TSTP Solution File: GRP355-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP355-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art06.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 299.1s
% Output : Assurance 299.1s
% 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/GRP355-1+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 19)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 19)
% (binary-posweight-lex-big-order 30 #f 3 19)
% (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_c6),sk_c8) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c8),sk_c7) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c8,U),sk_c6) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% was split for some strategies as:
% -equal(multiply(sk_c8,U),sk_c6) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6).
% -equal(multiply(Y,sk_c8),sk_c7) | -equal(inverse(Y),sk_c8).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(multiply(sk_c7,sk_c6),sk_c8).
%
% 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(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c8),sk_c7) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c8,U),sk_c6) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,U),sk_c6) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(26,40,0,57,0,0,5722,50,59,5753,0,59,11687,50,123,11718,0,123,17901,50,201,17932,0,201,24233,50,250,24264,0,250,30699,50,305,30730,0,305,37275,50,370,37306,0,370,43996,50,453,44027,0,453,50863,50,575,50894,0,575,57911,50,778,57911,40,778,57942,0,778,69105,3,1079,69812,4,1229,70438,5,1379,70439,1,1379,70439,50,1379,70439,40,1379,70470,0,1379,70655,3,1688,70664,4,1842,70671,5,1980,70671,1,1980,70671,50,1980,70671,40,1980,70702,0,1980,93417,3,3482,94321,4,4231,95142,1,4981,95142,50,4981,95142,40,4981,95173,0,4981,108500,3,5732,109415,4,6107,110209,1,6482,110209,50,6482,110209,40,6482,110240,0,6482,123716,3,7233,124750,4,7608,125875,5,7983,125876,1,7983,125876,50,7983,125876,40,7983,125907,0,7983,159891,3,11886,161018,4,13834,161932,1,15784,161932,50,15794,161932,40,15794,161963,0,15794,200742,3,18345,201402,4,19620,201980,1,20895,201980,50,20897,201980,40,20897,202011,0,20897,225221,3,22399,227387,4,23148,234316,5,23898,234317,1,23898,234317,50,23899,234317,40,23899,234348,0,23899,255034,3,24650,255801,4,25025,256502,5,25400,256503,1,25400,256503,50,25401,256503,40,25401,256534,0,25401,282223,3,26602,283087,4,27202,283824,1,27802,283824,50,27803,283824,40,27803,283855,0,27803,303803,3,28554,304508,4,28929,305061,5,29304,305062,1,29304,305062,50,29304,305062,40,29304,305062,40,29304,305088,0,29304)
%
%
% START OF PROOF
% 305063 [] equal(X,X).
% 305064 [] equal(multiply(identity,X),X).
% 305065 [] equal(multiply(inverse(X),X),identity).
% 305066 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 305067 [] -equal(multiply(sk_c8,X),sk_c6) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 305068 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 305069 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c8).
% 305070 [?] ?
% 305075 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 305076 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 305077 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c8,sk_c5),sk_c6).
% 305082 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 305083 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 305084 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(multiply(sk_c8,sk_c5),sk_c6).
% 305113 [hyper:305067,305069,305068,binarycut:305070] equal(inverse(sk_c1),sk_c8).
% 305128 [para:305113.1.1,305065.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 305163 [hyper:305067,305077,305076,305075] equal(multiply(sk_c1,sk_c8),sk_c7).
% 305174 [hyper:305067,305084,305083,305082] equal(multiply(sk_c7,sk_c6),sk_c8).
% 305175 [para:305065.1.1,305066.1.1.1,demod:305064] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 305176 [para:305128.1.1,305066.1.1.1,demod:305064] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 305177 [para:305163.1.1,305066.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c1,multiply(sk_c8,X))).
% 305181 [para:305163.1.1,305176.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 305187 [para:305174.1.1,305175.1.2.2] equal(sk_c6,multiply(inverse(sk_c7),sk_c8)).
% 305188 [para:305176.1.2,305175.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c8),X)).
% 305195 [para:305181.1.2,305177.1.2.2,demod:305163] equal(multiply(sk_c7,sk_c7),sk_c7).
