SET007 Axioms: SET007+673.ax


%------------------------------------------------------------------------------
% File     : SET007+673 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Formal Topological Spaces
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : fintopo2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   92 (   2 unit)
%            Number of atoms       :  571 (  73 equality)
%            Maximal formula depth :   21 (   8 average)
%            Number of connectives :  588 ( 109 ~  ;   0  |; 200  &)
%                                         (  32 <=>; 247 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   21 (   1 propositional; 0-3 arity)
%            Number of functors    :   42 (   3 constant; 0-4 arity)
%            Number of variables   :  276 (   0 singleton; 255 !;  21 ?)
%            Maximal term depth    :    5 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_fintopo2,axiom,(
    ? [A] :
      ( l1_fintopo2(A)
      & v1_fintopo2(A) ) )).

fof(rc2_fintopo2,axiom,(
    ? [A] :
      ( l1_fintopo2(A)
      & ~ v3_struct_0(A)
      & v1_fintopo2(A) ) )).

fof(t1_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(B,C)
               => r1_tarski(k7_fin_topo(A,B),k7_fin_topo(A,C)) ) ) ) ) )).

fof(t2_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_fin_topo(A,B) = k5_subset_1(u1_struct_0(A),k8_fin_topo(A,B),k3_subset_1(u1_struct_0(A),k7_fin_topo(A,B))) ) ) )).

fof(t3_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_fin_topo(A,B) = k6_subset_1(u1_struct_0(A),k8_fin_topo(A,B),k7_fin_topo(A,B)) ) ) )).

fof(t4_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_fin_topo(k3_subset_1(u1_struct_0(A),B),A)
           => v5_fin_topo(B,A) ) ) ) )).

fof(t5_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_fin_topo(k3_subset_1(u1_struct_0(A),B),A)
           => v4_fin_topo(B,A) ) ) ) )).

fof(d1_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( ( r2_hidden(C,k1_fin_topo(A,B))
                        & r2_hidden(C,D) )
                     => k1_fintopo2(A,B,C,D) = k8_margrel1 )
                    & ( ~ ( r2_hidden(C,k1_fin_topo(A,B))
                          & r2_hidden(C,D) )
                     => k1_fintopo2(A,B,C,D) = k7_margrel1 ) ) ) ) ) ) )).

fof(d2_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( ( r2_hidden(C,k1_fin_topo(A,B))
                        & r2_hidden(C,k3_subset_1(u1_struct_0(A),D)) )
                     => k2_fintopo2(A,B,C,D) = k8_margrel1 )
                    & ( ~ ( r2_hidden(C,k1_fin_topo(A,B))
                          & r2_hidden(C,k3_subset_1(u1_struct_0(A),D)) )
                     => k2_fintopo2(A,B,C,D) = k7_margrel1 ) ) ) ) ) ) )).

fof(t6_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( k1_fintopo2(A,B,C,D) = k8_margrel1
                  <=> ( r2_hidden(C,k1_fin_topo(A,B))
                      & r2_hidden(C,D) ) ) ) ) ) ) )).

fof(t7_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( k2_fintopo2(A,B,C,D) = k8_margrel1
                  <=> ( r2_hidden(C,k1_fin_topo(A,B))
                      & r2_hidden(C,k3_subset_1(u1_struct_0(A),D)) ) ) ) ) ) ) )).

fof(t8_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k4_fin_topo(A,C))
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & k1_fintopo2(A,B,D,C) = k8_margrel1
                        & k2_fintopo2(A,B,E,C) = k8_margrel1 ) ) ) ) ) ) )).

fof(d3_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( r2_hidden(C,k1_fin_topo(A,B))
                 => k3_fintopo2(A,B,C) = k8_margrel1 )
                & ( ~ r2_hidden(C,k1_fin_topo(A,B))
                 => k3_fintopo2(A,B,C) = k7_margrel1 ) ) ) ) ) )).

fof(t9_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k3_fintopo2(A,B,C) = k8_margrel1
              <=> r2_hidden(C,k1_fin_topo(A,B)) ) ) ) ) )).

