TSTP Solution File: GRP233-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP233-1 : 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 298.3s
% Output : Assurance 298.3s
% 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/GRP233-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% was split for some strategies as:
% -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8).
% -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(inverse(sk_c8),sk_c7).
%
% Starting a split proof attempt with 5 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,1,181994,5,1502,181994,1,1502,181994,50,1502,181994,40,1502,182034,0,1502,194379,3,1803,195078,4,1953,195778,5,2103,195779,1,2103,195779,50,2103,195779,40,2103,195819,0,2103,196110,3,2414,196118,4,2555,196126,5,2705,196126,1,2705,196126,50,2705,196126,40,2705,196166,0,2705,214142,3,4208,215561,4,4956,216508,1,5706,216508,50,5706,216508,40,5706,216548,0,5706,227175,3,6459,228727,4,6832,230977,1,7207,230977,50,7207,230977,40,7207,231017,0,7207,247091,3,7958,247784,4,8333,248162,1,8708,248162,50,8708,248162,40,8708,248202,0,8708,323539,3,12610,324543,4,14560,324888,5,16510,324889,1,16510,324889,50,16512,324889,40,16512,324929,0,16512,374227,3,19065,375033,4,20338,375537,1,21613,375537,50,21614,375537,40,21614,375577,0,21614,415347,3,23125,415996,4,23865,416561,5,24615,416562,1,24615,416562,50,24617,416562,40,24617,416602,0,24617,437044,3,25374,437469,4,25743,437868,1,26118,437868,50,26118,437868,40,26118,437908,0,26118,461167,3,27319,461945,4,27919,462570,1,28519,462570,50,28520,462570,40,28520,462610,0,28520,478959,3,29272,479602,4,29646,480239,5,30021,480240,1,30021,480240,50,30021,480240,40,30021,480240,40,30021,480275,0,30021)
%
%
% START OF PROOF
% 480241 [] equal(X,X).
% 480245 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 480246 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 480247 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c8).
% 480248 [?] ?
% 480251 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 480252 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 480253 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c8,sk_c6),sk_c7).
% 480256 [?] ?
% 480257 [?] ?
% 480258 [?] ?
% 480321 [hyper:480245,480247,480246,binarycut:480248] equal(inverse(sk_c2),sk_c8).
% 480333 [hyper:480245,480251,demod:480321,cut:480241,binarycut:480256] equal(inverse(sk_c5),sk_c8).
% 480345 [hyper:480245,480252,demod:480321,cut:480241,binarycut:480257] equal(multiply(sk_c5,sk_c8),sk_c6).
% 480364 [hyper:480245,480253,demod:480321,cut:480241,binarycut:480258] equal(multiply(sk_c8,sk_c6),sk_c7).
% 480368 [hyper:480245,480364,480345,demod:480333,cut:480241] 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: 6
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(inverse(U),sk_c8) | -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: 6
%
%
% 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: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,1,181994,5,1502,181994,1,1502,181994,50,1502,181994,40,1502,182034,0,1502,194379,3,1803,195078,4,1953,195778,5,2103,195779,1,2103,195779,50,2103,195779,40,2103,195819,0,2103,196110,3,2414,196118,4,2555,196126,5,2705,196126,1,2705,196126,50,2705,196126,40,2705,196166,0,2705,214142,3,4208,215561,4,4956,216508,1,5706,216508,50,5706,216508,40,5706,216548,0,5706,227175,3,6459,228727,4,6832,230977,1,7207,230977,50,7207,230977,40,7207,231017,0,7207,247091,3,7958,247784,4,8333,248162,1,8708,248162,50,8708,248162,40,8708,248202,0,8708,323539,3,12610,324543,4,14560,324888,5,16510,324889,1,16510,324889,50,16512,324889,40,16512,324929,0,16512,374227,3,19065,375033,4,20338,375537,1,21613,375537,50,21614,375537,40,21614,375577,0,21614,415347,3,23125,415996,4,23865,416561,5,24615,416562,1,24615,416562,50,24617,416562,40,24617,416602,0,24617,437044,3,25374,437469,4,25743,437868,1,26118,437868,50,26118,437868,40,26118,437908,0,26118,461167,3,27319,461945,4,27919,462570,1,28519,462570,50,28520,462570,40,28520,462610,0,28520,478959,3,29272,479602,4,29646,480239,5,30021,480240,1,30021,480240,50,30021,480240,40,30021,480240,40,30021,480275,0,30021,480367,50,30022,480367,30,30022,480367,40,30022,480402,0,30022,480525,50,30022,480560,0,30028)
%
%
% START OF PROOF
% 480527 [] equal(multiply(identity,X),X).
