TSTP Solution File: GRP231-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP231-1 : 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 : art10.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 298.1s
% Output : Assurance 298.1s
% 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/GRP231-1+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(inverse(sk_c8),sk_c7) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Z),sk_c8) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% was split for some strategies as:
% -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8).
% -equal(inverse(Z),sk_c8) | -equal(multiply(Z,sk_c7),sk_c8).
% -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8).
% -equal(inverse(sk_c8),sk_c7).
%
% Starting a split proof attempt with 5 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Z),sk_c8) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,136929,4,1412,140063,5,1502,140065,1,1508,140065,50,1508,140065,40,1508,140105,0,1508,151477,3,1809,152110,4,1959,152778,5,2109,152779,1,2109,152779,50,2109,152779,40,2109,152819,0,2109,153584,3,2416,153595,4,2568,153656,5,2710,153656,1,2710,153656,50,2710,153656,40,2710,153696,0,2710,184995,3,4212,185681,4,4961,186467,1,5711,186467,50,5712,186467,40,5712,186507,0,5712,210120,3,6470,210640,4,6838,211091,5,7213,211092,1,7213,211092,50,7214,211092,40,7214,211132,0,7214,231111,3,7965,231659,4,8340,232257,5,8715,232258,1,8715,232258,50,8715,232258,40,8715,232298,0,8715,308131,3,12616,309033,4,14566,309389,1,16516,309389,50,16518,309389,40,16518,309429,0,16518,366627,3,19070,367439,4,20344,367683,1,21619,367683,50,21621,367683,40,21621,367723,0,21621,409908,3,23124,410655,4,23872,411260,5,24622,411261,1,24623,411261,50,24624,411261,40,24624,411301,0,24624,431423,3,25377,431993,4,25750,432681,1,26125,432681,50,26125,432681,40,26125,432721,0,26125,465683,3,27331,466372,4,27926,467036,5,28526,467037,1,28526,467037,50,28527,467037,40,28527,467077,0,28527,491775,3,29279,492288,4,29653,492836,1,30028,492836,50,30029,492836,40,30029,492836,40,30029,492871,0,30029)
%
%
% START OF PROOF
% 492837 [] equal(X,X).
% 492838 [] equal(multiply(identity,X),X).
% 492839 [] equal(multiply(inverse(X),X),identity).
% 492840 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 492841 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 492842 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 492843 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 492844 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(multiply(sk_c8,sk_c6),sk_c7).
% 492847 [] equal(inverse(sk_c3),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 492848 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 492849 [?] ?
% 492857 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 492858 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c2).
% 492859 [?] ?
% 492862 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 492863 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 492864 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(multiply(sk_c8,sk_c6),sk_c7).
% 492867 [] equal(inverse(sk_c8),sk_c7) | equal(inverse(sk_c5),sk_c8).
% 492868 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c8),sk_c7).
% 492869 [?] ?
% 492922 [hyper:492841,492848,492847,binarycut:492849] equal(inverse(sk_c3),sk_c8).
% 492929 [para:492922.1.1,492839.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 492947 [hyper:492841,492844,492843,492842] equal(multiply(sk_c3,sk_c7),sk_c8).
% 492959 [hyper:492841,492858,492857,binarycut:492859] equal(inverse(sk_c1),sk_c2).
% 492983 [hyper:492841,492868,492867,binarycut:492869] equal(inverse(sk_c8),sk_c7).
% 492987 [para:492983.1.1,492839.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 492994 [hyper:492841,492864,492863,492862] equal(multiply(sk_c1,sk_c2),sk_c8).
% 492995 [para:492839.1.1,492840.1.1.1,demod:492838] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 492996 [para:492929.1.1,492840.1.1.1,demod:492838] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 492997 [para:492947.1.1,492840.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c3,multiply(sk_c7,X))).
% 493006 [para:492947.1.1,492995.1.2.2,demod:492922] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 493010 [para:492994.1.1,492995.1.2.2,demod:492959] equal(sk_c2,multiply(sk_c2,sk_c8)).
