TSTP Solution File: GRP341-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP341-1 : 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 288.6s
% Output : Assurance 288.6s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP341-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 23)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 23)
% (binary-posweight-lex-big-order 30 #f 3 23)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(Z,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c5),sk_c6) | -equal(multiply(U,sk_c6),sk_c5) | -equal(inverse(U),sk_c6) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c7).
% was split for some strategies as:
% -equal(multiply(U,sk_c6),sk_c5) | -equal(inverse(U),sk_c6).
% -equal(multiply(Z,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7).
% -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6).
% -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7).
% -equal(multiply(sk_c6,sk_c7),sk_c5).
% -equal(inverse(sk_c5),sk_c6).
% -equal(multiply(sk_c5,sk_c7),sk_c6).
% -equal(multiply(sk_c5,sk_c6),sk_c7).
%
% Starting a split proof attempt with 8 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(Z,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c5),sk_c6) | -equal(multiply(U,sk_c6),sk_c5) | -equal(inverse(U),sk_c6) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c7).
% Split part used next: -equal(multiply(U,sk_c6),sk_c5) | -equal(inverse(U),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,1,85,0,1,1169,50,10,1214,0,10,2313,50,19,2358,0,19,3468,50,31,3513,0,31,4630,50,40,4675,0,40,5799,50,51,5844,0,51,6976,50,69,7021,0,70,8162,50,102,8207,0,103,9358,50,169,9403,0,169,10565,50,297,10610,0,297,11784,50,514,11829,0,514,13016,50,939,13016,40,939,13061,0,939,23549,3,1240,24275,4,1390,24985,5,1540,24986,1,1540,24986,50,1540,24986,40,1540,25031,0,1540,25256,3,1849,25265,4,2003,25272,5,2141,25272,1,2141,25272,50,2141,25272,40,2141,25317,0,2141,54374,3,3645,55166,4,4392,56177,1,5142,56177,50,5143,56177,40,5143,56222,0,5143,72428,3,5898,73343,4,6269,74142,1,6644,74142,50,6644,74142,40,6644,74187,0,6644,81359,3,7409,82768,4,7770,83962,1,8145,83962,50,8145,83962,40,8145,84007,0,8145,124469,3,12055,126395,4,13996,127754,1,15946,127754,50,15947,127754,40,15947,127799,0,15947,164307,3,18498,165757,4,19773,166591,1,21048,166591,50,21049,166591,40,21049,166636,0,21049,195188,3,22550,196365,4,23300,197101,5,24050,197102,1,24050,197102,50,24051,197102,40,24051,197147,0,24051,205424,3,24831,206257,4,25181,206392,5,25552,206392,1,25552,206392,50,25552,206392,40,25552,206437,0,25552,229505,3,26759,230575,4,27353,231049,5,27953,231050,1,27953,231050,50,27954,231050,40,27954,231095,0,27954,250104,3,28705,250893,4,29080,251180,1,29455,251180,50,29455,251180,40,29455,251180,40,29455,251220,0,29455)
%
%
% START OF PROOF
% 251181 [] equal(X,X).
% 251182 [] equal(multiply(identity,X),X).
% 251183 [] equal(multiply(inverse(X),X),identity).
% 251184 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 251185 [] -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6).
% 251188 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 251189 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(multiply(sk_c4,sk_c6),sk_c5).
% 251195 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 251196 [?] ?
% 251202 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 251203 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(multiply(sk_c4,sk_c6),sk_c5).
% 251209 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 251210 [?] ?
% 251216 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c4),sk_c6).
% 251217 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(multiply(sk_c4,sk_c6),sk_c5).
% 251224 [hyper:251185,251195,binarycut:251196] equal(inverse(sk_c2),sk_c6).
% 251226 [para:251224.1.1,251183.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 251230 [hyper:251185,251209,binarycut:251210] equal(inverse(sk_c1),sk_c7).
% 251231 [para:251230.1.1,251183.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 251257 [hyper:251185,251189,251188] equal(multiply(sk_c2,sk_c5),sk_c6).
% 251262 [hyper:251185,251203,251202] equal(multiply(sk_c1,sk_c6),sk_c7).
% 251267 [hyper:251185,251217,251216] equal(multiply(sk_c6,sk_c7),sk_c5).
% 251268 [para:251183.1.1,251184.1.1.1,demod:251182] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 251271 [para:251257.1.1,251184.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c2,multiply(sk_c5,X))).
% 251275 [para:251226.1.1,251268.1.2.2] equal(sk_c2,multiply(inverse(sk_c6),identity)).
% 251276 [para:251231.1.1,251268.1.2.2] equal(sk_c1,multiply(inverse(sk_c7),identity)).
% 251277 [para:251257.1.1,251268.1.2.2,demod:251224] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 251278 [para:251262.1.1,251268.1.2.2,demod:251230] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 251279 [para:251267.1.1,251268.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 251281 [para:251277.1.2,251268.1.2.2,demod:251279] equal(sk_c6,sk_c7).
% 251282 [para:251281.1.1,251226.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 251284 [para:251281.1.1,251267.1.1.1,demod:251278] equal(sk_c6,sk_c5).