fof(t10_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k7_fin_topo(A,C))
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( k3_fintopo2(A,B,D) = k8_margrel1
                     => k1_fintopo2(A,B,D,C) = k8_margrel1 ) ) ) ) ) ) )).

fof(t11_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k8_fin_topo(A,C))
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & k1_fintopo2(A,B,D,C) = k8_margrel1 ) ) ) ) ) )).

fof(d4_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( r2_hidden(B,C)
                 => k4_fintopo2(A,B,C) = k8_margrel1 )
                & ( ~ r2_hidden(B,C)
                 => k4_fintopo2(A,B,C) = k7_margrel1 ) ) ) ) ) )).

fof(t12_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( k4_fintopo2(A,B,C) = k8_margrel1
              <=> r2_hidden(B,C) ) ) ) ) )).

fof(t13_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k5_fin_topo(A,C))
              <=> ( ? [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                      & ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & k1_fintopo2(A,B,D,C) = k8_margrel1
                          & k2_fintopo2(A,B,E,C) = k8_margrel1 ) )
                  & k4_fintopo2(A,B,C) = k8_margrel1 ) ) ) ) ) )).

fof(t14_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k6_fin_topo(A,C))
              <=> ( ? [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                      & ? [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                          & k1_fintopo2(A,B,D,C) = k8_margrel1
                          & k2_fintopo2(A,B,E,C) = k8_margrel1 ) )
                  & k4_fintopo2(A,B,C) = k7_margrel1 ) ) ) ) ) )).

fof(d5_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( B = C
                 => k5_fintopo2(A,B,C) = k8_margrel1 )
                & ( B != C
                 => k5_fintopo2(A,B,C) = k7_margrel1 ) ) ) ) ) )).

fof(t15_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k5_fintopo2(A,B,C) = k8_margrel1
              <=> B = C ) ) ) ) )).

fof(t16_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k9_fin_topo(A,C))
              <=> ( k4_fintopo2(A,B,C) = k8_margrel1
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( k1_fintopo2(A,B,D,C) = k8_margrel1
                          & k5_fintopo2(A,B,D) = k7_margrel1 ) ) ) ) ) ) ) )).

fof(t17_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k10_fin_topo(A,C))
              <=> ( k4_fintopo2(A,B,C) = k8_margrel1
                  & ? [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                      & k1_fintopo2(A,B,D,C) = k8_margrel1
                      & k5_fintopo2(A,B,D) = k7_margrel1 ) ) ) ) ) ) )).

fof(t18_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k11_fin_topo(A,C))
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & k4_fintopo2(A,D,C) = k8_margrel1
                    & k3_fintopo2(A,D,B) = k8_margrel1 ) ) ) ) ) )).

fof(d6_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_fintopo2(A,B) = k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))),u1_fintopo2(A),B) ) ) )).

fof(d8_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ( v2_fintopo2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,k6_fintopo2(A,B))
                 => r2_hidden(B,C) ) ) ) ) ) )).

fof(t19_fintopo2,axiom,(
    $true )).

fof(t20_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k8_fintopo2(A,C))
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( r2_hidden(D,k6_fintopo2(A,B))
                     => ( ~ r1_xboole_0(D,C)
                        & ~ r1_xboole_0(D,k3_subset_1(u1_struct_0(A),C)) ) ) ) ) ) ) ) )).

fof(t21_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k9_fintopo2(A,C))
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ~ ( r2_hidden(D,k6_fintopo2(A,B))
                        & r1_xboole_0(D,C) ) ) ) ) ) ) )).

fof(t22_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k10_fintopo2(A,C))
              <=> ? [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                    & r2_hidden(D,k6_fintopo2(A,B))
                    & r1_tarski(D,C) ) ) ) ) ) )).

fof(t23_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k11_fintopo2(A,C))
              <=> ( r2_hidden(B,C)
                  & ? [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                      & r2_hidden(D,k6_fintopo2(A,B))
                      & r1_xboole_0(k6_subset_1(u1_struct_0(A),D,k1_struct_0(A,B)),C) ) ) ) ) ) ) )).

