TSTP Solution File: SET924+1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET924+1 : TPTP v3.4.2. Released v3.2.0.
% 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 15:41:46 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    :    3 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    6 (   0 sgn   2   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t67_zfmisc_1,plain,
    ( ( ~ in(a,b)
      | $equal(set_difference(singleton(a),b),singleton(a)) )
    & ( ~ $equal(set_difference(singleton(a),b),singleton(a))
      | $equal(set_difference(singleton(a),b),singleton(a)) )
    & ( ~ in(a,b)
      | in(a,b) )
    & ( ~ $equal(set_difference(singleton(a),b),singleton(a))
      | in(a,b) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET924+1.tptp',unknown),
    [] ).

cnf(141328456,plain,
    ( ~ in(a,b)
    | $equal(set_difference(singleton(a),b),singleton(a)) ),
    inference(rewrite,[status(thm)],[t67_zfmisc_1]),
    [] ).

cnf(141318424,plain,
    ( ~ $equal(set_difference(singleton(a),b),singleton(a))
    | in(a,b) ),
    inference(rewrite,[status(thm)],[t67_zfmisc_1]),
    [] ).

fof(l34_zfmisc_1,plain,
    ! [A,B] :
      ( ( ~ $equal(set_difference(singleton(A),B),singleton(A))
        | ~ in(A,B) )
      & ( $equal(set_difference(singleton(A),B),singleton(A))
        | in(A,B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET924+1.tptp',unknown),
    [] ).

cnf(141334912,plain,
    ( $equal(set_difference(singleton(A),B),singleton(A))
    | in(A,B) ),
    inference(rewrite,[status(thm)],[l34_zfmisc_1]),
    [] ).

cnf(151777160,plain,
    in(a,b),
    inference(resolution,[status(thm)],[141318424,141334912]),
    [] ).

cnf(151791216,plain,
    $equal(set_difference(singleton(a),b),singleton(a)),
    inference(resolution,[status(thm)],[141328456,151777160]),
    [] ).

cnf(141340616,plain,
    ( ~ $equal(set_difference(singleton(A),B),singleton(A))
    | ~ in(A,B) ),
    inference(rewrite,[status(thm)],[l34_zfmisc_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[151791216,141340616,151777160]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t67_zfmisc_1,plain,(((~in(a,b)|$equal(set_difference(singleton(a),b),singleton(a)))&(~$equal(set_difference(singleton(a),b),singleton(a))|$equal(set_difference(singleton(a),b),singleton(a)))&(~in(a,b)|in(a,b))&(~$equal(set_difference(singleton(a),b),singleton(a))|in(a,b)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET924+1.tptp',unknown),[]).
% 
% cnf(141328456,plain,(~in(a,b)|$equal(set_difference(singleton(a),b),singleton(a))),inference(rewrite,[status(thm)],[t67_zfmisc_1]),[]).
% 
% cnf(141318424,plain,(~$equal(set_difference(singleton(a),b),singleton(a))|in(a,b)),inference(rewrite,[status(thm)],[t67_zfmisc_1]),[]).
% 
% fof(l34_zfmisc_1,plain,(((~$equal(set_difference(singleton(A),B),singleton(A))|~in(A,B))&($equal(set_difference(singleton(A),B),singleton(A))|in(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET924+1.tptp',unknown),[]).
% 
% cnf(141334912,plain,($equal(set_difference(singleton(A),B),singleton(A))|in(A,B)),inference(rewrite,[status(thm)],[l34_zfmisc_1]),[]).
% 
% cnf(151777160,plain,(in(a,b)),inference(resolution,[status(thm)],[141318424,141334912]),[]).
% 
% cnf(151791216,plain,($equal(set_difference(singleton(a),b),singleton(a))),inference(resolution,[status(thm)],[141328456,151777160]),[]).
% 
% cnf(141340616,plain,(~$equal(set_difference(singleton(A),B),singleton(A))|~in(A,B)),inference(rewrite,[status(thm)],[l34_zfmisc_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[151791216,141340616,151777160]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------