TSTP Solution File: GRP391-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP391-1 : 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 : art04.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 299.1s
% Output : Assurance 299.1s
% 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/GRP391-1+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_c6),sk_c8) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c6,sk_c7),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(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8).
% -equal(inverse(sk_c6),sk_c8).
% -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(inverse(sk_c6),sk_c8) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c6,sk_c7),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(35,40,0,75,0,1,1566,50,18,1606,0,18,4011,50,45,4051,0,45,6379,50,70,6419,0,70,9081,50,92,9121,0,92,12036,50,119,12076,0,119,15409,50,156,15449,0,156,19118,50,210,19158,0,210,23329,50,300,23369,0,300,27960,50,464,28000,0,464,33177,50,710,33217,0,710,38898,50,1138,38898,40,1138,38938,0,1138,49034,3,1439,49791,4,1589,50522,1,1739,50522,50,1739,50522,40,1739,50562,0,1739,50805,3,2042,50816,4,2204,50824,5,2340,50824,1,2340,50824,50,2340,50824,40,2340,50864,0,2340,76500,3,3842,77549,4,4591,78468,5,5341,78469,1,5341,78469,50,5342,78469,40,5342,78509,0,5342,96427,3,6093,97230,4,6468,97949,1,6843,97949,50,6843,97949,40,6843,97989,0,6843,114169,3,7594,114620,4,7969,115447,1,8344,115447,50,8344,115447,40,8344,115487,0,8344,174651,3,12246,175875,4,14195,176453,1,16145,176453,50,16147,176453,40,16147,176493,0,16147,229590,3,18698,230417,4,19973,231151,5,21249,231152,1,21249,231152,50,21251,231152,40,21251,231192,0,21251,270769,3,22752,271303,4,23502,272291,5,24252,272292,1,24252,272292,50,24253,272292,40,24253,272332,0,24253,287058,3,25006,288049,4,25379,288962,5,25754,288963,1,25754,288963,50,25754,288963,40,25754,289003,0,25754,324625,3,26957,325154,4,27555,325642,1,28155,325642,50,28156,325642,40,28156,325682,0,28156,354880,3,28907,355351,4,29282,355874,5,29657,355875,1,29657,355875,50,29658,355875,40,29658,355875,40,29658,355910,0,29658,355989,50,29658,356024,0,29658)
%
%
% START OF PROOF
% 355991 [] equal(multiply(identity,X),X).
% 355992 [] equal(multiply(inverse(X),X),identity).
% 355993 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 355994 [] -equal(multiply(X,sk_c8),sk_c6) | -equal(inverse(X),sk_c6).
% 355995 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 355996 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 356001 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 356002 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 356007 [?] ?
% 356008 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c6).
% 356013 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 356014 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 356019 [?] ?
% 356020 [] equal(inverse(sk_c6),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 356027 [hyper:355994,356008,binarycut:356007] equal(inverse(sk_c1),sk_c2).
% 356028 [para:356027.1.1,355992.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 356032 [hyper:355994,356020,binarycut:356019] equal(inverse(sk_c6),sk_c8).
% 356033 [para:356032.1.1,355992.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 356039 [hyper:355994,355995,355996] equal(multiply(sk_c6,sk_c7),sk_c8).
% 356045 [hyper:355994,356002,356001] equal(multiply(sk_c2,sk_c7),sk_c8).
% 356051 [hyper:355994,356014,356013] equal(multiply(sk_c1,sk_c2),sk_c8).
% 356052 [para:355992.1.1,355993.1.1.1,demod:355991] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 356053 [para:356028.1.1,355993.1.1.1,demod:355991] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 356054 [para:356033.1.1,355993.1.1.1,demod:355991] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 356055 [para:356039.1.1,355993.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c6,multiply(sk_c7,X))).
% 356056 [para:356045.1.1,355993.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c2,multiply(sk_c7,X))).
% 356057 [para:356051.1.1,355993.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c2,X))).
% 356058 [para:356051.1.1,356053.1.2.2] equal(sk_c2,multiply(sk_c2,sk_c8)).
