TSTP Solution File: GRP329-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP329-1 : 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 : art06.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 298.5s
% Output : Assurance 298.5s
% 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/GRP329-1+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(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% was split for some strategies as:
% -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8).
% -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9).
% -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8).
% -equal(multiply(sk_c8,sk_c9),sk_c7).
% -equal(inverse(sk_c8),sk_c7).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(47,40,0,100,0,0,1190,50,14,1243,0,14,2569,50,37,2622,0,37,4065,50,54,4118,0,54,5623,50,75,5676,0,75,7244,50,101,7297,0,101,8957,50,137,9010,0,137,10762,50,190,10815,0,190,12689,50,281,12742,0,281,14738,50,448,14791,0,448,16939,50,696,16992,0,696,19292,50,1121,19292,40,1121,19345,0,1121,31102,3,1422,31752,4,1572,32363,5,1722,32364,1,1722,32364,50,1722,32364,40,1722,32417,0,1722,32701,3,2036,32710,4,2179,32728,5,2323,32728,1,2323,32728,50,2323,32728,40,2323,32781,0,2323,63928,3,3834,64710,4,4574,65648,1,5324,65648,50,5325,65648,40,5325,65701,0,5325,84364,3,6077,85134,4,6451,85852,5,6826,85853,1,6826,85853,50,6826,85853,40,6826,85906,0,6826,100323,3,7581,101035,4,7952,102213,1,8327,102213,50,8327,102213,40,8327,102266,0,8327,160646,3,12234,161466,4,14178,162102,5,16128,162103,1,16129,162103,50,16131,162103,40,16131,162156,0,16131,206393,3,18691,207016,4,19957,207502,5,21232,207503,1,21232,207503,50,21234,207503,40,21234,207556,0,21234,246476,3,22736,247212,4,23485,247784,1,24235,247784,50,24236,247784,40,24236,247837,0,24236,260135,3,24987,261304,4,25362,261871,5,25737,261871,1,25737,261871,50,25737,261871,40,25737,261924,0,25737,293605,3,26947,294292,4,27538,294908,5,28138,294909,1,28138,294909,50,28139,294909,40,28139,294962,0,28139,316073,3,28890,316627,4,29265,317073,1,29640,317073,50,29640,317073,40,29640,317073,40,29640,317120,0,29640)
%
%
% START OF PROOF
% 317074 [] equal(X,X).
% 317075 [] equal(multiply(identity,X),X).
% 317076 [] equal(multiply(inverse(X),X),identity).
% 317077 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 317078 [] -equal(multiply(X,sk_c9),sk_c7) | -equal(inverse(X),sk_c9).
% 317079 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 317080 [?] ?
% 317086 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c6),sk_c9).
% 317087 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 317093 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(inverse(sk_c6),sk_c9).
% 317094 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 317100 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c6),sk_c9).
% 317101 [?] ?
% 317107 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 317108 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 317114 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c6),sk_c9).
% 317115 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 317124 [hyper:317078,317079,binarycut:317080] equal(inverse(sk_c2),sk_c9).
% 317126 [para:317124.1.1,317076.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 317130 [hyper:317078,317100,binarycut:317101] equal(inverse(sk_c1),sk_c8).
% 317131 [para:317130.1.1,317076.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 317137 [hyper:317078,317087,317086] equal(multiply(sk_c2,sk_c9),sk_c3).
% 317149 [hyper:317078,317094,317093] equal(multiply(sk_c9,sk_c3),sk_c8).
% 317152 [hyper:317078,317108,317107] equal(multiply(sk_c1,sk_c8),sk_c9).
% 317161 [hyper:317078,317115,317114] equal(multiply(sk_c8,sk_c9),sk_c7).
% 317163 [para:317076.1.1,317077.1.1.1,demod:317075] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 317164 [para:317126.1.1,317077.1.1.1,demod:317075] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 317166 [para:317137.1.1,317077.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c9,X))).
% 317169 [para:317137.1.1,317164.1.2.2,demod:317149] equal(sk_c9,sk_c8).
% 317170 [para:317169.1.2,317131.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 317171 [para:317169.1.2,317152.1.1.2] equal(multiply(sk_c1,sk_c9),sk_c9).
% 317175 [para:317169.1.2,317161.1.1.1] equal(multiply(sk_c9,sk_c9),sk_c7).
% 317177 [?] ?
% 317179 [para:317126.1.1,317163.1.2.2] equal(sk_c2,multiply(inverse(sk_c9),identity)).
% 317181 [para:317149.1.1,317163.1.2.2] equal(sk_c3,multiply(inverse(sk_c9),sk_c8)).
