0,27880,290594,3,28638,291287,4,29006,291745,1,29381,291745,50,29381,291745,40,29381,291745,40,29381,291785,0,29381,291893,50,29381,291893,30,29381,291893,40,29381,291933,0,29381,292056,50,29381,292056,30,29381,292056,40,29381,292096,0,29387,292197,50,29388,292237,0,29388,292273,50,29388,292273,30,29388,292273,40,29388,292313,0,29388,292430,50,29389,292470,0,29393,292512,50,29393,292512,30,29393,292512,40,29393,292552,0,29393,292655,50,29394,292695,0,29399,292851,50,29401,292891,0,29401,293058,50,29406,293098,0,29406,293277,50,29413,293317,0,29418,293502,50,29428,293542,0,29428,293735,50,29446,293775,0,29450,293977,50,29483,294017,0,29483,294229,50,29550,294229,40,29550,294269,0,29550)
%
%
% START OF PROOF
% 294121 [?] ?
% 294231 [] equal(multiply(identity,X),X).
% 294232 [] equal(multiply(inverse(X),X),identity).
% 294233 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 294234 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 294263 [?] ?
% 294264 [?] ?
% 294265 [?] ?
% 294266 [?] ?
% 294268 [?] ?
% 294319 [input:294263,cut:294234] equal(inverse(sk_c4),sk_c7).
% 294320 [para:294319.1.1,294232.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 294322 [input:294265,cut:294234] equal(inverse(sk_c3),sk_c6).
% 294323 [para:294322.1.1,294232.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 294336 [input:294264,cut:294234] equal(multiply(sk_c4,sk_c7),sk_c5).
% 294337 [input:294266,cut:294234] equal(multiply(sk_c3,sk_c6),sk_c7).
% 294338 [input:294268,cut:294234] equal(multiply(sk_c7,sk_c5),sk_c6).
% 294363 [para:294320.1.1,294233.1.1.1,demod:294231] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 294366 [para:294323.1.1,294233.1.1.1,demod:294231] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 294384 [para:294338.1.1,294233.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c5,X))).
% 294392 [para:294336.1.1,294363.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c5)).
% 294397 [para:294392.1.2,294338.1.1] equal(sk_c7,sk_c6).
% 294398 [para:294392.1.2,294233.1.1.1,demod:294384] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 294399 [para:294397.1.2,294234.1.1.1] -equal(multiply(sk_c7,sk_c7),sk_c5).
% 294423 [para:294337.1.1,294366.1.2.2,demod:294398] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 294425 [para:294423.1.2,294399.1.1,cut:294121] 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_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(multiply(sk_c6,sk_c5),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 2
%
%
% 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(40,40,1,85,0,1,949,50,7,994,0,7,1873,50,14,1918,0,14,2806,50,22,2851,0,22,3745,50,28,3790,0,28,4691,50,38,4736,0,38,5645,50,53,5690,0,53,6607,50,81,6652,0,81,7579,50,140,7624,0,140,8561,50,268,8606,0,268,9555,50,472,9600,0,472,10561,50,860,10561,40,860,10606,0,861,21061,3,1162,21807,4,1312,22543,5,1462,22544,1,1462,22544,50,1462,22544,40,1462,22589,0,1462,22866,3,1772,22875,4,1914,22887,5,2063,22887,1,2063,22887,50,2063,22887,40,2063,22932,0,2063,49014,3,3572,50277,4,4314,51458,5,5064,51459,1,5064,51459,50,5065,51459,40,5065,51504,0,5065,67610,3,5816,68511,4,6191,69392,1,6566,69392,50,6566,69392,40,6566,69437,0,6566,76895,3,7321,78252,4,7692,79443,5,8067,79444,1,8067,79444,50,8067,79444,40,8067,79489,0,8067,135469,3,11970,136919,4,13918,137998,1,15868,137998,50,15870,137998,40,15870,138043,0,15870,184890,3,18421,185950,4,19696,187001,1,20971,187001,50,20973,187001,40,20973,187046,0,20973,227247,3,22474,227867,4,23224,229978,5,23974,229979,1,23974,229979,50,23976,229979,40,23976,230024,0,23976,235851,3,24760,236663,4,25102,236893,5,25477,236893,1,25477,236893,50,25477,236893,40,25477,236938,0,25478,267203,3,26679,268076,4,27279,268621,1,27879,268621,50,27880,268621,40,27880,268666,0,27880,290594,3,28638,291287,4,29006,291745,1,29381,291745,50,29381,291745,40,29381,291745,40,29381,291785,0,29381,291893,50,29381,291893,30,29381,291893,40,29381,291933,0,29381,292056,50,29381,292056,30,29381,292056,40,29381,292096,0,29387,292197,50,29388,292237,0,29388,292273,50,29388,292273,30,29388,292273,40,29388,292313,0,29388,292430,50,29389,292470,0,29393,292512,50,29393,292512,30,29393,292512,40,29393,292552,0,29393,292655,50,29394,292695,0,29399,292851,50,29401,292891,0,29401,293058,50,29406,293098,0,29406,293277,50,29413,293317,0,29418,293502,50,29428,293542,0,29428,293735,50,29446,293775,0,29450,293977,50,29483,294017,0,29483,294229,50,29550,294229,40,29550,294269,0,29550,294424,50,29551,294424,30,29551,294424,40,29551,294464,0,29551,294571,50,29551,294611,0,29555,294763,50,29557,294803,0,29558,294963,50,29561,295003,0,29561,295171,50,29567,295211,0,29571,295385,50,29580,295425,0,29580,295607,50,29595,295647,0,29600,295837,50,29628,295877,0,29628,296077,50,29691,296077,40,29691,296117,0,29691)
%
%
% START OF PROOF
% 296032 [?] ?
