TSTP Solution File: GRP342-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP342-1 : 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 : art05.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 298.7s
% Output : Assurance 298.7s
% 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/GRP342-1+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(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Z,U),sk_c8) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% was split for some strategies as:
% -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% -equal(multiply(Z,U),sk_c8) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c7),sk_c8).
% -equal(inverse(Y),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7).
% -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8).
% -equal(multiply(sk_c7,sk_c8),sk_c6).
% -equal(multiply(sk_c8,sk_c6),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(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Z,U),sk_c8) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,841,50,6,881,0,6,1923,50,21,1963,0,21,2986,50,36,3026,0,36,4151,50,49,4191,0,49,5395,50,67,5435,0,67,6767,50,95,6807,0,95,8243,50,140,8283,0,140,9873,50,221,9913,0,221,11633,50,375,11673,0,375,13573,50,612,13613,0,612,15669,50,1025,15669,40,1025,15709,0,1025,25193,3,1326,26038,4,1476,26841,5,1626,26842,1,1626,26842,50,1626,26842,40,1626,26882,0,1626,27504,3,1940,27515,4,2119,27600,5,2227,27600,1,2227,27600,50,2227,27600,40,2227,27640,0,2227,52486,3,3732,53513,4,4478,54516,5,5228,54517,1,5228,54517,50,5229,54517,40,5229,54557,0,5229,72264,3,5981,72952,4,6355,73571,1,6730,73571,50,6730,73571,40,6730,73611,0,6730,85756,3,7483,86924,4,7856,88333,5,8231,88334,5,8231,88335,1,8231,88335,50,8231,88335,40,8231,88375,0,8231,154923,3,12132,156037,4,14083,157175,5,16032,157176,1,16032,157176,50,16034,157176,40,16034,157216,0,16034,204884,3,18586,205906,4,19861,206710,5,21135,206711,1,21135,206711,50,21137,206711,40,21137,206751,0,21137,248057,3,22638,248827,4,23388,249613,1,24138,249613,50,24139,249613,40,24139,249653,0,24139,258107,3,24900,259011,4,25266,259496,5,25640,259496,1,25640,259496,50,25640,259496,40,25640,259536,0,25640,287548,3,26841,288342,4,27441,289132,1,28041,289132,50,28042,289132,40,28042,289172,0,28042,308818,3,28794,309546,4,29168,310057,1,29543,310057,50,29543,310057,40,29543,310057,40,29543,310092,0,29543,310194,50,29544,310229,0,29544)
%
%
% START OF PROOF
% 310196 [] equal(multiply(identity,X),X).
% 310197 [] equal(multiply(inverse(X),X),identity).
% 310198 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 310199 [] -equal(multiply(X,sk_c8),sk_c6) | -equal(inverse(X),sk_c8).
% 310200 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(inverse(sk_c5),sk_c8).
% 310201 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 310206 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c5),sk_c8).
% 310207 [?] ?
% 310212 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 310213 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 310218 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 310219 [?] ?
% 310224 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c5),sk_c8).
% 310225 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 310232 [hyper:310199,310206,binarycut:310207] equal(inverse(sk_c2),sk_c7).
% 310233 [para:310232.1.1,310197.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 310238 [hyper:310199,310218,binarycut:310219] equal(inverse(sk_c1),sk_c8).
% 310241 [para:310238.1.1,310197.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 310248 [hyper:310199,310201,310200] equal(multiply(sk_c2,sk_c6),sk_c7).
% 310254 [hyper:310199,310213,310212] equal(multiply(sk_c1,sk_c7),sk_c8).
% 310263 [hyper:310199,310225,310224] equal(multiply(sk_c7,sk_c8),sk_c6).
% 310267 [para:310197.1.1,310198.1.1.1,demod:310196] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 310268 [para:310233.1.1,310198.1.1.1,demod:310196] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 310269 [para:310241.1.1,310198.1.1.1,demod:310196] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 310270 [para:310248.1.1,310198.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c2,multiply(sk_c6,X))).
% 310271 [para:310254.1.1,310198.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c7,X))).
% 310273 [para:310248.1.1,310268.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 310275 [para:310254.1.1,310269.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 310278 [para:310197.1.1,310267.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 310279 [para:310233.1.1,310267.1.2.2] equal(sk_c2,multiply(inverse(sk_c7),identity)).
% 310280 [para:310241.1.1,310267.1.2.2] equal(sk_c1,multiply(inverse(sk_c8),identity)).
% 310281 [para:310263.1.1,310267.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 310282 [para:310198.1.1,310267.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 310284 [para:310273.1.2,310267.1.2.2,demod:310281] equal(sk_c7,sk_c8).
% 310286 [para:310267.1.2,310267.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 310287 [para:310284.1.1,310233.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 310289 [para:310284.1.1,310263.1.1.1,demod:310275] equal(sk_c7,sk_c6).