% 317185 [para:317170.1.1,317163.1.2.2,demod:317179] equal(sk_c1,sk_c2).
% 317186 [para:317171.1.1,317163.1.2.2,demod:317161,317130] equal(sk_c9,sk_c7).
% 317191 [para:317185.1.2,317137.1.1.1,demod:317171] equal(sk_c9,sk_c3).
% 317201 [para:317191.1.1,317164.1.2.1] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 317205 [para:317191.1.1,317186.1.1] equal(sk_c3,sk_c7).
% 317209 [para:317205.1.1,317149.1.1.2] equal(multiply(sk_c9,sk_c7),sk_c8).
% 317213 [para:317191.1.1,317175.1.1.1] equal(multiply(sk_c3,sk_c9),sk_c7).
% 317218 [para:317164.1.2,317166.1.2.2,demod:317201] equal(X,multiply(sk_c2,X)).
% 317219 [para:317185.1.2,317166.1.2.1,demod:317177] equal(multiply(sk_c3,X),multiply(sk_c9,X)).
% 317220 [para:317186.1.1,317166.1.2.2.1,demod:317218] equal(multiply(sk_c3,X),multiply(sk_c7,X)).
% 317221 [para:317218.1.2,317164.1.2.2,demod:317220,317219] equal(X,multiply(sk_c7,X)).
% 317223 [para:317221.1.2,317163.1.2.2] equal(X,multiply(inverse(sk_c7),X)).
% 317239 [para:317223.1.2,317076.1.1] equal(sk_c7,identity).
% 317243 [para:317239.1.1,317209.1.1.2,demod:317221,317220,317219] equal(identity,sk_c8).
% 317246 [para:317243.1.2,317181.1.2.2,demod:317179] equal(sk_c3,sk_c2).
% 317247 [para:317246.1.2,317124.1.1.1] equal(inverse(sk_c3),sk_c9).
% 317258 [hyper:317078,317247,demod:317213,cut:317074] 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(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% 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(47,40,0,100,0,0,1190,50,14,1243,0,14,2569,50,37,2622,0,37,4065,50,54,4118,0,54,5623,50,75,5676,0,75,7244,50,101,7297,0,101,8957,50,137,9010,0,137,10762,50,190,10815,0,190,12689,50,281,12742,0,281,14738,50,448,14791,0,448,16939,50,696,16992,0,696,19292,50,1121,19292,40,1121,19345,0,1121,31102,3,1422,31752,4,1572,32363,5,1722,32364,1,1722,32364,50,1722,32364,40,1722,32417,0,1722,32701,3,2036,32710,4,2179,32728,5,2323,32728,1,2323,32728,50,2323,32728,40,2323,32781,0,2323,63928,3,3834,64710,4,4574,65648,1,5324,65648,50,5325,65648,40,5325,65701,0,5325,84364,3,6077,85134,4,6451,85852,5,6826,85853,1,6826,85853,50,6826,85853,40,6826,85906,0,6826,100323,3,7581,101035,4,7952,102213,1,8327,102213,50,8327,102213,40,8327,102266,0,8327,160646,3,12234,161466,4,14178,162102,5,16128,162103,1,16129,162103,50,16131,162103,40,16131,162156,0,16131,206393,3,18691,207016,4,19957,207502,5,21232,207503,1,21232,207503,50,21234,207503,40,21234,207556,0,21234,246476,3,22736,247212,4,23485,247784,1,24235,247784,50,24236,247784,40,24236,247837,0,24236,260135,3,24987,261304,4,25362,261871,5,25737,261871,1,25737,261871,50,25737,261871,40,25737,261924,0,25737,293605,3,26947,294292,4,27538,294908,5,28138,294909,1,28138,294909,50,28139,294909,40,28139,294962,0,28139,316073,3,28890,316627,4,29265,317073,1,29640,317073,50,29640,317073,40,29640,317073,40,29640,317120,0,29640,317257,50,29642,317257,30,29642,317257,40,29642,317304,0,29642)
%
%
% START OF PROOF
% 317258 [] equal(X,X).
% 317262 [] -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8).
% 317286 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 317287 [?] ?
% 317293 [?] ?
% 317294 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 317319 [hyper:317262,317286,binarycut:317293] equal(inverse(sk_c5),sk_c8).
% 317321 [hyper:317262,317286,binarycut:317287] equal(inverse(sk_c1),sk_c8).
% 317350 [hyper:317262,317294,demod:317321,cut:317258] equal(multiply(sk_c5,sk_c8),sk_c9).
