TSTP Solution File: GRP318-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP318-1 : 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 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/GRP318-1+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 31)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 31)
% (binary-posweight-lex-big-order 30 #f 3 31)
% (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_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c12,Y),sk_c11) | -equal(multiply(Z,sk_c12),Y) | -equal(inverse(Z),sk_c12) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% was split for some strategies as:
% -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X3),X1) | -equal(inverse(X2),X3) | -equal(multiply(X2,X1),X3).
% -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11).
% -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12).
% -equal(multiply(sk_c12,Y),sk_c11) | -equal(multiply(Z,sk_c12),Y) | -equal(inverse(Z),sk_c12).
% -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c11).
% -equal(multiply(sk_c11,sk_c12),sk_c10).
%
% 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_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c12,Y),sk_c11) | -equal(multiply(Z,sk_c12),Y) | -equal(inverse(Z),sk_c12) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X3),X1) | -equal(inverse(X2),X3) | -equal(multiply(X2,X1),X3).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,0,78420,4,1453,80229,5,1501,80229,1,1501,80229,50,1501,80229,40,1501,80303,0,1501,80816,5,2106,80819,1,2106,80819,50,2106,80819,40,2106,80893,0,2106,81406,5,2710,81409,1,2710,81409,50,2710,81409,40,2710,81483,0,2710,103455,3,4211,104729,4,4961,105997,5,5711,105998,1,5711,105998,50,5712,105998,40,5712,106072,0,5712,121899,3,6464,122859,4,6838,123570,5,7213,123571,1,7213,123571,50,7213,123571,40,7213,123645,0,7213,124361,5,8722,124362,1,8722,124362,50,8722,124362,40,8722,124436,0,8724,167150,3,12626,168708,4,14575,170031,1,16525,170031,50,16526,170031,40,16526,170105,0,16526,208131,3,19077,209290,4,20352,210184,1,21627,210184,50,21628,210184,40,21628,210258,0,21628,241578,3,23129,242447,4,23879,243330,5,24629,243331,1,24629,243331,50,24630,243331,40,24630,243405,0,24630,244133,5,26141,244134,1,26141,244134,50,26141,244134,40,26141,244208,0,26141,266381,3,27342,267160,4,27942,267886,1,28542,267886,50,28542,267886,40,28542,267960,0,28542,284025,3,29293,284588,4,29668,285181,1,30043,285181,50,30043,285181,40,30043,285181,40,30043,285310,0,30043)
%
%
% START OF PROOF
% 285183 [] equal(multiply(identity,X),X).
% 285184 [] equal(multiply(inverse(X),X),identity).
% 285185 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 285246 [] -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,X),sk_c12) | -equal(multiply(Z,X),U) | -equal(inverse(Z),U) | -equal(inverse(U),X) | -equal(inverse(Y),X).
% 285247 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst97,Y).
% 285248 [] -equal(multiply(X,Y),sk_c12) | -equal(inverse(X),Y) | $spltprd1($spltcnst98,Y).
% 285249 [] -equal(multiply(X,sk_c11),sk_c12) | $spltprd1($spltcnst99,X).
% 285250 [] -$spltprd1($spltcnst98,X) | -$spltprd1($spltcnst97,X) | -$spltprd1($spltcnst99,X).
% 285251 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c2),sk_c12).
% 285252 [] equal(inverse(sk_c2),sk_c12) | equal(inverse(sk_c7),sk_c9).
% 285253 [] equal(inverse(sk_c2),sk_c12) | equal(inverse(sk_c8),sk_c7).
% 285254 [] equal(multiply(sk_c9,sk_c11),sk_c12) | equal(inverse(sk_c2),sk_c12).
% 285255 [] equal(inverse(sk_c2),sk_c12) | equal(inverse(sk_c6),sk_c9).
% 285256 [?] ?
% 285261 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 285262 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(inverse(sk_c7),sk_c9).
% 285263 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(inverse(sk_c8),sk_c7).
% 285264 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 285265 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(inverse(sk_c6),sk_c9).
% 285266 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 285271 [] equal(multiply(sk_c12,sk_c3),sk_c11) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 285272 [] equal(multiply(sk_c12,sk_c3),sk_c11) | equal(inverse(sk_c7),sk_c9).
% 285273 [] equal(multiply(sk_c12,sk_c3),sk_c11) | equal(inverse(sk_c8),sk_c7).
% 285274 [] equal(multiply(sk_c12,sk_c3),sk_c11) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 285275 [] equal(multiply(sk_c12,sk_c3),sk_c11) | equal(inverse(sk_c6),sk_c9).
% 285276 [] equal(multiply(sk_c12,sk_c3),sk_c11) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 285281 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c1),sk_c11).
% 285282 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c9).
% 285283 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c8),sk_c7).
% 285284 [] equal(multiply(sk_c9,sk_c11),sk_c12) | equal(inverse(sk_c1),sk_c11).
% 285285 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c9).
% 285286 [?] ?
% 285291 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 285292 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(inverse(sk_c7),sk_c9).
% 285293 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(inverse(sk_c8),sk_c7).
% 285294 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 285295 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(inverse(sk_c6),sk_c9).
% 285296 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 285301 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 285302 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(inverse(sk_c7),sk_c9).
% 285303 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(inverse(sk_c8),sk_c7).
% 285304 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 285305 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(inverse(sk_c6),sk_c9).
% 285306 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 285377 [hyper:285248,285255,binarycut:285256] equal(inverse(sk_c2),sk_c12) | $spltprd1($spltcnst98,sk_c9).
% 285487 [hyper:285248,285285,binarycut:285286] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst98,sk_c9).
% 285591 [hyper:285247,285251,285252,285253] equal(inverse(sk_c2),sk_c12) | $spltprd1($spltcnst97,sk_c9).
