%------------------------------------------------------------------------------
% File     : SEU134+1 : TPTP v8.2.0. Released v3.3.0.
% Domain   : Set theory
% Problem  : MPTP bushy problem t37_xboole_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-t37_xboole_1 [Urb07]

% Status   : Theorem
% Rating   : 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.03 v6.0.0, 0.04 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v4.1.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.12 v3.7.0, 0.05 v3.3.0
% Syntax   : Number of formulae    :   14 (   8 unt;   0 def)
%            Number of atoms       :   21 (   6 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   12 (   5   ~;   0   |;   3   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-2 aty)
%            Number of variables   :   17 (  15   !;   2   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Translated by MPTP 0.2 from the original problem in the Mizar
%            library, www.mizar.org
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
    ! [A,B] :
      ( in(A,B)
     => ~ in(B,A) ) ).

fof(rc1_xboole_0,axiom,
    ? [A] : empty(A) ).

fof(rc2_xboole_0,axiom,
    ? [A] : ~ empty(A) ).

fof(t7_boole,axiom,
    ! [A,B] :
      ~ ( in(A,B)
        & empty(B) ) ).

fof(t8_boole,axiom,
    ! [A,B] :
      ~ ( empty(A)
        & A != B
        & empty(B) ) ).

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

fof(dt_k1_xboole_0,axiom,
    $true ).

fof(dt_k4_xboole_0,axiom,
    $true ).

fof(fc1_xboole_0,axiom,
    empty(empty_set) ).

fof(t3_boole,axiom,
    ! [A] : set_difference(A,empty_set) = A ).

fof(t4_boole,axiom,
    ! [A] : set_difference(empty_set,A) = empty_set ).

fof(t6_boole,axiom,
    ! [A] :
      ( empty(A)
     => A = empty_set ) ).

fof(t37_xboole_1,conjecture,
    ! [A,B] :
      ( set_difference(A,B) = empty_set
    <=> subset(A,B) ) ).

fof(l32_xboole_1,axiom,
    ! [A,B] :
      ( set_difference(A,B) = empty_set
    <=> subset(A,B) ) ).

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