% 356060 [para:356039.1.1,356054.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 356063 [para:355992.1.1,356052.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 356067 [para:355993.1.1,356052.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 356068 [para:356053.1.2,356052.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 356070 [para:356052.1.2,356052.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 356072 [para:356068.1.2,355992.1.1,demod:356051] equal(sk_c8,identity).
% 356073 [para:356068.1.2,356052.1.2,demod:356057] equal(X,multiply(sk_c8,X)).
% 356076 [para:356072.1.1,356033.1.1.1,demod:355991] equal(sk_c6,identity).
% 356078 [para:356072.1.1,356054.1.2.1,demod:355991] equal(X,multiply(sk_c6,X)).
% 356079 [para:356072.1.1,356060.1.2.1,demod:355991] equal(sk_c7,sk_c8).
% 356083 [para:356076.1.1,356055.1.2.1,demod:355991,356073] equal(X,multiply(sk_c7,X)).
% 356084 [para:356079.1.2,356058.1.2.2,demod:356045] equal(sk_c2,sk_c8).
% 356090 [para:356056.1.2,356057.1.2.2,demod:356073,356083] equal(X,multiply(sk_c1,X)).
% 356092 [para:356084.1.2,356060.1.2.1,demod:356058] equal(sk_c7,sk_c2).
% 356127 [para:356070.1.2,355992.1.1] equal(multiply(X,inverse(X)),identity).
% 356129 [para:356070.1.2,356063.1.2] equal(X,multiply(X,identity)).
% 356138 [para:356129.1.2,356063.1.2] equal(X,inverse(inverse(X))).
% 356140 [para:356127.1.1,356067.1.2.2.2,demod:356129] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 356142 [para:356053.1.2,356140.1.2.1.1,demod:356090] equal(inverse(X),multiply(inverse(X),sk_c2)).
% 356143 [para:356054.1.2,356140.1.2.1.1,demod:356078] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 356150 [para:356142.1.2,356070.1.2,demod:356138] equal(multiply(X,sk_c2),X).
% 356151 [para:356092.1.2,356150.1.1.2] equal(multiply(X,sk_c7),X).
% 356153 [para:356039.1.1,356151.1.1] equal(sk_c8,sk_c6).
% 356157 [para:356143.1.2,356070.1.2,demod:356138] equal(multiply(X,sk_c8),X).
% 356158 [hyper:355994,356157,demod:356032,cut:356153] 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 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c6),sk_c8) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c6,sk_c7),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 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(35,40,0,75,0,1,1566,50,18,1606,0,18,4011,50,45,4051,0,45,6379,50,70,6419,0,70,9081,50,92,9121,0,92,12036,50,119,12076,0,119,15409,50,156,15449,0,156,19118,50,210,19158,0,210,23329,50,300,23369,0,300,27960,50,464,28000,0,464,33177,50,710,33217,0,710,38898,50,1138,38898,40,1138,38938,0,1138,49034,3,1439,49791,4,1589,50522,1,1739,50522,50,1739,50522,40,1739,50562,0,1739,50805,3,2042,50816,4,2204,50824,5,2340,50824,1,2340,50824,50,2340,50824,40,2340,50864,0,2340,76500,3,3842,77549,4,4591,78468,5,5341,78469,1,5341,78469,50,5342,78469,40,5342,78509,0,5342,96427,3,6093,97230,4,6468,97949,1,6843,97949,50,6843,97949,40,6843,97989,0,6843,114169,3,7594,114620,4,7969,115447,1,8344,115447,50,8344,115447,40,8344,115487,0,8344,174651,3,12246,175875,4,14195,176453,1,16145,176453,50,16147,176453,40,16147,176493,0,16147,229590,3,18698,230417,4,19973,231151,5,21249,231152,1,21249,231152,50,21251,231152,40,21251,231192,0,21251,270769,3,22752,271303,4,23502,272291,5,24252,272292,1,24252,272292,50,24253,272292,40,24253,272332,0,24253,287058,3,25006,288049,4,25379,288962,5,25754,288963,1,25754,288963,50,25754,288963,40,25754,289003,0,25754,324625,3,26957,325154,4,27555,325642,1,28155,325642,50,28156,325642,40,28156,325682,0,28156,354880,3,28907,355351,4,29282,355874,5,29657,355875,1,29657,355875,50,29658,355875,40,29658,355875,40,29658,355910,0,29658,355989,50,29658,356024,0,29658,356157,50,29659,356157,30,29659,356157,40,29659,356192,0,29664,356282,50,29664,356317,0,29664)
%
%
% START OF PROOF
% 356284 [] equal(multiply(identity,X),X).
