TSTP Solution File: GRP310-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP310-1 : 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 : art03.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 299.3s
% Output : Assurance 299.3s
% 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/GRP310-1+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_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% was split for some strategies as:
% -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8).
% -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% -equal(multiply(sk_c8,sk_c7),sk_c6).
% -equal(inverse(sk_c8),sk_c6).
% -equal(multiply(sk_c6,sk_c7),sk_c8).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(31,40,1,66,0,2,141196,5,1503,141198,1,1503,141198,50,1503,141198,40,1503,141233,0,1503,154093,3,1804,154741,4,1954,155280,5,2104,155281,1,2104,155281,50,2104,155281,40,2104,155316,0,2104,155611,3,2411,155629,4,2575,155635,5,2705,155635,1,2705,155635,50,2705,155635,40,2705,155670,0,2705,184757,3,4206,185556,4,4956,186154,5,5706,186155,1,5706,186155,50,5707,186155,40,5707,186190,0,5707,204870,3,6458,205508,4,6833,205997,5,7208,205998,1,7208,205998,50,7208,205998,40,7208,206033,0,7208,218374,3,7959,218812,4,8334,219224,50,8704,219224,40,8704,219259,0,8704,277512,3,12606,278509,4,14555,279354,1,16505,279354,50,16507,279354,40,16507,279389,0,16507,323479,3,19060,324373,4,20333,325329,5,21608,325330,1,21608,325330,50,21609,325330,40,21609,325365,0,21609,375126,3,23111,375504,4,23860,375957,1,24611,375957,50,24613,375957,40,24613,375992,0,24613,392883,3,25364,393624,4,25739,394459,5,26114,394460,1,26114,394460,50,26114,394460,40,26114,394495,0,26114,427207,3,27316,427603,4,27915,428080,1,28515,428080,50,28516,428080,40,28516,428115,0,28516,459155,3,29267,459628,4,29642,460123,1,30017,460123,50,30018,460123,40,30018,460123,40,30018,460154,0,30018)
%
%
% START OF PROOF
% 460124 [] equal(X,X).
% 460128 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 460129 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 460130 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c8).
% 460131 [?] ?
% 460134 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c4),sk_c8).
% 460135 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 460136 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 460139 [?] ?
% 460140 [?] ?
% 460141 [?] ?
% 460186 [hyper:460128,460130,460129,binarycut:460131] equal(inverse(sk_c1),sk_c8).
% 460198 [hyper:460128,460134,demod:460186,cut:460124,binarycut:460139] equal(inverse(sk_c4),sk_c8).
% 460210 [hyper:460128,460135,demod:460186,cut:460124,binarycut:460140] equal(multiply(sk_c4,sk_c8),sk_c5).
% 460232 [hyper:460128,460136,demod:460186,cut:460124,binarycut:460141] equal(multiply(sk_c8,sk_c5),sk_c7).
% 460245 [hyper:460128,460232,460210,demod:460198,cut:460124] 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 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% 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(31,40,1,66,0,2,141196,5,1503,141198,1,1503,141198,50,1503,141198,40,1503,141233,0,1503,154093,3,1804,154741,4,1954,155280,5,2104,155281,1,2104,155281,50,2104,155281,40,2104,155316,0,2104,155611,3,2411,155629,4,2575,155635,5,2705,155635,1,2705,155635,50,2705,155635,40,2705,155670,0,2705,184757,3,4206,185556,4,4956,186154,5,5706,186155,1,5706,186155,50,5707,186155,40,5707,186190,0,5707,204870,3,6458,205508,4,6833,205997,5,7208,205998,1,7208,205998,50,7208,205998,40,7208,206033,0,7208,218374,3,7959,218812,4,8334,219224,50,8704,219224,40,8704,219259,0,8704,277512,3,12606,278509,4,14555,279354,1,16505,279354,50,16507,279354,40,16507,279389,0,16507,323479,3,19060,324373,4,20333,325329,5,21608,325330,1,21608,325330,50,21609,325330,40,21609,325365,0,21609,375126,3,23111,375504,4,23860,375957,1,24611,375957,50,24613,375957,40,24613,375992,0,24613,392883,3,25364,393624,4,25739,394459,5,26114,394460,1,26114,394460,50,26114,394460,40,26114,394495,0,26114,427207,3,27316,427603,4,27915,428080,1,28515,428080,50,28516,428080,40,28516,428115,0,28516,459155,3,29267,459628,4,29642,460123,1,30017,460123,50,30018,460123,40,30018,460123,40,30018,460154,0,30018,460244,50,30018,460244,30,30018,460244,40,30018,460275,0,30018,460390,50,30019,460421,0,30023)
%
%
% START OF PROOF
% 460392 [] equal(multiply(identity,X),X).
