TSTP Solution File: GRP316-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP316-1 : 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 : art09.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 299.5s
% Output : Assurance 299.5s
% 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/GRP316-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% was split for some strategies as:
% -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8).
% -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(multiply(sk_c7,sk_c8),sk_c6).
% -equal(multiply(sk_c6,sk_c8),sk_c7).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,724,50,6,764,0,6,1583,50,16,1623,0,16,2527,50,29,2567,0,29,3517,50,41,3557,0,41,4554,50,55,4594,0,55,5659,50,78,5699,0,78,6832,50,115,6872,0,115,8095,50,184,8135,0,184,9448,50,320,9488,0,320,10913,50,540,10953,0,540,12490,50,936,12490,40,936,12530,0,936,23049,3,1237,23772,4,1387,24469,5,1537,24470,1,1537,24470,50,1537,24470,40,1537,24510,0,1537,24745,3,1850,24754,4,1996,24763,5,2138,24763,1,2138,24763,50,2138,24763,40,2138,24803,0,2138,49758,3,3639,50740,4,4389,51859,5,5139,51860,1,5139,51860,50,5140,51860,40,5140,51900,0,5140,68657,3,5893,69516,4,6266,70252,5,6641,70253,1,6641,70253,50,6641,70253,40,6641,70293,0,6641,83124,3,7395,83594,4,7767,84884,5,8142,84885,1,8142,84885,50,8142,84885,40,8142,84925,0,8142,164596,3,12066,165417,4,13993,166205,1,15943,166205,50,15946,166205,40,15946,166245,0,15946,231466,3,18498,232119,4,19772,232966,1,21047,232966,50,21049,232966,40,21049,233006,0,21049,279404,3,22550,280123,4,23300,280908,5,24051,280909,1,24051,280909,50,24052,280909,40,24052,280949,0,24052,290581,3,24804,292040,4,25178,292513,5,25553,292513,1,25553,292513,50,25553,292513,40,25553,292553,0,25553,333232,3,26755,333821,4,27354,334420,1,27954,334420,50,27955,334420,40,27955,334460,0,27955,358920,3,28707,359537,4,29081,360102,1,29456,360102,50,29456,360102,40,29456,360102,40,29456,360137,0,29456,360233,50,29457,360268,0,29457)
%
%
% START OF PROOF
% 360235 [] equal(multiply(identity,X),X).
% 360236 [] equal(multiply(inverse(X),X),identity).
% 360237 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 360238 [] -equal(multiply(X,sk_c6),sk_c8) | -equal(inverse(X),sk_c6).
% 360239 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 360240 [?] ?
% 360245 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(inverse(sk_c5),sk_c6).
% 360246 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c5,sk_c6),sk_c8).
% 360251 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 360252 [?] ?
% 360257 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 360258 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c5,sk_c6),sk_c8).
% 360263 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c5),sk_c6).
% 360264 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c5,sk_c6),sk_c8).
% 360271 [hyper:360238,360239,binarycut:360240] equal(inverse(sk_c2),sk_c7).
% 360272 [para:360271.1.1,360236.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 360279 [hyper:360238,360251,binarycut:360252] equal(inverse(sk_c1),sk_c8).
% 360280 [para:360279.1.1,360236.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 360284 [hyper:360238,360246,360245] equal(multiply(sk_c2,sk_c7),sk_c6).
% 360291 [hyper:360238,360258,360257] equal(multiply(sk_c1,sk_c8),sk_c7).
% 360297 [hyper:360238,360264,360263] equal(multiply(sk_c7,sk_c8),sk_c6).
% 360298 [para:360236.1.1,360237.1.1.1,demod:360235] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 360299 [para:360272.1.1,360237.1.1.1,demod:360235] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 360300 [para:360280.1.1,360237.1.1.1,demod:360235] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 360301 [para:360284.1.1,360237.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c2,multiply(sk_c7,X))).
% 360302 [para:360291.1.1,360237.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c1,multiply(sk_c8,X))).
% 360303 [para:360297.1.1,360237.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c8,X))).
% 360304 [para:360284.1.1,360299.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 360306 [para:360291.1.1,360300.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 360309 [para:360236.1.1,360298.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 360311 [para:360280.1.1,360298.1.2.2] equal(sk_c1,multiply(inverse(sk_c8),identity)).
% 360313 [para:360237.1.1,360298.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 360314 [para:360299.1.2,360298.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c7),X)).
% 360316 [para:360298.1.2,360298.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 360319 [para:360299.1.2,360301.1.2.2] equal(multiply(sk_c6,multiply(sk_c2,X)),multiply(sk_c2,X)).
