%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SEU167+3 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art02.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 15:50:41 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   13 (   6 unt;   0 def)
%            Number of atoms       :   25 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   24 (  12   ~;   9   |;   3   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   18 (   0 sgn   6   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t118_zfmisc_1,plain,
    ! [C,A,B] :
      ( ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
        | ~ subset(A,B) )
      & ( subset(cartesian_product2(A,C),cartesian_product2(B,C))
        | ~ subset(A,B) ) ),
    file('/tmp/SystemOnTPTP15710/SEU167+3.p',unknown),
    [] ).

cnf(166016920,plain,
    ( subset(cartesian_product2(A,C),cartesian_product2(B,C))
    | ~ subset(A,B) ),
    inference(rewrite,[status(thm)],[t118_zfmisc_1]),
    [] ).

fof(t119_zfmisc_1,plain,
    ( subset(a,b)
    & subset(c,d)
    & ~ subset(cartesian_product2(a,c),cartesian_product2(b,d)) ),
    file('/tmp/SystemOnTPTP15710/SEU167+3.p',unknown),
    [] ).

cnf(166111344,plain,
    subset(a,b),
    inference(rewrite,[status(thm)],[t119_zfmisc_1]),
    [] ).

cnf(179381816,plain,
    subset(cartesian_product2(a,A),cartesian_product2(b,A)),
    inference(resolution,[status(thm)],[166016920,166111344]),
    [] ).

fof(t1_xboole_1,plain,
    ! [A,B,C] :
      ( ~ subset(A,B)
      | ~ subset(B,C)
      | subset(A,C) ),
    file('/tmp/SystemOnTPTP15710/SEU167+3.p',unknown),
    [] ).

cnf(166118368,plain,
    ( ~ subset(A,B)
    | ~ subset(B,C)
    | subset(A,C) ),
    inference(rewrite,[status(thm)],[t1_xboole_1]),
    [] ).

cnf(166092920,plain,
    ~ subset(cartesian_product2(a,c),cartesian_product2(b,d)),
    inference(rewrite,[status(thm)],[t119_zfmisc_1]),
    [] ).

cnf(179360520,plain,
    ( ~ subset(cartesian_product2(a,c),A)
    | ~ subset(A,cartesian_product2(b,d)) ),
    inference(resolution,[status(thm)],[166118368,166092920]),
    [] ).

cnf(166026848,plain,
    ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
    | ~ subset(A,B) ),
    inference(rewrite,[status(thm)],[t118_zfmisc_1]),
    [] ).

cnf(166104352,plain,
    subset(c,d),
    inference(rewrite,[status(thm)],[t119_zfmisc_1]),
    [] ).

cnf(179194664,plain,
    subset(cartesian_product2(A,c),cartesian_product2(A,d)),
    inference(resolution,[status(thm)],[166026848,166104352]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[179381816,179360520,179194664]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t118_zfmisc_1,plain,(((subset(cartesian_product2(C,A),cartesian_product2(C,B))|~subset(A,B))&(subset(cartesian_product2(A,C),cartesian_product2(B,C))|~subset(A,B)))),file('/tmp/SystemOnTPTP15710/SEU167+3.p',unknown),[]).
% 
% cnf(166016920,plain,(subset(cartesian_product2(A,C),cartesian_product2(B,C))|~subset(A,B)),inference(rewrite,[status(thm)],[t118_zfmisc_1]),[]).
% 
% fof(t119_zfmisc_1,plain,((subset(a,b)&subset(c,d)&~subset(cartesian_product2(a,c),cartesian_product2(b,d)))),file('/tmp/SystemOnTPTP15710/SEU167+3.p',unknown),[]).
% 
% cnf(166111344,plain,(subset(a,b)),inference(rewrite,[status(thm)],[t119_zfmisc_1]),[]).
% 
% cnf(179381816,plain,(subset(cartesian_product2(a,A),cartesian_product2(b,A))),inference(resolution,[status(thm)],[166016920,166111344]),[]).
% 
% fof(t1_xboole_1,plain,(~subset(A,B)|~subset(B,C)|subset(A,C)),file('/tmp/SystemOnTPTP15710/SEU167+3.p',unknown),[]).
% 
% cnf(166118368,plain,(~subset(A,B)|~subset(B,C)|subset(A,C)),inference(rewrite,[status(thm)],[t1_xboole_1]),[]).
% 
% cnf(166092920,plain,(~subset(cartesian_product2(a,c),cartesian_product2(b,d))),inference(rewrite,[status(thm)],[t119_zfmisc_1]),[]).
% 
% cnf(179360520,plain,(~subset(cartesian_product2(a,c),A)|~subset(A,cartesian_product2(b,d))),inference(resolution,[status(thm)],[166118368,166092920]),[]).
% 
% cnf(166026848,plain,(subset(cartesian_product2(C,A),cartesian_product2(C,B))|~subset(A,B)),inference(rewrite,[status(thm)],[t118_zfmisc_1]),[]).
% 
% cnf(166104352,plain,(subset(c,d)),inference(rewrite,[status(thm)],[t119_zfmisc_1]),[]).
% 
% cnf(179194664,plain,(subset(cartesian_product2(A,c),cartesian_product2(A,d))),inference(resolution,[status(thm)],[166026848,166104352]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[179381816,179360520,179194664]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------