%------------------------------------------------------------------------------
% File     : SEU247+1 : TPTP v9.0.0. Released v3.3.0.
% Domain   : Set theory
% Problem  : MPTP bushy problem t18_wellord1
% 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-t18_wellord1 [Urb07]

% Status   : Theorem
% Rating   : 0.09 v9.0.0, 0.11 v8.1.0, 0.14 v7.5.0, 0.16 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.17 v6.0.0, 0.09 v5.5.0, 0.11 v5.4.0, 0.14 v5.3.0, 0.15 v5.2.0, 0.05 v5.0.0, 0.04 v4.0.0, 0.08 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0
% Syntax   : Number of formulae    :   11 (   4 unt;   0 def)
%            Number of atoms       :   18 (   6 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   0   ~;   0   |;   0   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   0 con; 2-2 aty)
%            Number of variables   :   19 (  19   !;   0   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Translated by MPTP 0.2 from the original problem in the Mizar
%            library, www.mizar.org
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).

fof(d6_wellord1,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ) ).

fof(dt_k2_wellord1,axiom,
    ! [A,B] :
      ( relation(A)
     => relation(relation_restriction(A,B)) ) ).

fof(dt_k2_zfmisc_1,axiom,
    $true ).

fof(dt_k3_xboole_0,axiom,
    $true ).

fof(dt_k7_relat_1,axiom,
    ! [A,B] :
      ( relation(A)
     => relation(relation_dom_restriction(A,B)) ) ).

fof(dt_k8_relat_1,axiom,
    ! [A,B] :
      ( relation(B)
     => relation(relation_rng_restriction(A,B)) ) ).

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

fof(t140_relat_1,axiom,
    ! [A,B,C] :
      ( relation(C)
     => relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)) ) ).

fof(t17_wellord1,axiom,
    ! [A,B] :
      ( relation(B)
     => relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A) ) ).

fof(t18_wellord1,conjecture,
    ! [A,B] :
      ( relation(B)
     => relation_restriction(B,A) = relation_rng_restriction(A,relation_dom_restriction(B,A)) ) ).

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