% 360320 [para:360304.1.2,360301.1.2.2,demod:360284] equal(multiply(sk_c6,sk_c6),sk_c6).
% 360322 [para:360320.1.1,360298.1.2.2,demod:360236] equal(sk_c6,identity).
% 360323 [para:360322.1.1,360304.1.2.2] equal(sk_c7,multiply(sk_c7,identity)).
% 360328 [para:360306.1.2,360302.1.2.2,demod:360291] equal(multiply(sk_c7,sk_c7),sk_c7).
% 360330 [para:360328.1.1,360298.1.2.2,demod:360284,360314] equal(sk_c7,sk_c6).
% 360331 [para:360328.1.1,360301.1.2.2,demod:360284] equal(multiply(sk_c6,sk_c7),sk_c6).
% 360334 [para:360330.1.1,360299.1.2.1,demod:360319] equal(X,multiply(sk_c2,X)).
% 360336 [para:360330.1.1,360328.1.1.1,demod:360331] equal(sk_c6,sk_c7).
% 360337 [para:360336.1.2,360299.1.2.1,demod:360334] equal(X,multiply(sk_c6,X)).
% 360340 [para:360280.1.1,360303.1.2.2,demod:360323,360337] equal(sk_c1,sk_c7).
% 360344 [para:360340.1.2,360284.1.1.2,demod:360334] equal(sk_c1,sk_c6).
% 360379 [para:360316.1.2,360236.1.1] equal(multiply(X,inverse(X)),identity).
% 360381 [para:360316.1.2,360309.1.2] equal(X,multiply(X,identity)).
% 360382 [para:360381.1.2,360309.1.2] equal(X,inverse(inverse(X))).
% 360384 [para:360381.1.2,360311.1.2] equal(sk_c1,inverse(sk_c8)).
% 360385 [para:360379.1.1,360313.1.2.2.2,demod:360381] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 360387 [para:360299.1.2,360385.1.2.1.1,demod:360334] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 360396 [para:360387.1.2,360316.1.2,demod:360382] equal(multiply(X,sk_c7),X).
% 360397 [para:360330.1.1,360396.1.1.2] equal(multiply(X,sk_c6),X).
% 360402 [hyper:360238,360397,demod:360384,cut:360344] 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(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,724,50,6,764,0,6,1583,50,16,1623,0,16,2527,50,29,2567,0,29,3517,50,41,3557,0,41,4554,50,55,4594,0,55,5659,50,78,5699,0,78,6832,50,115,6872,0,115,8095,50,184,8135,0,184,9448,50,320,9488,0,320,10913,50,540,10953,0,540,12490,50,936,12490,40,936,12530,0,936,23049,3,1237,23772,4,1387,24469,5,1537,24470,1,1537,24470,50,1537,24470,40,1537,24510,0,1537,24745,3,1850,24754,4,1996,24763,5,2138,24763,1,2138,24763,50,2138,24763,40,2138,24803,0,2138,49758,3,3639,50740,4,4389,51859,5,5139,51860,1,5139,51860,50,5140,51860,40,5140,51900,0,5140,68657,3,5893,69516,4,6266,70252,5,6641,70253,1,6641,70253,50,6641,70253,40,6641,70293,0,6641,83124,3,7395,83594,4,7767,84884,5,8142,84885,1,8142,84885,50,8142,84885,40,8142,84925,0,8142,164596,3,12066,165417,4,13993,166205,1,15943,166205,50,15946,166205,40,15946,166245,0,15946,231466,3,18498,232119,4,19772,232966,1,21047,232966,50,21049,232966,40,21049,233006,0,21049,279404,3,22550,280123,4,23300,280908,5,24051,280909,1,24051,280909,50,24052,280909,40,24052,280949,0,24052,290581,3,24804,292040,4,25178,292513,5,25553,292513,1,25553,292513,50,25553,292513,40,25553,292553,0,25553,333232,3,26755,333821,4,27354,334420,1,27954,334420,50,27955,334420,40,27955,334460,0,27955,358920,3,28707,359537,4,29081,360102,1,29456,360102,50,29456,360102,40,29456,360102,40,29456,360137,0,29456,360233,50,29457,360268,0,29457,360401,50,29458,360401,30,29458,360401,40,29458,360436,0,29463)
%
%
% START OF PROOF
% 360402 [] equal(X,X).
% 360403 [] equal(multiply(identity,X),X).
% 360404 [] equal(multiply(inverse(X),X),identity).
% 360405 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 360406 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 360409 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 360410 [] equal(multiply(sk_c3,sk_c8),sk_c4) | equal(inverse(sk_c2),sk_c7).
% 360411 [?] ?
% 360415 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 360416 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c8),sk_c4).
