TSTP Solution File: GRP280-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP280-1 : 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 : art01.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 289.1s
% Output : Assurance 289.1s
% 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/GRP280-1+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 23)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 23)
% (binary-posweight-lex-big-order 30 #f 3 23)
% (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_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% was split for some strategies as:
% -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9).
% -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9).
% -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% -equal(multiply(sk_c9,sk_c8),sk_c7).
% -equal(multiply(sk_c9,sk_c7),sk_c8).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1116,50,10,1162,0,10,2664,50,38,2710,0,38,4507,50,68,4553,0,68,6501,50,99,6547,0,99,8668,50,140,8714,0,140,11013,50,196,11059,0,196,13559,50,279,13605,0,279,16333,50,413,16379,0,413,19358,50,619,19404,0,619,22661,50,916,22661,40,916,22707,0,916,34032,3,1217,34721,4,1367,35382,5,1517,35383,1,1517,35383,50,1517,35383,40,1517,35429,0,1517,35658,3,1831,35666,4,1976,35674,5,2118,35674,1,2118,35674,50,2118,35674,40,2118,35720,0,2118,53935,3,3619,55033,4,4369,56488,1,5119,56488,50,5119,56488,40,5119,56534,0,5119,65415,3,5870,67125,50,6144,67125,40,6144,67171,0,6144,79709,3,6895,80460,4,7270,81545,5,7645,81546,5,7645,81546,1,7645,81546,50,7645,81546,40,7645,81592,0,7645,142135,3,11546,143257,4,13496,144326,1,15447,144326,50,15449,144326,40,15449,144372,0,15449,195137,3,18004,196034,4,19276,196754,1,20550,196754,50,20551,196754,40,20551,196800,0,20551,240677,3,22054,241464,4,22802,242120,1,23552,242120,50,23554,242120,40,23554,242166,0,23554,262766,3,24305,263300,4,24680,263837,5,25055,263838,1,25055,263838,50,25055,263838,40,25055,263884,0,25055,292200,3,26256,292907,4,26856,293667,1,27456,293667,50,27457,293667,40,27457,293713,0,27457,309026,3,28209,309524,4,28583,310024,1,28958,310024,50,28958,310024,40,28958,310024,40,28958,310065,0,28958)
%
%
% START OF PROOF
% 310026 [] equal(multiply(identity,X),X).
% 310027 [] equal(multiply(inverse(X),X),identity).
% 310028 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 310029 [] -equal(multiply(X,sk_c9),sk_c7) | -equal(inverse(X),sk_c9).
% 310030 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 310031 [?] ?
% 310036 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c6),sk_c9).
% 310037 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 310042 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(inverse(sk_c6),sk_c9).
% 310043 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 310048 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 310049 [?] ?
% 310054 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(inverse(sk_c6),sk_c9).
% 310055 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 310060 [] equal(multiply(sk_c9,sk_c8),sk_c7) | equal(inverse(sk_c6),sk_c9).
% 310061 [] equal(multiply(sk_c9,sk_c8),sk_c7) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 310069 [hyper:310029,310030,binarycut:310031] equal(inverse(sk_c2),sk_c9).
% 310071 [para:310069.1.1,310027.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 310079 [hyper:310029,310048,binarycut:310049] equal(inverse(sk_c1),sk_c9).
% 310082 [para:310079.1.1,310027.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 310087 [hyper:310029,310037,310036] equal(multiply(sk_c2,sk_c9),sk_c3).
% 310093 [hyper:310029,310043,310042] equal(multiply(sk_c9,sk_c3),sk_c8).
% 310099 [hyper:310029,310055,310054] equal(multiply(sk_c1,sk_c9),sk_c8).
% 310106 [hyper:310029,310061,310060] equal(multiply(sk_c9,sk_c8),sk_c7).
% 310107 [para:310027.1.1,310028.1.1.1,demod:310026] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 310108 [para:310071.1.1,310028.1.1.1,demod:310026] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 310114 [para:310087.1.1,310108.1.2.2,demod:310093] equal(sk_c9,sk_c8).
% 310118 [para:310114.1.1,310093.1.1.1] equal(multiply(sk_c8,sk_c3),sk_c8).
% 310124 [para:310071.1.1,310107.1.2.2] equal(sk_c2,multiply(inverse(sk_c9),identity)).
% 310125 [para:310082.1.1,310107.1.2.2,demod:310124] equal(sk_c1,sk_c2).