% 460393 [] equal(multiply(inverse(X),X),identity).
% 460394 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 460395 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 460399 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 460400 [?] ?
% 460404 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c3),sk_c8).
% 460405 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 460409 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 460410 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 460414 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 460415 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 460419 [] equal(inverse(sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 460420 [?] ?
% 460429 [hyper:460395,460399,binarycut:460400] equal(inverse(sk_c1),sk_c8).
% 460432 [para:460429.1.1,460393.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 460442 [hyper:460395,460419,binarycut:460420] equal(inverse(sk_c8),sk_c6).
% 460443 [para:460442.1.1,460393.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 460463 [hyper:460395,460405,460404] equal(multiply(sk_c1,sk_c8),sk_c2).
% 460468 [hyper:460395,460410,460409] equal(multiply(sk_c8,sk_c2),sk_c7).
% 460473 [hyper:460395,460415,460414] equal(multiply(sk_c6,sk_c7),sk_c8).
% 460475 [para:460393.1.1,460394.1.1.1,demod:460392] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 460476 [para:460432.1.1,460394.1.1.1,demod:460392] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 460481 [para:460463.1.1,460476.1.2.2,demod:460468] equal(sk_c8,sk_c7).
% 460484 [para:460481.1.1,460442.1.1.1] equal(inverse(sk_c7),sk_c6).
% 460485 [para:460481.1.1,460443.1.1.2,demod:460473] equal(sk_c8,identity).
% 460492 [para:460393.1.1,460475.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 460497 [para:460394.1.1,460475.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 460498 [para:460476.1.2,460475.1.2.2,demod:460442] equal(multiply(sk_c1,X),multiply(sk_c6,X)).
% 460500 [para:460475.1.2,460475.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 460502 [para:460485.1.1,460432.1.1.1,demod:460392] equal(sk_c1,identity).
% 460503 [para:460485.1.1,460442.1.1.1] equal(inverse(identity),sk_c6).
% 460506 [para:460485.1.1,460476.1.2.1,demod:460392,460498] equal(X,multiply(sk_c6,X)).
% 460519 [para:460502.1.1,460429.1.1.1,demod:460503] equal(sk_c6,sk_c8).
% 460547 [para:460476.1.2,460497.1.2.2.2,demod:460506,460498] equal(X,multiply(inverse(multiply(Y,sk_c8)),multiply(Y,X))).
% 460554 [para:460500.1.2,460393.1.1] equal(multiply(X,inverse(X)),identity).
% 460556 [para:460500.1.2,460492.1.2] equal(X,multiply(X,identity)).
% 460557 [para:460556.1.2,460492.1.2] equal(X,inverse(inverse(X))).
% 460561 [para:460554.1.1,460547.1.2.2,demod:460556] equal(inverse(X),inverse(multiply(X,sk_c8))).
% 460572 [para:460561.1.2,460492.1.2.1.1,demod:460556,460557] equal(multiply(X,sk_c8),X).