% 356285 [] equal(multiply(inverse(X),X),identity).
% 356286 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 356287 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 356290 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 356291 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c6).
% 356296 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 356297 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c6).
% 356302 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c4),sk_c7).
% 356303 [?] ?
% 356308 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 356309 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c6).
% 356314 [] equal(inverse(sk_c6),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 356315 [?] ?
% 356321 [hyper:356287,356302,binarycut:356303] equal(inverse(sk_c1),sk_c2).
% 356323 [para:356321.1.1,356285.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 356327 [hyper:356287,356314,binarycut:356315] equal(inverse(sk_c6),sk_c8).
% 356328 [para:356327.1.1,356285.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 356338 [hyper:356287,356291,356290] equal(multiply(sk_c6,sk_c7),sk_c8).
% 356351 [hyper:356287,356297,356296] equal(multiply(sk_c2,sk_c7),sk_c8).
% 356355 [hyper:356287,356309,356308] equal(multiply(sk_c1,sk_c2),sk_c8).
% 356356 [para:356285.1.1,356286.1.1.1,demod:356284] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 356357 [para:356323.1.1,356286.1.1.1,demod:356284] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 356358 [para:356328.1.1,356286.1.1.1,demod:356284] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 356359 [para:356338.1.1,356286.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c6,multiply(sk_c7,X))).
% 356360 [para:356351.1.1,356286.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c2,multiply(sk_c7,X))).
% 356361 [para:356355.1.1,356286.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c2,X))).
% 356362 [para:356355.1.1,356357.1.2.2] equal(sk_c2,multiply(sk_c2,sk_c8)).
% 356364 [para:356338.1.1,356358.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 356365 [para:356364.1.2,356286.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c8,X))).
% 356367 [para:356285.1.1,356356.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 356371 [para:356286.1.1,356356.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 356372 [para:356357.1.2,356356.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 356374 [para:356356.1.2,356356.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 356376 [para:356372.1.2,356285.1.1,demod:356355] equal(sk_c8,identity).
% 356377 [para:356372.1.2,356356.1.2,demod:356361] equal(X,multiply(sk_c8,X)).
% 356380 [para:356376.1.1,356328.1.1.1,demod:356284] equal(sk_c6,identity).
% 356383 [para:356376.1.1,356364.1.2.1,demod:356284] equal(sk_c7,sk_c8).
% 356387 [para:356380.1.1,356359.1.2.1,demod:356284,356377] equal(X,multiply(sk_c7,X)).
% 356388 [para:356383.1.2,356362.1.2.2,demod:356351] equal(sk_c2,sk_c8).
% 356394 [para:356360.1.2,356361.1.2.2,demod:356377,356387] equal(X,multiply(sk_c1,X)).
% 356396 [para:356388.1.2,356364.1.2.1,demod:356362] equal(sk_c7,sk_c2).
% 356408 [para:356364.1.2,356365.1.2.2,demod:356377,356387] equal(sk_c8,sk_c7).
% 356431 [para:356374.1.2,356285.1.1] equal(multiply(X,inverse(X)),identity).
% 356433 [para:356374.1.2,356367.1.2] equal(X,multiply(X,identity)).
% 356442 [para:356433.1.2,356367.1.2] equal(X,inverse(inverse(X))).
% 356444 [para:356431.1.1,356371.1.2.2.2,demod:356433] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 356446 [para:356357.1.2,356444.1.2.1.1,demod:356394] equal(inverse(X),multiply(inverse(X),sk_c2)).
% 356454 [para:356446.1.2,356374.1.2,demod:356442] equal(multiply(X,sk_c2),X).