% 310290 [para:310284.1.1,310268.1.2.1] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 310298 [para:310289.1.1,310284.1.1] equal(sk_c6,sk_c8).
% 310303 [para:310287.1.1,310267.1.2.2,demod:310280] equal(sk_c2,sk_c1).
% 310305 [para:310268.1.2,310271.1.2.2,demod:310290] equal(X,multiply(sk_c1,X)).
% 310309 [para:310303.1.1,310268.1.2.2.1,demod:310305] equal(X,multiply(sk_c7,X)).
% 310310 [para:310303.1.1,310270.1.2.1,demod:310305,310309] equal(X,multiply(sk_c6,X)).
% 310312 [para:310309.1.2,310268.1.2] equal(X,multiply(sk_c2,X)).
% 310317 [para:310310.1.2,310267.1.2.2] equal(X,multiply(inverse(sk_c6),X)).
% 310322 [para:310317.1.2,310197.1.1] equal(sk_c6,identity).
% 310328 [para:310322.1.1,310281.1.2.2,demod:310279] equal(sk_c8,sk_c2).
% 310329 [para:310328.1.1,310298.1.2] equal(sk_c6,sk_c2).
% 310332 [para:310329.1.2,310232.1.1.1] equal(inverse(sk_c6),sk_c7).
% 310341 [para:310268.1.2,310282.1.2.2.2,demod:310312] equal(X,multiply(inverse(multiply(Y,sk_c7)),multiply(Y,X))).
% 310348 [para:310286.1.2,310278.1.2] equal(X,multiply(X,identity)).
% 310349 [para:310197.1.1,310341.1.2.2,demod:310348] equal(X,inverse(multiply(inverse(X),sk_c7))).
% 310351 [para:310348.1.2,310278.1.2] equal(X,inverse(inverse(X))).
% 310360 [para:310349.1.2,310278.1.2.1.1,demod:310348] equal(multiply(inverse(X),sk_c7),inverse(X)).
% 310375 [para:310360.1.1,310286.1.2,demod:310351] equal(multiply(X,sk_c7),X).
% 310376 [para:310284.1.1,310375.1.1.2] equal(multiply(X,sk_c8),X).
% 310377 [hyper:310199,310376,demod:310332,cut:310284] 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(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Z,U),sk_c8) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Z,U),sk_c8) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c7),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,841,50,6,881,0,6,1923,50,21,1963,0,21,2986,50,36,3026,0,36,4151,50,49,4191,0,49,5395,50,67,5435,0,67,6767,50,95,6807,0,95,8243,50,140,8283,0,140,9873,50,221,9913,0,221,11633,50,375,11673,0,375,13573,50,612,13613,0,612,15669,50,1025,15669,40,1025,15709,0,1025,25193,3,1326,26038,4,1476,26841,5,1626,26842,1,1626,26842,50,1626,26842,40,1626,26882,0,1626,27504,3,1940,27515,4,2119,27600,5,2227,27600,1,2227,27600,50,2227,27600,40,2227,27640,0,2227,52486,3,3732,53513,4,4478,54516,5,5228,54517,1,5228,54517,50,5229,54517,40,5229,54557,0,5229,72264,3,5981,72952,4,6355,73571,1,6730,73571,50,6730,73571,40,6730,73611,0,6730,85756,3,7483,86924,4,7856,88333,5,8231,88334,5,8231,88335,1,8231,88335,50,8231,88335,40,8231,88375,0,8231,154923,3,12132,156037,4,14083,157175,5,16032,157176,1,16032,157176,50,16034,157176,40,16034,157216,0,16034,204884,3,18586,205906,4,19861,206710,5,21135,206711,1,21135,206711,50,21137,206711,40,21137,206751,0,21137,248057,3,22638,248827,4,23388,249613,1,24138,249613,50,24139,249613,40,24139,249653,0,24139,258107,3,24900,259011,4,25266,259496,5,25640,259496,1,25640,259496,50,25640,259496,40,25640,259536,0,25640,287548,3,26841,288342,4,27441,289132,1,28041,289132,50,28042,289132,40,28042,289172,0,28042,308818,3,28794,309546,4,29168,310057,1,29543,310057,50,29543,310057,40,29543,310057,40,29543,310092,0,29543,310194,50,29544,310229,0,29544,310376,50,29545,310376,30,29545,310376,40,29545,310411,0,29551)
%
%
% START OF PROOF
% 310378 [] equal(multiply(identity,X),X).
% 310379 [] equal(multiply(inverse(X),X),identity).
% 310380 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 310381 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,X),sk_c8) | -equal(inverse(Y),X).
% 310384 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 310385 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(inverse(sk_c3),sk_c4).
