TSTP Solution File: GRP360-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP360-1 : 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 : art09.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 298.7s
% Output : Assurance 298.7s
% 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/GRP360-1+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_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% was split for some strategies as:
% -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7).
% -equal(multiply(sk_c6,sk_c5),sk_c7).
% -equal(inverse(sk_c7),sk_c5).
% -equal(multiply(sk_c6,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_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,64,0,0,502,50,3,536,0,3,1304,50,11,1338,0,11,2271,50,25,2305,0,25,3324,50,38,3358,0,38,4464,50,52,4498,0,52,5732,50,74,5766,0,74,7128,50,110,7162,0,110,8694,50,178,8728,0,178,10430,50,311,10464,0,311,12378,50,536,12412,0,536,14538,50,931,14538,40,931,14572,0,931,25333,3,1232,26067,4,1382,26748,5,1532,26749,1,1532,26749,50,1532,26749,40,1532,26783,0,1532,26986,3,1845,26994,4,1988,27002,5,2133,27002,1,2133,27002,50,2133,27002,40,2133,27036,0,2133,50724,3,3635,52129,4,4384,53236,5,5134,53237,1,5134,53237,50,5134,53237,40,5134,53271,0,5134,67934,3,5885,68962,4,6260,69985,1,6635,69985,50,6635,69985,40,6635,70019,0,6635,81676,3,7408,82672,4,7761,84186,1,8136,84186,50,8136,84186,40,8136,84220,0,8136,149960,3,12038,150956,4,13988,151868,5,15937,151869,1,15938,151869,50,15940,151869,40,15940,151903,0,15940,200249,3,18491,201075,4,19766,201774,5,21041,201775,1,21041,201775,50,21043,201775,40,21043,201809,0,21047,234240,3,22553,235332,4,23298,236424,5,24048,236425,1,24048,236425,50,24049,236425,40,24049,236459,0,24049,245565,3,24801,246783,4,25175,247333,5,25550,247333,1,25550,247333,50,25550,247333,40,25550,247367,0,25550,276481,3,26751,277047,4,27351,277668,1,27951,277668,50,27952,277668,40,27952,277702,0,27952,298591,3,28703,299353,4,29078,299933,5,29453,299934,1,29453,299934,50,29454,299934,40,29454,299934,40,29454,299964,0,29454,300044,50,29454,300074,0,29454)
%
%
% START OF PROOF
% 300046 [] equal(multiply(identity,X),X).
% 300047 [] equal(multiply(inverse(X),X),identity).
% 300048 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 300049 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 300050 [?] ?
% 300051 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 300055 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 300056 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c4),sk_c6).
% 300060 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 300061 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 300065 [?] ?
% 300066 [] equal(inverse(sk_c7),sk_c5) | equal(inverse(sk_c4),sk_c6).
% 300070 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 300071 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 300077 [hyper:300049,300051,binarycut:300050] equal(inverse(sk_c1),sk_c7).
% 300078 [para:300077.1.1,300047.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 300085 [hyper:300049,300066,binarycut:300065] equal(inverse(sk_c7),sk_c5).
% 300086 [para:300085.1.1,300047.1.1.1] equal(multiply(sk_c5,sk_c7),identity).
% 300089 [hyper:300049,300056,300055] equal(multiply(sk_c1,sk_c7),sk_c2).
% 300099 [hyper:300049,300060,300061] equal(multiply(sk_c7,sk_c2),sk_c6).
% 300103 [hyper:300049,300070,300071] equal(multiply(sk_c6,sk_c5),sk_c7).
% 300104 [para:300047.1.1,300048.1.1.1,demod:300046] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 300105 [para:300078.1.1,300048.1.1.1,demod:300046] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 300106 [para:300086.1.1,300048.1.1.1,demod:300046] equal(X,multiply(sk_c5,multiply(sk_c7,X))).
% 300107 [para:300089.1.1,300048.1.1.1] equal(multiply(sk_c2,X),multiply(sk_c1,multiply(sk_c7,X))).