% 305197 [para:305195.1.1,305175.1.2.2,demod:305065] equal(sk_c7,identity).
% 305198 [para:305197.1.1,305174.1.1.1,demod:305064] equal(sk_c6,sk_c8).
% 305201 [para:305198.1.1,305174.1.1.2] equal(multiply(sk_c7,sk_c8),sk_c8).
% 305213 [para:305201.1.1,305175.1.2.2,demod:305187] equal(sk_c8,sk_c6).
% 305214 [hyper:305067,305188,demod:305113,305181,305163,305188,cut:305213,cut:305063] 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 19
% 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(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c8),sk_c7) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c8,U),sk_c6) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% clause depth limited to 10
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(26,40,0,57,0,0,5722,50,59,5753,0,59,11687,50,123,11718,0,123,17901,50,201,17932,0,201,24233,50,250,24264,0,250,30699,50,305,30730,0,305,37275,50,370,37306,0,370,43996,50,453,44027,0,453,50863,50,575,50894,0,575,57911,50,778,57911,40,778,57942,0,778,69105,3,1079,69812,4,1229,70438,5,1379,70439,1,1379,70439,50,1379,70439,40,1379,70470,0,1379,70655,3,1688,70664,4,1842,70671,5,1980,70671,1,1980,70671,50,1980,70671,40,1980,70702,0,1980,93417,3,3482,94321,4,4231,95142,1,4981,95142,50,4981,95142,40,4981,95173,0,4981,108500,3,5732,109415,4,6107,110209,1,6482,110209,50,6482,110209,40,6482,110240,0,6482,123716,3,7233,124750,4,7608,125875,5,7983,125876,1,7983,125876,50,7983,125876,40,7983,125907,0,7983,159891,3,11886,161018,4,13834,161932,1,15784,161932,50,15794,161932,40,15794,161963,0,15794,200742,3,18345,201402,4,19620,201980,1,20895,201980,50,20897,201980,40,20897,202011,0,20897,225221,3,22399,227387,4,23148,234316,5,23898,234317,1,23898,234317,50,23899,234317,40,23899,234348,0,23899,255034,3,24650,255801,4,25025,256502,5,25400,256503,1,25400,256503,50,25401,256503,40,25401,256534,0,25401,282223,3,26602,283087,4,27202,283824,1,27802,283824,50,27803,283824,40,27803,283855,0,27803,303803,3,28554,304508,4,28929,305061,5,29304,305062,1,29304,305062,50,29304,305062,40,29304,305062,40,29304,305088,0,29304,305213,50,29305,305213,30,29305,305213,40,29305,305239,0,29305,305300,50,29305,305326,0,29311,305436,50,29313,305462,0,29313,305588,50,29333,305614,0,29333,305761,50,29358,305787,0,29363,305957,50,29385,305983,0,29385,306190,50,29436,306216,0,29440,306467,50,29553,306493,0,29553,306804,4,29780)
%
%
% START OF PROOF
% 306469 [] equal(multiply(identity,X),X).
% 306470 [] equal(multiply(inverse(X),X),identity).
% 306471 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 306472 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6).
% 306476 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c6).
% 306477 [?] ?
% 306483 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 306484 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 306490 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(inverse(sk_c3),sk_c6).
% 306491 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 306497 [hyper:306472,306476,binarycut:306477] equal(inverse(sk_c1),sk_c8).
% 306500 [para:306497.1.1,306470.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 306514 [hyper:306472,306484,306483] equal(multiply(sk_c1,sk_c8),sk_c7).
% 306519 [hyper:306472,306491,306490] equal(multiply(sk_c7,sk_c6),sk_c8).
% 306520 [para:306470.1.1,306471.1.1.1,demod:306469] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 306521 [para:306500.1.1,306471.1.1.1,demod:306469] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 306522 [para:306514.1.1,306471.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c1,multiply(sk_c8,X))).
% 306523 [para:306519.1.1,306471.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c7,multiply(sk_c6,X))).
% 306524 [para:306514.1.1,306521.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 306525 [para:306524.1.2,306471.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c8,multiply(sk_c7,X))).
% 306526 [para:306519.1.1,306525.1.2.2] equal(multiply(sk_c8,sk_c6),multiply(sk_c8,sk_c8)).