% 310386 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(multiply(sk_c3,sk_c4),sk_c8).
% 310390 [?] ?
% 310391 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c4).
% 310392 [?] ?
% 310396 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 310397 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c3),sk_c4).
% 310398 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c3,sk_c4),sk_c8).
% 310402 [?] ?
% 310403 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c4).
% 310404 [?] ?
% 310408 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 310409 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c4).
% 310410 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c3,sk_c4),sk_c8).
% 310420 [hyper:310381,310391,binarycut:310392,binarycut:310390] equal(inverse(sk_c2),sk_c7).
% 310423 [para:310420.1.1,310379.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 310433 [hyper:310381,310403,binarycut:310404,binarycut:310402] equal(inverse(sk_c1),sk_c8).
% 310436 [para:310433.1.1,310379.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 310474 [hyper:310381,310386,310384,310385] equal(multiply(sk_c2,sk_c6),sk_c7).
% 310495 [hyper:310381,310398,310396,310397] equal(multiply(sk_c1,sk_c7),sk_c8).
% 310512 [hyper:310381,310410,310408,310409] equal(multiply(sk_c7,sk_c8),sk_c6).
% 310513 [para:310379.1.1,310380.1.1.1,demod:310378] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 310514 [para:310423.1.1,310380.1.1.1,demod:310378] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 310515 [para:310436.1.1,310380.1.1.1,demod:310378] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 310517 [para:310495.1.1,310380.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c7,X))).
% 310521 [para:310474.1.1,310514.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 310525 [para:310495.1.1,310515.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 310531 [para:310436.1.1,310513.1.2.2] equal(sk_c1,multiply(inverse(sk_c8),identity)).
% 310532 [para:310512.1.1,310513.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 310534 [para:310521.1.2,310513.1.2.2,demod:310532] equal(sk_c7,sk_c8).
% 310536 [para:310534.1.1,310423.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 310538 [para:310534.1.1,310512.1.1.1,demod:310525] equal(sk_c7,sk_c6).
% 310539 [para:310534.1.1,310514.1.2.1] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 310547 [para:310538.1.1,310534.1.1] equal(sk_c6,sk_c8).
% 310552 [para:310536.1.1,310513.1.2.2,demod:310531] equal(sk_c2,sk_c1).
% 310554 [para:310514.1.2,310517.1.2.2,demod:310539] equal(X,multiply(sk_c1,X)).
% 310558 [para:310552.1.1,310514.1.2.2.1,demod:310554] equal(X,multiply(sk_c7,X)).
% 310564 [para:310558.1.2,310423.1.1] equal(sk_c2,identity).
% 310567 [para:310564.1.1,310420.1.1.1] equal(inverse(identity),sk_c7).
% 310570 [hyper:310381,310567,demod:310521,310378,cut:310534,cut:310547] 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(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Z,U),sk_c8) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(inverse(Y),sk_c7) | -equal(multiply(Y,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 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(35,40,0,75,0,0,841,50,6,881,0,6,1923,50,21,1963,0,21,2986,50,36,3026,0,36,4151,50,49,4191,0,49,5395,50,67,5435,0,67,6767,50,95,6807,0,95,8243,50,140,8283,0,140,9873,50,221,9913,0,221,11633,50,375,11673,0,375,13573,50,612,13613,0,612,15669,50,1025,15669,40,1025,15709,0,1025,25193,3,1326,26038,4,1476,26841,5,1626,26842,1,1626,26842,50,1626,26842,40,1626,26882,0,1626,27504,3,1940,27515,4,2119,27600,5,2227,27600,1,2227,27600,50,2227,27600,40,2227,27640,0,2227,52486,3,3732,53513,4,4478,54516,5,5228,54517,1,5228,54517,50,5229,54517,40,5229,54557,0,5229,72264,3,5981,72952,4,6355,73571,1,6730,73571,50,6730,73571,40,6730,73611,0,6730,85756,3,7483,86924,4,7856,88333,5,8231,88334,5,8231,88335,1,8231,88335,50,8231,88335,40,8231,88375,0,8231,154923,3,12132,156037,4,14083,157175,5,16032,157176,1,16032,157176,50,16034,157176,40,16034,157216,0,16034,204884,3,18586,205906,4,19861,206710,5,21135,206711,1,21135,206711,50,21137,206711,40,21137,206751,0,21137,248057,3,22638,248827,4,23388,249613,1,24138,249613,50,24139,249613,40,24139,249653,0,24139,258107,3,24900,259011,4,25266,259496,5,25640,259496,1,25640,259496,50,25640,259496,40,25640,259536,0,25640,287548,3,26841,288342,4,27441,289132,1,28041,289132,50,28042,289132,40,28042,289172,0,28042,308818,3,28794,309546,4,29168,310057,1,29543,310057,50,29543,310057,40,29543,310057,40,29543,310092,0,29543,310194,50,29544,310229,0,29544,310376,50,29545,310376,30,29545,310376,40,29545,310411,0,29551,310569,50,29551,310569,30,29551,310569,40,29551,310604,0,29551,310715,50,29552,310750,0,29552)
%
%
% START OF PROOF
% 310717 [] equal(multiply(identity,X),X).