% 360417 [] equal(multiply(sk_c2,sk_c7),sk_c6) | equal(multiply(sk_c8,sk_c4),sk_c7).
% 360421 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 360422 [] equal(multiply(sk_c3,sk_c8),sk_c4) | equal(inverse(sk_c1),sk_c8).
% 360423 [?] ?
% 360427 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 360428 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c3,sk_c8),sk_c4).
% 360429 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c8,sk_c4),sk_c7).
% 360433 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 360434 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c3,sk_c8),sk_c4).
% 360435 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c8,sk_c4),sk_c7).
% 360463 [hyper:360406,360410,360409,binarycut:360411] equal(inverse(sk_c2),sk_c7).
% 360464 [para:360463.1.1,360404.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 360480 [hyper:360406,360422,360421,binarycut:360423] equal(inverse(sk_c1),sk_c8).
% 360487 [para:360480.1.1,360404.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 360519 [hyper:360406,360417,360416,360415] equal(multiply(sk_c2,sk_c7),sk_c6).
% 360533 [hyper:360406,360429,360428,360427] equal(multiply(sk_c1,sk_c8),sk_c7).
% 360550 [hyper:360406,360435,360434,360433] equal(multiply(sk_c7,sk_c8),sk_c6).
% 360554 [para:360404.1.1,360405.1.1.1,demod:360403] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 360555 [para:360464.1.1,360405.1.1.1,demod:360403] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 360556 [para:360487.1.1,360405.1.1.1,demod:360403] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 360557 [para:360519.1.1,360405.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c2,multiply(sk_c7,X))).
% 360558 [para:360533.1.1,360405.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c1,multiply(sk_c8,X))).
% 360559 [para:360550.1.1,360405.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c8,X))).
% 360562 [para:360519.1.1,360555.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 360566 [para:360533.1.1,360556.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 360569 [para:360403.1.1,360554.1.2.2] equal(X,multiply(inverse(identity),X)).
% 360574 [para:360555.1.2,360554.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c7),X)).
% 360580 [para:360555.1.2,360557.1.2.2] equal(multiply(sk_c6,multiply(sk_c2,X)),multiply(sk_c2,X)).
% 360581 [para:360562.1.2,360557.1.2.2,demod:360519] equal(multiply(sk_c6,sk_c6),sk_c6).
% 360583 [para:360581.1.1,360554.1.2.2,demod:360404] equal(sk_c6,identity).
% 360584 [para:360583.1.1,360562.1.2.2] equal(sk_c7,multiply(sk_c7,identity)).
% 360591 [para:360566.1.2,360558.1.2.2,demod:360533] equal(multiply(sk_c7,sk_c7),sk_c7).
% 360593 [para:360591.1.1,360554.1.2.2,demod:360519,360574] equal(sk_c7,sk_c6).
% 360594 [para:360591.1.1,360557.1.2.2,demod:360519] equal(multiply(sk_c6,sk_c7),sk_c6).
% 360597 [para:360593.1.1,360555.1.2.1,demod:360580] equal(X,multiply(sk_c2,X)).
% 360599 [para:360593.1.1,360591.1.1.1,demod:360594] equal(sk_c6,sk_c7).
% 360600 [para:360599.1.2,360555.1.2.1,demod:360597] equal(X,multiply(sk_c6,X)).
% 360603 [para:360597.1.2,360555.1.2.2] equal(X,multiply(sk_c7,X)).
% 360609 [para:360487.1.1,360559.1.2.2,demod:360584,360600] equal(sk_c1,sk_c7).
% 360610 [para:360556.1.2,360559.1.2.2,demod:360603,360600] equal(multiply(sk_c1,X),X).
% 360611 [para:360559.1.2,360554.1.2.2,demod:360597,360574,360600] equal(multiply(sk_c8,X),X).
% 360612 [para:360609.1.2,360464.1.1.1,demod:360610] equal(sk_c2,identity).
% 360618 [para:360612.1.1,360463.1.1.1] equal(inverse(identity),sk_c7).