% 317353 [hyper:317262,317350,demod:317319,cut:317258] 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(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),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(47,40,0,100,0,0,1190,50,14,1243,0,14,2569,50,37,2622,0,37,4065,50,54,4118,0,54,5623,50,75,5676,0,75,7244,50,101,7297,0,101,8957,50,137,9010,0,137,10762,50,190,10815,0,190,12689,50,281,12742,0,281,14738,50,448,14791,0,448,16939,50,696,16992,0,696,19292,50,1121,19292,40,1121,19345,0,1121,31102,3,1422,31752,4,1572,32363,5,1722,32364,1,1722,32364,50,1722,32364,40,1722,32417,0,1722,32701,3,2036,32710,4,2179,32728,5,2323,32728,1,2323,32728,50,2323,32728,40,2323,32781,0,2323,63928,3,3834,64710,4,4574,65648,1,5324,65648,50,5325,65648,40,5325,65701,0,5325,84364,3,6077,85134,4,6451,85852,5,6826,85853,1,6826,85853,50,6826,85853,40,6826,85906,0,6826,100323,3,7581,101035,4,7952,102213,1,8327,102213,50,8327,102213,40,8327,102266,0,8327,160646,3,12234,161466,4,14178,162102,5,16128,162103,1,16129,162103,50,16131,162103,40,16131,162156,0,16131,206393,3,18691,207016,4,19957,207502,5,21232,207503,1,21232,207503,50,21234,207503,40,21234,207556,0,21234,246476,3,22736,247212,4,23485,247784,1,24235,247784,50,24236,247784,40,24236,247837,0,24236,260135,3,24987,261304,4,25362,261871,5,25737,261871,1,25737,261871,50,25737,261871,40,25737,261924,0,25737,293605,3,26947,294292,4,27538,294908,5,28138,294909,1,28138,294909,50,28139,294909,40,28139,294962,0,28139,316073,3,28890,316627,4,29265,317073,1,29640,317073,50,29640,317073,40,29640,317073,40,29640,317120,0,29640,317257,50,29642,317257,30,29642,317257,40,29642,317304,0,29642,317352,50,29642,317352,30,29642,317352,40,29642,317399,0,29648)
%
%
% START OF PROOF
% 317354 [] equal(multiply(identity,X),X).
% 317355 [] equal(multiply(inverse(X),X),identity).
% 317356 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 317357 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 317362 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c4),sk_c8).
% 317363 [?] ?
% 317369 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 317370 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 317376 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 317377 [] equal(multiply(sk_c9,sk_c3),sk_c8) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 317383 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 317384 [?] ?
% 317390 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(inverse(sk_c4),sk_c8).
% 317391 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 317397 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 317398 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 317406 [hyper:317357,317362,binarycut:317363] equal(inverse(sk_c2),sk_c9).
% 317408 [para:317406.1.1,317355.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 317420 [hyper:317357,317383,binarycut:317384] equal(inverse(sk_c1),sk_c8).
% 317424 [para:317420.1.1,317355.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 317445 [hyper:317357,317370,317369] equal(multiply(sk_c2,sk_c9),sk_c3).
% 317465 [hyper:317357,317377,317376] equal(multiply(sk_c9,sk_c3),sk_c8).
% 317470 [hyper:317357,317391,317390] equal(multiply(sk_c1,sk_c8),sk_c9).
% 317475 [hyper:317357,317398,317397] equal(multiply(sk_c8,sk_c9),sk_c7).
% 317476 [para:317355.1.1,317356.1.1.1,demod:317354] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 317477 [para:317408.1.1,317356.1.1.1,demod:317354] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 317479 [para:317445.1.1,317356.1.1.1] equal(multiply(sk_c3,X),multiply(sk_c2,multiply(sk_c9,X))).
% 317482 [para:317445.1.1,317477.1.2.2,demod:317465] equal(sk_c9,sk_c8).
% 317483 [para:317482.1.2,317424.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 317484 [para:317482.1.2,317470.1.1.2] equal(multiply(sk_c1,sk_c9),sk_c9).
% 317488 [para:317484.1.1,317356.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c1,multiply(sk_c9,X))).
% 317490 [para:317408.1.1,317476.1.2.2] equal(sk_c2,multiply(inverse(sk_c9),identity)).
% 317493 [para:317470.1.1,317476.1.2.2,demod:317475,317420] equal(sk_c8,sk_c7).
% 317496 [para:317483.1.1,317476.1.2.2,demod:317490] equal(sk_c1,sk_c2).
% 317497 [para:317484.1.1,317476.1.2.2,demod:317475,317420] equal(sk_c9,sk_c7).
% 317498 [para:317493.1.1,317424.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 317502 [para:317496.1.2,317445.1.1.1,demod:317484] equal(sk_c9,sk_c3).
