TSTP Solution File: GRP334-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP334-1 : 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 : art07.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 297.5s
% Output : Assurance 297.5s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP334-1+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_c6,sk_c7),sk_c5) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c6,Z),sk_c5) | -equal(multiply(U,sk_c6),Z) | -equal(inverse(U),sk_c6).
% was split for some strategies as:
% -equal(multiply(sk_c6,Z),sk_c5) | -equal(multiply(U,sk_c6),Z) | -equal(inverse(U),sk_c6).
% -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6).
% -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6).
% -equal(multiply(sk_c6,sk_c7),sk_c5).
% -equal(inverse(sk_c6),sk_c5).
% -equal(inverse(sk_c7),sk_c5).
%
% 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_c6,sk_c7),sk_c5) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c6,Z),sk_c5) | -equal(multiply(U,sk_c6),Z) | -equal(inverse(U),sk_c6).
% Split part used next: -equal(multiply(sk_c6,Z),sk_c5) | -equal(multiply(U,sk_c6),Z) | -equal(inverse(U),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(26,40,0,56,0,0,8546,50,101,8576,0,101,17776,50,221,17806,0,221,27596,50,315,27626,0,315,37762,50,407,37792,0,407,48191,50,514,48221,0,514,58968,50,650,58998,0,650,70093,50,840,70093,40,840,70123,0,840,82717,3,1141,83370,4,1291,83923,1,1441,83923,50,1441,83923,40,1441,83953,0,1441,84158,3,1742,84171,4,1916,84178,5,2042,84178,1,2042,84178,50,2042,84178,40,2042,84208,0,2042,124707,3,3543,125341,4,4293,125947,1,5043,125947,50,5044,125947,40,5044,125977,0,5044,152436,3,5801,152909,4,6170,153331,5,6545,153332,1,6545,153332,50,6546,153332,40,6546,153362,0,6546,167568,3,7297,168548,4,7672,169334,5,8047,169335,1,8047,169335,50,8047,169335,40,8047,169365,0,8047,239605,3,11948,240468,4,13899,241819,1,15848,241819,50,15850,241819,40,15850,241849,0,15850,286060,3,18401,286993,4,19676,287996,5,20951,287997,1,20951,287997,50,20953,287997,40,20953,288027,0,20953,333333,3,22459,334228,4,23204,335159,5,23954,335160,1,23954,335160,50,23956,335160,40,23956,335190,0,23956,356347,3,24707,356811,4,25082,357044,1,25457,357044,50,25457,357044,40,25457,357074,0,25457,380935,3,26658,381917,4,27258,382957,5,27858,382958,1,27858,382958,50,27859,382958,40,27859,382988,0,27859,415275,3,28618,415751,4,28985,416205,5,29360,416206,1,29360,416206,50,29361,416206,40,29361,416206,40,29361,416232,0,29361)
%
%
% START OF PROOF
% 416207 [] equal(X,X).
% 416211 [] -equal(multiply(sk_c6,X),sk_c5) | -equal(multiply(Y,sk_c6),X) | -equal(inverse(Y),sk_c6).
% 416222 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 416223 [] equal(multiply(sk_c3,sk_c6),sk_c4) | equal(inverse(sk_c1),sk_c6).
% 416224 [?] ?
% 416227 [?] ?
% 416228 [?] ?
% 416229 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(multiply(sk_c6,sk_c4),sk_c5).
% 416232 [] equal(multiply(sk_c6,sk_c7),sk_c5).
% 416267 [hyper:416211,416222,416232,binarycut:416227] equal(inverse(sk_c3),sk_c6).
% 416312 [hyper:416211,416223,demod:416267,cut:416207,binarycut:416224] equal(inverse(sk_c1),sk_c6).
% 416316 [hyper:416211,416223,416232,binarycut:416228] equal(multiply(sk_c3,sk_c6),sk_c4).
% 416332 [hyper:416211,416229,demod:416312,416232,cut:416207,cut:416207] equal(multiply(sk_c6,sk_c4),sk_c5).
% 416344 [hyper:416211,416316,demod:416267,416332,cut:416207,cut:416207] 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: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c6,Z),sk_c5) | -equal(multiply(U,sk_c6),Z) | -equal(inverse(U),sk_c6).
