TSTP Solution File: GRP321-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP321-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art03.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 297.6s
% Output : Assurance 297.6s
% 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/GRP321-1+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_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c8).
% was split for some strategies as:
% -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% -equal(multiply(sk_c7,sk_c8),sk_c6).
% -equal(multiply(sk_c6,sk_c7),sk_c8).
%
% 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_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c8).
% Split part used next: -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,829,50,7,869,0,7,1826,50,20,1866,0,20,2924,50,36,2964,0,36,4076,50,49,4116,0,49,5283,50,66,5323,0,66,6570,50,92,6610,0,92,7937,50,132,7977,0,132,9410,50,206,9450,0,206,10989,50,348,11029,0,348,12700,50,574,12740,0,574,14543,50,981,14543,40,981,14583,0,981,25020,3,1282,25663,4,1432,26355,1,1582,26355,50,1582,26355,40,1582,26395,0,1582,26746,3,1895,26758,4,2053,26775,5,2183,26775,1,2183,26775,50,2183,26775,40,2183,26815,0,2183,51505,3,3688,52651,4,4434,53598,5,5184,53599,1,5184,53599,50,5185,53599,40,5185,53639,0,5185,70600,3,5936,71182,4,6311,71983,5,6686,71984,1,6686,71984,50,6686,71984,40,6686,72024,0,6686,82919,3,7454,84094,4,7812,85724,5,8187,85725,1,8187,85725,50,8187,85725,40,8187,85765,0,8187,161847,3,12090,162596,4,14038,163382,5,15988,163383,1,15988,163383,50,15991,163383,40,15991,163423,0,15991,221612,3,18551,222268,4,19817,222939,1,21092,222939,50,21094,222939,40,21094,222979,0,21094,267531,3,22596,268223,4,23345,268987,5,24095,268988,1,24095,268988,50,24097,268988,40,24097,269028,0,24097,278747,3,24853,280008,4,25227,280688,5,25598,280688,1,25598,280688,50,25598,280688,40,25598,280728,0,25598,312313,3,26800,312862,4,27399,313290,5,27999,313291,1,27999,313291,50,28000,313291,40,28000,313331,0,28000,336477,3,28751,337052,4,29126,337689,1,29501,337689,50,29502,337689,40,29502,337689,40,29502,337724,0,29502)
%
%
% START OF PROOF
% 337691 [] equal(multiply(identity,X),X).
% 337692 [] equal(multiply(inverse(X),X),identity).
% 337693 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 337694 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 337696 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 337697 [?] ?
% 337701 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c7).
% 337702 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 337706 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 337707 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 337711 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 337712 [?] ?
% 337716 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 337717 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 337721 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c5),sk_c7).
% 337722 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 337727 [hyper:337694,337696,binarycut:337697] equal(inverse(sk_c2),sk_c8).
% 337728 [para:337727.1.1,337692.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 337734 [hyper:337694,337711,binarycut:337712] equal(inverse(sk_c1),sk_c7).
% 337737 [para:337734.1.1,337692.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 337745 [hyper:337694,337702,337701] equal(multiply(sk_c2,sk_c8),sk_c3).
% 337761 [hyper:337694,337707,337706] equal(multiply(sk_c8,sk_c3),sk_c7).
% 337765 [hyper:337694,337717,337716] equal(multiply(sk_c1,sk_c7),sk_c8).
% 337769 [hyper:337694,337722,337721] equal(multiply(sk_c7,sk_c8),sk_c6).
% 337770 [para:337692.1.1,337693.1.1.1,demod:337691] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 337771 [para:337728.1.1,337693.1.1.1,demod:337691] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 337773 [para:337745.1.1,337693.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c8,X))).
% 337777 [para:337745.1.1,337771.1.2.2,demod:337761] equal(sk_c8,sk_c7).
% 337778 [para:337777.1.2,337737.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 337779 [para:337777.1.2,337765.1.1.2] equal(multiply(sk_c1,sk_c8),sk_c8).
% 337782 [para:337779.1.1,337693.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c8,X))).
% 337784 [para:337728.1.1,337770.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 337787 [para:337765.1.1,337770.1.2.2,demod:337769,337734] equal(sk_c7,sk_c6).
% 337790 [para:337778.1.1,337770.1.2.2,demod:337784] equal(sk_c1,sk_c2).
% 337791 [para:337779.1.1,337770.1.2.2,demod:337769,337734] equal(sk_c8,sk_c6).
