TSTP Solution File: GRP228-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP228-1 : 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 : art08.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 297.9s
% Output : Assurance 297.9s
% 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/GRP228-1+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 27)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 27)
% (binary-posweight-lex-big-order 30 #f 3 27)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(inverse(sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(U,sk_c9),sk_c10) | -equal(multiply(V,W),sk_c10) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c10) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% was split for some strategies as:
% -equal(multiply(V,W),sk_c10) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c10) | -equal(inverse(X2),W) | -equal(inverse(X1),X2) | -equal(multiply(X1,W),X2).
% -equal(inverse(U),sk_c10) | -equal(multiply(U,sk_c9),sk_c10).
% -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10).
% -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10).
% -equal(inverse(sk_c10),sk_c9).
%
% Starting a split proof attempt with 5 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(inverse(sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(U,sk_c9),sk_c10) | -equal(multiply(V,W),sk_c10) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c10) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(V,W),sk_c10) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c10) | -equal(inverse(X2),W) | -equal(inverse(X1),X2) | -equal(multiply(X1,W),X2).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(50,40,0,108,0,0,231422,4,1141,237021,5,1501,237022,5,1501,237022,1,1501,237022,50,1501,237022,40,1501,237080,0,1501,243525,3,1806,244676,4,1952,245451,5,2102,245451,1,2102,245451,50,2102,245451,40,2102,245509,0,2102,248009,3,2415,248088,4,2553,248974,5,2703,248974,1,2703,248974,50,2703,248974,40,2703,249032,0,2703,268862,3,4204,270501,4,4954,272101,5,5704,272102,1,5704,272102,50,5704,272102,40,5704,272160,0,5705,286200,3,6456,287405,4,6831,288547,1,7206,288547,50,7206,288547,40,7206,288605,0,7206,301313,3,8082,302231,4,8332,303759,5,8707,303760,1,8707,303760,50,8707,303760,40,8707,303818,0,8707,352045,3,12608,352956,4,14558,353565,1,16508,353565,50,16510,353565,40,16510,353623,0,16510,394132,3,19061,395226,4,20336,396137,5,21611,396138,1,21611,396138,50,21612,396138,40,21612,396196,0,21612,426839,3,23113,427724,4,23863,428720,5,24613,428721,1,24613,428721,50,24614,428721,40,24614,428779,0,24614,441481,3,25380,443035,4,25741,444952,5,26115,444953,1,26115,444953,50,26115,444953,40,26115,445011,0,26115,466403,3,27316,467465,4,27916,468497,1,28516,468497,50,28516,468497,40,28516,468555,0,28516,485968,3,29267,486568,4,29642,487178,1,30017,487178,50,30017,487178,40,30017,487178,40,30017,487277,0,30017)
%
%
% START OF PROOF
% 487179 [] equal(X,X).
% 487180 [] equal(multiply(identity,X),X).
% 487181 [] equal(multiply(inverse(X),X),identity).
% 487182 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 487228 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,X),sk_c10) | -equal(multiply(Z,X),U) | -equal(inverse(Z),U) | -equal(inverse(U),X) | -equal(inverse(Y),X).
% 487229 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst85,Y).
% 487230 [] -equal(multiply(X,Y),sk_c10) | -equal(inverse(X),Y) | $spltprd1($spltcnst86,Y).
% 487231 [] -equal(multiply(X,sk_c9),sk_c10) | $spltprd1($spltcnst87,X).
% 487232 [] -$spltprd1($spltcnst86,X) | -$spltprd1($spltcnst85,X) | -$spltprd1($spltcnst87,X).
% 487233 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c10).
% 487234 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 487235 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 487236 [] equal(multiply(sk_c8,sk_c9),sk_c10) | equal(inverse(sk_c2),sk_c10).
% 487237 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 487238 [?] ?
% 487242 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 487243 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c6),sk_c8).
% 487244 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c7),sk_c6).
% 487245 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(multiply(sk_c8,sk_c9),sk_c10).
% 487246 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 487247 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c10).
% 487251 [] equal(multiply(sk_c10,sk_c3),sk_c9) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 487252 [] equal(multiply(sk_c10,sk_c3),sk_c9) | equal(inverse(sk_c6),sk_c8).
% 487253 [] equal(multiply(sk_c10,sk_c3),sk_c9) | equal(inverse(sk_c7),sk_c6).
% 487254 [] equal(multiply(sk_c10,sk_c3),sk_c9) | equal(multiply(sk_c8,sk_c9),sk_c10).