% Split part used next: -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),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: 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 19
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(26,40,0,56,0,0,8546,50,101,8576,0,101,17776,50,221,17806,0,221,27596,50,315,27626,0,315,37762,50,407,37792,0,407,48191,50,514,48221,0,514,58968,50,650,58998,0,650,70093,50,840,70093,40,840,70123,0,840,82717,3,1141,83370,4,1291,83923,1,1441,83923,50,1441,83923,40,1441,83953,0,1441,84158,3,1742,84171,4,1916,84178,5,2042,84178,1,2042,84178,50,2042,84178,40,2042,84208,0,2042,124707,3,3543,125341,4,4293,125947,1,5043,125947,50,5044,125947,40,5044,125977,0,5044,152436,3,5801,152909,4,6170,153331,5,6545,153332,1,6545,153332,50,6546,153332,40,6546,153362,0,6546,167568,3,7297,168548,4,7672,169334,5,8047,169335,1,8047,169335,50,8047,169335,40,8047,169365,0,8047,239605,3,11948,240468,4,13899,241819,1,15848,241819,50,15850,241819,40,15850,241849,0,15850,286060,3,18401,286993,4,19676,287996,5,20951,287997,1,20951,287997,50,20953,287997,40,20953,288027,0,20953,333333,3,22459,334228,4,23204,335159,5,23954,335160,1,23954,335160,50,23956,335160,40,23956,335190,0,23956,356347,3,24707,356811,4,25082,357044,1,25457,357044,50,25457,357044,40,25457,357074,0,25457,380935,3,26658,381917,4,27258,382957,5,27858,382958,1,27858,382958,50,27859,382958,40,27859,382988,0,27859,415275,3,28618,415751,4,28985,416205,5,29360,416206,1,29360,416206,50,29361,416206,40,29361,416206,40,29361,416232,0,29361,416343,50,29361,416343,30,29361,416343,40,29361,416369,0,29361,416438,50,29361,416464,0,29368)
%
%
% START OF PROOF
% 416440 [] equal(multiply(identity,X),X).
% 416441 [] equal(multiply(inverse(X),X),identity).
% 416442 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 416443 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 416444 [?] ?
% 416445 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c4).
% 416446 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(multiply(sk_c6,sk_c4),sk_c5).
% 416447 [?] ?
% 416448 [?] ?
% 416449 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 416450 [] equal(multiply(sk_c3,sk_c6),sk_c4) | equal(inverse(sk_c2),sk_c6).
% 416451 [] equal(multiply(sk_c6,sk_c4),sk_c5) | equal(inverse(sk_c2),sk_c6).
% 416452 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c7),sk_c5).
% 416453 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c6),sk_c5).
% 416464 [] equal(multiply(sk_c6,sk_c7),sk_c5).
% 416467 [hyper:416443,416449,binarycut:416444] equal(inverse(sk_c3),sk_c6).
% 416471 [para:416467.1.1,416441.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 416475 [hyper:416443,416452,binarycut:416447] equal(inverse(sk_c7),sk_c5).
% 416476 [para:416475.1.1,416441.1.1.1] equal(multiply(sk_c5,sk_c7),identity).
% 416482 [hyper:416443,416453,binarycut:416448] equal(inverse(sk_c6),sk_c5).
% 416483 [para:416482.1.1,416441.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 416486 [hyper:416443,416450,binarycut:416445] equal(multiply(sk_c3,sk_c6),sk_c4).
% 416492 [hyper:416443,416451,binarycut:416446] equal(multiply(sk_c6,sk_c4),sk_c5).
% 416493 [para:416464.1.1,416442.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c6,multiply(sk_c7,X))).
% 416494 [para:416441.1.1,416442.1.1.1,demod:416440] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 416495 [para:416471.1.1,416442.1.1.1,demod:416440] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 416496 [para:416476.1.1,416442.1.1.1,demod:416440] equal(X,multiply(sk_c5,multiply(sk_c7,X))).
% 416500 [para:416486.1.1,416495.1.2.2,demod:416492] equal(sk_c6,sk_c5).