% 493015 [para:493010.1.2,492995.1.2.2,demod:492839] equal(sk_c8,identity).
% 493018 [para:493015.1.1,493006.1.2.1,demod:492838] equal(sk_c7,sk_c8).
% 493019 [para:493015.1.1,493006.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 493024 [para:493015.1.1,492996.1.2.1,demod:492838] equal(X,multiply(sk_c3,X)).
% 493040 [hyper:492841,492997,demod:492983,493019,493024,492987,cut:492837,cut:493018] 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: 6
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Z),sk_c8) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(inverse(U),sk_c8) | -equal(multiply(U,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: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,136929,4,1412,140063,5,1502,140065,1,1508,140065,50,1508,140065,40,1508,140105,0,1508,151477,3,1809,152110,4,1959,152778,5,2109,152779,1,2109,152779,50,2109,152779,40,2109,152819,0,2109,153584,3,2416,153595,4,2568,153656,5,2710,153656,1,2710,153656,50,2710,153656,40,2710,153696,0,2710,184995,3,4212,185681,4,4961,186467,1,5711,186467,50,5712,186467,40,5712,186507,0,5712,210120,3,6470,210640,4,6838,211091,5,7213,211092,1,7213,211092,50,7214,211092,40,7214,211132,0,7214,231111,3,7965,231659,4,8340,232257,5,8715,232258,1,8715,232258,50,8715,232258,40,8715,232298,0,8715,308131,3,12616,309033,4,14566,309389,1,16516,309389,50,16518,309389,40,16518,309429,0,16518,366627,3,19070,367439,4,20344,367683,1,21619,367683,50,21621,367683,40,21621,367723,0,21621,409908,3,23124,410655,4,23872,411260,5,24622,411261,1,24623,411261,50,24624,411261,40,24624,411301,0,24624,431423,3,25377,431993,4,25750,432681,1,26125,432681,50,26125,432681,40,26125,432721,0,26125,465683,3,27331,466372,4,27926,467036,5,28526,467037,1,28526,467037,50,28527,467037,40,28527,467077,0,28527,491775,3,29279,492288,4,29653,492836,1,30028,492836,50,30029,492836,40,30029,492836,40,30029,492871,0,30029,493039,50,30029,493039,30,30029,493039,40,30029,493074,0,30029)
%
%
% START OF PROOF
% 493040 [] equal(X,X).
% 493044 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c8).
% 493048 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 493049 [?] ?
% 493053 [?] ?
% 493054 [] equal(inverse(sk_c3),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 493084 [hyper:493044,493054,binarycut:493049] equal(inverse(sk_c4),sk_c8).
% 493086 [hyper:493044,493054,binarycut:493053] equal(inverse(sk_c3),sk_c8).
% 493105 [hyper:493044,493048,demod:493086,cut:493040] equal(multiply(sk_c4,sk_c7),sk_c8).
% 493107 [hyper:493044,493105,demod:493084,cut:493040] 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: 6
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Z),sk_c8) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(inverse(Z),sk_c8) | -equal(multiply(Z,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: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,136929,4,1412,140063,5,1502,140065,1,1508,140065,50,1508,140065,40,1508,140105,0,1508,151477,3,1809,152110,4,1959,152778,5,2109,152779,1,2109,152779,50,2109,152779,40,2109,152819,0,2109,153584,3,2416,153595,4,2568,153656,5,2710,153656,1,2710,153656,50,2710,153656,40,2710,153696,0,2710,184995,3,4212,185681,4,4961,186467,1,5711,186467,50,5712,186467,40,5712,186507,0,5712,210120,3,6470,210640,4,6838,211091,5,7213,211092,1,7213,211092,50,7214,211092,40,7214,211132,0,7214,231111,3,7965,231659,4,8340,232257,5,8715,232258,1,8715,232258,50,8715,232258,40,8715,232298,0,8715,308131,3,12616,309033,4,14566,309389,1,16516,309389,50,16518,309389,40,16518,309429,0,16518,366627,3,19070,367439,4,20344,367683,1,21619,367683,50,21621,367683,40,21621,367723,0,21621,409908,3,23124,410655,4,23872,411260,5,24622,411261,1,24623,411261,50,24624,411261,40,24624,411301,0,24624,431423,3,25377,431993,4,25750,432681,1,26125,432681,50,26125,432681,40,26125,432721,0,26125,465683,3,27331,466372,4,27926,467036,5,28526,467037,1,28526,467037,50,28527,467037,40,28527,467077,0,28527,491775,3,29279,492288,4,29653,492836,1,30028,492836,50,30029,492836,40,30029,492836,40,30029,492871,0,30029,493039,50,30029,493039,30,30029,493039,40,30029,493074,0,30029,493106,50,30029,493106,30,30029,493106,40,30029,493141,0,30034)
%
%
% START OF PROOF
% 493107 [] equal(X,X).