% 487255 [] equal(multiply(sk_c10,sk_c3),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 487256 [] equal(multiply(sk_c10,sk_c3),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c10).
% 487260 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 487261 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 487262 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 487263 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c8,sk_c9),sk_c10).
% 487264 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 487265 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c8),sk_c10).
% 487269 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c10).
% 487270 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 487271 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 487272 [] equal(multiply(sk_c8,sk_c9),sk_c10) | equal(inverse(sk_c1),sk_c10).
% 487273 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 487274 [?] ?
% 487344 [hyper:487230,487237,binarycut:487238] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst86,sk_c8).
% 487432 [hyper:487230,487273,binarycut:487274] equal(inverse(sk_c1),sk_c10) | $spltprd1($spltcnst86,sk_c8).
% 487494 [hyper:487229,487233,487234,487235] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst85,sk_c8).
% 487525 [hyper:487231,487236] equal(inverse(sk_c2),sk_c10) | $spltprd1($spltcnst87,sk_c8).
% 487536 [hyper:487232,487525,487494,487344] equal(inverse(sk_c2),sk_c10).
% 487543 [para:487536.1.1,487181.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 487840 [hyper:487229,487269,487270,487271] equal(inverse(sk_c1),sk_c10) | $spltprd1($spltcnst85,sk_c8).
% 487929 [hyper:487231,487272] equal(inverse(sk_c1),sk_c10) | $spltprd1($spltcnst87,sk_c8).
% 487969 [hyper:487232,487929,487840,487432] equal(inverse(sk_c1),sk_c10).
% 488005 [para:487969.1.1,487181.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 488246 [hyper:487228,487247,487245,487246,487243,487242,487244] equal(multiply(sk_c2,sk_c10),sk_c3).
% 488373 [hyper:487228,487256,487254,487255,487252,487251,487253] equal(multiply(sk_c10,sk_c3),sk_c9).
% 488537 [hyper:487228,487265,487263,487264,487261,487260,487262] equal(multiply(sk_c1,sk_c9),sk_c10).
% 488561 [para:487181.1.1,487182.1.1.1,demod:487180] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 488562 [para:487543.1.1,487182.1.1.1,demod:487180] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 488563 [para:488005.1.1,487182.1.1.1,demod:487180] equal(X,multiply(sk_c10,multiply(sk_c1,X))).
% 488582 [para:488246.1.1,488562.1.2.2,demod:488373] equal(sk_c10,sk_c9).
% 488624 [para:488537.1.1,488563.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 488626 [para:488582.1.1,488624.1.2.1] equal(sk_c9,multiply(sk_c9,sk_c10)).
% 488627 [para:488582.1.1,488624.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c9)).
% 488629 [para:488582.1.1,488626.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c9)).
% 488673 [para:487543.1.1,488561.1.2.2] equal(sk_c2,multiply(inverse(sk_c10),identity)).
% 488683 [para:488373.1.1,488561.1.2.2] equal(sk_c3,multiply(inverse(sk_c10),sk_c9)).
% 488688 [para:488624.1.2,488561.1.2.2,demod:488683] equal(sk_c10,sk_c3).
% 488689 [para:488626.1.2,488561.1.2.2,demod:487181] equal(sk_c10,identity).
% 488691 [para:488629.1.2,488561.1.2.2,demod:487181] equal(sk_c9,identity).
% 488707 [para:488689.1.1,487543.1.1.1,demod:487180] equal(sk_c2,identity).
% 488712 [para:488689.1.1,488624.1.2.1,demod:487180] equal(sk_c9,sk_c10).
% 488715 [para:488707.1.1,487536.1.1.1] equal(inverse(identity),sk_c10).
% 489370 [para:488691.1.1,488683.1.2.2,demod:488673] equal(sk_c3,sk_c2).
% 489371 [para:489370.1.2,487536.1.1.1] equal(inverse(sk_c3),sk_c10).
% 489427 [hyper:487228,489371,487180,488246,demod:488627,cut:488712,demod:488715,cut:487179,demod:487536,cut:488688] 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 27
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(inverse(sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(U,sk_c9),sk_c10) | -equal(multiply(V,W),sk_c10) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c10) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(inverse(U),sk_c10) | -equal(multiply(U,sk_c9),sk_c10).
