TSTP Solution File: GRP239-1 by Gandalf---c-2.6

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Gandalf---c-2.6
% Problem  : GRP239-1 : 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 299.7s
% Output   : Assurance 299.7s
% 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/GRP239-1+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 25)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 25)
% (binary-posweight-lex-big-order 30 #f 3 25)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
% 
% 
% SOS clause 
% -equal(inverse(sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c8),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,X1),sk_c8) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c9),sk_c8).
% was split for some strategies as: 
% -equal(multiply(W,X1),sk_c8) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c9),sk_c8).
% -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8).
% -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c8),sk_c9).
% -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9).
% -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9).
% -equal(inverse(sk_c9),sk_c8).
% 
% Starting a split proof attempt with 6 components.
% 
% Split component 1 started.
% 
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split: 
% -equal(inverse(sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c8),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,X1),sk_c8) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c9),sk_c8).
% Split part used next: -equal(multiply(W,X1),sk_c8) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c9),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
% 
% 
% timer checkpoints: c(47,40,1,100,0,1,112597,4,1279,118632,5,1502,118632,1,1502,118632,50,1502,118632,40,1502,118685,0,1502,130224,3,1803,130899,4,1953,131499,5,2103,131500,1,2103,131500,50,2103,131500,40,2103,131553,0,2103,133025,3,2406,133038,4,2558,133205,5,2704,133205,1,2704,133205,50,2704,133205,40,2704,133258,0,2704,163368,3,4205,164082,4,4955,164808,1,5705,164808,50,5706,164808,40,5706,164861,0,5706,185179,3,6457,185864,4,6832,186536,5,7207,186537,1,7207,186537,50,7208,186537,40,7208,186590,0,7208,203914,3,7979,204701,4,8334,205700,1,8709,205700,50,8709,205700,40,8709,205753,0,8710,322216,3,12611,323042,4,14562,323479,1,16512,323479,50,16514,323479,40,16514,323532,0,16514,398255,3,19065,398792,4,20341,399389,5,21616,399390,1,21616,399390,50,21618,399390,40,21618,399443,0,21618,449844,3,23120,450433,4,23869,450819,1,24619,450819,50,24621,450819,40,24621,450872,0,24621,455487,5,26124,455490,1,26126,455490,50,26126,455490,40,26126,455543,0,26126,506389,3,27328,506786,4,27927,507088,1,28527,507088,50,28529,507088,40,28529,507141,0,28529,549461,3,29281,549757,4,29655,550055,1,30030,550055,50,30031,550055,40,30031,550055,40,30031,550102,0,30031)
% 
% 
% START OF PROOF
% 550057 [] equal(multiply(identity,X),X).
% 550058 [] equal(multiply(inverse(X),X),identity).
% 550059 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 550060 [] -equal(multiply(X,sk_c9),sk_c8) | -equal(multiply(Y,X),sk_c8) | -equal(inverse(Y),X).
% 550061 [?] ?
% 550062 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c6),sk_c7).
% 550063 [?] ?
% 550068 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c7,sk_c9),sk_c8).
% 550069 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c6),sk_c7).
% 550070 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c6,sk_c7),sk_c8).
% 550075 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(multiply(sk_c7,sk_c9),sk_c8).
% 550076 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(inverse(sk_c6),sk_c7).
% 550077 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(multiply(sk_c6,sk_c7),sk_c8).
% 550082 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(multiply(sk_c7,sk_c9),sk_c8).
% 550083 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(inverse(sk_c6),sk_c7).
% 550084 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(multiply(sk_c6,sk_c7),sk_c8).
% 550089 [?] ?
% 550090 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c6),sk_c7).
% 550091 [?] ?
% 550096 [?] ?
% 550097 [] equal(inverse(sk_c9),sk_c8) | equal(inverse(sk_c6),sk_c7).
% 550098 [?] ?
% 550108 [hyper:550060,550062,binarycut:550063,binarycut:550061] equal(inverse(sk_c2),sk_c9).
% 550110 [para:550108.1.1,550058.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 550115 [hyper:550060,550090,binarycut:550091,binarycut:550089] equal(inverse(sk_c1),sk_c9).