% 306529 [para:306470.1.1,306520.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 306530 [para:306500.1.1,306520.1.2.2] equal(sk_c1,multiply(inverse(sk_c8),identity)).
% 306532 [para:306471.1.1,306520.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 306533 [para:306521.1.2,306520.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c8),X)).
% 306534 [para:306526.1.1,306520.1.2.2,demod:306522,306533] equal(sk_c6,multiply(sk_c7,sk_c8)).
% 306535 [para:306520.1.2,306520.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 306538 [para:306524.1.2,306522.1.2.2,demod:306514] equal(multiply(sk_c7,sk_c7),sk_c7).
% 306540 [para:306526.1.1,306522.1.2.2,demod:306534,306522,306519] equal(sk_c8,sk_c6).
% 306542 [para:306534.1.2,306471.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c8,X))).
% 306545 [para:306540.1.2,306523.1.2.2.1,demod:306542] equal(multiply(sk_c8,X),multiply(sk_c6,X)).
% 306546 [para:306538.1.1,306520.1.2.2,demod:306470] equal(sk_c7,identity).
% 306547 [para:306546.1.1,306524.1.2.2] equal(sk_c8,multiply(sk_c8,identity)).
% 306558 [para:306519.1.1,306532.1.2.1.1,demod:306522,306533,306542,306545] equal(X,multiply(sk_c7,X)).
% 306573 [para:306535.1.2,306470.1.1] equal(multiply(X,inverse(X)),identity).
% 306575 [para:306535.1.2,306529.1.2] equal(X,multiply(X,identity)).
% 306577 [para:306575.1.2,306529.1.2] equal(X,inverse(inverse(X))).
% 306578 [para:306575.1.2,306530.1.2] equal(sk_c1,inverse(sk_c8)).
% 306584 [para:306573.1.1,306532.1.2.2.2,demod:306575] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 306592 [para:306521.1.2,306584.1.2.1.1] equal(inverse(multiply(sk_c1,X)),multiply(inverse(X),sk_c8)).
% 306598 [para:306584.1.2,306584.1.2.1.1,demod:306577] equal(inverse(X),multiply(Y,inverse(multiply(X,Y)))).
% 306600 [para:306598.1.2,306471.1.1] equal(inverse(X),multiply(Y,multiply(Z,inverse(multiply(X,multiply(Y,Z)))))).
% 306602 [para:306471.1.1,306598.1.2.2.1] equal(inverse(multiply(X,Y)),multiply(Z,inverse(multiply(X,multiply(Y,Z))))).
% 306605 [para:306598.1.2,306523.1.2.2,demod:306558] equal(multiply(sk_c8,inverse(multiply(X,sk_c6))),inverse(X)).
% 306611 [para:306605.1.1,306520.1.2.2,demod:306578] equal(inverse(multiply(X,sk_c6)),multiply(sk_c1,inverse(X))).
% 306613 [para:306611.1.1,306529.1.2.1.1,demod:306547,306471,306577,306592] equal(multiply(X,sk_c6),multiply(X,sk_c8)).
% 306621 [para:306600.1.2,306471.1.1,demod:306471] equal(inverse(X),multiply(Y,multiply(Z,multiply(U,inverse(multiply(X,multiply(Y,multiply(Z,U)))))))).
% 306626 [para:306471.1.1,306602.1.2.2.1,demod:306471] equal(inverse(multiply(X,multiply(Y,Z))),multiply(U,inverse(multiply(X,multiply(Y,multiply(Z,U)))))).
% 306654 [para:306621.1.2,306471.1.1,demod:306471] equal(inverse(X),multiply(Y,multiply(Z,multiply(U,multiply(V,inverse(multiply(X,multiply(Y,multiply(Z,multiply(U,V)))))))))).
% 306663 [para:306471.1.1,306626.1.2.2.1,demod:306471] equal(inverse(multiply(X,multiply(Y,multiply(Z,U)))),multiply(V,inverse(multiply(X,multiply(Y,multiply(Z,multiply(U,V))))))).
