%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL009-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:39:43 EDT 2009
% Result : Unsatisfiable 13.5s
% Output : Refutation 13.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 15 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(condensed_detachment,plain,
! [A,B] :
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL009-1.tptp',unknown),
[] ).
cnf(164147104,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(yql,plain,
! [A,B,C] : is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL009-1.tptp',unknown),
[] ).
cnf(164151960,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C)))),
inference(rewrite,[status(thm)],[yql]),
[] ).
cnf(171935488,plain,
( ~ is_a_theorem(equivalent(A,B))
| is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C))) ),
inference(resolution,[status(thm)],[164147104,164151960]),
[] ).
cnf(172098760,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(equivalent(C,B))
| is_a_theorem(equivalent(A,C)) ),
inference(resolution,[status(thm)],[171935488,164147104]),
[] ).
cnf(172233568,plain,
( ~ is_a_theorem(equivalent(A,equivalent(equivalent(D,C),equivalent(B,D))))
| is_a_theorem(equivalent(equivalent(B,C),A)) ),
inference(resolution,[status(thm)],[172098760,164151960]),
[] ).
cnf(171955120,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(B,C),equivalent(equivalent(D,C),equivalent(B,D))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[164147104,164151960]),
[] ).
cnf(172245288,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolution,[status(thm)],[172098760,164151960]),
[] ).
cnf(172363656,plain,
is_a_theorem(equivalent(equivalent(C,equivalent(A,B)),equivalent(equivalent(A,B),C))),
inference(resolution,[status(thm)],[172245288,171935488]),
[] ).
cnf(172543456,plain,
is_a_theorem(equivalent(equivalent(equivalent(C,B),equivalent(A,C)),equivalent(A,B))),
inference(resolution,[status(thm)],[171955120,172363656]),
[] ).
cnf(173149096,plain,
( ~ is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))
| is_a_theorem(equivalent(A,B)) ),
inference(resolution,[status(thm)],[172543456,164147104]),
[] ).
cnf(172341248,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),C))
| is_a_theorem(C) ),
inference(resolution,[status(thm)],[172245288,164147104]),
[] ).
cnf(174049528,plain,
is_a_theorem(equivalent(A,A)),
inference(resolution,[status(thm)],[172341248,172543456]),
[] ).
cnf(174096976,plain,
( ~ is_a_theorem(equivalent(B,A))
| is_a_theorem(equivalent(A,B)) ),
inference(resolution,[status(thm)],[174049528,172098760]),
[] ).
cnf(175785832,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(C,B)))),
inference(resolution,[status(thm)],[172233568,172363656]),
[] ).
cnf(176202152,plain,
is_a_theorem(equivalent(equivalent(equivalent(B,A),B),A)),
inference(resolution,[status(thm)],[173149096,175785832]),
[] ).
cnf(176394384,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,A),B))),
inference(resolution,[status(thm)],[174096976,176202152]),
[] ).
cnf(176898336,plain,
is_a_theorem(equivalent(equivalent(B,equivalent(B,A)),A)),
inference(resolution,[status(thm)],[173149096,176394384]),
[] ).
cnf(177190888,plain,
is_a_theorem(equivalent(equivalent(B,A),equivalent(equivalent(C,equivalent(C,A)),B))),
inference(resolution,[status(thm)],[171935488,176898336]),
[] ).
cnf(197945024,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(A,B),C))),
inference(resolution,[status(thm)],[172233568,177190888]),
[] ).
fof(prove_ec_5,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL009-1.tptp',unknown),
[] ).
cnf(164156176,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
inference(rewrite,[status(thm)],[prove_ec_5]),
[] ).
cnf(172290552,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),A))
| ~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),A)) ),
inference(resolution,[status(thm)],[172098760,164156176]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[197945024,172290552,174049528]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 13 seconds
% START OF PROOF SEQUENCE
% fof(condensed_detachment,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL009-1.tptp',unknown),[]).
%
% cnf(164147104,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(yql,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL009-1.tptp',unknown),[]).
%
% cnf(164151960,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C))))),inference(rewrite,[status(thm)],[yql]),[]).
%
% cnf(171935488,plain,(~is_a_theorem(equivalent(A,B))|is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))),inference(resolution,[status(thm)],[164147104,164151960]),[]).
%
% cnf(172098760,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(equivalent(C,B))|is_a_theorem(equivalent(A,C))),inference(resolution,[status(thm)],[171935488,164147104]),[]).
%
% cnf(172233568,plain,(~is_a_theorem(equivalent(A,equivalent(equivalent(D,C),equivalent(B,D))))|is_a_theorem(equivalent(equivalent(B,C),A))),inference(resolution,[status(thm)],[172098760,164151960]),[]).
%
% cnf(171955120,plain,(~is_a_theorem(equivalent(equivalent(equivalent(B,C),equivalent(equivalent(D,C),equivalent(B,D))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[164147104,164151960]),[]).
%
% cnf(172245288,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B)))),inference(resolution,[status(thm)],[172098760,164151960]),[]).
%
% cnf(172363656,plain,(is_a_theorem(equivalent(equivalent(C,equivalent(A,B)),equivalent(equivalent(A,B),C)))),inference(resolution,[status(thm)],[172245288,171935488]),[]).
%
% cnf(172543456,plain,(is_a_theorem(equivalent(equivalent(equivalent(C,B),equivalent(A,C)),equivalent(A,B)))),inference(resolution,[status(thm)],[171955120,172363656]),[]).
%
% cnf(173149096,plain,(~is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))|is_a_theorem(equivalent(A,B))),inference(resolution,[status(thm)],[172543456,164147104]),[]).
%
% cnf(172341248,plain,(~is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),C))|is_a_theorem(C)),inference(resolution,[status(thm)],[172245288,164147104]),[]).
%
% cnf(174049528,plain,(is_a_theorem(equivalent(A,A))),inference(resolution,[status(thm)],[172341248,172543456]),[]).
%
% cnf(174096976,plain,(~is_a_theorem(equivalent(B,A))|is_a_theorem(equivalent(A,B))),inference(resolution,[status(thm)],[174049528,172098760]),[]).
%
% cnf(175785832,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(C,B))))),inference(resolution,[status(thm)],[172233568,172363656]),[]).
%
% cnf(176202152,plain,(is_a_theorem(equivalent(equivalent(equivalent(B,A),B),A))),inference(resolution,[status(thm)],[173149096,175785832]),[]).
%
% cnf(176394384,plain,(is_a_theorem(equivalent(A,equivalent(equivalent(B,A),B)))),inference(resolution,[status(thm)],[174096976,176202152]),[]).
%
% cnf(176898336,plain,(is_a_theorem(equivalent(equivalent(B,equivalent(B,A)),A))),inference(resolution,[status(thm)],[173149096,176394384]),[]).
%
% cnf(177190888,plain,(is_a_theorem(equivalent(equivalent(B,A),equivalent(equivalent(C,equivalent(C,A)),B)))),inference(resolution,[status(thm)],[171935488,176898336]),[]).
%
% cnf(197945024,plain,(is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(A,B),C)))),inference(resolution,[status(thm)],[172233568,177190888]),[]).
%
% fof(prove_ec_5,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL009-1.tptp',unknown),[]).
%
% cnf(164156176,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))),inference(rewrite,[status(thm)],[prove_ec_5]),[]).
%
% cnf(172290552,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),c),A))|~is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),A))),inference(resolution,[status(thm)],[172098760,164156176]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[197945024,172290552,174049528]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------