% 337792 [para:337787.1.1,337737.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 337796 [para:337790.1.2,337745.1.1.1,demod:337779] equal(sk_c8,sk_c3).
% 337807 [para:337796.1.1,337771.1.2.1] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 337821 [para:337771.1.2,337773.1.2.2,demod:337807] equal(X,multiply(sk_c2,X)).
% 337822 [para:337790.1.2,337773.1.2.1,demod:337782] equal(multiply(sk_c3,X),multiply(sk_c8,X)).
% 337823 [para:337791.1.1,337773.1.2.2.1,demod:337821] equal(multiply(sk_c3,X),multiply(sk_c6,X)).
% 337824 [para:337821.1.2,337771.1.2.2,demod:337823,337822] equal(X,multiply(sk_c6,X)).
% 337827 [para:337824.1.2,337792.1.1] equal(sk_c1,identity).
% 337828 [para:337827.1.1,337734.1.1.1] equal(inverse(identity),sk_c7).
% 337829 [hyper:337694,337828,demod:337691,cut:337787] 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_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c8).
% Split part used next: -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,829,50,7,869,0,7,1826,50,20,1866,0,20,2924,50,36,2964,0,36,4076,50,49,4116,0,49,5283,50,66,5323,0,66,6570,50,92,6610,0,92,7937,50,132,7977,0,132,9410,50,206,9450,0,206,10989,50,348,11029,0,348,12700,50,574,12740,0,574,14543,50,981,14543,40,981,14583,0,981,25020,3,1282,25663,4,1432,26355,1,1582,26355,50,1582,26355,40,1582,26395,0,1582,26746,3,1895,26758,4,2053,26775,5,2183,26775,1,2183,26775,50,2183,26775,40,2183,26815,0,2183,51505,3,3688,52651,4,4434,53598,5,5184,53599,1,5184,53599,50,5185,53599,40,5185,53639,0,5185,70600,3,5936,71182,4,6311,71983,5,6686,71984,1,6686,71984,50,6686,71984,40,6686,72024,0,6686,82919,3,7454,84094,4,7812,85724,5,8187,85725,1,8187,85725,50,8187,85725,40,8187,85765,0,8187,161847,3,12090,162596,4,14038,163382,5,15988,163383,1,15988,163383,50,15991,163383,40,15991,163423,0,15991,221612,3,18551,222268,4,19817,222939,1,21092,222939,50,21094,222939,40,21094,222979,0,21094,267531,3,22596,268223,4,23345,268987,5,24095,268988,1,24095,268988,50,24097,268988,40,24097,269028,0,24097,278747,3,24853,280008,4,25227,280688,5,25598,280688,1,25598,280688,50,25598,280688,40,25598,280728,0,25598,312313,3,26800,312862,4,27399,313290,5,27999,313291,1,27999,313291,50,28000,313291,40,28000,313331,0,28000,336477,3,28751,337052,4,29126,337689,1,29501,337689,50,29502,337689,40,29502,337689,40,29502,337724,0,29502,337828,50,29502,337828,30,29502,337828,40,29502,337863,0,29502)
%
%
% START OF PROOF
% 337830 [] equal(multiply(identity,X),X).
% 337831 [] equal(multiply(inverse(X),X),identity).
% 337832 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 337833 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 337837 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 337838 [?] ?
% 337842 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 337843 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 337847 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 337848 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 337852 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 337853 [?] ?
% 337857 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 337858 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 337862 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 337863 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 337869 [hyper:337833,337837,binarycut:337838] equal(inverse(sk_c2),sk_c8).
% 337872 [para:337869.1.1,337831.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 337878 [hyper:337833,337852,binarycut:337853] equal(inverse(sk_c1),sk_c7).
% 337879 [para:337878.1.1,337831.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 337895 [hyper:337833,337843,337842] equal(multiply(sk_c2,sk_c8),sk_c3).
% 337904 [hyper:337833,337848,337847] equal(multiply(sk_c8,sk_c3),sk_c7).
% 337909 [hyper:337833,337858,337857] equal(multiply(sk_c1,sk_c7),sk_c8).
% 337914 [hyper:337833,337863,337862] equal(multiply(sk_c7,sk_c8),sk_c6).
% 337915 [para:337831.1.1,337832.1.1.1,demod:337830] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 337916 [para:337872.1.1,337832.1.1.1,demod:337830] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 337918 [para:337895.1.1,337832.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c8,X))).