% 416504 [para:416500.1.1,416483.1.1.2] equal(multiply(sk_c5,sk_c5),identity).
% 416508 [para:416500.1.1,416493.1.2.1,demod:416496] equal(multiply(sk_c5,X),X).
% 416514 [para:416441.1.1,416494.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 416520 [para:416494.1.2,416494.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 416534 [para:416483.1.1,416508.1.1] equal(identity,sk_c6).
% 416537 [para:416520.1.2,416441.1.1] equal(multiply(X,inverse(X)),identity).
% 416538 [para:416520.1.2,416494.1.2] equal(X,multiply(Y,multiply(inverse(Y),X))).
% 416539 [para:416520.1.2,416514.1.2] equal(X,multiply(X,identity)).
% 416561 [para:416537.1.1,416538.1.2.2,demod:416539] equal(inverse(inverse(X)),X).
% 416562 [hyper:416443,416561,demod:416504,416482,cut:416534] 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 4
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c6,Z),sk_c5) | -equal(multiply(U,sk_c6),Z) | -equal(inverse(U),sk_c6).
% Split part used next: -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),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: 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 19
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(26,40,0,56,0,0,8546,50,101,8576,0,101,17776,50,221,17806,0,221,27596,50,315,27626,0,315,37762,50,407,37792,0,407,48191,50,514,48221,0,514,58968,50,650,58998,0,650,70093,50,840,70093,40,840,70123,0,840,82717,3,1141,83370,4,1291,83923,1,1441,83923,50,1441,83923,40,1441,83953,0,1441,84158,3,1742,84171,4,1916,84178,5,2042,84178,1,2042,84178,50,2042,84178,40,2042,84208,0,2042,124707,3,3543,125341,4,4293,125947,1,5043,125947,50,5044,125947,40,5044,125977,0,5044,152436,3,5801,152909,4,6170,153331,5,6545,153332,1,6545,153332,50,6546,153332,40,6546,153362,0,6546,167568,3,7297,168548,4,7672,169334,5,8047,169335,1,8047,169335,50,8047,169335,40,8047,169365,0,8047,239605,3,11948,240468,4,13899,241819,1,15848,241819,50,15850,241819,40,15850,241849,0,15850,286060,3,18401,286993,4,19676,287996,5,20951,287997,1,20951,287997,50,20953,287997,40,20953,288027,0,20953,333333,3,22459,334228,4,23204,335159,5,23954,335160,1,23954,335160,50,23956,335160,40,23956,335190,0,23956,356347,3,24707,356811,4,25082,357044,1,25457,357044,50,25457,357044,40,25457,357074,0,25457,380935,3,26658,381917,4,27258,382957,5,27858,382958,1,27858,382958,50,27859,382958,40,27859,382988,0,27859,415275,3,28618,415751,4,28985,416205,5,29360,416206,1,29360,416206,50,29361,416206,40,29361,416206,40,29361,416232,0,29361,416343,50,29361,416343,30,29361,416343,40,29361,416369,0,29361,416438,50,29361,416464,0,29368,416561,50,29368,416561,30,29368,416561,40,29368,416587,0,29368,416668,50,29369,416694,0,29369)
%
%
% START OF PROOF
% 416670 [] equal(multiply(identity,X),X).
% 416671 [] equal(multiply(inverse(X),X),identity).
% 416672 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 416673 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6).
% 416684 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 416685 [] equal(multiply(sk_c3,sk_c6),sk_c4) | equal(inverse(sk_c1),sk_c6).
% 416686 [] equal(multiply(sk_c6,sk_c4),sk_c5) | equal(inverse(sk_c1),sk_c6).
% 416687 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c7),sk_c5).
% 416688 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c6),sk_c5).
% 416689 [?] ?
% 416690 [?] ?
% 416691 [?] ?
% 416692 [?] ?
% 416693 [?] ?
% 416694 [] equal(multiply(sk_c6,sk_c7),sk_c5).
% 416707 [hyper:416673,416684,binarycut:416689] equal(inverse(sk_c3),sk_c6).
% 416711 [para:416707.1.1,416671.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 416716 [hyper:416673,416687,binarycut:416692] equal(inverse(sk_c7),sk_c5).