% 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 27
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(50,40,0,108,0,0,231422,4,1141,237021,5,1501,237022,5,1501,237022,1,1501,237022,50,1501,237022,40,1501,237080,0,1501,243525,3,1806,244676,4,1952,245451,5,2102,245451,1,2102,245451,50,2102,245451,40,2102,245509,0,2102,248009,3,2415,248088,4,2553,248974,5,2703,248974,1,2703,248974,50,2703,248974,40,2703,249032,0,2703,268862,3,4204,270501,4,4954,272101,5,5704,272102,1,5704,272102,50,5704,272102,40,5704,272160,0,5705,286200,3,6456,287405,4,6831,288547,1,7206,288547,50,7206,288547,40,7206,288605,0,7206,301313,3,8082,302231,4,8332,303759,5,8707,303760,1,8707,303760,50,8707,303760,40,8707,303818,0,8707,352045,3,12608,352956,4,14558,353565,1,16508,353565,50,16510,353565,40,16510,353623,0,16510,394132,3,19061,395226,4,20336,396137,5,21611,396138,1,21611,396138,50,21612,396138,40,21612,396196,0,21612,426839,3,23113,427724,4,23863,428720,5,24613,428721,1,24613,428721,50,24614,428721,40,24614,428779,0,24614,441481,3,25380,443035,4,25741,444952,5,26115,444953,1,26115,444953,50,26115,444953,40,26115,445011,0,26115,466403,3,27316,467465,4,27916,468497,1,28516,468497,50,28516,468497,40,28516,468555,0,28516,485968,3,29267,486568,4,29642,487178,1,30017,487178,50,30017,487178,40,30017,487178,40,30017,487277,0,30017,489426,50,30024,489426,30,30024,489426,40,30024,489476,0,30024)
%
%
% START OF PROOF
% 489427 [] equal(X,X).
% 489431 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c10).
% 489465 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c9),sk_c10).
% 489466 [?] ?
% 489474 [?] ?
% 489475 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 489512 [hyper:489431,489475,binarycut:489466] equal(inverse(sk_c4),sk_c10).
% 489514 [hyper:489431,489475,binarycut:489474] equal(inverse(sk_c1),sk_c10).
% 489545 [hyper:489431,489465,demod:489514,cut:489427] equal(multiply(sk_c4,sk_c9),sk_c10).
% 489547 [hyper:489431,489545,demod:489512,cut:489427] 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 27
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(inverse(sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(U,sk_c9),sk_c10) | -equal(multiply(V,W),sk_c10) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c10) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10).
% 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 27
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(50,40,0,108,0,0,231422,4,1141,237021,5,1501,237022,5,1501,237022,1,1501,237022,50,1501,237022,40,1501,237080,0,1501,243525,3,1806,244676,4,1952,245451,5,2102,245451,1,2102,245451,50,2102,245451,40,2102,245509,0,2102,248009,3,2415,248088,4,2553,248974,5,2703,248974,1,2703,248974,50,2703,248974,40,2703,249032,0,2703,268862,3,4204,270501,4,4954,272101,5,5704,272102,1,5704,272102,50,5704,272102,40,5704,272160,0,5705,286200,3,6456,287405,4,6831,288547,1,7206,288547,50,7206,288547,40,7206,288605,0,7206,301313,3,8082,302231,4,8332,303759,5,8707,303760,1,8707,303760,50,8707,303760,40,8707,303818,0,8707,352045,3,12608,352956,4,14558,353565,1,16508,353565,50,16510,353565,40,16510,353623,0,16510,394132,3,19061,395226,4,20336,396137,5,21611,396138,1,21611,396138,50,21612,396138,40,21612,396196,0,21612,426839,3,23113,427724,4,23863,428720,5,24613,428721,1,24613,428721,50,24614,428721,40,24614,428779,0,24614,441481,3,25380,443035,4,25741,444952,5,26115,444953,1,26115,444953,50,26115,444953,40,26115,445011,0,26115,466403,3,27316,467465,4,27916,468497,1,28516,468497,50,28516,468497,40,28516,468555,0,28516,485968,3,29267,486568,4,29642,487178,1,30017,487178,50,30017,487178,40,30017,487178,40,30017,487277,0,30017,489426,50,30024,489426,30,30024,489426,40,30024,489476,0,30024,489546,50,30024,489546,30,30024,489546,40,30024,489596,0,30028)
%
%
% START OF PROOF
% 489547 [] equal(X,X).
% 489548 [] equal(multiply(identity,X),X).
% 489549 [] equal(multiply(inverse(X),X),identity).