% 251286 [para:251284.1.1,251226.1.1.1] equal(multiply(sk_c5,sk_c2),identity).
% 251287 [para:251284.1.1,251262.1.1.2] equal(multiply(sk_c1,sk_c5),sk_c7).
% 251288 [para:251284.1.1,251267.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 251289 [para:251284.1.1,251277.1.2.1] equal(sk_c5,multiply(sk_c5,sk_c6)).
% 251291 [para:251284.1.1,251281.1.1] equal(sk_c5,sk_c7).
% 251297 [para:251282.1.1,251268.1.2.2,demod:251276] equal(sk_c2,sk_c1).
% 251310 [para:251287.1.1,251184.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c1,multiply(sk_c5,X))).
% 251312 [para:251297.1.1,251271.1.2.1,demod:251310] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 251313 [para:251286.1.1,251271.1.2.2,demod:251226] equal(identity,multiply(sk_c2,identity)).
% 251315 [para:251288.1.1,251268.1.2.2,demod:251183] equal(sk_c7,identity).
% 251317 [para:251315.1.1,251231.1.1.1,demod:251182] equal(sk_c1,identity).
% 251318 [para:251315.1.1,251267.1.1.2,demod:251312] equal(multiply(sk_c7,identity),sk_c5).
% 251319 [para:251315.1.1,251291.1.2] equal(sk_c5,identity).
% 251325 [para:251317.1.1,251230.1.1.1] equal(inverse(identity),sk_c7).
% 251327 [para:251319.1.1,251257.1.1.2,demod:251313] equal(identity,sk_c6).
% 251332 [para:251327.1.2,251275.1.2.1.1,demod:251318,251325] equal(sk_c2,sk_c5).
% 251333 [para:251332.1.1,251224.1.1.1] equal(inverse(sk_c5),sk_c6).
% 251337 [hyper:251185,251333,demod:251289,cut:251181] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(Z,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c5),sk_c6) | -equal(multiply(U,sk_c6),sk_c5) | -equal(inverse(U),sk_c6) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c7).
% Split part used next: -equal(multiply(Z,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,1,85,0,1,1169,50,10,1214,0,10,2313,50,19,2358,0,19,3468,50,31,3513,0,31,4630,50,40,4675,0,40,5799,50,51,5844,0,51,6976,50,69,7021,0,70,8162,50,102,8207,0,103,9358,50,169,9403,0,169,10565,50,297,10610,0,297,11784,50,514,11829,0,514,13016,50,939,13016,40,939,13061,0,939,23549,3,1240,24275,4,1390,24985,5,1540,24986,1,1540,24986,50,1540,24986,40,1540,25031,0,1540,25256,3,1849,25265,4,2003,25272,5,2141,25272,1,2141,25272,50,2141,25272,40,2141,25317,0,2141,54374,3,3645,55166,4,4392,56177,1,5142,56177,50,5143,56177,40,5143,56222,0,5143,72428,3,5898,73343,4,6269,74142,1,6644,74142,50,6644,74142,40,6644,74187,0,6644,81359,3,7409,82768,4,7770,83962,1,8145,83962,50,8145,83962,40,8145,84007,0,8145,124469,3,12055,126395,4,13996,127754,1,15946,127754,50,15947,127754,40,15947,127799,0,15947,164307,3,18498,165757,4,19773,166591,1,21048,166591,50,21049,166591,40,21049,166636,0,21049,195188,3,22550,196365,4,23300,197101,5,24050,197102,1,24050,197102,50,24051,197102,40,24051,197147,0,24051,205424,3,24831,206257,4,25181,206392,5,25552,206392,1,25552,206392,50,25552,206392,40,25552,206437,0,25552,229505,3,26759,230575,4,27353,231049,5,27953,231050,1,27953,231050,50,27954,231050,40,27954,231095,0,27954,250104,3,28705,250893,4,29080,251180,1,29455,251180,50,29455,251180,40,29455,251180,40,29455,251220,0,29455,251336,50,29455,251336,30,29455,251336,40,29455,251376,0,29455)
%
%
% START OF PROOF
% 251338 [] equal(multiply(identity,X),X).
% 251339 [] equal(multiply(inverse(X),X),identity).
% 251340 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 251341 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 251347 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 251348 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(multiply(sk_c3,sk_c7),sk_c6).
% 251354 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 251355 [?] ?
% 251361 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 251362 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(multiply(sk_c3,sk_c7),sk_c6).
% 251368 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 251369 [?] ?
% 251375 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c3),sk_c7).
% 251376 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(multiply(sk_c3,sk_c7),sk_c6).
% 251382 [hyper:251341,251354,binarycut:251355] equal(inverse(sk_c2),sk_c6).
% 251383 [para:251382.1.1,251339.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 251394 [hyper:251341,251368,binarycut:251369] equal(inverse(sk_c1),sk_c7).
% 251397 [para:251394.1.1,251339.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 251420 [hyper:251341,251348,251347] equal(multiply(sk_c2,sk_c5),sk_c6).
% 251428 [hyper:251341,251362,251361] equal(multiply(sk_c1,sk_c6),sk_c7).