% 416717 [para:416716.1.1,416671.1.1.1] equal(multiply(sk_c5,sk_c7),identity).
% 416720 [hyper:416673,416688,binarycut:416693] equal(inverse(sk_c6),sk_c5).
% 416722 [para:416720.1.1,416671.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 416731 [hyper:416673,416685,binarycut:416690] equal(multiply(sk_c3,sk_c6),sk_c4).
% 416734 [hyper:416673,416686,binarycut:416691] equal(multiply(sk_c6,sk_c4),sk_c5).
% 416735 [para:416694.1.1,416672.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c6,multiply(sk_c7,X))).
% 416736 [para:416671.1.1,416672.1.1.1,demod:416670] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 416737 [para:416711.1.1,416672.1.1.1,demod:416670] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 416738 [para:416717.1.1,416672.1.1.1,demod:416670] equal(X,multiply(sk_c5,multiply(sk_c7,X))).
% 416742 [para:416731.1.1,416737.1.2.2,demod:416734] equal(sk_c6,sk_c5).
% 416750 [para:416742.1.1,416735.1.2.1,demod:416738] equal(multiply(sk_c5,X),X).
% 416756 [para:416671.1.1,416736.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 416762 [para:416736.1.2,416736.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 416775 [para:416717.1.1,416750.1.1] equal(identity,sk_c7).
% 416779 [para:416762.1.2,416671.1.1] equal(multiply(X,inverse(X)),identity).
% 416780 [para:416762.1.2,416736.1.2] equal(X,multiply(Y,multiply(inverse(Y),X))).
% 416781 [para:416762.1.2,416756.1.2] equal(X,multiply(X,identity)).
% 416803 [para:416779.1.1,416780.1.2.2,demod:416781] equal(inverse(inverse(X)),X).
% 416804 [hyper:416673,416803,demod:416722,416720,cut:416775] 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 4
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c6,Z),sk_c5) | -equal(multiply(U,sk_c6),Z) | -equal(inverse(U),sk_c6).
% Split part used next: -equal(multiply(sk_c6,sk_c7),sk_c5).
% 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: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(26,40,0,56,0,0,8546,50,101,8576,0,101,17776,50,221,17806,0,221,27596,50,315,27626,0,315,37762,50,407,37792,0,407,48191,50,514,48221,0,514,58968,50,650,58998,0,650,70093,50,840,70093,40,840,70123,0,840,82717,3,1141,83370,4,1291,83923,1,1441,83923,50,1441,83923,40,1441,83953,0,1441,84158,3,1742,84171,4,1916,84178,5,2042,84178,1,2042,84178,50,2042,84178,40,2042,84208,0,2042,124707,3,3543,125341,4,4293,125947,1,5043,125947,50,5044,125947,40,5044,125977,0,5044,152436,3,5801,152909,4,6170,153331,5,6545,153332,1,6545,153332,50,6546,153332,40,6546,153362,0,6546,167568,3,7297,168548,4,7672,169334,5,8047,169335,1,8047,169335,50,8047,169335,40,8047,169365,0,8047,239605,3,11948,240468,4,13899,241819,1,15848,241819,50,15850,241819,40,15850,241849,0,15850,286060,3,18401,286993,4,19676,287996,5,20951,287997,1,20951,287997,50,20953,287997,40,20953,288027,0,20953,333333,3,22459,334228,4,23204,335159,5,23954,335160,1,23954,335160,50,23956,335160,40,23956,335190,0,23956,356347,3,24707,356811,4,25082,357044,1,25457,357044,50,25457,357044,40,25457,357074,0,25457,380935,3,26658,381917,4,27258,382957,5,27858,382958,1,27858,382958,50,27859,382958,40,27859,382988,0,27859,415275,3,28618,415751,4,28985,416205,5,29360,416206,1,29360,416206,50,29361,416206,40,29361,416206,40,29361,416232,0,29361,416343,50,29361,416343,30,29361,416343,40,29361,416369,0,29361,416438,50,29361,416464,0,29368,416561,50,29368,416561,30,29368,416561,40,29368,416587,0,29368,416668,50,29369,416694,0,29369,416803,50,29369,416803,30,29369,416803,40,29369,416829,0,29374)
%
%
% START OF PROOF
% 416808 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 416829 [] equal(multiply(sk_c6,sk_c7),sk_c5).