% 489550 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 489551 [] -equal(multiply(sk_c10,X),sk_c9) | -equal(multiply(Y,sk_c10),X) | -equal(inverse(Y),sk_c10).
% 489553 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c6),sk_c8).
% 489554 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c7),sk_c6).
% 489556 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c5),sk_c8).
% 489557 [] equal(multiply(sk_c5,sk_c8),sk_c10) | equal(inverse(sk_c2),sk_c10).
% 489558 [] equal(multiply(sk_c4,sk_c9),sk_c10) | equal(inverse(sk_c2),sk_c10).
% 489559 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 489560 [] equal(inverse(sk_c2),sk_c10) | equal(inverse(sk_c10),sk_c9).
% 489562 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c6),sk_c8).
% 489563 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c7),sk_c6).
% 489565 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 489566 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c10).
% 489567 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(multiply(sk_c4,sk_c9),sk_c10).
% 489568 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c4),sk_c10).
% 489569 [] equal(multiply(sk_c2,sk_c10),sk_c3) | equal(inverse(sk_c10),sk_c9).
% 489571 [?] ?
% 489572 [?] ?
% 489574 [?] ?
% 489575 [?] ?
% 489576 [?] ?
% 489577 [?] ?
% 489578 [?] ?
% 489677 [hyper:489551,489562,binarycut:489571,binarycut:489553] equal(inverse(sk_c6),sk_c8).
% 489678 [para:489677.1.1,489549.1.1.1] equal(multiply(sk_c8,sk_c6),identity).
% 489681 [hyper:489551,489563,binarycut:489572,binarycut:489554] equal(inverse(sk_c7),sk_c6).
% 489682 [para:489681.1.1,489549.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 489692 [hyper:489551,489565,binarycut:489574,binarycut:489556] equal(inverse(sk_c5),sk_c8).
% 489693 [para:489692.1.1,489549.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 489702 [hyper:489551,489568,binarycut:489577,binarycut:489559] equal(inverse(sk_c4),sk_c10).
% 489709 [para:489702.1.1,489549.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 489714 [hyper:489551,489569,binarycut:489578,binarycut:489560] equal(inverse(sk_c10),sk_c9).
% 489718 [hyper:489551,489566,489557,binarycut:489575] equal(multiply(sk_c5,sk_c8),sk_c10).
% 489725 [hyper:489551,489567,489558,binarycut:489576] equal(multiply(sk_c4,sk_c9),sk_c10).
% 489726 [para:489549.1.1,489550.1.1.1,demod:489548] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 489727 [para:489678.1.1,489550.1.1.1,demod:489548] equal(X,multiply(sk_c8,multiply(sk_c6,X))).
% 489728 [para:489682.1.1,489550.1.1.1,demod:489548] equal(X,multiply(sk_c6,multiply(sk_c7,X))).
% 489730 [para:489693.1.1,489550.1.1.1,demod:489548] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 489732 [para:489709.1.1,489550.1.1.1,demod:489548] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 489733 [para:489718.1.1,489550.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c5,multiply(sk_c8,X))).
% 489738 [para:489682.1.1,489727.1.2.2] equal(sk_c7,multiply(sk_c8,identity)).
% 489739 [para:489738.1.2,489550.1.1.1,demod:489548] equal(multiply(sk_c7,X),multiply(sk_c8,X)).
% 489746 [para:489718.1.1,489730.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c10)).
% 489750 [para:489725.1.1,489732.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 489767 [para:489678.1.1,489726.1.2.2] equal(sk_c6,multiply(inverse(sk_c8),identity)).
% 489768 [para:489693.1.1,489726.1.2.2,demod:489767] equal(sk_c5,sk_c6).
% 489775 [para:489768.1.2,489728.1.2.1,demod:489733,489739] equal(X,multiply(sk_c10,X)).
% 489782 [para:489775.1.2,489750.1.2] equal(sk_c9,sk_c10).
% 489827 [hyper:489551,489733,demod:489714,489750,489718,489746,cut:489547,cut:489782] 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 27
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(inverse(sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(U,sk_c9),sk_c10) | -equal(multiply(V,W),sk_c10) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c10) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10).
