%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET080-7 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art06.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 15:27:34 EDT 2009

% Result   : Unsatisfiable 0.3s
% Output   : Refutation 0.3s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    8 (   6 unt;   0 def)
%            Number of atoms       :   10 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    6 (   4   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :    2 (   0 sgn   1   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_null_class_in_its_singleton_1,plain,
    ~ member(null_class,singleton(null_class)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-7.tptp',unknown),
    [] ).

cnf(166736544,plain,
    ~ member(null_class,singleton(null_class)),
    inference(rewrite,[status(thm)],[prove_null_class_in_its_singleton_1]),
    [] ).

fof(set_in_its_singleton,plain,
    ! [A] :
      ( ~ member(A,universal_class)
      | member(A,singleton(A)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-7.tptp',unknown),
    [] ).

cnf(166728768,plain,
    ( ~ member(A,universal_class)
    | member(A,singleton(A)) ),
    inference(rewrite,[status(thm)],[set_in_its_singleton]),
    [] ).

fof(null_class_is_a_set,plain,
    member(null_class,universal_class),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-7.tptp',unknown),
    [] ).

cnf(166597536,plain,
    member(null_class,universal_class),
    inference(rewrite,[status(thm)],[null_class_is_a_set]),
    [] ).

cnf(178154320,plain,
    member(null_class,singleton(null_class)),
    inference(resolution,[status(thm)],[166728768,166597536]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[166736544,178154320]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_null_class_in_its_singleton_1,plain,(~member(null_class,singleton(null_class))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-7.tptp',unknown),[]).
% 
% cnf(166736544,plain,(~member(null_class,singleton(null_class))),inference(rewrite,[status(thm)],[prove_null_class_in_its_singleton_1]),[]).
% 
% fof(set_in_its_singleton,plain,(~member(A,universal_class)|member(A,singleton(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-7.tptp',unknown),[]).
% 
% cnf(166728768,plain,(~member(A,universal_class)|member(A,singleton(A))),inference(rewrite,[status(thm)],[set_in_its_singleton]),[]).
% 
% fof(null_class_is_a_set,plain,(member(null_class,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET080-7.tptp',unknown),[]).
% 
% cnf(166597536,plain,(member(null_class,universal_class)),inference(rewrite,[status(thm)],[null_class_is_a_set]),[]).
% 
% cnf(178154320,plain,(member(null_class,singleton(null_class))),inference(resolution,[status(thm)],[166728768,166597536]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[166736544,178154320]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------