% 416830 [hyper:416808,416829] 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: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c6,Z),sk_c5) | -equal(multiply(U,sk_c6),Z) | -equal(inverse(U),sk_c6).
% Split part used next: -equal(inverse(sk_c6),sk_c5).
% 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: 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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(26,40,0,56,0,0,8546,50,101,8576,0,101,17776,50,221,17806,0,221,27596,50,315,27626,0,315,37762,50,407,37792,0,407,48191,50,514,48221,0,514,58968,50,650,58998,0,650,70093,50,840,70093,40,840,70123,0,840,82717,3,1141,83370,4,1291,83923,1,1441,83923,50,1441,83923,40,1441,83953,0,1441,84158,3,1742,84171,4,1916,84178,5,2042,84178,1,2042,84178,50,2042,84178,40,2042,84208,0,2042,124707,3,3543,125341,4,4293,125947,1,5043,125947,50,5044,125947,40,5044,125977,0,5044,152436,3,5801,152909,4,6170,153331,5,6545,153332,1,6545,153332,50,6546,153332,40,6546,153362,0,6546,167568,3,7297,168548,4,7672,169334,5,8047,169335,1,8047,169335,50,8047,169335,40,8047,169365,0,8047,239605,3,11948,240468,4,13899,241819,1,15848,241819,50,15850,241819,40,15850,241849,0,15850,286060,3,18401,286993,4,19676,287996,5,20951,287997,1,20951,287997,50,20953,287997,40,20953,288027,0,20953,333333,3,22459,334228,4,23204,335159,5,23954,335160,1,23954,335160,50,23956,335160,40,23956,335190,0,23956,356347,3,24707,356811,4,25082,357044,1,25457,357044,50,25457,357044,40,25457,357074,0,25457,380935,3,26658,381917,4,27258,382957,5,27858,382958,1,27858,382958,50,27859,382958,40,27859,382988,0,27859,415275,3,28618,415751,4,28985,416205,5,29360,416206,1,29360,416206,50,29361,416206,40,29361,416206,40,29361,416232,0,29361,416343,50,29361,416343,30,29361,416343,40,29361,416369,0,29361,416438,50,29361,416464,0,29368,416561,50,29368,416561,30,29368,416561,40,29368,416587,0,29368,416668,50,29369,416694,0,29369,416803,50,29369,416803,30,29369,416803,40,29369,416829,0,29374,416829,50,29374,416829,30,29374,416829,40,29374,416855,0,29374,416950,50,29375,416976,0,29380,417140,50,29382,417166,0,29382,417346,50,29385,417372,0,29385,417565,50,29390,417591,0,29394,417790,50,29401,417816,0,29401,418023,50,29414,418049,0,29419,418264,50,29445,418290,0,29446,418515,50,29504,418541,0,29504,418776,50,29616,418776,40,29616,418802,0,29616)
%
%
% START OF PROOF
% 418778 [] equal(multiply(identity,X),X).
% 418779 [] equal(multiply(inverse(X),X),identity).
% 418780 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 418781 [] -equal(inverse(sk_c6),sk_c5).
% 418786 [?] ?
% 418791 [?] ?
% 418796 [?] ?
% 418801 [?] ?
% 418802 [] equal(multiply(sk_c6,sk_c7),sk_c5).
% 418811 [input:418791,cut:418781] equal(inverse(sk_c2),sk_c6).
% 418812 [para:418811.1.1,418779.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 418820 [input:418796,cut:418781] equal(inverse(sk_c1),sk_c6).
% 418821 [para:418820.1.1,418779.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 418824 [input:418786,cut:418781] equal(multiply(sk_c2,sk_c5),sk_c6).
% 418835 [input:418801,cut:418781] equal(multiply(sk_c1,sk_c6),sk_c7).
% 418842 [para:418779.1.1,418780.1.1.1,demod:418778] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 418844 [para:418812.1.1,418780.1.1.1,demod:418778] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 418847 [para:418821.1.1,418780.1.1.1,demod:418778] equal(X,multiply(sk_c6,multiply(sk_c1,X))).