% 360634 [hyper:360406,360569,360533,demod:360611,360603,360618,demod:360480,cut:360402] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,724,50,6,764,0,6,1583,50,16,1623,0,16,2527,50,29,2567,0,29,3517,50,41,3557,0,41,4554,50,55,4594,0,55,5659,50,78,5699,0,78,6832,50,115,6872,0,115,8095,50,184,8135,0,184,9448,50,320,9488,0,320,10913,50,540,10953,0,540,12490,50,936,12490,40,936,12530,0,936,23049,3,1237,23772,4,1387,24469,5,1537,24470,1,1537,24470,50,1537,24470,40,1537,24510,0,1537,24745,3,1850,24754,4,1996,24763,5,2138,24763,1,2138,24763,50,2138,24763,40,2138,24803,0,2138,49758,3,3639,50740,4,4389,51859,5,5139,51860,1,5139,51860,50,5140,51860,40,5140,51900,0,5140,68657,3,5893,69516,4,6266,70252,5,6641,70253,1,6641,70253,50,6641,70253,40,6641,70293,0,6641,83124,3,7395,83594,4,7767,84884,5,8142,84885,1,8142,84885,50,8142,84885,40,8142,84925,0,8142,164596,3,12066,165417,4,13993,166205,1,15943,166205,50,15946,166205,40,15946,166245,0,15946,231466,3,18498,232119,4,19772,232966,1,21047,232966,50,21049,232966,40,21049,233006,0,21049,279404,3,22550,280123,4,23300,280908,5,24051,280909,1,24051,280909,50,24052,280909,40,24052,280949,0,24052,290581,3,24804,292040,4,25178,292513,5,25553,292513,1,25553,292513,50,25553,292513,40,25553,292553,0,25553,333232,3,26755,333821,4,27354,334420,1,27954,334420,50,27955,334420,40,27955,334460,0,27955,358920,3,28707,359537,4,29081,360102,1,29456,360102,50,29456,360102,40,29456,360102,40,29456,360137,0,29456,360233,50,29457,360268,0,29457,360401,50,29458,360401,30,29458,360401,40,29458,360436,0,29463,360633,50,29464,360633,30,29464,360633,40,29464,360668,0,29464,360770,50,29465,360805,0,29465)
%
%
% START OF PROOF
% 360772 [] equal(multiply(identity,X),X).
% 360773 [] equal(multiply(inverse(X),X),identity).
% 360774 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 360775 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 360776 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 360777 [] equal(multiply(sk_c5,sk_c6),sk_c8) | equal(inverse(sk_c2),sk_c7).
% 360778 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 360779 [] equal(multiply(sk_c3,sk_c8),sk_c4) | equal(inverse(sk_c2),sk_c7).
% 360780 [] equal(multiply(sk_c8,sk_c4),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 360781 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 360782 [?] ?
% 360783 [?] ?
% 360784 [?] ?
% 360785 [?] ?
% 360786 [?] ?
% 360787 [?] ?
% 360808 [hyper:360775,360776,binarycut:360782] equal(inverse(sk_c5),sk_c6).
% 360809 [para:360808.1.1,360773.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 360813 [hyper:360775,360778,binarycut:360784] equal(inverse(sk_c3),sk_c8).
% 360814 [para:360813.1.1,360773.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 360817 [hyper:360775,360777,binarycut:360783] equal(multiply(sk_c5,sk_c6),sk_c8).
% 360820 [hyper:360775,360779,binarycut:360785] equal(multiply(sk_c3,sk_c8),sk_c4).
% 360823 [hyper:360775,360780,binarycut:360786] equal(multiply(sk_c8,sk_c4),sk_c7).
% 360826 [hyper:360775,360781,binarycut:360787] equal(multiply(sk_c6,sk_c8),sk_c7).
% 360827 [para:360773.1.1,360774.1.1.1,demod:360772] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 360828 [para:360809.1.1,360774.1.1.1,demod:360772] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 360829 [para:360814.1.1,360774.1.1.1,demod:360772] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 360830 [para:360817.1.1,360774.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c5,multiply(sk_c6,X))).
% 360831 [para:360820.1.1,360774.1.1.1] equal(multiply(sk_c4,X),multiply(sk_c3,multiply(sk_c8,X))).
% 360832 [para:360823.1.1,360774.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c4,X))).
% 360833 [para:360826.1.1,360774.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c8,X))).
% 360834 [para:360817.1.1,360828.1.2.2,demod:360826] equal(sk_c6,sk_c7).
% 360835 [para:360820.1.1,360829.1.2.2,demod:360823] equal(sk_c8,sk_c7).
% 360836 [para:360835.1.2,360834.1.2] equal(sk_c6,sk_c8).
% 360839 [para:360773.1.1,360827.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 360840 [para:360809.1.1,360827.1.2.2] equal(sk_c5,multiply(inverse(sk_c6),identity)).
% 360843 [para:360774.1.1,360827.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 360844 [para:360826.1.1,360827.1.2.2] equal(sk_c8,multiply(inverse(sk_c6),sk_c7)).
% 360847 [para:360827.1.2,360827.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 360848 [para:360836.1.2,360814.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 360849 [para:360836.1.2,360820.1.1.2] equal(multiply(sk_c3,sk_c6),sk_c4).
% 360853 [para:360848.1.1,360827.1.2.2,demod:360840] equal(sk_c3,sk_c5).