% 550118 [para:550115.1.1,550058.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 550123 [hyper:550060,550097,binarycut:550098,binarycut:550096] equal(inverse(sk_c9),sk_c8).
% 550131 [para:550123.1.1,550058.1.1.1] equal(multiply(sk_c8,sk_c9),identity).
% 550146 [hyper:550060,550070,550068,550069] equal(multiply(sk_c2,sk_c9),sk_c3).
% 550183 [hyper:550060,550077,550075,550076] equal(multiply(sk_c9,sk_c3),sk_c8).
% 550196 [hyper:550060,550084,550082,550083] equal(multiply(sk_c1,sk_c8),sk_c9).
% 550197 [para:550058.1.1,550059.1.1.1,demod:550057] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 550198 [para:550110.1.1,550059.1.1.1,demod:550057] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 550199 [para:550118.1.1,550059.1.1.1,demod:550057] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 550206 [para:550146.1.1,550198.1.2.2,demod:550183] equal(sk_c9,sk_c8).
% 550209 [para:550206.1.1,550123.1.1.1] equal(inverse(sk_c8),sk_c8).
% 550211 [para:550206.1.1,550146.1.1.2] equal(multiply(sk_c2,sk_c8),sk_c3).
% 550212 [para:550206.1.1,550183.1.1.1] equal(multiply(sk_c8,sk_c3),sk_c8).
% 550219 [para:550110.1.1,550197.1.2.2,demod:550123] equal(sk_c2,multiply(sk_c8,identity)).
% 550220 [para:550118.1.1,550197.1.2.2,demod:550219,550123] equal(sk_c1,sk_c2).
% 550221 [para:550131.1.1,550197.1.2.2,demod:550219,550209] equal(sk_c9,sk_c2).
% 550224 [para:550198.1.2,550197.1.2.2,demod:550123] equal(multiply(sk_c2,X),multiply(sk_c8,X)).
% 550229 [para:550221.1.1,550183.1.1.1] equal(multiply(sk_c2,sk_c3),sk_c8).
% 550237 [para:550206.1.1,550199.1.2.1,demod:550224] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 550238 [para:550199.1.2,550197.1.2.2,demod:550224,550123] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 550239 [para:550211.1.1,550059.1.1.1,demod:550237,550238,550224] equal(multiply(sk_c3,X),X).
% 550240 [para:550220.1.2,550211.1.1.1,demod:550196] equal(sk_c9,sk_c3).
% 550248 [para:550240.1.1,550146.1.1.2,demod:550229] equal(sk_c8,sk_c3).
% 550263 [hyper:550060,550212,demod:550209,550239,cut:550206,cut:550248] 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 25
% 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(inverse(sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c8),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,X1),sk_c8) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c9),sk_c8).
% Split part used next: -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 25
% clause depth limited to 3
% seconds given: 4
% 
% 
% ********* EMPTY CLAUSE DERIVED *********
% 
% 
% timer checkpoints: c(47,40,1,100,0,1,112597,4,1279,118632,5,1502,118632,1,1502,118632,50,1502,118632,40,1502,118685,0,1502,130224,3,1803,130899,4,1953,131499,5,2103,131500,1,2103,131500,50,2103,131500,40,2103,131553,0,2103,133025,3,2406,133038,4,2558,133205,5,2704,133205,1,2704,133205,50,2704,133205,40,2704,133258,0,2704,163368,3,4205,164082,4,4955,164808,1,5705,164808,50,5706,164808,40,5706,164861,0,5706,185179,3,6457,185864,4,6832,186536,5,7207,186537,1,7207,186537,50,7208,186537,40,7208,186590,0,7208,203914,3,7979,204701,4,8334,205700,1,8709,205700,50,8709,205700,40,8709,205753,0,8710,322216,3,12611,323042,4,14562,323479,1,16512,323479,50,16514,323479,40,16514,323532,0,16514,398255,3,19065,398792,4,20341,399389,5,21616,399390,1,21616,399390,50,21618,399390,40,21618,399443,0,21618,449844,3,23120,450433,4,23869,450819,1,24619,450819,50,24621,450819,40,24621,450872,0,24621,455487,5,26124,455490,1,26126,455490,50,26126,455490,40,26126,455543,0,26126,506389,3,27328,506786,4,27927,507088,1,28527,507088,50,28529,507088,40,28529,507141,0,28529,549461,3,29281,549757,4,29655,550055,1,30030,550055,50,30031,550055,40,30031,550055,40,30031,550102,0,30031,550262,50,30032,550262,30,30032,550262,40,30032,550309,0,30032)
% 
% 
% START OF PROOF
% 550264 [] equal(multiply(identity,X),X).