fof(d13_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k12_fintopo2(A,B) = k6_subset_1(u1_struct_0(A),B,k11_fintopo2(A,B)) ) ) )).

fof(t24_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k12_fintopo2(A,C))
              <=> ( r2_hidden(B,C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( r2_hidden(D,k6_fintopo2(A,B))
                          & r1_xboole_0(k6_subset_1(u1_struct_0(A),D,k1_struct_0(A,B)),C) ) ) ) ) ) ) ) )).

fof(t25_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(B,C)
               => r1_tarski(k9_fintopo2(A,B),k9_fintopo2(A,C)) ) ) ) ) )).

fof(t26_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(B,C)
               => r1_tarski(k10_fintopo2(A,B),k10_fintopo2(A,C)) ) ) ) ) )).

fof(t27_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k4_subset_1(u1_struct_0(A),k9_fintopo2(A,B),k9_fintopo2(A,C)),k9_fintopo2(A,k4_subset_1(u1_struct_0(A),B,C))) ) ) ) )).

fof(t28_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k9_fintopo2(A,k5_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),k9_fintopo2(A,B),k9_fintopo2(A,C))) ) ) ) )).

fof(t29_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k4_subset_1(u1_struct_0(A),k10_fintopo2(A,B),k10_fintopo2(A,C)),k10_fintopo2(A,k4_subset_1(u1_struct_0(A),B,C))) ) ) ) )).

fof(t30_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k10_fintopo2(A,k5_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),k10_fintopo2(A,B),k10_fintopo2(A,C))) ) ) ) )).

fof(t31_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ~ ( r2_hidden(C,k6_fintopo2(A,B))
                        & r2_hidden(D,k6_fintopo2(A,B))
                        & ! [E] :
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                           => ~ ( r2_hidden(E,k6_fintopo2(A,B))
                                & r1_tarski(E,k5_subset_1(u1_struct_0(A),C,D)) ) ) ) ) ) )
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => k9_fintopo2(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k9_fintopo2(A,B),k9_fintopo2(A,C)) ) ) ) ) )).

fof(t32_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ~ ( r2_hidden(C,k6_fintopo2(A,B))
                        & r2_hidden(D,k6_fintopo2(A,B))
                        & ! [E] :
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                           => ~ ( r2_hidden(E,k6_fintopo2(A,B))
                                & r1_tarski(E,k5_subset_1(u1_struct_0(A),C,D)) ) ) ) ) ) )
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => k5_subset_1(u1_struct_0(A),k10_fintopo2(A,B),k10_fintopo2(A,C)) = k10_fintopo2(A,k5_subset_1(u1_struct_0(A),B,C)) ) ) ) ) )).

fof(t33_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ! [F] :
                            ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                           => ~ ( r2_hidden(E,k6_fintopo2(A,D))
                                & r2_hidden(F,k6_fintopo2(A,D))
                                & ! [G] :
                                    ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                                   => ~ ( r2_hidden(G,k6_fintopo2(A,D))
                                        & r1_tarski(G,k5_subset_1(u1_struct_0(A),E,F)) ) ) ) ) ) )
               => r1_tarski(k8_fintopo2(A,k4_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k8_fintopo2(A,B),k8_fintopo2(A,C))) ) ) ) ) )).

fof(t34_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ( ( v2_fintopo2(A)
          & ! [B] :
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
             => ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => k8_fintopo2(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k8_fintopo2(A,B),k8_fintopo2(A,C)) ) ) )
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ~ ( r2_hidden(C,k6_fintopo2(A,B))
                        & r2_hidden(D,k6_fintopo2(A,B))
                        & ! [E] :
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                           => ~ ( r2_hidden(E,k6_fintopo2(A,B))
                                & r1_tarski(E,k5_subset_1(u1_struct_0(A),C,D)) ) ) ) ) ) ) ) ) )).

fof(t35_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k11_fintopo2(A,C))
              <=> ( r2_hidden(B,C)
                  & ~ r2_hidden(B,k9_fintopo2(A,k6_subset_1(u1_struct_0(A),C,k1_struct_0(A,B)))) ) ) ) ) ) )).