% 251436 [hyper:251341,251376,251375] equal(multiply(sk_c6,sk_c7),sk_c5).
% 251437 [para:251339.1.1,251340.1.1.1,demod:251338] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 251445 [para:251397.1.1,251437.1.2.2] equal(sk_c1,multiply(inverse(sk_c7),identity)).
% 251446 [para:251420.1.1,251437.1.2.2,demod:251382] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 251447 [para:251428.1.1,251437.1.2.2,demod:251394] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 251448 [para:251436.1.1,251437.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 251450 [para:251446.1.2,251437.1.2.2,demod:251448] equal(sk_c6,sk_c7).
% 251451 [para:251450.1.1,251383.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 251453 [para:251450.1.1,251436.1.1.1,demod:251447] equal(sk_c6,sk_c5).
% 251457 [para:251453.1.1,251436.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 251466 [para:251451.1.1,251437.1.2.2,demod:251445] equal(sk_c2,sk_c1).
% 251467 [para:251466.1.1,251382.1.1.1,demod:251394] equal(sk_c7,sk_c6).
% 251484 [para:251457.1.1,251437.1.2.2,demod:251339] equal(sk_c7,identity).
% 251486 [para:251484.1.1,251397.1.1.1,demod:251338] equal(sk_c1,identity).
% 251494 [para:251486.1.1,251394.1.1.1] equal(inverse(identity),sk_c7).
% 251501 [hyper:251341,251494,demod:251338,cut:251467] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(Z,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c5),sk_c6) | -equal(multiply(U,sk_c6),sk_c5) | -equal(inverse(U),sk_c6) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c7).
% Split part used next: -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,1,85,0,1,1169,50,10,1214,0,10,2313,50,19,2358,0,19,3468,50,31,3513,0,31,4630,50,40,4675,0,40,5799,50,51,5844,0,51,6976,50,69,7021,0,70,8162,50,102,8207,0,103,9358,50,169,9403,0,169,10565,50,297,10610,0,297,11784,50,514,11829,0,514,13016,50,939,13016,40,939,13061,0,939,23549,3,1240,24275,4,1390,24985,5,1540,24986,1,1540,24986,50,1540,24986,40,1540,25031,0,1540,25256,3,1849,25265,4,2003,25272,5,2141,25272,1,2141,25272,50,2141,25272,40,2141,25317,0,2141,54374,3,3645,55166,4,4392,56177,1,5142,56177,50,5143,56177,40,5143,56222,0,5143,72428,3,5898,73343,4,6269,74142,1,6644,74142,50,6644,74142,40,6644,74187,0,6644,81359,3,7409,82768,4,7770,83962,1,8145,83962,50,8145,83962,40,8145,84007,0,8145,124469,3,12055,126395,4,13996,127754,1,15946,127754,50,15947,127754,40,15947,127799,0,15947,164307,3,18498,165757,4,19773,166591,1,21048,166591,50,21049,166591,40,21049,166636,0,21049,195188,3,22550,196365,4,23300,197101,5,24050,197102,1,24050,197102,50,24051,197102,40,24051,197147,0,24051,205424,3,24831,206257,4,25181,206392,5,25552,206392,1,25552,206392,50,25552,206392,40,25552,206437,0,25552,229505,3,26759,230575,4,27353,231049,5,27953,231050,1,27953,231050,50,27954,231050,40,27954,231095,0,27954,250104,3,28705,250893,4,29080,251180,1,29455,251180,50,29455,251180,40,29455,251180,40,29455,251220,0,29455,251336,50,29455,251336,30,29455,251336,40,29455,251376,0,29455,251500,50,29455,251500,30,29455,251500,40,29455,251540,0,29457)
%
%
% START OF PROOF
% 251502 [] equal(multiply(identity,X),X).
% 251503 [] equal(multiply(inverse(X),X),identity).
% 251504 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 251505 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 251506 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 251507 [?] ?
% 251508 [?] ?
% 251509 [?] ?
% 251510 [?] ?
% 251511 [?] ?
% 251512 [?] ?
% 251513 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c6).
% 251514 [] equal(multiply(sk_c5,sk_c7),sk_c6) | equal(inverse(sk_c2),sk_c6).
% 251515 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 251516 [] equal(multiply(sk_c4,sk_c6),sk_c5) | equal(inverse(sk_c2),sk_c6).
% 251517 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c5),sk_c6).
% 251518 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 251519 [] equal(multiply(sk_c3,sk_c7),sk_c6) | equal(inverse(sk_c2),sk_c6).
% 251543 [hyper:251505,251515,binarycut:251508] equal(inverse(sk_c4),sk_c6).
% 251546 [para:251543.1.1,251503.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 251550 [hyper:251505,251517,binarycut:251510] equal(inverse(sk_c5),sk_c6).
% 251554 [para:251550.1.1,251503.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 251558 [hyper:251505,251518,binarycut:251511] equal(inverse(sk_c3),sk_c7).
% 251565 [hyper:251505,251513,binarycut:251506] equal(multiply(sk_c5,sk_c6),sk_c7).
% 251568 [hyper:251505,251514,binarycut:251507] equal(multiply(sk_c5,sk_c7),sk_c6).