% 337922 [para:337895.1.1,337916.1.2.2,demod:337904] equal(sk_c8,sk_c7).
% 337923 [para:337922.1.2,337879.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 337924 [para:337922.1.2,337909.1.1.2] equal(multiply(sk_c1,sk_c8),sk_c8).
% 337925 [para:337922.1.2,337914.1.1.1] equal(multiply(sk_c8,sk_c8),sk_c6).
% 337927 [?] ?
% 337929 [para:337872.1.1,337915.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 337931 [para:337904.1.1,337915.1.2.2] equal(sk_c3,multiply(inverse(sk_c8),sk_c7)).
% 337935 [para:337923.1.1,337915.1.2.2,demod:337929] equal(sk_c1,sk_c2).
% 337936 [para:337924.1.1,337915.1.2.2,demod:337914,337878] equal(sk_c8,sk_c6).
% 337941 [para:337935.1.2,337895.1.1.1,demod:337924] equal(sk_c8,sk_c3).
% 337943 [para:337936.1.1,337895.1.1.2] equal(multiply(sk_c2,sk_c6),sk_c3).
% 337952 [para:337941.1.1,337916.1.2.1] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 337955 [para:337941.1.1,337936.1.1] equal(sk_c3,sk_c6).
% 337959 [para:337955.1.1,337904.1.1.2] equal(multiply(sk_c8,sk_c6),sk_c7).
% 337961 [para:337941.1.1,337925.1.1.1] equal(multiply(sk_c3,sk_c8),sk_c6).
% 337966 [para:337916.1.2,337918.1.2.2,demod:337952] equal(X,multiply(sk_c2,X)).
% 337967 [para:337935.1.2,337918.1.2.1,demod:337927] equal(multiply(sk_c3,X),multiply(sk_c8,X)).
% 337968 [para:337936.1.1,337918.1.2.2.1,demod:337966] equal(multiply(sk_c3,X),multiply(sk_c6,X)).
% 337969 [para:337966.1.2,337916.1.2.2,demod:337968,337967] equal(X,multiply(sk_c6,X)).
% 337971 [para:337969.1.2,337915.1.2.2] equal(X,multiply(inverse(sk_c6),X)).
% 337977 [para:337943.1.1,337916.1.2.2,demod:337904] equal(sk_c6,sk_c7).
% 337983 [para:337971.1.2,337831.1.1] equal(sk_c6,identity).
% 337987 [para:337983.1.1,337959.1.1.2,demod:337969,337968,337967] equal(identity,sk_c7).
% 337990 [para:337987.1.2,337931.1.2.2,demod:337929] equal(sk_c3,sk_c2).
% 337991 [para:337990.1.2,337869.1.1.1] equal(inverse(sk_c3),sk_c8).
% 338002 [hyper:337833,337991,demod:337961,cut:337977] 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_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c8).
% Split part used next: -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,829,50,7,869,0,7,1826,50,20,1866,0,20,2924,50,36,2964,0,36,4076,50,49,4116,0,49,5283,50,66,5323,0,66,6570,50,92,6610,0,92,7937,50,132,7977,0,132,9410,50,206,9450,0,206,10989,50,348,11029,0,348,12700,50,574,12740,0,574,14543,50,981,14543,40,981,14583,0,981,25020,3,1282,25663,4,1432,26355,1,1582,26355,50,1582,26355,40,1582,26395,0,1582,26746,3,1895,26758,4,2053,26775,5,2183,26775,1,2183,26775,50,2183,26775,40,2183,26815,0,2183,51505,3,3688,52651,4,4434,53598,5,5184,53599,1,5184,53599,50,5185,53599,40,5185,53639,0,5185,70600,3,5936,71182,4,6311,71983,5,6686,71984,1,6686,71984,50,6686,71984,40,6686,72024,0,6686,82919,3,7454,84094,4,7812,85724,5,8187,85725,1,8187,85725,50,8187,85725,40,8187,85765,0,8187,161847,3,12090,162596,4,14038,163382,5,15988,163383,1,15988,163383,50,15991,163383,40,15991,163423,0,15991,221612,3,18551,222268,4,19817,222939,1,21092,222939,50,21094,222939,40,21094,222979,0,21094,267531,3,22596,268223,4,23345,268987,5,24095,268988,1,24095,268988,50,24097,268988,40,24097,269028,0,24097,278747,3,24853,280008,4,25227,280688,5,25598,280688,1,25598,280688,50,25598,280688,40,25598,280728,0,25598,312313,3,26800,312862,4,27399,313290,5,27999,313291,1,27999,313291,50,28000,313291,40,28000,313331,0,28000,336477,3,28751,337052,4,29126,337689,1,29501,337689,50,29502,337689,40,29502,337689,40,29502,337724,0,29502,337828,50,29502,337828,30,29502,337828,40,29502,337863,0,29502,338001,50,29502,338001,30,29502,338001,40,29502,338036,0,29507)
%
%
% START OF PROOF
% 338003 [] equal(multiply(identity,X),X).