% 550265 [] equal(multiply(inverse(X),X),identity).
% 550266 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 550267 [] -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8).
% 550271 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 550272 [?] ?
% 550278 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 550279 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 550285 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 550286 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 550292 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 550293 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 550299 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 550300 [?] ?
% 550306 [] equal(inverse(sk_c9),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 550307 [?] ?
% 550313 [hyper:550267,550271,binarycut:550272] equal(inverse(sk_c2),sk_c9).
% 550316 [para:550313.1.1,550265.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 550320 [hyper:550267,550299,binarycut:550300] equal(inverse(sk_c1),sk_c9).
% 550321 [para:550320.1.1,550265.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 550329 [hyper:550267,550306,binarycut:550307] equal(inverse(sk_c9),sk_c8).
% 550346 [hyper:550267,550279,550278] equal(multiply(sk_c2,sk_c9),sk_c3).
% 550362 [hyper:550267,550286,550285] equal(multiply(sk_c9,sk_c3),sk_c8).
% 550372 [hyper:550267,550293,550292] equal(multiply(sk_c1,sk_c8),sk_c9).
% 550376 [para:550265.1.1,550266.1.1.1,demod:550264] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 550377 [para:550316.1.1,550266.1.1.1,demod:550264] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 550378 [para:550321.1.1,550266.1.1.1,demod:550264] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 550383 [para:550346.1.1,550377.1.2.2,demod:550362] equal(sk_c9,sk_c8).
% 550388 [para:550383.1.1,550346.1.1.2] equal(multiply(sk_c2,sk_c8),sk_c3).
% 550394 [para:550316.1.1,550376.1.2.2,demod:550329] equal(sk_c2,multiply(sk_c8,identity)).
% 550395 [para:550321.1.1,550376.1.2.2,demod:550394,550329] equal(sk_c1,sk_c2).
% 550399 [para:550377.1.2,550376.1.2.2,demod:550329] equal(multiply(sk_c2,X),multiply(sk_c8,X)).
% 550410 [para:550383.1.1,550378.1.2.1,demod:550399] equal(X,multiply(sk_c2,multiply(sk_c1,X))).
% 550411 [para:550378.1.2,550376.1.2.2,demod:550399,550329] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 550412 [para:550388.1.1,550266.1.1.1,demod:550410,550411,550399] equal(multiply(sk_c3,X),X).
% 550413 [para:550395.1.2,550388.1.1.1,demod:550372] equal(sk_c9,sk_c3).
% 550416 [para:550413.1.1,550321.1.1.1,demod:550412] equal(sk_c1,identity).
% 550417 [para:550413.1.1,550329.1.1.1] equal(inverse(sk_c3),sk_c8).
% 550425 [para:550416.1.1,550372.1.1.1,demod:550264] equal(sk_c8,sk_c9).
% 550434 [hyper:550267,550417,demod:550412,cut:550425] 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 25
% 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(inverse(sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c8),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,X1),sk_c8) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c9),sk_c8).