% 285620 [hyper:285249,285254] equal(inverse(sk_c2),sk_c12) | $spltprd1($spltcnst99,sk_c9).
% 285631 [hyper:285250,285620,285591,285377] equal(inverse(sk_c2),sk_c12).
% 285638 [para:285631.1.1,285184.1.1.1] equal(multiply(sk_c12,sk_c2),identity).
% 285783 [hyper:285247,285281,285282,285283] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst97,sk_c9).
% 285826 [hyper:285249,285284] equal(inverse(sk_c1),sk_c11) | $spltprd1($spltcnst99,sk_c9).
% 285839 [hyper:285250,285826,285487,285783] equal(inverse(sk_c1),sk_c11).
% 285846 [para:285839.1.1,285184.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 286221 [hyper:285246,285266,285264,285261,285263,285262,285265] equal(multiply(sk_c2,sk_c12),sk_c3).
% 286483 [hyper:285246,285276,285274,285275,285272,285271,285273] equal(multiply(sk_c12,sk_c3),sk_c11).
% 286642 [hyper:285246,285296,285294,285295,285292,285291,285293] equal(multiply(sk_c1,sk_c11),sk_c12).
% 286738 [hyper:285246,285306,285304,285305,285302,285301,285303] equal(multiply(sk_c11,sk_c12),sk_c10).
% 286746 [para:285184.1.1,285185.1.1.1,demod:285183] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 286747 [para:285638.1.1,285185.1.1.1,demod:285183] equal(X,multiply(sk_c12,multiply(sk_c2,X))).
% 286748 [para:285846.1.1,285185.1.1.1,demod:285183] equal(X,multiply(sk_c11,multiply(sk_c1,X))).
% 286765 [para:286221.1.1,286747.1.2.2,demod:286483] equal(sk_c12,sk_c11).
% 286770 [para:286765.1.2,285846.1.1.1] equal(multiply(sk_c12,sk_c1),identity).
% 286771 [para:286765.1.2,286642.1.1.2] equal(multiply(sk_c1,sk_c12),sk_c12).
% 286773 [para:286765.1.2,286738.1.1.1] equal(multiply(sk_c12,sk_c12),sk_c10).
% 286780 [para:286770.1.1,285185.1.1.1,demod:285183] equal(X,multiply(sk_c12,multiply(sk_c1,X))).
% 286809 [para:286642.1.1,286748.1.2.2,demod:286738] equal(sk_c11,sk_c10).
% 286810 [para:286771.1.1,286748.1.2.2,demod:286738] equal(sk_c12,sk_c10).
% 286811 [para:286809.1.1,285846.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 286814 [para:286809.1.1,286738.1.1.1] equal(multiply(sk_c10,sk_c12),sk_c10).
% 286816 [para:286810.1.1,285638.1.1.1] equal(multiply(sk_c10,sk_c2),identity).
% 286929 [para:285638.1.1,286746.1.2.2] equal(sk_c2,multiply(inverse(sk_c12),identity)).
% 286941 [para:286747.1.2,286746.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c12),X)).
% 286942 [para:286770.1.1,286746.1.2.2,demod:286929] equal(sk_c1,sk_c2).
% 286945 [para:286811.1.1,286746.1.2.2] equal(sk_c1,multiply(inverse(sk_c10),identity)).
% 286946 [para:286814.1.1,286746.1.2.2,demod:285184] equal(sk_c12,identity).
% 286947 [para:286816.1.1,286746.1.2.2,demod:286945] equal(sk_c2,sk_c1).
% 286951 [para:286780.1.2,286746.1.2.2,demod:286941] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 286953 [para:286942.1.2,285631.1.1.1,demod:285839] equal(sk_c11,sk_c12).
% 286965 [para:286946.1.1,285638.1.1.1,demod:285183] equal(sk_c2,identity).
% 286969 [para:286946.1.1,286747.1.2.1,demod:285183,286951] equal(X,multiply(sk_c1,X)).
% 286972 [para:286946.1.1,286773.1.1.2] equal(multiply(sk_c12,identity),sk_c10).
% 286977 [para:286947.1.1,286747.1.2.2.1,demod:286969] equal(X,multiply(sk_c12,X)).
% 286982 [para:286965.1.1,285631.1.1.1] equal(inverse(identity),sk_c12).
% 287403 [para:286946.1.1,286929.1.2.1.1,demod:286972,286982] equal(sk_c2,sk_c10).
% 287404 [para:287403.1.1,285631.1.1.1] equal(inverse(sk_c10),sk_c12).
% 287474 [hyper:285246,287404,286771,286814,demod:286977,cut:286953,demod:285839,cut:286953,demod:287404,cut:286810] 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 31
% 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_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c12,Y),sk_c11) | -equal(multiply(Z,sk_c12),Y) | -equal(inverse(Z),sk_c12) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11).
% 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,0,78420,4,1453,80229,5,1501,80229,1,1501,80229,50,1501,80229,40,1501,80303,0,1501,80816,5,2106,80819,1,2106,80819,50,2106,80819,40,2106,80893,0,2106,81406,5,2710,81409,1,2710,81409,50,2710,81409,40,2710,81483,0,2710,103455,3,4211,104729,4,4961,105997,5,5711,105998,1,5711,105998,50,5712,105998,40,5712,106072,0,5712,121899,3,6464,122859,4,6838,123570,5,7213,123571,1,7213,123571,50,7213,123571,40,7213,123645,0,7213,124361,5,8722,124362,1,8722,124362,50,8722,124362,40,8722,124436,0,8724,167150,3,12626,168708,4,14575,170031,1,16525,170031,50,16526,170031,40,16526,170105,0,16526,208131,3,19077,209290,4,20352,210184,1,21627,210184,50,21628,210184,40,21628,210258,0,21628,241578,3,23129,242447,4,23879,243330,5,24629,243331,1,24629,243331,50,24630,243331,40,24630,243405,0,24630,244133,5,26141,244134,1,26141,244134,50,26141,244134,40,26141,244208,0,26141,266381,3,27342,267160,4,27942,267886,1,28542,267886,50,28542,267886,40,28542,267960,0,28542,284025,3,29293,284588,4,29668,285181,1,30043,285181,50,30043,285181,40,30043,285181,40,30043,285310,0,30043,287473,50,30051,287473,30,30051,287473,40,30051,287538,0,30051)
%
%
% START OF PROOF
% 287475 [] equal(multiply(identity,X),X).