% 338004 [] equal(multiply(inverse(X),X),identity).
% 338005 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 338006 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 338007 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(inverse(sk_c2),sk_c8).
% 338008 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 338009 [] equal(multiply(sk_c5,sk_c7),sk_c6) | equal(inverse(sk_c2),sk_c8).
% 338010 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 338011 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c8).
% 338012 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c6,sk_c7),sk_c8).
% 338013 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c7).
% 338014 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c7),sk_c6).
% 338015 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 338016 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 338017 [?] ?
% 338018 [?] ?
% 338019 [?] ?
% 338020 [?] ?
% 338021 [?] ?
% 338077 [hyper:338006,338012,338007,binarycut:338017] equal(multiply(sk_c6,sk_c7),sk_c8).
% 338080 [hyper:338006,338013,binarycut:338018,binarycut:338008] equal(inverse(sk_c5),sk_c7).
% 338081 [para:338080.1.1,338004.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 338084 [hyper:338006,338015,binarycut:338020,binarycut:338010] equal(inverse(sk_c4),sk_c8).
% 338094 [hyper:338006,338014,338009,binarycut:338019] equal(multiply(sk_c5,sk_c7),sk_c6).
% 338098 [para:338084.1.1,338004.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 338108 [hyper:338006,338016,338011,binarycut:338021] equal(multiply(sk_c4,sk_c8),sk_c7).
% 338111 [para:338004.1.1,338005.1.1.1,demod:338003] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 338112 [para:338077.1.1,338005.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c6,multiply(sk_c7,X))).
% 338113 [para:338081.1.1,338005.1.1.1,demod:338003] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 338115 [para:338098.1.1,338005.1.1.1,demod:338003] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 338121 [para:338094.1.1,338113.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 338131 [para:338081.1.1,338111.1.2.2] equal(sk_c5,multiply(inverse(sk_c7),identity)).
% 338132 [para:338098.1.1,338111.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 338133 [para:338113.1.2,338111.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c7),X)).
% 338134 [para:338115.1.2,338111.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c8),X)).
% 338142 [para:338121.1.2,338112.1.2.2,demod:338077] equal(multiply(sk_c8,sk_c6),sk_c8).
% 338144 [para:338142.1.1,338111.1.2.2,demod:338108,338134] equal(sk_c6,sk_c7).
% 338145 [para:338144.1.2,338077.1.1.2] equal(multiply(sk_c6,sk_c6),sk_c8).
% 338149 [para:338144.1.2,338121.1.2.1,demod:338145] equal(sk_c7,sk_c8).
% 338154 [para:338149.1.1,338094.1.1.2] equal(multiply(sk_c5,sk_c8),sk_c6).
% 338157 [para:338149.1.1,338131.1.2.1.1,demod:338132] equal(sk_c5,sk_c4).
% 338159 [para:338157.1.1,338080.1.1.1,demod:338084] equal(sk_c8,sk_c7).
% 338199 [hyper:338006,338133,demod:338080,338142,338154,338133,cut:338159,cut:338149] 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_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c8).