% 460573 [hyper:460395,460572,demod:460484,cut:460519] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(31,40,1,66,0,2,141196,5,1503,141198,1,1503,141198,50,1503,141198,40,1503,141233,0,1503,154093,3,1804,154741,4,1954,155280,5,2104,155281,1,2104,155281,50,2104,155281,40,2104,155316,0,2104,155611,3,2411,155629,4,2575,155635,5,2705,155635,1,2705,155635,50,2705,155635,40,2705,155670,0,2705,184757,3,4206,185556,4,4956,186154,5,5706,186155,1,5706,186155,50,5707,186155,40,5707,186190,0,5707,204870,3,6458,205508,4,6833,205997,5,7208,205998,1,7208,205998,50,7208,205998,40,7208,206033,0,7208,218374,3,7959,218812,4,8334,219224,50,8704,219224,40,8704,219259,0,8704,277512,3,12606,278509,4,14555,279354,1,16505,279354,50,16507,279354,40,16507,279389,0,16507,323479,3,19060,324373,4,20333,325329,5,21608,325330,1,21608,325330,50,21609,325330,40,21609,325365,0,21609,375126,3,23111,375504,4,23860,375957,1,24611,375957,50,24613,375957,40,24613,375992,0,24613,392883,3,25364,393624,4,25739,394459,5,26114,394460,1,26114,394460,50,26114,394460,40,26114,394495,0,26114,427207,3,27316,427603,4,27915,428080,1,28515,428080,50,28516,428080,40,28516,428115,0,28516,459155,3,29267,459628,4,29642,460123,1,30017,460123,50,30018,460123,40,30018,460123,40,30018,460154,0,30018,460244,50,30018,460244,30,30018,460244,40,30018,460275,0,30018,460390,50,30019,460421,0,30023,460572,50,30023,460572,30,30023,460572,40,30023,460603,0,30023)
%
%
% START OF PROOF
% 460573 [] equal(X,X).
% 460577 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 460578 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 460579 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c8).
% 460580 [?] ?
% 460583 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c4),sk_c8).
% 460584 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 460585 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 460588 [?] ?
% 460589 [?] ?
% 460590 [?] ?
% 460635 [hyper:460577,460579,460578,binarycut:460580] equal(inverse(sk_c1),sk_c8).
% 460647 [hyper:460577,460583,demod:460635,cut:460573,binarycut:460588] equal(inverse(sk_c4),sk_c8).
% 460659 [hyper:460577,460584,demod:460635,cut:460573,binarycut:460589] equal(multiply(sk_c4,sk_c8),sk_c5).
% 460681 [hyper:460577,460585,demod:460635,cut:460573,binarycut:460590] equal(multiply(sk_c8,sk_c5),sk_c7).
% 460694 [hyper:460577,460681,460659,demod:460647,cut:460573] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,sk_c7),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(31,40,1,66,0,2,141196,5,1503,141198,1,1503,141198,50,1503,141198,40,1503,141233,0,1503,154093,3,1804,154741,4,1954,155280,5,2104,155281,1,2104,155281,50,2104,155281,40,2104,155316,0,2104,155611,3,2411,155629,4,2575,155635,5,2705,155635,1,2705,155635,50,2705,155635,40,2705,155670,0,2705,184757,3,4206,185556,4,4956,186154,5,5706,186155,1,5706,186155,50,5707,186155,40,5707,186190,0,5707,204870,3,6458,205508,4,6833,205997,5,7208,205998,1,7208,205998,50,7208,205998,40,7208,206033,0,7208,218374,3,7959,218812,4,8334,219224,50,8704,219224,40,8704,219259,0,8704,277512,3,12606,278509,4,14555,279354,1,16505,279354,50,16507,279354,40,16507,279389,0,16507,323479,3,19060,324373,4,20333,325329,5,21608,325330,1,21608,325330,50,21609,325330,40,21609,325365,0,21609,375126,3,23111,375504,4,23860,375957,1,24611,375957,50,24613,375957,40,24613,375992,0,24613,392883,3,25364,393624,4,25739,394459,5,26114,394460,1,26114,394460,50,26114,394460,40,26114,394495,0,26114,427207,3,27316,427603,4,27915,428080,1,28515,428080,50,28516,428080,40,28516,428115,0,28516,459155,3,29267,459628,4,29642,460123,1,30017,460123,50,30018,460123,40,30018,460123,40,30018,460154,0,30018,460244,50,30018,460244,30,30018,460244,40,30018,460275,0,30018,460390,50,30019,460421,0,30023,460572,50,30023,460572,30,30023,460572,40,30023,460603,0,30023,460693,50,30023,460693,30,30023,460693,40,30023,460724,0,30023)
%
%
% START OF PROOF
% 460698 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 460724 [] equal(multiply(sk_c8,sk_c7),sk_c6).