% 306851 [para:306654.1.1,306472.2.1,demod:306613,306598,306602,306626,306663] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c6).
% 306852 [binary:306514,306851,demod:306497,cut:306540] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% clause depth limited to 10
% seconds given: 6
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c8),sk_c7) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c8,U),sk_c6) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Y,sk_c8),sk_c7) | -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 19
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(26,40,0,57,0,0,5722,50,59,5753,0,59,11687,50,123,11718,0,123,17901,50,201,17932,0,201,24233,50,250,24264,0,250,30699,50,305,30730,0,305,37275,50,370,37306,0,370,43996,50,453,44027,0,453,50863,50,575,50894,0,575,57911,50,778,57911,40,778,57942,0,778,69105,3,1079,69812,4,1229,70438,5,1379,70439,1,1379,70439,50,1379,70439,40,1379,70470,0,1379,70655,3,1688,70664,4,1842,70671,5,1980,70671,1,1980,70671,50,1980,70671,40,1980,70702,0,1980,93417,3,3482,94321,4,4231,95142,1,4981,95142,50,4981,95142,40,4981,95173,0,4981,108500,3,5732,109415,4,6107,110209,1,6482,110209,50,6482,110209,40,6482,110240,0,6482,123716,3,7233,124750,4,7608,125875,5,7983,125876,1,7983,125876,50,7983,125876,40,7983,125907,0,7983,159891,3,11886,161018,4,13834,161932,1,15784,161932,50,15794,161932,40,15794,161963,0,15794,200742,3,18345,201402,4,19620,201980,1,20895,201980,50,20897,201980,40,20897,202011,0,20897,225221,3,22399,227387,4,23148,234316,5,23898,234317,1,23898,234317,50,23899,234317,40,23899,234348,0,23899,255034,3,24650,255801,4,25025,256502,5,25400,256503,1,25400,256503,50,25401,256503,40,25401,256534,0,25401,282223,3,26602,283087,4,27202,283824,1,27802,283824,50,27803,283824,40,27803,283855,0,27803,303803,3,28554,304508,4,28929,305061,5,29304,305062,1,29304,305062,50,29304,305062,40,29304,305062,40,29304,305088,0,29304,305213,50,29305,305213,30,29305,305213,40,29305,305239,0,29305,305300,50,29305,305326,0,29311,305436,50,29313,305462,0,29313,305588,50,29333,305614,0,29333,305761,50,29358,305787,0,29363,305957,50,29385,305983,0,29385,306190,50,29436,306216,0,29440,306467,50,29553,306493,0,29553,306804,4,29780,306851,50,29780,306851,30,29780,306851,40,29780,306877,0,29780)
%
%
% START OF PROOF
% 306852 [] equal(X,X).
% 306856 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 306862 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c2),sk_c8).
% 306863 [?] ?
% 306869 [?] ?
% 306870 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c2,sk_c8),sk_c7).
% 306891 [hyper:306856,306862,binarycut:306869] equal(inverse(sk_c2),sk_c8).
% 306893 [hyper:306856,306862,binarycut:306863] equal(inverse(sk_c1),sk_c8).
% 306907 [hyper:306856,306870,demod:306893,cut:306852] equal(multiply(sk_c2,sk_c8),sk_c7).