% Split part used next: -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 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
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,829,50,7,869,0,7,1826,50,20,1866,0,20,2924,50,36,2964,0,36,4076,50,49,4116,0,49,5283,50,66,5323,0,66,6570,50,92,6610,0,92,7937,50,132,7977,0,132,9410,50,206,9450,0,206,10989,50,348,11029,0,348,12700,50,574,12740,0,574,14543,50,981,14543,40,981,14583,0,981,25020,3,1282,25663,4,1432,26355,1,1582,26355,50,1582,26355,40,1582,26395,0,1582,26746,3,1895,26758,4,2053,26775,5,2183,26775,1,2183,26775,50,2183,26775,40,2183,26815,0,2183,51505,3,3688,52651,4,4434,53598,5,5184,53599,1,5184,53599,50,5185,53599,40,5185,53639,0,5185,70600,3,5936,71182,4,6311,71983,5,6686,71984,1,6686,71984,50,6686,71984,40,6686,72024,0,6686,82919,3,7454,84094,4,7812,85724,5,8187,85725,1,8187,85725,50,8187,85725,40,8187,85765,0,8187,161847,3,12090,162596,4,14038,163382,5,15988,163383,1,15988,163383,50,15991,163383,40,15991,163423,0,15991,221612,3,18551,222268,4,19817,222939,1,21092,222939,50,21094,222939,40,21094,222979,0,21094,267531,3,22596,268223,4,23345,268987,5,24095,268988,1,24095,268988,50,24097,268988,40,24097,269028,0,24097,278747,3,24853,280008,4,25227,280688,5,25598,280688,1,25598,280688,50,25598,280688,40,25598,280728,0,25598,312313,3,26800,312862,4,27399,313290,5,27999,313291,1,27999,313291,50,28000,313291,40,28000,313331,0,28000,336477,3,28751,337052,4,29126,337689,1,29501,337689,50,29502,337689,40,29502,337689,40,29502,337724,0,29502,337828,50,29502,337828,30,29502,337828,40,29502,337863,0,29502,338001,50,29502,338001,30,29502,338001,40,29502,338036,0,29507,338198,50,29508,338198,30,29508,338198,40,29508,338233,0,29508,338325,50,29508,338360,0,29508)
%
%
% START OF PROOF
% 338327 [] equal(multiply(identity,X),X).
% 338328 [] equal(multiply(inverse(X),X),identity).
% 338329 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 338330 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% 338346 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c7).
% 338347 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 338348 [] equal(multiply(sk_c5,sk_c7),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 338349 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 338350 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 338351 [?] ?
% 338352 [?] ?
% 338353 [?] ?
% 338354 [?] ?
% 338355 [?] ?
% 338367 [hyper:338330,338347,binarycut:338352] equal(inverse(sk_c5),sk_c7).
% 338371 [para:338367.1.1,338328.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 338375 [hyper:338330,338349,binarycut:338354] equal(inverse(sk_c4),sk_c8).
% 338376 [para:338375.1.1,338328.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 338385 [hyper:338330,338346,binarycut:338351] equal(multiply(sk_c6,sk_c7),sk_c8).
% 338391 [hyper:338330,338348,binarycut:338353] equal(multiply(sk_c5,sk_c7),sk_c6).
% 338395 [hyper:338330,338350,binarycut:338355] equal(multiply(sk_c4,sk_c8),sk_c7).
% 338396 [para:338328.1.1,338329.1.1.1,demod:338327] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 338397 [para:338371.1.1,338329.1.1.1,demod:338327] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 338398 [para:338376.1.1,338329.1.1.1,demod:338327] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 338399 [para:338385.1.1,338329.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c6,multiply(sk_c7,X))).
% 338400 [para:338391.1.1,338329.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c5,multiply(sk_c7,X))).
% 338402 [para:338391.1.1,338397.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 338407 [para:338328.1.1,338396.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 338408 [para:338371.1.1,338396.1.2.2] equal(sk_c5,multiply(inverse(sk_c7),identity)).
% 338409 [para:338376.1.1,338396.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 338411 [para:338329.1.1,338396.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 338413 [para:338398.1.2,338396.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c8),X)).
% 338414 [para:338396.1.2,338396.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 338416 [para:338397.1.2,338399.1.2.2] equal(multiply(sk_c8,multiply(sk_c5,X)),multiply(sk_c6,X)).
% 338417 [para:338402.1.2,338399.1.2.2,demod:338385] equal(multiply(sk_c8,sk_c6),sk_c8).
% 338420 [para:338417.1.1,338396.1.2.2,demod:338395,338413] equal(sk_c6,sk_c7).
% 338422 [para:338420.1.2,338385.1.1.2] equal(multiply(sk_c6,sk_c6),sk_c8).
% 338424 [para:338420.1.2,338397.1.2.1] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 338425 [para:338420.1.2,338402.1.2.1,demod:338422] equal(sk_c7,sk_c8).
% 338430 [para:338425.1.1,338397.1.2.1,demod:338416] equal(X,multiply(sk_c6,X)).
% 338432 [para:338425.1.1,338420.1.2] equal(sk_c6,sk_c8).
