TSTP Solution File: GRP308-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP308-1 : 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 : art06.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 297.1s
% Output : Assurance 297.1s
% 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/GRP308-1+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_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% was split for some strategies as:
% -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7).
% -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8).
% -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% -equal(multiply(sk_c8,sk_c7),sk_c6).
% -equal(inverse(sk_c8),sk_c6).
% -equal(multiply(sk_c6,sk_c7),sk_c8).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% Split part used next: -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,1,87,0,1,13458,50,234,13504,0,234,28069,50,378,28115,0,378,43727,50,531,43773,0,531,59837,50,695,59883,0,695,76546,50,892,76546,40,892,76592,0,892,87047,3,1193,87767,4,1343,88474,1,1493,88474,50,1493,88474,40,1493,88520,0,1493,88859,3,1805,88868,4,1947,88892,5,2094,88892,1,2094,88892,50,2094,88892,40,2094,88938,0,2094,127304,3,3595,127767,4,4345,127922,5,5095,127923,1,5095,127923,50,5096,127923,40,5096,127969,0,5096,150402,3,5848,150970,4,6222,151471,1,6597,151471,50,6597,151471,40,6597,151517,0,6597,162732,3,7350,164114,4,7723,166107,5,8098,166108,1,8098,166108,50,8098,166108,40,8098,166154,0,8098,229406,3,12000,230162,4,13949,230522,1,15899,230522,50,15902,230522,40,15902,230568,0,15902,284798,3,18453,285464,4,19728,285778,5,21003,285779,1,21003,285779,50,21004,285779,40,21004,285825,0,21004,329643,3,22507,330318,4,23255,330839,5,24005,330840,1,24005,330840,50,24006,330840,40,24006,330886,0,24006,339840,3,24767,340971,4,25132,341710,5,25507,341710,1,25507,341710,50,25507,341710,40,25507,341756,0,25507,381061,3,26708,381610,4,27309,382001,1,27908,382001,50,27910,382001,40,27910,382047,0,27910,411117,3,28661,411604,4,29036,411961,1,29411,411961,50,29412,411961,40,29412,411961,40,29412,412002,0,29412)
%
%
% START OF PROOF
% 411963 [] equal(multiply(identity,X),X).
% 411964 [] equal(multiply(inverse(X),X),identity).
% 411965 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 411966 [] -equal(multiply(X,sk_c8),sk_c6) | -equal(inverse(X),sk_c6).
% 411967 [?] ?
% 411968 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 411973 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 411974 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c5),sk_c6).
% 411979 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 411980 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 411985 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 411986 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 411991 [?] ?
% 411992 [] equal(inverse(sk_c8),sk_c6) | equal(inverse(sk_c5),sk_c6).
% 411997 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 411998 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c5),sk_c6).
% 412005 [hyper:411966,411968,binarycut:411967] equal(inverse(sk_c1),sk_c8).
% 412006 [para:412005.1.1,411964.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 412014 [hyper:411966,411992,binarycut:411991] equal(inverse(sk_c8),sk_c6).
% 412017 [para:412014.1.1,411964.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 412021 [hyper:411966,411974,411973] equal(multiply(sk_c1,sk_c8),sk_c2).
% 412027 [hyper:411966,411979,411980] equal(multiply(sk_c8,sk_c2),sk_c7).
% 412033 [hyper:411966,411986,411985] equal(multiply(sk_c6,sk_c7),sk_c8).
% 412039 [hyper:411966,411998,411997] equal(multiply(sk_c8,sk_c7),sk_c6).
% 412041 [para:412006.1.1,411965.1.1.1,demod:411963] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 412043 [para:412021.1.1,411965.1.1.1] equal(multiply(sk_c2,X),multiply(sk_c1,multiply(sk_c8,X))).
% 412047 [para:412021.1.1,412041.1.2.2,demod:412027] equal(sk_c8,sk_c7).
% 412049 [para:412047.1.1,412014.1.1.1] equal(inverse(sk_c7),sk_c6).
% 412050 [para:412047.1.1,412017.1.1.2,demod:412033] equal(sk_c8,identity).
% 412055 [para:412050.1.1,412006.1.1.1,demod:411963] equal(sk_c1,identity).