% 310127 [para:310099.1.1,310107.1.2.2,demod:310106,310079] equal(sk_c9,sk_c7).
% 310131 [para:310125.1.2,310087.1.1.1,demod:310099] equal(sk_c8,sk_c3).
% 310132 [para:310127.1.1,310071.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 310139 [para:310127.1.1,310114.1.1] equal(sk_c7,sk_c8).
% 310144 [para:310139.1.2,310131.1.1] equal(sk_c7,sk_c3).
% 310151 [para:310118.1.1,310107.1.2.2,demod:310027] equal(sk_c3,identity).
% 310155 [para:310151.1.1,310144.1.2] equal(sk_c7,identity).
% 310169 [para:310155.1.1,310132.1.1.1,demod:310026] equal(sk_c2,identity).
% 310170 [para:310169.1.1,310069.1.1.1] equal(inverse(identity),sk_c9).
% 310178 [hyper:310029,310170,demod:310026,cut:310127] 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 23
% 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_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9).
% 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 23
% 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 23
% clause depth limited to 4
% seconds given: 4
%
%
% **** EMPTY CLAUSE DERIVED ****
%
%
% timer checkpoints: c(41,40,0,87,0,0,1116,50,10,1162,0,10,2664,50,38,2710,0,38,4507,50,68,4553,0,68,6501,50,99,6547,0,99,8668,50,140,8714,0,140,11013,50,196,11059,0,196,13559,50,279,13605,0,279,16333,50,413,16379,0,413,19358,50,619,19404,0,619,22661,50,916,22661,40,916,22707,0,916,34032,3,1217,34721,4,1367,35382,5,1517,35383,1,1517,35383,50,1517,35383,40,1517,35429,0,1517,35658,3,1831,35666,4,1976,35674,5,2118,35674,1,2118,35674,50,2118,35674,40,2118,35720,0,2118,53935,3,3619,55033,4,4369,56488,1,5119,56488,50,5119,56488,40,5119,56534,0,5119,65415,3,5870,67125,50,6144,67125,40,6144,67171,0,6144,79709,3,6895,80460,4,7270,81545,5,7645,81546,5,7645,81546,1,7645,81546,50,7645,81546,40,7645,81592,0,7645,142135,3,11546,143257,4,13496,144326,1,15447,144326,50,15449,144326,40,15449,144372,0,15449,195137,3,18004,196034,4,19276,196754,1,20550,196754,50,20551,196754,40,20551,196800,0,20551,240677,3,22054,241464,4,22802,242120,1,23552,242120,50,23554,242120,40,23554,242166,0,23554,262766,3,24305,263300,4,24680,263837,5,25055,263838,1,25055,263838,50,25055,263838,40,25055,263884,0,25055,292200,3,26256,292907,4,26856,293667,1,27456,293667,50,27457,293667,40,27457,293713,0,27457,309026,3,28209,309524,4,28583,310024,1,28958,310024,50,28958,310024,40,28958,310024,40,28958,310065,0,28958,310177,50,28959,310177,30,28959,310177,40,28959,310218,0,28959,310434,50,28960,310475,0,28965)
%
%
% START OF PROOF
% 310436 [] equal(multiply(identity,X),X).
% 310437 [] equal(multiply(inverse(X),X),identity).
% 310438 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 310439 [] -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(Y,X),sk_c9) | -equal(inverse(Y),X).
% 310442 [?] ?
% 310443 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c4),sk_c5).
% 310444 [?] ?
% 310448 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 310449 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c4),sk_c5).
% 310450 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c4,sk_c5),sk_c9).
% 310454 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 310455 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(inverse(sk_c4),sk_c5).
% 310456 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(multiply(sk_c4,sk_c5),sk_c9).
% 310460 [?] ?
% 310461 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c4),sk_c5).
% 310462 [?] ?
% 310466 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 310467 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(inverse(sk_c4),sk_c5).
% 310468 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(multiply(sk_c4,sk_c5),sk_c9).
% 310472 [] equal(multiply(sk_c9,sk_c8),sk_c7) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 310473 [] equal(multiply(sk_c9,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c5).
% 310474 [] equal(multiply(sk_c9,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c5),sk_c9).
% 310484 [hyper:310439,310443,binarycut:310444,binarycut:310442] equal(inverse(sk_c2),sk_c9).