% 251571 [hyper:251505,251516,binarycut:251509] equal(multiply(sk_c4,sk_c6),sk_c5).
% 251574 [hyper:251505,251519,binarycut:251512] equal(multiply(sk_c3,sk_c7),sk_c6).
% 251575 [para:251503.1.1,251504.1.1.1,demod:251502] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 251576 [para:251546.1.1,251504.1.1.1,demod:251502] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 251583 [para:251571.1.1,251576.1.2.2,demod:251554] equal(sk_c6,identity).
% 251584 [para:251583.1.1,251546.1.1.1,demod:251502] equal(sk_c4,identity).
% 251592 [para:251584.1.1,251576.1.2.2.1,demod:251502] equal(X,multiply(sk_c6,X)).
% 251593 [para:251546.1.1,251575.1.2.2] equal(sk_c4,multiply(inverse(sk_c6),identity)).
% 251594 [para:251554.1.1,251575.1.2.2,demod:251593] equal(sk_c5,sk_c4).
% 251597 [para:251568.1.1,251575.1.2.2,demod:251592,251550] equal(sk_c7,sk_c6).
% 251605 [para:251594.1.2,251571.1.1.1,demod:251565] equal(sk_c7,sk_c5).
% 251614 [para:251605.1.1,251574.1.1.2] equal(multiply(sk_c3,sk_c5),sk_c6).
% 251627 [hyper:251505,251614,demod:251558,cut:251597] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(Z,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c5),sk_c6) | -equal(multiply(U,sk_c6),sk_c5) | -equal(inverse(U),sk_c6) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c7).
% Split part used next: -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,1,85,0,1,1169,50,10,1214,0,10,2313,50,19,2358,0,19,3468,50,31,3513,0,31,4630,50,40,4675,0,40,5799,50,51,5844,0,51,6976,50,69,7021,0,70,8162,50,102,8207,0,103,9358,50,169,9403,0,169,10565,50,297,10610,0,297,11784,50,514,11829,0,514,13016,50,939,13016,40,939,13061,0,939,23549,3,1240,24275,4,1390,24985,5,1540,24986,1,1540,24986,50,1540,24986,40,1540,25031,0,1540,25256,3,1849,25265,4,2003,25272,5,2141,25272,1,2141,25272,50,2141,25272,40,2141,25317,0,2141,54374,3,3645,55166,4,4392,56177,1,5142,56177,50,5143,56177,40,5143,56222,0,5143,72428,3,5898,73343,4,6269,74142,1,6644,74142,50,6644,74142,40,6644,74187,0,6644,81359,3,7409,82768,4,7770,83962,1,8145,83962,50,8145,83962,40,8145,84007,0,8145,124469,3,12055,126395,4,13996,127754,1,15946,127754,50,15947,127754,40,15947,127799,0,15947,164307,3,18498,165757,4,19773,166591,1,21048,166591,50,21049,166591,40,21049,166636,0,21049,195188,3,22550,196365,4,23300,197101,5,24050,197102,1,24050,197102,50,24051,197102,40,24051,197147,0,24051,205424,3,24831,206257,4,25181,206392,5,25552,206392,1,25552,206392,50,25552,206392,40,25552,206437,0,25552,229505,3,26759,230575,4,27353,231049,5,27953,231050,1,27953,231050,50,27954,231050,40,27954,231095,0,27954,250104,3,28705,250893,4,29080,251180,1,29455,251180,50,29455,251180,40,29455,251180,40,29455,251220,0,29455,251336,50,29455,251336,30,29455,251336,40,29455,251376,0,29455,251500,50,29455,251500,30,29455,251500,40,29455,251540,0,29457,251626,50,29458,251626,30,29458,251626,40,29458,251666,0,29458,251771,50,29458,251811,0,29458)
%
%
% START OF PROOF
% 251741 [?] ?
% 251772 [] equal(X,X).
% 251776 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 251791 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 251795 [?] ?
% 251798 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 251802 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 251824 [hyper:251776,251802,binarycut:251795] equal(inverse(sk_c5),sk_c6).
% 251841 [hyper:251776,251791,demod:251824,cut:251741] equal(multiply(sk_c1,sk_c6),sk_c7).
% 251846 [hyper:251776,251798,demod:251824,cut:251741] equal(inverse(sk_c1),sk_c7).
% 251848 [hyper:251776,251846,demod:251841,cut:251772] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 2
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(Z,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c5),sk_c6) | -equal(multiply(U,sk_c6),sk_c5) | -equal(inverse(U),sk_c6) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c7).