% 317512 [para:317502.1.1,317477.1.2.1] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 317527 [para:317477.1.2,317479.1.2.2,demod:317512] equal(X,multiply(sk_c2,X)).
% 317528 [para:317496.1.2,317479.1.2.1,demod:317488] equal(multiply(sk_c3,X),multiply(sk_c9,X)).
% 317529 [para:317497.1.1,317479.1.2.2.1,demod:317527] equal(multiply(sk_c3,X),multiply(sk_c7,X)).
% 317530 [para:317527.1.2,317477.1.2.2,demod:317529,317528] equal(X,multiply(sk_c7,X)).
% 317533 [para:317530.1.2,317498.1.1] equal(sk_c1,identity).
% 317534 [para:317533.1.1,317420.1.1.1] equal(inverse(identity),sk_c8).
% 317535 [hyper:317357,317534,demod:317354,cut:317493] 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(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 25
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(47,40,0,100,0,0,1190,50,14,1243,0,14,2569,50,37,2622,0,37,4065,50,54,4118,0,54,5623,50,75,5676,0,75,7244,50,101,7297,0,101,8957,50,137,9010,0,137,10762,50,190,10815,0,190,12689,50,281,12742,0,281,14738,50,448,14791,0,448,16939,50,696,16992,0,696,19292,50,1121,19292,40,1121,19345,0,1121,31102,3,1422,31752,4,1572,32363,5,1722,32364,1,1722,32364,50,1722,32364,40,1722,32417,0,1722,32701,3,2036,32710,4,2179,32728,5,2323,32728,1,2323,32728,50,2323,32728,40,2323,32781,0,2323,63928,3,3834,64710,4,4574,65648,1,5324,65648,50,5325,65648,40,5325,65701,0,5325,84364,3,6077,85134,4,6451,85852,5,6826,85853,1,6826,85853,50,6826,85853,40,6826,85906,0,6826,100323,3,7581,101035,4,7952,102213,1,8327,102213,50,8327,102213,40,8327,102266,0,8327,160646,3,12234,161466,4,14178,162102,5,16128,162103,1,16129,162103,50,16131,162103,40,16131,162156,0,16131,206393,3,18691,207016,4,19957,207502,5,21232,207503,1,21232,207503,50,21234,207503,40,21234,207556,0,21234,246476,3,22736,247212,4,23485,247784,1,24235,247784,50,24236,247784,40,24236,247837,0,24236,260135,3,24987,261304,4,25362,261871,5,25737,261871,1,25737,261871,50,25737,261871,40,25737,261924,0,25737,293605,3,26947,294292,4,27538,294908,5,28138,294909,1,28138,294909,50,28139,294909,40,28139,294962,0,28139,316073,3,28890,316627,4,29265,317073,1,29640,317073,50,29640,317073,40,29640,317073,40,29640,317120,0,29640,317257,50,29642,317257,30,29642,317257,40,29642,317304,0,29642,317352,50,29642,317352,30,29642,317352,40,29642,317399,0,29648,317534,50,29648,317534,30,29648,317534,40,29648,317581,0,29648)
%
%
% START OF PROOF
% 317536 [] equal(multiply(identity,X),X).
% 317537 [] equal(multiply(inverse(X),X),identity).
% 317538 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 317539 [] -equal(multiply(sk_c9,X),sk_c8) | -equal(multiply(Y,sk_c9),X) | -equal(inverse(Y),sk_c9).
% 317540 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 317541 [] equal(multiply(sk_c6,sk_c9),sk_c7) | equal(inverse(sk_c2),sk_c9).
% 317542 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 317543 [] equal(multiply(sk_c5,sk_c8),sk_c9) | equal(inverse(sk_c2),sk_c9).
% 317544 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c4),sk_c8).
% 317545 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c9).
% 317546 [] equal(inverse(sk_c2),sk_c9) | equal(inverse(sk_c8),sk_c7).
% 317547 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c6),sk_c9).
% 317548 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 317549 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 317550 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 317551 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 317552 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 317553 [] equal(multiply(sk_c2,sk_c9),sk_c3) | equal(inverse(sk_c8),sk_c7).
% 317554 [?] ?
% 317555 [?] ?
% 317556 [?] ?
% 317557 [?] ?
% 317558 [?] ?
% 317559 [?] ?
% 317560 [?] ?
% 317631 [hyper:317539,317547,binarycut:317554,binarycut:317540] equal(inverse(sk_c6),sk_c9).
% 317641 [para:317631.1.1,317537.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 317651 [hyper:317539,317548,317541,binarycut:317555] equal(multiply(sk_c6,sk_c9),sk_c7).