% 412056 [para:412050.1.1,412014.1.1.1] equal(inverse(identity),sk_c6).
% 412061 [para:412050.1.1,412041.1.2.1,demod:411963] equal(X,multiply(sk_c1,X)).
% 412064 [para:412055.1.1,412005.1.1.1,demod:412056] equal(sk_c6,sk_c8).
% 412066 [para:412055.1.1,412021.1.1.1,demod:411963] equal(sk_c8,sk_c2).
% 412080 [para:412064.1.2,412039.1.1.1,demod:412033] equal(sk_c8,sk_c6).
% 412086 [para:412066.1.1,412041.1.2.1,demod:412061] equal(X,multiply(sk_c2,X)).
% 412089 [para:412047.1.1,412043.1.2.2.1,demod:412061,412086] equal(X,multiply(sk_c7,X)).
% 412090 [hyper:411966,412049,demod:412089,cut:412080] 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: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% Split part used next: -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),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: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,1,87,0,1,13458,50,234,13504,0,234,28069,50,378,28115,0,378,43727,50,531,43773,0,531,59837,50,695,59883,0,695,76546,50,892,76546,40,892,76592,0,892,87047,3,1193,87767,4,1343,88474,1,1493,88474,50,1493,88474,40,1493,88520,0,1493,88859,3,1805,88868,4,1947,88892,5,2094,88892,1,2094,88892,50,2094,88892,40,2094,88938,0,2094,127304,3,3595,127767,4,4345,127922,5,5095,127923,1,5095,127923,50,5096,127923,40,5096,127969,0,5096,150402,3,5848,150970,4,6222,151471,1,6597,151471,50,6597,151471,40,6597,151517,0,6597,162732,3,7350,164114,4,7723,166107,5,8098,166108,1,8098,166108,50,8098,166108,40,8098,166154,0,8098,229406,3,12000,230162,4,13949,230522,1,15899,230522,50,15902,230522,40,15902,230568,0,15902,284798,3,18453,285464,4,19728,285778,5,21003,285779,1,21003,285779,50,21004,285779,40,21004,285825,0,21004,329643,3,22507,330318,4,23255,330839,5,24005,330840,1,24005,330840,50,24006,330840,40,24006,330886,0,24006,339840,3,24767,340971,4,25132,341710,5,25507,341710,1,25507,341710,50,25507,341710,40,25507,341756,0,25507,381061,3,26708,381610,4,27309,382001,1,27908,382001,50,27910,382001,40,27910,382047,0,27910,411117,3,28661,411604,4,29036,411961,1,29411,411961,50,29412,411961,40,29412,411961,40,29412,412002,0,29412,412089,50,29412,412089,30,29412,412089,40,29412,412130,0,29412)
%
%
% START OF PROOF
% 412091 [] equal(multiply(identity,X),X).
% 412092 [] equal(multiply(inverse(X),X),identity).
% 412093 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 412094 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 412097 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 412098 [?] ?
% 412103 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c4),sk_c7).
% 412104 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c4,sk_c7),sk_c6).
% 412109 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 412110 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c6).
% 412115 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 412116 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c6).
% 412121 [] equal(inverse(sk_c8),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 412122 [?] ?
% 412127 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 412128 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c7),sk_c6).
% 412134 [hyper:412094,412097,binarycut:412098] equal(inverse(sk_c1),sk_c8).
% 412136 [para:412134.1.1,412092.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 412141 [hyper:412094,412121,binarycut:412122] equal(inverse(sk_c8),sk_c6).
% 412142 [para:412141.1.1,412092.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 412155 [hyper:412094,412104,412103] equal(multiply(sk_c1,sk_c8),sk_c2).
% 412175 [hyper:412094,412110,412109] equal(multiply(sk_c8,sk_c2),sk_c7).
% 412179 [hyper:412094,412116,412115] equal(multiply(sk_c6,sk_c7),sk_c8).
% 412186 [hyper:412094,412128,412127] equal(multiply(sk_c8,sk_c7),sk_c6).
% 412189 [para:412136.1.1,412093.1.1.1,demod:412091] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 412197 [para:412155.1.1,412189.1.2.2,demod:412175] equal(sk_c8,sk_c7).
