%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET025-8 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art04.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 15:24:37 EDT 2009

% Result   : Unsatisfiable 4.7s
% Output   : Refutation 4.7s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   10 (   8 unt;   0 def)
%            Number of atoms       :   12 (   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    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :    6 (   2 sgn   3   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(ordered_pairs_are_small1,plain,
    ! [A,B] : little_set(ordered_pair(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-8.tptp',unknown),
    [] ).

cnf(155440136,plain,
    little_set(ordered_pair(A,B)),
    inference(rewrite,[status(thm)],[ordered_pairs_are_small1]),
    [] ).

fof(ordered_pair_predicate3,plain,
    ! [A] :
      ( ~ ordered_pair_predicate(A)
      | $equal(ordered_pair(f2(A),f3(A)),A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-8.tptp',unknown),
    [] ).

cnf(153806192,plain,
    ( ~ ordered_pair_predicate(A)
    | $equal(ordered_pair(f2(A),f3(A)),A) ),
    inference(rewrite,[status(thm)],[ordered_pair_predicate3]),
    [] ).

fof(an_ordered_pair_predicate,plain,
    ordered_pair_predicate(a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-8.tptp',unknown),
    [] ).

cnf(155447944,plain,
    ordered_pair_predicate(a),
    inference(rewrite,[status(thm)],[an_ordered_pair_predicate]),
    [] ).

cnf(165406064,plain,
    $equal(ordered_pair(f2(a),f3(a)),a),
    inference(resolution,[status(thm)],[153806192,155447944]),
    [] ).

fof(prove_predicate_is_small,plain,
    ~ little_set(a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-8.tptp',unknown),
    [] ).

cnf(155454024,plain,
    ~ little_set(a),
    inference(rewrite,[status(thm)],[prove_predicate_is_small]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[155440136,165406064,155454024,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 5 seconds
% START OF PROOF SEQUENCE
% fof(ordered_pairs_are_small1,plain,(little_set(ordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-8.tptp',unknown),[]).
% 
% cnf(155440136,plain,(little_set(ordered_pair(A,B))),inference(rewrite,[status(thm)],[ordered_pairs_are_small1]),[]).
% 
% fof(ordered_pair_predicate3,plain,(~ordered_pair_predicate(A)|$equal(ordered_pair(f2(A),f3(A)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-8.tptp',unknown),[]).
% 
% cnf(153806192,plain,(~ordered_pair_predicate(A)|$equal(ordered_pair(f2(A),f3(A)),A)),inference(rewrite,[status(thm)],[ordered_pair_predicate3]),[]).
% 
% fof(an_ordered_pair_predicate,plain,(ordered_pair_predicate(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-8.tptp',unknown),[]).
% 
% cnf(155447944,plain,(ordered_pair_predicate(a)),inference(rewrite,[status(thm)],[an_ordered_pair_predicate]),[]).
% 
% cnf(165406064,plain,($equal(ordered_pair(f2(a),f3(a)),a)),inference(resolution,[status(thm)],[153806192,155447944]),[]).
% 
% fof(prove_predicate_is_small,plain,(~little_set(a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-8.tptp',unknown),[]).
% 
% cnf(155454024,plain,(~little_set(a)),inference(rewrite,[status(thm)],[prove_predicate_is_small]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[155440136,165406064,155454024,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------