% Split part used next: -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c8),sk_c9).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 25
% clause depth limited to 3
% seconds given: 4
% 
% 
% ********* EMPTY CLAUSE DERIVED *********
% 
% 
% timer checkpoints: c(47,40,1,100,0,1,112597,4,1279,118632,5,1502,118632,1,1502,118632,50,1502,118632,40,1502,118685,0,1502,130224,3,1803,130899,4,1953,131499,5,2103,131500,1,2103,131500,50,2103,131500,40,2103,131553,0,2103,133025,3,2406,133038,4,2558,133205,5,2704,133205,1,2704,133205,50,2704,133205,40,2704,133258,0,2704,163368,3,4205,164082,4,4955,164808,1,5705,164808,50,5706,164808,40,5706,164861,0,5706,185179,3,6457,185864,4,6832,186536,5,7207,186537,1,7207,186537,50,7208,186537,40,7208,186590,0,7208,203914,3,7979,204701,4,8334,205700,1,8709,205700,50,8709,205700,40,8709,205753,0,8710,322216,3,12611,323042,4,14562,323479,1,16512,323479,50,16514,323479,40,16514,323532,0,16514,398255,3,19065,398792,4,20341,399389,5,21616,399390,1,21616,399390,50,21618,399390,40,21618,399443,0,21618,449844,3,23120,450433,4,23869,450819,1,24619,450819,50,24621,450819,40,24621,450872,0,24621,455487,5,26124,455490,1,26126,455490,50,26126,455490,40,26126,455543,0,26126,506389,3,27328,506786,4,27927,507088,1,28527,507088,50,28529,507088,40,28529,507141,0,28529,549461,3,29281,549757,4,29655,550055,1,30030,550055,50,30031,550055,40,30031,550055,40,30031,550102,0,30031,550262,50,30032,550262,30,30032,550262,40,30032,550309,0,30032,550433,50,30033,550433,30,30033,550433,40,30033,550480,0,30039)
% 
% 
% START OF PROOF
% 550434 [] equal(X,X).
% 550438 [] -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c9).
% 550465 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(multiply(sk_c4,sk_c8),sk_c9).
% 550466 [?] ?
% 550472 [?] ?
% 550473 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c4),sk_c9).
% 550509 [hyper:550438,550473,binarycut:550466] equal(inverse(sk_c4),sk_c9).
% 550511 [hyper:550438,550473,binarycut:550472] equal(inverse(sk_c1),sk_c9).
% 550544 [hyper:550438,550465,demod:550511,cut:550434] equal(multiply(sk_c4,sk_c8),sk_c9).
% 550548 [hyper:550438,550544,demod:550509,cut:550434] 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 25
% 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(inverse(sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c8),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,X1),sk_c8) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c9),sk_c8).
% Split part used next: -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 25
% clause depth limited to 3
% seconds given: 4
% 
% 
% ********* EMPTY CLAUSE DERIVED *********
% 
% 
% timer checkpoints: c(47,40,1,100,0,1,112597,4,1279,118632,5,1502,118632,1,1502,118632,50,1502,118632,40,1502,118685,0,1502,130224,3,1803,130899,4,1953,131499,5,2103,131500,1,2103,131500,50,2103,131500,40,2103,131553,0,2103,133025,3,2406,133038,4,2558,133205,5,2704,133205,1,2704,133205,50,2704,133205,40,2704,133258,0,2704,163368,3,4205,164082,4,4955,164808,1,5705,164808,50,5706,164808,40,5706,164861,0,5706,185179,3,6457,185864,4,6832,186536,5,7207,186537,1,7207,186537,50,7208,186537,40,7208,186590,0,7208,203914,3,7979,204701,4,8334,205700,1,8709,205700,50,8709,205700,40,8709,205753,0,8710,322216,3,12611,323042,4,14562,323479,1,16512,323479,50,16514,323479,40,16514,323532,0,16514,398255,3,19065,398792,4,20341,399389,5,21616,399390,1,21616,399390,50,21618,399390,40,21618,399443,0,21618,449844,3,23120,450433,4,23869,450819,1,24619,450819,50,24621,450819,40,24621,450872,0,24621,455487,5,26124,455490,1,26126,455490,50,26126,455490,40,26126,455543,0,26126,506389,3,27328,506786,4,27927,507088,1,28527,507088,50,28529,507088,40,28529,507141,0,28529,549461,3,29281,549757,4,29655,550055,1,30030,550055,50,30031,550055,40,30031,550055,40,30031,550102,0,30031,550262,50,30032,550262,30,30032,550262,40,30032,550309,0,30032,550433,50,30033,550433,30,30033,550433,40,30033,550480,0,30039,550547,50,30039,550547,30,30039,550547,40,30039,550594,0,30039)
% 
% 
% START OF PROOF
% 550549 [] equal(multiply(identity,X),X).