% 300108 [para:300099.1.1,300048.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c2,X))).
% 300110 [para:300089.1.1,300105.1.2.2,demod:300099] equal(sk_c7,sk_c6).
% 300111 [para:300110.1.2,300103.1.1.1] equal(multiply(sk_c7,sk_c5),sk_c7).
% 300113 [para:300047.1.1,300104.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 300116 [para:300099.1.1,300104.1.2.2,demod:300085] equal(sk_c2,multiply(sk_c5,sk_c6)).
% 300117 [para:300048.1.1,300104.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 300119 [para:300105.1.2,300104.1.2.2,demod:300085] equal(multiply(sk_c1,X),multiply(sk_c5,X)).
% 300120 [para:300104.1.2,300104.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 300121 [para:300111.1.1,300048.1.1.1,demod:300105,300119] equal(multiply(sk_c7,X),X).
% 300140 [para:300107.1.2,300105.1.2.2,demod:300108,300121] equal(X,multiply(sk_c6,X)).
% 300145 [para:300140.1.2,300104.1.2.2] equal(X,multiply(inverse(sk_c6),X)).
% 300147 [para:300110.1.2,300116.1.2.2,demod:300086] equal(sk_c2,identity).
% 300148 [para:300147.1.1,300099.1.1.2,demod:300121] equal(identity,sk_c6).
% 300169 [para:300120.1.2,300047.1.1] equal(multiply(X,inverse(X)),identity).
% 300171 [para:300120.1.2,300113.1.2] equal(X,multiply(X,identity)).
% 300175 [para:300171.1.2,300113.1.2] equal(X,inverse(inverse(X))).
% 300177 [para:300171.1.2,300145.1.2] equal(identity,inverse(sk_c6)).
% 300182 [para:300169.1.1,300117.1.2.2.2,demod:300171] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 300186 [para:300106.1.2,300182.1.2.1.1,demod:300121] equal(inverse(X),multiply(inverse(X),sk_c5)).
% 300195 [para:300186.1.2,300120.1.2,demod:300175] equal(multiply(X,sk_c5),X).
% 300196 [hyper:300049,300195,demod:300177,cut:300148] 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 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),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 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(30,40,0,64,0,0,502,50,3,536,0,3,1304,50,11,1338,0,11,2271,50,25,2305,0,25,3324,50,38,3358,0,38,4464,50,52,4498,0,52,5732,50,74,5766,0,74,7128,50,110,7162,0,110,8694,50,178,8728,0,178,10430,50,311,10464,0,311,12378,50,536,12412,0,536,14538,50,931,14538,40,931,14572,0,931,25333,3,1232,26067,4,1382,26748,5,1532,26749,1,1532,26749,50,1532,26749,40,1532,26783,0,1532,26986,3,1845,26994,4,1988,27002,5,2133,27002,1,2133,27002,50,2133,27002,40,2133,27036,0,2133,50724,3,3635,52129,4,4384,53236,5,5134,53237,1,5134,53237,50,5134,53237,40,5134,53271,0,5134,67934,3,5885,68962,4,6260,69985,1,6635,69985,50,6635,69985,40,6635,70019,0,6635,81676,3,7408,82672,4,7761,84186,1,8136,84186,50,8136,84186,40,8136,84220,0,8136,149960,3,12038,150956,4,13988,151868,5,15937,151869,1,15938,151869,50,15940,151869,40,15940,151903,0,15940,200249,3,18491,201075,4,19766,201774,5,21041,201775,1,21041,201775,50,21043,201775,40,21043,201809,0,21047,234240,3,22553,235332,4,23298,236424,5,24048,236425,1,24048,236425,50,24049,236425,40,24049,236459,0,24049,245565,3,24801,246783,4,25175,247333,5,25550,247333,1,25550,247333,50,25550,247333,40,25550,247367,0,25550,276481,3,26751,277047,4,27351,277668,1,27951,277668,50,27952,277668,40,27952,277702,0,27952,298591,3,28703,299353,4,29078,299933,5,29453,299934,1,29453,299934,50,29454,299934,40,29454,299934,40,29454,299964,0,29454,300044,50,29454,300074,0,29454,300195,50,29455,300195,30,29455,300195,40,29455,300225,0,29461,300317,50,29461,300347,0,29461)
%
%
% START OF PROOF
% 300319 [] equal(multiply(identity,X),X).