% 306909 [hyper:306856,306907,demod:306891,cut:306852] 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 19
% 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(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c8),sk_c7) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c8,U),sk_c6) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),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 19
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(26,40,0,57,0,0,5722,50,59,5753,0,59,11687,50,123,11718,0,123,17901,50,201,17932,0,201,24233,50,250,24264,0,250,30699,50,305,30730,0,305,37275,50,370,37306,0,370,43996,50,453,44027,0,453,50863,50,575,50894,0,575,57911,50,778,57911,40,778,57942,0,778,69105,3,1079,69812,4,1229,70438,5,1379,70439,1,1379,70439,50,1379,70439,40,1379,70470,0,1379,70655,3,1688,70664,4,1842,70671,5,1980,70671,1,1980,70671,50,1980,70671,40,1980,70702,0,1980,93417,3,3482,94321,4,4231,95142,1,4981,95142,50,4981,95142,40,4981,95173,0,4981,108500,3,5732,109415,4,6107,110209,1,6482,110209,50,6482,110209,40,6482,110240,0,6482,123716,3,7233,124750,4,7608,125875,5,7983,125876,1,7983,125876,50,7983,125876,40,7983,125907,0,7983,159891,3,11886,161018,4,13834,161932,1,15784,161932,50,15794,161932,40,15794,161963,0,15794,200742,3,18345,201402,4,19620,201980,1,20895,201980,50,20897,201980,40,20897,202011,0,20897,225221,3,22399,227387,4,23148,234316,5,23898,234317,1,23898,234317,50,23899,234317,40,23899,234348,0,23899,255034,3,24650,255801,4,25025,256502,5,25400,256503,1,25400,256503,50,25401,256503,40,25401,256534,0,25401,282223,3,26602,283087,4,27202,283824,1,27802,283824,50,27803,283824,40,27803,283855,0,27803,303803,3,28554,304508,4,28929,305061,5,29304,305062,1,29304,305062,50,29304,305062,40,29304,305062,40,29304,305088,0,29304,305213,50,29305,305213,30,29305,305213,40,29305,305239,0,29305,305300,50,29305,305326,0,29311,305436,50,29313,305462,0,29313,305588,50,29333,305614,0,29333,305761,50,29358,305787,0,29363,305957,50,29385,305983,0,29385,306190,50,29436,306216,0,29440,306467,50,29553,306493,0,29553,306804,4,29780,306851,50,29780,306851,30,29780,306851,40,29780,306877,0,29780,306908,50,29781,306908,30,29781,306908,40,29781,306934,0,29785)
%
%
% START OF PROOF
% 306909 [] equal(X,X).
% 306913 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 306919 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c2),sk_c8).
% 306920 [?] ?
% 306926 [?] ?
% 306927 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c2,sk_c8),sk_c7).
% 306948 [hyper:306913,306919,binarycut:306926] equal(inverse(sk_c2),sk_c8).
% 306950 [hyper:306913,306919,binarycut:306920] equal(inverse(sk_c1),sk_c8).
% 306964 [hyper:306913,306927,demod:306950,cut:306909] equal(multiply(sk_c2,sk_c8),sk_c7).
% 306966 [hyper:306913,306964,demod:306948,cut:306909] 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 19
% 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(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(Y,sk_c8),sk_c7) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(sk_c8,U),sk_c6) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c7,sk_c6),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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% clause depth limited to 10
% 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(26,40,0,57,0,0,5722,50,59,5753,0,59,11687,50,123,11718,0,123,17901,50,201,17932,0,201,24233,50,250,24264,0,250,30699,50,305,30730,0,305,37275,50,370,37306,0,370,43996,50,453,44027,0,453,50863,50,575,50894,0,575,57911,50,778,57911,40,778,57942,0,778,69105,3,1079,69812,4,1229,70438,5,1379,70439,1,1379,70439,50,1379,70439,40,1379,70470,0,1379,70655,3,1688,70664,4,1842,70671,5,1980,70671,1,1980,70671,50,1980,70671,40,1980,70702,0,1980,93417,3,3482,94321,4,4231,95142,1,4981,95142,50,4981,95142,40,4981,95173,0,4981,108500,3,5732,109415,4,6107,110209,1,6482,110209,50,6482,110209,40,6482,110240,0,6482,123716,3,7233,124750,4,7608,125875,5,7983,125876,1,7983,125876,50,7983,125876,40,7983,125907,0,7983,159891,3,11886,161018,4,13834,161932,1,15784,161932,50,15794,161932,40,15794,161963,0,15794,200742,3,18345,201402,4,19620,201980,1,20895,201980,50,20897,201980,40,20897,202011,0,20897,225221,3,22399,227387,4,23148,234316,5,23898,234317,1,23898,234317,50,23899,234317,40,23899,234348,0,23899,255034,3,24650,255801,4,25025,256502,5,25400,256503,1,25400,256503,50,25401,256503,40,25401,256534,0,25401,282223,3,26602,283087,4,27202,283824,1,27802,283824,50,27803,283824,40,27803,283855,0,27803,303803,3,28554,304508,4,28929,305061,5,29304,305062,1,29304,305062,50,29304,305062,40,29304,305062,40,29304,305088,0,29304,305213,50,29305,305213,30,29305,305213,40,29305,305239,0,29305,305300,50,29305,305326,0,29311,305436,50,29313,305462,0,29313,305588,50,29333,305614,0,29333,305761,50,29358,305787,0,29363,305957,50,29385,305983,0,29385,306190,50,29436,306216,0,29440,306467,50,29553,306493,0,29553,306804,4,29780,306851,50,29780,306851,30,29780,306851,40,29780,306877,0,29780,306908,50,29781,306908,30,29781,306908,40,29781,306934,0,29785,306965,50,29785,306965,30,29785,306965,40,29785,306991,0,29785,307080,50,29786,307106,0,29786,307253,50,29790,307279,0,29794,307440,50,29802,307466,0,29802,307645,50,29817,307671,0,29821,307872,50,29847,307898,0,29847,308133,50,29901,308159,0,29901,308436,50,30006,308462,0,30006,308797,50,30235,308797,40,30235,308823,0,30235)
%
%
% START OF PROOF
% 308540 [?] ?
