%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET118-7 : 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 15:28:54 EDT 2009

% Result   : Unsatisfiable 0.3s
% Output   : Refutation 0.3s
% 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 :   11 (   7   ~;   4   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :    9 (   2 sgn   4   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_corollary_2_to_ordered_pairs_are_sets_1,plain,
    member(x,cross_product(universal_class,universal_class)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET118-7.tptp',unknown),
    [] ).

cnf(155902536,plain,
    member(x,cross_product(universal_class,universal_class)),
    inference(rewrite,[status(thm)],[prove_corollary_2_to_ordered_pairs_are_sets_1]),
    [] ).

fof(class_elements_are_sets,plain,
    ! [A] : subclass(A,universal_class),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET118-7.tptp',unknown),
    [] ).

cnf(154394008,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/SET118-7.tptp',unknown),
    [] ).

cnf(154363552,plain,
    ( ~ subclass(A,B)
    | ~ member(C,A)
    | member(C,B) ),
    inference(rewrite,[status(thm)],[subclass_members]),
    [] ).

fof(prove_corollary_2_to_ordered_pairs_are_sets_2,plain,
    ~ member(x,universal_class),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET118-7.tptp',unknown),
    [] ).

cnf(155907368,plain,
    ~ member(x,universal_class),
    inference(rewrite,[status(thm)],[prove_corollary_2_to_ordered_pairs_are_sets_2]),
    [] ).

cnf(168689896,plain,
    ~ member(x,A),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[154394008,154363552,155907368]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[155902536,168689896]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_corollary_2_to_ordered_pairs_are_sets_1,plain,(member(x,cross_product(universal_class,universal_class))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET118-7.tptp',unknown),[]).
% 
% cnf(155902536,plain,(member(x,cross_product(universal_class,universal_class))),inference(rewrite,[status(thm)],[prove_corollary_2_to_ordered_pairs_are_sets_1]),[]).
% 
% fof(class_elements_are_sets,plain,(subclass(A,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET118-7.tptp',unknown),[]).
% 
% cnf(154394008,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/SET118-7.tptp',unknown),[]).
% 
% cnf(154363552,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
% 
% fof(prove_corollary_2_to_ordered_pairs_are_sets_2,plain,(~member(x,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET118-7.tptp',unknown),[]).
% 
% cnf(155907368,plain,(~member(x,universal_class)),inference(rewrite,[status(thm)],[prove_corollary_2_to_ordered_pairs_are_sets_2]),[]).
% 
% cnf(168689896,plain,(~member(x,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[154394008,154363552,155907368]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[155902536,168689896]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------