% 412199 [para:412197.1.1,412141.1.1.1] equal(inverse(sk_c7),sk_c6).
% 412200 [para:412197.1.1,412142.1.1.2,demod:412179] equal(sk_c8,identity).
% 412203 [para:412197.1.1,412186.1.1.1] equal(multiply(sk_c7,sk_c7),sk_c6).
% 412205 [para:412200.1.1,412136.1.1.1,demod:412091] equal(sk_c1,identity).
% 412206 [para:412200.1.1,412141.1.1.1] equal(inverse(identity),sk_c6).
% 412214 [para:412205.1.1,412134.1.1.1,demod:412206] equal(sk_c6,sk_c8).
% 412231 [para:412214.1.2,412197.1.1] equal(sk_c6,sk_c7).
% 412240 [hyper:412094,412203,demod:412199,cut:412231] 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: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% Split part used next: -equal(multiply(Z,sk_c8),sk_c7) | -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 23
% 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 23
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,1,87,0,1,13458,50,234,13504,0,234,28069,50,378,28115,0,378,43727,50,531,43773,0,531,59837,50,695,59883,0,695,76546,50,892,76546,40,892,76592,0,892,87047,3,1193,87767,4,1343,88474,1,1493,88474,50,1493,88474,40,1493,88520,0,1493,88859,3,1805,88868,4,1947,88892,5,2094,88892,1,2094,88892,50,2094,88892,40,2094,88938,0,2094,127304,3,3595,127767,4,4345,127922,5,5095,127923,1,5095,127923,50,5096,127923,40,5096,127969,0,5096,150402,3,5848,150970,4,6222,151471,1,6597,151471,50,6597,151471,40,6597,151517,0,6597,162732,3,7350,164114,4,7723,166107,5,8098,166108,1,8098,166108,50,8098,166108,40,8098,166154,0,8098,229406,3,12000,230162,4,13949,230522,1,15899,230522,50,15902,230522,40,15902,230568,0,15902,284798,3,18453,285464,4,19728,285778,5,21003,285779,1,21003,285779,50,21004,285779,40,21004,285825,0,21004,329643,3,22507,330318,4,23255,330839,5,24005,330840,1,24005,330840,50,24006,330840,40,24006,330886,0,24006,339840,3,24767,340971,4,25132,341710,5,25507,341710,1,25507,341710,50,25507,341710,40,25507,341756,0,25507,381061,3,26708,381610,4,27309,382001,1,27908,382001,50,27910,382001,40,27910,382047,0,27910,411117,3,28661,411604,4,29036,411961,1,29411,411961,50,29412,411961,40,29412,411961,40,29412,412002,0,29412,412089,50,29412,412089,30,29412,412089,40,29412,412130,0,29412,412239,50,29412,412239,30,29412,412239,40,29412,412280,0,29418,412389,50,29418,412430,0,29418)
%
%
% START OF PROOF
% 412391 [] equal(multiply(identity,X),X).
% 412392 [] equal(multiply(inverse(X),X),identity).
% 412393 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 412394 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 412399 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 412400 [?] ?
% 412405 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c3),sk_c8).
% 412406 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 412411 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 412412 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 412417 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 412418 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 412423 [] equal(inverse(sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 412424 [?] ?
% 412439 [hyper:412394,412399,binarycut:412400] equal(inverse(sk_c1),sk_c8).
% 412442 [para:412439.1.1,412392.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 412449 [hyper:412394,412423,binarycut:412424] equal(inverse(sk_c8),sk_c6).
% 412450 [para:412449.1.1,412392.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 412470 [hyper:412394,412406,412405] equal(multiply(sk_c1,sk_c8),sk_c2).
% 412479 [hyper:412394,412412,412411] equal(multiply(sk_c8,sk_c2),sk_c7).
% 412484 [hyper:412394,412418,412417] equal(multiply(sk_c6,sk_c7),sk_c8).
% 412490 [para:412392.1.1,412393.1.1.1,demod:412391] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 412491 [para:412442.1.1,412393.1.1.1,demod:412391] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 412497 [para:412470.1.1,412491.1.2.2,demod:412479] equal(sk_c8,sk_c7).
