%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET891+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art10.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 15:40:49 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% 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    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :    8 (   0 sgn   4   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t41_enumset1,plain,
    ! [A,B] : $equal(set_union2(singleton(A),singleton(B)),unordered_pair(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET891+1.tptp',unknown),
    [] ).

cnf(148413832,plain,
    $equal(set_union2(singleton(A),singleton(B)),unordered_pair(A,B)),
    inference(rewrite,[status(thm)],[t41_enumset1]),
    [] ).

fof(t32_zfmisc_1,plain,
    ~ $equal(union(unordered_pair(singleton(a),singleton(b))),unordered_pair(a,b)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET891+1.tptp',unknown),
    [] ).

cnf(148514088,plain,
    ~ $equal(union(unordered_pair(singleton(a),singleton(b))),unordered_pair(a,b)),
    inference(rewrite,[status(thm)],[t32_zfmisc_1]),
    [] ).

fof(l52_zfmisc_1,plain,
    ! [A,B] : $equal(union(unordered_pair(A,B)),set_union2(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET891+1.tptp',unknown),
    [] ).

cnf(148449928,plain,
    $equal(union(unordered_pair(A,B)),set_union2(A,B)),
    inference(rewrite,[status(thm)],[l52_zfmisc_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[148413832,148514088,148449928,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t41_enumset1,plain,($equal(set_union2(singleton(A),singleton(B)),unordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET891+1.tptp',unknown),[]).
% 
% cnf(148413832,plain,($equal(set_union2(singleton(A),singleton(B)),unordered_pair(A,B))),inference(rewrite,[status(thm)],[t41_enumset1]),[]).
% 
% fof(t32_zfmisc_1,plain,(~$equal(union(unordered_pair(singleton(a),singleton(b))),unordered_pair(a,b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET891+1.tptp',unknown),[]).
% 
% cnf(148514088,plain,(~$equal(union(unordered_pair(singleton(a),singleton(b))),unordered_pair(a,b))),inference(rewrite,[status(thm)],[t32_zfmisc_1]),[]).
% 
% fof(l52_zfmisc_1,plain,($equal(union(unordered_pair(A,B)),set_union2(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET891+1.tptp',unknown),[]).
% 
% cnf(148449928,plain,($equal(union(unordered_pair(A,B)),set_union2(A,B))),inference(rewrite,[status(thm)],[l52_zfmisc_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[148413832,148514088,148449928,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------