%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SEU303+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art03.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 15:55:19 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   11 (   6 unt;   0 def)
%            Number of atoms       :   22 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   22 (  11   ~;   8   |;   3   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :    6 (   0 sgn   3   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t26_finset_1,plain,
    ( relation(a)
    & function(a)
    & finite(relation_dom(a))
    & ~ finite(relation_rng(a)) ),
    file('/tmp/SystemOnTPTP16464/SEU303+1.p',unknown),
    [] ).

cnf(162736632,plain,
    finite(relation_dom(a)),
    inference(rewrite,[status(thm)],[t26_finset_1]),
    [] ).

cnf(162743992,plain,
    function(a),
    inference(rewrite,[status(thm)],[t26_finset_1]),
    [] ).

cnf(162751016,plain,
    relation(a),
    inference(rewrite,[status(thm)],[t26_finset_1]),
    [] ).

fof(fc13_finset_1,plain,
    ! [A,B] :
      ( ~ relation(A)
      | ~ function(A)
      | ~ finite(B)
      | finite(relation_image(A,B)) ),
    file('/tmp/SystemOnTPTP16464/SEU303+1.p',unknown),
    [] ).

cnf(162649200,plain,
    ( ~ relation(A)
    | ~ function(A)
    | ~ finite(B)
    | finite(relation_image(A,B)) ),
    inference(rewrite,[status(thm)],[fc13_finset_1]),
    [] ).

fof(t146_relat_1,plain,
    ! [A] :
      ( ~ relation(A)
      | $equal(relation_image(A,relation_dom(A)),relation_rng(A)) ),
    file('/tmp/SystemOnTPTP16464/SEU303+1.p',unknown),
    [] ).

cnf(162676408,plain,
    ( ~ relation(A)
    | $equal(relation_image(A,relation_dom(A)),relation_rng(A)) ),
    inference(rewrite,[status(thm)],[t146_relat_1]),
    [] ).

cnf(162727536,plain,
    ~ finite(relation_rng(a)),
    inference(rewrite,[status(thm)],[t26_finset_1]),
    [] ).

cnf(178532304,plain,
    ~ finite(relation_image(a,relation_dom(a))),
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[162751016,162676408,162727536,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[162736632,162743992,162751016,162649200,178532304]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t26_finset_1,plain,((relation(a)&function(a)&finite(relation_dom(a))&~finite(relation_rng(a)))),file('/tmp/SystemOnTPTP16464/SEU303+1.p',unknown),[]).
% 
% cnf(162736632,plain,(finite(relation_dom(a))),inference(rewrite,[status(thm)],[t26_finset_1]),[]).
% 
% cnf(162743992,plain,(function(a)),inference(rewrite,[status(thm)],[t26_finset_1]),[]).
% 
% cnf(162751016,plain,(relation(a)),inference(rewrite,[status(thm)],[t26_finset_1]),[]).
% 
% fof(fc13_finset_1,plain,(~relation(A)|~function(A)|~finite(B)|finite(relation_image(A,B))),file('/tmp/SystemOnTPTP16464/SEU303+1.p',unknown),[]).
% 
% cnf(162649200,plain,(~relation(A)|~function(A)|~finite(B)|finite(relation_image(A,B))),inference(rewrite,[status(thm)],[fc13_finset_1]),[]).
% 
% fof(t146_relat_1,plain,(~relation(A)|$equal(relation_image(A,relation_dom(A)),relation_rng(A))),file('/tmp/SystemOnTPTP16464/SEU303+1.p',unknown),[]).
% 
% cnf(162676408,plain,(~relation(A)|$equal(relation_image(A,relation_dom(A)),relation_rng(A))),inference(rewrite,[status(thm)],[t146_relat_1]),[]).
% 
% cnf(162727536,plain,(~finite(relation_rng(a))),inference(rewrite,[status(thm)],[t26_finset_1]),[]).
% 
% cnf(178532304,plain,(~finite(relation_image(a,relation_dom(a)))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[162751016,162676408,162727536,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[162736632,162743992,162751016,162649200,178532304]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------