%------------------------------------------------------------------------------
% File     : SEU167+1 : TPTP v8.2.0. Released v3.3.0.
% Domain   : Set theory
% Problem  : MPTP bushy problem t119_zfmisc_1
% Version  : [Urb07] axioms : Especial.
% English  :

% Refs     : [Ban01] Bancerek et al. (2001), On the Characterizations of Co
%          : [Urb07] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb07]
% Names    : bushy-t119_zfmisc_1 [Urb07]

% Status   : Theorem
% Rating   : 0.06 v8.2.0, 0.07 v7.5.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v5.5.0, 0.04 v5.4.0, 0.00 v5.3.0, 0.09 v5.2.0, 0.00 v4.0.1, 0.05 v3.7.0, 0.00 v3.3.0
% Syntax   : Number of formulae    :    5 (   2 unt;   0 def)
%            Number of atoms       :   11 (   0 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :    6 (   0   ~;   0   |;   3   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :   12 (  12   !;   0   ?)
% SPC      : FOF_THM_RFO_NEQ

% Comments : Translated by MPTP 0.2 from the original problem in the Mizar
%            library, www.mizar.org
%------------------------------------------------------------------------------
fof(dt_k2_zfmisc_1,axiom,
    $true ).

fof(reflexivity_r1_tarski,axiom,
    ! [A,B] : subset(A,A) ).

fof(t118_zfmisc_1,axiom,
    ! [A,B,C] :
      ( subset(A,B)
     => ( subset(cartesian_product2(A,C),cartesian_product2(B,C))
        & subset(cartesian_product2(C,A),cartesian_product2(C,B)) ) ) ).

fof(t119_zfmisc_1,conjecture,
    ! [A,B,C,D] :
      ( ( subset(A,B)
        & subset(C,D) )
     => subset(cartesian_product2(A,C),cartesian_product2(B,D)) ) ).

fof(t1_xboole_1,axiom,
    ! [A,B,C] :
      ( ( subset(A,B)
        & subset(B,C) )
     => subset(A,C) ) ).

%------------------------------------------------------------------------------