% 300320 [] equal(multiply(inverse(X),X),identity).
% 300321 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 300322 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 300325 [?] ?
% 300326 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 300330 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 300331 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c3),sk_c7).
% 300335 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 300336 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 300340 [?] ?
% 300341 [] equal(inverse(sk_c7),sk_c5) | equal(inverse(sk_c3),sk_c7).
% 300345 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 300346 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 300353 [hyper:300322,300326,binarycut:300325] equal(inverse(sk_c1),sk_c7).
% 300356 [para:300353.1.1,300320.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 300362 [hyper:300322,300341,binarycut:300340] equal(inverse(sk_c7),sk_c5).
% 300363 [para:300362.1.1,300320.1.1.1] equal(multiply(sk_c5,sk_c7),identity).
% 300370 [hyper:300322,300331,300330] equal(multiply(sk_c1,sk_c7),sk_c2).
% 300382 [hyper:300322,300335,300336] equal(multiply(sk_c7,sk_c2),sk_c6).
% 300386 [hyper:300322,300345,300346] equal(multiply(sk_c6,sk_c5),sk_c7).
% 300387 [para:300320.1.1,300321.1.1.1,demod:300319] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 300388 [para:300356.1.1,300321.1.1.1,demod:300319] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 300390 [para:300370.1.1,300321.1.1.1] equal(multiply(sk_c2,X),multiply(sk_c1,multiply(sk_c7,X))).
% 300391 [para:300382.1.1,300321.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c2,X))).
% 300393 [para:300370.1.1,300388.1.2.2,demod:300382] equal(sk_c7,sk_c6).
% 300394 [para:300393.1.2,300386.1.1.1] equal(multiply(sk_c7,sk_c5),sk_c7).
% 300396 [para:300320.1.1,300387.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 300400 [para:300321.1.1,300387.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 300402 [para:300388.1.2,300387.1.2.2,demod:300362] equal(multiply(sk_c1,X),multiply(sk_c5,X)).
% 300403 [para:300387.1.2,300387.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 300404 [para:300394.1.1,300321.1.1.1,demod:300388,300402] equal(multiply(sk_c7,X),X).
% 300405 [para:300394.1.1,300387.1.2.2,demod:300363,300362] equal(sk_c5,identity).
% 300408 [para:300405.1.1,300363.1.1.1,demod:300319] equal(sk_c7,identity).
% 300416 [para:300408.1.1,300394.1.1.1,demod:300319] equal(sk_c5,sk_c7).
% 300423 [para:300390.1.2,300388.1.2.2,demod:300391,300404] equal(X,multiply(sk_c6,X)).
% 300454 [para:300403.1.2,300320.1.1] equal(multiply(X,inverse(X)),identity).
% 300456 [para:300403.1.2,300396.1.2] equal(X,multiply(X,identity)).
% 300460 [para:300456.1.2,300396.1.2] equal(X,inverse(inverse(X))).
% 300467 [para:300454.1.1,300400.1.2.2.2,demod:300456] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 300473 [para:300423.1.2,300467.1.2.1.1] equal(inverse(X),multiply(inverse(X),sk_c6)).
% 300482 [para:300473.1.2,300403.1.2,demod:300460] equal(multiply(X,sk_c6),X).