% 317658 [hyper:317539,317549,binarycut:317556,binarycut:317542] equal(inverse(sk_c5),sk_c8).
% 317659 [para:317658.1.1,317537.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 317665 [hyper:317539,317550,317543,binarycut:317557] equal(multiply(sk_c5,sk_c8),sk_c9).
% 317668 [hyper:317539,317551,binarycut:317558,binarycut:317544] equal(inverse(sk_c4),sk_c8).
% 317669 [para:317668.1.1,317537.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 317672 [hyper:317539,317553,binarycut:317560,binarycut:317546] equal(inverse(sk_c8),sk_c7).
% 317676 [hyper:317539,317552,317545,binarycut:317559] equal(multiply(sk_c4,sk_c8),sk_c7).
% 317677 [para:317672.1.1,317537.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 317679 [para:317641.1.1,317538.1.1.1,demod:317536] equal(X,multiply(sk_c9,multiply(sk_c6,X))).
% 317680 [para:317651.1.1,317538.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c6,multiply(sk_c9,X))).
% 317681 [para:317659.1.1,317538.1.1.1,demod:317536] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 317683 [para:317669.1.1,317538.1.1.1,demod:317536] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 317685 [para:317677.1.1,317538.1.1.1,demod:317536] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 317688 [para:317651.1.1,317679.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c7)).
% 317692 [para:317665.1.1,317681.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c9)).
% 317696 [para:317676.1.1,317683.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 317697 [para:317696.1.2,317538.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c8,multiply(sk_c7,X))).
% 317700 [para:317659.1.1,317685.1.2.2] equal(sk_c5,multiply(sk_c7,identity)).
% 317701 [para:317669.1.1,317685.1.2.2,demod:317700] equal(sk_c4,sk_c5).
% 317703 [para:317692.1.2,317685.1.2.2,demod:317677] equal(sk_c9,identity).
% 317704 [para:317683.1.2,317685.1.2.2] equal(multiply(sk_c4,X),multiply(sk_c7,X)).
% 317707 [para:317701.1.2,317681.1.2.2.1,demod:317697,317704] equal(X,multiply(sk_c8,X)).
% 317708 [para:317703.1.1,317641.1.1.1,demod:317536] equal(sk_c6,identity).
% 317712 [para:317703.1.1,317692.1.2.2,demod:317707] equal(sk_c8,identity).
% 317716 [para:317708.1.1,317631.1.1.1] equal(inverse(identity),sk_c9).
% 317717 [para:317708.1.1,317679.1.2.2.1,demod:317536] equal(X,multiply(sk_c9,X)).
% 317719 [para:317712.1.1,317659.1.1.1,demod:317536] equal(sk_c5,identity).
% 317722 [para:317712.1.1,317676.1.1.2,demod:317700,317704] equal(sk_c5,sk_c7).
% 317723 [para:317712.1.1,317692.1.2.1,demod:317536] equal(sk_c8,sk_c9).
% 317725 [para:317719.1.1,317658.1.1.1,demod:317716] equal(sk_c9,sk_c8).
% 317733 [para:317722.1.1,317658.1.1.1] equal(inverse(sk_c7),sk_c8).
% 317736 [hyper:317539,317680,demod:317733,317688,317651,317717,cut:317725,cut:317723] 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(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),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(47,40,0,100,0,0,1190,50,14,1243,0,14,2569,50,37,2622,0,37,4065,50,54,4118,0,54,5623,50,75,5676,0,75,7244,50,101,7297,0,101,8957,50,137,9010,0,137,10762,50,190,10815,0,190,12689,50,281,12742,0,281,14738,50,448,14791,0,448,16939,50,696,16992,0,696,19292,50,1121,19292,40,1121,19345,0,1121,31102,3,1422,31752,4,1572,32363,5,1722,32364,1,1722,32364,50,1722,32364,40,1722,32417,0,1722,32701,3,2036,32710,4,2179,32728,5,2323,32728,1,2323,32728,50,2323,32728,40,2323,32781,0,2323,63928,3,3834,64710,4,4574,65648,1,5324,65648,50,5325,65648,40,5325,65701,0,5325,84364,3,6077,85134,4,6451,85852,5,6826,85853,1,6826,85853,50,6826,85853,40,6826,85906,0,6826,100323,3,7581,101035,4,7952,102213,1,8327,102213,50,8327,102213,40,8327,102266,0,8327,160646,3,12234,161466,4,14178,162102,5,16128,162103,1,16129,162103,50,16131,162103,40,16131,162156,0,16131,206393,3,18691,207016,4,19957,207502,5,21232,207503,1,21232,207503,50,21234,207503,40,21234,207556,0,21234,246476,3,22736,247212,4,23485,247784,1,24235,247784,50,24236,247784,40,24236,247837,0,24236,260135,3,24987,261304,4,25362,261871,5,25737,261871,1,25737,261871,50,25737,261871,40,25737,261924,0,25737,293605,3,26947,294292,4,27538,294908,5,28138,294909,1,28138,294909,50,28139,294909,40,28139,294962,0,28139,316073,3,28890,316627,4,29265,317073,1,29640,317073,50,29640,317073,40,29640,317073,40,29640,317120,0,29640,317257,50,29642,317257,30,29642,317257,40,29642,317304,0,29642,317352,50,29642,317352,30,29642,317352,40,29642,317399,0,29648,317534,50,29648,317534,30,29648,317534,40,29648,317581,0,29648,317735,50,29648,317735,30,29648,317735,40,29648,317782,0,29648)
%
%
% START OF PROOF
% 317736 [] equal(X,X).