% 287476 [] equal(multiply(inverse(X),X),identity).
% 287477 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 287478 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 287485 [] equal(inverse(sk_c2),sk_c12) | equal(inverse(sk_c5),sk_c11).
% 287486 [?] ?
% 287495 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(inverse(sk_c5),sk_c11).
% 287496 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(multiply(sk_c5,sk_c11),sk_c10).
% 287505 [] equal(multiply(sk_c12,sk_c3),sk_c11) | equal(inverse(sk_c5),sk_c11).
% 287506 [] equal(multiply(sk_c12,sk_c3),sk_c11) | equal(multiply(sk_c5,sk_c11),sk_c10).
% 287515 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c5),sk_c11).
% 287516 [?] ?
% 287525 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(inverse(sk_c5),sk_c11).
% 287526 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c5,sk_c11),sk_c10).
% 287535 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(inverse(sk_c5),sk_c11).
% 287536 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(multiply(sk_c5,sk_c11),sk_c10).
% 287545 [hyper:287478,287485,binarycut:287486] equal(inverse(sk_c2),sk_c12).
% 287546 [para:287545.1.1,287476.1.1.1] equal(multiply(sk_c12,sk_c2),identity).
% 287560 [hyper:287478,287515,binarycut:287516] equal(inverse(sk_c1),sk_c11).
% 287563 [para:287560.1.1,287476.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 287589 [hyper:287478,287496,287495] equal(multiply(sk_c2,sk_c12),sk_c3).
% 287603 [hyper:287478,287506,287505] equal(multiply(sk_c12,sk_c3),sk_c11).
% 287609 [hyper:287478,287526,287525] equal(multiply(sk_c1,sk_c11),sk_c12).
% 287615 [hyper:287478,287536,287535] equal(multiply(sk_c11,sk_c12),sk_c10).
% 287616 [para:287476.1.1,287477.1.1.1,demod:287475] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 287617 [para:287546.1.1,287477.1.1.1,demod:287475] equal(X,multiply(sk_c12,multiply(sk_c2,X))).
% 287619 [para:287589.1.1,287477.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c12,X))).
% 287623 [para:287589.1.1,287617.1.2.2,demod:287603] equal(sk_c12,sk_c11).
% 287624 [para:287623.1.2,287563.1.1.1] equal(multiply(sk_c12,sk_c1),identity).
% 287625 [para:287623.1.2,287609.1.1.2] equal(multiply(sk_c1,sk_c12),sk_c12).
% 287630 [para:287546.1.1,287616.1.2.2] equal(sk_c2,multiply(inverse(sk_c12),identity)).
% 287633 [para:287609.1.1,287616.1.2.2,demod:287615,287560] equal(sk_c11,sk_c10).
% 287636 [para:287624.1.1,287616.1.2.2,demod:287630] equal(sk_c1,sk_c2).
% 287638 [para:287633.1.1,287563.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 287643 [para:287636.1.2,287545.1.1.1,demod:287560] equal(sk_c11,sk_c12).
% 287644 [para:287636.1.2,287589.1.1.1,demod:287625] equal(sk_c12,sk_c3).
% 287650 [para:287633.1.1,287643.1.1] equal(sk_c10,sk_c12).
% 287654 [para:287617.1.2,287619.1.2.2] equal(multiply(sk_c3,multiply(sk_c2,X)),multiply(sk_c2,X)).
% 287661 [para:287644.1.1,287617.1.2.1,demod:287654] equal(X,multiply(sk_c2,X)).
% 287665 [para:287650.1.2,287617.1.2.1,demod:287661] equal(X,multiply(sk_c10,X)).
% 287669 [para:287665.1.2,287616.1.2.2] equal(X,multiply(inverse(sk_c10),X)).
% 287671 [para:287638.1.1,287616.1.2.2,demod:287669] equal(sk_c1,identity).
% 287672 [para:287671.1.1,287560.1.1.1] equal(inverse(identity),sk_c11).
% 287673 [hyper:287478,287672,demod:287475,cut:287633] 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c12,Y),sk_c11) | -equal(multiply(Z,sk_c12),Y) | -equal(inverse(Z),sk_c12) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12).