% 356455 [para:356396.1.2,356454.1.1.2] equal(multiply(X,sk_c7),X).
% 356457 [hyper:356287,356455,demod:356327,cut:356408] 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 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c6),sk_c8) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c6,sk_c7),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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,1,1566,50,18,1606,0,18,4011,50,45,4051,0,45,6379,50,70,6419,0,70,9081,50,92,9121,0,92,12036,50,119,12076,0,119,15409,50,156,15449,0,156,19118,50,210,19158,0,210,23329,50,300,23369,0,300,27960,50,464,28000,0,464,33177,50,710,33217,0,710,38898,50,1138,38898,40,1138,38938,0,1138,49034,3,1439,49791,4,1589,50522,1,1739,50522,50,1739,50522,40,1739,50562,0,1739,50805,3,2042,50816,4,2204,50824,5,2340,50824,1,2340,50824,50,2340,50824,40,2340,50864,0,2340,76500,3,3842,77549,4,4591,78468,5,5341,78469,1,5341,78469,50,5342,78469,40,5342,78509,0,5342,96427,3,6093,97230,4,6468,97949,1,6843,97949,50,6843,97949,40,6843,97989,0,6843,114169,3,7594,114620,4,7969,115447,1,8344,115447,50,8344,115447,40,8344,115487,0,8344,174651,3,12246,175875,4,14195,176453,1,16145,176453,50,16147,176453,40,16147,176493,0,16147,229590,3,18698,230417,4,19973,231151,5,21249,231152,1,21249,231152,50,21251,231152,40,21251,231192,0,21251,270769,3,22752,271303,4,23502,272291,5,24252,272292,1,24252,272292,50,24253,272292,40,24253,272332,0,24253,287058,3,25006,288049,4,25379,288962,5,25754,288963,1,25754,288963,50,25754,288963,40,25754,289003,0,25754,324625,3,26957,325154,4,27555,325642,1,28155,325642,50,28156,325642,40,28156,325682,0,28156,354880,3,28907,355351,4,29282,355874,5,29657,355875,1,29657,355875,50,29658,355875,40,29658,355875,40,29658,355910,0,29658,355989,50,29658,356024,0,29658,356157,50,29659,356157,30,29659,356157,40,29659,356192,0,29664,356282,50,29664,356317,0,29664,356456,50,29665,356456,30,29665,356456,40,29665,356491,0,29665)
%
%
% START OF PROOF
% 356458 [] equal(multiply(identity,X),X).
% 356459 [] equal(multiply(inverse(X),X),identity).
% 356460 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 356461 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 356466 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 356467 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 356478 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c3),sk_c8).
% 356479 [?] ?
% 356484 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 356485 [] equal(multiply(sk_c1,sk_c2),sk_c8) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 356490 [] equal(inverse(sk_c6),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 356491 [?] ?
% 356497 [hyper:356461,356478,binarycut:356479] equal(inverse(sk_c1),sk_c2).
% 356498 [para:356497.1.1,356459.1.1.1] equal(multiply(sk_c2,sk_c1),identity).
% 356509 [hyper:356461,356490,binarycut:356491] equal(inverse(sk_c6),sk_c8).
% 356512 [para:356509.1.1,356459.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 356528 [hyper:356461,356467,356466] equal(multiply(sk_c6,sk_c7),sk_c8).
% 356542 [hyper:356461,356485,356484] equal(multiply(sk_c1,sk_c2),sk_c8).
% 356543 [para:356459.1.1,356460.1.1.1,demod:356458] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 356544 [para:356498.1.1,356460.1.1.1,demod:356458] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 356545 [para:356512.1.1,356460.1.1.1,demod:356458] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 356546 [para:356528.1.1,356460.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c6,multiply(sk_c7,X))).
% 356548 [para:356542.1.1,356460.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c2,X))).
% 356551 [para:356528.1.1,356545.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 356552 [para:356551.1.2,356460.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c8,X))).
% 356557 [para:356544.1.2,356543.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c2),X)).
% 356560 [para:356557.1.2,356459.1.1,demod:356542] equal(sk_c8,identity).