% 480528 [] equal(multiply(inverse(X),X),identity).
% 480529 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 480530 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c8).
% 480534 [?] ?
% 480535 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 480539 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 480540 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 480544 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 480545 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 480549 [?] ?
% 480550 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 480554 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 480555 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 480559 [?] ?
% 480560 [] equal(inverse(sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 480567 [hyper:480530,480535,binarycut:480534] equal(inverse(sk_c2),sk_c8).
% 480570 [para:480567.1.1,480528.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 480583 [hyper:480530,480550,binarycut:480549] equal(inverse(sk_c1),sk_c8).
% 480586 [para:480583.1.1,480528.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 480594 [hyper:480530,480560,binarycut:480559] equal(inverse(sk_c8),sk_c7).
% 480595 [para:480594.1.1,480528.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 480614 [hyper:480530,480539,480540] equal(multiply(sk_c2,sk_c8),sk_c3).
% 480619 [hyper:480530,480544,480545] equal(multiply(sk_c8,sk_c3),sk_c7).
% 480624 [hyper:480530,480554,480555] equal(multiply(sk_c1,sk_c8),sk_c7).
% 480625 [para:480528.1.1,480529.1.1.1,demod:480527] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 480626 [para:480570.1.1,480529.1.1.1,demod:480527] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 480627 [para:480586.1.1,480529.1.1.1,demod:480527] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 480630 [para:480619.1.1,480529.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c3,X))).
% 480632 [para:480614.1.1,480626.1.2.2,demod:480619] equal(sk_c8,sk_c7).
% 480635 [para:480632.1.1,480594.1.1.1] equal(inverse(sk_c7),sk_c7).
% 480642 [para:480528.1.1,480625.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 480643 [para:480570.1.1,480625.1.2.2,demod:480594] equal(sk_c2,multiply(sk_c7,identity)).
% 480644 [para:480586.1.1,480625.1.2.2,demod:480643,480594] equal(sk_c1,sk_c2).
% 480645 [para:480595.1.1,480625.1.2.2,demod:480643,480635] equal(sk_c8,sk_c2).
% 480648 [para:480529.1.1,480625.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 480649 [para:480626.1.2,480625.1.2.2,demod:480594] equal(multiply(sk_c2,X),multiply(sk_c7,X)).
% 480650 [para:480625.1.2,480625.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 480651 [para:480644.1.2,480614.1.1.1,demod:480624] equal(sk_c7,sk_c3).
% 480658 [para:480645.1.1,480632.1.1] equal(sk_c2,sk_c7).
% 480662 [para:480651.1.1,480635.1.1.1] equal(inverse(sk_c3),sk_c7).
% 480664 [para:480627.1.2,480625.1.2.2,demod:480649,480594] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 480665 [para:480658.1.2,480651.1.1] equal(sk_c2,sk_c3).
% 480667 [para:480665.1.1,480567.1.1.1,demod:480662] equal(sk_c7,sk_c8).
% 480669 [para:480665.1.1,480626.1.2.2.1,demod:480664,480649,480630] equal(X,multiply(sk_c1,X)).
% 480693 [para:480626.1.2,480648.1.2.2.2,demod:480669,480664] equal(X,multiply(inverse(multiply(Y,sk_c8)),multiply(Y,X))).
% 480700 [para:480650.1.2,480528.1.1] equal(multiply(X,inverse(X)),identity).
% 480702 [para:480650.1.2,480642.1.2] equal(X,multiply(X,identity)).
% 480705 [para:480702.1.2,480642.1.2] equal(X,inverse(inverse(X))).
% 480707 [para:480700.1.1,480693.1.2.2,demod:480702] equal(inverse(X),inverse(multiply(X,sk_c8))).
% 480717 [para:480707.1.2,480642.1.2.1.1,demod:480702,480705] equal(multiply(X,sk_c8),X).
