TSTP Solution File: GRP336-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP336-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art08.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 297.9s
% Output : Assurance 297.9s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP336-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 27)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 27)
% (binary-posweight-lex-big-order 30 #f 3 27)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c10) | -equal(multiply(V,sk_c9),sk_c10) | -equal(multiply(W,X1),sk_c9) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c8),sk_c9).
% was split for some strategies as:
% -equal(multiply(W,X1),sk_c9) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c8),sk_c9).
% -equal(inverse(V),sk_c10) | -equal(multiply(V,sk_c9),sk_c10).
% -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10).
% -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9).
% -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10).
% -equal(multiply(sk_c9,sk_c10),sk_c8).
% -equal(multiply(sk_c10,sk_c8),sk_c9).
%
% 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_c9,sk_c10),sk_c8) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c10) | -equal(multiply(V,sk_c9),sk_c10) | -equal(multiply(W,X1),sk_c9) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c8),sk_c9).
% Split part used next: -equal(multiply(W,X1),sk_c9) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c8),sk_c9).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,112,0,1,2349,50,26,2408,0,26,5517,50,62,5576,0,62,9086,50,108,9145,0,108,12896,50,165,12955,0,165,16947,50,238,17006,0,238,21318,50,333,21377,0,334,26010,50,466,26069,0,466,31102,50,666,31161,0,667,36595,50,944,36595,40,944,36654,0,944,48609,3,1245,49300,4,1395,49950,5,1545,49951,1,1545,49951,50,1545,49951,40,1545,50010,0,1545,50327,3,1847,50337,4,2008,50347,5,2146,50347,1,2146,50347,50,2146,50347,40,2146,50406,0,2146,82156,3,3658,83050,4,4397,83820,5,5147,83821,1,5147,83821,50,5148,83821,40,5148,83880,0,5148,101839,3,5901,102750,4,6274,103672,5,6649,103673,1,6649,103673,50,6649,103673,40,6649,103732,0,6649,112501,3,7450,114266,4,7775,116192,5,8150,116193,5,8150,116193,1,8150,116193,50,8150,116193,40,8150,116252,0,8150,190871,3,12052,192105,4,14002,193102,5,15952,193103,1,15952,193103,50,15954,193103,40,15954,193162,0,15954,252259,3,18507,253215,4,19780,254000,5,21055,254001,1,21055,254001,50,21057,254001,40,21057,254060,0,21057,296683,3,22559,297394,4,23308,298176,5,24058,298177,1,24058,298177,50,24059,298177,40,24059,298236,0,24059,319089,3,24810,319632,4,25185,320134,5,25560,320135,1,25560,320135,50,25561,320135,40,25561,320194,0,25561,350703,3,26763,351491,4,27362,352102,1,27962,352102,50,27963,352102,40,27963,352161,0,27963,374211,3,28715,374860,4,29089,375279,5,29464,375280,1,29464,375280,50,29464,375280,40,29464,375280,40,29464,375333,0,29464)
%
%
% START OF PROOF
% 375281 [] equal(X,X).
% 375282 [] equal(multiply(identity,X),X).
% 375283 [] equal(multiply(inverse(X),X),identity).
% 375284 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 375285 [] -equal(multiply(X,sk_c8),sk_c9) | -equal(multiply(Y,X),sk_c9) | -equal(inverse(Y),X).
% 375286 [] equal(multiply(sk_c3,sk_c10),sk_c9) | equal(multiply(sk_c7,sk_c8),sk_c9).
% 375287 [] equal(multiply(sk_c3,sk_c10),sk_c9) | equal(inverse(sk_c6),sk_c7).
% 375288 [] equal(multiply(sk_c3,sk_c10),sk_c9) | equal(multiply(sk_c6,sk_c7),sk_c9).
% 375294 [?] ?
% 375295 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c6),sk_c7).
% 375296 [?] ?
% 375302 [] equal(multiply(sk_c2,sk_c3),sk_c9) | equal(multiply(sk_c7,sk_c8),sk_c9).
% 375303 [] equal(multiply(sk_c2,sk_c3),sk_c9) | equal(inverse(sk_c6),sk_c7).
% 375304 [] equal(multiply(sk_c2,sk_c3),sk_c9) | equal(multiply(sk_c6,sk_c7),sk_c9).
% 375310 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c7,sk_c8),sk_c9).
% 375311 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(inverse(sk_c6),sk_c7).
% 375312 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c6,sk_c7),sk_c9).
% 375318 [?] ?
% 375319 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c6),sk_c7).
% 375320 [?] ?
% 375326 [] equal(multiply(sk_c9,sk_c10),sk_c8) | equal(multiply(sk_c7,sk_c8),sk_c9).