% 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,0,78420,4,1453,80229,5,1501,80229,1,1501,80229,50,1501,80229,40,1501,80303,0,1501,80816,5,2106,80819,1,2106,80819,50,2106,80819,40,2106,80893,0,2106,81406,5,2710,81409,1,2710,81409,50,2710,81409,40,2710,81483,0,2710,103455,3,4211,104729,4,4961,105997,5,5711,105998,1,5711,105998,50,5712,105998,40,5712,106072,0,5712,121899,3,6464,122859,4,6838,123570,5,7213,123571,1,7213,123571,50,7213,123571,40,7213,123645,0,7213,124361,5,8722,124362,1,8722,124362,50,8722,124362,40,8722,124436,0,8724,167150,3,12626,168708,4,14575,170031,1,16525,170031,50,16526,170031,40,16526,170105,0,16526,208131,3,19077,209290,4,20352,210184,1,21627,210184,50,21628,210184,40,21628,210258,0,21628,241578,3,23129,242447,4,23879,243330,5,24629,243331,1,24629,243331,50,24630,243331,40,24630,243405,0,24630,244133,5,26141,244134,1,26141,244134,50,26141,244134,40,26141,244208,0,26141,266381,3,27342,267160,4,27942,267886,1,28542,267886,50,28542,267886,40,28542,267960,0,28542,284025,3,29293,284588,4,29668,285181,1,30043,285181,50,30043,285181,40,30043,285181,40,30043,285310,0,30043,287473,50,30051,287473,30,30051,287473,40,30051,287538,0,30051,287672,50,30051,287672,30,30051,287672,40,30051,287737,0,30056)
%
%
% START OF PROOF
% 287674 [] equal(multiply(identity,X),X).
% 287675 [] equal(multiply(inverse(X),X),identity).
% 287676 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 287677 [] -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12).
% 287686 [] equal(inverse(sk_c2),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 287687 [?] ?
% 287696 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(inverse(sk_c4),sk_c12).
% 287697 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 287706 [] equal(multiply(sk_c12,sk_c3),sk_c11) | equal(inverse(sk_c4),sk_c12).
% 287707 [] equal(multiply(sk_c12,sk_c3),sk_c11) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 287716 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c4),sk_c12).
% 287717 [?] ?
% 287726 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 287727 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 287736 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(inverse(sk_c4),sk_c12).
% 287737 [] equal(multiply(sk_c11,sk_c12),sk_c10) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 287752 [hyper:287677,287686,binarycut:287687] equal(inverse(sk_c2),sk_c12).
% 287755 [para:287752.1.1,287675.1.1.1] equal(multiply(sk_c12,sk_c2),identity).
% 287764 [hyper:287677,287716,binarycut:287717] equal(inverse(sk_c1),sk_c11).
% 287765 [para:287764.1.1,287675.1.1.1] equal(multiply(sk_c11,sk_c1),identity).
% 287789 [hyper:287677,287697,287696] equal(multiply(sk_c2,sk_c12),sk_c3).
% 287806 [hyper:287677,287707,287706] equal(multiply(sk_c12,sk_c3),sk_c11).
% 287813 [hyper:287677,287727,287726] equal(multiply(sk_c1,sk_c11),sk_c12).
% 287820 [hyper:287677,287737,287736] equal(multiply(sk_c11,sk_c12),sk_c10).
% 287821 [para:287675.1.1,287676.1.1.1,demod:287674] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 287822 [para:287755.1.1,287676.1.1.1,demod:287674] equal(X,multiply(sk_c12,multiply(sk_c2,X))).
% 287824 [para:287789.1.1,287676.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c12,X))).
% 287828 [para:287789.1.1,287822.1.2.2,demod:287806] equal(sk_c12,sk_c11).
% 287829 [para:287828.1.2,287765.1.1.1] equal(multiply(sk_c12,sk_c1),identity).
% 287830 [para:287828.1.2,287813.1.1.2] equal(multiply(sk_c1,sk_c12),sk_c12).
% 287833 [?] ?
% 287835 [para:287755.1.1,287821.1.2.2] equal(sk_c2,multiply(inverse(sk_c12),identity)).
% 287837 [para:287806.1.1,287821.1.2.2] equal(sk_c3,multiply(inverse(sk_c12),sk_c11)).
% 287838 [para:287813.1.1,287821.1.2.2,demod:287820,287764] equal(sk_c11,sk_c10).
% 287841 [para:287829.1.1,287821.1.2.2,demod:287835] equal(sk_c1,sk_c2).
% 287842 [para:287830.1.1,287821.1.2.2,demod:287820,287764] equal(sk_c12,sk_c10).
% 287848 [para:287841.1.2,287752.1.1.1,demod:287764] equal(sk_c11,sk_c12).
% 287849 [para:287841.1.2,287789.1.1.1,demod:287830] equal(sk_c12,sk_c3).
% 287851 [para:287842.1.1,287789.1.1.2] equal(multiply(sk_c2,sk_c10),sk_c3).
% 287855 [para:287838.1.1,287848.1.1] equal(sk_c10,sk_c12).
% 287856 [para:287755.1.1,287824.1.2.2] equal(multiply(sk_c3,sk_c2),multiply(sk_c2,identity)).
% 287859 [para:287822.1.2,287824.1.2.2] equal(multiply(sk_c3,multiply(sk_c2,X)),multiply(sk_c2,X)).
% 287860 [para:287829.1.1,287824.1.2.2,demod:287856] equal(multiply(sk_c3,sk_c1),multiply(sk_c3,sk_c2)).
% 287861 [para:287841.1.2,287824.1.2.1,demod:287833] equal(multiply(sk_c3,X),multiply(sk_c12,X)).
% 287863 [para:287849.1.1,287755.1.1.1,demod:287860] equal(multiply(sk_c3,sk_c1),identity).
% 287866 [para:287849.1.1,287822.1.2.1,demod:287859] equal(X,multiply(sk_c2,X)).
% 287870 [para:287855.1.2,287822.1.2.1,demod:287866] equal(X,multiply(sk_c10,X)).
% 287871 [para:287855.1.2,287824.1.2.2.1,demod:287866,287870] equal(multiply(sk_c3,X),X).
% 287874 [para:287870.1.2,287821.1.2.2] equal(X,multiply(inverse(sk_c10),X)).
% 287883 [para:287874.1.2,287675.1.1] equal(sk_c10,identity).
% 287885 [para:287883.1.1,287851.1.1.2,demod:287863,287860,287856] equal(identity,sk_c3).