% 412499 [para:412497.1.1,412449.1.1.1] equal(inverse(sk_c7),sk_c6).
% 412500 [para:412497.1.1,412450.1.1.2,demod:412484] equal(sk_c8,identity).
% 412505 [para:412500.1.1,412442.1.1.1,demod:412391] equal(sk_c1,identity).
% 412506 [para:412500.1.1,412449.1.1.1] equal(inverse(identity),sk_c6).
% 412511 [para:412500.1.1,412491.1.2.1,demod:412391] equal(X,multiply(sk_c1,X)).
% 412514 [para:412505.1.1,412439.1.1.1,demod:412506] equal(sk_c6,sk_c8).
% 412519 [para:412392.1.1,412490.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 412523 [para:412393.1.1,412490.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 412524 [para:412490.1.2,412490.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 412543 [para:412524.1.2,412392.1.1] equal(multiply(X,inverse(X)),identity).
% 412545 [para:412524.1.2,412519.1.2] equal(X,multiply(X,identity)).
% 412561 [para:412545.1.2,412519.1.2] equal(X,inverse(inverse(X))).
% 412563 [para:412543.1.1,412523.1.2.2.2,demod:412545] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 412571 [para:412491.1.2,412563.1.2.1.1,demod:412511] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 412584 [para:412571.1.2,412524.1.2,demod:412561] equal(multiply(X,sk_c8),X).
% 412585 [hyper:412394,412584,demod:412499,cut:412514] 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: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% Split part used next: -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),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 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,1,87,0,1,13458,50,234,13504,0,234,28069,50,378,28115,0,378,43727,50,531,43773,0,531,59837,50,695,59883,0,695,76546,50,892,76546,40,892,76592,0,892,87047,3,1193,87767,4,1343,88474,1,1493,88474,50,1493,88474,40,1493,88520,0,1493,88859,3,1805,88868,4,1947,88892,5,2094,88892,1,2094,88892,50,2094,88892,40,2094,88938,0,2094,127304,3,3595,127767,4,4345,127922,5,5095,127923,1,5095,127923,50,5096,127923,40,5096,127969,0,5096,150402,3,5848,150970,4,6222,151471,1,6597,151471,50,6597,151471,40,6597,151517,0,6597,162732,3,7350,164114,4,7723,166107,5,8098,166108,1,8098,166108,50,8098,166108,40,8098,166154,0,8098,229406,3,12000,230162,4,13949,230522,1,15899,230522,50,15902,230522,40,15902,230568,0,15902,284798,3,18453,285464,4,19728,285778,5,21003,285779,1,21003,285779,50,21004,285779,40,21004,285825,0,21004,329643,3,22507,330318,4,23255,330839,5,24005,330840,1,24005,330840,50,24006,330840,40,24006,330886,0,24006,339840,3,24767,340971,4,25132,341710,5,25507,341710,1,25507,341710,50,25507,341710,40,25507,341756,0,25507,381061,3,26708,381610,4,27309,382001,1,27908,382001,50,27910,382001,40,27910,382047,0,27910,411117,3,28661,411604,4,29036,411961,1,29411,411961,50,29412,411961,40,29412,411961,40,29412,412002,0,29412,412089,50,29412,412089,30,29412,412089,40,29412,412130,0,29412,412239,50,29412,412239,30,29412,412239,40,29412,412280,0,29418,412389,50,29418,412430,0,29418,412584,50,29419,412584,30,29419,412584,40,29419,412625,0,29419)
%
%
% START OF PROOF
% 412585 [] equal(X,X).
% 412586 [] equal(multiply(identity,X),X).
% 412587 [] equal(multiply(inverse(X),X),identity).
% 412588 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 412589 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 412590 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 412591 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 412592 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 412593 [] equal(multiply(sk_c4,sk_c7),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 412594 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 412595 [] equal(multiply(sk_c3,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 412596 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 412597 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c5),sk_c6).
% 412598 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c4),sk_c7).
% 412599 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c4,sk_c7),sk_c6).
% 412600 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c3),sk_c8).
% 412601 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 412602 [?] ?
% 412603 [?] ?
% 412604 [?] ?
% 412605 [?] ?