% 317740 [] -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8).
% 317764 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 317765 [?] ?
% 317771 [?] ?
% 317772 [] equal(multiply(sk_c1,sk_c8),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 317797 [hyper:317740,317764,binarycut:317771] equal(inverse(sk_c5),sk_c8).
% 317799 [hyper:317740,317764,binarycut:317765] equal(inverse(sk_c1),sk_c8).
% 317828 [hyper:317740,317772,demod:317799,cut:317736] equal(multiply(sk_c5,sk_c8),sk_c9).
% 317831 [hyper:317740,317828,demod:317797,cut:317736] 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(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(sk_c8,sk_c9),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 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(47,40,0,100,0,0,1190,50,14,1243,0,14,2569,50,37,2622,0,37,4065,50,54,4118,0,54,5623,50,75,5676,0,75,7244,50,101,7297,0,101,8957,50,137,9010,0,137,10762,50,190,10815,0,190,12689,50,281,12742,0,281,14738,50,448,14791,0,448,16939,50,696,16992,0,696,19292,50,1121,19292,40,1121,19345,0,1121,31102,3,1422,31752,4,1572,32363,5,1722,32364,1,1722,32364,50,1722,32364,40,1722,32417,0,1722,32701,3,2036,32710,4,2179,32728,5,2323,32728,1,2323,32728,50,2323,32728,40,2323,32781,0,2323,63928,3,3834,64710,4,4574,65648,1,5324,65648,50,5325,65648,40,5325,65701,0,5325,84364,3,6077,85134,4,6451,85852,5,6826,85853,1,6826,85853,50,6826,85853,40,6826,85906,0,6826,100323,3,7581,101035,4,7952,102213,1,8327,102213,50,8327,102213,40,8327,102266,0,8327,160646,3,12234,161466,4,14178,162102,5,16128,162103,1,16129,162103,50,16131,162103,40,16131,162156,0,16131,206393,3,18691,207016,4,19957,207502,5,21232,207503,1,21232,207503,50,21234,207503,40,21234,207556,0,21234,246476,3,22736,247212,4,23485,247784,1,24235,247784,50,24236,247784,40,24236,247837,0,24236,260135,3,24987,261304,4,25362,261871,5,25737,261871,1,25737,261871,50,25737,261871,40,25737,261924,0,25737,293605,3,26947,294292,4,27538,294908,5,28138,294909,1,28138,294909,50,28139,294909,40,28139,294962,0,28139,316073,3,28890,316627,4,29265,317073,1,29640,317073,50,29640,317073,40,29640,317073,40,29640,317120,0,29640,317257,50,29642,317257,30,29642,317257,40,29642,317304,0,29642,317352,50,29642,317352,30,29642,317352,40,29642,317399,0,29648,317534,50,29648,317534,30,29648,317534,40,29648,317581,0,29648,317735,50,29648,317735,30,29648,317735,40,29648,317782,0,29648,317830,50,29648,317830,30,29648,317830,40,29648,317877,0,29653,318004,50,29653,318051,0,29653,318238,50,29656,318285,0,29660,318479,50,29664,318526,0,29664,318728,50,29671,318775,0,29671,318983,50,29680,319030,0,29685,319246,50,29702,319293,0,29702,319517,50,29732,319564,0,29736,319798,50,29796,319845,0,29796,320089,50,29923,320089,40,29923,320136,0,29923)
%
%
% START OF PROOF
% 319936 [?] ?
% 320091 [] equal(multiply(identity,X),X).
% 320092 [] equal(multiply(inverse(X),X),identity).