% 308799 [] equal(multiply(identity,X),X).
% 308800 [] equal(multiply(inverse(X),X),identity).
% 308801 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 308802 [] -equal(multiply(sk_c7,sk_c6),sk_c8).
% 308817 [?] ?
% 308818 [?] ?
% 308819 [?] ?
% 308820 [?] ?
% 308821 [?] ?
% 308847 [input:308817,cut:308802] equal(inverse(sk_c4),sk_c8).
% 308848 [para:308847.1.1,308800.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 308849 [input:308820,cut:308802] equal(inverse(sk_c3),sk_c6).
% 308850 [para:308849.1.1,308800.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 308860 [input:308818,cut:308802] equal(multiply(sk_c4,sk_c8),sk_c5).
% 308861 [input:308819,cut:308802] equal(multiply(sk_c8,sk_c5),sk_c6).
% 308862 [input:308821,cut:308802] equal(multiply(sk_c3,sk_c6),sk_c7).
% 308865 [para:308800.1.1,308801.1.1.1,demod:308799] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 308873 [para:308848.1.1,308801.1.1.1,demod:308799] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 308876 [para:308850.1.1,308801.1.1.1,demod:308799] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 308888 [para:308861.1.1,308801.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c8,multiply(sk_c5,X))).
% 308894 [para:308860.1.1,308873.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 308897 [para:308894.1.2,308861.1.1] equal(sk_c8,sk_c6).
% 308898 [para:308894.1.2,308801.1.1.1,demod:308888] equal(multiply(sk_c8,X),multiply(sk_c6,X)).
% 308899 [para:308897.1.2,308802.1.1.2] -equal(multiply(sk_c7,sk_c8),sk_c8).
% 308912 [para:308862.1.1,308876.1.2.2,demod:308898] equal(sk_c6,multiply(sk_c8,sk_c7)).
% 308939 [para:308861.1.1,308865.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),sk_c6)).
% 308949 [para:308912.1.2,308865.1.2.2,demod:308939] equal(sk_c7,sk_c5).
% 308965 [para:308949.1.1,308899.1.1.1,cut:308540] 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: 35916
% derived clauses: 6195982
% kept clauses: 213756
% kept size sum: 625269
% kept mid-nuclei: 48798
% kept new demods: 5596
% forw unit-subs: 3428759
% forw double-subs: 2279572
% forw overdouble-subs: 157702
% backward subs: 21046
% fast unit cutoff: 49196
% full unit cutoff: 0
% dbl unit cutoff: 12280
% real runtime : 303.49
% process. runtime: 302.36
% specific non-discr-tree subsumption statistics:
% tried: 5862624
% length fails: 526352
% strength fails: 1494714
% predlist fails: 221557
% aux str. fails: 814205
% by-lit fails: 807119
% full subs tried: 1030049
% full subs fail: 932549
%
% ; 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/GRP355-1+eq_r.in")
%
%------------------------------------------------------------------------------