% Split part used next: -equal(multiply(sk_c6,sk_c7),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,1,85,0,1,1169,50,10,1214,0,10,2313,50,19,2358,0,19,3468,50,31,3513,0,31,4630,50,40,4675,0,40,5799,50,51,5844,0,51,6976,50,69,7021,0,70,8162,50,102,8207,0,103,9358,50,169,9403,0,169,10565,50,297,10610,0,297,11784,50,514,11829,0,514,13016,50,939,13016,40,939,13061,0,939,23549,3,1240,24275,4,1390,24985,5,1540,24986,1,1540,24986,50,1540,24986,40,1540,25031,0,1540,25256,3,1849,25265,4,2003,25272,5,2141,25272,1,2141,25272,50,2141,25272,40,2141,25317,0,2141,54374,3,3645,55166,4,4392,56177,1,5142,56177,50,5143,56177,40,5143,56222,0,5143,72428,3,5898,73343,4,6269,74142,1,6644,74142,50,6644,74142,40,6644,74187,0,6644,81359,3,7409,82768,4,7770,83962,1,8145,83962,50,8145,83962,40,8145,84007,0,8145,124469,3,12055,126395,4,13996,127754,1,15946,127754,50,15947,127754,40,15947,127799,0,15947,164307,3,18498,165757,4,19773,166591,1,21048,166591,50,21049,166591,40,21049,166636,0,21049,195188,3,22550,196365,4,23300,197101,5,24050,197102,1,24050,197102,50,24051,197102,40,24051,197147,0,24051,205424,3,24831,206257,4,25181,206392,5,25552,206392,1,25552,206392,50,25552,206392,40,25552,206437,0,25552,229505,3,26759,230575,4,27353,231049,5,27953,231050,1,27953,231050,50,27954,231050,40,27954,231095,0,27954,250104,3,28705,250893,4,29080,251180,1,29455,251180,50,29455,251180,40,29455,251180,40,29455,251220,0,29455,251336,50,29455,251336,30,29455,251336,40,29455,251376,0,29455,251500,50,29455,251500,30,29455,251500,40,29455,251540,0,29457,251626,50,29458,251626,30,29458,251626,40,29458,251666,0,29458,251771,50,29458,251811,0,29458,251847,50,29458,251847,30,29458,251847,40,29458,251887,0,29460,251984,50,29461,252024,0,29461,252136,50,29462,252176,0,29464,252290,50,29464,252330,0,29464,252479,50,29468,252519,0,29468,252675,50,29474,252715,0,29476,252899,50,29488,252939,0,29488,253135,50,29514,253175,0,29514,253386,50,29564,253386,40,29564,253426,0,29564)
%
%
% START OF PROOF
% 253252 [?] ?
% 253388 [] equal(multiply(identity,X),X).
% 253389 [] equal(multiply(inverse(X),X),identity).
% 253390 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 253391 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 253422 [?] ?
% 253423 [?] ?
% 253424 [?] ?
% 253477 [input:253422,cut:253391] equal(inverse(sk_c4),sk_c6).
% 253478 [para:253477.1.1,253389.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 253480 [input:253424,cut:253391] equal(inverse(sk_c5),sk_c6).
% 253481 [para:253480.1.1,253389.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 253495 [input:253423,cut:253391] equal(multiply(sk_c4,sk_c6),sk_c5).
% 253524 [para:253478.1.1,253390.1.1.1,demod:253388] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 253549 [para:253495.1.1,253524.1.2.2,demod:253481] equal(sk_c6,identity).
% 253550 [para:253549.1.1,253391.1.1.1,demod:253388,cut:253252] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(Z,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c5),sk_c6) | -equal(multiply(U,sk_c6),sk_c5) | -equal(inverse(U),sk_c6) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c7).
% Split part used next: -equal(inverse(sk_c5),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,1,85,0,1,1169,50,10,1214,0,10,2313,50,19,2358,0,19,3468,50,31,3513,0,31,4630,50,40,4675,0,40,5799,50,51,5844,0,51,6976,50,69,7021,0,70,8162,50,102,8207,0,103,9358,50,169,9403,0,169,10565,50,297,10610,0,297,11784,50,514,11829,0,514,13016,50,939,13016,40,939,13061,0,939,23549,3,1240,24275,4,1390,24985,5,1540,24986,1,1540,24986,50,1540,24986,40,1540,25031,0,1540,25256,3,1849,25265,4,2003,25272,5,2141,25272,1,2141,25272,50,2141,25272,40,2141,25317,0,2141,54374,3,3645,55166,4,4392,56177,1,5142,56177,50,5143,56177,40,5143,56222,0,5143,72428,3,5898,73343,4,6269,74142,1,6644,74142,50,6644,74142,40,6644,74187,0,6644,81359,3,7409,82768,4,7770,83962,1,8145,83962,50,8145,83962,40,8145,84007,0,8145,124469,3,12055,126395,4,13996,127754,1,15946,127754,50,15947,127754,40,15947,127799,0,15947,164307,3,18498,165757,4,19773,166591,1,21048,166591,50,21049,166591,40,21049,166636,0,21049,195188,3,22550,196365,4,23300,197101,5,24050,197102,1,24050,197102,50,24051,197102,40,24051,197147,0,24051,205424,3,24831,206257,4,25181,206392,5,25552,206392,1,25552,206392,50,25552,206392,40,25552,206437,0,25552,229505,3,26759,230575,4,27353,231049,5,27953,231050,1,27953,231050,50,27954,231050,40,27954,231095,0,27954,250104,3,28705,250893,4,29080,251180,1,29455,251180,50,29455,251180,40,29455,251180,40,29455,251220,0,29455,251336,50,29455,251336,30,29455,251336,40,29455,251376,0,29455,251500,50,29455,251500,30,29455,251500,40,29455,251540,0,29457,251626,50,29458,251626,30,29458,251626,40,29458,251666,0,29458,251771,50,29458,251811,0,29458,251847,50,29458,251847,30,29458,251847,40,29458,251887,0,29460,251984,50,29461,252024,0,29461,252136,50,29462,252176,0,29464,252290,50,29464,252330,0,29464,252479,50,29468,252519,0,29468,252675,50,29474,252715,0,29476,252899,50,29488,252939,0,29488,253135,50,29514,253175,0,29514,253386,50,29564,253386,40,29564,253426,0,29564,253549,50,29564,253549,30,29564,253549,40,29564,253589,0,29564)
%
%
% START OF PROOF
% 253551 [] equal(multiply(identity,X),X).