% 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 27
% clause depth limited to 3
% seconds given: 6
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(50,40,0,108,0,0,231422,4,1141,237021,5,1501,237022,5,1501,237022,1,1501,237022,50,1501,237022,40,1501,237080,0,1501,243525,3,1806,244676,4,1952,245451,5,2102,245451,1,2102,245451,50,2102,245451,40,2102,245509,0,2102,248009,3,2415,248088,4,2553,248974,5,2703,248974,1,2703,248974,50,2703,248974,40,2703,249032,0,2703,268862,3,4204,270501,4,4954,272101,5,5704,272102,1,5704,272102,50,5704,272102,40,5704,272160,0,5705,286200,3,6456,287405,4,6831,288547,1,7206,288547,50,7206,288547,40,7206,288605,0,7206,301313,3,8082,302231,4,8332,303759,5,8707,303760,1,8707,303760,50,8707,303760,40,8707,303818,0,8707,352045,3,12608,352956,4,14558,353565,1,16508,353565,50,16510,353565,40,16510,353623,0,16510,394132,3,19061,395226,4,20336,396137,5,21611,396138,1,21611,396138,50,21612,396138,40,21612,396196,0,21612,426839,3,23113,427724,4,23863,428720,5,24613,428721,1,24613,428721,50,24614,428721,40,24614,428779,0,24614,441481,3,25380,443035,4,25741,444952,5,26115,444953,1,26115,444953,50,26115,444953,40,26115,445011,0,26115,466403,3,27316,467465,4,27916,468497,1,28516,468497,50,28516,468497,40,28516,468555,0,28516,485968,3,29267,486568,4,29642,487178,1,30017,487178,50,30017,487178,40,30017,487178,40,30017,487277,0,30017,489426,50,30024,489426,30,30024,489426,40,30024,489476,0,30024,489546,50,30024,489546,30,30024,489546,40,30024,489596,0,30028,489826,50,30029,489826,30,30029,489826,40,30029,489876,0,30029)
%
%
% START OF PROOF
% 489827 [] equal(X,X).
% 489831 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c10).
% 489865 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c4,sk_c9),sk_c10).
% 489866 [?] ?
% 489874 [?] ?
% 489875 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c4),sk_c10).
% 489912 [hyper:489831,489875,binarycut:489866] equal(inverse(sk_c4),sk_c10).
% 489914 [hyper:489831,489875,binarycut:489874] equal(inverse(sk_c1),sk_c10).
% 489945 [hyper:489831,489865,demod:489914,cut:489827] equal(multiply(sk_c4,sk_c9),sk_c10).
% 489947 [hyper:489831,489945,demod:489912,cut:489827] 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 27
% clause depth limited to 3
% seconds given: 6
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(sk_c10,Y),sk_c9) | -equal(multiply(Z,sk_c10),Y) | -equal(inverse(Z),sk_c10) | -equal(inverse(sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(U,sk_c9),sk_c10) | -equal(multiply(V,W),sk_c10) | -equal(inverse(V),W) | -equal(multiply(W,sk_c9),sk_c10) | -equal(inverse(X1),X2) | -equal(inverse(X2),W) | -equal(multiply(X1,W),X2).
% Split part used next: -equal(inverse(sk_c10),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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% clause depth limited to 10
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 27
% clause depth limited to 11
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 27
% clause depth limited to 12
% seconds given: 6
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(50,40,0,108,0,0,231422,4,1141,237021,5,1501,237022,5,1501,237022,1,1501,237022,50,1501,237022,40,1501,237080,0,1501,243525,3,1806,244676,4,1952,245451,5,2102,245451,1,2102,245451,50,2102,245451,40,2102,245509,0,2102,248009,3,2415,248088,4,2553,248974,5,2703,248974,1,2703,248974,50,2703,248974,40,2703,249032,0,2703,268862,3,4204,270501,4,4954,272101,5,5704,272102,1,5704,272102,50,5704,272102,40,5704,272160,0,5705,286200,3,6456,287405,4,6831,288547,1,7206,288547,50,7206,288547,40,7206,288605,0,7206,301313,3,8082,302231,4,8332,303759,5,8707,303760,1,8707,303760,50,8707,303760,40,8707,303818,0,8707,352045,3,12608,352956,4,14558,353565,1,16508,353565,50,16510,353565,40,16510,353623,0,16510,394132,3,19061,395226,4,20336,396137,5,21611,396138,1,21611,396138,50,21612,396138,40,21612,396196,0,21612,426839,3,23113,427724,4,23863,428720,5,24613,428721,1,24613,428721,50,24614,428721,40,24614,428779,0,24614,441481,3,25380,443035,4,25741,444952,5,26115,444953,1,26115,444953,50,26115,444953,40,26115,445011,0,26115,466403,3,27316,467465,4,27916,468497,1,28516,468497,50,28516,468497,40,28516,468555,0,28516,485968,3,29267,486568,4,29642,487178,1,30017,487178,50,30017,487178,40,30017,487178,40,30017,487277,0,30017,489426,50,30024,489426,30,30024,489426,40,30024,489476,0,30024,489546,50,30024,489546,30,30024,489546,40,30024,489596,0,30028,489826,50,30029,489826,30,30029,489826,40,30029,489876,0,30029,489946,50,30029,489946,30,30029,489946,40,30029,489996,0,30029,490103,50,30029,490153,0,30034,490311,50,30037,490361,0,30037,490527,50,30040,490577,0,30045,490751,50,30051,490801,0,30051,490981,50,30059,491031,0,30059,491219,50,30074,491269,0,30079,491465,50,30107,491515,0,30107,491721,50,30167,491771,0,30167,491987,50,30281,492037,0,30281,492265,50,30507,492265,40,30507,492315,0,30508)
%
%
% START OF PROOF
% 492267 [] equal(multiply(identity,X),X).