% 310718 [] equal(multiply(inverse(X),X),identity).
% 310719 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 310720 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 310721 [?] ?
% 310722 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 310723 [?] ?
% 310724 [?] ?
% 310725 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(multiply(sk_c3,sk_c4),sk_c8).
% 310726 [?] ?
% 310727 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c5),sk_c8).
% 310728 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c7).
% 310729 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c2),sk_c7).
% 310730 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c4).
% 310731 [] equal(multiply(sk_c3,sk_c4),sk_c8) | equal(inverse(sk_c2),sk_c7).
% 310732 [] equal(multiply(sk_c8,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 310753 [hyper:310720,310727,binarycut:310721] equal(inverse(sk_c5),sk_c8).
% 310754 [para:310753.1.1,310718.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 310758 [hyper:310720,310730,binarycut:310724] equal(inverse(sk_c3),sk_c4).
% 310759 [para:310758.1.1,310718.1.1.1] equal(multiply(sk_c4,sk_c3),identity).
% 310765 [hyper:310720,310728,binarycut:310722] equal(multiply(sk_c5,sk_c8),sk_c6).
% 310768 [hyper:310720,310729,binarycut:310723] equal(multiply(sk_c4,sk_c7),sk_c8).
% 310774 [hyper:310720,310731,binarycut:310725] equal(multiply(sk_c3,sk_c4),sk_c8).
% 310778 [hyper:310720,310732,binarycut:310726] equal(multiply(sk_c8,sk_c6),sk_c7).
% 310780 [para:310718.1.1,310719.1.1.1,demod:310717] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 310781 [para:310754.1.1,310719.1.1.1,demod:310717] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 310782 [para:310759.1.1,310719.1.1.1,demod:310717] equal(X,multiply(sk_c4,multiply(sk_c3,X))).
% 310783 [para:310765.1.1,310719.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c5,multiply(sk_c8,X))).
% 310784 [para:310768.1.1,310719.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c4,multiply(sk_c7,X))).
% 310788 [para:310778.1.1,310719.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c6,X))).
% 310789 [para:310765.1.1,310781.1.2.2,demod:310778] equal(sk_c8,sk_c7).
% 310790 [para:310789.1.2,310768.1.1.2] equal(multiply(sk_c4,sk_c8),sk_c8).
% 310792 [para:310774.1.1,310782.1.2.2,demod:310790] equal(sk_c4,sk_c8).
% 310794 [para:310718.1.1,310780.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 310796 [para:310759.1.1,310780.1.2.2] equal(sk_c3,multiply(inverse(sk_c4),identity)).
% 310798 [para:310719.1.1,310780.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 310801 [para:310782.1.2,310780.1.2.2] equal(multiply(sk_c3,X),multiply(inverse(sk_c4),X)).
% 310802 [para:310780.1.2,310780.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 310803 [para:310792.1.2,310754.1.1.1] equal(multiply(sk_c4,sk_c5),identity).
% 310804 [para:310792.1.2,310765.1.1.2] equal(multiply(sk_c5,sk_c4),sk_c6).
% 310808 [para:310803.1.1,310780.1.2.2,demod:310796] equal(sk_c5,sk_c3).
% 310813 [para:310804.1.1,310781.1.2.2,demod:310778] equal(sk_c4,sk_c7).
% 310814 [para:310808.1.1,310804.1.1.1,demod:310774] equal(sk_c8,sk_c6).
% 310815 [para:310813.1.2,310789.1.2] equal(sk_c8,sk_c4).
% 310818 [para:310783.1.2,310781.1.2.2,demod:310788] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 310819 [?] ?
% 310820 [para:310808.1.1,310783.1.2.1] equal(multiply(sk_c6,X),multiply(sk_c3,multiply(sk_c8,X))).
% 310824 [para:310814.1.1,310781.1.2.1,demod:310819] equal(X,multiply(sk_c5,X)).
% 310827 [para:310815.1.1,310781.1.2.1,demod:310824] equal(X,multiply(sk_c4,X)).
% 310828 [para:310815.1.1,310783.1.2.2.1,demod:310824,310827] equal(multiply(sk_c6,X),X).
% 310833 [para:310784.1.2,310780.1.2.2,demod:310828,310820,310801,310818] equal(multiply(sk_c8,X),X).
% 310839 [para:310828.1.1,310780.1.2.2] equal(X,multiply(inverse(sk_c6),X)).