% 310487 [para:310484.1.1,310437.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 310500 [hyper:310439,310461,binarycut:310462,binarycut:310460] equal(inverse(sk_c1),sk_c9).
% 310503 [para:310500.1.1,310437.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 310536 [hyper:310439,310450,310448,310449] equal(multiply(sk_c2,sk_c9),sk_c3).
% 310547 [hyper:310439,310456,310454,310455] equal(multiply(sk_c9,sk_c3),sk_c8).
% 310558 [hyper:310439,310468,310466,310467] equal(multiply(sk_c1,sk_c9),sk_c8).
% 310569 [hyper:310439,310474,310472,310473] equal(multiply(sk_c9,sk_c8),sk_c7).
% 310570 [para:310437.1.1,310438.1.1.1,demod:310436] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 310571 [para:310487.1.1,310438.1.1.1,demod:310436] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 310572 [para:310503.1.1,310438.1.1.1,demod:310436] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 310573 [para:310536.1.1,310438.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c9,X))).
% 310579 [para:310536.1.1,310571.1.2.2,demod:310547] equal(sk_c9,sk_c8).
% 310583 [para:310579.1.1,310547.1.1.1] equal(multiply(sk_c8,sk_c3),sk_c8).
% 310586 [para:310579.1.1,310571.1.2.1] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 310589 [para:310436.1.1,310570.1.2.2] equal(X,multiply(inverse(identity),X)).
% 310590 [para:310437.1.1,310570.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 310592 [para:310487.1.1,310570.1.2.2] equal(sk_c2,multiply(inverse(sk_c9),identity)).
% 310593 [para:310503.1.1,310570.1.2.2,demod:310592] equal(sk_c1,sk_c2).
% 310594 [para:310547.1.1,310570.1.2.2] equal(sk_c3,multiply(inverse(sk_c9),sk_c8)).
% 310595 [para:310558.1.1,310570.1.2.2,demod:310569,310500] equal(sk_c9,sk_c7).
% 310596 [para:310438.1.1,310570.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 310598 [para:310571.1.2,310570.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c9),X)).
% 310600 [para:310570.1.2,310570.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 310601 [para:310593.1.2,310536.1.1.1,demod:310558] equal(sk_c8,sk_c3).
% 310602 [para:310595.1.1,310487.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 310609 [para:310595.1.1,310579.1.1] equal(sk_c7,sk_c8).
% 310614 [para:310609.1.2,310601.1.1] equal(sk_c7,sk_c3).
% 310618 [para:310572.1.2,310570.1.2.2,demod:310598] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 310623 [para:310583.1.1,310570.1.2.2,demod:310437] equal(sk_c3,identity).
% 310626 [para:310623.1.1,310547.1.1.2] equal(multiply(sk_c9,identity),sk_c8).
% 310627 [para:310623.1.1,310614.1.2] equal(sk_c7,identity).
% 310633 [para:310571.1.2,310573.1.2.2,demod:310618] equal(multiply(sk_c3,multiply(sk_c1,X)),multiply(sk_c1,X)).
% 310642 [para:310627.1.1,310602.1.1.1,demod:310436] equal(sk_c2,identity).
% 310643 [para:310642.1.1,310484.1.1.1] equal(inverse(identity),sk_c9).
% 310644 [para:310642.1.1,310487.1.1.2,demod:310626] equal(sk_c8,identity).
% 310645 [para:310642.1.1,310536.1.1.1,demod:310436] equal(sk_c9,sk_c3).
% 310650 [para:310645.1.1,310571.1.2.1,demod:310633,310618] equal(X,multiply(sk_c1,X)).
% 310678 [para:310644.1.1,310594.1.2.2,demod:310592] equal(sk_c3,sk_c2).
% 310680 [para:310678.1.2,310593.1.2] equal(sk_c1,sk_c3).
% 310682 [para:310680.1.2,310614.1.2] equal(sk_c7,sk_c1).
% 310721 [para:310682.1.2,310500.1.1.1] equal(inverse(sk_c7),sk_c9).
% 310736 [para:310600.1.2,310437.1.1] equal(multiply(X,inverse(X)),identity).
% 310738 [para:310600.1.2,310590.1.2] equal(X,multiply(X,identity)).
% 310742 [para:310738.1.2,310589.1.2,demod:310643] equal(identity,sk_c9).