% 296079 [] equal(multiply(identity,X),X).
% 296080 [] equal(multiply(inverse(X),X),identity).
% 296081 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 296082 [] -equal(multiply(sk_c6,sk_c5),sk_c7).
% 296089 [?] ?
% 296096 [?] ?
% 296117 [?] ?
% 296150 [input:296096,cut:296082] equal(inverse(sk_c2),sk_c6).
% 296151 [para:296150.1.1,296080.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 296167 [input:296089,cut:296082] equal(multiply(sk_c2,sk_c5),sk_c6).
% 296187 [input:296117,cut:296082] equal(multiply(sk_c6,sk_c7),sk_c5).
% 296188 [para:296080.1.1,296081.1.1.1,demod:296079] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 296199 [para:296151.1.1,296081.1.1.1,demod:296079] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 296239 [para:296167.1.1,296199.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 296303 [para:296187.1.1,296188.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 296306 [para:296239.1.2,296188.1.2.2,demod:296303] equal(sk_c6,sk_c7).
% 296312 [para:296306.1.1,296082.1.1.1,cut:296032] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(multiply(sk_c7,sk_c5),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 2
%
%
% 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(40,40,1,85,0,1,949,50,7,994,0,7,1873,50,14,1918,0,14,2806,50,22,2851,0,22,3745,50,28,3790,0,28,4691,50,38,4736,0,38,5645,50,53,5690,0,53,6607,50,81,6652,0,81,7579,50,140,7624,0,140,8561,50,268,8606,0,268,9555,50,472,9600,0,472,10561,50,860,10561,40,860,10606,0,861,21061,3,1162,21807,4,1312,22543,5,1462,22544,1,1462,22544,50,1462,22544,40,1462,22589,0,1462,22866,3,1772,22875,4,1914,22887,5,2063,22887,1,2063,22887,50,2063,22887,40,2063,22932,0,2063,49014,3,3572,50277,4,4314,51458,5,5064,51459,1,5064,51459,50,5065,51459,40,5065,51504,0,5065,67610,3,5816,68511,4,6191,69392,1,6566,69392,50,6566,69392,40,6566,69437,0,6566,76895,3,7321,78252,4,7692,79443,5,8067,79444,1,8067,79444,50,8067,79444,40,8067,79489,0,8067,135469,3,11970,136919,4,13918,137998,1,15868,137998,50,15870,137998,40,15870,138043,0,15870,184890,3,18421,185950,4,19696,187001,1,20971,187001,50,20973,187001,40,20973,187046,0,20973,227247,3,22474,227867,4,23224,229978,5,23974,229979,1,23974,229979,50,23976,229979,40,23976,230024,0,23976,235851,3,24760,236663,4,25102,236893,5,25477,236893,1,25477,236893,50,25477,236893,40,25477,236938,0,25478,267203,3,26679,268076,4,27279,268621,1,27879,268621,50,27880,268621,40,27880,268666,0,27880,290594,3,28638,291287,4,29006,291745,1,29381,291745,50,29381,291745,40,29381,291745,40,29381,291785,0,29381,291893,50,29381,291893,30,29381,291893,40,29381,291933,0,29381,292056,50,29381,292056,30,29381,292056,40,29381,292096,0,29387,292197,50,29388,292237,0,29388,292273,50,29388,292273,30,29388,292273,40,29388,292313,0,29388,292430,50,29389,292470,0,29393,292512,50,29393,292512,30,29393,292512,40,29393,292552,0,29393,292655,50,29394,292695,0,29399,292851,50,29401,292891,0,29401,293058,50,29406,293098,0,29406,293277,50,29413,293317,0,29418,293502,50,29428,293542,0,29428,293735,50,29446,293775,0,29450,293977,50,29483,294017,0,29483,294229,50,29550,294229,40,29550,294269,0,29550,294424,50,29551,294424,30,29551,294424,40,29551,294464,0,29551,294571,50,29551,294611,0,29555,294763,50,29557,294803,0,29558,294963,50,29561,295003,0,29561,295171,50,29567,295211,0,29571,295385,50,29580,295425,0,29580,295607,50,29595,295647,0,29600,295837,50,29628,295877,0,29628,296077,50,29691,296077,40,29691,296117,0,29691,296311,50,29691,296311,30,29691,296311,40,29691,296351,0,29691,296458,50,29692,296498,0,29696,296650,50,29699,296690,0,29699,296850,50,29703,296890,0,29703,297058,50,29708,297098,0,29713,297272,50,29721,297312,0,29721,297494,50,29737,297534,0,29741,297724,50,29771,297764,0,29771,297964,50,29832,297964,40,29832,298004,0,29832)
%
%
% START OF PROOF
% 297919 [?] ?