% 287888 [para:287885.1.2,287806.1.1.2,demod:287871,287861] equal(identity,sk_c11).
% 287890 [para:287888.1.2,287837.1.2.2,demod:287835] equal(sk_c3,sk_c2).
% 287892 [para:287890.1.2,287752.1.1.1] equal(inverse(sk_c3),sk_c12).
% 287901 [hyper:287677,287892,demod:287871,cut:287828] 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 31
% 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_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c12,Y),sk_c11) | -equal(multiply(Z,sk_c12),Y) | -equal(inverse(Z),sk_c12) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(sk_c12,Y),sk_c11) | -equal(multiply(Z,sk_c12),Y) | -equal(inverse(Z),sk_c12).
% 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 31
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,0,78420,4,1453,80229,5,1501,80229,1,1501,80229,50,1501,80229,40,1501,80303,0,1501,80816,5,2106,80819,1,2106,80819,50,2106,80819,40,2106,80893,0,2106,81406,5,2710,81409,1,2710,81409,50,2710,81409,40,2710,81483,0,2710,103455,3,4211,104729,4,4961,105997,5,5711,105998,1,5711,105998,50,5712,105998,40,5712,106072,0,5712,121899,3,6464,122859,4,6838,123570,5,7213,123571,1,7213,123571,50,7213,123571,40,7213,123645,0,7213,124361,5,8722,124362,1,8722,124362,50,8722,124362,40,8722,124436,0,8724,167150,3,12626,168708,4,14575,170031,1,16525,170031,50,16526,170031,40,16526,170105,0,16526,208131,3,19077,209290,4,20352,210184,1,21627,210184,50,21628,210184,40,21628,210258,0,21628,241578,3,23129,242447,4,23879,243330,5,24629,243331,1,24629,243331,50,24630,243331,40,24630,243405,0,24630,244133,5,26141,244134,1,26141,244134,50,26141,244134,40,26141,244208,0,26141,266381,3,27342,267160,4,27942,267886,1,28542,267886,50,28542,267886,40,28542,267960,0,28542,284025,3,29293,284588,4,29668,285181,1,30043,285181,50,30043,285181,40,30043,285181,40,30043,285310,0,30043,287473,50,30051,287473,30,30051,287473,40,30051,287538,0,30051,287672,50,30051,287672,30,30051,287672,40,30051,287737,0,30056,287900,50,30057,287900,30,30057,287900,40,30057,287965,0,30057)
%
%
% START OF PROOF
% 287901 [] equal(X,X).
% 287902 [] equal(multiply(identity,X),X).
% 287903 [] equal(multiply(inverse(X),X),identity).
% 287904 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 287905 [] -equal(multiply(sk_c12,X),sk_c11) | -equal(multiply(Y,sk_c12),X) | -equal(inverse(Y),sk_c12).
% 287907 [] equal(inverse(sk_c2),sk_c12) | equal(inverse(sk_c7),sk_c9).
% 287908 [] equal(inverse(sk_c2),sk_c12) | equal(inverse(sk_c8),sk_c7).
% 287910 [] equal(inverse(sk_c2),sk_c12) | equal(inverse(sk_c6),sk_c9).
% 287911 [] equal(multiply(sk_c6,sk_c9),sk_c12) | equal(inverse(sk_c2),sk_c12).
% 287914 [] equal(inverse(sk_c2),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 287915 [] equal(multiply(sk_c4,sk_c12),sk_c11) | equal(inverse(sk_c2),sk_c12).
% 287917 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(inverse(sk_c7),sk_c9).
% 287918 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(inverse(sk_c8),sk_c7).
% 287920 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(inverse(sk_c6),sk_c9).
% 287921 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 287924 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(inverse(sk_c4),sk_c12).
% 287925 [] equal(multiply(sk_c2,sk_c12),sk_c3) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 287927 [?] ?
% 287928 [?] ?
% 287930 [?] ?
% 287931 [?] ?
% 287934 [?] ?
% 287935 [?] ?
% 288033 [hyper:287905,287917,binarycut:287927,binarycut:287907] equal(inverse(sk_c7),sk_c9).
% 288034 [para:288033.1.1,287903.1.1.1] equal(multiply(sk_c9,sk_c7),identity).
% 288037 [hyper:287905,287918,binarycut:287928,binarycut:287908] equal(inverse(sk_c8),sk_c7).
% 288045 [para:288037.1.1,287903.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 288048 [hyper:287905,287920,binarycut:287930,binarycut:287910] equal(inverse(sk_c6),sk_c9).
% 288049 [para:288048.1.1,287903.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 288064 [hyper:287905,287921,287911,binarycut:287931] equal(multiply(sk_c6,sk_c9),sk_c12).
% 288067 [hyper:287905,287924,binarycut:287934,binarycut:287914] equal(inverse(sk_c4),sk_c12).
% 288088 [hyper:287905,287925,287915,binarycut:287935] equal(multiply(sk_c4,sk_c12),sk_c11).
% 288092 [para:288034.1.1,287904.1.1.1,demod:287902] equal(X,multiply(sk_c9,multiply(sk_c7,X))).
% 288094 [para:288045.1.1,287904.1.1.1,demod:287902] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 288098 [para:288064.1.1,287904.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c6,multiply(sk_c9,X))).
% 288106 [para:288045.1.1,288092.1.2.2] equal(sk_c8,multiply(sk_c9,identity)).
% 288107 [para:288106.1.2,287904.1.1.1,demod:287902] equal(multiply(sk_c8,X),multiply(sk_c9,X)).
% 288126 [para:288107.1.1,288094.1.2.2] equal(X,multiply(sk_c7,multiply(sk_c9,X))).
% 288129 [para:288034.1.1,288126.1.2.2] equal(sk_c7,multiply(sk_c7,identity)).