% 375327 [] equal(multiply(sk_c9,sk_c10),sk_c8) | equal(inverse(sk_c6),sk_c7).
% 375328 [] equal(multiply(sk_c9,sk_c10),sk_c8) | equal(multiply(sk_c6,sk_c7),sk_c9).
% 375340 [hyper:375285,375295,binarycut:375296,binarycut:375294] equal(inverse(sk_c2),sk_c3).
% 375342 [para:375340.1.1,375283.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 375347 [hyper:375285,375319,binarycut:375320,binarycut:375318] equal(inverse(sk_c1),sk_c10).
% 375350 [para:375347.1.1,375283.1.1.1] equal(multiply(sk_c10,sk_c1),identity).
% 375394 [hyper:375285,375288,375286,375287] equal(multiply(sk_c3,sk_c10),sk_c9).
% 375425 [hyper:375285,375304,375302,375303] equal(multiply(sk_c2,sk_c3),sk_c9).
% 375438 [hyper:375285,375312,375310,375311] equal(multiply(sk_c1,sk_c9),sk_c10).
% 375451 [hyper:375285,375328,375326,375327] equal(multiply(sk_c9,sk_c10),sk_c8).
% 375452 [para:375283.1.1,375284.1.1.1,demod:375282] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 375453 [para:375342.1.1,375284.1.1.1,demod:375282] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 375454 [para:375350.1.1,375284.1.1.1,demod:375282] equal(X,multiply(sk_c10,multiply(sk_c1,X))).
% 375455 [para:375394.1.1,375284.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c3,multiply(sk_c10,X))).
% 375456 [para:375425.1.1,375284.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c2,multiply(sk_c3,X))).
% 375457 [para:375438.1.1,375284.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c1,multiply(sk_c9,X))).
% 375458 [para:375451.1.1,375284.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c9,multiply(sk_c10,X))).
% 375461 [para:375425.1.1,375453.1.2.2] equal(sk_c3,multiply(sk_c3,sk_c9)).
% 375465 [para:375438.1.1,375454.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 375470 [para:375342.1.1,375452.1.2.2] equal(sk_c2,multiply(inverse(sk_c3),identity)).
% 375472 [para:375394.1.1,375452.1.2.2] equal(sk_c10,multiply(inverse(sk_c3),sk_c9)).
% 375474 [para:375453.1.2,375452.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c3),X)).
% 375478 [para:375472.1.2,375284.1.1.1,demod:375474] equal(multiply(sk_c10,X),multiply(sk_c2,multiply(sk_c9,X))).
% 375482 [para:375465.1.2,375455.1.2.2,demod:375461,375451] equal(sk_c8,sk_c3).
% 375487 [para:375482.1.2,375461.1.2.1] equal(sk_c3,multiply(sk_c8,sk_c9)).
% 375501 [para:375394.1.1,375456.1.2.2,demod:375451] equal(sk_c8,multiply(sk_c2,sk_c9)).
% 375503 [para:375461.1.2,375456.1.2.2,demod:375425] equal(multiply(sk_c9,sk_c9),sk_c9).
% 375504 [para:375455.1.2,375456.1.2.2,demod:375478,375458] equal(multiply(sk_c8,X),multiply(sk_c10,X)).
% 375505 [para:375501.1.2,375453.1.2.2] equal(sk_c9,multiply(sk_c3,sk_c8)).
% 375511 [para:375503.1.1,375452.1.2.2,demod:375283] equal(sk_c9,identity).
% 375512 [para:375503.1.1,375457.1.2.2,demod:375438,375487,375504] equal(sk_c3,sk_c10).
% 375514 [para:375511.1.1,375451.1.1.1,demod:375282] equal(sk_c10,sk_c8).
% 375516 [para:375511.1.1,375472.1.2.2,demod:375470] equal(sk_c10,sk_c2).
% 375525 [para:375512.1.2,375465.1.2.2,demod:375504] equal(sk_c9,multiply(sk_c8,sk_c3)).
% 375540 [para:375516.1.1,375514.1.1] equal(sk_c2,sk_c8).
% 375549 [para:375540.1.1,375340.1.1.1] equal(inverse(sk_c8),sk_c3).
% 375551 [hyper:375285,375549,demod:375505,375525,cut:375281,cut:375281] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 27
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c10) | -equal(multiply(V,sk_c9),sk_c10) | -equal(multiply(W,X1),sk_c9) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c8),sk_c9).