% 310847 [para:310839.1.2,310718.1.1] equal(sk_c6,identity).
% 310848 [para:310847.1.1,310778.1.1.2,demod:310833] equal(identity,sk_c7).
% 310867 [para:310778.1.1,310798.1.2.1.1,demod:310833,310828] equal(X,multiply(inverse(sk_c7),X)).
% 310878 [para:310802.1.2,310718.1.1] equal(multiply(X,inverse(X)),identity).
% 310880 [para:310802.1.2,310794.1.2] equal(X,multiply(X,identity)).
% 310881 [para:310880.1.2,310794.1.2] equal(X,inverse(inverse(X))).
% 310884 [para:310880.1.2,310867.1.2] equal(identity,inverse(sk_c7)).
% 310887 [para:310878.1.1,310798.1.2.2.2,demod:310880] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 310889 [para:310781.1.2,310887.1.2.1.1,demod:310824] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 310900 [para:310889.1.2,310802.1.2,demod:310881] equal(multiply(X,sk_c8),X).
% 310902 [para:310814.1.1,310900.1.1.2] equal(multiply(X,sk_c6),X).
% 310909 [hyper:310720,310902,demod:310884,cut:310848] 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(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Z,U),sk_c8) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,841,50,6,881,0,6,1923,50,21,1963,0,21,2986,50,36,3026,0,36,4151,50,49,4191,0,49,5395,50,67,5435,0,67,6767,50,95,6807,0,95,8243,50,140,8283,0,140,9873,50,221,9913,0,221,11633,50,375,11673,0,375,13573,50,612,13613,0,612,15669,50,1025,15669,40,1025,15709,0,1025,25193,3,1326,26038,4,1476,26841,5,1626,26842,1,1626,26842,50,1626,26842,40,1626,26882,0,1626,27504,3,1940,27515,4,2119,27600,5,2227,27600,1,2227,27600,50,2227,27600,40,2227,27640,0,2227,52486,3,3732,53513,4,4478,54516,5,5228,54517,1,5228,54517,50,5229,54517,40,5229,54557,0,5229,72264,3,5981,72952,4,6355,73571,1,6730,73571,50,6730,73571,40,6730,73611,0,6730,85756,3,7483,86924,4,7856,88333,5,8231,88334,5,8231,88335,1,8231,88335,50,8231,88335,40,8231,88375,0,8231,154923,3,12132,156037,4,14083,157175,5,16032,157176,1,16032,157176,50,16034,157176,40,16034,157216,0,16034,204884,3,18586,205906,4,19861,206710,5,21135,206711,1,21135,206711,50,21137,206711,40,21137,206751,0,21137,248057,3,22638,248827,4,23388,249613,1,24138,249613,50,24139,249613,40,24139,249653,0,24139,258107,3,24900,259011,4,25266,259496,5,25640,259496,1,25640,259496,50,25640,259496,40,25640,259536,0,25640,287548,3,26841,288342,4,27441,289132,1,28041,289132,50,28042,289132,40,28042,289172,0,28042,308818,3,28794,309546,4,29168,310057,1,29543,310057,50,29543,310057,40,29543,310057,40,29543,310092,0,29543,310194,50,29544,310229,0,29544,310376,50,29545,310376,30,29545,310376,40,29545,310411,0,29551,310569,50,29551,310569,30,29551,310569,40,29551,310604,0,29551,310715,50,29552,310750,0,29552,310908,50,29555,310908,30,29555,310908,40,29555,310943,0,29559,311062,50,29560,311097,0,29560)
%
%
% START OF PROOF
% 311064 [] equal(multiply(identity,X),X).
% 311065 [] equal(multiply(inverse(X),X),identity).
% 311066 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 311067 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c8).
% 311080 [?] ?
% 311081 [?] ?
% 311082 [?] ?
% 311083 [?] ?
% 311084 [?] ?
% 311085 [?] ?
% 311086 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 311087 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 311088 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 311089 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c4).
% 311090 [] equal(multiply(sk_c3,sk_c4),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 311091 [] equal(multiply(sk_c8,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 311104 [hyper:311067,311086,binarycut:311080] equal(inverse(sk_c5),sk_c8).
% 311108 [para:311104.1.1,311065.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 311112 [hyper:311067,311089,binarycut:311083] equal(inverse(sk_c3),sk_c4).
% 311114 [para:311112.1.1,311065.1.1.1] equal(multiply(sk_c4,sk_c3),identity).
% 311126 [hyper:311067,311087,binarycut:311081] equal(multiply(sk_c5,sk_c8),sk_c6).
% 311130 [hyper:311067,311088,binarycut:311082] equal(multiply(sk_c4,sk_c7),sk_c8).
% 311137 [hyper:311067,311090,binarycut:311084] equal(multiply(sk_c3,sk_c4),sk_c8).