% 412606 [?] ?
% 412607 [?] ?
% 412673 [hyper:412589,412597,binarycut:412603,binarycut:412591] equal(inverse(sk_c5),sk_c6).
% 412674 [para:412673.1.1,412587.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 412677 [hyper:412589,412598,binarycut:412604,binarycut:412592] equal(inverse(sk_c4),sk_c7).
% 412682 [hyper:412589,412596,412590,binarycut:412602] equal(multiply(sk_c5,sk_c8),sk_c6).
% 412685 [para:412677.1.1,412587.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 412690 [hyper:412589,412600,binarycut:412606,binarycut:412594] equal(inverse(sk_c3),sk_c8).
% 412707 [hyper:412589,412599,412593,binarycut:412605] equal(multiply(sk_c4,sk_c7),sk_c6).
% 412714 [hyper:412589,412601,412595,binarycut:412607] equal(multiply(sk_c3,sk_c8),sk_c7).
% 412719 [para:412587.1.1,412588.1.1.1,demod:412586] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 412720 [para:412674.1.1,412588.1.1.1,demod:412586] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 412721 [para:412682.1.1,412588.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c5,multiply(sk_c8,X))).
% 412722 [para:412685.1.1,412588.1.1.1,demod:412586] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 412736 [para:412707.1.1,412719.1.2.2,demod:412677] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 412740 [para:412736.1.2,412719.1.2.2,demod:412587] equal(sk_c6,identity).
% 412741 [para:412740.1.1,412674.1.1.1,demod:412586] equal(sk_c5,identity).
% 412748 [para:412741.1.1,412720.1.2.2.1,demod:412586] equal(X,multiply(sk_c6,X)).
% 412753 [para:412721.1.2,412720.1.2.2,demod:412748] equal(multiply(sk_c8,X),X).
% 412767 [hyper:412589,412722,412714,demod:412753,412722,demod:412690,cut:412585] 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: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% Split part used next: -equal(multiply(sk_c8,sk_c7),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,1,87,0,1,13458,50,234,13504,0,234,28069,50,378,28115,0,378,43727,50,531,43773,0,531,59837,50,695,59883,0,695,76546,50,892,76546,40,892,76592,0,892,87047,3,1193,87767,4,1343,88474,1,1493,88474,50,1493,88474,40,1493,88520,0,1493,88859,3,1805,88868,4,1947,88892,5,2094,88892,1,2094,88892,50,2094,88892,40,2094,88938,0,2094,127304,3,3595,127767,4,4345,127922,5,5095,127923,1,5095,127923,50,5096,127923,40,5096,127969,0,5096,150402,3,5848,150970,4,6222,151471,1,6597,151471,50,6597,151471,40,6597,151517,0,6597,162732,3,7350,164114,4,7723,166107,5,8098,166108,1,8098,166108,50,8098,166108,40,8098,166154,0,8098,229406,3,12000,230162,4,13949,230522,1,15899,230522,50,15902,230522,40,15902,230568,0,15902,284798,3,18453,285464,4,19728,285778,5,21003,285779,1,21003,285779,50,21004,285779,40,21004,285825,0,21004,329643,3,22507,330318,4,23255,330839,5,24005,330840,1,24005,330840,50,24006,330840,40,24006,330886,0,24006,339840,3,24767,340971,4,25132,341710,5,25507,341710,1,25507,341710,50,25507,341710,40,25507,341756,0,25507,381061,3,26708,381610,4,27309,382001,1,27908,382001,50,27910,382001,40,27910,382047,0,27910,411117,3,28661,411604,4,29036,411961,1,29411,411961,50,29412,411961,40,29412,411961,40,29412,412002,0,29412,412089,50,29412,412089,30,29412,412089,40,29412,412130,0,29412,412239,50,29412,412239,30,29412,412239,40,29412,412280,0,29418,412389,50,29418,412430,0,29418,412584,50,29419,412584,30,29419,412584,40,29419,412625,0,29419,412766,50,29419,412766,30,29419,412766,40,29419,412807,0,29424,412930,50,29425,412971,0,29425,413150,50,29428,413191,0,29433,413378,50,29437,413419,0,29437,413614,50,29443,413655,0,29443,413856,50,29453,413897,0,29457,414106,50,29474,414147,0,29474,414364,50,29506,414405,0,29510,414632,50,29572,414673,0,29572,414910,50,29700,414910,40,29700,414951,0,29700)
%
%
% START OF PROOF
% 414755 [?] ?
