%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET242-6 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art07.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 15:30:41 EDT 2009

% Result   : Unsatisfiable 2.1s
% Output   : Refutation 2.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   12 (  10 unt;   0 def)
%            Number of atoms       :   16 (   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    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   12 (   0 sgn   6   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_restriction_alternate_defn5_2,plain,
    member(z,cross_product(x,y)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET242-6.tptp',unknown),
    [] ).

cnf(155201352,plain,
    member(z,cross_product(x,y)),
    inference(rewrite,[status(thm)],[prove_restriction_alternate_defn5_2]),
    [] ).

fof(prove_restriction_alternate_defn5_1,plain,
    member(z,xr),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET242-6.tptp',unknown),
    [] ).

cnf(155197576,plain,
    member(z,xr),
    inference(rewrite,[status(thm)],[prove_restriction_alternate_defn5_1]),
    [] ).

fof(intersection3,plain,
    ! [A,B,C] :
      ( ~ member(A,B)
      | ~ member(A,C)
      | member(A,intersection(B,C)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET242-6.tptp',unknown),
    [] ).

cnf(154204440,plain,
    ( ~ member(A,B)
    | ~ member(A,C)
    | member(A,intersection(B,C)) ),
    inference(rewrite,[status(thm)],[intersection3]),
    [] ).

fof(prove_restriction_alternate_defn5_3,plain,
    ~ member(z,restrict(xr,x,y)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET242-6.tptp',unknown),
    [] ).

cnf(155210560,plain,
    ~ member(z,restrict(xr,x,y)),
    inference(rewrite,[status(thm)],[prove_restriction_alternate_defn5_3]),
    [] ).

fof(restriction1,plain,
    ! [A,B,C] : $equal(intersection(A,cross_product(B,C)),restrict(A,B,C)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET242-6.tptp',unknown),
    [] ).

cnf(154246288,plain,
    $equal(intersection(A,cross_product(B,C)),restrict(A,B,C)),
    inference(rewrite,[status(thm)],[restriction1]),
    [] ).

cnf(171426176,plain,
    ~ member(z,intersection(xr,cross_product(x,y))),
    inference(paramodulation,[status(thm)],[155210560,154246288,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[155201352,155197576,154204440,171426176]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(prove_restriction_alternate_defn5_2,plain,(member(z,cross_product(x,y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET242-6.tptp',unknown),[]).
% 
% cnf(155201352,plain,(member(z,cross_product(x,y))),inference(rewrite,[status(thm)],[prove_restriction_alternate_defn5_2]),[]).
% 
% fof(prove_restriction_alternate_defn5_1,plain,(member(z,xr)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET242-6.tptp',unknown),[]).
% 
% cnf(155197576,plain,(member(z,xr)),inference(rewrite,[status(thm)],[prove_restriction_alternate_defn5_1]),[]).
% 
% fof(intersection3,plain,(~member(A,B)|~member(A,C)|member(A,intersection(B,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET242-6.tptp',unknown),[]).
% 
% cnf(154204440,plain,(~member(A,B)|~member(A,C)|member(A,intersection(B,C))),inference(rewrite,[status(thm)],[intersection3]),[]).
% 
% fof(prove_restriction_alternate_defn5_3,plain,(~member(z,restrict(xr,x,y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET242-6.tptp',unknown),[]).
% 
% cnf(155210560,plain,(~member(z,restrict(xr,x,y))),inference(rewrite,[status(thm)],[prove_restriction_alternate_defn5_3]),[]).
% 
% fof(restriction1,plain,($equal(intersection(A,cross_product(B,C)),restrict(A,B,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET242-6.tptp',unknown),[]).
% 
% cnf(154246288,plain,($equal(intersection(A,cross_product(B,C)),restrict(A,B,C))),inference(rewrite,[status(thm)],[restriction1]),[]).
% 
% cnf(171426176,plain,(~member(z,intersection(xr,cross_product(x,y)))),inference(paramodulation,[status(thm)],[155210560,154246288,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[155201352,155197576,154204440,171426176]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------