% 356561 [para:356557.1.2,356543.1.2,demod:356548] equal(X,multiply(sk_c8,X)).
% 356565 [para:356560.1.1,356512.1.1.1,demod:356458] equal(sk_c6,identity).
% 356571 [para:356565.1.1,356509.1.1.1] equal(inverse(identity),sk_c8).
% 356572 [para:356565.1.1,356546.1.2.1,demod:356458,356561] equal(X,multiply(sk_c7,X)).
% 356591 [para:356551.1.2,356552.1.2.2,demod:356561,356572] equal(sk_c8,sk_c7).
% 356595 [hyper:356461,356571,demod:356458,cut:356591] 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(inverse(sk_c6),sk_c8) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c6,sk_c7),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(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: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,1,1566,50,18,1606,0,18,4011,50,45,4051,0,45,6379,50,70,6419,0,70,9081,50,92,9121,0,92,12036,50,119,12076,0,119,15409,50,156,15449,0,156,19118,50,210,19158,0,210,23329,50,300,23369,0,300,27960,50,464,28000,0,464,33177,50,710,33217,0,710,38898,50,1138,38898,40,1138,38938,0,1138,49034,3,1439,49791,4,1589,50522,1,1739,50522,50,1739,50522,40,1739,50562,0,1739,50805,3,2042,50816,4,2204,50824,5,2340,50824,1,2340,50824,50,2340,50824,40,2340,50864,0,2340,76500,3,3842,77549,4,4591,78468,5,5341,78469,1,5341,78469,50,5342,78469,40,5342,78509,0,5342,96427,3,6093,97230,4,6468,97949,1,6843,97949,50,6843,97949,40,6843,97989,0,6843,114169,3,7594,114620,4,7969,115447,1,8344,115447,50,8344,115447,40,8344,115487,0,8344,174651,3,12246,175875,4,14195,176453,1,16145,176453,50,16147,176453,40,16147,176493,0,16147,229590,3,18698,230417,4,19973,231151,5,21249,231152,1,21249,231152,50,21251,231152,40,21251,231192,0,21251,270769,3,22752,271303,4,23502,272291,5,24252,272292,1,24252,272292,50,24253,272292,40,24253,272332,0,24253,287058,3,25006,288049,4,25379,288962,5,25754,288963,1,25754,288963,50,25754,288963,40,25754,289003,0,25754,324625,3,26957,325154,4,27555,325642,1,28155,325642,50,28156,325642,40,28156,325682,0,28156,354880,3,28907,355351,4,29282,355874,5,29657,355875,1,29657,355875,50,29658,355875,40,29658,355875,40,29658,355910,0,29658,355989,50,29658,356024,0,29658,356157,50,29659,356157,30,29659,356157,40,29659,356192,0,29664,356282,50,29664,356317,0,29664,356456,50,29665,356456,30,29665,356456,40,29665,356491,0,29665,356594,50,29666,356594,30,29666,356594,40,29666,356629,0,29671)
%
%
% START OF PROOF
% 356596 [] equal(multiply(identity,X),X).
% 356597 [] equal(multiply(inverse(X),X),identity).
% 356598 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 356599 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,X),sk_c8) | -equal(inverse(Y),X).
% 356606 [?] ?
% 356607 [?] ?
% 356608 [?] ?
% 356609 [?] ?
% 356610 [?] ?
% 356611 [?] ?
% 356612 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c2).
% 356613 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c5),sk_c6).
% 356614 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c4),sk_c7).
% 356615 [] equal(multiply(sk_c4,sk_c7),sk_c6) | equal(inverse(sk_c1),sk_c2).
% 356616 [] equal(inverse(sk_c1),sk_c2) | equal(inverse(sk_c3),sk_c8).
% 356617 [] equal(multiply(sk_c3,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c2).
% 356618 [?] ?
% 356619 [?] ?
% 356620 [?] ?
% 356621 [?] ?
% 356622 [?] ?
% 356623 [?] ?
% 356634 [hyper:356599,356613,binarycut:356619,binarycut:356607] equal(inverse(sk_c5),sk_c6).