% 311140 [hyper:311067,311091,binarycut:311085] equal(multiply(sk_c8,sk_c6),sk_c7).
% 311141 [para:311065.1.1,311066.1.1.1,demod:311064] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 311142 [para:311108.1.1,311066.1.1.1,demod:311064] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 311143 [para:311114.1.1,311066.1.1.1,demod:311064] equal(X,multiply(sk_c4,multiply(sk_c3,X))).
% 311144 [para:311126.1.1,311066.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c5,multiply(sk_c8,X))).
% 311145 [para:311130.1.1,311066.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c4,multiply(sk_c7,X))).
% 311147 [para:311140.1.1,311066.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c6,X))).
% 311148 [para:311126.1.1,311142.1.2.2,demod:311140] equal(sk_c8,sk_c7).
% 311149 [para:311148.1.2,311130.1.1.2] equal(multiply(sk_c4,sk_c8),sk_c8).
% 311151 [para:311137.1.1,311143.1.2.2,demod:311149] equal(sk_c4,sk_c8).
% 311153 [para:311065.1.1,311141.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 311154 [para:311108.1.1,311141.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),identity)).
% 311155 [para:311114.1.1,311141.1.2.2] equal(sk_c3,multiply(inverse(sk_c4),identity)).
% 311157 [para:311066.1.1,311141.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 311160 [para:311143.1.2,311141.1.2.2] equal(multiply(sk_c3,X),multiply(inverse(sk_c4),X)).
% 311161 [para:311141.1.2,311141.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 311162 [para:311151.1.2,311108.1.1.1] equal(multiply(sk_c4,sk_c5),identity).
% 311163 [para:311151.1.2,311126.1.1.2] equal(multiply(sk_c5,sk_c4),sk_c6).
% 311167 [para:311162.1.1,311141.1.2.2,demod:311155] equal(sk_c5,sk_c3).
% 311172 [para:311163.1.1,311142.1.2.2,demod:311140] equal(sk_c4,sk_c7).
% 311173 [para:311167.1.1,311163.1.1.1,demod:311137] equal(sk_c8,sk_c6).
% 311174 [para:311172.1.2,311148.1.2] equal(sk_c8,sk_c4).
% 311177 [para:311144.1.2,311142.1.2.2,demod:311147] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 311178 [?] ?
% 311179 [para:311167.1.1,311144.1.2.1] equal(multiply(sk_c6,X),multiply(sk_c3,multiply(sk_c8,X))).
% 311183 [para:311173.1.1,311142.1.2.1,demod:311178] equal(X,multiply(sk_c5,X)).
% 311186 [para:311174.1.1,311142.1.2.1,demod:311183] equal(X,multiply(sk_c4,X)).
% 311187 [para:311174.1.1,311144.1.2.2.1,demod:311183,311186] equal(multiply(sk_c6,X),X).
% 311192 [para:311145.1.2,311141.1.2.2,demod:311187,311179,311160,311177] equal(multiply(sk_c8,X),X).
% 311233 [para:311161.1.2,311065.1.1] equal(multiply(X,inverse(X)),identity).
% 311235 [para:311161.1.2,311153.1.2] equal(X,multiply(X,identity)).
% 311236 [para:311235.1.2,311153.1.2] equal(X,inverse(inverse(X))).
% 311237 [para:311235.1.2,311154.1.2] equal(sk_c5,inverse(sk_c8)).
% 311242 [para:311233.1.1,311157.1.2.2.2,demod:311235] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 311244 [para:311142.1.2,311242.1.2.1.1,demod:311183] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 311251 [para:311177.1.2,311242.1.2.1.1,demod:311192] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 311255 [para:311244.1.2,311161.1.2,demod:311236] equal(multiply(X,sk_c8),X).
% 311258 [para:311255.1.1,311183.1.2] equal(sk_c8,sk_c5).
% 311263 [para:311258.1.1,311237.1.2.1,demod:311104] equal(sk_c5,sk_c8).
% 311265 [para:311251.1.2,311161.1.2,demod:311236] equal(multiply(X,sk_c7),X).