% 360854 [para:360853.1.2,360817.1.1.1,demod:360849] equal(sk_c4,sk_c8).
% 360855 [para:360854.1.2,360814.1.1.1] equal(multiply(sk_c4,sk_c3),identity).
% 360858 [para:360854.1.2,360829.1.2.1] equal(X,multiply(sk_c4,multiply(sk_c3,X))).
% 360863 [para:360830.1.2,360828.1.2.2,demod:360833] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 360866 [para:360853.1.2,360830.1.2.1] equal(multiply(sk_c8,X),multiply(sk_c3,multiply(sk_c6,X))).
% 360868 [para:360849.1.1,360774.1.1.1,demod:360866] equal(multiply(sk_c4,X),multiply(sk_c8,X)).
% 360875 [para:360831.1.2,360829.1.2.2,demod:360863,360832,360868] equal(multiply(sk_c4,X),multiply(sk_c6,X)).
% 360876 [para:360829.1.2,360831.1.2.2,demod:360858] equal(X,multiply(sk_c3,X)).
% 360878 [para:360876.1.2,360829.1.2.2,demod:360875,360868] equal(X,multiply(sk_c6,X)).
% 360884 [para:360855.1.1,360827.1.2.2] equal(sk_c3,multiply(inverse(sk_c4),identity)).
% 360888 [para:360884.1.2,360774.1.1.1,demod:360772,360876] equal(X,multiply(inverse(sk_c4),X)).
% 360889 [para:360888.1.2,360773.1.1] equal(sk_c4,identity).
% 360890 [para:360889.1.1,360823.1.1.2,demod:360878,360875,360868] equal(identity,sk_c7).
% 360911 [para:360890.1.2,360844.1.2.2,demod:360840] equal(sk_c8,sk_c5).
% 360917 [para:360911.1.1,360836.1.2] equal(sk_c6,sk_c5).
% 360921 [para:360917.1.2,360808.1.1.1] equal(inverse(sk_c6),sk_c6).
% 360924 [para:360847.1.2,360773.1.1] equal(multiply(X,inverse(X)),identity).
% 360926 [para:360847.1.2,360839.1.2] equal(X,multiply(X,identity)).
% 360927 [para:360926.1.2,360839.1.2] equal(X,inverse(inverse(X))).
% 360935 [para:360924.1.1,360843.1.2.2.2,demod:360926] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 360944 [para:360863.1.2,360935.1.2.1.1,demod:360878] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 360955 [para:360944.1.2,360847.1.2,demod:360927] equal(multiply(X,sk_c7),X).
% 360956 [hyper:360775,360955,demod:360921,cut:360834] 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 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,724,50,6,764,0,6,1583,50,16,1623,0,16,2527,50,29,2567,0,29,3517,50,41,3557,0,41,4554,50,55,4594,0,55,5659,50,78,5699,0,78,6832,50,115,6872,0,115,8095,50,184,8135,0,184,9448,50,320,9488,0,320,10913,50,540,10953,0,540,12490,50,936,12490,40,936,12530,0,936,23049,3,1237,23772,4,1387,24469,5,1537,24470,1,1537,24470,50,1537,24470,40,1537,24510,0,1537,24745,3,1850,24754,4,1996,24763,5,2138,24763,1,2138,24763,50,2138,24763,40,2138,24803,0,2138,49758,3,3639,50740,4,4389,51859,5,5139,51860,1,5139,51860,50,5140,51860,40,5140,51900,0,5140,68657,3,5893,69516,4,6266,70252,5,6641,70253,1,6641,70253,50,6641,70253,40,6641,70293,0,6641,83124,3,7395,83594,4,7767,84884,5,8142,84885,1,8142,84885,50,8142,84885,40,8142,84925,0,8142,164596,3,12066,165417,4,13993,166205,1,15943,166205,50,15946,166205,40,15946,166245,0,15946,231466,3,18498,232119,4,19772,232966,1,21047,232966,50,21049,232966,40,21049,233006,0,21049,279404,3,22550,280123,4,23300,280908,5,24051,280909,1,24051,280909,50,24052,280909,40,24052,280949,0,24052,290581,3,24804,292040,4,25178,292513,5,25553,292513,1,25553,292513,50,25553,292513,40,25553,292553,0,25553,333232,3,26755,333821,4,27354,334420,1,27954,334420,50,27955,334420,40,27955,334460,0,27955,358920,3,28707,359537,4,29081,360102,1,29456,360102,50,29456,360102,40,29456,360102,40,29456,360137,0,29456,360233,50,29457,360268,0,29457,360401,50,29458,360401,30,29458,360401,40,29458,360436,0,29463,360633,50,29464,360633,30,29464,360633,40,29464,360668,0,29464,360770,50,29465,360805,0,29465,360955,50,29467,360955,30,29467,360955,40,29467,360990,0,29472)
%
%
% START OF PROOF
% 360956 [] equal(X,X).