% 297966 [] equal(multiply(identity,X),X).
% 297967 [] equal(multiply(inverse(X),X),identity).
% 297968 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 297969 [] -equal(multiply(sk_c7,sk_c5),sk_c6).
% 297975 [?] ?
% 297982 [?] ?
% 298003 [?] ?
% 298034 [input:297982,cut:297969] equal(inverse(sk_c2),sk_c6).
% 298035 [para:298034.1.1,297967.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 298044 [input:297975,cut:297969] equal(multiply(sk_c2,sk_c5),sk_c6).
% 298071 [input:298003,cut:297969] equal(multiply(sk_c6,sk_c7),sk_c5).
% 298073 [para:297967.1.1,297968.1.1.1,demod:297966] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 298083 [para:298035.1.1,297968.1.1.1,demod:297966] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 298120 [para:298044.1.1,298083.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 298179 [para:298071.1.1,298073.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 298183 [para:298120.1.2,298073.1.2.2,demod:298179] equal(sk_c6,sk_c7).
% 298189 [para:298183.1.1,297969.1.2,cut:297919] 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 8 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(inverse(sk_c7),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 2
%
%
% 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(40,40,1,85,0,1,949,50,7,994,0,7,1873,50,14,1918,0,14,2806,50,22,2851,0,22,3745,50,28,3790,0,28,4691,50,38,4736,0,38,5645,50,53,5690,0,53,6607,50,81,6652,0,81,7579,50,140,7624,0,140,8561,50,268,8606,0,268,9555,50,472,9600,0,472,10561,50,860,10561,40,860,10606,0,861,21061,3,1162,21807,4,1312,22543,5,1462,22544,1,1462,22544,50,1462,22544,40,1462,22589,0,1462,22866,3,1772,22875,4,1914,22887,5,2063,22887,1,2063,22887,50,2063,22887,40,2063,22932,0,2063,49014,3,3572,50277,4,4314,51458,5,5064,51459,1,5064,51459,50,5065,51459,40,5065,51504,0,5065,67610,3,5816,68511,4,6191,69392,1,6566,69392,50,6566,69392,40,6566,69437,0,6566,76895,3,7321,78252,4,7692,79443,5,8067,79444,1,8067,79444,50,8067,79444,40,8067,79489,0,8067,135469,3,11970,136919,4,13918,137998,1,15868,137998,50,15870,137998,40,15870,138043,0,15870,184890,3,18421,185950,4,19696,187001,1,20971,187001,50,20973,187001,40,20973,187046,0,20973,227247,3,22474,227867,4,23224,229978,5,23974,229979,1,23974,229979,50,23976,229979,40,23976,230024,0,23976,235851,3,24760,236663,4,25102,236893,5,25477,236893,1,25477,236893,50,25477,236893,40,25477,236938,0,25478,267203,3,26679,268076,4,27279,268621,1,27879,268621,50,27880,268621,40,27880,268666,0,27880,290594,3,28638,291287,4,29006,291745,1,29381,291745,50,29381,291745,40,29381,291745,40,29381,291785,0,29381,291893,50,29381,291893,30,29381,291893,40,29381,291933,0,29381,292056,50,29381,292056,30,29381,292056,40,29381,292096,0,29387,292197,50,29388,292237,0,29388,292273,50,29388,292273,30,29388,292273,40,29388,292313,0,29388,292430,50,29389,292470,0,29393,292512,50,29393,292512,30,29393,292512,40,29393,292552,0,29393,292655,50,29394,292695,0,29399,292851,50,29401,292891,0,29401,293058,50,29406,293098,0,29406,293277,50,29413,293317,0,29418,293502,50,29428,293542,0,29428,293735,50,29446,293775,0,29450,293977,50,29483,294017,0,29483,294229,50,29550,294229,40,29550,294269,0,29550,294424,50,29551,294424,30,29551,294424,40,29551,294464,0,29551,294571,50,29551,294611,0,29555,294763,50,29557,294803,0,29558,294963,50,29561,295003,0,29561,295171,50,29567,295211,0,29571,295385,50,29580,295425,0,29580,295607,50,29595,295647,0,29600,295837,50,29628,295877,0,29628,296077,50,29691,296077,40,29691,296117,0,29691,296311,50,29691,296311,30,29691,296311,40,29691,296351,0,