% 253552 [] equal(multiply(inverse(X),X),identity).
% 253553 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 253554 [] -equal(inverse(sk_c5),sk_c6).
% 253559 [?] ?
% 253566 [?] ?
% 253573 [?] ?
% 253580 [?] ?
% 253587 [?] ?
% 253592 [input:253566,cut:253554] equal(inverse(sk_c2),sk_c6).
% 253593 [para:253592.1.1,253552.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 253596 [input:253580,cut:253554] equal(inverse(sk_c1),sk_c7).
% 253597 [para:253596.1.1,253552.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 253601 [input:253559,cut:253554] equal(multiply(sk_c2,sk_c5),sk_c6).
% 253610 [input:253573,cut:253554] equal(multiply(sk_c1,sk_c6),sk_c7).
% 253618 [input:253587,cut:253554] equal(multiply(sk_c6,sk_c7),sk_c5).
% 253627 [para:253552.1.1,253553.1.1.1,demod:253551] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 253628 [para:253593.1.1,253553.1.1.1,demod:253551] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 253629 [para:253597.1.1,253553.1.1.1,demod:253551] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 253631 [para:253610.1.1,253553.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c1,multiply(sk_c6,X))).
% 253633 [para:253601.1.1,253628.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 253635 [para:253610.1.1,253629.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 253638 [para:253593.1.1,253627.1.2.2] equal(sk_c2,multiply(inverse(sk_c6),identity)).
% 253642 [para:253618.1.1,253627.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 253644 [para:253633.1.2,253627.1.2.2,demod:253642] equal(sk_c6,sk_c7).
% 253650 [para:253644.1.1,253618.1.1.1,demod:253635] equal(sk_c6,sk_c5).
% 253651 [para:253644.1.1,253628.1.2.1] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 253660 [para:253650.1.1,253644.1.1] equal(sk_c5,sk_c7).
% 253666 [para:253628.1.2,253631.1.2.2,demod:253651] equal(X,multiply(sk_c1,X)).
% 253668 [para:253650.1.1,253631.1.2.2.1,demod:253666] equal(multiply(sk_c7,X),multiply(sk_c5,X)).
% 253669 [para:253666.1.2,253629.1.2.2,demod:253668] equal(X,multiply(sk_c5,X)).
% 253673 [para:253669.1.2,253627.1.2.2] equal(X,multiply(inverse(sk_c5),X)).
% 253683 [para:253673.1.2,253552.1.1] equal(sk_c5,identity).
% 253689 [para:253683.1.1,253642.1.2.2,demod:253638] equal(sk_c7,sk_c2).
% 253690 [para:253689.1.1,253660.1.2] equal(sk_c5,sk_c2).
% 253694 [para:253690.1.2,253592.1.1.1,cut:253554] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(Z,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c5),sk_c6) | -equal(multiply(U,sk_c6),sk_c5) | -equal(inverse(U),sk_c6) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c7).