% 360957 [] equal(multiply(identity,X),X).
% 360958 [] equal(multiply(inverse(X),X),identity).
% 360959 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 360960 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 360973 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 360974 [] equal(multiply(sk_c5,sk_c6),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 360975 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 360976 [] equal(multiply(sk_c3,sk_c8),sk_c4) | equal(inverse(sk_c1),sk_c8).
% 360977 [] equal(multiply(sk_c8,sk_c4),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 360978 [] equal(multiply(sk_c6,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 360979 [?] ?
% 360980 [?] ?
% 360981 [?] ?
% 360982 [?] ?
% 360983 [?] ?
% 360984 [?] ?
% 360997 [hyper:360960,360973,binarycut:360979] equal(inverse(sk_c5),sk_c6).
% 360998 [para:360997.1.1,360958.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 361001 [hyper:360960,360975,binarycut:360981] equal(inverse(sk_c3),sk_c8).
% 361005 [para:361001.1.1,360958.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 361016 [hyper:360960,360974,binarycut:360980] equal(multiply(sk_c5,sk_c6),sk_c8).
% 361019 [hyper:360960,360976,binarycut:360982] equal(multiply(sk_c3,sk_c8),sk_c4).
% 361023 [hyper:360960,360977,binarycut:360983] equal(multiply(sk_c8,sk_c4),sk_c7).
% 361027 [hyper:360960,360978,binarycut:360984] equal(multiply(sk_c6,sk_c8),sk_c7).
% 361029 [para:360958.1.1,360959.1.1.1,demod:360957] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 361030 [para:360998.1.1,360959.1.1.1,demod:360957] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 361031 [para:361005.1.1,360959.1.1.1,demod:360957] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 361032 [para:361016.1.1,360959.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c5,multiply(sk_c6,X))).
% 361033 [para:361019.1.1,360959.1.1.1] equal(multiply(sk_c4,X),multiply(sk_c3,multiply(sk_c8,X))).
% 361034 [para:361023.1.1,360959.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c4,X))).
% 361037 [para:361027.1.1,360959.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c8,X))).
% 361038 [para:361016.1.1,361030.1.2.2,demod:361027] equal(sk_c6,sk_c7).
% 361039 [para:361019.1.1,361031.1.2.2,demod:361023] equal(sk_c8,sk_c7).
% 361040 [para:361039.1.2,361038.1.2] equal(sk_c6,sk_c8).
% 361043 [para:360998.1.1,361029.1.2.2] equal(sk_c5,multiply(inverse(sk_c6),identity)).
% 361044 [para:361005.1.1,361029.1.2.2] equal(sk_c3,multiply(inverse(sk_c8),identity)).
% 361045 [para:361023.1.1,361029.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),sk_c7)).
% 361047 [para:361030.1.2,361029.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c6),X)).
% 361049 [para:361040.1.2,361005.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 361050 [para:361040.1.2,361019.1.1.2] equal(multiply(sk_c3,sk_c6),sk_c4).
% 361054 [para:361049.1.1,361029.1.2.2,demod:361043] equal(sk_c3,sk_c5).
% 361055 [para:361054.1.2,361016.1.1.1,demod:361050] equal(sk_c4,sk_c8).
% 361059 [para:361055.1.2,361031.1.2.1] equal(X,multiply(sk_c4,multiply(sk_c3,X))).
% 361064 [para:361032.1.2,361030.1.2.2,demod:361037] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 361067 [para:361054.1.2,361032.1.2.1] equal(multiply(sk_c8,X),multiply(sk_c3,multiply(sk_c6,X))).
% 361069 [para:361050.1.1,360959.1.1.1,demod:361067] equal(multiply(sk_c4,X),multiply(sk_c8,X)).
% 361075 [para:361033.1.2,361031.1.2.2,demod:361064,361034,361069] equal(multiply(sk_c4,X),multiply(sk_c6,X)).
% 361076 [para:361031.1.2,361033.1.2.2,demod:361059] equal(X,multiply(sk_c3,X)).
% 361078 [para:361076.1.2,361031.1.2.2,demod:361075,361069] equal(X,multiply(sk_c6,X)).
% 361086 [para:361047.1.2,360958.1.1,demod:361016] equal(sk_c8,identity).
% 361090 [para:361086.1.1,361027.1.1.2,demod:361078] equal(identity,sk_c7).
% 361096 [para:361090.1.2,361045.1.2.2,demod:361044] equal(sk_c4,sk_c3).
