%------------------------------------------------------------------------------
% File     : SET916+1 : TPTP v8.2.0. Released v3.2.0.
% Domain   : Set theory
% Problem  : ~ ( ~ in(A,B) & ~ in(C,B) & ~ disjoint(unordered_pair(A,C),B) )
% Version  : [Urb06] axioms : Especial.
% English  :

% Refs     : [Byl90] Bylinski (1990), Some Basic Properties of Sets
%          : [Urb06] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb06]
% Names    : zfmisc_1__t57_zfmisc_1 [Urb06]

% Status   : Theorem
% Rating   : 0.44 v8.2.0, 0.42 v8.1.0, 0.39 v7.5.0, 0.47 v7.4.0, 0.37 v7.3.0, 0.34 v7.2.0, 0.31 v7.1.0, 0.39 v7.0.0, 0.33 v6.4.0, 0.42 v6.3.0, 0.46 v6.2.0, 0.48 v6.1.0, 0.60 v6.0.0, 0.61 v5.5.0, 0.59 v5.4.0, 0.64 v5.3.0, 0.63 v5.2.0, 0.50 v5.1.0, 0.52 v5.0.0, 0.54 v4.1.0, 0.61 v4.0.1, 0.57 v4.0.0, 0.58 v3.7.0, 0.60 v3.5.0, 0.58 v3.3.0, 0.57 v3.2.0
% Syntax   : Number of formulae    :   11 (   5 unt;   0 def)
%            Number of atoms       :   24 (   7 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   23 (  10   ~;   1   |;   6   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   0 prp; 1-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 2-2 aty)
%            Number of variables   :   27 (  24   !;   3   ?)
% 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(commutativity_k2_tarski,axiom,
    ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).

fof(commutativity_k3_xboole_0,axiom,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).

fof(d2_tarski,axiom,
    ! [A,B,C] :
      ( C = unordered_pair(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( D = A
            | D = B ) ) ) ).

fof(d3_xboole_0,axiom,
    ! [A,B,C] :
      ( C = set_intersection2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ) ).

fof(idempotence_k3_xboole_0,axiom,
    ! [A,B] : set_intersection2(A,A) = A ).

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

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

fof(symmetry_r1_xboole_0,axiom,
    ! [A,B] :
      ( disjoint(A,B)
     => disjoint(B,A) ) ).

fof(t4_xboole_0,axiom,
    ! [A,B] :
      ( ~ ( ~ disjoint(A,B)
          & ! [C] : ~ in(C,set_intersection2(A,B)) )
      & ~ ( ? [C] : in(C,set_intersection2(A,B))
          & disjoint(A,B) ) ) ).

fof(t57_zfmisc_1,conjecture,
    ! [A,B,C] :
      ~ ( ~ in(A,B)
        & ~ in(C,B)
        & ~ disjoint(unordered_pair(A,C),B) ) ).

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