% Split part used next: -equal(multiply(sk_c5,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: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,1,85,0,1,1169,50,10,1214,0,10,2313,50,19,2358,0,19,3468,50,31,3513,0,31,4630,50,40,4675,0,40,5799,50,51,5844,0,51,6976,50,69,7021,0,70,8162,50,102,8207,0,103,9358,50,169,9403,0,169,10565,50,297,10610,0,297,11784,50,514,11829,0,514,13016,50,939,13016,40,939,13061,0,939,23549,3,1240,24275,4,1390,24985,5,1540,24986,1,1540,24986,50,1540,24986,40,1540,25031,0,1540,25256,3,1849,25265,4,2003,25272,5,2141,25272,1,2141,25272,50,2141,25272,40,2141,25317,0,2141,54374,3,3645,55166,4,4392,56177,1,5142,56177,50,5143,56177,40,5143,56222,0,5143,72428,3,5898,73343,4,6269,74142,1,6644,74142,50,6644,74142,40,6644,74187,0,6644,81359,3,7409,82768,4,7770,83962,1,8145,83962,50,8145,83962,40,8145,84007,0,8145,124469,3,12055,126395,4,13996,127754,1,15946,127754,50,15947,127754,40,15947,127799,0,15947,164307,3,18498,165757,4,19773,166591,1,21048,166591,50,21049,166591,40,21049,166636,0,21049,195188,3,22550,196365,4,23300,197101,5,24050,197102,1,24050,197102,50,24051,197102,40,24051,197147,0,24051,205424,3,24831,206257,4,25181,206392,5,25552,206392,1,25552,206392,50,25552,206392,40,25552,206437,0,25552,229505,3,26759,230575,4,27353,231049,5,27953,231050,1,27953,231050,50,27954,231050,40,27954,231095,0,27954,250104,3,28705,250893,4,29080,251180,1,29455,251180,50,29455,251180,40,29455,251180,40,29455,251220,0,29455,251336,50,29455,251336,30,29455,251336,40,29455,251376,0,29455,251500,50,29455,251500,30,29455,251500,40,29455,251540,0,29457,251626,50,29458,251626,30,29458,251626,40,29458,251666,0,29458,251771,50,29458,251811,0,29458,251847,50,29458,251847,30,29458,251847,40,29458,251887,0,29460,251984,50,29461,252024,0,29461,252136,50,29462,252176,0,29464,252290,50,29464,252330,0,29464,252479,50,29468,252519,0,29468,252675,50,29474,252715,0,29476,252899,50,29488,252939,0,29488,253135,50,29514,253175,0,29514,253386,50,29564,253386,40,29564,253426,0,29564,253549,50,29564,253549,30,29564,253549,40,29564,253589,0,29564,253693,50,29565,253693,30,29565,253693,40,29565,253733,0,29566,253840,50,29567,253880,0,29567,254056,50,29569,254096,0,29570,254289,50,29572,254329,0,29574,254535,50,29578,254575,0,29578,254787,50,29585,254827,0,29586,255047,50,29600,255087,0,29600,255315,50,29628,255355,0,29628,255593,50,29684,255593,40,29684,255633,0,29684)
%
%
% START OF PROOF
% 255425 [?] ?
% 255595 [] equal(multiply(identity,X),X).
% 255596 [] equal(multiply(inverse(X),X),identity).
% 255597 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 255598 [] -equal(multiply(sk_c5,sk_c7),sk_c6).
% 255600 [?] ?
% 255607 [?] ?
% 255614 [?] ?
% 255621 [?] ?
% 255627 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 255628 [?] ?
% 255653 [input:255600,cut:255598] equal(multiply(sk_c2,sk_c5),sk_c6).
% 255662 [input:255607,cut:255598] equal(inverse(sk_c2),sk_c6).
% 255663 [para:255662.1.1,255596.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 255676 [input:255621,cut:255598] equal(inverse(sk_c1),sk_c7).
% 255677 [para:255676.1.1,255596.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 255687 [input:255614,cut:255598] equal(multiply(sk_c1,sk_c6),sk_c7).
% 255697 [input:255628,cut:255598] equal(multiply(sk_c6,sk_c7),sk_c5).
% 255700 [para:255596.1.1,255597.1.1.1,demod:255595] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 255706 [para:255663.1.1,255597.1.1.1,demod:255595] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 255714 [para:255677.1.1,255597.1.1.1,demod:255595] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 255737 [para:255653.1.1,255706.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 255743 [para:255687.1.1,255714.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 255788 [para:255697.1.1,255700.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 255793 [para:255737.1.2,255700.1.2.2,demod:255788] equal(sk_c6,sk_c7).
% 255799 [para:255793.1.1,255598.1.2] -equal(multiply(sk_c5,sk_c7),sk_c7).
% 255813 [para:255627.1.1,255793.2.1.2,cut:255799] equal(multiply(sk_c6,sk_c7),sk_c5).
% 255822 [para:255793.1.1,255813.1.1.1,demod:255743] equal(sk_c6,sk_c5).
% 255823 [para:255822.1.1,255598.1.2,cut:255425] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 8 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(Z,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c5),sk_c6) | -equal(multiply(U,sk_c6),sk_c5) | -equal(inverse(U),sk_c6) | -equal(multiply(sk_c5,sk_c7),sk_c6) | -equal(multiply(sk_c5,sk_c6),sk_c7).
