%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET053-6 : TPTP v3.4.2. Bugfixed v2.1.0.
% 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 15:25:40 EDT 2009

% Result   : Unsatisfiable 3.5s
% Output   : Refutation 3.5s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   13 (   9 unt;   0 def)
%            Number of atoms       :   19 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   16 (  10   ~;   6   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   20 (   7 sgn   8   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_corollary_2_to_cartesian_product_1,plain,
    member(ordered_pair(u,v),cross_product(x,y)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET053-6.tptp',unknown),
    [] ).

cnf(166798992,plain,
    member(ordered_pair(u,v),cross_product(x,y)),
    inference(rewrite,[status(thm)],[prove_corollary_2_to_cartesian_product_1]),
    [] ).

fof(cartesian_product2,plain,
    ! [A,B,C,D] :
      ( ~ member(ordered_pair(A,B),cross_product(C,D))
      | member(B,D) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET053-6.tptp',unknown),
    [] ).

cnf(165971264,plain,
    ( ~ member(ordered_pair(A,B),cross_product(C,D))
    | member(B,D) ),
    inference(rewrite,[status(thm)],[cartesian_product2]),
    [] ).

fof(class_elements_are_sets,plain,
    ! [A] : subclass(A,universal_class),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET053-6.tptp',unknown),
    [] ).

cnf(165871456,plain,
    subclass(A,universal_class),
    inference(rewrite,[status(thm)],[class_elements_are_sets]),
    [] ).

fof(subclass_members,plain,
    ! [A,B,C] :
      ( ~ subclass(A,B)
      | ~ member(C,A)
      | member(C,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET053-6.tptp',unknown),
    [] ).

cnf(165841096,plain,
    ( ~ subclass(A,B)
    | ~ member(C,A)
    | member(C,B) ),
    inference(rewrite,[status(thm)],[subclass_members]),
    [] ).

fof(prove_corollary_2_to_cartesian_product_2,plain,
    ~ member(v,universal_class),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET053-6.tptp',unknown),
    [] ).

cnf(166803808,plain,
    ~ member(v,universal_class),
    inference(rewrite,[status(thm)],[prove_corollary_2_to_cartesian_product_2]),
    [] ).

cnf(189446456,plain,
    ~ member(v,A),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[165871456,165841096,166803808]),
    [] ).

cnf(189556648,plain,
    ~ member(ordered_pair(A,v),cross_product(B,C)),
    inference(resolution,[status(thm)],[165971264,189446456]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[166798992,189556648]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 3 seconds
% START OF PROOF SEQUENCE
% fof(prove_corollary_2_to_cartesian_product_1,plain,(member(ordered_pair(u,v),cross_product(x,y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET053-6.tptp',unknown),[]).
% 
% cnf(166798992,plain,(member(ordered_pair(u,v),cross_product(x,y))),inference(rewrite,[status(thm)],[prove_corollary_2_to_cartesian_product_1]),[]).
% 
% fof(cartesian_product2,plain,(~member(ordered_pair(A,B),cross_product(C,D))|member(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET053-6.tptp',unknown),[]).
% 
% cnf(165971264,plain,(~member(ordered_pair(A,B),cross_product(C,D))|member(B,D)),inference(rewrite,[status(thm)],[cartesian_product2]),[]).
% 
% fof(class_elements_are_sets,plain,(subclass(A,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET053-6.tptp',unknown),[]).
% 
% cnf(165871456,plain,(subclass(A,universal_class)),inference(rewrite,[status(thm)],[class_elements_are_sets]),[]).
% 
% fof(subclass_members,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET053-6.tptp',unknown),[]).
% 
% cnf(165841096,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
% 
% fof(prove_corollary_2_to_cartesian_product_2,plain,(~member(v,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET053-6.tptp',unknown),[]).
% 
% cnf(166803808,plain,(~member(v,universal_class)),inference(rewrite,[status(thm)],[prove_corollary_2_to_cartesian_product_2]),[]).
% 
% cnf(189446456,plain,(~member(v,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165871456,165841096,166803808]),[]).
% 
% cnf(189556648,plain,(~member(ordered_pair(A,v),cross_product(B,C))),inference(resolution,[status(thm)],[165971264,189446456]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[166798992,189556648]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------