% 480720 [para:480632.1.1,480717.1.1.2] equal(multiply(X,sk_c7),X).
% 480725 [hyper:480530,480720,demod:480594,cut:480667] 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: 6
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -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: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,1,181994,5,1502,181994,1,1502,181994,50,1502,181994,40,1502,182034,0,1502,194379,3,1803,195078,4,1953,195778,5,2103,195779,1,2103,195779,50,2103,195779,40,2103,195819,0,2103,196110,3,2414,196118,4,2555,196126,5,2705,196126,1,2705,196126,50,2705,196126,40,2705,196166,0,2705,214142,3,4208,215561,4,4956,216508,1,5706,216508,50,5706,216508,40,5706,216548,0,5706,227175,3,6459,228727,4,6832,230977,1,7207,230977,50,7207,230977,40,7207,231017,0,7207,247091,3,7958,247784,4,8333,248162,1,8708,248162,50,8708,248162,40,8708,248202,0,8708,323539,3,12610,324543,4,14560,324888,5,16510,324889,1,16510,324889,50,16512,324889,40,16512,324929,0,16512,374227,3,19065,375033,4,20338,375537,1,21613,375537,50,21614,375537,40,21614,375577,0,21614,415347,3,23125,415996,4,23865,416561,5,24615,416562,1,24615,416562,50,24617,416562,40,24617,416602,0,24617,437044,3,25374,437469,4,25743,437868,1,26118,437868,50,26118,437868,40,26118,437908,0,26118,461167,3,27319,461945,4,27919,462570,1,28519,462570,50,28520,462570,40,28520,462610,0,28520,478959,3,29272,479602,4,29646,480239,5,30021,480240,1,30021,480240,50,30021,480240,40,30021,480240,40,30021,480275,0,30021,480367,50,30022,480367,30,30022,480367,40,30022,480402,0,30022,480525,50,30022,480560,0,30028,480724,50,30029,480724,30,30029,480724,40,30029,480759,0,30029)
%
%
% START OF PROOF
% 480725 [] equal(X,X).
% 480729 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 480730 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 480731 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c8).
% 480732 [?] ?
% 480735 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 480736 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 480737 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c8,sk_c6),sk_c7).
% 480740 [?] ?
% 480741 [?] ?
% 480742 [?] ?
% 480805 [hyper:480729,480731,480730,binarycut:480732] equal(inverse(sk_c2),sk_c8).
% 480817 [hyper:480729,480735,demod:480805,cut:480725,binarycut:480740] equal(inverse(sk_c5),sk_c8).
% 480829 [hyper:480729,480736,demod:480805,cut:480725,binarycut:480741] equal(multiply(sk_c5,sk_c8),sk_c6).
% 480848 [hyper:480729,480737,demod:480805,cut:480725,binarycut:480742] equal(multiply(sk_c8,sk_c6),sk_c7).
% 480852 [hyper:480729,480848,480829,demod:480817,cut:480725] 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: 6
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% 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: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,1,181994,5,1502,181994,1,1502,181994,50,1502,181994,40,1502,182034,0,1502,194379,3,1803,195078,4,1953,195778,5,2103,195779,1,2103,195779,50,2103,195779,40,2103,195819,0,2103,196110,3,2414,196118,4,2555,196126,5,2705,196126,1,2705,196126,50,2705,196126,40,2705,196166,0,2705,214142,3,4208,215561,4,4956,216508,1,5706,216508,50,5706,216508,40,5706,216548,0,5706,227175,3,6459,228727,4,6832,230977,1,7207,230977,50,7207,230977,40,7207,231017,0,7207,247091,3,7958,247784,4,8333,248162,1,8708,248162,50,8708,248162,40,8708,248202,0,8708,323539,3,12610,324543,4,14560,324888,5,16510,324889,1,16510,324889,50,16512,324889,40,16512,324929,0,16512,374227,3,19065,375033,4,20338,375537,1,21613,375537,50,21614,375537,40,21614,375577,0,21614,415347,3,23125,415996,4,23865,416561,5,24615,416562,1,24615,416562,50,24617,416562,40,24617,416602,0,24617,437044,3,25374,437469,4,25743,437868,1,26118,437868,50,26118,437868,40,26118,437908,0,26118,461167,3,27319,461945,4,27919,462570,1,28519,462570,50,28520,462570,40,28520,462610,0,28520,478959,3,29272,479602,4,29646,480239,5,30021,480240,1,30021,480240,50,30021,480240,40,30021,480240,40,30021,480275,0,30021,480367,50,30022,480367,30,30022,480367,40,30022,480402,0,30022,480525,50,30022,480560,0,30028,480724,50,30029,480724,30,30029,480724,40,30029,480759,0,30029,480851,50,30029,480851,30,30029,480851,40,30029,480886,0,30029)
%
%
% START OF PROOF
% 480853 [] equal(multiply(identity,X),X).