% 320093 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 320094 [] -equal(multiply(sk_c8,sk_c9),sk_c7).
% 320132 [?] ?
% 320133 [?] ?
% 320203 [input:320132,cut:320094] equal(inverse(sk_c5),sk_c8).
% 320204 [para:320203.1.1,320092.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 320223 [input:320133,cut:320094] equal(multiply(sk_c5,sk_c8),sk_c9).
% 320256 [para:320204.1.1,320093.1.1.1,demod:320091] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 320295 [para:320223.1.1,320256.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c9)).
% 320296 [para:320295.1.2,320094.1.1,cut:319936] 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 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c9,Y),sk_c8) | -equal(multiply(Z,sk_c9),Y) | -equal(inverse(Z),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(inverse(sk_c8),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 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(47,40,0,100,0,0,1190,50,14,1243,0,14,2569,50,37,2622,0,37,4065,50,54,4118,0,54,5623,50,75,5676,0,75,7244,50,101,7297,0,101,8957,50,137,9010,0,137,10762,50,190,10815,0,190,12689,50,281,12742,0,281,14738,50,448,14791,0,448,16939,50,696,16992,0,696,19292,50,1121,19292,40,1121,19345,0,1121,31102,3,1422,31752,4,1572,32363,5,1722,32364,1,1722,32364,50,1722,32364,40,1722,32417,0,1722,32701,3,2036,32710,4,2179,32728,5,2323,32728,1,2323,32728,50,2323,32728,40,2323,32781,0,2323,63928,3,3834,64710,4,4574,65648,1,5324,65648,50,5325,65648,40,5325,65701,0,5325,84364,3,6077,85134,4,6451,85852,5,6826,85853,1,6826,85853,50,6826,85853,40,6826,85906,0,6826,100323,3,7581,101035,4,7952,102213,1,8327,102213,50,8327,102213,40,8327,102266,0,8327,160646,3,12234,161466,4,14178,162102,5,16128,162103,1,16129,162103,50,16131,162103,40,16131,162156,0,16131,206393,3,18691,207016,4,19957,207502,5,21232,207503,1,21232,207503,50,21234,207503,40,21234,207556,0,21234,246476,3,22736,247212,4,23485,247784,1,24235,247784,50,24236,247784,40,24236,247837,0,24236,260135,3,24987,261304,4,25362,261871,5,25737,261871,1,25737,261871,50,25737,261871,40,25737,261924,0,25737,293605,3,26947,294292,4,27538,294908,5,28138,294909,1,28138,294909,50,28139,294909,40,28139,294962,0,28139,316073,3,28890,316627,4,29265,317073,1,29640,317073,50,29640,317073,40,29640,317073,40,29640,317120,0,29640,317257,50,29642,317257,30,29642,317257,40,29642,317304,0,29642,317352,50,29642,317352,30,29642,317352,40,29642,317399,0,29648,317534,50,29648,317534,30,29648,317534,40,29648,317581,0,29648,317735,50,29648,317735,30,29648,317735,40,29648,317782,0,29648,317830,50,29648,317830,30,29648,317830,40,29648,317877,0,29653,318004,50,29653,318051,0,29653,318238,50,29656,318285,0,29660,318479,50,29664,318526,0,29664,318728,50,29671,318775,0,29671,318983,50,29680,319030,0,29685,319246,50,29702,319293,0,29702,319517,50,29732,319564,0,29736,319798,50,29796,319845,0,29796,320089,50,29923,320089,40,29923,320136,0,29923,320295,50,29923,320295,30,29923,320295,40,29923,320342,0,29923,320473,50,29924,320520,0,29929,320707,50,29932,320754,0,29932,320941,50,29936,320988,0,29936,321196,50,29944,321243,0,29948,321458,50,29959,321505,0,29959,321728,50,29978,321775,0,29982,322007,50,30017,322054,0,30017,322296,50,30087,322343,0,30087,322596,50,30217,322596,40,30217,322643,0,30217)
%
%
% START OF PROOF
% 322598 [] equal(multiply(identity,X),X).
% 322599 [] equal(multiply(inverse(X),X),identity).
% 322600 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 322601 [] -equal(inverse(sk_c8),sk_c7).
% 322608 [?] ?
% 322615 [?] ?
% 322622 [?] ?
% 322629 [?] ?
% 322636 [?] ?
% 322643 [?] ?
% 322655 [input:322608,cut:322601] equal(inverse(sk_c2),sk_c9).
% 322656 [para:322655.1.1,322599.1.1.1] equal(multiply(sk_c9,sk_c2),identity).
% 322667 [input:322629,cut:322601] equal(inverse(sk_c1),sk_c8).