% Split part used next: -equal(inverse(V),sk_c10) | -equal(multiply(V,sk_c9),sk_c10).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 27
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,112,0,1,2349,50,26,2408,0,26,5517,50,62,5576,0,62,9086,50,108,9145,0,108,12896,50,165,12955,0,165,16947,50,238,17006,0,238,21318,50,333,21377,0,334,26010,50,466,26069,0,466,31102,50,666,31161,0,667,36595,50,944,36595,40,944,36654,0,944,48609,3,1245,49300,4,1395,49950,5,1545,49951,1,1545,49951,50,1545,49951,40,1545,50010,0,1545,50327,3,1847,50337,4,2008,50347,5,2146,50347,1,2146,50347,50,2146,50347,40,2146,50406,0,2146,82156,3,3658,83050,4,4397,83820,5,5147,83821,1,5147,83821,50,5148,83821,40,5148,83880,0,5148,101839,3,5901,102750,4,6274,103672,5,6649,103673,1,6649,103673,50,6649,103673,40,6649,103732,0,6649,112501,3,7450,114266,4,7775,116192,5,8150,116193,5,8150,116193,1,8150,116193,50,8150,116193,40,8150,116252,0,8150,190871,3,12052,192105,4,14002,193102,5,15952,193103,1,15952,193103,50,15954,193103,40,15954,193162,0,15954,252259,3,18507,253215,4,19780,254000,5,21055,254001,1,21055,254001,50,21057,254001,40,21057,254060,0,21057,296683,3,22559,297394,4,23308,298176,5,24058,298177,1,24058,298177,50,24059,298177,40,24059,298236,0,24059,319089,3,24810,319632,4,25185,320134,5,25560,320135,1,25560,320135,50,25561,320135,40,25561,320194,0,25561,350703,3,26763,351491,4,27362,352102,1,27962,352102,50,27963,352102,40,27963,352161,0,27963,374211,3,28715,374860,4,29089,375279,5,29464,375280,1,29464,375280,50,29464,375280,40,29464,375280,40,29464,375333,0,29464,375550,50,29464,375550,30,29464,375550,40,29464,375603,0,29464)
%
%
% START OF PROOF
% 375551 [] equal(X,X).
% 375555 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c10).
% 375583 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c9),sk_c10).
% 375584 [?] ?
% 375591 [?] ?
% 375592 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c5),sk_c10).
% 375617 [hyper:375555,375592,binarycut:375584] equal(inverse(sk_c5),sk_c10).
% 375619 [hyper:375555,375592,binarycut:375591] equal(inverse(sk_c1),sk_c10).
% 375651 [hyper:375555,375583,demod:375619,cut:375551] equal(multiply(sk_c5,sk_c9),sk_c10).
% 375653 [hyper:375555,375651,demod:375617,cut:375551] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 27
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c10) | -equal(multiply(V,sk_c9),sk_c10) | -equal(multiply(W,X1),sk_c9) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c8),sk_c9).
% Split part used next: -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 27
% clause depth limited to 3
% seconds given: 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% clause depth limited to 10
% 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(53,40,0,112,0,1,2349,50,26,2408,0,26,5517,50,62,5576,0,62,9086,50,108,9145,0,108,12896,50,165,12955,0,165,16947,50,238,17006,0,238,21318,50,333,21377,0,334,26010,50,466,26069,0,466,31102,50,666,31161,0,667,36595,50,944,36595,40,944,36654,0,944,48609,3,1245,49300,4,1395,49950,5,1545,49951,1,1545,49951,50,1545,49951,40,1545,50010,0,1545,50327,3,1847,50337,4,2008,50347,5,2146,50347,1,2146,50347,50,2146,50347,40,2146,50406,0,2146,82156,3,3658,83050,4,4397,83820,5,5147,83821,1,5147,83821,50,5148,83821,40,5148,83880,0,5148,101839,3,5901,102750,4,6274,103672,5,6649,103673,1,6649,103673,50,6649,103673,40,6649,103732,0,6649,112501,3,7450,114266,4,7775,116192,5,8150,116193,5,8150,116193,1,8150,116193,50,8150,116193,40,8150,116252,0,8150,190871,3,12052,192105,4,14002,193102,5,15952,193103,1,15952,193103,50,15954,193103,40,15954,193162,0,15954,252259,3,18507,253215,4,19780,254000,5,21055,254001,1,21055,254001,50,21057,254001,40,21057,254060,0,21057,296683,3,22559,297394,4,23308,298176,5,24058,298177,1,24058,298177,50,24059,298177,40,24059,298236,0,24059,319089,3,24810,319632,4,25185,320134,5,25560,320135,1,25560,320135,50,25561,320135,40,25561,320194,0,25561,350703,3,26763,351491,4,27362,352102,1,27962,352102,50,27963,352102,40,27963,352161,0,27963,374211,3,28715,374860,4,29089,375279,5,29464,375280,1,29464,375280,50,29464,375280,40,29464,375280,40,29464,375333,0,29464,375550,50,29464,375550,30,29464,375550,40,29464,375603,0,29464,375652,50,29464,375652,30,29464,375652,40,29464,375705,0,29470,375893,50,29471,375946,0,29471,376189,50,29476,376242,0,29480,376495,50,29487,376548,0,29487,376811,50,29498,376864,0,29504,377138,50,29520,377191,0,29520,377480,50,29548,377533,0,29553,377838,50,29603,377891,0,29603,378215,50,29703,378215,40,29703,378268,0,29703)
%
%
% START OF PROOF
% 378063 [?] ?
