%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET643+3 : TPTP v3.4.2. Released v2.2.0.
% 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 15:34:24 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   12 (   6 unt;   0 def)
%            Number of atoms       :   25 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   26 (  13   ~;  11   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   16 (   1 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(p19,plain,
    ! [A] : ilf_type(A,set_type),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET643+3.tptp',unknown),
    [] ).

cnf(175105400,plain,
    ilf_type(A,set_type),
    inference(rewrite,[status(thm)],[p19]),
    [] ).

fof(p1,plain,
    ! [A,B,C] :
      ( ~ ilf_type(A,set_type)
      | ~ ilf_type(B,set_type)
      | ~ ilf_type(C,set_type)
      | ~ subset(A,cross_product(B,C))
      | ilf_type(A,relation_type(B,C)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET643+3.tptp',unknown),
    [] ).

cnf(174593960,plain,
    ( ~ ilf_type(A,set_type)
    | ~ ilf_type(B,set_type)
    | ~ ilf_type(C,set_type)
    | ~ subset(A,cross_product(B,C))
    | ilf_type(A,relation_type(B,C)) ),
    inference(rewrite,[status(thm)],[p1]),
    [] ).

cnf(183210176,plain,
    ( ~ subset(A,cross_product(B,C))
    | ilf_type(A,relation_type(B,C)) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[175105400,174593960,175105400]),
    [] ).

fof(p10,plain,
    ! [A] :
      ( ~ ilf_type(A,set_type)
      | subset(A,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET643+3.tptp',unknown),
    [] ).

cnf(174869896,plain,
    ( ~ ilf_type(A,set_type)
    | subset(A,A) ),
    inference(rewrite,[status(thm)],[p10]),
    [] ).

cnf(183062512,plain,
    subset(A,A),
    inference(resolution,[status(thm)],[174869896,175105400]),
    [] ).

cnf(184318608,plain,
    ilf_type(cross_product(A,B),relation_type(A,B)),
    inference(resolution,[status(thm)],[183210176,183062512]),
    [] ).

fof(prove_relset_1_5,plain,
    ( ilf_type(b,set_type)
    & ilf_type(c,set_type)
    & ~ ilf_type(cross_product(b,c),relation_type(b,c)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET643+3.tptp',unknown),
    [] ).

cnf(175161944,plain,
    ~ ilf_type(cross_product(b,c),relation_type(b,c)),
    inference(rewrite,[status(thm)],[prove_relset_1_5]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[184318608,175161944]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(p19,plain,(ilf_type(A,set_type)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET643+3.tptp',unknown),[]).
% 
% cnf(175105400,plain,(ilf_type(A,set_type)),inference(rewrite,[status(thm)],[p19]),[]).
% 
% fof(p1,plain,(~ilf_type(A,set_type)|~ilf_type(B,set_type)|~ilf_type(C,set_type)|~subset(A,cross_product(B,C))|ilf_type(A,relation_type(B,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET643+3.tptp',unknown),[]).
% 
% cnf(174593960,plain,(~ilf_type(A,set_type)|~ilf_type(B,set_type)|~ilf_type(C,set_type)|~subset(A,cross_product(B,C))|ilf_type(A,relation_type(B,C))),inference(rewrite,[status(thm)],[p1]),[]).
% 
% cnf(183210176,plain,(~subset(A,cross_product(B,C))|ilf_type(A,relation_type(B,C))),inference(forward_subsumption_resolution__resolution,[status(thm)],[175105400,174593960,175105400]),[]).
% 
% fof(p10,plain,(~ilf_type(A,set_type)|subset(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET643+3.tptp',unknown),[]).
% 
% cnf(174869896,plain,(~ilf_type(A,set_type)|subset(A,A)),inference(rewrite,[status(thm)],[p10]),[]).
% 
% cnf(183062512,plain,(subset(A,A)),inference(resolution,[status(thm)],[174869896,175105400]),[]).
% 
% cnf(184318608,plain,(ilf_type(cross_product(A,B),relation_type(A,B))),inference(resolution,[status(thm)],[183210176,183062512]),[]).
% 
% fof(prove_relset_1_5,plain,((ilf_type(b,set_type)&ilf_type(c,set_type)&~ilf_type(cross_product(b,c),relation_type(b,c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET643+3.tptp',unknown),[]).
% 
% cnf(175161944,plain,(~ilf_type(cross_product(b,c),relation_type(b,c))),inference(rewrite,[status(thm)],[prove_relset_1_5]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[184318608,175161944]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------