% Split part used next: -equal(multiply(sk_c5,sk_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 2
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,1,85,0,1,1169,50,10,1214,0,10,2313,50,19,2358,0,19,3468,50,31,3513,0,31,4630,50,40,4675,0,40,5799,50,51,5844,0,51,6976,50,69,7021,0,70,8162,50,102,8207,0,103,9358,50,169,9403,0,169,10565,50,297,10610,0,297,11784,50,514,11829,0,514,13016,50,939,13016,40,939,13061,0,939,23549,3,1240,24275,4,1390,24985,5,1540,24986,1,1540,24986,50,1540,24986,40,1540,25031,0,1540,25256,3,1849,25265,4,2003,25272,5,2141,25272,1,2141,25272,50,2141,25272,40,2141,25317,0,2141,54374,3,3645,55166,4,4392,56177,1,5142,56177,50,5143,56177,40,5143,56222,0,5143,72428,3,5898,73343,4,6269,74142,1,6644,74142,50,6644,74142,40,6644,74187,0,6644,81359,3,7409,82768,4,7770,83962,1,8145,83962,50,8145,83962,40,8145,84007,0,8145,124469,3,12055,126395,4,13996,127754,1,15946,127754,50,15947,127754,40,15947,127799,0,15947,164307,3,18498,165757,4,19773,166591,1,21048,166591,50,21049,166591,40,21049,166636,0,21049,195188,3,22550,196365,4,23300,197101,5,24050,197102,1,24050,197102,50,24051,197102,40,24051,197147,0,24051,205424,3,24831,206257,4,25181,206392,5,25552,206392,1,25552,206392,50,25552,206392,40,25552,206437,0,25552,229505,3,26759,230575,4,27353,231049,5,27953,231050,1,27953,231050,50,27954,231050,40,27954,231095,0,27954,250104,3,28705,250893,4,29080,251180,1,29455,251180,50,29455,251180,40,29455,251180,40,29455,251220,0,29455,251336,50,29455,251336,30,29455,251336,40,29455,251376,0,29455,251500,50,29455,251500,30,29455,251500,40,29455,251540,0,29457,251626,50,29458,251626,30,29458,251626,40,29458,251666,0,29458,251771,50,29458,251811,0,29458,251847,50,29458,251847,30,29458,251847,40,29458,251887,0,29460,251984,50,29461,252024,0,29461,252136,50,29462,252176,0,29464,252290,50,29464,252330,0,29464,252479,50,29468,252519,0,29468,252675,50,29474,252715,0,29476,252899,50,29488,252939,0,29488,253135,50,29514,253175,0,29514,253386,50,29564,253386,40,29564,253426,0,29564,253549,50,29564,253549,30,29564,253549,40,29564,253589,0,29564,253693,50,29565,253693,30,29565,253693,40,29565,253733,0,29566,253840,50,29567,253880,0,29567,254056,50,29569,254096,0,29570,254289,50,29572,254329,0,29574,254535,50,29578,254575,0,29578,254787,50,29585,254827,0,29586,255047,50,29600,255087,0,29600,255315,50,29628,255355,0,29628,255593,50,29684,255593,40,29684,255633,0,29684,255822,50,29684,255822,30,29684,255822,40,29684,255862,0,29685,255969,50,29685,256009,0,29687,256185,50,29689,256225,0,29689,256418,50,29692,256458,0,29692,256664,50,29696,256704,0,29698,256916,50,29705,256956,0,29705,257176,50,29720,257216,0,29720,257444,50,29747,257484,0,29747,257722,50,29804,257722,40,29804,257762,0,29804)
%
%
% START OF PROOF
% 257723 [] equal(X,X).
% 257724 [] equal(multiply(identity,X),X).
% 257725 [] equal(multiply(inverse(X),X),identity).
% 257726 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 257727 [] -equal(multiply(sk_c5,sk_c6),sk_c7).
% 257728 [?] ?
% 257735 [?] ?
% 257742 [?] ?
% 257749 [?] ?
% 257756 [?] ?
% 257766 [input:257728,cut:257727] equal(multiply(sk_c2,sk_c5),sk_c6).
% 257789 [input:257735,cut:257727] equal(inverse(sk_c2),sk_c6).
% 257790 [para:257789.1.1,257725.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 257802 [input:257749,cut:257727] equal(inverse(sk_c1),sk_c7).
% 257803 [para:257802.1.1,257725.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 257806 [input:257742,cut:257727] equal(multiply(sk_c1,sk_c6),sk_c7).
% 257822 [input:257756,cut:257727] equal(multiply(sk_c6,sk_c7),sk_c5).
% 257827 [para:257725.1.1,257726.1.1.1,demod:257724] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 257830 [para:257790.1.1,257726.1.1.1,demod:257724] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 257839 [para:257803.1.1,257726.1.1.1,demod:257724] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 257860 [para:257766.1.1,257830.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 257865 [para:257806.1.1,257839.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 257905 [para:257822.1.1,257827.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 257912 [para:257860.1.2,257827.1.2.2,demod:257905] equal(sk_c6,sk_c7).
% 257934 [para:257912.1.1,257822.1.1.1,demod:257865] equal(sk_c6,sk_c5).
% 257958 [para:257934.1.1,257860.1.2.1] equal(sk_c5,multiply(sk_c5,sk_c6)).
% 257961 [para:257934.1.1,257912.1.1] equal(sk_c5,sk_c7).
% 257963 [para:257961.1.2,257727.1.2,demod:257958,cut:257723] 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: 38461
% derived clauses: 5720440
% kept clauses: 205116
% kept size sum: 827473
% kept mid-nuclei: 7922
% kept new demods: 4506
% forw unit-subs: 2199650
% forw double-subs: 3115515
% forw overdouble-subs: 147158
% backward subs: 13727
% fast unit cutoff: 20735
% full unit cutoff: 0
% dbl unit cutoff: 7147
% real runtime : 299.87
% process. runtime: 298.4
% specific non-discr-tree subsumption statistics:
% tried: 35586919
% length fails: 3913250
% strength fails: 10183223
% predlist fails: 1556012
% aux str. fails: 3340556
% by-lit fails: 11185322
% full subs tried: 788470
% full subs fail: 711943
%
% ; 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/GRP341-1+eq_r.in")
%
%------------------------------------------------------------------------------