%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET095-7 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art01.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 15:28:18 EDT 2009

% Result   : Unsatisfiable 0.8s
% Output   : Refutation 0.8s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   10 (   8 unt;   0 def)
%            Number of atoms       :   14 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   10 (   6   ~;   4   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 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(unordered_pair_is_subset,plain,
    ! [A,B,C] :
      ( ~ member(A,B)
      | ~ member(C,B)
      | subclass(unordered_pair(A,C),B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095-7.tptp',unknown),
    [] ).

cnf(158440696,plain,
    ( ~ member(A,B)
    | ~ member(C,B)
    | subclass(unordered_pair(A,C),B) ),
    inference(rewrite,[status(thm)],[unordered_pair_is_subset]),
    [] ).

fof(prove_property_of_singletons2_1,plain,
    member(x,y),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095-7.tptp',unknown),
    [] ).

cnf(158601488,plain,
    member(x,y),
    inference(rewrite,[status(thm)],[prove_property_of_singletons2_1]),
    [] ).

cnf(170818640,plain,
    subclass(unordered_pair(x,x),y),
    inference(resolution,[status(thm)],[158440696,158601488]),
    [] ).

fof(prove_property_of_singletons2_2,plain,
    ~ subclass(singleton(x),y),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095-7.tptp',unknown),
    [] ).

cnf(158605400,plain,
    ~ subclass(singleton(x),y),
    inference(rewrite,[status(thm)],[prove_property_of_singletons2_2]),
    [] ).

fof(singleton_set,plain,
    ! [A] : $equal(singleton(A),unordered_pair(A,A)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095-7.tptp',unknown),
    [] ).

cnf(157371296,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)],[170818640,158605400,157371296,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(unordered_pair_is_subset,plain,(~member(A,B)|~member(C,B)|subclass(unordered_pair(A,C),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095-7.tptp',unknown),[]).
% 
% cnf(158440696,plain,(~member(A,B)|~member(C,B)|subclass(unordered_pair(A,C),B)),inference(rewrite,[status(thm)],[unordered_pair_is_subset]),[]).
% 
% fof(prove_property_of_singletons2_1,plain,(member(x,y)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095-7.tptp',unknown),[]).
% 
% cnf(158601488,plain,(member(x,y)),inference(rewrite,[status(thm)],[prove_property_of_singletons2_1]),[]).
% 
% cnf(170818640,plain,(subclass(unordered_pair(x,x),y)),inference(resolution,[status(thm)],[158440696,158601488]),[]).
% 
% fof(prove_property_of_singletons2_2,plain,(~subclass(singleton(x),y)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095-7.tptp',unknown),[]).
% 
% cnf(158605400,plain,(~subclass(singleton(x),y)),inference(rewrite,[status(thm)],[prove_property_of_singletons2_2]),[]).
% 
% fof(singleton_set,plain,($equal(singleton(A),unordered_pair(A,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET095-7.tptp',unknown),[]).
% 
% cnf(157371296,plain,($equal(singleton(A),unordered_pair(A,A))),inference(rewrite,[status(thm)],[singleton_set]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[170818640,158605400,157371296,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------