% 338433 [para:338432.1.2,338376.1.1.1,demod:338430] equal(sk_c4,identity).
% 338436 [para:338433.1.1,338375.1.1.1] equal(inverse(identity),sk_c8).
% 338439 [para:338433.1.1,338398.1.2.2.1,demod:338327] equal(X,multiply(sk_c8,X)).
% 338441 [para:338397.1.2,338400.1.2.2,demod:338424] equal(X,multiply(sk_c5,X)).
% 338443 [para:338430.1.2,338396.1.2.2] equal(X,multiply(inverse(sk_c6),X)).
% 338444 [para:338430.1.2,338399.1.2,demod:338439] equal(X,multiply(sk_c7,X)).
% 338448 [para:338443.1.2,338328.1.1] equal(sk_c6,identity).
% 338449 [para:338448.1.1,338402.1.2.2,demod:338444] equal(sk_c7,identity).
% 338467 [para:338414.1.2,338328.1.1] equal(multiply(X,inverse(X)),identity).
% 338469 [para:338414.1.2,338407.1.2] equal(X,multiply(X,identity)).
% 338470 [para:338469.1.2,338407.1.2] equal(X,inverse(inverse(X))).
% 338472 [para:338469.1.2,338408.1.2] equal(sk_c5,inverse(sk_c7)).
% 338473 [para:338469.1.2,338409.1.2] equal(sk_c4,inverse(sk_c8)).
% 338474 [para:338449.1.1,338472.1.2.1,demod:338436] equal(sk_c5,sk_c8).
% 338483 [para:338474.1.2,338473.1.2.1,demod:338367] equal(sk_c4,sk_c7).
% 338487 [para:338467.1.1,338411.1.2.2.2,demod:338469] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 338489 [para:338397.1.2,338487.1.2.1.1,demod:338441] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 338497 [para:338489.1.2,338414.1.2,demod:338470] equal(multiply(X,sk_c7),X).
% 338499 [hyper:338330,338497,demod:338473,cut:338483] 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 4
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c7),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(35,40,0,75,0,0,829,50,7,869,0,7,1826,50,20,1866,0,20,2924,50,36,2964,0,36,4076,50,49,4116,0,49,5283,50,66,5323,0,66,6570,50,92,6610,0,92,7937,50,132,7977,0,132,9410,50,206,9450,0,206,10989,50,348,11029,0,348,12700,50,574,12740,0,574,14543,50,981,14543,40,981,14583,0,981,25020,3,1282,25663,4,1432,26355,1,1582,26355,50,1582,26355,40,1582,26395,0,1582,26746,3,1895,26758,4,2053,26775,5,2183,26775,1,2183,26775,50,2183,26775,40,2183,26815,0,2183,51505,3,3688,52651,4,4434,53598,5,5184,53599,1,5184,53599,50,5185,53599,40,5185,53639,0,5185,70600,3,5936,71182,4,6311,71983,5,6686,71984,1,6686,71984,50,6686,71984,40,6686,72024,0,6686,82919,3,7454,84094,4,7812,85724,5,8187,85725,1,8187,85725,50,8187,85725,40,8187,85765,0,8187,161847,3,12090,162596,4,14038,163382,5,15988,163383,1,15988,163383,50,15991,163383,40,15991,163423,0,15991,221612,3,18551,222268,4,19817,222939,1,21092,222939,50,21094,222939,40,21094,222979,0,21094,267531,3,22596,268223,4,23345,268987,5,24095,268988,1,24095,268988,50,24097,268988,40,24097,269028,0,24097,278747,3,24853,280008,4,25227,280688,5,25598,280688,1,25598,280688,50,25598,280688,40,25598,280728,0,25598,312313,3,26800,312862,4,27399,313290,5,27999,313291,1,27999,313291,50,28000,313291,40,28000,313331,0,28000,336477,3,28751,337052,4,29126,337689,1,29501,337689,50,29502,337689,40,29502,337689,40,29502,337724,0,29502,337828,50,29502,337828,30,29502,337828,40,29502,337863,0,29502,338001,50,29502,338001,30,29502,338001,40,29502,338036,0,29507,338198,50,29508,338198,30,29508,338198,40,29508,338233,0,29508,338325,50,29508,338360,0,29508,338498,50,29509,338498,30,29509,338498,40,29509,338533,0,29514,338651,50,29515,338686,0,29515,338838,50,29517,338873,0,29523,339033,50,29526,339068,0,29526,339236,50,29532,339271,0,29532,339445,50,29541,339480,0,29545,339662,50,29561,339697,0,29561,339887,50,29591,339922,0,29595,340122,50,29654,340157,0,29654,340367,50,29771,340367,40,29771,340402,0,29771)
%
%
% START OF PROOF
% 340255 [?] ?