% 414912 [] equal(multiply(identity,X),X).
% 414913 [] equal(multiply(inverse(X),X),identity).
% 414914 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 414915 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 414950 [?] ?
% 414951 [?] ?
% 415007 [input:414950,cut:414915] equal(inverse(sk_c3),sk_c8).
% 415008 [para:415007.1.1,414913.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 415023 [input:414951,cut:414915] equal(multiply(sk_c3,sk_c8),sk_c7).
% 415051 [para:415008.1.1,414914.1.1.1,demod:414912] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 415095 [para:415023.1.1,415051.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 415096 [para:415095.1.2,414915.1.1,cut:414755] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% Split part used next: -equal(inverse(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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,1,87,0,1,13458,50,234,13504,0,234,28069,50,378,28115,0,378,43727,50,531,43773,0,531,59837,50,695,59883,0,695,76546,50,892,76546,40,892,76592,0,892,87047,3,1193,87767,4,1343,88474,1,1493,88474,50,1493,88474,40,1493,88520,0,1493,88859,3,1805,88868,4,1947,88892,5,2094,88892,1,2094,88892,50,2094,88892,40,2094,88938,0,2094,127304,3,3595,127767,4,4345,127922,5,5095,127923,1,5095,127923,50,5096,127923,40,5096,127969,0,5096,150402,3,5848,150970,4,6222,151471,1,6597,151471,50,6597,151471,40,6597,151517,0,6597,162732,3,7350,164114,4,7723,166107,5,8098,166108,1,8098,166108,50,8098,166108,40,8098,166154,0,8098,229406,3,12000,230162,4,13949,230522,1,15899,230522,50,15902,230522,40,15902,230568,0,15902,284798,3,18453,285464,4,19728,285778,5,21003,285779,1,21003,285779,50,21004,285779,40,21004,285825,0,21004,329643,3,22507,330318,4,23255,330839,5,24005,330840,1,24005,330840,50,24006,330840,40,24006,330886,0,24006,339840,3,24767,340971,4,25132,341710,5,25507,341710,1,25507,341710,50,25507,341710,40,25507,341756,0,25507,381061,3,26708,381610,4,27309,382001,1,27908,382001,50,27910,382001,40,27910,382047,0,27910,411117,3,28661,411604,4,29036,411961,1,29411,411961,50,29412,411961,40,29412,411961,40,29412,412002,0,29412,412089,50,29412,412089,30,29412,412089,40,29412,412130,0,29412,412239,50,29412,412239,30,29412,412239,40,29412,412280,0,29418,412389,50,29418,412430,0,29418,412584,50,29419,412584,30,29419,412584,40,29419,412625,0,29419,412766,50,29419,412766,30,29419,412766,40,29419,412807,0,29424,412930,50,29425,412971,0,29425,413150,50,29428,413191,0,29433,413378,50,29437,413419,0,29437,413614,50,29443,413655,0,29443,413856,50,29453,413897,0,29457,414106,50,29474,414147,0,29474,414364,50,29506,414405,0,29510,414632,50,29572,414673,0,29572,414910,50,29700,414910,40,29700,414951,0,29700,415095,50,29700,415095,30,29700,415095,40,29700,415136,0,29700,415259,50,29701,415300,0,29706,415479,50,29709,415520,0,29709,415707,50,29714,415748,0,29714,415943,50,29720,415984,0,29725,416185,50,29734,416226,0,29735,416435,50,29752,416476,0,29756,416693,50,29788,416734,0,29788,416961,50,29859,417002,0,29859,417239,50,29986,417239,40,29986,417280,0,29986)
%
%
% START OF PROOF
% 415257 [?] ?
% 417241 [] equal(multiply(identity,X),X).
% 417242 [] equal(multiply(inverse(X),X),identity).
% 417243 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 417244 [] -equal(inverse(sk_c8),sk_c6).
% 417269 [?] ?