% 550550 [] equal(multiply(inverse(X),X),identity).
% 550551 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 550552 [] -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9).
% 550553 [] equal(multiply(sk_c7,sk_c9),sk_c8) | equal(inverse(sk_c2),sk_c9).
% 550554 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c6),sk_c7).
% 550555 [] equal(multiply(sk_c6,sk_c7),sk_c8) | equal(inverse(sk_c2),sk_c9).
% 550556 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 550557 [] equal(multiply(sk_c5,sk_c8),sk_c9) | equal(inverse(sk_c2),sk_c9).
% 550558 [] equal(multiply(sk_c4,sk_c8),sk_c9) | equal(inverse(sk_c2),sk_c9).
% 550559 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c4),sk_c9).
% 550560 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c7,sk_c9),sk_c8).
% 550561 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c6),sk_c7).
% 550562 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c6,sk_c7),sk_c8).
% 550563 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 550564 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 550565 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c4,sk_c8),sk_c9).
% 550566 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c4),sk_c9).
% 550567 [?] ?
% 550568 [?] ?
% 550569 [?] ?
% 550570 [?] ?
% 550571 [?] ?
% 550572 [?] ?
% 550573 [?] ?
% 550668 [hyper:550552,550560,550553,binarycut:550567] equal(multiply(sk_c7,sk_c9),sk_c8).
% 550675 [hyper:550552,550561,binarycut:550568,binarycut:550554] equal(inverse(sk_c6),sk_c7).
% 550676 [para:550675.1.1,550550.1.1.1] equal(multiply(sk_c7,sk_c6),identity).
% 550679 [hyper:550552,550563,binarycut:550570,binarycut:550556] equal(inverse(sk_c5),sk_c8).
% 550684 [hyper:550552,550562,550555,binarycut:550569] equal(multiply(sk_c6,sk_c7),sk_c8).
% 550685 [para:550679.1.1,550550.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 550688 [hyper:550552,550566,binarycut:550573,binarycut:550559] equal(inverse(sk_c4),sk_c9).
% 550695 [para:550688.1.1,550550.1.1.1] equal(multiply(sk_c9,sk_c4),identity).
% 550701 [hyper:550552,550564,550557,binarycut:550571] equal(multiply(sk_c5,sk_c8),sk_c9).
% 550711 [hyper:550552,550565,550558,binarycut:550572] equal(multiply(sk_c4,sk_c8),sk_c9).
% 550712 [para:550550.1.1,550551.1.1.1,demod:550549] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 550713 [para:550668.1.1,550551.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c7,multiply(sk_c9,X))).
% 550714 [para:550676.1.1,550551.1.1.1,demod:550549] equal(X,multiply(sk_c7,multiply(sk_c6,X))).
% 550716 [para:550685.1.1,550551.1.1.1,demod:550549] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 550717 [para:550695.1.1,550551.1.1.1,demod:550549] equal(X,multiply(sk_c9,multiply(sk_c4,X))).
% 550718 [para:550701.1.1,550551.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c5,multiply(sk_c8,X))).
% 550719 [para:550711.1.1,550551.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c4,multiply(sk_c8,X))).
% 550722 [para:550684.1.1,550714.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 550723 [para:550722.1.2,550551.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c7,multiply(sk_c8,X))).
% 550726 [para:550701.1.1,550716.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c9)).
% 550730 [para:550711.1.1,550717.1.2.2] equal(sk_c8,multiply(sk_c9,sk_c9)).
% 550735 [para:550668.1.1,550712.1.2.2] equal(sk_c9,multiply(inverse(sk_c7),sk_c8)).
% 550739 [para:550714.1.2,550712.1.2.2] equal(multiply(sk_c6,X),multiply(inverse(sk_c7),X)).