% 361100 [para:361096.1.2,361001.1.1.1] equal(inverse(sk_c4),sk_c8).
% 361111 [hyper:360960,361100,demod:361027,361075,cut:360956] 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(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(sk_c7,sk_c8),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,724,50,6,764,0,6,1583,50,16,1623,0,16,2527,50,29,2567,0,29,3517,50,41,3557,0,41,4554,50,55,4594,0,55,5659,50,78,5699,0,78,6832,50,115,6872,0,115,8095,50,184,8135,0,184,9448,50,320,9488,0,320,10913,50,540,10953,0,540,12490,50,936,12490,40,936,12530,0,936,23049,3,1237,23772,4,1387,24469,5,1537,24470,1,1537,24470,50,1537,24470,40,1537,24510,0,1537,24745,3,1850,24754,4,1996,24763,5,2138,24763,1,2138,24763,50,2138,24763,40,2138,24803,0,2138,49758,3,3639,50740,4,4389,51859,5,5139,51860,1,5139,51860,50,5140,51860,40,5140,51900,0,5140,68657,3,5893,69516,4,6266,70252,5,6641,70253,1,6641,70253,50,6641,70253,40,6641,70293,0,6641,83124,3,7395,83594,4,7767,84884,5,8142,84885,1,8142,84885,50,8142,84885,40,8142,84925,0,8142,164596,3,12066,165417,4,13993,166205,1,15943,166205,50,15946,166205,40,15946,166245,0,15946,231466,3,18498,232119,4,19772,232966,1,21047,232966,50,21049,232966,40,21049,233006,0,21049,279404,3,22550,280123,4,23300,280908,5,24051,280909,1,24051,280909,50,24052,280909,40,24052,280949,0,24052,290581,3,24804,292040,4,25178,292513,5,25553,292513,1,25553,292513,50,25553,292513,40,25553,292553,0,25553,333232,3,26755,333821,4,27354,334420,1,27954,334420,50,27955,334420,40,27955,334460,0,27955,358920,3,28707,359537,4,29081,360102,1,29456,360102,50,29456,360102,40,29456,360102,40,29456,360137,0,29456,360233,50,29457,360268,0,29457,360401,50,29458,360401,30,29458,360401,40,29458,360436,0,29463,360633,50,29464,360633,30,29464,360633,40,29464,360668,0,29464,360770,50,29465,360805,0,29465,360955,50,29467,360955,30,29467,360955,40,29467,360990,0,29472,361110,50,29472,361110,30,29472,361110,40,29472,361145,0,29473,361250,50,29473,361285,0,29478,361447,50,29481,361482,0,29481,361654,50,29485,361689,0,29485,361884,50,29492,361919,0,29496,362121,50,29508,362156,0,29508,362366,50,29527,362401,0,29531,362620,50,29566,362655,0,29566,362884,50,29637,362919,0,29637,363159,50,29768,363159,40,29768,363194,0,29768)
%
%
% START OF PROOF
% 363160 [] equal(X,X).
% 363161 [] equal(multiply(identity,X),X).
% 363162 [] equal(multiply(inverse(X),X),identity).
% 363163 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 363164 [] -equal(multiply(sk_c7,sk_c8),sk_c6).
% 363189 [?] ?
% 363190 [?] ?
% 363194 [?] ?
% 363232 [input:363189,cut:363164] equal(inverse(sk_c5),sk_c6).
% 363233 [para:363232.1.1,363162.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 363247 [input:363190,cut:363164] equal(multiply(sk_c5,sk_c6),sk_c8).
% 363250 [input:363194,cut:363164] equal(multiply(sk_c6,sk_c8),sk_c7).
% 363269 [para:363233.1.1,363163.1.1.1,demod:363161] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 363300 [para:363247.1.1,363269.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c8)).
% 363305 [para:363300.1.2,363250.1.1] equal(sk_c6,sk_c7).
