SET007 Axioms: SET007+915.ax


%------------------------------------------------------------------------------
% File     : SET007+915 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Borel Families of Subsets of 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    : topgen_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  124 (   4 unit)
%            Number of atoms       :  768 (  39 equality)
%            Maximal formula depth :   24 (   7 average)
%            Number of connectives :  776 ( 132 ~  ;   1  |; 373  &)
%                                         (  23 <=>; 247 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   63 (   0 propositional; 1-3 arity)
%            Number of functors    :   45 (   7 constant; 0-4 arity)
%            Number of variables   :  257 (   0 singleton; 245 !;  12 ?)
%            Maximal term depth    :    4 (   1 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(fc1_topgen_4,axiom,
    ( v1_membered(k3_numbers)
    & v2_membered(k3_numbers)
    & v3_membered(k3_numbers)
    & ~ v1_xboole_0(k3_numbers)
    & ~ v1_finset_1(k3_numbers)
    & v1_card_4(k3_numbers) )).

fof(cc1_topgen_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v6_group_1(A)
       => v5_waybel23(A) ) ) )).

fof(fc2_topgen_4,axiom,
    ( v1_membered(k1_numbers)
    & v2_membered(k1_numbers)
    & ~ v1_xboole_0(k1_numbers)
    & ~ v1_finset_1(k1_numbers)
    & ~ v1_card_4(k1_numbers) )).

fof(cc2_topgen_4,axiom,(
    ! [A] :
      ( ~ v1_card_4(A)
     => ~ v1_finset_1(A) ) )).

fof(cc3_topgen_4,axiom,(
    ! [A] :
      ( ~ v1_finset_1(A)
     => ~ v1_realset1(A) ) )).

fof(rc1_topgen_4,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & ~ v1_card_4(A) ) )).

fof(cc4_topgen_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v5_waybel23(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v7_topgen_1(A) ) ) ) )).

fof(cc5_topgen_4,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( ~ v1_xboole_0(B)
          & v1_prob_1(B,A)
          & v1_measure1(B,A) )
       => ( ~ v1_xboole_0(B)
          & v1_finsub_1(B)
          & v2_finsub_1(B)
          & v1_prob_1(B,A)
          & v1_measure1(B,A)
          & v3_topgen_4(B,A) ) ) ) )).

fof(cc6_topgen_4,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v3_topgen_4(B,A)
       => ~ v1_xboole_0(B) ) ) )).

fof(cc7_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ( v1_prob_1(B,u1_struct_0(A))
              & v1_topgen_4(B,A)
              & v3_topgen_4(B,u1_struct_0(A)) )
           => ( v2_topgen_4(B,A)
              & v4_topgen_4(B,u1_struct_0(A)) ) ) ) ) )).

fof(cc8_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ( v1_prob_1(B,u1_struct_0(A))
              & v2_topgen_4(B,A)
              & v4_topgen_4(B,u1_struct_0(A)) )
           => ( ~ v1_xboole_0(B)
              & v1_topgen_4(B,A)
              & v3_topgen_4(B,u1_struct_0(A)) ) ) ) ) )).

fof(fc3_topgen_4,axiom,(
    ! [A,B] :
      ( ( v1_card_4(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => v1_card_4(k7_setfam_1(A,B)) ) )).

fof(cc9_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_xboole_0(B)
           => ( v1_tops_2(B,A)
              & v2_tops_2(B,A) ) ) ) ) )).

fof(rc2_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
          & v1_tops_2(B,A)
          & v2_tops_2(B,A)
          & v1_card_4(B) ) ) )).

fof(cc10_topgen_4,axiom,(
    ! [A] :
      ( v1_xboole_0(A)
     => v1_card_4(A) ) )).

fof(fc4_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_membered(k1_pre_topc(A))
        & v2_membered(k1_pre_topc(A))
        & v3_membered(k1_pre_topc(A))
        & v4_membered(k1_pre_topc(A))
        & v5_membered(k1_pre_topc(A))
        & v1_xboole_0(k1_pre_topc(A))
        & v3_pre_topc(k1_pre_topc(A),A)
        & v4_pre_topc(k1_pre_topc(A),A)
        & v2_tops_1(k1_pre_topc(A),A)
        & v3_tops_1(k1_pre_topc(A),A)
        & v2_connsp_1(k1_pre_topc(A),A)
        & v1_ordinal1(k1_pre_topc(A))
        & v2_ordinal1(k1_pre_topc(A))
        & v3_ordinal1(k1_pre_topc(A))
        & v1_finset_1(k1_pre_topc(A))
        & v6_compts_1(k1_pre_topc(A),A)
        & v1_card_4(k1_pre_topc(A))
        & v2_topgen_1(k1_pre_topc(A),A)
        & v5_topgen_1(k1_pre_topc(A),A)
        & v6_topgen_1(k1_pre_topc(A),A)
        & v5_topgen_4(k1_pre_topc(A),A)
        & v6_topgen_4(k1_pre_topc(A),A) ) ) )).