% 550748 [para:550717.1.2,550713.1.2.2] equal(multiply(sk_c8,multiply(sk_c4,X)),multiply(sk_c7,X)).
% 550749 [para:550730.1.2,550713.1.2.2,demod:550722,550726] equal(sk_c8,sk_c7).
% 550755 [para:550749.1.1,550735.1.2.2,demod:550684,550739] equal(sk_c9,sk_c8).
% 550759 [para:550755.1.1,550717.1.2.1,demod:550748] equal(X,multiply(sk_c7,X)).
% 550761 [para:550755.1.1,550713.1.2.2.1,demod:550759,550723] equal(multiply(sk_c8,X),X).
% 550765 [para:550759.1.2,550714.1.2] equal(X,multiply(sk_c6,X)).
% 550766 [para:550759.1.2,550713.1.2,demod:550761] equal(X,multiply(sk_c9,X)).
% 550775 [para:550749.1.1,550718.1.2.2.1,demod:550759,550766] equal(X,multiply(sk_c5,X)).
% 550784 [para:550716.1.2,550719.1.2.2,demod:550766,550775] equal(X,multiply(sk_c4,X)).
% 550787 [hyper:550552,550765,550688,demod:550766,550765,demod:550784,cut:550755] 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 25
% 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(inverse(sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c8),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,X1),sk_c8) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c9),sk_c8).
% Split part used next: -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 25
% clause depth limited to 3
% seconds given: 4
% 
% 
% ********* EMPTY CLAUSE DERIVED *********
% 
% 
% timer checkpoints: c(47,40,1,100,0,1,112597,4,1279,118632,5,1502,118632,1,1502,118632,50,1502,118632,40,1502,118685,0,1502,130224,3,1803,130899,4,1953,131499,5,2103,131500,1,2103,131500,50,2103,131500,40,2103,131553,0,2103,133025,3,2406,133038,4,2558,133205,5,2704,133205,1,2704,133205,50,2704,133205,40,2704,133258,0,2704,163368,3,4205,164082,4,4955,164808,1,5705,164808,50,5706,164808,40,5706,164861,0,5706,185179,3,6457,185864,4,6832,186536,5,7207,186537,1,7207,186537,50,7208,186537,40,7208,186590,0,7208,203914,3,7979,204701,4,8334,205700,1,8709,205700,50,8709,205700,40,8709,205753,0,8710,322216,3,12611,323042,4,14562,323479,1,16512,323479,50,16514,323479,40,16514,323532,0,16514,398255,3,19065,398792,4,20341,399389,5,21616,399390,1,21616,399390,50,21618,399390,40,21618,399443,0,21618,449844,3,23120,450433,4,23869,450819,1,24619,450819,50,24621,450819,40,24621,450872,0,24621,455487,5,26124,455490,1,26126,455490,50,26126,455490,40,26126,455543,0,26126,506389,3,27328,506786,4,27927,507088,1,28527,507088,50,28529,507088,40,28529,507141,0,28529,549461,3,29281,549757,4,29655,550055,1,30030,550055,50,30031,550055,40,30031,550055,40,30031,550102,0,30031,550262,50,30032,550262,30,30032,550262,40,30032,550309,0,30032,550433,50,30033,550433,30,30033,550433,40,30033,550480,0,30039,550547,50,30039,550547,30,30039,550547,40,30039,550594,0,30039,550786,50,30039,550786,30,30039,550786,40,30039,550833,0,30039)
% 
% 
% START OF PROOF
% 550787 [] equal(X,X).
% 550791 [] -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c9).
% 550818 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(multiply(sk_c4,sk_c8),sk_c9).
% 550819 [?] ?
% 550825 [?] ?
% 550826 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c4),sk_c9).
% 550862 [hyper:550791,550826,binarycut:550819] equal(inverse(sk_c4),sk_c9).
% 550864 [hyper:550791,550826,binarycut:550825] equal(inverse(sk_c1),sk_c9).
% 550897 [hyper:550791,550818,demod:550864,cut:550787] equal(multiply(sk_c4,sk_c8),sk_c9).