% 378216 [] equal(X,X).
% 378217 [] equal(multiply(identity,X),X).
% 378218 [] equal(multiply(inverse(X),X),identity).
% 378219 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 378220 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(inverse(X),sk_c10).
% 378277 [para:378218.1.1,378220.1.1,cut:378063] -equal(inverse(inverse(sk_c10)),sk_c10).
% 378378 [para:378218.1.1,378219.1.1.1,demod:378217] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 378465 [para:378218.1.1,378378.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 378580 [para:378378.1.2,378378.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 378661 [para:378580.1.2,378465.1.2] equal(X,multiply(X,identity)).
% 378667 [para:378661.1.2,378465.1.2] equal(X,inverse(inverse(X))).
% 378678 [para:378667.1.2,378277.1.1,cut:378216] 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 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c10) | -equal(multiply(V,sk_c9),sk_c10) | -equal(multiply(W,X1),sk_c9) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c8),sk_c9).
% Split part used next: -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 27
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,112,0,1,2349,50,26,2408,0,26,5517,50,62,5576,0,62,9086,50,108,9145,0,108,12896,50,165,12955,0,165,16947,50,238,17006,0,238,21318,50,333,21377,0,334,26010,50,466,26069,0,466,31102,50,666,31161,0,667,36595,50,944,36595,40,944,36654,0,944,48609,3,1245,49300,4,1395,49950,5,1545,49951,1,1545,49951,50,1545,49951,40,1545,50010,0,1545,50327,3,1847,50337,4,2008,50347,5,2146,50347,1,2146,50347,50,2146,50347,40,2146,50406,0,2146,82156,3,3658,83050,4,4397,83820,5,5147,83821,1,5147,83821,50,5148,83821,40,5148,83880,0,5148,101839,3,5901,102750,4,6274,103672,5,6649,103673,1,6649,103673,50,6649,103673,40,6649,103732,0,6649,112501,3,7450,114266,4,7775,116192,5,8150,116193,5,8150,116193,1,8150,116193,50,8150,116193,40,8150,116252,0,8150,190871,3,12052,192105,4,14002,193102,5,15952,193103,1,15952,193103,50,15954,193103,40,15954,193162,0,15954,252259,3,18507,253215,4,19780,254000,5,21055,254001,1,21055,254001,50,21057,254001,40,21057,254060,0,21057,296683,3,22559,297394,4,23308,298176,5,24058,298177,1,24058,298177,50,24059,298177,40,24059,298236,0,24059,319089,3,24810,319632,4,25185,320134,5,25560,320135,1,25560,320135,50,25561,320135,40,25561,320194,0,25561,350703,3,26763,351491,4,27362,352102,1,27962,352102,50,27963,352102,40,27963,352161,0,27963,374211,3,28715,374860,4,29089,375279,5,29464,375280,1,29464,375280,50,29464,375280,40,29464,375280,40,29464,375333,0,29464,375550,50,29464,375550,30,29464,375550,40,29464,375603,0,29464,375652,50,29464,375652,30,29464,375652,40,29464,375705,0,29470,375893,50,29471,375946,0,29471,376189,50,29476,376242,0,29480,376495,50,29487,376548,0,29487,376811,50,29498,376864,0,29504,377138,50,29520,377191,0,29520,377480,50,29548,377533,0,29553,377838,50,29603,377891,0,29603,378215,50,29703,378215,40,29703,378268,0,29703,378677,50,29704,378677,30,29704,378677,40,29704,378730,0,29704)
%
%
% START OF PROOF
% 378678 [] equal(X,X).
% 378679 [] equal(multiply(identity,X),X).
% 378680 [] equal(multiply(inverse(X),X),identity).
% 378681 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 378682 [] -equal(multiply(X,sk_c10),sk_c9) | -equal(multiply(Y,X),sk_c9) | -equal(inverse(Y),X).
% 378686 [?] ?
% 378687 [?] ?