% 310755 [para:310736.1.1,310596.1.2.2.2,demod:310738] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 310765 [para:310571.1.2,310755.1.2.1.1,demod:310650,310618] equal(inverse(X),multiply(inverse(X),sk_c9)).
% 310770 [para:310586.1.2,310755.1.2.1.1,demod:310650,310618] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 310776 [hyper:310439,310765,demod:310770,310736,310765,cut:310742,slowcut:310721] 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 23
% 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_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9).
% 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 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1116,50,10,1162,0,10,2664,50,38,2710,0,38,4507,50,68,4553,0,68,6501,50,99,6547,0,99,8668,50,140,8714,0,140,11013,50,196,11059,0,196,13559,50,279,13605,0,279,16333,50,413,16379,0,413,19358,50,619,19404,0,619,22661,50,916,22661,40,916,22707,0,916,34032,3,1217,34721,4,1367,35382,5,1517,35383,1,1517,35383,50,1517,35383,40,1517,35429,0,1517,35658,3,1831,35666,4,1976,35674,5,2118,35674,1,2118,35674,50,2118,35674,40,2118,35720,0,2118,53935,3,3619,55033,4,4369,56488,1,5119,56488,50,5119,56488,40,5119,56534,0,5119,65415,3,5870,67125,50,6144,67125,40,6144,67171,0,6144,79709,3,6895,80460,4,7270,81545,5,7645,81546,5,7645,81546,1,7645,81546,50,7645,81546,40,7645,81592,0,7645,142135,3,11546,143257,4,13496,144326,1,15447,144326,50,15449,144326,40,15449,144372,0,15449,195137,3,18004,196034,4,19276,196754,1,20550,196754,50,20551,196754,40,20551,196800,0,20551,240677,3,22054,241464,4,22802,242120,1,23552,242120,50,23554,242120,40,23554,242166,0,23554,262766,3,24305,263300,4,24680,263837,5,25055,263838,1,25055,263838,50,25055,263838,40,25055,263884,0,25055,292200,3,26256,292907,4,26856,293667,1,27456,293667,50,27457,293667,40,27457,293713,0,27457,309026,3,28209,309524,4,28583,310024,1,28958,310024,50,28958,310024,40,28958,310024,40,28958,310065,0,28958,310177,50,28959,310177,30,28959,310177,40,28959,310218,0,28959,310434,50,28960,310475,0,28965,310775,50,28966,310775,30,28966,310775,40,28966,310816,0,28966)
%
%
% START OF PROOF
% 310776 [] equal(X,X).
% 310780 [] -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9).
% 310781 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 310782 [] equal(multiply(sk_c6,sk_c9),sk_c7) | equal(inverse(sk_c2),sk_c9).
% 310786 [?] ?
% 310787 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c6),sk_c9).
% 310788 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 310792 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c9,sk_c7),sk_c8).
% 310793 [?] ?
% 310794 [?] ?
% 310798 [?] ?
% 310846 [hyper:310780,310782,310781,binarycut:310786] equal(inverse(sk_c2),sk_c9).
% 310858 [hyper:310780,310787,demod:310846,cut:310776,binarycut:310793] equal(inverse(sk_c6),sk_c9).
% 310870 [hyper:310780,310788,demod:310846,cut:310776,binarycut:310794] equal(multiply(sk_c6,sk_c9),sk_c7).
% 310909 [hyper:310780,310792,demod:310846,cut:310776,binarycut:310798] equal(multiply(sk_c9,sk_c7),sk_c8).