% 300483 [hyper:300322,300482,demod:300362,cut:300416] 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_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),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 19
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(30,40,0,64,0,0,502,50,3,536,0,3,1304,50,11,1338,0,11,2271,50,25,2305,0,25,3324,50,38,3358,0,38,4464,50,52,4498,0,52,5732,50,74,5766,0,74,7128,50,110,7162,0,110,8694,50,178,8728,0,178,10430,50,311,10464,0,311,12378,50,536,12412,0,536,14538,50,931,14538,40,931,14572,0,931,25333,3,1232,26067,4,1382,26748,5,1532,26749,1,1532,26749,50,1532,26749,40,1532,26783,0,1532,26986,3,1845,26994,4,1988,27002,5,2133,27002,1,2133,27002,50,2133,27002,40,2133,27036,0,2133,50724,3,3635,52129,4,4384,53236,5,5134,53237,1,5134,53237,50,5134,53237,40,5134,53271,0,5134,67934,3,5885,68962,4,6260,69985,1,6635,69985,50,6635,69985,40,6635,70019,0,6635,81676,3,7408,82672,4,7761,84186,1,8136,84186,50,8136,84186,40,8136,84220,0,8136,149960,3,12038,150956,4,13988,151868,5,15937,151869,1,15938,151869,50,15940,151869,40,15940,151903,0,15940,200249,3,18491,201075,4,19766,201774,5,21041,201775,1,21041,201775,50,21043,201775,40,21043,201809,0,21047,234240,3,22553,235332,4,23298,236424,5,24048,236425,1,24048,236425,50,24049,236425,40,24049,236459,0,24049,245565,3,24801,246783,4,25175,247333,5,25550,247333,1,25550,247333,50,25550,247333,40,25550,247367,0,25550,276481,3,26751,277047,4,27351,277668,1,27951,277668,50,27952,277668,40,27952,277702,0,27952,298591,3,28703,299353,4,29078,299933,5,29453,299934,1,29453,299934,50,29454,299934,40,29454,299934,40,29454,299964,0,29454,300044,50,29454,300074,0,29454,300195,50,29455,300195,30,29455,300195,40,29455,300225,0,29461,300317,50,29461,300347,0,29461,300482,50,29462,300482,30,29462,300482,40,29462,300512,0,29462)
%
%
% START OF PROOF
% 300483 [] equal(X,X).
% 300484 [] equal(multiply(identity,X),X).
% 300485 [] equal(multiply(inverse(X),X),identity).
% 300486 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 300487 [] -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7).
% 300488 [] equal(multiply(sk_c4,sk_c5),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 300489 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 300490 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 300491 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 300492 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 300493 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 300494 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c4),sk_c6).
% 300495 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 300496 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c3),sk_c7).
% 300497 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c6,sk_c7),sk_c5).
% 300498 [?] ?
% 300499 [?] ?
% 300500 [?] ?
% 300501 [?] ?
% 300502 [?] ?
% 300553 [hyper:300487,300493,300488,binarycut:300498] equal(multiply(sk_c4,sk_c5),sk_c6).
% 300556 [hyper:300487,300494,binarycut:300499,binarycut:300489] equal(inverse(sk_c4),sk_c6).
% 300560 [hyper:300487,300496,binarycut:300501,binarycut:300491] equal(inverse(sk_c3),sk_c7).
% 300568 [hyper:300487,300495,300490,binarycut:300500] equal(multiply(sk_c3,sk_c6),sk_c7).
% 300580 [hyper:300487,300497,300492,binarycut:300502] equal(multiply(sk_c6,sk_c7),sk_c5).
% 300585 [para:300485.1.1,300486.1.1.1,demod:300484] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 300594 [para:300553.1.1,300585.1.2.2,demod:300556] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 300596 [para:300568.1.1,300585.1.2.2,demod:300560] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 300598 [para:300580.1.1,300585.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 300600 [para:300594.1.2,300585.1.2.2,demod:300598] equal(sk_c6,sk_c7).
% 300604 [para:300600.1.1,300568.1.1.2] equal(multiply(sk_c3,sk_c7),sk_c7).