% 378688 [] equal(multiply(sk_c3,sk_c10),sk_c9) | equal(multiply(sk_c10,sk_c8),sk_c9).
% 378689 [?] ?
% 378690 [?] ?
% 378694 [] equal(multiply(sk_c5,sk_c9),sk_c10) | equal(inverse(sk_c2),sk_c3).
% 378695 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c5),sk_c10).
% 378696 [] equal(multiply(sk_c10,sk_c8),sk_c9) | equal(inverse(sk_c2),sk_c3).
% 378697 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c4),sk_c10).
% 378698 [] equal(multiply(sk_c4,sk_c10),sk_c9) | equal(inverse(sk_c2),sk_c3).
% 378702 [?] ?
% 378703 [?] ?
% 378704 [?] ?
% 378705 [?] ?
% 378706 [?] ?
% 378743 [hyper:378682,378695,binarycut:378703,binarycut:378687] equal(inverse(sk_c5),sk_c10).
% 378751 [hyper:378682,378697,binarycut:378705,binarycut:378689] equal(inverse(sk_c4),sk_c10).
% 378789 [hyper:378682,378694,binarycut:378702,binarycut:378686] equal(multiply(sk_c5,sk_c9),sk_c10).
% 378800 [hyper:378682,378696,binarycut:378704,binarycut:378688] equal(multiply(sk_c10,sk_c8),sk_c9).
% 378808 [hyper:378682,378698,binarycut:378706,binarycut:378690] equal(multiply(sk_c4,sk_c10),sk_c9).
% 378815 [para:378680.1.1,378681.1.1.1,demod:378679] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 378834 [para:378789.1.1,378815.1.2.2,demod:378743] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 378835 [para:378800.1.1,378815.1.2.2] equal(sk_c8,multiply(inverse(sk_c10),sk_c9)).
% 378841 [para:378834.1.2,378815.1.2.2,demod:378835] equal(sk_c10,sk_c8).
% 378845 [para:378841.1.1,378808.1.1.2] equal(multiply(sk_c4,sk_c8),sk_c9).
% 378846 [para:378841.1.1,378834.1.2.1] equal(sk_c9,multiply(sk_c8,sk_c10)).
% 378868 [hyper:378682,378845,demod:378751,378846,cut:378678,cut:378841] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 27
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c10) | -equal(multiply(V,sk_c9),sk_c10) | -equal(multiply(W,X1),sk_c9) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c8),sk_c9).
% Split part used next: -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 27
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,112,0,1,2349,50,26,2408,0,26,5517,50,62,5576,0,62,9086,50,108,9145,0,108,12896,50,165,12955,0,165,16947,50,238,17006,0,238,21318,50,333,21377,0,334,26010,50,466,26069,0,466,31102,50,666,31161,0,667,36595,50,944,36595,40,944,36654,0,944,48609,3,1245,49300,4,1395,49950,5,1545,49951,1,1545,49951,50,1545,49951,40,1545,50010,0,1545,50327,3,1847,50337,4,2008,50347,5,2146,50347,1,2146,50347,50,2146,50347,40,2146,50406,0,2146,82156,3,3658,83050,4,4397,83820,5,5147,83821,1,5147,83821,50,5148,83821,40,5148,83880,0,5148,101839,3,5901,102750,4,6274,103672,5,6649,103673,1,6649,103673,50,6649,103673,40,6649,103732,0,6649,112501,3,7450,114266,4,7775,116192,5,8150,116193,5,8150,116193,1,8150,116193,50,8150,116193,40,8150,116252,0,8150,190871,3,12052,192105,4,14002,193102,5,15952,193103,1,15952,193103,50,15954,193103,40,15954,193162,0,15954,252259,3,18507,253215,4,19780,254000,5,21055,254001,1,21055,254001,50,21057,254001,40,21057,254060,0,21057,296683,3,22559,297394,4,23308,298176,5,24058,298177,1,24058,298177,50,24059,298177,40,24059,298236,0,24059,319089,3,24810,319632,4,25185,320134,5,25560,320135,1,25560,320135,50,25561,320135,40,25561,320194,0,25561,350703,3,26763,351491,4,27362,352102,1,27962,352102,50,27963,352102,40,27963,352161,0,27963,374211,3,28715,374860,4,29089,375279,5,29464,375280,1,29464,375280,50,29464,375280,40,29464,375280,40,29464,375333,0,29464,375550,50,29464,375550,30,29464,375550,40,29464,375603,0,29464,375652,50,29464,375652,30,29464,375652,40,29464,375705,0,29470,375893,50,29471,375946,0,29471,376189,50,29476,376242,0,29480,376495,50,29487,376548,0,29487,376811,50,29498,376864,0,29504,377138,50,29520,377191,0,29520,377480,50,29548,377533,0,29553,377838,50,29603,377891,0,29603,378215,50,29703,378215,40,29703,378268,0,29703,378677,50,29704,378677,30,29704,378677,40,29704,378730,0,29704,378867,50,29704,378867,30,29704,378867,40,29704,378920,0,29708)
%
%
% START OF PROOF
% 378868 [] equal(X,X).