% 310913 [hyper:310780,310909,310870,demod:310858,cut:310776] 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 23
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% 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 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1116,50,10,1162,0,10,2664,50,38,2710,0,38,4507,50,68,4553,0,68,6501,50,99,6547,0,99,8668,50,140,8714,0,140,11013,50,196,11059,0,196,13559,50,279,13605,0,279,16333,50,413,16379,0,413,19358,50,619,19404,0,619,22661,50,916,22661,40,916,22707,0,916,34032,3,1217,34721,4,1367,35382,5,1517,35383,1,1517,35383,50,1517,35383,40,1517,35429,0,1517,35658,3,1831,35666,4,1976,35674,5,2118,35674,1,2118,35674,50,2118,35674,40,2118,35720,0,2118,53935,3,3619,55033,4,4369,56488,1,5119,56488,50,5119,56488,40,5119,56534,0,5119,65415,3,5870,67125,50,6144,67125,40,6144,67171,0,6144,79709,3,6895,80460,4,7270,81545,5,7645,81546,5,7645,81546,1,7645,81546,50,7645,81546,40,7645,81592,0,7645,142135,3,11546,143257,4,13496,144326,1,15447,144326,50,15449,144326,40,15449,144372,0,15449,195137,3,18004,196034,4,19276,196754,1,20550,196754,50,20551,196754,40,20551,196800,0,20551,240677,3,22054,241464,4,22802,242120,1,23552,242120,50,23554,242120,40,23554,242166,0,23554,262766,3,24305,263300,4,24680,263837,5,25055,263838,1,25055,263838,50,25055,263838,40,25055,263884,0,25055,292200,3,26256,292907,4,26856,293667,1,27456,293667,50,27457,293667,40,27457,293713,0,27457,309026,3,28209,309524,4,28583,310024,1,28958,310024,50,28958,310024,40,28958,310024,40,28958,310065,0,28958,310177,50,28959,310177,30,28959,310177,40,28959,310218,0,28959,310434,50,28960,310475,0,28965,310775,50,28966,310775,30,28966,310775,40,28966,310816,0,28966,310912,50,28966,310912,30,28966,310912,40,28966,310953,0,28967)
%
%
% START OF PROOF
% 310914 [] equal(multiply(identity,X),X).
% 310915 [] equal(multiply(inverse(X),X),identity).
% 310916 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 310917 [] -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% 310936 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 310937 [] equal(multiply(sk_c6,sk_c9),sk_c7) | equal(inverse(sk_c1),sk_c9).
% 310939 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c4),sk_c5).
% 310940 [] equal(multiply(sk_c4,sk_c5),sk_c9) | equal(inverse(sk_c1),sk_c9).
% 310941 [] equal(multiply(sk_c9,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c9).
% 310942 [?] ?
% 310943 [?] ?
% 310945 [?] ?
% 310946 [?] ?
% 310947 [?] ?
% 310962 [hyper:310917,310936,binarycut:310942] equal(inverse(sk_c6),sk_c9).
% 310966 [para:310962.1.1,310915.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 310970 [hyper:310917,310939,binarycut:310945] equal(inverse(sk_c4),sk_c5).
% 310987 [hyper:310917,310937,binarycut:310943] equal(multiply(sk_c6,sk_c9),sk_c7).
% 310994 [hyper:310917,310940,binarycut:310946] equal(multiply(sk_c4,sk_c5),sk_c9).
% 310997 [hyper:310917,310941,binarycut:310947] equal(multiply(sk_c9,sk_c7),sk_c8).
% 310998 [para:310915.1.1,310916.1.1.1,demod:310914] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 310999 [para:310966.1.1,310916.1.1.1,demod:310914] equal(X,multiply(sk_c9,multiply(sk_c6,X))).
% 311005 [para:310987.1.1,310999.1.2.2,demod:310997] equal(sk_c9,sk_c8).
% 311015 [para:310994.1.1,310998.1.2.2,demod:310970] equal(sk_c5,multiply(sk_c5,sk_c9)).
% 311025 [para:311015.1.2,310998.1.2.2,demod:310915] equal(sk_c9,identity).
% 311032 [para:311025.1.1,310966.1.1.1,demod:310914] equal(sk_c6,identity).
% 311041 [para:311032.1.1,310962.1.1.1] equal(inverse(identity),sk_c9).