fof(t36_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ( v2_fintopo2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => r1_tarski(B,k9_fintopo2(A,B)) ) ) ) )).

fof(t37_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ( v2_fintopo2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => r1_tarski(k10_fintopo2(A,B),B) ) ) ) )).

fof(t38_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_subset_1(u1_struct_0(A),k9_fintopo2(A,k3_subset_1(u1_struct_0(A),B))) = k10_fintopo2(A,B) ) ) )).

fof(t39_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_subset_1(u1_struct_0(A),k10_fintopo2(A,k3_subset_1(u1_struct_0(A),B))) = k9_fintopo2(A,B) ) ) )).

fof(t40_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k8_fintopo2(A,B) = k5_subset_1(u1_struct_0(A),k9_fintopo2(A,B),k9_fintopo2(A,k3_subset_1(u1_struct_0(A),B))) ) ) )).

fof(t41_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k8_fintopo2(A,B) = k5_subset_1(u1_struct_0(A),k9_fintopo2(A,B),k3_subset_1(u1_struct_0(A),k10_fintopo2(A,B))) ) ) )).

fof(t42_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k8_fintopo2(A,B) = k8_fintopo2(A,k3_subset_1(u1_struct_0(A),B)) ) ) )).

fof(t43_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k8_fintopo2(A,B) = k6_subset_1(u1_struct_0(A),k9_fintopo2(A,B),k10_fintopo2(A,B)) ) ) )).

fof(d14_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k13_fintopo2(A,B) = k5_subset_1(u1_struct_0(A),B,k8_fintopo2(A,B)) ) ) )).

fof(d15_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k14_fintopo2(A,B) = k5_subset_1(u1_struct_0(A),k3_subset_1(u1_struct_0(A),B),k8_fintopo2(A,B)) ) ) )).

fof(t44_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k8_fintopo2(A,B) = k4_subset_1(u1_struct_0(A),k13_fintopo2(A,B),k14_fintopo2(A,B)) ) ) )).

fof(d16_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_fintopo2(B,A)
          <=> B = k10_fintopo2(A,B) ) ) ) )).

fof(d17_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_fintopo2(B,A)
          <=> B = k9_fintopo2(A,B) ) ) ) )).

fof(t45_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_fintopo2(k3_subset_1(u1_struct_0(A),B),A)
           => v4_fintopo2(B,A) ) ) ) )).

fof(t46_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_fintopo2(k3_subset_1(u1_struct_0(A),B),A)
           => v3_fintopo2(B,A) ) ) ) )).

fof(t47_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v2_fintopo2(A)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => r2_hidden(k1_struct_0(A,D),k6_fintopo2(A,D)) ) )
               => k9_fintopo2(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k9_fintopo2(A,B),k9_fintopo2(A,C)) ) ) ) ) )).

fof(t48_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v2_fintopo2(A)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => r2_hidden(k1_struct_0(A,D),k6_fintopo2(A,D)) ) )
               => k4_subset_1(u1_struct_0(A),k10_fintopo2(A,B),k10_fintopo2(A,C)) = k10_fintopo2(A,k4_subset_1(u1_struct_0(A),B,C)) ) ) ) ) )).

fof(dt_l1_fintopo2,axiom,(
    ! [A] :
      ( l1_fintopo2(A)
     => l1_struct_0(A) ) )).

fof(existence_l1_fintopo2,axiom,(
    ? [A] : l1_fintopo2(A) )).

fof(abstractness_v1_fintopo2,axiom,(
    ! [A] :
      ( l1_fintopo2(A)
     => ( v1_fintopo2(A)
       => A = g1_fintopo2(u1_struct_0(A),u1_fintopo2(A)) ) ) )).

fof(dt_k1_fintopo2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k1_fintopo2(A,B,C,D),k6_margrel1) ) )).

fof(dt_k2_fintopo2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k2_fintopo2(A,B,C,D),k6_margrel1) ) )).