% 378872 [] -equal(multiply(X,sk_c9),sk_c10) | -equal(inverse(X),sk_c10).
% 378900 [] equal(multiply(sk_c1,sk_c9),sk_c10) | equal(multiply(sk_c5,sk_c9),sk_c10).
% 378901 [?] ?
% 378908 [?] ?
% 378909 [] equal(inverse(sk_c1),sk_c10) | equal(inverse(sk_c5),sk_c10).
% 378934 [hyper:378872,378909,binarycut:378901] equal(inverse(sk_c5),sk_c10).
% 378936 [hyper:378872,378909,binarycut:378908] equal(inverse(sk_c1),sk_c10).
% 378968 [hyper:378872,378900,demod:378936,cut:378868] equal(multiply(sk_c5,sk_c9),sk_c10).
% 378970 [hyper:378872,378968,demod:378934,cut:378868] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 27
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c9,sk_c10),sk_c8) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c10) | -equal(multiply(V,sk_c9),sk_c10) | -equal(multiply(W,X1),sk_c9) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c8),sk_c9).
% Split part used next: -equal(multiply(sk_c9,sk_c10),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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% clause depth limited to 10
% 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(53,40,0,112,0,1,2349,50,26,2408,0,26,5517,50,62,5576,0,62,9086,50,108,9145,0,108,12896,50,165,12955,0,165,16947,50,238,17006,0,238,21318,50,333,21377,0,334,26010,50,466,26069,0,466,31102,50,666,31161,0,667,36595,50,944,36595,40,944,36654,0,944,48609,3,1245,49300,4,1395,49950,5,1545,49951,1,1545,49951,50,1545,49951,40,1545,50010,0,1545,50327,3,1847,50337,4,2008,50347,5,2146,50347,1,2146,50347,50,2146,50347,40,2146,50406,0,2146,82156,3,3658,83050,4,4397,83820,5,5147,83821,1,5147,83821,50,5148,83821,40,5148,83880,0,5148,101839,3,5901,102750,4,6274,103672,5,6649,103673,1,6649,103673,50,6649,103673,40,6649,103732,0,6649,112501,3,7450,114266,4,7775,116192,5,8150,116193,5,8150,116193,1,8150,116193,50,8150,116193,40,8150,116252,0,8150,190871,3,12052,192105,4,14002,193102,5,15952,193103,1,15952,193103,50,15954,193103,40,15954,193162,0,15954,252259,3,18507,253215,4,19780,254000,5,21055,254001,1,21055,254001,50,21057,254001,40,21057,254060,0,21057,296683,3,22559,297394,4,23308,298176,5,24058,298177,1,24058,298177,50,24059,298177,40,24059,298236,0,24059,319089,3,24810,319632,4,25185,320134,5,25560,320135,1,25560,320135,50,25561,320135,40,25561,320194,0,25561,350703,3,26763,351491,4,27362,352102,1,27962,352102,50,27963,352102,40,27963,352161,0,27963,374211,3,28715,374860,4,29089,375279,5,29464,375280,1,29464,375280,50,29464,375280,40,29464,375280,40,29464,375333,0,29464,375550,50,29464,375550,30,29464,375550,40,29464,375603,0,29464,375652,50,29464,375652,30,29464,375652,40,29464,375705,0,29470,375893,50,29471,375946,0,29471,376189,50,29476,376242,0,29480,376495,50,29487,376548,0,29487,376811,50,29498,376864,0,29504,377138,50,29520,377191,0,29520,377480,50,29548,377533,0,29553,377838,50,29603,377891,0,29603,378215,50,29703,378215,40,29703,378268,0,29703,378677,50,29704,378677,30,29704,378677,40,29704,378730,0,29704,378867,50,29704,378867,30,29704,378867,40,29704,378920,0,29708,378969,50,29708,378969,30,29708,378969,40,29708,379022,0,29708,379187,50,29709,379240,0,29714,379467,50,29720,379520,0,29720,379757,50,29729,379810,0,29734,380057,50,29748,380110,0,29748,380369,50,29768,380422,0,29773,380696,50,29808,380749,0,29808,381039,50,29872,381092,0,29872,381401,50,29987,381401,40,29987,381454,0,29987)
%
%
% START OF PROOF
% 381403 [] equal(multiply(identity,X),X).