% 492268 [] equal(multiply(inverse(X),X),identity).
% 492269 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 492270 [] -equal(inverse(sk_c10),sk_c9).
% 492279 [?] ?
% 492288 [?] ?
% 492297 [?] ?
% 492306 [?] ?
% 492315 [?] ?
% 492330 [input:492279,cut:492270] equal(inverse(sk_c2),sk_c10).
% 492331 [para:492330.1.1,492268.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 492345 [input:492315,cut:492270] equal(inverse(sk_c1),sk_c10).
% 492346 [para:492345.1.1,492268.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 492358 [input:492288,cut:492270] equal(multiply(sk_c2,sk_c10),sk_c3).
% 492368 [input:492297,cut:492270] equal(multiply(sk_c10,sk_c3),sk_c9).
% 492378 [input:492306,cut:492270] equal(multiply(sk_c1,sk_c9),sk_c10).
% 492403 [para:492268.1.1,492269.1.1.1,demod:492267] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 492405 [para:492331.1.1,492269.1.1.1,demod:492267] equal(X,multiply(sk_c10,multiply(sk_c2,X))).
% 492408 [para:492346.1.1,492269.1.1.1,demod:492267] equal(X,multiply(sk_c10,multiply(sk_c1,X))).
% 492422 [para:492368.1.1,492269.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c10,multiply(sk_c3,X))).
% 492458 [para:492358.1.1,492405.1.2.2] equal(sk_c10,multiply(sk_c10,sk_c3)).
% 492463 [para:492458.1.2,492368.1.1] equal(sk_c10,sk_c9).
% 492464 [para:492458.1.2,492269.1.1.1,demod:492422] equal(multiply(sk_c10,X),multiply(sk_c9,X)).
% 492465 [para:492463.1.1,492270.1.1.1] -equal(inverse(sk_c9),sk_c9).
% 492496 [para:492378.1.1,492408.1.2.2,demod:492464] equal(sk_c9,multiply(sk_c9,sk_c10)).
% 492563 [para:492496.1.2,492403.1.2.2,demod:492268] equal(sk_c10,identity).
% 492581 [para:492563.1.1,492346.1.1.1,demod:492267] equal(sk_c1,identity).
% 492596 [para:492563.1.1,492463.1.1] equal(identity,sk_c9).
% 492609 [para:492581.1.1,492345.1.1.1] equal(inverse(identity),sk_c10).
% 492613 [para:492596.1.2,492465.1.1.1,demod:492609,cut:492463] 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: 37721
% derived clauses: 3968487
% kept clauses: 207447
% kept size sum: 293402
% kept mid-nuclei: 233268
% kept new demods: 2133
% forw unit-subs: 715569
% forw double-subs: 2572063
% forw overdouble-subs: 187579
% backward subs: 15669
% fast unit cutoff: 36196
% full unit cutoff: 0
% dbl unit cutoff: 9542
% real runtime : 307.49
% process. runtime: 305.9
% specific non-discr-tree subsumption statistics:
% tried: 19506573
% length fails: 1642373
% strength fails: 6430627
% predlist fails: 1339646
% aux str. fails: 2997386
% by-lit fails: 1757195
% full subs tried: 3922086
% full subs fail: 3802692
%
% ; 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/GRP228-1+eq_r.in")
%
%------------------------------------------------------------------------------