% 418868 [para:418824.1.1,418844.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 418873 [para:418835.1.1,418847.1.2.2,demod:418802] equal(sk_c6,sk_c5).
% 418877 [para:418873.1.1,418802.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 418895 [para:418873.1.1,418868.1.2.1] equal(sk_c5,multiply(sk_c5,sk_c6)).
% 418962 [para:418802.1.1,418842.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 418965 [para:418812.1.1,418842.1.2.2] equal(sk_c2,multiply(inverse(sk_c6),identity)).
% 418969 [para:418821.1.1,418842.1.2.2,demod:418965] equal(sk_c1,sk_c2).
% 418990 [para:418868.1.2,418842.1.2.2,demod:418962] equal(sk_c6,sk_c7).
% 418994 [para:418877.1.1,418842.1.2.2,demod:418779] equal(sk_c7,identity).
% 418998 [para:418895.1.2,418842.1.2.2,demod:418779] equal(sk_c6,identity).
% 419006 [para:418969.1.2,418811.1.1.1] equal(inverse(sk_c1),sk_c6).
% 419010 [para:418990.1.1,418781.1.1.1] -equal(inverse(sk_c7),sk_c5).
% 419036 [para:418998.1.1,418821.1.1.1,demod:418778] equal(sk_c1,identity).
% 419049 [para:419036.1.1,419006.1.1.1] equal(inverse(identity),sk_c6).
% 419050 [para:418994.1.1,419010.1.1.1,demod:419049,cut:418873] 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_c6,sk_c7),sk_c5) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(inverse(sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c6,Z),sk_c5) | -equal(multiply(U,sk_c6),Z) | -equal(inverse(U),sk_c6).
% Split part used next: -equal(inverse(sk_c7),sk_c5).
% 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: 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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(26,40,0,56,0,0,8546,50,101,8576,0,101,17776,50,221,17806,0,221,27596,50,315,27626,0,315,37762,50,407,37792,0,407,48191,50,514,48221,0,514,58968,50,650,58998,0,650,70093,50,840,70093,40,840,70123,0,840,82717,3,1141,83370,4,1291,83923,1,1441,83923,50,1441,83923,40,1441,83953,0,1441,84158,3,1742,84171,4,1916,84178,5,2042,84178,1,2042,84178,50,2042,84178,40,2042,84208,0,2042,124707,3,3543,125341,4,4293,125947,1,5043,125947,50,5044,125947,40,5044,125977,0,5044,152436,3,5801,152909,4,6170,153331,5,6545,153332,1,6545,153332,50,6546,153332,40,6546,153362,0,6546,167568,3,7297,168548,4,7672,169334,5,8047,169335,1,8047,169335,50,8047,169335,40,8047,169365,0,8047,239605,3,11948,240468,4,13899,241819,1,15848,241819,50,15850,241819,40,15850,241849,0,15850,286060,3,18401,286993,4,19676,287996,5,20951,287997,1,20951,287997,50,20953,287997,40,20953,288027,0,20953,333333,3,22459,334228,4,23204,335159,5,23954,335160,1,23954,335160,50,23956,335160,40,23956,335190,0,23956,356347,3,24707,356811,4,25082,357044,1,25457,357044,50,25457,357044,40,25457,357074,0,25457,380935,3,26658,381917,4,27258,382957,5,27858,382958,1,27858,382958,50,27859,382958,40,27859,382988,0,27859,415275,3,28618,415751,4,28985,416205,5,29360,416206,1,29360,416206,50,29361,416206,40,29361,416206,40,29361,416232,0,29361,416343,50,29361,416343,30,29361,416343,40,29361,416369,0,29361,416438,50,29361,416464,0,29368,416561,50,29368,416561,30,29368,416561,40,29368,416587,0,29368,416668,50,29369,416694,0,29369,416803,50,29369,416803,30,29369,416803,40,29369,416829,0,29374,416829,50,29374,416829,30,29374,416829,40,29374,416855,0,29374,416950,50,29375,416976,0,29380,417140,50,29382,417166,0,29382,417346,50,29385,417372,0,29385,417565,50,29390,417591,0,29394,417790,50,29401,417816,0,29401,418023,50,29414,418049,0,29419,418264,50,29445,418290,0,29446,418515,50,29504,418541,0,29504,418776,50,29616,418776,40,29616,418802,0,29616,419049,50,29617,419049,30,29617,419049,40,29617,419075,0,29617,419170,50,29618,419196,0,29622,419360,50,29625,419386,0,29625,419566,50,29628,419592,0,29628,419785,50,29632,419811,0,29637,420010,50,29644,420036,0,29644,420243,50,29658,420269,0,29663,420484,50,29689,420510,0,29689,420735,50,29747,420761,0,29747,420996,50,29858,420996,40,29858,421022,0,29858)
%
%
% START OF PROOF
% 420998 [] equal(multiply(identity,X),X).