% 381404 [] equal(multiply(inverse(X),X),identity).
% 381405 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 381406 [] -equal(multiply(sk_c9,sk_c10),sk_c8).
% 381450 [?] ?
% 381451 [?] ?
% 381452 [?] ?
% 381453 [?] ?
% 381454 [?] ?
% 381518 [input:381451,cut:381406] equal(inverse(sk_c5),sk_c10).
% 381519 [para:381518.1.1,381404.1.1.1] equal(multiply(sk_c10,sk_c5),identity).
% 381520 [input:381453,cut:381406] equal(inverse(sk_c4),sk_c10).
% 381521 [para:381520.1.1,381404.1.1.1] equal(multiply(sk_c10,sk_c4),identity).
% 381540 [input:381450,cut:381406] equal(multiply(sk_c5,sk_c9),sk_c10).
% 381541 [input:381452,cut:381406] equal(multiply(sk_c10,sk_c8),sk_c9).
% 381542 [input:381454,cut:381406] equal(multiply(sk_c4,sk_c10),sk_c9).
% 381544 [para:381404.1.1,381405.1.1.1,demod:381403] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 381575 [para:381519.1.1,381405.1.1.1,demod:381403] equal(X,multiply(sk_c10,multiply(sk_c5,X))).
% 381578 [para:381521.1.1,381405.1.1.1,demod:381403] equal(X,multiply(sk_c10,multiply(sk_c4,X))).
% 381605 [para:381540.1.1,381405.1.1.1] equal(multiply(sk_c10,X),multiply(sk_c5,multiply(sk_c9,X))).
% 381621 [para:381540.1.1,381575.1.2.2] equal(sk_c9,multiply(sk_c10,sk_c10)).
% 381704 [para:381541.1.1,381544.1.2.2] equal(sk_c8,multiply(inverse(sk_c10),sk_c9)).
% 381710 [para:381575.1.2,381544.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c10),X)).
% 381711 [para:381621.1.2,381544.1.2.2,demod:381704] equal(sk_c10,sk_c8).
% 381712 [para:381578.1.2,381544.1.2.2,demod:381710] equal(multiply(sk_c4,X),multiply(sk_c5,X)).
% 381743 [para:381711.1.1,381542.1.1.2] equal(multiply(sk_c4,sk_c8),sk_c9).
% 381754 [para:381743.1.1,381405.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c4,multiply(sk_c8,X))).
% 381764 [para:381704.1.2,381405.1.1.1,demod:381605,381710] equal(multiply(sk_c8,X),multiply(sk_c10,X)).
% 381768 [para:381764.1.2,381544.1.2.2,demod:381754,381712,381710] equal(X,multiply(sk_c9,X)).
% 381769 [para:381768.1.2,381406.1.1,cut:381711] 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_c9,sk_c10),sk_c8) | -equal(inverse(X),sk_c10) | -equal(multiply(X,sk_c9),sk_c10) | -equal(multiply(Y,Z),sk_c9) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c10),sk_c9) | -equal(multiply(U,sk_c10),sk_c9) | -equal(inverse(U),sk_c10) | -equal(multiply(sk_c10,sk_c8),sk_c9) | -equal(inverse(V),sk_c10) | -equal(multiply(V,sk_c9),sk_c10) | -equal(multiply(W,X1),sk_c9) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c8),sk_c9).