% 550901 [hyper:550791,550897,demod:550862,cut:550787] 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 25
% clause depth limited to 3
% seconds given: 4
% 
% 
% Split component 6 started.
% 
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split: 
% -equal(inverse(sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c8),sk_c9) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,X1),sk_c8) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c9),sk_c8).
% Split part used next: -equal(inverse(sk_c9),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 25
% 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 25
% 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 25
% 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 25
% 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 25
% 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 25
% 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 25
% 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 25
% 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 25
% 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(47,40,1,100,0,1,112597,4,1279,118632,5,1502,118632,1,1502,118632,50,1502,118632,40,1502,118685,0,1502,130224,3,1803,130899,4,1953,131499,5,2103,131500,1,2103,131500,50,2103,131500,40,2103,131553,0,2103,133025,3,2406,133038,4,2558,133205,5,2704,133205,1,2704,133205,50,2704,133205,40,2704,133258,0,2704,163368,3,4205,164082,4,4955,164808,1,5705,164808,50,5706,164808,40,5706,164861,0,5706,185179,3,6457,185864,4,6832,186536,5,7207,186537,1,7207,186537,50,7208,186537,40,7208,186590,0,7208,203914,3,7979,204701,4,8334,205700,1,8709,205700,50,8709,205700,40,8709,205753,0,8710,322216,3,12611,323042,4,14562,323479,1,16512,323479,50,16514,323479,40,16514,323532,0,16514,398255,3,19065,398792,4,20341,399389,5,21616,399390,1,21616,399390,50,21618,399390,40,21618,399443,0,21618,449844,3,23120,450433,4,23869,450819,1,24619,450819,50,24621,450819,40,24621,450872,0,24621,455487,5,26124,455490,1,26126,455490,50,26126,455490,40,26126,455543,0,26126,506389,3,27328,506786,4,27927,507088,1,28527,507088,50,28529,507088,40,28529,507141,0,28529,549461,3,29281,549757,4,29655,550055,1,30030,550055,50,30031,550055,40,30031,550055,40,30031,550102,0,30031,550262,50,30032,550262,30,30032,550262,40,30032,550309,0,30032,550433,50,30033,550433,30,30033,550433,40,30033,550480,0,30039,550547,50,30039,550547,30,30039,550547,40,30039,550594,0,30039,550786,50,30039,550786,30,30039,550786,40,30039,550833,0,30039,550900,50,30040,550900,30,30040,550900,40,30040,550947,0,30044,551073,50,30045,551120,0,30045,551304,50,30048,551351,0,30052,551543,50,30056,551590,0,30056,551790,50,30062,551837,0,30062,552043,50,30071,552090,0,30076,552304,50,30092,552351,0,30093,552573,50,30123,552620,0,30127,552852,50,30187,552899,0,30187,553141,50,30310,553141,40,30310,553188,0,30310)
% 
% 
% START OF PROOF
% 553143 [] equal(multiply(identity,X),X).
% 553144 [] equal(multiply(inverse(X),X),identity).
% 553145 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 553146 [] -equal(inverse(sk_c9),sk_c8).
% 553182 [?] ?
% 553183 [?] ?
% 553184 [?] ?
% 553185 [?] ?
% 553186 [?] ?
% 553188 [?] ?
% 553211 [input:553183,cut:553146] equal(inverse(sk_c6),sk_c7).
% 553212 [para:553211.1.1,553144.1.1.1] equal(multiply(sk_c7,sk_c6),identity).
% 553213 [input:553185,cut:553146] equal(inverse(sk_c5),sk_c8).
% 553214 [para:553213.1.1,553144.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 553215 [input:553188,cut:553146] equal(inverse(sk_c4),sk_c9).
% 553216 [para:553215.1.1,553144.1.1.1] equal(multiply(sk_c9,sk_c4),identity).
% 553241 [input:553182,cut:553146] equal(multiply(sk_c7,sk_c9),sk_c8).
% 553242 [input:553184,cut:553146] equal(multiply(sk_c6,sk_c7),sk_c8).
% 553243 [input:553186,cut:553146] equal(multiply(sk_c5,sk_c8),sk_c9).