% 288130 [para:288049.1.1,288126.1.2.2,demod:288129] equal(sk_c6,sk_c7).
% 288134 [para:288130.1.2,288094.1.2.1,demod:288098,288107] equal(X,multiply(sk_c12,X)).
% 288138 [hyper:287905,288134,288088,demod:288134,demod:288067,cut:287901] 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 31
% 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_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c12,Y),sk_c11) | -equal(multiply(Z,sk_c12),Y) | -equal(inverse(Z),sk_c12) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c11).
% 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 31
% 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 31
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(65,40,0,139,0,0,78420,4,1453,80229,5,1501,80229,1,1501,80229,50,1501,80229,40,1501,80303,0,1501,80816,5,2106,80819,1,2106,80819,50,2106,80819,40,2106,80893,0,2106,81406,5,2710,81409,1,2710,81409,50,2710,81409,40,2710,81483,0,2710,103455,3,4211,104729,4,4961,105997,5,5711,105998,1,5711,105998,50,5712,105998,40,5712,106072,0,5712,121899,3,6464,122859,4,6838,123570,5,7213,123571,1,7213,123571,50,7213,123571,40,7213,123645,0,7213,124361,5,8722,124362,1,8722,124362,50,8722,124362,40,8722,124436,0,8724,167150,3,12626,168708,4,14575,170031,1,16525,170031,50,16526,170031,40,16526,170105,0,16526,208131,3,19077,209290,4,20352,210184,1,21627,210184,50,21628,210184,40,21628,210258,0,21628,241578,3,23129,242447,4,23879,243330,5,24629,243331,1,24629,243331,50,24630,243331,40,24630,243405,0,24630,244133,5,26141,244134,1,26141,244134,50,26141,244134,40,26141,244208,0,26141,266381,3,27342,267160,4,27942,267886,1,28542,267886,50,28542,267886,40,28542,267960,0,28542,284025,3,29293,284588,4,29668,285181,1,30043,285181,50,30043,285181,40,30043,285181,40,30043,285310,0,30043,287473,50,30051,287473,30,30051,287473,40,30051,287538,0,30051,287672,50,30051,287672,30,30051,287672,40,30051,287737,0,30056,287900,50,30057,287900,30,30057,287900,40,30057,287965,0,30057,288137,50,30057,288137,30,30057,288137,40,30057,288202,0,30062,288397,50,30064,288462,0,30064)
%
%
% START OF PROOF
% 288399 [] equal(multiply(identity,X),X).
% 288400 [] equal(multiply(inverse(X),X),identity).
% 288401 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 288402 [] -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c11).
% 288433 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c1),sk_c11).
% 288434 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c7),sk_c9).
% 288435 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c8),sk_c7).
% 288436 [] equal(multiply(sk_c9,sk_c11),sk_c12) | equal(inverse(sk_c1),sk_c11).
% 288437 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c6),sk_c9).
% 288438 [] equal(multiply(sk_c6,sk_c9),sk_c12) | equal(inverse(sk_c1),sk_c11).
% 288439 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c5),sk_c11).
% 288440 [] equal(multiply(sk_c5,sk_c11),sk_c10) | equal(inverse(sk_c1),sk_c11).
% 288441 [] equal(inverse(sk_c1),sk_c11) | equal(inverse(sk_c4),sk_c12).
% 288442 [] equal(multiply(sk_c4,sk_c12),sk_c11) | equal(inverse(sk_c1),sk_c11).
% 288443 [?] ?
% 288444 [?] ?
% 288445 [?] ?
% 288446 [?] ?
% 288447 [?] ?
% 288448 [?] ?
% 288449 [?] ?
% 288450 [?] ?
% 288451 [?] ?
% 288452 [?] ?
% 288473 [hyper:288402,288434,binarycut:288444] equal(inverse(sk_c7),sk_c9).
% 288474 [para:288473.1.1,288400.1.1.1] equal(multiply(sk_c9,sk_c7),identity).
% 288478 [hyper:288402,288435,binarycut:288445] equal(inverse(sk_c8),sk_c7).
% 288479 [para:288478.1.1,288400.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 288482 [hyper:288402,288437,binarycut:288447] equal(inverse(sk_c6),sk_c9).
% 288486 [para:288482.1.1,288400.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 288489 [hyper:288402,288439,binarycut:288449] equal(inverse(sk_c5),sk_c11).
% 288493 [para:288489.1.1,288400.1.1.1] equal(multiply(sk_c11,sk_c5),identity).
% 288498 [hyper:288402,288441,binarycut:288451] equal(inverse(sk_c4),sk_c12).
% 288499 [para:288498.1.1,288400.1.1.1] equal(multiply(sk_c12,sk_c4),identity).
% 288505 [hyper:288402,288433,binarycut:288443] equal(multiply(sk_c8,sk_c9),sk_c7).
% 288509 [hyper:288402,288436,binarycut:288446] equal(multiply(sk_c9,sk_c11),sk_c12).
% 288515 [hyper:288402,288438,binarycut:288448] equal(multiply(sk_c6,sk_c9),sk_c12).
% 288519 [hyper:288402,288440,binarycut:288450] equal(multiply(sk_c5,sk_c11),sk_c10).
% 288522 [hyper:288402,288442,binarycut:288452] equal(multiply(sk_c4,sk_c12),sk_c11).
% 288523 [para:288400.1.1,288401.1.1.1,demod:288399] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 288524 [para:288474.1.1,288401.1.1.1,demod:288399] equal(X,multiply(sk_c9,multiply(sk_c7,X))).
% 288525 [para:288479.1.1,288401.1.1.1,demod:288399] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 288526 [para:288486.1.1,288401.1.1.1,demod:288399] equal(X,multiply(sk_c9,multiply(sk_c6,X))).