% 460725 [hyper:460698,460724] 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_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(inverse(sk_c8),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 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(31,40,1,66,0,2,141196,5,1503,141198,1,1503,141198,50,1503,141198,40,1503,141233,0,1503,154093,3,1804,154741,4,1954,155280,5,2104,155281,1,2104,155281,50,2104,155281,40,2104,155316,0,2104,155611,3,2411,155629,4,2575,155635,5,2705,155635,1,2705,155635,50,2705,155635,40,2705,155670,0,2705,184757,3,4206,185556,4,4956,186154,5,5706,186155,1,5706,186155,50,5707,186155,40,5707,186190,0,5707,204870,3,6458,205508,4,6833,205997,5,7208,205998,1,7208,205998,50,7208,205998,40,7208,206033,0,7208,218374,3,7959,218812,4,8334,219224,50,8704,219224,40,8704,219259,0,8704,277512,3,12606,278509,4,14555,279354,1,16505,279354,50,16507,279354,40,16507,279389,0,16507,323479,3,19060,324373,4,20333,325329,5,21608,325330,1,21608,325330,50,21609,325330,40,21609,325365,0,21609,375126,3,23111,375504,4,23860,375957,1,24611,375957,50,24613,375957,40,24613,375992,0,24613,392883,3,25364,393624,4,25739,394459,5,26114,394460,1,26114,394460,50,26114,394460,40,26114,394495,0,26114,427207,3,27316,427603,4,27915,428080,1,28515,428080,50,28516,428080,40,28516,428115,0,28516,459155,3,29267,459628,4,29642,460123,1,30017,460123,50,30018,460123,40,30018,460123,40,30018,460154,0,30018,460244,50,30018,460244,30,30018,460244,40,30018,460275,0,30018,460390,50,30019,460421,0,30023,460572,50,30023,460572,30,30023,460572,40,30023,460603,0,30023,460693,50,30023,460693,30,30023,460693,40,30023,460724,0,30023,460724,50,30023,460724,30,30023,460724,40,30023,460755,0,30027,460882,50,30028,460913,0,30028,461089,50,30032,461120,0,30036,461304,50,30041,461335,0,30041,461527,50,30047,461558,0,30047,461756,50,30058,461787,0,30062,461993,50,30080,462024,0,30080,462238,50,30112,462269,0,30117,462493,50,30179,462524,0,30179,462758,50,30306,462758,40,30306,462789,0,30306)
%
%
% START OF PROOF
% 462760 [] equal(multiply(identity,X),X).
% 462761 [] equal(multiply(inverse(X),X),identity).
% 462762 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 462763 [] -equal(inverse(sk_c8),sk_c6).
% 462784 [?] ?
% 462785 [?] ?
% 462786 [?] ?
% 462787 [?] ?
% 462788 [?] ?
% 462789 [] equal(multiply(sk_c8,sk_c7),sk_c6).
% 462796 [input:462784,cut:462763] equal(inverse(sk_c4),sk_c8).
% 462797 [para:462796.1.1,462761.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 462798 [input:462787,cut:462763] equal(inverse(sk_c3),sk_c8).