fof(dt_k3_fintopo2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k3_fintopo2(A,B,C),k6_margrel1) ) )).

fof(dt_k4_fintopo2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k4_fintopo2(A,B,C),k6_margrel1) ) )).

fof(dt_k5_fintopo2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k5_fintopo2(A,B,C),k6_margrel1) ) )).

fof(dt_k6_fintopo2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k6_fintopo2(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k7_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k7_fintopo2(A))
        & v1_fintopo2(k7_fintopo2(A))
        & l1_fintopo2(k7_fintopo2(A)) ) ) )).

fof(dt_k8_fintopo2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k8_fintopo2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k9_fintopo2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k9_fintopo2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k10_fintopo2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k10_fintopo2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k11_fintopo2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k11_fintopo2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k12_fintopo2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k12_fintopo2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k13_fintopo2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k13_fintopo2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k14_fintopo2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k14_fintopo2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_u1_fintopo2,axiom,(
    ! [A] :
      ( l1_fintopo2(A)
     => ( v1_funct_1(u1_fintopo2(A))
        & v1_funct_2(u1_fintopo2(A),u1_struct_0(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
        & m2_relset_1(u1_fintopo2(A),u1_struct_0(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) )).

fof(dt_g1_fintopo2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_relset_1(B,A,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( v1_fintopo2(g1_fintopo2(A,B))
        & l1_fintopo2(g1_fintopo2(A,B)) ) ) )).

fof(free_g1_fintopo2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_relset_1(B,A,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C,D] :
          ( g1_fintopo2(A,B) = g1_fintopo2(C,D)
         => ( A = C
            & B = D ) ) ) )).

fof(d7_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_fintopo2(B)
            & l1_fintopo2(B) )
         => ( B = k7_fintopo2(A)
          <=> ( u1_struct_0(B) = u1_struct_0(A)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(B))
                 => k6_fintopo2(B,C) = a_3_0_fintopo2(A,B,C) ) ) ) ) ) )).

fof(d9_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k8_fintopo2(A,B) = a_2_0_fintopo2(A,B) ) ) )).

fof(d10_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k9_fintopo2(A,B) = a_2_1_fintopo2(A,B) ) ) )).

fof(d11_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k10_fintopo2(A,B) = a_2_2_fintopo2(A,B) ) ) )).

fof(d12_fintopo2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_fintopo2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k11_fintopo2(A,B) = a_2_3_fintopo2(A,B) ) ) )).

fof(fraenkel_a_3_0_fintopo2,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v1_fintopo2(C)
        & l1_fintopo2(C)
        & m1_subset_1(D,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_0_fintopo2(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
            & A = E
            & r2_hidden(E,u1_pre_topc(B))
            & r2_hidden(D,E) ) ) ) )).

fof(fraenkel_a_2_0_fintopo2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_fintopo2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_0_fintopo2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ! [E] :
                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
               => ( r2_hidden(E,k6_fintopo2(B,D))
                 => ( ~ r1_xboole_0(E,C)
                    & ~ r1_xboole_0(E,k3_subset_1(u1_struct_0(B),C)) ) ) ) ) ) ) )).

fof(fraenkel_a_2_1_fintopo2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_fintopo2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_1_fintopo2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ! [E] :
                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
               => ~ ( r2_hidden(E,k6_fintopo2(B,D))
                    & r1_xboole_0(E,C) ) ) ) ) ) )).

fof(fraenkel_a_2_2_fintopo2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_fintopo2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_2_fintopo2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ? [E] :
                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                & r2_hidden(E,k6_fintopo2(B,D))
                & r1_tarski(E,C) ) ) ) ) )).

fof(fraenkel_a_2_3_fintopo2,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_fintopo2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_3_fintopo2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r2_hidden(D,C)
            & ? [E] :
                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                & r2_hidden(E,k6_fintopo2(B,D))
                & r1_xboole_0(k6_subset_1(u1_struct_0(B),E,k1_struct_0(B,D)),C) ) ) ) ) )).
%------------------------------------------------------------------------------