% 417270 [?] ?
% 417271 [?] ?
% 417272 [?] ?
% 417273 [?] ?
% 417274 [?] ?
% 417276 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c5),sk_c6).
% 417292 [input:417270,cut:417244] equal(inverse(sk_c5),sk_c6).
% 417293 [para:417292.1.1,417242.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 417294 [input:417271,cut:417244] equal(inverse(sk_c4),sk_c7).
% 417295 [para:417294.1.1,417242.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 417298 [input:417273,cut:417244] equal(inverse(sk_c3),sk_c8).
% 417313 [input:417269,cut:417244] equal(multiply(sk_c5,sk_c8),sk_c6).
% 417314 [input:417272,cut:417244] equal(multiply(sk_c4,sk_c7),sk_c6).
% 417316 [input:417274,cut:417244] equal(multiply(sk_c3,sk_c8),sk_c7).
% 417335 [para:417242.1.1,417243.1.1.1,demod:417241] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 417381 [para:417293.1.1,417335.1.2.2] equal(sk_c5,multiply(inverse(sk_c6),identity)).
% 417383 [para:417295.1.1,417335.1.2.2] equal(sk_c4,multiply(inverse(sk_c7),identity)).
% 417399 [para:417313.1.1,417335.1.2.2] equal(sk_c8,multiply(inverse(sk_c5),sk_c6)).
% 417400 [para:417314.1.1,417335.1.2.2] equal(sk_c7,multiply(inverse(sk_c4),sk_c6)).
% 417403 [para:417316.1.1,417335.1.2.2] equal(sk_c8,multiply(inverse(sk_c3),sk_c7)).
% 417423 [para:417335.1.2,417335.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 417424 [para:417381.1.2,417243.1.1.1,demod:417241] equal(multiply(sk_c5,X),multiply(inverse(sk_c6),X)).
% 417425 [para:417383.1.2,417243.1.1.1,demod:417241] equal(multiply(sk_c4,X),multiply(inverse(sk_c7),X)).
% 417435 [para:417400.1.2,417335.1.2.2,demod:417423] equal(sk_c6,multiply(sk_c4,sk_c7)).
% 417438 [para:417298.1.1,417403.1.2.1] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 417441 [para:417438.1.2,417276.1.1] equal(inverse(sk_c5),sk_c6) | equal(sk_c8,sk_c6).
% 417449 [para:417441.2.1,417244.1.1.1,cut:415257] equal(inverse(sk_c5),sk_c6).
% 417455 [para:417424.1.2,417242.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 417458 [para:417455.1.1,417335.1.2.2,demod:417449] equal(sk_c6,multiply(sk_c6,identity)).
% 417459 [para:417425.1.2,417242.1.1,demod:417435] equal(sk_c6,identity).
% 417464 [para:417459.1.1,417399.1.2.2,demod:417458,417449] equal(sk_c8,sk_c6).
% 417469 [para:417464.1.1,417244.1.1.1,cut:415257] 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_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,1,87,0,1,13458,50,234,13504,0,234,28069,50,378,28115,0,378,43727,50,531,43773,0,531,59837,50,695,59883,0,695,76546,50,892,76546,40,892,76592,0,892,87047,3,1193,87767,4,1343,88474,1,1493,88474,50,1493,88474,40,1493,88520,0,1493,88859,3,1805,88868,4,1947,88892,5,2094,88892,1,2094,88892,50,2094,88892,40,2094,88938,0,2094,127304,3,3595,127767,4,4345,127922,5,5095,127923,1,5095,127923,50,5096,127923,40,5096,127969,0,5096,150402,3,5848,150970,4,6222,151471,1,6597,151471,50,6597,151471,40,6597,151517,0,6597,162732,3,7350,164114,4,7723,166107,5,8098,166108,1,8098,166108,50,8098,166108,40,8098,166154,0,8098,229406,3,12000,230162,4,13949,230522,1,15899,230522,50,15902,230522,40,15902,230568,0,15902,284798,3,18453,285464,4,19728,285778,5,21003,285779,1,21003,285779,50,21004,285779,40,21004,285825,0,21004,329643,3,22507,330318,4,23255,330839,5,24005,330840,1,24005,330840,50,24006,330840,40,24006,330886,0,24006,339840,3,24767,340971,4,25132,341710,5,25507,341710,1,25507,341710,50,25507,341710,40,25507,341756,0,25507,381061