% 462799 [para:462798.1.1,462761.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 462813 [input:462785,cut:462763] equal(multiply(sk_c4,sk_c8),sk_c5).
% 462814 [input:462786,cut:462763] equal(multiply(sk_c8,sk_c5),sk_c7).
% 462816 [input:462788,cut:462763] equal(multiply(sk_c3,sk_c8),sk_c7).
% 462829 [para:462789.1.1,462762.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c8,multiply(sk_c7,X))).
% 462830 [para:462761.1.1,462762.1.1.1,demod:462760] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 462831 [para:462797.1.1,462762.1.1.1,demod:462760] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 462832 [para:462799.1.1,462762.1.1.1,demod:462760] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 462845 [para:462814.1.1,462762.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c5,X))).
% 462862 [para:462813.1.1,462831.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 462864 [para:462862.1.2,462814.1.1] equal(sk_c8,sk_c7).
% 462865 [para:462862.1.2,462762.1.1.1,demod:462845] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 462866 [para:462864.1.1,462763.1.1.1] -equal(inverse(sk_c7),sk_c6).
% 462868 [para:462864.1.1,462797.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 462869 [para:462864.1.1,462799.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 462879 [para:462864.1.1,462813.1.1.2] equal(multiply(sk_c4,sk_c7),sk_c5).
% 462880 [para:462864.1.1,462814.1.1.1] equal(multiply(sk_c7,sk_c5),sk_c7).
% 462881 [para:462864.1.1,462816.1.1.2] equal(multiply(sk_c3,sk_c7),sk_c7).
% 462892 [para:462868.1.1,462829.1.2.2,demod:462865] equal(multiply(sk_c6,sk_c4),multiply(sk_c7,identity)).
% 462898 [para:462797.1.1,462830.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 462899 [para:462799.1.1,462830.1.2.2,demod:462898] equal(sk_c3,sk_c4).
% 462937 [para:462869.1.1,462829.1.2.2,demod:462892,462865] equal(multiply(sk_c6,sk_c3),multiply(sk_c6,sk_c4)).
% 462940 [para:462899.1.2,462879.1.1.1,demod:462881] equal(sk_c7,sk_c5).
% 462945 [para:462816.1.1,462832.1.2.2,demod:462789] equal(sk_c8,sk_c6).
% 462950 [para:462940.1.1,462866.1.1.1] -equal(inverse(sk_c5),sk_c6).
% 462958 [para:462945.1.1,462797.1.1.1,demod:462937] equal(multiply(sk_c6,sk_c3),identity).
% 462976 [para:462880.1.1,462830.1.2.2,demod:462761] equal(sk_c5,identity).
% 462979 [para:462976.1.1,462814.1.1.2,demod:462958,462937,462892,462865] equal(identity,sk_c7).
% 462985 [para:462979.1.2,462868.1.1.1,demod:462760] equal(sk_c4,identity).
% 462988 [para:462979.1.2,462940.1.1] equal(identity,sk_c5).
% 463000 [para:462985.1.1,462796.1.1.1] equal(inverse(identity),sk_c8).