% 340369 [] equal(multiply(identity,X),X).
% 340370 [] equal(multiply(inverse(X),X),identity).
% 340371 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 340372 [] -equal(multiply(sk_c7,sk_c8),sk_c6).
% 340398 [?] ?
% 340399 [?] ?
% 340400 [?] ?
% 340401 [?] ?
% 340402 [?] ?
% 340441 [input:340399,cut:340372] equal(inverse(sk_c5),sk_c7).
% 340442 [para:340441.1.1,340370.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 340444 [input:340401,cut:340372] equal(inverse(sk_c4),sk_c8).
% 340445 [para:340444.1.1,340370.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 340456 [input:340398,cut:340372] equal(multiply(sk_c6,sk_c7),sk_c8).
% 340457 [input:340400,cut:340372] equal(multiply(sk_c5,sk_c7),sk_c6).
% 340458 [input:340402,cut:340372] equal(multiply(sk_c4,sk_c8),sk_c7).
% 340462 [para:340370.1.1,340371.1.1.1,demod:340369] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 340481 [para:340442.1.1,340371.1.1.1,demod:340369] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 340482 [para:340445.1.1,340371.1.1.1,demod:340369] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 340510 [para:340457.1.1,340481.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 340517 [para:340458.1.1,340482.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 340560 [para:340456.1.1,340462.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c8)).
% 340567 [para:340481.1.2,340462.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c7),X)).
% 340568 [para:340510.1.2,340462.1.2.2,demod:340567] equal(sk_c6,multiply(sk_c5,sk_c7)).
% 340571 [para:340462.1.2,340462.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 340573 [para:340560.1.2,340462.1.2.2,demod:340571] equal(sk_c8,multiply(sk_c6,sk_c7)).
% 340580 [para:340567.1.2,340370.1.1,demod:340568] equal(sk_c6,identity).
% 340589 [para:340580.1.1,340456.1.1.1,demod:340369] equal(sk_c7,sk_c8).
% 340591 [para:340580.1.1,340573.1.2.1,demod:340369] equal(sk_c8,sk_c7).
% 340607 [para:340589.1.1,340517.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c8)).
% 340611 [para:340591.1.2,340372.1.1.1,demod:340607,cut:340255] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c7),sk_c6) | -equal(inverse(V),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c8).
% Split part used next: -equal(multiply(sk_c6,sk_c7),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
%
%
% 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(35,40,0,75,0,0,829,50,7,869,0,7,1826,50,20,1866,0,20,2924,50,36,2964,0,36,4076,50,49,4116,0,49,5283,50,66,5323,0,66,6570,50,92,6610,0,92,7937,50,132,7977,0,132,9410,50,206,9450,0,206,10989,50,348,11029,0,348,12700,50,574,12740,0,574,14543,50,981,14543,40,981,14583,0,981,25020,3,1282,25663,4,1432,26355,1,1582,26355,50,1582,26355,40,1582,26395,0,1582,26746,3,1895,26758,4,2053,26775,5,2183,26775,1,2183,26775,50,2183,26775,40,2183,26815,0,2183,51505,3,3688,52651,4,4434,53598,5,5184,53599,1,5184,53599,50,5185,53599,40,5185,53639,0,5185,70600,3,5936,71182,4,6311,71983,5,6686,71984,1,6686,71984,50,6686,71984,40,6686,72024,0,6686,82919,3,7454,84094,4,7812,85724,5,8187,85725,1,8187,85725,50,8187,85725,40,8187,85765,0,8187,161847,3,12090,162596,4,14038,163382,5,15988,163383,1,15988,163383,50,15991,163383,40,15991,163423,0,15991,221612,3,18551,222268,4,19817,222939,1,21092,222939,50,21094,222939,40,21094,222979,0,21094,267531,3,22596,268223,4,23345,268987,5,24095,268988,1,24095,268988,50,24097,268988,40,24097,269028,0,24097,278747,3,24853,280008,4,25227,280688,5,25598,280688,1,25598,280688,50,25598,280688,40,25598,280728,0,25598,312313,3,26800,312862,4,27399,313290,5,27999,313291,1,27999,313291,50,28000,313291,40,28000