% 288527 [para:288493.1.1,288401.1.1.1,demod:288399] equal(X,multiply(sk_c11,multiply(sk_c5,X))).
% 288528 [para:288499.1.1,288401.1.1.1,demod:288399] equal(X,multiply(sk_c12,multiply(sk_c4,X))).
% 288529 [para:288505.1.1,288401.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c9,X))).
% 288531 [para:288515.1.1,288401.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c6,multiply(sk_c9,X))).
% 288534 [para:288479.1.1,288524.1.2.2] equal(sk_c8,multiply(sk_c9,identity)).
% 288535 [para:288534.1.2,288401.1.1.1,demod:288399] equal(multiply(sk_c8,X),multiply(sk_c9,X)).
% 288536 [para:288505.1.1,288525.1.2.2] equal(sk_c9,multiply(sk_c7,sk_c7)).
% 288539 [para:288400.1.1,288523.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 288540 [para:288474.1.1,288523.1.2.2] equal(sk_c7,multiply(inverse(sk_c9),identity)).
% 288542 [para:288486.1.1,288523.1.2.2,demod:288540] equal(sk_c6,sk_c7).
% 288544 [para:288499.1.1,288523.1.2.2] equal(sk_c4,multiply(inverse(sk_c12),identity)).
% 288546 [para:288515.1.1,288523.1.2.2,demod:288482] equal(sk_c9,multiply(sk_c9,sk_c12)).
% 288549 [para:288401.1.1,288523.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 288550 [para:288524.1.2,288523.1.2.2] equal(multiply(sk_c7,X),multiply(inverse(sk_c9),X)).
% 288551 [para:288523.1.2,288523.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 288553 [para:288542.1.2,288525.1.2.1,demod:288531,288535] equal(X,multiply(sk_c12,X)).
% 288554 [para:288553.1.2,288499.1.1] equal(sk_c4,identity).
% 288555 [para:288553.1.2,288523.1.2.2] equal(X,multiply(inverse(sk_c12),X)).
% 288557 [para:288554.1.1,288522.1.1.1,demod:288399] equal(sk_c12,sk_c11).
% 288558 [para:288557.1.2,288493.1.1.1,demod:288553] equal(sk_c5,identity).
% 288559 [para:288557.1.2,288509.1.1.2,demod:288546] equal(sk_c9,sk_c12).
% 288562 [para:288558.1.1,288519.1.1.1,demod:288399] equal(sk_c11,sk_c10).
% 288563 [para:288526.1.2,288523.1.2.2,demod:288550] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 288566 [para:288559.1.2,288553.1.2.1] equal(X,multiply(sk_c9,X)).
% 288568 [para:288562.1.1,288509.1.1.2,demod:288566] equal(sk_c10,sk_c12).
% 288573 [para:288568.1.2,288553.1.2.1] equal(X,multiply(sk_c10,X)).
% 288574 [para:288568.1.2,288559.1.2] equal(sk_c9,sk_c10).
% 288581 [para:288574.1.1,288524.1.2.1,demod:288573,288563] equal(X,multiply(sk_c6,X)).
% 288582 [para:288574.1.1,288534.1.2.1,demod:288573] equal(sk_c8,identity).
% 288584 [para:288557.1.2,288527.1.2.1,demod:288553] equal(X,multiply(sk_c5,X)).
% 288591 [para:288528.1.2,288523.1.2.2,demod:288555] equal(multiply(sk_c4,X),X).
% 288593 [para:288582.1.1,288505.1.1.1,demod:288399] equal(sk_c9,sk_c7).
% 288595 [para:288474.1.1,288529.1.2.2,demod:288534,288535,288536] equal(sk_c9,sk_c8).
% 288602 [para:288593.1.2,288473.1.1.1] equal(inverse(sk_c9),sk_c9).
% 288647 [para:288559.1.2,288544.1.2.1.1,demod:288534,288602] equal(sk_c4,sk_c8).
% 288648 [para:288647.1.2,288595.1.2] equal(sk_c9,sk_c4).
% 288653 [para:288648.1.1,288515.1.1.2,demod:288581] equal(sk_c4,sk_c12).
% 288656 [para:288653.1.2,288522.1.1.2,demod:288591] equal(sk_c4,sk_c11).
% 288681 [para:288551.1.2,288400.1.1] equal(multiply(X,inverse(X)),identity).
% 288683 [para:288551.1.2,288539.1.2] equal(X,multiply(X,identity)).
% 288684 [para:288683.1.2,288539.1.2] equal(X,inverse(inverse(X))).
% 288686 [para:288683.1.2,288544.1.2] equal(sk_c4,inverse(sk_c12)).
% 288687 [para:288681.1.1,288549.1.2.2.2,demod:288683] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 288693 [para:288527.1.2,288687.1.2.1.1,demod:288584] equal(inverse(X),multiply(inverse(X),sk_c11)).
% 288710 [para:288693.1.2,288551.1.2,demod:288684] equal(multiply(X,sk_c11),X).