29691,296458,50,29692,296498,0,29696,296650,50,29699,296690,0,29699,296850,50,29703,296890,0,29703,297058,50,29708,297098,0,29713,297272,50,29721,297312,0,29721,297494,50,29737,297534,0,29741,297724,50,29771,297764,0,29771,297964,50,29832,297964,40,29832,298004,0,29832,298188,50,29833,298188,30,29833,298188,40,29833,298228,0,29833,298335,50,29833,298375,0,29838,298527,50,29840,298567,0,29841,298727,50,29844,298767,0,29844,298935,50,29850,298975,0,29854,299149,50,29863,299189,0,29863,299371,50,29878,299411,0,29883,299601,50,29911,299641,0,29911,299841,50,29973,299841,40,29973,299881,0,29973)
%
%
% START OF PROOF
% 299843 [] equal(multiply(identity,X),X).
% 299844 [] equal(multiply(inverse(X),X),identity).
% 299845 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 299846 [] -equal(inverse(sk_c7),sk_c5).
% 299851 [?] ?
% 299858 [?] ?
% 299865 [?] ?
% 299872 [?] ?
% 299879 [?] ?
% 299890 [input:299858,cut:299846] equal(inverse(sk_c2),sk_c6).
% 299891 [para:299890.1.1,299844.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 299899 [input:299872,cut:299846] equal(inverse(sk_c1),sk_c7).
% 299900 [para:299899.1.1,299844.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 299903 [input:299851,cut:299846] equal(multiply(sk_c2,sk_c5),sk_c6).
% 299914 [input:299865,cut:299846] equal(multiply(sk_c1,sk_c6),sk_c7).
% 299924 [input:299879,cut:299846] equal(multiply(sk_c6,sk_c7),sk_c5).
% 299941 [para:299844.1.1,299845.1.1.1,demod:299843] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 299943 [para:299891.1.1,299845.1.1.1,demod:299843] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 299946 [para:299900.1.1,299845.1.1.1,demod:299843] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 299985 [para:299903.1.1,299943.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 299989 [para:299914.1.1,299946.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 300018 [para:299924.1.1,299941.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 300037 [para:299985.1.2,299941.1.2.2,demod:300018] equal(sk_c6,sk_c7).
% 300055 [para:300037.1.1,299924.1.1.1,demod:299989] equal(sk_c6,sk_c5).
% 300076 [para:300055.1.1,299924.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 300083 [para:300055.1.1,300037.1.1] equal(sk_c5,sk_c7).
% 300084 [para:300037.1.1,300055.1.1] equal(sk_c7,sk_c5).
% 300085 [para:300083.1.2,299846.1.1.1] -equal(inverse(sk_c5),sk_c5).
% 300120 [para:300076.1.1,299941.1.2.2,demod:299844] equal(sk_c7,identity).
% 300124 [para:300120.1.1,299900.1.1.1,demod:299843] equal(sk_c1,identity).
% 300133 [para:300120.1.1,300083.1.2] equal(sk_c5,identity).
% 300141 [para:300124.1.1,299899.1.1.1] equal(inverse(identity),sk_c7).
% 300150 [para:300133.1.1,300085.1.1.1,demod:300141,cut:300084] 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: 39654
% derived clauses: 6650118
% kept clauses: 250630
% kept size sum: 322569
% kept mid-nuclei: 6246
% kept new demods: 6522
% forw unit-subs: 2530257
% forw double-subs: 3568355
% forw overdouble-subs: 249053
% backward subs: 10589
% fast unit cutoff: 20780
% full unit cutoff: 0
% dbl unit cutoff: 6272
% real runtime : 300.42
% process. runtime: 299.74
% specific non-discr-tree subsumption statistics:
% tried: 42514228
% length fails: 5011660
% strength fails: 11814612
% predlist fails: 1665156
% aux str. fails: 5646720
% by-lit fails: 11181546
% full subs tried: 1296807
% full subs fail: 1214871
%
% ; 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/GRP346-1+eq_r.in")
%
%------------------------------------------------------------------------------