% 300628 [hyper:300487,300604,demod:300560,300596,cut:300483,cut:300483] 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 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c6,sk_c5),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 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(30,40,0,64,0,0,502,50,3,536,0,3,1304,50,11,1338,0,11,2271,50,25,2305,0,25,3324,50,38,3358,0,38,4464,50,52,4498,0,52,5732,50,74,5766,0,74,7128,50,110,7162,0,110,8694,50,178,8728,0,178,10430,50,311,10464,0,311,12378,50,536,12412,0,536,14538,50,931,14538,40,931,14572,0,931,25333,3,1232,26067,4,1382,26748,5,1532,26749,1,1532,26749,50,1532,26749,40,1532,26783,0,1532,26986,3,1845,26994,4,1988,27002,5,2133,27002,1,2133,27002,50,2133,27002,40,2133,27036,0,2133,50724,3,3635,52129,4,4384,53236,5,5134,53237,1,5134,53237,50,5134,53237,40,5134,53271,0,5134,67934,3,5885,68962,4,6260,69985,1,6635,69985,50,6635,69985,40,6635,70019,0,6635,81676,3,7408,82672,4,7761,84186,1,8136,84186,50,8136,84186,40,8136,84220,0,8136,149960,3,12038,150956,4,13988,151868,5,15937,151869,1,15938,151869,50,15940,151869,40,15940,151903,0,15940,200249,3,18491,201075,4,19766,201774,5,21041,201775,1,21041,201775,50,21043,201775,40,21043,201809,0,21047,234240,3,22553,235332,4,23298,236424,5,24048,236425,1,24048,236425,50,24049,236425,40,24049,236459,0,24049,245565,3,24801,246783,4,25175,247333,5,25550,247333,1,25550,247333,50,25550,247333,40,25550,247367,0,25550,276481,3,26751,277047,4,27351,277668,1,27951,277668,50,27952,277668,40,27952,277702,0,27952,298591,3,28703,299353,4,29078,299933,5,29453,299934,1,29453,299934,50,29454,299934,40,29454,299934,40,29454,299964,0,29454,300044,50,29454,300074,0,29454,300195,50,29455,300195,30,29455,300195,40,29455,300225,0,29461,300317,50,29461,300347,0,29461,300482,50,29462,300482,30,29462,300482,40,29462,300512,0,29462,300627,50,29462,300627,30,29462,300627,40,29462,300657,0,29467,300749,50,29467,300779,0,29467,300921,50,29470,300951,0,29475,301101,50,29479,301131,0,29479,301289,50,29484,301319,0,29484,301483,50,29493,301513,0,29497,301685,50,29512,301715,0,29512,301895,50,29540,301925,0,29545,302115,50,29602,302145,0,29602,302345,50,29717,302345,40,29717,302375,0,29717)
%
%
% START OF PROOF
% 302290 [?] ?
% 302347 [] equal(multiply(identity,X),X).
% 302348 [] equal(multiply(inverse(X),X),identity).
% 302349 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 302350 [] -equal(multiply(sk_c6,sk_c5),sk_c7).
% 302371 [?] ?
% 302372 [?] ?
% 302375 [?] ?
% 302410 [input:302372,cut:302350] equal(inverse(sk_c4),sk_c6).
% 302411 [para:302410.1.1,302348.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 302422 [input:302371,cut:302350] equal(multiply(sk_c4,sk_c5),sk_c6).
% 302424 [input:302375,cut:302350] equal(multiply(sk_c6,sk_c7),sk_c5).
% 302425 [para:302348.1.1,302349.1.1.1,demod:302347] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 302440 [para:302411.1.1,302349.1.1.1,demod:302347] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 302461 [para:302422.1.1,302440.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 302508 [para:302424.1.1,302425.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 302512 [para:302461.1.2,302425.1.2.2,demod:302508] equal(sk_c6,sk_c7).