% 288711 [hyper:288402,288710,demod:288686,cut:288656] 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 31
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c11,sk_c12),sk_c10) | -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c11) | -equal(multiply(sk_c12,Y),sk_c11) | -equal(multiply(Z,sk_c12),Y) | -equal(inverse(Z),sk_c12) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(sk_c11,sk_c12),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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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 31
% 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(65,40,0,139,0,0,78420,4,1453,80229,5,1501,80229,1,1501,80229,50,1501,80229,40,1501,80303,0,1501,80816,5,2106,80819,1,2106,80819,50,2106,80819,40,2106,80893,0,2106,81406,5,2710,81409,1,2710,81409,50,2710,81409,40,2710,81483,0,2710,103455,3,4211,104729,4,4961,105997,5,5711,105998,1,5711,105998,50,5712,105998,40,5712,106072,0,5712,121899,3,6464,122859,4,6838,123570,5,7213,123571,1,7213,123571,50,7213,123571,40,7213,123645,0,7213,124361,5,8722,124362,1,8722,124362,50,8722,124362,40,8722,124436,0,8724,167150,3,12626,168708,4,14575,170031,1,16525,170031,50,16526,170031,40,16526,170105,0,16526,208131,3,19077,209290,4,20352,210184,1,21627,210184,50,21628,210184,40,21628,210258,0,21628,241578,3,23129,242447,4,23879,243330,5,24629,243331,1,24629,243331,50,24630,243331,40,24630,243405,0,24630,244133,5,26141,244134,1,26141,244134,50,26141,244134,40,26141,244208,0,26141,266381,3,27342,267160,4,27942,267886,1,28542,267886,50,28542,267886,40,28542,267960,0,28542,284025,3,29293,284588,4,29668,285181,1,30043,285181,50,30043,285181,40,30043,285181,40,30043,285310,0,30043,287473,50,30051,287473,30,30051,287473,40,30051,287538,0,30051,287672,50,30051,287672,30,30051,287672,40,30051,287737,0,30056,287900,50,30057,287900,30,30057,287900,40,30057,287965,0,30057,288137,50,30057,288137,30,30057,288137,40,30057,288202,0,30062,288397,50,30064,288462,0,30064,288710,50,30066,288710,30,30066,288710,40,30066,288775,0,30072,288983,50,30074,289048,0,30074,289308,50,30078,289373,0,30083,289641,50,30090,289706,0,30090,289985,50,30099,290050,0,30103,290336,50,30117,290401,0,30117,290695,50,30138,290760,0,30143,291063,50,30181,291128,0,30181,291441,50,30256,291506,0,30256,291830,50,30394,291830,40,30394,291895,0,30394)
%
%
% START OF PROOF
% 291626 [?] ?
% 291832 [] equal(multiply(identity,X),X).
% 291833 [] equal(multiply(inverse(X),X),identity).
% 291834 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 291835 [] -equal(multiply(sk_c11,sk_c12),sk_c10).
% 291887 [?] ?
% 291888 [?] ?
% 291890 [?] ?
% 291891 [?] ?
% 291894 [?] ?
% 291895 [?] ?
% 291981 [input:291887,cut:291835] equal(inverse(sk_c7),sk_c9).
% 291982 [para:291981.1.1,291833.1.1.1] equal(multiply(sk_c9,sk_c7),identity).
% 291983 [input:291888,cut:291835] equal(inverse(sk_c8),sk_c7).
% 291984 [para:291983.1.1,291833.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 291986 [input:291890,cut:291835] equal(inverse(sk_c6),sk_c9).
% 291987 [para:291986.1.1,291833.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 291991 [input:291894,cut:291835] equal(inverse(sk_c4),sk_c12).
% 291992 [para:291991.1.1,291833.1.1.1] equal(multiply(sk_c12,sk_c4),identity).
% 292013 [input:291891,cut:291835] equal(multiply(sk_c6,sk_c9),sk_c12).
% 292015 [input:291895,cut:291835] equal(multiply(sk_c4,sk_c12),sk_c11).
% 292052 [para:291982.1.1,291834.1.1.1,demod:291832] equal(X,multiply(sk_c9,multiply(sk_c7,X))).
% 292055 [para:291984.1.1,291834.1.1.1,demod:291832] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 292060 [para:291992.1.1,291834.1.1.1,demod:291832] equal(X,multiply(sk_c12,multiply(sk_c4,X))).
% 292089 [para:292013.1.1,291834.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c6,multiply(sk_c9,X))).
% 292092 [para:291984.1.1,292052.1.2.2] equal(sk_c8,multiply(sk_c9,identity)).
% 292093 [para:292092.1.2,291834.1.1.1,demod:291832] equal(multiply(sk_c8,X),multiply(sk_c9,X)).
% 292124 [para:292015.1.1,292060.1.2.2] equal(sk_c12,multiply(sk_c12,sk_c11)).
% 292128 [para:292093.1.1,292055.1.2.2] equal(X,multiply(sk_c7,multiply(sk_c9,X))).
% 292132 [para:291982.1.1,292128.1.2.2] equal(sk_c7,multiply(sk_c7,identity)).
% 292133 [para:291987.1.1,292128.1.2.2,demod:292132] equal(sk_c6,sk_c7).
% 292141 [para:292133.1.2,292055.1.2.1,demod:292089,292093] equal(X,multiply(sk_c12,X)).
% 292159 [para:292141.1.2,292124.1.2] equal(sk_c12,sk_c11).
% 292167 [para:292159.1.2,291835.1.1.1,demod:292141,cut:291626] 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: 34040
% derived clauses: 2942472
% kept clauses: 167813
% kept size sum: 253707
% kept mid-nuclei: 66780
% kept new demods: 2957
% forw unit-subs: 493503
% forw double-subs: 1997058
% forw overdouble-subs: 131196
% backward subs: 17482
% fast unit cutoff: 24754
% full unit cutoff: 0
% dbl unit cutoff: 21531
% real runtime : 305.64
% process. runtime: 303.95
% specific non-discr-tree subsumption statistics:
% tried: 55373007
% length fails: 9075720
% strength fails: 16655740
% predlist fails: 299287
% aux str. fails: 9476831
% by-lit fails: 8443705
% full subs tried: 4973681
% full subs fail: 4892977
%
% ; 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/GRP318-1+eq_r.in")
%
%------------------------------------------------------------------------------