% 463002 [para:462988.1.2,462950.1.1.1,demod:463000,cut:462945] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c8) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c6,sk_c7),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(31,40,1,66,0,2,141196,5,1503,141198,1,1503,141198,50,1503,141198,40,1503,141233,0,1503,154093,3,1804,154741,4,1954,155280,5,2104,155281,1,2104,155281,50,2104,155281,40,2104,155316,0,2104,155611,3,2411,155629,4,2575,155635,5,2705,155635,1,2705,155635,50,2705,155635,40,2705,155670,0,2705,184757,3,4206,185556,4,4956,186154,5,5706,186155,1,5706,186155,50,5707,186155,40,5707,186190,0,5707,204870,3,6458,205508,4,6833,205997,5,7208,205998,1,7208,205998,50,7208,205998,40,7208,206033,0,7208,218374,3,7959,218812,4,8334,219224,50,8704,219224,40,8704,219259,0,8704,277512,3,12606,278509,4,14555,279354,1,16505,279354,50,16507,279354,40,16507,279389,0,16507,323479,3,19060,324373,4,20333,325329,5,21608,325330,1,21608,325330,50,21609,325330,40,21609,325365,0,21609,375126,3,23111,375504,4,23860,375957,1,24611,375957,50,24613,375957,40,24613,375992,0,24613,392883,3,25364,393624,4,25739,394459,5,26114,394460,1,26114,394460,50,26114,394460,40,26114,394495,0,26114,427207,3,27316,427603,4,27915,428080,1,28515,428080,50,28516,428080,40,28516,428115,0,28516,459155,3,29267,459628,4,29642,460123,1,30017,460123,50,30018,460123,40,30018,460123,40,30018,460154,0,30018,460244,50,30018,460244,30,30018,460244,40,30018,460275,0,30018,460390,50,30019,460421,0,30023,460572,50,30023,460572,30,30023,460572,40,30023,460603,0,30023,460693,50,30023,460693,30,30023,460693,40,30023,460724,0,30023,460724,50,30023,460724,30,30023,460724,40,30023,460755,0,30027,460882,50,30028,460913,0,30028,461089,50,30032,461120,0,30036,461304,50,30041,461335,0,30041,461527,50,30047,461558,0,30047,461756,50,30058,461787,0,30062,461993,50,30080,462024,0,30080,462238,50,30112,462269,0,30117,462493,50,30179,462524,0,30179,462758,50,30306,462758,40,30306,462789,0,30306,463001,50,30307,463001,30,30307,463001,40,30307,463032,0,30307,463159,50,30308,463190,0,30313,463366,50,30316,463397,0,30316,463581,50,30321,463612,0,30321,463804,50,30327,463835,0,30332,464033,50,30342,464064,0,30342,464270,50,30360,464301,0,30364,464515,50,30396,464546,0,30396,464770,50,30462,464801,0,30462,465035,50,30586,465035,40,30586,465066,0,30586)
%
%
% START OF PROOF
% 464892 [?] ?
% 465037 [] equal(multiply(identity,X),X).
% 465038 [] equal(multiply(inverse(X),X),identity).
% 465039 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 465040 [] -equal(multiply(sk_c6,sk_c7),sk_c8).
% 465056 [?] ?
% 465057 [?] ?
% 465058 [?] ?
% 465093 [input:465056,cut:465040] equal(inverse(sk_c4),sk_c8).
% 465094 [para:465093.1.1,465038.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 465113 [input:465057,cut:465040] equal(multiply(sk_c4,sk_c8),sk_c5).
% 465114 [input:465058,cut:465040] equal(multiply(sk_c8,sk_c5),sk_c7).
% 465128 [para:465094.1.1,465039.1.1.1,demod:465037] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 465155 [para:465113.1.1,465128.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 465160 [para:465155.1.2,465114.1.1] equal(sk_c8,sk_c7).
% 465162 [para:465160.1.1,465040.1.2,cut:464892] 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: 31982
% derived clauses: 5918150
% kept clauses: 289859
% kept size sum: 412387
% kept mid-nuclei: 117675
% kept new demods: 4243
% forw unit-subs: 2077477
% forw double-subs: 3022624
% forw overdouble-subs: 242886
% backward subs: 23761
% fast unit cutoff: 40342
% full unit cutoff: 0
% dbl unit cutoff: 27884
% real runtime : 306.99
% process. runtime: 305.86
% specific non-discr-tree subsumption statistics:
% tried: 16200156
% length fails: 1593020
% strength fails: 4837966
% predlist fails: 1062240
% aux str. fails: 2133122
% by-lit fails: 3124809
% full subs tried: 889532
% full subs fail: 775332
%
% ; 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/GRP310-1+eq_r.in")
%
%------------------------------------------------------------------------------