% 311073 [hyper:310917,311041,demod:310914,cut:311005] 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 23
% 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_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(sk_c9,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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,0,87,0,0,1116,50,10,1162,0,10,2664,50,38,2710,0,38,4507,50,68,4553,0,68,6501,50,99,6547,0,99,8668,50,140,8714,0,140,11013,50,196,11059,0,196,13559,50,279,13605,0,279,16333,50,413,16379,0,413,19358,50,619,19404,0,619,22661,50,916,22661,40,916,22707,0,916,34032,3,1217,34721,4,1367,35382,5,1517,35383,1,1517,35383,50,1517,35383,40,1517,35429,0,1517,35658,3,1831,35666,4,1976,35674,5,2118,35674,1,2118,35674,50,2118,35674,40,2118,35720,0,2118,53935,3,3619,55033,4,4369,56488,1,5119,56488,50,5119,56488,40,5119,56534,0,5119,65415,3,5870,67125,50,6144,67125,40,6144,67171,0,6144,79709,3,6895,80460,4,7270,81545,5,7645,81546,5,7645,81546,1,7645,81546,50,7645,81546,40,7645,81592,0,7645,142135,3,11546,143257,4,13496,144326,1,15447,144326,50,15449,144326,40,15449,144372,0,15449,195137,3,18004,196034,4,19276,196754,1,20550,196754,50,20551,196754,40,20551,196800,0,20551,240677,3,22054,241464,4,22802,242120,1,23552,242120,50,23554,242120,40,23554,242166,0,23554,262766,3,24305,263300,4,24680,263837,5,25055,263838,1,25055,263838,50,25055,263838,40,25055,263884,0,25055,292200,3,26256,292907,4,26856,293667,1,27456,293667,50,27457,293667,40,27457,293713,0,27457,309026,3,28209,309524,4,28583,310024,1,28958,310024,50,28958,310024,40,28958,310024,40,28958,310065,0,28958,310177,50,28959,310177,30,28959,310177,40,28959,310218,0,28959,310434,50,28960,310475,0,28965,310775,50,28966,310775,30,28966,310775,40,28966,310816,0,28966,310912,50,28966,310912,30,28966,310912,40,28966,310953,0,28967,311072,50,28967,311072,30,28967,311072,40,28967,311113,0,28972,311254,50,28973,311295,0,28973,311482,50,28976,311523,0,28981,311718,50,28986,311759,0,28986,311962,50,28993,312003,0,28993,312212,50,29003,312253,0,29008,312470,50,29026,312511,0,29026,312736,50,29058,312777,0,29062,313012,50,29125,313053,0,29125,313298,50,29253,313298,40,29253,313339,0,29253)
%
%
% START OF PROOF
% 313170 [?] ?
% 313300 [] equal(multiply(identity,X),X).
% 313301 [] equal(multiply(inverse(X),X),identity).
% 313302 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 313303 [] -equal(multiply(sk_c9,sk_c8),sk_c7).
% 313334 [?] ?
% 313335 [?] ?
% 313336 [?] ?
% 313337 [?] ?
% 313338 [?] ?
% 313339 [?] ?
% 313382 [input:313334,cut:313303] equal(inverse(sk_c6),sk_c9).
% 313383 [para:313382.1.1,313301.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 313384 [input:313337,cut:313303] equal(inverse(sk_c4),sk_c5).
% 313385 [para:313384.1.1,313301.1.1.1] equal(multiply(sk_c5,sk_c4),identity).
% 313400 [input:313335,cut:313303] equal(multiply(sk_c6,sk_c9),sk_c7).
% 313401 [input:313336,cut:313303] equal(multiply(sk_c5,sk_c8),sk_c9).
% 313402 [input:313338,cut:313303] equal(multiply(sk_c4,sk_c5),sk_c9).
% 313403 [input:313339,cut:313303] equal(multiply(sk_c9,sk_c7),sk_c8).
% 313426 [para:313383.1.1,313302.1.1.1,demod:313300] equal(X,multiply(sk_c9,multiply(sk_c6,X))).
% 313427 [para:313385.1.1,313302.1.1.1,demod:313300] equal(X,multiply(sk_c5,multiply(sk_c4,X))).
% 313464 [para:313400.1.1,313426.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c7)).
% 313470 [para:313464.1.2,313403.1.1] equal(sk_c9,sk_c8).
% 313518 [para:313402.1.1,313427.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c9)).
% 313520 [para:313470.1.1,313518.1.2.2] equal(sk_c5,multiply(sk_c5,sk_c8)).
% 313526 [para:313520.1.2,313401.1.1] equal(sk_c5,sk_c9).
