%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET077-6 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art06.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 15:27:21 EDT 2009

% Result   : Unsatisfiable 0.2s
% Output   : Refutation 0.2s
% 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    :    2 (   1 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 (   2 sgn   3   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(unordered_pairs_in_universal,plain,
    ! [A,B] : member(unordered_pair(A,B),universal_class),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET077-6.tptp',unknown),
    [] ).

cnf(165284480,plain,
    member(unordered_pair(A,B),universal_class),
    inference(rewrite,[status(thm)],[unordered_pairs_in_universal]),
    [] ).

fof(prove_singletons_are_sets_1,plain,
    ~ member(singleton(x),universal_class),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET077-6.tptp',unknown),
    [] ).

cnf(166127592,plain,
    ~ member(singleton(x),universal_class),
    inference(rewrite,[status(thm)],[prove_singletons_are_sets_1]),
    [] ).

fof(singleton_set,plain,
    ! [A] : $equal(singleton(A),unordered_pair(A,A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET077-6.tptp',unknown),
    [] ).

cnf(165294520,plain,
    $equal(singleton(A),unordered_pair(A,A)),
    inference(rewrite,[status(thm)],[singleton_set]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[165284480,166127592,165294520,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(unordered_pairs_in_universal,plain,(member(unordered_pair(A,B),universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET077-6.tptp',unknown),[]).
% 
% cnf(165284480,plain,(member(unordered_pair(A,B),universal_class)),inference(rewrite,[status(thm)],[unordered_pairs_in_universal]),[]).
% 
% fof(prove_singletons_are_sets_1,plain,(~member(singleton(x),universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET077-6.tptp',unknown),[]).
% 
% cnf(166127592,plain,(~member(singleton(x),universal_class)),inference(rewrite,[status(thm)],[prove_singletons_are_sets_1]),[]).
% 
% fof(singleton_set,plain,($equal(singleton(A),unordered_pair(A,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET077-6.tptp',unknown),[]).
% 
% cnf(165294520,plain,($equal(singleton(A),unordered_pair(A,A))),inference(rewrite,[status(thm)],[singleton_set]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[165284480,166127592,165294520,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------