% Split part used next: -equal(multiply(sk_c10,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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% 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 27
% clause depth limited to 10
% 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(53,40,0,112,0,1,2349,50,26,2408,0,26,5517,50,62,5576,0,62,9086,50,108,9145,0,108,12896,50,165,12955,0,165,16947,50,238,17006,0,238,21318,50,333,21377,0,334,26010,50,466,26069,0,466,31102,50,666,31161,0,667,36595,50,944,36595,40,944,36654,0,944,48609,3,1245,49300,4,1395,49950,5,1545,49951,1,1545,49951,50,1545,49951,40,1545,50010,0,1545,50327,3,1847,50337,4,2008,50347,5,2146,50347,1,2146,50347,50,2146,50347,40,2146,50406,0,2146,82156,3,3658,83050,4,4397,83820,5,5147,83821,1,5147,83821,50,5148,83821,40,5148,83880,0,5148,101839,3,5901,102750,4,6274,103672,5,6649,103673,1,6649,103673,50,6649,103673,40,6649,103732,0,6649,112501,3,7450,114266,4,7775,116192,5,8150,116193,5,8150,116193,1,8150,116193,50,8150,116193,40,8150,116252,0,8150,190871,3,12052,192105,4,14002,193102,5,15952,193103,1,15952,193103,50,15954,193103,40,15954,193162,0,15954,252259,3,18507,253215,4,19780,254000,5,21055,254001,1,21055,254001,50,21057,254001,40,21057,254060,0,21057,296683,3,22559,297394,4,23308,298176,5,24058,298177,1,24058,298177,50,24059,298177,40,24059,298236,0,24059,319089,3,24810,319632,4,25185,320134,5,25560,320135,1,25560,320135,50,25561,320135,40,25561,320194,0,25561,350703,3,26763,351491,4,27362,352102,1,27962,352102,50,27963,352102,40,27963,352161,0,27963,374211,3,28715,374860,4,29089,375279,5,29464,375280,1,29464,375280,50,29464,375280,40,29464,375280,40,29464,375333,0,29464,375550,50,29464,375550,30,29464,375550,40,29464,375603,0,29464,375652,50,29464,375652,30,29464,375652,40,29464,375705,0,29470,375893,50,29471,375946,0,29471,376189,50,29476,376242,0,29480,376495,50,29487,376548,0,29487,376811,50,29498,376864,0,29504,377138,50,29520,377191,0,29520,377480,50,29548,377533,0,29553,377838,50,29603,377891,0,29603,378215,50,29703,378215,40,29703,378268,0,29703,378677,50,29704,378677,30,29704,378677,40,29704,378730,0,29704,378867,50,29704,378867,30,29704,378867,40,29704,378920,0,29708,378969,50,29708,378969,30,29708,378969,40,29708,379022,0,29708,379187,50,29709,379240,0,29714,379467,50,29720,379520,0,29720,379757,50,29729,379810,0,29734,380057,50,29748,380110,0,29748,380369,50,29768,380422,0,29773,380696,50,29808,380749,0,29808,381039,50,29872,381092,0,29872,381401,50,29987,381401,40,29987,381454,0,29987,381768,50,29988,381768,30,29988,381768,40,29988,381821,0,29988,381965,50,29989,382018,0,29993,382220,50,29998,382273,0,29998,382485,50,30005,382538,0,30010,382762,50,30022,382815,0,30022,383051,50,30039,383104,0,30044,383357,50,30077,383410,0,30077,383680,50,30140,383733,0,30141,384025,50,30265,384025,40,30265,384078,0,30265)
%
%
% START OF PROOF
% 383858 [?] ?
% 384027 [] equal(multiply(identity,X),X).
% 384028 [] equal(multiply(inverse(X),X),identity).
% 384029 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 384030 [] -equal(multiply(sk_c10,sk_c8),sk_c9).
% 384044 [?] ?
% 384052 [?] ?
% 384076 [?] ?
% 384111 [input:384044,cut:384030] equal(inverse(sk_c2),sk_c3).
% 384112 [para:384111.1.1,384028.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 384152 [input:384052,cut:384030] equal(multiply(sk_c2,sk_c3),sk_c9).
% 384163 [input:384076,cut:384030] equal(multiply(sk_c9,sk_c10),sk_c8).
% 384168 [para:384028.1.1,384029.1.1.1,demod:384027] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 384179 [para:384112.1.1,384029.1.1.1,demod:384027] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 384238 [para:384152.1.1,384179.1.2.2] equal(sk_c3,multiply(sk_c3,sk_c9)).
% 384323 [para:384179.1.2,384168.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c3),X)).
% 384324 [para:384238.1.2,384168.1.2.2,demod:384323] equal(sk_c9,multiply(sk_c2,sk_c3)).
% 384350 [para:384323.1.2,384028.1.1,demod:384324] equal(sk_c9,identity).
% 384370 [para:384350.1.1,384163.1.1.1,demod:384027] equal(sk_c10,sk_c8).
% 384375 [para:384370.1.1,384030.1.1.1,cut:383858] 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: 36894
% derived clauses: 5854665
% kept clauses: 305319
% kept size sum: 51000
% kept mid-nuclei: 30200
% kept new demods: 5672
% forw unit-subs: 1987858
% forw double-subs: 3217787
% forw overdouble-subs: 266078
% backward subs: 8571
% fast unit cutoff: 20527
% full unit cutoff: 0
% dbl unit cutoff: 11154
% real runtime : 305.12
% process. runtime: 302.66
% specific non-discr-tree subsumption statistics:
% tried: 28067277
% length fails: 2371802
% strength fails: 7433258
% predlist fails: 1753606
% aux str. fails: 3219335
% by-lit fails: 7508769
% full subs tried: 819229
% full subs fail: 718299
%
% ; 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/GRP336-1+eq_r.in")
%
%------------------------------------------------------------------------------