% 420999 [] equal(multiply(inverse(X),X),identity).
% 421000 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 421001 [] -equal(inverse(sk_c7),sk_c5).
% 421005 [?] ?
% 421010 [?] ?
% 421015 [?] ?
% 421020 [?] ?
% 421022 [] equal(multiply(sk_c6,sk_c7),sk_c5).
% 421028 [input:421010,cut:421001] equal(inverse(sk_c2),sk_c6).
% 421029 [para:421028.1.1,420999.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 421036 [input:421015,cut:421001] equal(inverse(sk_c1),sk_c6).
% 421037 [para:421036.1.1,420999.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 421040 [input:421005,cut:421001] equal(multiply(sk_c2,sk_c5),sk_c6).
% 421051 [input:421020,cut:421001] equal(multiply(sk_c1,sk_c6),sk_c7).
% 421062 [para:420999.1.1,421000.1.1.1,demod:420998] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 421064 [para:421029.1.1,421000.1.1.1,demod:420998] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 421067 [para:421037.1.1,421000.1.1.1,demod:420998] equal(X,multiply(sk_c6,multiply(sk_c1,X))).
% 421087 [para:421040.1.1,421064.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 421091 [para:421051.1.1,421067.1.2.2,demod:421022] equal(sk_c6,sk_c5).
% 421094 [para:421091.1.1,421022.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 421119 [para:421091.1.1,421087.1.2.1] equal(sk_c5,multiply(sk_c5,sk_c6)).
% 421132 [para:421091.1.1,421119.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c5)).
% 421140 [para:421029.1.1,421062.1.2.2] equal(sk_c2,multiply(inverse(sk_c6),identity)).
% 421144 [para:421037.1.1,421062.1.2.2,demod:421140] equal(sk_c1,sk_c2).
% 421171 [para:421094.1.1,421062.1.2.2,demod:420999] equal(sk_c7,identity).
% 421174 [para:421119.1.2,421062.1.2.2,demod:420999] equal(sk_c6,identity).
% 421177 [para:421132.1.2,421062.1.2.2,demod:420999] equal(sk_c5,identity).
% 421181 [para:421144.1.2,421028.1.1.1] equal(inverse(sk_c1),sk_c6).
% 421198 [para:421171.1.1,421001.1.1.1] -equal(inverse(identity),sk_c5).
% 421203 [para:421174.1.1,421037.1.1.1,demod:420998] equal(sk_c1,identity).
% 421211 [para:421203.1.1,421181.1.1.1] equal(inverse(identity),sk_c6).
% 421213 [para:421177.1.1,421198.1.2,demod:421211,cut:421174] 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: 31750
% derived clauses: 6690297
% kept clauses: 319842
% kept size sum: 983620
% kept mid-nuclei: 67591
% kept new demods: 4117
% forw unit-subs: 2237554
% forw double-subs: 3554914
% forw overdouble-subs: 326610
% backward subs: 9072
% fast unit cutoff: 36466
% full unit cutoff: 0
% dbl unit cutoff: 3731
% real runtime : 301.39
% process. runtime: 298.59
% specific non-discr-tree subsumption statistics:
% tried: 17505990
% length fails: 2103076
% strength fails: 3675507
% predlist fails: 458651
% aux str. fails: 2359063
% by-lit fails: 3066523
% full subs tried: 1333378
% full subs fail: 1202399
%
% ; 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/GRP334-1+eq_r.in")
%
%------------------------------------------------------------------------------