% 480854 [] equal(multiply(inverse(X),X),identity).
% 480855 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 480856 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 480872 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 480873 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 480874 [] equal(multiply(sk_c8,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 480875 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 480876 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 480877 [?] ?
% 480878 [?] ?
% 480879 [?] ?
% 480880 [?] ?
% 480881 [?] ?
% 480896 [hyper:480856,480872,binarycut:480877] equal(inverse(sk_c5),sk_c8).
% 480900 [para:480896.1.1,480854.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 480904 [hyper:480856,480876,binarycut:480881] equal(inverse(sk_c4),sk_c8).
% 480908 [para:480904.1.1,480854.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 480921 [hyper:480856,480873,binarycut:480878] equal(multiply(sk_c5,sk_c8),sk_c6).
% 480924 [hyper:480856,480874,binarycut:480879] equal(multiply(sk_c8,sk_c6),sk_c7).
% 480927 [hyper:480856,480875,binarycut:480880] equal(multiply(sk_c4,sk_c7),sk_c8).
% 480928 [para:480854.1.1,480855.1.1.1,demod:480853] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 480929 [para:480900.1.1,480855.1.1.1,demod:480853] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 480934 [para:480921.1.1,480929.1.2.2,demod:480924] equal(sk_c8,sk_c7).
% 480937 [para:480934.1.1,480921.1.1.2] equal(multiply(sk_c5,sk_c7),sk_c6).
% 480938 [para:480934.1.1,480924.1.1.1] equal(multiply(sk_c7,sk_c6),sk_c7).
% 480943 [para:480900.1.1,480928.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),identity)).
% 480944 [para:480908.1.1,480928.1.2.2,demod:480943] equal(sk_c4,sk_c5).
% 480950 [para:480944.1.2,480937.1.1.1,demod:480927] equal(sk_c8,sk_c6).
% 480951 [para:480950.1.1,480900.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 480960 [para:480938.1.1,480928.1.2.2,demod:480854] equal(sk_c6,identity).
% 480971 [para:480960.1.1,480951.1.1.1,demod:480853] equal(sk_c5,identity).
% 480972 [para:480971.1.1,480896.1.1.1] equal(inverse(identity),sk_c8).
% 480986 [hyper:480856,480972,demod:480853,cut:480934] 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: 6
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(inverse(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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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: 6
%
%
% 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 12
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,1,181994,5,1502,181994,1,1502,181994,50,1502,181994,40,1502,182034,0,1502,194379,3,1803,195078,4,1953,195778,5,2103,195779,1,2103,195779,50,2103,195779,40,2103,195819,0,2103,196110,3,2414,196118,4,2555,196126,5,2705,196126,1,2705,196126,50,2705,196126,40,2705,196166,0,2705,214142,3,4208,215561,4,4956,216508,1,5706,216508,50,5706,216508,40,5706,216548,0,5706,227175,3,6459,228727,4,6832,230977,1,7207,230977,50,7207,230977,40,7207,231017,0,7207,247091,3,7958,247784,4,8333,248162,1,8708,248162,50,8708,248162,40,8708,248202,0,8708,323539,3,12610,324543,4,14560,324888,5,16510,324889,1,16510,324889,50,16512,324889,40,16512,324929,0,16512,374227,3,19065,375033,4,20338,375537,1,21613,375537,50,21614,375537,40,21614,375577,0,21614,415347,3,23125,415996,4,23865,416561,5,24615,416562,1,24615,416562,50,24617,416562,40,24617,416602,0,24617,437044,3,25374,437469,4,25743,437868,1,26118,437868,50,26118,437868,40,26118,437908,0,26118,461167,3,27319,461945,4,27919,462570,1,28519,462570,