% 322668 [para:322667.1.1,322599.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 322676 [input:322615,cut:322601] equal(multiply(sk_c2,sk_c9),sk_c3).
% 322684 [input:322622,cut:322601] equal(multiply(sk_c9,sk_c3),sk_c8).
% 322695 [input:322636,cut:322601] equal(multiply(sk_c1,sk_c8),sk_c9).
% 322703 [input:322643,cut:322601] equal(multiply(sk_c8,sk_c9),sk_c7).
% 322723 [para:322599.1.1,322600.1.1.1,demod:322598] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 322725 [para:322656.1.1,322600.1.1.1,demod:322598] equal(X,multiply(sk_c9,multiply(sk_c2,X))).
% 322727 [para:322668.1.1,322600.1.1.1,demod:322598] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 322737 [para:322684.1.1,322600.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c9,multiply(sk_c3,X))).
% 322773 [para:322676.1.1,322725.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c3)).
% 322777 [para:322773.1.2,322684.1.1] equal(sk_c9,sk_c8).
% 322778 [para:322773.1.2,322600.1.1.1,demod:322737] equal(multiply(sk_c9,X),multiply(sk_c8,X)).
% 322781 [para:322777.1.2,322668.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 322789 [para:322777.1.2,322695.1.1.2] equal(multiply(sk_c1,sk_c9),sk_c9).
% 322794 [para:322777.1.2,322703.1.1.1] equal(multiply(sk_c9,sk_c9),sk_c7).
% 322803 [para:322781.1.1,322600.1.1.1,demod:322598] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 322810 [para:322695.1.1,322727.1.2.2,demod:322794,322778] equal(sk_c8,sk_c7).
% 322811 [para:322789.1.1,322727.1.2.2,demod:322794,322778] equal(sk_c9,sk_c7).
% 322812 [para:322810.1.1,322601.1.1.1] -equal(inverse(sk_c7),sk_c7).
% 322822 [para:322810.1.1,322695.1.1.2] equal(multiply(sk_c1,sk_c7),sk_c9).
% 322827 [para:322810.1.1,322703.1.1.1] equal(multiply(sk_c7,sk_c9),sk_c7).
% 322842 [para:322811.1.1,322676.1.1.2] equal(multiply(sk_c2,sk_c7),sk_c3).
% 322862 [para:322822.1.1,322600.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c1,multiply(sk_c7,X))).
% 322878 [para:322810.1.1,322778.1.2.1] equal(multiply(sk_c9,X),multiply(sk_c7,X)).
% 322940 [para:322725.1.2,322723.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c9),X)).
% 322943 [para:322794.1.1,322723.1.2.2,demod:322842,322940] equal(sk_c9,sk_c3).
% 322944 [para:322727.1.2,322723.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c8),X)).
% 322947 [para:322827.1.1,322723.1.2.2,demod:322599] equal(sk_c9,identity).
% 322954 [para:322778.1.2,322723.1.2.2,demod:322862,322944,322878] equal(X,multiply(sk_c7,X)).
% 322955 [para:322803.1.2,322723.1.2.2,demod:322940] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 322957 [para:322878.1.1,322723.1.2.2,demod:322955,322940,322954] equal(X,multiply(sk_c1,X)).
% 322973 [para:322943.1.1,322725.1.2.1,demod:322957,322955] equal(X,multiply(sk_c3,X)).
% 322975 [para:322943.1.1,322781.1.1.1,demod:322973] equal(sk_c1,identity).
% 322992 [para:322947.1.1,322703.1.1.2,demod:322954,322878,322778] equal(identity,sk_c7).
% 323011 [para:322975.1.1,322667.1.1.1] equal(inverse(identity),sk_c8).
% 323031 [para:322992.1.2,322812.1.1.1,demod:323011,cut:322810] 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: 32737
% derived clauses: 5412913
% kept clauses: 268579
% kept size sum: 28462
% kept mid-nuclei: 14598
% kept new demods: 4390
% forw unit-subs: 2003565
% forw double-subs: 2841220
% forw overdouble-subs: 243422
% backward subs: 12156
% fast unit cutoff: 28404
% full unit cutoff: 0
% dbl unit cutoff: 8200
% real runtime : 303.97
% process. runtime: 302.19
% specific non-discr-tree subsumption statistics:
% tried: 28049414
% length fails: 2281106
% strength fails: 7470326
% predlist fails: 980959
% aux str. fails: 2836169
% by-lit fails: 7012125
% full subs tried: 1879118
% full subs fail: 1750140
%
% ; 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/GRP329-1+eq_r.in")
%
%------------------------------------------------------------------------------