% 356637 [para:356634.1.1,356597.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 356641 [hyper:356599,356614,binarycut:356620,binarycut:356608] equal(inverse(sk_c4),sk_c7).
% 356645 [para:356641.1.1,356597.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 356649 [hyper:356599,356616,binarycut:356622,binarycut:356610] equal(inverse(sk_c3),sk_c8).
% 356662 [hyper:356599,356612,binarycut:356618,binarycut:356606] equal(multiply(sk_c5,sk_c8),sk_c6).
% 356670 [hyper:356599,356615,binarycut:356621,binarycut:356609] equal(multiply(sk_c4,sk_c7),sk_c6).
% 356673 [hyper:356599,356617,binarycut:356623,binarycut:356611] equal(multiply(sk_c3,sk_c8),sk_c7).
% 356674 [para:356597.1.1,356598.1.1.1,demod:356596] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 356676 [para:356645.1.1,356598.1.1.1,demod:356596] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 356687 [para:356670.1.1,356676.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 356694 [para:356673.1.1,356674.1.2.2,demod:356649] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 356699 [para:356694.1.2,356674.1.2.2,demod:356597] equal(sk_c7,identity).
% 356700 [para:356699.1.1,356645.1.1.1,demod:356596] equal(sk_c4,identity).
% 356703 [para:356699.1.1,356687.1.2.1,demod:356596] equal(sk_c7,sk_c6).
% 356705 [para:356700.1.1,356641.1.1.1] equal(inverse(identity),sk_c7).
% 356707 [para:356700.1.1,356676.1.2.2.1,demod:356596] equal(X,multiply(sk_c7,X)).
% 356708 [para:356703.1.2,356637.1.1.1,demod:356707] equal(sk_c5,identity).
% 356716 [para:356708.1.1,356662.1.1.1,demod:356596] equal(sk_c8,sk_c6).
% 356723 [para:356716.1.2,356687.1.2.2,demod:356707] equal(sk_c7,sk_c8).
% 356728 [hyper:356599,356705,demod:356707,356596,cut:356723,cut:356723] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c6),sk_c8) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c6,sk_c7),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_c6),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(35,40,0,75,0,1,1566,50,18,1606,0,18,4011,50,45,4051,0,45,6379,50,70,6419,0,70,9081,50,92,9121,0,92,12036,50,119,12076,0,119,15409,50,156,15449,0,156,19118,50,210,19158,0,210,23329,50,300,23369,0,300,27960,50,464,28000,0,464,33177,50,710,33217,0,710,38898,50,1138,38898,40,1138,38938,0,1138,49034,3,1439,49791,4,1589,50522,1,1739,50522,50,1739,50522,40,1739,50562,0,1739,50805,3,2042,50816,4,2204,50824,5,2340,50824,1,2340,50824,50,2340,50824,40,2340,50864,0,2340,76500,3,3842,77549,4,4591,78468,5,5341,78469,1,5341,78469,50,5342,78469,40,5342,78509,0,5342,96427,3,6093,97230,4,6468,97949,1,6843,97949,50,6843,97949,40,6843,97989,0,6843,114169,3,7594,114620,4,7969,115447,1,8344,115447,50,8344,115447,40,8344,115487,0,8344,174651,3,12246,175875,4,14195,176453,1,16145,176453,50,16147,176453,40,16147,176493,0,16147,229590,3,18698,230417,4,19973,231151,5,21249,231152,1,21249,231152,50,21251,231152,40,21251,231192,0,21251,270769,3,22752,271303,4,23502,272291,5,24252,272292,1,24252,272292,50,24253,272292,40,24253,272332,0,24253,287058,3,25006,288049,4,25379,288962,5,25754,288963,1,25754,288963,50,25754,288963,40,25754,289003,0,25754,324625,3,26957,325154,4,27555,325642,1,28155,325642,50,28156,325642,40,28156,325682,0,28156,354880,3,28907,355351,4,29282,355874,5,29657,355875,1,29657,355875,50,29658,355875,40,29658,355875,40,29658,355910,0,29658,355989,50,29658,356024,0,29658,356157,50,29659,356157,30,29659,356157,40,29659,356192,0,29664,356282,50,29664,356317,0,29664,356456,50,29665,356456,30,29665,356456,40,29665,356491,0,29665,356594,50,29666,356594,30,29666,356594,40,29666,356629,0,29671,356727,50,29672,356727,30,29672,356727,40,29672,356762,0,29672,356896,50,29673,356931,0,29678,357131,50,29681,357166,0,29681,357383,50,29685,357418,0,29685,357648,50,29691,357683,0,29696,357919,50,29704,357954,0,29704,358198,50,29719,358233,0,29724,358485,50,29754,358520,0,29754,358782,50,29818,358817,0,29818,359089,50,29938,359089,40,29938,359124,0,29938)
%
%
% START OF PROOF
% 358925 [?] ?