% 493111 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c8).
% 493115 [] equal(multiply(sk_c3,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 493116 [?] ?
% 493120 [?] ?
% 493121 [] equal(inverse(sk_c3),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 493151 [hyper:493111,493121,binarycut:493116] equal(inverse(sk_c4),sk_c8).
% 493153 [hyper:493111,493121,binarycut:493120] equal(inverse(sk_c3),sk_c8).
% 493172 [hyper:493111,493115,demod:493153,cut:493107] equal(multiply(sk_c4,sk_c7),sk_c8).
% 493174 [hyper:493111,493172,demod:493151,cut:493107] 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: 6
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Z),sk_c8) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,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: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,136929,4,1412,140063,5,1502,140065,1,1508,140065,50,1508,140065,40,1508,140105,0,1508,151477,3,1809,152110,4,1959,152778,5,2109,152779,1,2109,152779,50,2109,152779,40,2109,152819,0,2109,153584,3,2416,153595,4,2568,153656,5,2710,153656,1,2710,153656,50,2710,153656,40,2710,153696,0,2710,184995,3,4212,185681,4,4961,186467,1,5711,186467,50,5712,186467,40,5712,186507,0,5712,210120,3,6470,210640,4,6838,211091,5,7213,211092,1,7213,211092,50,7214,211092,40,7214,211132,0,7214,231111,3,7965,231659,4,8340,232257,5,8715,232258,1,8715,232258,50,8715,232258,40,8715,232298,0,8715,308131,3,12616,309033,4,14566,309389,1,16516,309389,50,16518,309389,40,16518,309429,0,16518,366627,3,19070,367439,4,20344,367683,1,21619,367683,50,21621,367683,40,21621,367723,0,21621,409908,3,23124,410655,4,23872,411260,5,24622,411261,1,24623,411261,50,24624,411261,40,24624,411301,0,24624,431423,3,25377,431993,4,25750,432681,1,26125,432681,50,26125,432681,40,26125,432721,0,26125,465683,3,27331,466372,4,27926,467036,5,28526,467037,1,28526,467037,50,28527,467037,40,28527,467077,0,28527,491775,3,29279,492288,4,29653,492836,1,30028,492836,50,30029,492836,40,30029,492836,40,30029,492871,0,30029,493039,50,30029,493039,30,30029,493039,40,30029,493074,0,30029,493106,50,30029,493106,30,30029,493106,40,30029,493141,0,30034,493173,50,30034,493173,30,30034,493173,40,30034,493208,0,30034)
%
%
% START OF PROOF
% 493174 [] equal(X,X).
% 493175 [] equal(multiply(identity,X),X).
% 493176 [] equal(multiply(inverse(X),X),identity).
% 493177 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 493178 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,X),sk_c8) | -equal(inverse(Y),X).
% 493189 [?] ?
% 493190 [?] ?
% 493191 [?] ?
% 493192 [?] ?
% 493193 [?] ?
% 493194 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c8).
% 493195 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c2).
% 493196 [] equal(multiply(sk_c8,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c2).
% 493197 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c2).
% 493198 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c4),sk_c8).
% 493199 [?] ?
% 493200 [?] ?
