%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET101-7 : 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 15:28:31 EDT 2009

% Result   : Unsatisfiable 1.1s
% Output   : Refutation 1.1s
% 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 :    5 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   12 (   3 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(singletons_are_sets,plain,
    ! [A] : member(singleton(A),universal_class),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-7.tptp',unknown),
    [] ).

cnf(162671368,plain,
    member(singleton(A),universal_class),
    inference(rewrite,[status(thm)],[singletons_are_sets]),
    [] ).

fof(unordered_pair2,plain,
    ! [A,B] :
      ( ~ member(A,universal_class)
      | member(A,unordered_pair(A,B)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-7.tptp',unknown),
    [] ).

cnf(161577336,plain,
    ( ~ member(A,universal_class)
    | member(A,unordered_pair(A,B)) ),
    inference(rewrite,[status(thm)],[unordered_pair2]),
    [] ).

fof(ordered_pair,plain,
    ! [A,B] : $equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-7.tptp',unknown),
    [] ).

cnf(161606400,plain,
    $equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B)),
    inference(rewrite,[status(thm)],[ordered_pair]),
    [] ).

cnf(198605984,plain,
    member(singleton(A),ordered_pair(A,B)),
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[162671368,161577336,161606400,theory(equality)]),
    [] ).

fof(prove_singleton_member_of_ordered_pair_1,plain,
    ~ member(singleton(x),ordered_pair(x,y)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-7.tptp',unknown),
    [] ).

cnf(162889208,plain,
    ~ member(singleton(x),ordered_pair(x,y)),
    inference(rewrite,[status(thm)],[prove_singleton_member_of_ordered_pair_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[198605984,162889208]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(singletons_are_sets,plain,(member(singleton(A),universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-7.tptp',unknown),[]).
% 
% cnf(162671368,plain,(member(singleton(A),universal_class)),inference(rewrite,[status(thm)],[singletons_are_sets]),[]).
% 
% fof(unordered_pair2,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-7.tptp',unknown),[]).
% 
% cnf(161577336,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),inference(rewrite,[status(thm)],[unordered_pair2]),[]).
% 
% fof(ordered_pair,plain,($equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-7.tptp',unknown),[]).
% 
% cnf(161606400,plain,($equal(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),ordered_pair(A,B))),inference(rewrite,[status(thm)],[ordered_pair]),[]).
% 
% cnf(198605984,plain,(member(singleton(A),ordered_pair(A,B))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[162671368,161577336,161606400,theory(equality)]),[]).
% 
% fof(prove_singleton_member_of_ordered_pair_1,plain,(~member(singleton(x),ordered_pair(x,y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET101-7.tptp',unknown),[]).
% 
% cnf(162889208,plain,(~member(singleton(x),ordered_pair(x,y))),inference(rewrite,[status(thm)],[prove_singleton_member_of_ordered_pair_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[198605984,162889208]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------