,313331,0,28000,336477,3,28751,337052,4,29126,337689,1,29501,337689,50,29502,337689,40,29502,337689,40,29502,337724,0,29502,337828,50,29502,337828,30,29502,337828,40,29502,337863,0,29502,338001,50,29502,338001,30,29502,338001,40,29502,338036,0,29507,338198,50,29508,338198,30,29508,338198,40,29508,338233,0,29508,338325,50,29508,338360,0,29508,338498,50,29509,338498,30,29509,338498,40,29509,338533,0,29514,338651,50,29515,338686,0,29515,338838,50,29517,338873,0,29523,339033,50,29526,339068,0,29526,339236,50,29532,339271,0,29532,339445,50,29541,339480,0,29545,339662,50,29561,339697,0,29561,339887,50,29591,339922,0,29595,340122,50,29654,340157,0,29654,340367,50,29771,340367,40,29771,340402,0,29771,340610,50,29772,340610,30,29772,340610,40,29772,340645,0,29772,340758,50,29773,340793,0,29777,340958,50,29780,340993,0,29780,341165,50,29784,341200,0,29784,341380,50,29790,341415,0,29795,341601,50,29804,341636,0,29804,341830,50,29820,341865,0,29825,342067,50,29854,342102,0,29854,342314,50,29917,342349,0,29917,342571,50,30035,342571,40,30035,342606,0,30035)
%
%
% START OF PROOF
% 342518 [?] ?
% 342573 [] equal(multiply(identity,X),X).
% 342574 [] equal(multiply(inverse(X),X),identity).
% 342575 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 342576 [] -equal(multiply(sk_c6,sk_c7),sk_c8).
% 342577 [?] ?
% 342582 [?] ?
% 342587 [?] ?
% 342592 [?] ?
% 342597 [?] ?
% 342602 [?] ?
% 342610 [input:342577,cut:342576] equal(inverse(sk_c2),sk_c8).
% 342611 [para:342610.1.1,342574.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 342630 [input:342592,cut:342576] equal(inverse(sk_c1),sk_c7).
% 342631 [para:342630.1.1,342574.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 342632 [input:342582,cut:342576] equal(multiply(sk_c2,sk_c8),sk_c3).
% 342649 [input:342587,cut:342576] equal(multiply(sk_c8,sk_c3),sk_c7).
% 342652 [input:342597,cut:342576] equal(multiply(sk_c1,sk_c7),sk_c8).
% 342655 [input:342602,cut:342576] equal(multiply(sk_c7,sk_c8),sk_c6).
% 342663 [para:342611.1.1,342575.1.1.1,demod:342573] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 342671 [para:342631.1.1,342575.1.1.1,demod:342573] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 342684 [para:342649.1.1,342575.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c3,X))).
% 342699 [para:342632.1.1,342663.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c3)).
% 342702 [para:342699.1.2,342649.1.1] equal(sk_c8,sk_c7).
% 342703 [para:342699.1.2,342575.1.1.1,demod:342684] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 342715 [para:342702.1.2,342652.1.1.2] equal(multiply(sk_c1,sk_c8),sk_c8).
% 342717 [para:342702.1.2,342655.1.1.1] equal(multiply(sk_c8,sk_c8),sk_c6).
% 342729 [para:342715.1.1,342671.1.2.2,demod:342717,342703] equal(sk_c8,sk_c6).
% 342747 [para:342729.1.1,342576.1.2,cut:342518] 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: 33037
% derived clauses: 5004234
% kept clauses: 293379
% kept size sum: 334167
% kept mid-nuclei: 11216
% kept new demods: 4262
% forw unit-subs: 1627171
% forw double-subs: 2672656
% forw overdouble-subs: 362043
% backward subs: 10323
% fast unit cutoff: 20026
% full unit cutoff: 0
% dbl unit cutoff: 6604
% real runtime : 303.5
% process. runtime: 300.36
% specific non-discr-tree subsumption statistics:
% tried: 44372727
% length fails: 4903764
% strength fails: 15615189
% predlist fails: 3472850
% aux str. fails: 6054378
% by-lit fails: 7820280
% full subs tried: 1990746
% full subs fail: 1876941
%
% ; 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/GRP321-1+eq_r.in")
%
%------------------------------------------------------------------------------