% 493201 [?] ?
% 493202 [?] ?
% 493203 [?] ?
% 493220 [hyper:493178,493194,binarycut:493199,binarycut:493189] equal(inverse(sk_c5),sk_c8).
% 493224 [para:493220.1.1,493176.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 493228 [hyper:493178,493198,binarycut:493203,binarycut:493193] equal(inverse(sk_c4),sk_c8).
% 493237 [para:493228.1.1,493176.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 493259 [hyper:493178,493195,binarycut:493200,binarycut:493190] equal(multiply(sk_c5,sk_c8),sk_c6).
% 493262 [hyper:493178,493196,binarycut:493201,binarycut:493191] equal(multiply(sk_c8,sk_c6),sk_c7).
% 493267 [hyper:493178,493197,binarycut:493202,binarycut:493192] equal(multiply(sk_c4,sk_c7),sk_c8).
% 493274 [para:493176.1.1,493177.1.1.1,demod:493175] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 493275 [para:493224.1.1,493177.1.1.1,demod:493175] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 493282 [para:493259.1.1,493275.1.2.2,demod:493262] equal(sk_c8,sk_c7).
% 493285 [para:493282.1.1,493259.1.1.2] equal(multiply(sk_c5,sk_c7),sk_c6).
% 493286 [para:493282.1.1,493262.1.1.1] equal(multiply(sk_c7,sk_c6),sk_c7).
% 493293 [para:493224.1.1,493274.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),identity)).
% 493294 [para:493237.1.1,493274.1.2.2,demod:493293] equal(sk_c4,sk_c5).
% 493296 [para:493267.1.1,493274.1.2.2,demod:493228] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 493300 [para:493294.1.2,493285.1.1.1,demod:493267] equal(sk_c8,sk_c6).
% 493301 [para:493300.1.1,493224.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 493310 [para:493286.1.1,493274.1.2.2,demod:493176] equal(sk_c6,identity).
% 493319 [para:493282.1.1,493296.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c7)).
% 493323 [para:493310.1.1,493301.1.1.1,demod:493175] equal(sk_c5,identity).
% 493324 [para:493323.1.1,493220.1.1.1] equal(inverse(identity),sk_c8).
% 493327 [para:493323.1.1,493294.1.2] equal(sk_c4,identity).
% 493336 [para:493327.1.1,493267.1.1.1,demod:493175] equal(sk_c7,sk_c8).
% 493338 [hyper:493178,493324,demod:493319,493175,cut:493174,cut:493336] 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: 6
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Z),sk_c8) | -equal(multiply(Z,sk_c7),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(inverse(sk_c8),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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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 12
% seconds given: 6
%
%
% 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(35,40,0,75,0,0,136929,4,1412,140063,5,1502,140065,1,1508,140065,50,1508,140065,40,1508,140105,0,1508,151477,3,1809,152110,4,1959,152778,5,2109,152779,1,2109,152779,50,2109,152779,40,2109,152819,0,2109,153584,3,2416,153595,4,2568,153656,5,2710,153656,1,2710,153656,50,2710,153656,40,2710,153696,0,2710,184995,3,4212,185681,4,4961,186467,1,5711,186467,50,5712,186467,40,5712,186507,0,5712,210120,3,6470,210640,4,6838,211091,5,7213,211092,1,7213,211092,50,7214,211092,40,7214,211132,0,7214,231111,3,7965,231659,4,8340,232257,5,8715,232258,1,8715,232258,50,8715,232258,40,8715,232298,0,8715,308131,3,12616,309033,4,14566,309389,1,16516,309389,50,16518,309389,40,16518,309429,0,16518,366627,3,19070,367439,4,20344,367683,1,21619,367683,50,21621,367683,40,21621,367723,0,21621,409908,3,23124,410655,4,23872,411260,5,24622,411261,1,24623,411261,50,24624,411261,40,24624,411301,0,24624,431423,3,25377,431993,4,25750,432681,1,26125,432681,50,26125,432681,40,26125,432721,0,26125,465683,3,27331,466372,4,27926,467036,5,28526,467037,1,28526,467037,50,28527,467037,40,28527,467077,0,28527,491775,3,29279,492288,4,29653,492836,1,30028,492836,50,30029,492836,40,30029,492836,40,30029,492871,0,30029,493039,50,30029,493039,30,30029,493039,40,30029,493074,0,30029,493106,50,30029,493106,30,30029,493106,40,30029,493141,0,30034,493173,50,30034,493173,30,30034,493173,40,30034,493208,0,30034,493337,50,30034,493337,30,30034,493337,40,30034,493372,0,30034,493478,50,30034,493513,0,30039,493660,50,30042,493695,0,30042,493850,50,30046,493885,0,30050,494048,50,30055,494083,0,30055,494252,50,30064,494287,0,30064,494464,50,30079,494499,0,30084,494684,50,30112,494719,0,30112,494914,50,30173,494949,0,30173,495154,50,30289,495189,0,30289,495406,50,30518,495406,40,30518,495441,0,30518)
%
%
% START OF PROOF
% 495408 [] equal(multiply(identity,X),X).