% 302516 [para:302512.1.1,302350.1.1.1,cut:302290] 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 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),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(30,40,0,64,0,0,502,50,3,536,0,3,1304,50,11,1338,0,11,2271,50,25,2305,0,25,3324,50,38,3358,0,38,4464,50,52,4498,0,52,5732,50,74,5766,0,74,7128,50,110,7162,0,110,8694,50,178,8728,0,178,10430,50,311,10464,0,311,12378,50,536,12412,0,536,14538,50,931,14538,40,931,14572,0,931,25333,3,1232,26067,4,1382,26748,5,1532,26749,1,1532,26749,50,1532,26749,40,1532,26783,0,1532,26986,3,1845,26994,4,1988,27002,5,2133,27002,1,2133,27002,50,2133,27002,40,2133,27036,0,2133,50724,3,3635,52129,4,4384,53236,5,5134,53237,1,5134,53237,50,5134,53237,40,5134,53271,0,5134,67934,3,5885,68962,4,6260,69985,1,6635,69985,50,6635,69985,40,6635,70019,0,6635,81676,3,7408,82672,4,7761,84186,1,8136,84186,50,8136,84186,40,8136,84220,0,8136,149960,3,12038,150956,4,13988,151868,5,15937,151869,1,15938,151869,50,15940,151869,40,15940,151903,0,15940,200249,3,18491,201075,4,19766,201774,5,21041,201775,1,21041,201775,50,21043,201775,40,21043,201809,0,21047,234240,3,22553,235332,4,23298,236424,5,24048,236425,1,24048,236425,50,24049,236425,40,24049,236459,0,24049,245565,3,24801,246783,4,25175,247333,5,25550,247333,1,25550,247333,50,25550,247333,40,25550,247367,0,25550,276481,3,26751,277047,4,27351,277668,1,27951,277668,50,27952,277668,40,27952,277702,0,27952,298591,3,28703,299353,4,29078,299933,5,29453,299934,1,29453,299934,50,29454,299934,40,29454,299934,40,29454,299964,0,29454,300044,50,29454,300074,0,29454,300195,50,29455,300195,30,29455,300195,40,29455,300225,0,29461,300317,50,29461,300347,0,29461,300482,50,29462,300482,30,29462,300482,40,29462,300512,0,29462,300627,50,29462,300627,30,29462,300627,40,29462,300657,0,29467,300749,50,29467,300779,0,29467,300921,50,29470,300951,0,29475,301101,50,29479,301131,0,29479,301289,50,29484,301319,0,29484,301483,50,29493,301513,0,29497,301685,50,29512,301715,0,29512,301895,50,29540,301925,0,29545,302115,50,29602,302145,0,29602,302345,50,29717,302345,40,29717,302375,0,29717,302515,50,29718,302515,30,29718,302515,40,29718,302545,0,29718,302637,50,29719,302667,0,29723,302809,50,29726,302839,0,29726,302989,50,29729,303019,0,29729,303177,50,29735,303207,0,29739,303371,50,29748,303401,0,29748,303573,50,29763,303603,0,29768,303783,50,29797,303813,0,29797,304003,50,29858,304033,0,29858,304233,50,29973,304233,40,29973,304263,0,29973)
%
%
% START OF PROOF
% 304108 [?] ?
% 304235 [] equal(multiply(identity,X),X).
% 304236 [] equal(multiply(inverse(X),X),identity).
% 304237 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 304238 [] -equal(inverse(sk_c7),sk_c5).
% 304254 [?] ?
% 304255 [?] ?
% 304256 [?] ?
% 304257 [?] ?
% 304258 [?] ?
% 304272 [input:304255,cut:304238] equal(inverse(sk_c4),sk_c6).
% 304273 [para:304272.1.1,304236.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 304274 [input:304257,cut:304238] equal(inverse(sk_c3),sk_c7).
% 304275 [para:304274.1.1,304236.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 304285 [input:304254,cut:304238] equal(multiply(sk_c4,sk_c5),sk_c6).