% 359091 [] equal(multiply(identity,X),X).
% 359092 [] equal(multiply(inverse(X),X),identity).
% 359093 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 359094 [] -equal(inverse(sk_c6),sk_c8).
% 359121 [?] ?
% 359122 [?] ?
% 359137 [input:359121,cut:359094] equal(inverse(sk_c4),sk_c7).
% 359138 [para:359137.1.1,359092.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 359160 [input:359122,cut:359094] equal(multiply(sk_c4,sk_c7),sk_c6).
% 359173 [para:359092.1.1,359093.1.1.1,demod:359091] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 359216 [para:359138.1.1,359173.1.2.2] equal(sk_c4,multiply(inverse(sk_c7),identity)).
% 359235 [para:359160.1.1,359173.1.2.2] equal(sk_c7,multiply(inverse(sk_c4),sk_c6)).
% 359249 [para:359173.1.2,359173.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 359251 [para:359216.1.2,359093.1.1.1,demod:359091] equal(multiply(sk_c4,X),multiply(inverse(sk_c7),X)).
% 359262 [para:359235.1.2,359173.1.2.2,demod:359249] equal(sk_c6,multiply(sk_c4,sk_c7)).
% 359413 [para:359251.1.2,359092.1.1,demod:359262] equal(sk_c6,identity).
% 359416 [para:359413.1.1,359094.1.1.1,cut:358925] 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(inverse(sk_c6),sk_c8) | -equal(multiply(X,Y),sk_c8) | -equal(inverse(X),Y) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(multiply(sk_c6,sk_c7),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 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(35,40,0,75,0,1,1566,50,18,1606,0,18,4011,50,45,4051,0,45,6379,50,70,6419,0,70,9081,50,92,9121,0,92,12036,50,119,12076,0,119,15409,50,156,15449,0,156,19118,50,210,19158,0,210,23329,50,300,23369,0,300,27960,50,464,28000,0,464,33177,50,710,33217,0,710,38898,50,1138,38898,40,1138,38938,0,1138,49034,3,1439,49791,4,1589,50522,1,1739,50522,50,1739,50522,40,1739,50562,0,1739,50805,3,2042,50816,4,2204,50824,5,2340,50824,1,2340,50824,50,2340,50824,40,2340,50864,0,2340,76500,3,3842,77549,4,4591,78468,5,5341,78469,1,5341,78469,50,5342,78469,40,5342,78509,0,5342,96427,3,6093,97230,4,6468,97949,1,6843,97949,50,6843,97949,40,6843,97989,0,6843,114169,3,7594,114620,4,7969,115447,1,8344,115447,50,8344,115447,40,8344,115487,0,8344,174651,3,12246,175875,4,14195,176453,1,16145,176453,50,16147,176453,40,16147,176493,0,16147,229590,3,18698,230417,4,19973,231151,5,21249,231152,1,21249,231152,50,21251,231152,40,21251,231192,0,21251,270769,3,22752,271303,4,23502,272291,5,24252,272292,1,24252,272292,50,24253,272292,40,24253,272332,0,24253,287058,3,25006,288049,4,25379,288962,5,25754,288963,1,25754,288963,50,25754,288963,40,25754,289003,0,25754,324625,3,26957,325154,4,27555,325642,1,28155,325642,50,28156,325642,40,28156,325682,0,28156,354880,3,28907,355351,4,29282,355874,5,29657,355875,1,29657,355875,50,29658,355875,40,29658,355875,40,29658,355910,0,29658,355989,50,29658,356024,0,29658,356157,50,29659,356157,30,29659,356157,40,29659,356192,0,29664,356282,50,29664,356317,0,29664,356456,50,29665,356456,30,29665,356456,40,29665,356491,0,29665,356594,50,29666,356594,30,29666,356594,40,29666,356629,0,29671,356727,50,29672,356727,30,29672,356727,40,29672,356762,0,29672,356896,50