% 495409 [] equal(multiply(inverse(X),X),identity).
% 495410 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 495411 [] -equal(inverse(sk_c8),sk_c7).
% 495437 [?] ?
% 495438 [?] ?
% 495439 [?] ?
% 495440 [?] ?
% 495441 [?] ?
% 495456 [input:495437,cut:495411] equal(inverse(sk_c5),sk_c8).
% 495457 [para:495456.1.1,495409.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 495459 [input:495441,cut:495411] equal(inverse(sk_c4),sk_c8).
% 495460 [para:495459.1.1,495409.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 495480 [input:495438,cut:495411] equal(multiply(sk_c5,sk_c8),sk_c6).
% 495481 [input:495439,cut:495411] equal(multiply(sk_c8,sk_c6),sk_c7).
% 495483 [input:495440,cut:495411] equal(multiply(sk_c4,sk_c7),sk_c8).
% 495495 [para:495409.1.1,495410.1.1.1,demod:495408] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 495497 [para:495457.1.1,495410.1.1.1,demod:495408] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 495500 [para:495460.1.1,495410.1.1.1,demod:495408] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 495517 [para:495481.1.1,495410.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c6,X))).
% 495534 [para:495480.1.1,495497.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 495538 [para:495534.1.2,495481.1.1] equal(sk_c8,sk_c7).
% 495539 [para:495534.1.2,495410.1.1.1,demod:495517] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 495540 [para:495538.1.1,495411.1.1.1] -equal(inverse(sk_c7),sk_c7).
% 495565 [para:495483.1.1,495500.1.2.2,demod:495539] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 495619 [para:495565.1.2,495495.1.2.2,demod:495409] equal(sk_c8,identity).
% 495638 [para:495619.1.1,495457.1.1.1,demod:495408] equal(sk_c5,identity).
% 495651 [para:495619.1.1,495538.1.1] equal(identity,sk_c7).
% 495666 [para:495638.1.1,495456.1.1.1] equal(inverse(identity),sk_c8).
% 495682 [para:495651.1.2,495540.1.1.1,demod:495666,cut:495538] 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: 26475
% derived clauses: 5968472
% kept clauses: 324540
% kept size sum: 15331
% kept mid-nuclei: 116797
% kept new demods: 2091
% forw unit-subs: 1754661
% forw double-subs: 3455312
% forw overdouble-subs: 264937
% backward subs: 7347
% fast unit cutoff: 25235
% full unit cutoff: 0
% dbl unit cutoff: 26652
% real runtime : 307.55
% process. runtime: 305.19
% specific non-discr-tree subsumption statistics:
% tried: 29282577
% length fails: 3542098
% strength fails: 9576898
% predlist fails: 1091762
% aux str. fails: 3643321
% by-lit fails: 3990837
% full subs tried: 2291707
% full subs fail: 2150673
%
% ; 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/GRP231-1+eq_r.in")
%
%------------------------------------------------------------------------------