% 311266 [hyper:311067,311265,demod:311237,cut:311263] 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 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Z,U),sk_c8) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% 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(35,40,0,75,0,0,841,50,6,881,0,6,1923,50,21,1963,0,21,2986,50,36,3026,0,36,4151,50,49,4191,0,49,5395,50,67,5435,0,67,6767,50,95,6807,0,95,8243,50,140,8283,0,140,9873,50,221,9913,0,221,11633,50,375,11673,0,375,13573,50,612,13613,0,612,15669,50,1025,15669,40,1025,15709,0,1025,25193,3,1326,26038,4,1476,26841,5,1626,26842,1,1626,26842,50,1626,26842,40,1626,26882,0,1626,27504,3,1940,27515,4,2119,27600,5,2227,27600,1,2227,27600,50,2227,27600,40,2227,27640,0,2227,52486,3,3732,53513,4,4478,54516,5,5228,54517,1,5228,54517,50,5229,54517,40,5229,54557,0,5229,72264,3,5981,72952,4,6355,73571,1,6730,73571,50,6730,73571,40,6730,73611,0,6730,85756,3,7483,86924,4,7856,88333,5,8231,88334,5,8231,88335,1,8231,88335,50,8231,88335,40,8231,88375,0,8231,154923,3,12132,156037,4,14083,157175,5,16032,157176,1,16032,157176,50,16034,157176,40,16034,157216,0,16034,204884,3,18586,205906,4,19861,206710,5,21135,206711,1,21135,206711,50,21137,206711,40,21137,206751,0,21137,248057,3,22638,248827,4,23388,249613,1,24138,249613,50,24139,249613,40,24139,249653,0,24139,258107,3,24900,259011,4,25266,259496,5,25640,259496,1,25640,259496,50,25640,259496,40,25640,259536,0,25640,287548,3,26841,288342,4,27441,289132,1,28041,289132,50,28042,289132,40,28042,289172,0,28042,308818,3,28794,309546,4,29168,310057,1,29543,310057,50,29543,310057,40,29543,310057,40,29543,310092,0,29543,310194,50,29544,310229,0,29544,310376,50,29545,310376,30,29545,310376,40,29545,310411,0,29551,310569,50,29551,310569,30,29551,310569,40,29551,310604,0,29551,310715,50,29552,310750,0,29552,310908,50,29555,310908,30,29555,310908,40,29555,310943,0,29559,311062,50,29560,311097,0,29560,311265,50,29562,311265,30,29562,311265,40,29562,311300,0,29568,311435,50,29569,311470,0,29569,311649,50,29572,311684,0,29572,311871,50,29576,311906,0,29581,312101,50,29587,312136,0,29587,312337,50,29598,312372,0,29602,312581,50,29620,312616,0,29620,312833,50,29651,312868,0,29652,313095,50,29719,313130,0,29719,313367,50,29842,313367,40,29842,313402,0,29842)
%
%
% START OF PROOF
% 313223 [?] ?
% 313369 [] equal(multiply(identity,X),X).
% 313370 [] equal(multiply(inverse(X),X),identity).
% 313371 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 313372 [] -equal(multiply(sk_c7,sk_c8),sk_c6).
% 313397 [?] ?
% 313398 [?] ?
% 313399 [?] ?
% 313400 [?] ?
% 313401 [?] ?
% 313402 [?] ?
% 313441 [input:313397,cut:313372] equal(inverse(sk_c5),sk_c8).
% 313442 [para:313441.1.1,313370.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 313444 [input:313400,cut:313372] equal(inverse(sk_c3),sk_c4).
% 313445 [para:313444.1.1,313370.1.1.1] equal(multiply(sk_c4,sk_c3),identity).
% 313455 [input:313398,cut:313372] equal(multiply(sk_c5,sk_c8),sk_c6).
% 313456 [input:313399,cut:313372] equal(multiply(sk_c4,sk_c7),sk_c8).
% 313457 [input:313401,cut:313372] equal(multiply(sk_c3,sk_c4),sk_c8).
% 313458 [input:313402,cut:313372] equal(multiply(sk_c8,sk_c6),sk_c7).
% 313479 [para:313442.1.1,313371.1.1.1,demod:313369] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 313480 [para:313445.1.1,313371.1.1.1,demod:313369] equal(X,multiply(sk_c4,multiply(sk_c3,X))).
% 313504 [para:313455.1.1,313479.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 313509 [para:313504.1.2,313458.1.1] equal(sk_c8,sk_c7).
% 313511 [para:313509.1.2,313372.1.1.1] -equal(multiply(sk_c8,sk_c8),sk_c6).
% 313523 [para:313509.1.2,313456.1.1.2] equal(multiply(sk_c4,sk_c8),sk_c8).
% 313533 [para:313457.1.1,313480.1.2.2,demod:313523] equal(sk_c4,sk_c8).
