%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SEU158+3 : TPTP v3.4.2. Released v3.2.0.
% 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 15:49:54 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    2
% Syntax   : Number of formulae    :    9 (   3 unt;   0 def)
%            Number of atoms       :   23 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   24 (  10   ~;  10   |;   4   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :    6 (   0 sgn   2   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(l2_zfmisc_1,plain,
    ! [A,B] :
      ( ( ~ subset(singleton(A),B)
        | in(A,B) )
      & ( subset(singleton(A),B)
        | ~ in(A,B) ) ),
    file('/tmp/SystemOnTPTP5907/SEU158+3.p',unknown),
    [] ).

cnf(156638512,plain,
    ( subset(singleton(A),B)
    | ~ in(A,B) ),
    inference(rewrite,[status(thm)],[l2_zfmisc_1]),
    [] ).

fof(t37_zfmisc_1,plain,
    ( ( in(a,b)
      | subset(singleton(a),b) )
    & ( ~ subset(singleton(a),b)
      | subset(singleton(a),b) )
    & ( in(a,b)
      | ~ in(a,b) )
    & ( ~ subset(singleton(a),b)
      | ~ in(a,b) ) ),
    file('/tmp/SystemOnTPTP5907/SEU158+3.p',unknown),
    [] ).

cnf(156633024,plain,
    ( in(a,b)
    | subset(singleton(a),b) ),
    inference(rewrite,[status(thm)],[t37_zfmisc_1]),
    [] ).

cnf(167127904,plain,
    subset(singleton(a),b),
    inference(resolution,[status(thm)],[156638512,156633024]),
    [] ).

cnf(156622232,plain,
    ( ~ subset(singleton(a),b)
    | ~ in(a,b) ),
    inference(rewrite,[status(thm)],[t37_zfmisc_1]),
    [] ).

cnf(156644024,plain,
    ( ~ subset(singleton(A),B)
    | in(A,B) ),
    inference(rewrite,[status(thm)],[l2_zfmisc_1]),
    [] ).

cnf(167132264,plain,
    in(a,b),
    inference(resolution,[status(thm)],[156644024,167127904]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[167127904,156622232,167132264]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l2_zfmisc_1,plain,(((~subset(singleton(A),B)|in(A,B))&(subset(singleton(A),B)|~in(A,B)))),file('/tmp/SystemOnTPTP5907/SEU158+3.p',unknown),[]).
% 
% cnf(156638512,plain,(subset(singleton(A),B)|~in(A,B)),inference(rewrite,[status(thm)],[l2_zfmisc_1]),[]).
% 
% fof(t37_zfmisc_1,plain,(((in(a,b)|subset(singleton(a),b))&(~subset(singleton(a),b)|subset(singleton(a),b))&(in(a,b)|~in(a,b))&(~subset(singleton(a),b)|~in(a,b)))),file('/tmp/SystemOnTPTP5907/SEU158+3.p',unknown),[]).
% 
% cnf(156633024,plain,(in(a,b)|subset(singleton(a),b)),inference(rewrite,[status(thm)],[t37_zfmisc_1]),[]).
% 
% cnf(167127904,plain,(subset(singleton(a),b)),inference(resolution,[status(thm)],[156638512,156633024]),[]).
% 
% cnf(156622232,plain,(~subset(singleton(a),b)|~in(a,b)),inference(rewrite,[status(thm)],[t37_zfmisc_1]),[]).
% 
% cnf(156644024,plain,(~subset(singleton(A),B)|in(A,B)),inference(rewrite,[status(thm)],[l2_zfmisc_1]),[]).
% 
% cnf(167132264,plain,(in(a,b)),inference(resolution,[status(thm)],[156644024,167127904]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[167127904,156622232,167132264]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------