% 313528 [para:313526.1.2,313303.1.1.1,demod:313520,cut:313170] 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_c9,sk_c8),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(U,V),sk_c9) | -equal(inverse(U),V) | -equal(multiply(V,sk_c8),sk_c9) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(sk_c9,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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(41,40,0,87,0,0,1116,50,10,1162,0,10,2664,50,38,2710,0,38,4507,50,68,4553,0,68,6501,50,99,6547,0,99,8668,50,140,8714,0,140,11013,50,196,11059,0,196,13559,50,279,13605,0,279,16333,50,413,16379,0,413,19358,50,619,19404,0,619,22661,50,916,22661,40,916,22707,0,916,34032,3,1217,34721,4,1367,35382,5,1517,35383,1,1517,35383,50,1517,35383,40,1517,35429,0,1517,35658,3,1831,35666,4,1976,35674,5,2118,35674,1,2118,35674,50,2118,35674,40,2118,35720,0,2118,53935,3,3619,55033,4,4369,56488,1,5119,56488,50,5119,56488,40,5119,56534,0,5119,65415,3,5870,67125,50,6144,67125,40,6144,67171,0,6144,79709,3,6895,80460,4,7270,81545,5,7645,81546,5,7645,81546,1,7645,81546,50,7645,81546,40,7645,81592,0,7645,142135,3,11546,143257,4,13496,144326,1,15447,144326,50,15449,144326,40,15449,144372,0,15449,195137,3,18004,196034,4,19276,196754,1,20550,196754,50,20551,196754,40,20551,196800,0,20551,240677,3,22054,241464,4,22802,242120,1,23552,242120,50,23554,242120,40,23554,242166,0,23554,262766,3,24305,263300,4,24680,263837,5,25055,263838,1,25055,263838,50,25055,263838,40,25055,263884,0,25055,292200,3,26256,292907,4,26856,293667,1,27456,293667,50,27457,293667,40,27457,293713,0,27457,309026,3,28209,309524,4,28583,310024,1,28958,310024,50,28958,310024,40,28958,310024,40,28958,310065,0,28958,310177,50,28959,310177,30,28959,310177,40,28959,310218,0,28959,310434,50,28960,310475,0,28965,310775,50,28966,310775,30,28966,310775,40,28966,310816,0,28966,310912,50,28966,310912,30,28966,310912,40,28966,310953,0,28967,311072,50,28967,311072,30,28967,311072,40,28967,311113,0,28972,311254,50,28973,311295,0,28973,311482,50,28976,311523,0,28981,311718,50,28986,311759,0,28986,311962,50,28993,312003,0,28993,312212,50,29003,312253,0,29008,312470,50,29026,312511,0,29026,312736,50,29058,312777,0,29062,313012,50,29125,313053,0,29125,313298,50,29253,313298,40,29253,313339,0,29253,313527,50,29253,313527,30,29253,313527,40,29253,313568,0,29253,313708,50,29254,313749,0,29259,313939,50,29263,313980,0,29263,314178,50,29268,314219,0,29268,314425,50,29276,314466,0,29280,314678,50,29291,314719,0,29291,314939,50,29310,314980,0,29315,315208,50,29348,315249,0,29348,315487,50,29418,315528,0,29418,315776,50,29546,315776,40,29546,315817,0,29546)
%
%
% START OF PROOF
% 315719 [?] ?
% 315778 [] equal(multiply(identity,X),X).
% 315779 [] equal(multiply(inverse(X),X),identity).
% 315780 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 315781 [] -equal(multiply(sk_c9,sk_c7),sk_c8).
% 315787 [?] ?
% 315793 [?] ?
% 315799 [?] ?
% 315836 [input:315787,cut:315781] equal(inverse(sk_c2),sk_c9).
% 315837 [para:315836.1.1,315779.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 315868 [input:315793,cut:315781] equal(multiply(sk_c2,sk_c9),sk_c3).
% 315873 [input:315799,cut:315781] equal(multiply(sk_c9,sk_c3),sk_c8).
% 315886 [para:315837.1.1,315780.1.1.1,demod:315778] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 315936 [para:315868.1.1,315886.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c3)).
% 315942 [para:315936.1.2,315873.1.1] equal(sk_c9,sk_c8).
% 315944 [para:315942.1.1,315781.1.1.1,cut:315719] 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: 41509
% derived clauses: 4440103
% kept clauses: 250280
% kept size sum: 942319
% kept mid-nuclei: 18834
% kept new demods: 4526
% forw unit-subs: 1297772
% forw double-subs: 2669587
% forw overdouble-subs: 158018
% backward subs: 31032
% fast unit cutoff: 25535
% full unit cutoff: 0
% dbl unit cutoff: 7306
% real runtime : 296.66
% process. runtime: 295.47
% specific non-discr-tree subsumption statistics:
% tried: 27870379
% length fails: 3038714
% strength fails: 9237534
% predlist fails: 1467998
% aux str. fails: 4734167
% by-lit fails: 5404941
% full subs tried: 908094
% full subs fail: 830197
%
% ; 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/GRP280-1+eq_r.in")
%
%------------------------------------------------------------------------------