% 313549 [para:313533.1.2,313511.1.1.1,demod:313523,cut:313223] 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(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Z,U),sk_c8) | -equal(inverse(Z),U) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(V,sk_c8),sk_c6) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,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 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(35,40,0,75,0,0,841,50,6,881,0,6,1923,50,21,1963,0,21,2986,50,36,3026,0,36,4151,50,49,4191,0,49,5395,50,67,5435,0,67,6767,50,95,6807,0,95,8243,50,140,8283,0,140,9873,50,221,9913,0,221,11633,50,375,11673,0,375,13573,50,612,13613,0,612,15669,50,1025,15669,40,1025,15709,0,1025,25193,3,1326,26038,4,1476,26841,5,1626,26842,1,1626,26842,50,1626,26842,40,1626,26882,0,1626,27504,3,1940,27515,4,2119,27600,5,2227,27600,1,2227,27600,50,2227,27600,40,2227,27640,0,2227,52486,3,3732,53513,4,4478,54516,5,5228,54517,1,5228,54517,50,5229,54517,40,5229,54557,0,5229,72264,3,5981,72952,4,6355,73571,1,6730,73571,50,6730,73571,40,6730,73611,0,6730,85756,3,7483,86924,4,7856,88333,5,8231,88334,5,8231,88335,1,8231,88335,50,8231,88335,40,8231,88375,0,8231,154923,3,12132,156037,4,14083,157175,5,16032,157176,1,16032,157176,50,16034,157176,40,16034,157216,0,16034,204884,3,18586,205906,4,19861,206710,5,21135,206711,1,21135,206711,50,21137,206711,40,21137,206751,0,21137,248057,3,22638,248827,4,23388,249613,1,24138,249613,50,24139,249613,40,24139,249653,0,24139,258107,3,24900,259011,4,25266,259496,5,25640,259496,1,25640,259496,50,25640,259496,40,25640,259536,0,25640,287548,3,26841,288342,4,27441,289132,1,28041,289132,50,28042,289132,40,28042,289172,0,28042,308818,3,28794,309546,4,29168,310057,1,29543,310057,50,29543,310057,40,29543,310057,40,29543,310092,0,29543,310194,50,29544,310229,0,29544,310376,50,29545,310376,30,29545,310376,40,29545,310411,0,29551,310569,50,29551,310569,30,29551,310569,40,29551,310604,0,29551,310715,50,29552,310750,0,29552,310908,50,29555,310908,30,29555,310908,40,29555,310943,0,29559,311062,50,29560,311097,0,29560,311265,50,29562,311265,30,29562,311265,40,29562,311300,0,29568,311435,50,29569,311470,0,29569,311649,50,29572,311684,0,29572,311871,50,29576,311906,0,29581,312101,50,29587,312136,0,29587,312337,50,29598,312372,0,29602,312581,50,29620,312616,0,29620,312833,50,29651,312868,0,29652,313095,50,29719,313130,0,29719,313367,50,29842,313367,40,29842,313402,0,29842,313548,50,29843,313548,30,29843,313548,40,29843,313583,0,29843,313688,50,29843,313723,0,29848,313872,50,29850,313907,0,29850,314064,50,29854,314099,0,29854,314264,50,29860,314299,0,29865,314470,50,29873,314505,0,29874,314684,50,29889,314719,0,29894,314906,50,29923,314941,0,29923,315138,50,29986,315173,0,29986,315380,50,30102,315380,40,30102,315415,0,30103)
%
%
% START OF PROOF
% 315325 [?] ?
% 315382 [] equal(multiply(identity,X),X).
% 315383 [] equal(multiply(inverse(X),X),identity).
% 315384 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 315385 [] -equal(multiply(sk_c8,sk_c6),sk_c7).
% 315391 [?] ?
% 315397 [?] ?
% 315415 [?] ?
% 315439 [input:315397,cut:315385] equal(inverse(sk_c2),sk_c7).
% 315440 [para:315439.1.1,315383.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 315460 [input:315391,cut:315385] equal(multiply(sk_c2,sk_c6),sk_c7).
% 315471 [input:315415,cut:315385] equal(multiply(sk_c7,sk_c8),sk_c6).
% 315474 [para:315383.1.1,315384.1.1.1,demod:315382] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 315482 [para:315440.1.1,315384.1.1.1,demod:315382] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 315521 [para:315460.1.1,315482.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 315574 [para:315471.1.1,315474.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 315579 [para:315521.1.2,315474.1.2.2,demod:315574] equal(sk_c7,sk_c8).
% 315583 [para:315579.1.1,315385.1.2,cut:315325] 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: 35812
% derived clauses: 5910273
% kept clauses: 261786
% kept size sum: 319522
% kept mid-nuclei: 11989
% kept new demods: 4617
% forw unit-subs: 2409810
% forw double-subs: 2908270
% forw overdouble-subs: 275512
% backward subs: 8603
% fast unit cutoff: 17783
% full unit cutoff: 0
% dbl unit cutoff: 7296
% real runtime : 302.61
% process. runtime: 301.3
% specific non-discr-tree subsumption statistics:
% tried: 41637359
% length fails: 4485448
% strength fails: 14752516
% predlist fails: 3389136
% aux str. fails: 5587779
% by-lit fails: 6707742
% full subs tried: 1806339
% full subs fail: 1694457
%
% ; 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/GRP342-1+eq_r.in")
%
%------------------------------------------------------------------------------