,29673,356931,0,29678,357131,50,29681,357166,0,29681,357383,50,29685,357418,0,29685,357648,50,29691,357683,0,29696,357919,50,29704,357954,0,29704,358198,50,29719,358233,0,29724,358485,50,29754,358520,0,29754,358782,50,29818,358817,0,29818,359089,50,29938,359089,40,29938,359124,0,29938,359415,50,29939,359415,30,29939,359415,40,29939,359450,0,29939,359585,50,29940,359620,0,29945,359819,50,29948,359854,0,29948,360070,50,29952,360105,0,29953,360334,50,29958,360369,0,29963,360604,50,29972,360639,0,29972,360882,50,29988,360917,0,29992,361168,50,30022,361203,0,30022,361464,50,30086,361499,0,30086,361770,50,30205,361770,40,30205,361805,0,30206)
%
%
% START OF PROOF
% 361608 [?] ?
% 361772 [] equal(multiply(identity,X),X).
% 361773 [] equal(multiply(inverse(X),X),identity).
% 361774 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 361775 [] -equal(multiply(sk_c6,sk_c7),sk_c8).
% 361776 [?] ?
% 361777 [?] ?
% 361780 [?] ?
% 361781 [?] ?
% 361809 [input:361776,cut:361775] equal(multiply(sk_c5,sk_c8),sk_c6).
% 361825 [input:361777,cut:361775] equal(inverse(sk_c5),sk_c6).
% 361826 [para:361825.1.1,361773.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 361829 [input:361780,cut:361775] equal(inverse(sk_c3),sk_c8).
% 361830 [para:361829.1.1,361773.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 361839 [input:361781,cut:361775] equal(multiply(sk_c3,sk_c8),sk_c7).
% 361867 [para:361773.1.1,361774.1.1.1,demod:361772] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 361868 [para:361809.1.1,361774.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c5,multiply(sk_c8,X))).
% 361869 [para:361826.1.1,361774.1.1.1,demod:361772] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 361871 [para:361830.1.1,361774.1.1.1,demod:361772] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 361896 [para:361809.1.1,361869.1.2.2] equal(sk_c8,multiply(sk_c6,sk_c6)).
% 361900 [para:361839.1.1,361871.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 361936 [para:361869.1.2,361867.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c6),X)).
% 361937 [para:361896.1.2,361867.1.2.2,demod:361936] equal(sk_c6,multiply(sk_c5,sk_c8)).
% 361953 [para:361900.1.2,361868.1.2.2,demod:361937] equal(multiply(sk_c6,sk_c7),sk_c6).
% 361954 [para:361953.1.1,361775.1.1,cut:361608] 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: 33599
% derived clauses: 5657185
% kept clauses: 285491
% kept size sum: 878510
% kept mid-nuclei: 28985
% kept new demods: 4597
% forw unit-subs: 1673147
% forw double-subs: 3208460
% forw overdouble-subs: 413589
% backward subs: 11336
% fast unit cutoff: 30962
% full unit cutoff: 0
% dbl unit cutoff: 14769
% real runtime : 303.28
% process. runtime: 302.6
% specific non-discr-tree subsumption statistics:
% tried: 24778181
% length fails: 3304219
% strength fails: 7213458
% predlist fails: 1506189
% aux str. fails: 2610211
% by-lit fails: 4252273
% full subs tried: 1900091
% full subs fail: 1703556
%
% ; 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/GRP391-1+eq_r.in")
%
%------------------------------------------------------------------------------