% 304286 [input:304256,cut:304238] equal(multiply(sk_c3,sk_c6),sk_c7).
% 304287 [input:304258,cut:304238] equal(multiply(sk_c6,sk_c7),sk_c5).
% 304300 [para:304236.1.1,304237.1.1.1,demod:304235] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 304302 [para:304273.1.1,304237.1.1.1,demod:304235] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 304303 [para:304275.1.1,304237.1.1.1,demod:304235] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 304329 [para:304285.1.1,304302.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 304332 [para:304286.1.1,304303.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 304354 [para:304287.1.1,304300.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 304369 [para:304329.1.2,304300.1.2.2,demod:304354] equal(sk_c6,sk_c7).
% 304378 [para:304369.1.1,304287.1.1.1,demod:304332] equal(sk_c6,sk_c5).
% 304390 [para:304378.1.1,304287.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 304397 [para:304378.1.1,304369.1.1] equal(sk_c5,sk_c7).
% 304399 [para:304397.1.1,304238.1.2] -equal(inverse(sk_c7),sk_c7).
% 304420 [para:304390.1.1,304300.1.2.2,demod:304236] equal(sk_c7,identity).
% 304434 [para:304420.1.1,304399.1.1.1,cut:304108] 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_c5),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),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
%
%
% 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(30,40,0,64,0,0,502,50,3,536,0,3,1304,50,11,1338,0,11,2271,50,25,2305,0,25,3324,50,38,3358,0,38,4464,50,52,4498,0,52,5732,50,74,5766,0,74,7128,50,110,7162,0,110,8694,50,178,8728,0,178,10430,50,311,10464,0,311,12378,50,536,12412,0,536,14538,50,931,14538,40,931,14572,0,931,25333,3,1232,26067,4,1382,26748,5,1532,26749,1,1532,26749,50,1532,26749,40,1532,26783,0,1532,26986,3,1845,26994,4,1988,27002,5,2133,27002,1,2133,27002,50,2133,27002,40,2133,27036,0,2133,50724,3,3635,52129,4,4384,53236,5,5134,53237,1,5134,53237,50,5134,53237,40,5134,53271,0,5134,67934,3,5885,68962,4,6260,69985,1,6635,69985,50,6635,69985,40,6635,70019,0,6635,81676,3,7408,82672,4,7761,84186,1,8136,84186,50,8136,84186,40,8136,84220,0,8136,149960,3,12038,150956,4,13988,151868,5,15937,151869,1,15938,151869,50,15940,151869,40,15940,151903,0,15940,200249,3,18491,201075,4,19766,201774,5,21041,201775,1,21041,201775,50,21043,201775,40,21043,201809,0,21047,234240,3,22553,235332,4,23298,236424,5,24048,236425,1,24048,236425,50,24049,236425,40,24049,236459,0,24049,245565,3,24801,246783,4,25175,247333,5,25550,247333,1,25550,247333,50,25550,247333,40,25550,247367,0,25550,276481,3,26751,277047,4,27351,277668,1,27951,277668,50,27952,277668,40,27952,277702,0,27952,298591,3,28703,299353,4,29078,299933,5,29453,299934,1,29453,299934,50,29454,299934,40,29454,299934,40,29454,299964,0,29454,300044,50,29454,300074,0,29454,300195,50,29455,300195,30,29455,300195,40,29455,300225,0,29461,300317,50,29461,300347,0,29461,300482,50,29462,300482,30,29462,300482,40,29462,300512,0,29462,300627,50,29462,300627,30,29462,300627,40,29462,300657,0,29467,300749,50,29467,300779,0,29467,300921,50,29470,300951,0,29475,301101,50,29479,301131,0,29479,301289,50,29484,301319,0,29484,301483,50,29493,301513,0,29497,301685,50,29512,301715,0,29512,301895,50,29540,301925,0,29545,302115,50,29602,302145,0,29602,302345,50,29717,302345,40,29717,302375,0,29717,302515,50,29718,302515,30,29718,302515,40,29718,302545,0,29718,302637,50,29719,302667,0,29723,302809,50,29726,302839,0,29726,302989,50,29729,303019,0,29729,303177,50,29735,303207,0,29739,303371,50,29748,303401,0,29748,303573,50,29763,303603,0,29768,303783,50,29797,303813,0,29797,304003,50,29858,304033,0,29858,304233,50,29973,304233,40,29973,304263,0,29973,304433,50,29974,304433,30,29974,304433,40,29974,304463,0,29974,304555,50,29975,304585,0,29979,304721,50,29982,304751,0,29982,304895,50,29985,304925,0,29985,305077,50,29990,305107,0,29995,305265,50,30003,305295,0,30003,305461,50,30018,305491,0,30022,305665,50,30050,305695,0,30050,305879,50,30110,305909,0,30110,306103,50,30223,306103,40,30223,306133,0,30223)
%
%
% START OF PROOF
% 306033 [?] ?