% 553264 [para:553144.1.1,553145.1.1.1,demod:553143] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 553267 [para:553212.1.1,553145.1.1.1,demod:553143] equal(X,multiply(sk_c7,multiply(sk_c6,X))).
% 553268 [para:553214.1.1,553145.1.1.1,demod:553143] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 553270 [para:553216.1.1,553145.1.1.1,demod:553143] equal(X,multiply(sk_c9,multiply(sk_c4,X))).
% 553292 [para:553242.1.1,553145.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c6,multiply(sk_c7,X))).
% 553318 [para:553242.1.1,553267.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 553323 [para:553243.1.1,553268.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c9)).
% 553336 [para:553212.1.1,553264.1.2.2] equal(sk_c6,multiply(inverse(sk_c7),identity)).
% 553337 [para:553214.1.1,553264.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),identity)).
% 553363 [para:553241.1.1,553264.1.2.2] equal(sk_c9,multiply(inverse(sk_c7),sk_c8)).
% 553364 [para:553242.1.1,553264.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c8)).
% 553388 [para:553267.1.2,553264.1.2.2] equal(multiply(sk_c6,X),multiply(inverse(sk_c7),X)).
% 553389 [para:553318.1.2,553264.1.2.2,demod:553388] equal(sk_c8,multiply(sk_c6,sk_c7)).
% 553410 [para:553388.1.2,553144.1.1,demod:553389] equal(sk_c8,identity).
% 553411 [para:553388.1.2,553264.1.2,demod:553292] equal(X,multiply(sk_c8,X)).
% 553428 [para:553410.1.1,553268.1.2.1,demod:553143] equal(X,multiply(sk_c5,X)).
% 553429 [para:553410.1.1,553323.1.2.1,demod:553143] equal(sk_c8,sk_c9).
% 553430 [para:553410.1.1,553363.1.2.2,demod:553336] equal(sk_c9,sk_c6).
% 553431 [para:553410.1.1,553364.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),identity)).
% 553447 [para:553429.1.2,553241.1.1.2,demod:553318] equal(sk_c7,sk_c8).
% 553454 [para:553429.1.2,553270.1.2.1,demod:553411] equal(X,multiply(sk_c4,X)).
% 553478 [para:553430.1.1,553323.1.2.2,demod:553411] equal(sk_c8,sk_c6).
% 553479 [para:553430.1.1,553270.1.2.1,demod:553454] equal(X,multiply(sk_c6,X)).
% 553499 [para:553447.1.2,553337.1.2.1.1,demod:553336] equal(sk_c5,sk_c6).
% 553513 [para:553478.1.1,553337.1.2.1.1,demod:553431] equal(sk_c5,sk_c7).
% 553531 [para:553499.1.2,553211.1.1.1] equal(inverse(sk_c5),sk_c7).
% 553537 [para:553513.1.2,553242.1.1.2,demod:553479] equal(sk_c5,sk_c8).
% 553550 [para:553537.1.2,553243.1.1.2,demod:553428] equal(sk_c5,sk_c9).
% 553554 [para:553550.1.2,553146.1.1.1,demod:553531,cut:553447] 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:    23259
%  derived clauses:   4467372
%  kept clauses:      374247
%  kept size sum:     15003
%  kept mid-nuclei:   87164
%  kept new demods:   2172
%  forw unit-subs:    1318424
%  forw double-subs: 2262573
%  forw overdouble-subs: 305504
%  backward subs:     7317
%  fast unit cutoff:  24626
%  full unit cutoff:  0
%  dbl  unit cutoff:  29578
%  real runtime  :  303.77
%  process. runtime:  303.11
% specific non-discr-tree subsumption statistics: 
%  tried:           57974365
%  length fails:    9872409
%  strength fails:  16873480
%  predlist fails:  1249500
%  aux str. fails:  5853740
%  by-lit fails:    7822970
%  full subs tried: 4229435
%  full subs fail:  4068551
% 
% ; 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/GRP239-1+eq_r.in")
% 
%------------------------------------------------------------------------------