,3,26708,381610,4,27309,382001,1,27908,382001,50,27910,382001,40,27910,382047,0,27910,411117,3,28661,411604,4,29036,411961,1,29411,411961,50,29412,411961,40,29412,411961,40,29412,412002,0,29412,412089,50,29412,412089,30,29412,412089,40,29412,412130,0,29412,412239,50,29412,412239,30,29412,412239,40,29412,412280,0,29418,412389,50,29418,412430,0,29418,412584,50,29419,412584,30,29419,412584,40,29419,412625,0,29419,412766,50,29419,412766,30,29419,412766,40,29419,412807,0,29424,412930,50,29425,412971,0,29425,413150,50,29428,413191,0,29433,413378,50,29437,413419,0,29437,413614,50,29443,413655,0,29443,413856,50,29453,413897,0,29457,414106,50,29474,414147,0,29474,414364,50,29506,414405,0,29510,414632,50,29572,414673,0,29572,414910,50,29700,414910,40,29700,414951,0,29700,415095,50,29700,415095,30,29700,415095,40,29700,415136,0,29700,415259,50,29701,415300,0,29706,415479,50,29709,415520,0,29709,415707,50,29714,415748,0,29714,415943,50,29720,415984,0,29725,416185,50,29734,416226,0,29735,416435,50,29752,416476,0,29756,416693,50,29788,416734,0,29788,416961,50,29859,417002,0,29859,417239,50,29986,417239,40,29986,417280,0,29986,417468,50,29986,417468,30,29986,417468,40,29986,417509,0,29987,417632,50,29987,417673,0,29992,417852,50,29995,417893,0,29995,418080,50,30000,418121,0,30000,418316,50,30006,418357,0,30011,418558,50,30021,418599,0,30021,418808,50,30038,418849,0,30042,419066,50,30074,419107,0,30074,419334,50,30140,419375,0,30140,419612,50,30271,419612,40,30271,419653,0,30271)
%
%
% START OF PROOF
% 419468 [?] ?
% 419614 [] equal(multiply(identity,X),X).
% 419615 [] equal(multiply(inverse(X),X),identity).
% 419616 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 419617 [] -equal(multiply(sk_c6,sk_c7),sk_c8).
% 419638 [?] ?
% 419639 [?] ?
% 419693 [input:419638,cut:419617] equal(inverse(sk_c4),sk_c7).
% 419694 [para:419693.1.1,419615.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 419718 [input:419639,cut:419617] equal(multiply(sk_c4,sk_c7),sk_c6).
% 419726 [para:419615.1.1,419616.1.1.1,demod:419614] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 419741 [para:419694.1.1,419616.1.1.1,demod:419614] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 419782 [para:419718.1.1,419741.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 419825 [para:419741.1.2,419726.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c7),X)).
% 419826 [para:419782.1.2,419726.1.2.2,demod:419825] equal(sk_c6,multiply(sk_c4,sk_c7)).
% 419835 [para:419825.1.2,419615.1.1,demod:419826] equal(sk_c6,identity).
% 419838 [para:419835.1.1,419617.1.1.1,demod:419614,cut:419468] 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: 30990
% derived clauses: 6024897
% kept clauses: 310830
% kept size sum: 413403
% kept mid-nuclei: 67346
% kept new demods: 5583
% forw unit-subs: 2663637
% forw double-subs: 2587063
% forw overdouble-subs: 323401
% backward subs: 12073
% fast unit cutoff: 24905
% full unit cutoff: 0
% dbl unit cutoff: 13104
% real runtime : 306.42
% process. runtime: 302.70
% specific non-discr-tree subsumption statistics:
% tried: 42533800
% length fails: 5264269
% strength fails: 12895090
% predlist fails: 2987487
% aux str. fails: 6111324
% by-lit fails: 6554353
% full subs tried: 2202543
% full subs fail: 2060488
%
% ; 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/GRP308-1+eq_r.in")
%
%------------------------------------------------------------------------------