% 363307 [para:363305.1.2,363164.1.1.1,demod:363300,cut:363160] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c8),sk_c7) | -equal(multiply(sk_c8,Z),sk_c7) | -equal(multiply(U,sk_c8),Z) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c6),sk_c8) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(sk_c6,sk_c8),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,724,50,6,764,0,6,1583,50,16,1623,0,16,2527,50,29,2567,0,29,3517,50,41,3557,0,41,4554,50,55,4594,0,55,5659,50,78,5699,0,78,6832,50,115,6872,0,115,8095,50,184,8135,0,184,9448,50,320,9488,0,320,10913,50,540,10953,0,540,12490,50,936,12490,40,936,12530,0,936,23049,3,1237,23772,4,1387,24469,5,1537,24470,1,1537,24470,50,1537,24470,40,1537,24510,0,1537,24745,3,1850,24754,4,1996,24763,5,2138,24763,1,2138,24763,50,2138,24763,40,2138,24803,0,2138,49758,3,3639,50740,4,4389,51859,5,5139,51860,1,5139,51860,50,5140,51860,40,5140,51900,0,5140,68657,3,5893,69516,4,6266,70252,5,6641,70253,1,6641,70253,50,6641,70253,40,6641,70293,0,6641,83124,3,7395,83594,4,7767,84884,5,8142,84885,1,8142,84885,50,8142,84885,40,8142,84925,0,8142,164596,3,12066,165417,4,13993,166205,1,15943,166205,50,15946,166205,40,15946,166245,0,15946,231466,3,18498,232119,4,19772,232966,1,21047,232966,50,21049,232966,40,21049,233006,0,21049,279404,3,22550,280123,4,23300,280908,5,24051,280909,1,24051,280909,50,24052,280909,40,24052,280949,0,24052,290581,3,24804,292040,4,25178,292513,5,25553,292513,1,25553,292513,50,25553,292513,40,25553,292553,0,25553,333232,3,26755,333821,4,27354,334420,1,27954,334420,50,27955,334420,40,27955,334460,0,27955,358920,3,28707,359537,4,29081,360102,1,29456,360102,50,29456,360102,40,29456,360102,40,29456,360137,0,29456,360233,50,29457,360268,0,29457,360401,50,29458,360401,30,29458,360401,40,29458,360436,0,29463,360633,50,29464,360633,30,29464,360633,40,29464,360668,0,29464,360770,50,29465,360805,0,29465,360955,50,29467,360955,30,29467,360955,40,29467,360990,0,29472,361110,50,29472,361110,30,29472,361110,40,29472,361145,0,29473,361250,50,29473,361285,0,29478,361447,50,29481,361482,0,29481,361654,50,29485,361689,0,29485,361884,50,29492,361919,0,29496,362121,50,29508,362156,0,29508,362366,50,29527,362401,0,29531,362620,50,29566,362655,0,29566,362884,50,29637,362919,0,29637,363159,50,29768,363159,40,29768,363194,0,29768,363306,50,29769,363306,30,29769,363306,40,29769,363341,0,29769,363452,50,29770,363487,0,29774,363636,50,29777,363671,0,29777,363828,50,29780,363863,0,29780,364028,50,29786,364063,0,29790,364234,50,29799,364269,0,29799,364448,50,29814,364483,0,29818,364670,50,29846,364705,0,29846,364902,50,29907,364937,0,29907,365144,50,30021,365144,40,30021,365179,0,30021)
%
%
% START OF PROOF
% 365036 [?] ?
% 365146 [] equal(multiply(identity,X),X).
% 365147 [] equal(multiply(inverse(X),X),identity).
% 365148 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 365149 [] -equal(multiply(sk_c6,sk_c8),sk_c7).
% 365155 [?] ?
% 365161 [?] ?
% 365198 [input:365155,cut:365149] equal(inverse(sk_c2),sk_c7).
% 365199 [para:365198.1.1,365147.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 365227 [input:365161,cut:365149] equal(multiply(sk_c2,sk_c7),sk_c6).
% 365236 [para:365147.1.1,365148.1.1.1,demod:365146] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 365240 [para:365199.1.1,365148.1.1.1,demod:365146] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 365281 [para:365227.1.1,365240.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 365338 [para:365240.1.2,365236.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c7),X)).
% 365339 [para:365281.1.2,365236.1.2.2,demod:365338] equal(sk_c6,multiply(sk_c2,sk_c7)).
% 365357 [para:365338.1.2,365147.1.1,demod:365339] equal(sk_c6,identity).
% 365361 [para:365357.1.1,365149.1.1.1,demod:365146,cut:365036] 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: 32798
% derived clauses: 5378430
% kept clauses: 316423
% kept size sum: 27682
% kept mid-nuclei: 9157
% kept new demods: 4416
% forw unit-subs: 1757173
% forw double-subs: 2900374
% forw overdouble-subs: 357710
% backward subs: 9743
% fast unit cutoff: 20044
% full unit cutoff: 0
% dbl unit cutoff: 8681
% real runtime : 300.95
% process. runtime: 300.22
% specific non-discr-tree subsumption statistics:
% tried: 38574734
% length fails: 4174930
% strength fails: 11500007
% predlist fails: 3690779
% aux str. fails: 4655208
% by-lit fails: 8092823
% full subs tried: 1450729
% full subs fail: 1294579
%
% ; 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/GRP316-1+eq_r.in")
%
%------------------------------------------------------------------------------