50,28520,462570,40,28520,462610,0,28520,478959,3,29272,479602,4,29646,480239,5,30021,480240,1,30021,480240,50,30021,480240,40,30021,480240,40,30021,480275,0,30021,480367,50,30022,480367,30,30022,480367,40,30022,480402,0,30022,480525,50,30022,480560,0,30028,480724,50,30029,480724,30,30029,480724,40,30029,480759,0,30029,480851,50,30029,480851,30,30029,480851,40,30029,480886,0,30029,480985,50,30029,480985,30,30029,480985,40,30029,481020,0,30034,481126,50,30034,481161,0,30034,481308,50,30037,481343,0,30041,481498,50,30044,481533,0,30044,481696,50,30050,481731,0,30050,481900,50,30058,481935,0,30062,482112,50,30078,482147,0,30078,482332,50,30106,482367,0,30111,482562,50,30167,482597,0,30167,482802,50,30281,482837,0,30281,483054,50,30515,483054,40,30515,483089,0,30515)
%
%
% START OF PROOF
% 483056 [] equal(multiply(identity,X),X).
% 483057 [] equal(multiply(inverse(X),X),identity).
% 483058 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 483059 [] -equal(inverse(sk_c8),sk_c7).
% 483085 [?] ?
% 483086 [?] ?
% 483087 [?] ?
% 483088 [?] ?
% 483089 [?] ?
% 483104 [input:483085,cut:483059] equal(inverse(sk_c5),sk_c8).
% 483105 [para:483104.1.1,483057.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 483108 [input:483089,cut:483059] equal(inverse(sk_c4),sk_c8).
% 483109 [para:483108.1.1,483057.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 483126 [input:483086,cut:483059] equal(multiply(sk_c5,sk_c8),sk_c6).
% 483127 [input:483087,cut:483059] equal(multiply(sk_c8,sk_c6),sk_c7).
% 483128 [input:483088,cut:483059] equal(multiply(sk_c4,sk_c7),sk_c8).
% 483143 [para:483057.1.1,483058.1.1.1,demod:483056] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 483145 [para:483105.1.1,483058.1.1.1,demod:483056] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 483147 [para:483109.1.1,483058.1.1.1,demod:483056] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 483163 [para:483127.1.1,483058.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c6,X))).
% 483182 [para:483126.1.1,483145.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 483186 [para:483182.1.2,483127.1.1] equal(sk_c8,sk_c7).
% 483187 [para:483182.1.2,483058.1.1.1,demod:483163] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 483188 [para:483186.1.1,483059.1.1.1] -equal(inverse(sk_c7),sk_c7).
% 483228 [para:483128.1.1,483147.1.2.2,demod:483187] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 483292 [para:483228.1.2,483143.1.2.2,demod:483057] equal(sk_c8,identity).
% 483310 [para:483292.1.1,483105.1.1.1,demod:483056] equal(sk_c5,identity).
% 483330 [para:483292.1.1,483186.1.1] equal(identity,sk_c7).
% 483340 [para:483310.1.1,483104.1.1.1] equal(inverse(identity),sk_c8).
% 483348 [para:483330.1.2,483188.1.1.1,demod:483340,cut:483186] 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: 38648
% derived clauses: 5595729
% kept clauses: 259347
% kept size sum: 874857
% kept mid-nuclei: 143441
% kept new demods: 2290
% forw unit-subs: 1225423
% forw double-subs: 3485803
% forw overdouble-subs: 218699
% backward subs: 32243
% fast unit cutoff: 46810
% full unit cutoff: 0
% dbl unit cutoff: 41988
% real runtime : 307.18
% process. runtime: 305.16
% specific non-discr-tree subsumption statistics:
% tried: 9122188
% length fails: 1044780
% strength fails: 2036975
% predlist fails: 404571
% aux str. fails: 1305795
% by-lit fails: 1081981
% full subs tried: 1181586
% full subs fail: 1046184
%
% ; 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/GRP233-1+eq_r.in")
%
%------------------------------------------------------------------------------