%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET025-4 : 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 15:24:32 EDT 2009

% Result   : Unsatisfiable 0.5s
% Output   : Refutation 0.5s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    7 (   7 unt;   0 def)
%            Number of atoms       :    7 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :    8 (   2 sgn   4   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(non_ordered_pair4,plain,
    ! [A,B] : little_set(non_ordered_pair(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-4.tptp',unknown),
    [] ).

cnf(152716768,plain,
    little_set(non_ordered_pair(A,B)),
    inference(rewrite,[status(thm)],[non_ordered_pair4]),
    [] ).

fof(prove_ordered_pairs_are_small,plain,
    ~ little_set(ordered_pair(a,b)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-4.tptp',unknown),
    [] ).

cnf(152618608,plain,
    ~ little_set(ordered_pair(a,b)),
    inference(rewrite,[status(thm)],[prove_ordered_pairs_are_small]),
    [] ).

fof(ordered_pair,plain,
    ! [A,B] : $equal(non_ordered_pair(singleton_set(A),non_ordered_pair(A,B)),ordered_pair(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-4.tptp',unknown),
    [] ).

cnf(152622016,plain,
    $equal(non_ordered_pair(singleton_set(A),non_ordered_pair(A,B)),ordered_pair(A,B)),
    inference(rewrite,[status(thm)],[ordered_pair]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[152716768,152618608,152622016,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(non_ordered_pair4,plain,(little_set(non_ordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-4.tptp',unknown),[]).
% 
% cnf(152716768,plain,(little_set(non_ordered_pair(A,B))),inference(rewrite,[status(thm)],[non_ordered_pair4]),[]).
% 
% fof(prove_ordered_pairs_are_small,plain,(~little_set(ordered_pair(a,b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-4.tptp',unknown),[]).
% 
% cnf(152618608,plain,(~little_set(ordered_pair(a,b))),inference(rewrite,[status(thm)],[prove_ordered_pairs_are_small]),[]).
% 
% fof(ordered_pair,plain,($equal(non_ordered_pair(singleton_set(A),non_ordered_pair(A,B)),ordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET025-4.tptp',unknown),[]).
% 
% cnf(152622016,plain,($equal(non_ordered_pair(singleton_set(A),non_ordered_pair(A,B)),ordered_pair(A,B))),inference(rewrite,[status(thm)],[ordered_pair]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[152716768,152618608,152622016,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------