% 306105 [] equal(multiply(identity,X),X).
% 306106 [] equal(multiply(inverse(X),X),identity).
% 306107 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 306108 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 306113 [?] ?
% 306118 [?] ?
% 306123 [?] ?
% 306128 [?] ?
% 306133 [?] ?
% 306150 [input:306113,cut:306108] equal(inverse(sk_c1),sk_c7).
% 306151 [para:306150.1.1,306106.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 306166 [input:306128,cut:306108] equal(inverse(sk_c7),sk_c5).
% 306167 [para:306166.1.1,306106.1.1.1] equal(multiply(sk_c5,sk_c7),identity).
% 306170 [input:306118,cut:306108] equal(multiply(sk_c1,sk_c7),sk_c2).
% 306179 [input:306123,cut:306108] equal(multiply(sk_c7,sk_c2),sk_c6).
% 306182 [input:306133,cut:306108] equal(multiply(sk_c6,sk_c5),sk_c7).
% 306188 [para:306151.1.1,306107.1.1.1,demod:306105] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 306197 [para:306167.1.1,306107.1.1.1,demod:306105] equal(X,multiply(sk_c5,multiply(sk_c7,X))).
% 306209 [para:306179.1.1,306107.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c2,X))).
% 306219 [para:306170.1.1,306188.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c2)).
% 306224 [para:306219.1.2,306179.1.1] equal(sk_c7,sk_c6).
% 306225 [para:306219.1.2,306107.1.1.1,demod:306209] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 306237 [para:306224.1.2,306182.1.1.1] equal(multiply(sk_c7,sk_c5),sk_c7).
% 306248 [para:306219.1.2,306197.1.2.2,demod:306167] equal(sk_c2,identity).
% 306249 [para:306237.1.1,306197.1.2.2,demod:306167] equal(sk_c5,identity).
% 306254 [para:306248.1.1,306179.1.1.2] equal(multiply(sk_c7,identity),sk_c6).
% 306259 [para:306249.1.1,306167.1.1.1,demod:306105] equal(sk_c7,identity).
% 306266 [para:306259.1.1,306108.1.1.2,demod:306254,306225,cut:306033] 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: 35990
% derived clauses: 5915595
% kept clauses: 254324
% kept size sum: 35881
% kept mid-nuclei: 9204
% kept new demods: 5298
% forw unit-subs: 2155680
% forw double-subs: 3200350
% forw overdouble-subs: 251993
% backward subs: 9010
% fast unit cutoff: 14096
% full unit cutoff: 0
% dbl unit cutoff: 9490
% real runtime : 303.86
% process. runtime: 302.24
% specific non-discr-tree subsumption statistics:
% tried: 43185505
% length fails: 4212657
% strength fails: 10322564
% predlist fails: 3454326
% aux str. fails: 6405235
% by-lit fails: 9293604
% full subs tried: 1888074
% full subs fail: 1787513
%
% ; 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/GRP360-1+eq_r.in")
%
%------------------------------------------------------------------------------