TSTP Solution File: LCL008-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL008-1 : 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 13:39:41 EDT 2009
% Result : Unsatisfiable 0.5s
% Output : Refutation 0.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_ec_4,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL008-1.tptp',unknown),
[] ).
cnf(149404416,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))),
inference(rewrite,[status(thm)],[prove_ec_4]),
[] ).
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/LCL008-1.tptp',unknown),
[] ).
cnf(149395616,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/LCL008-1.tptp',unknown),
[] ).
cnf(149400440,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C)))),
inference(rewrite,[status(thm)],[yql]),
[] ).
cnf(157271152,plain,
( ~ is_a_theorem(equivalent(A,B))
| is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C))) ),
inference(resolution,[status(thm)],[149395616,149400440]),
[] ).
cnf(157289856,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)],[149395616,149400440]),
[] ).
cnf(157452128,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(D,C),equivalent(B,D))),equivalent(equivalent(B,C),A))),
inference(resolution,[status(thm)],[157271152,149400440]),
[] ).
cnf(160206456,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(D,C),equivalent(B,D))),equivalent(equivalent(B,C),A)),E))
| is_a_theorem(E) ),
inference(resolution,[status(thm)],[157452128,149395616]),
[] ).
cnf(164992856,plain,
is_a_theorem(equivalent(equivalent(D,B),equivalent(equivalent(D,A),equivalent(equivalent(C,B),equivalent(A,C))))),
inference(resolution,[status(thm)],[160206456,157452128]),
[] ).
cnf(165029936,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(E,C),equivalent(equivalent(E,B),equivalent(equivalent(D,C),equivalent(B,D)))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[149395616,164992856]),
[] ).
cnf(165193928,plain,
is_a_theorem(equivalent(equivalent(equivalent(C,B),A),equivalent(equivalent(A,C),B))),
inference(resolution,[status(thm)],[165029936,157452128]),
[] ).
cnf(165261040,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(C,B),equivalent(A,C)),A),B)),
inference(resolution,[status(thm)],[157289856,165193928]),
[] ).
cnf(165393960,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(C,A),equivalent(B,C)),B))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[149395616,165261040]),
[] ).
cnf(165491336,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,A)),B)),
inference(resolution,[status(thm)],[165393960,165261040]),
[] ).
cnf(165615208,plain,
is_a_theorem(equivalent(B,B)),
inference(resolution,[status(thm)],[157289856,165491336]),
[] ).
cnf(165686200,plain,
is_a_theorem(equivalent(equivalent(B,A),equivalent(A,B))),
inference(resolution,[status(thm)],[157271152,165615208]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[149404416,165686200]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_ec_4,plain,(~is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL008-1.tptp',unknown),[]).
%
% cnf(149404416,plain,(~is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a)))),inference(rewrite,[status(thm)],[prove_ec_4]),[]).
%
% 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/LCL008-1.tptp',unknown),[]).
%
% cnf(149395616,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/LCL008-1.tptp',unknown),[]).
%
% cnf(149400440,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C))))),inference(rewrite,[status(thm)],[yql]),[]).
%
% cnf(157271152,plain,(~is_a_theorem(equivalent(A,B))|is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))),inference(resolution,[status(thm)],[149395616,149400440]),[]).
%
% cnf(157289856,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)],[149395616,149400440]),[]).
%
% cnf(157452128,plain,(is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(D,C),equivalent(B,D))),equivalent(equivalent(B,C),A)))),inference(resolution,[status(thm)],[157271152,149400440]),[]).
%
% cnf(160206456,plain,(~is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(D,C),equivalent(B,D))),equivalent(equivalent(B,C),A)),E))|is_a_theorem(E)),inference(resolution,[status(thm)],[157452128,149395616]),[]).
%
% cnf(164992856,plain,(is_a_theorem(equivalent(equivalent(D,B),equivalent(equivalent(D,A),equivalent(equivalent(C,B),equivalent(A,C)))))),inference(resolution,[status(thm)],[160206456,157452128]),[]).
%
% cnf(165029936,plain,(~is_a_theorem(equivalent(equivalent(equivalent(E,C),equivalent(equivalent(E,B),equivalent(equivalent(D,C),equivalent(B,D)))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[149395616,164992856]),[]).
%
% cnf(165193928,plain,(is_a_theorem(equivalent(equivalent(equivalent(C,B),A),equivalent(equivalent(A,C),B)))),inference(resolution,[status(thm)],[165029936,157452128]),[]).
%
% cnf(165261040,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(C,B),equivalent(A,C)),A),B))),inference(resolution,[status(thm)],[157289856,165193928]),[]).
%
% cnf(165393960,plain,(~is_a_theorem(equivalent(equivalent(equivalent(C,A),equivalent(B,C)),B))|is_a_theorem(A)),inference(resolution,[status(thm)],[149395616,165261040]),[]).
%
% cnf(165491336,plain,(is_a_theorem(equivalent(equivalent(A,equivalent(B,A)),B))),inference(resolution,[status(thm)],[165393960,165261040]),[]).
%
% cnf(165615208,plain,(is_a_theorem(equivalent(B,B))),inference(resolution,[status(thm)],[157289856,165491336]),[]).
%
% cnf(165686200,plain,(is_a_theorem(equivalent(equivalent(B,A),equivalent(A,B)))),inference(resolution,[status(thm)],[157271152,165615208]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[149404416,165686200]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------