fof(fc5_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v3_pre_topc(k2_pre_topc(A),A)
        & v4_pre_topc(k2_pre_topc(A),A)
        & v1_tops_1(k2_pre_topc(A),A)
        & v5_topgen_4(k2_pre_topc(A),A)
        & v6_topgen_4(k2_pre_topc(A),A) ) ) )).

fof(cc11_topgen_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v7_topgen_4(A) )
       => ( v2_pre_topc(A)
          & v2_t_0topsp(A) ) ) ) )).

fof(cc12_topgen_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v1_urysohn1(A) )
       => ( v2_pre_topc(A)
          & v7_topgen_4(A) ) ) ) )).

fof(fc6_topgen_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & v1_card_4(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_membered(k4_topgen_4(A,B))
        & v2_membered(k4_topgen_4(A,B))
        & v3_membered(k4_topgen_4(A,B))
        & v4_membered(k4_topgen_4(A,B))
        & v5_membered(k4_topgen_4(A,B))
        & v1_xboole_0(k4_topgen_4(A,B))
        & v3_pre_topc(k4_topgen_4(A,B),A)
        & v4_pre_topc(k4_topgen_4(A,B),A)
        & v2_tops_1(k4_topgen_4(A,B),A)
        & v3_tops_1(k4_topgen_4(A,B),A)
        & v2_connsp_1(k4_topgen_4(A,B),A)
        & v1_ordinal1(k4_topgen_4(A,B))
        & v2_ordinal1(k4_topgen_4(A,B))
        & v3_ordinal1(k4_topgen_4(A,B))
        & v1_finset_1(k4_topgen_4(A,B))
        & v6_compts_1(k4_topgen_4(A,B),A)
        & v1_card_4(k4_topgen_4(A,B))
        & v2_topgen_1(k4_topgen_4(A,B),A)
        & v5_topgen_1(k4_topgen_4(A,B),A)
        & v6_topgen_1(k4_topgen_4(A,B),A) ) ) )).

fof(rc3_topgen_4,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v5_waybel23(A)
      & v7_topgen_1(A) ) )).

fof(fc7_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v1_xboole_0(k1_topgen_4(A))
        & v1_prob_1(k1_topgen_4(A),u1_struct_0(A))
        & v1_topgen_4(k1_topgen_4(A),A)
        & v2_topgen_4(k1_topgen_4(A),A)
        & v3_topgen_4(k1_topgen_4(A),u1_struct_0(A))
        & v4_topgen_4(k1_topgen_4(A),u1_struct_0(A)) ) ) )).

fof(rc4_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
          & ~ v1_xboole_0(B)
          & v1_prob_1(B,u1_struct_0(A))
          & v1_topgen_4(B,A)
          & v2_topgen_4(B,A)
          & v3_topgen_4(B,u1_struct_0(A))
          & v4_topgen_4(B,u1_struct_0(A)) ) ) )).

fof(fc8_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v1_xboole_0(k11_prob_1(u1_struct_0(A),k1_topgen_4(A)))
        & v1_finsub_1(k11_prob_1(u1_struct_0(A),k1_topgen_4(A)))
        & v2_finsub_1(k11_prob_1(u1_struct_0(A),k1_topgen_4(A)))
        & v1_prob_1(k11_prob_1(u1_struct_0(A),k1_topgen_4(A)),u1_struct_0(A))
        & v1_topgen_4(k11_prob_1(u1_struct_0(A),k1_topgen_4(A)),A)
        & v2_topgen_4(k11_prob_1(u1_struct_0(A),k1_topgen_4(A)),A)
        & v3_topgen_4(k11_prob_1(u1_struct_0(A),k1_topgen_4(A)),u1_struct_0(A))
        & v4_topgen_4(k11_prob_1(u1_struct_0(A),k1_topgen_4(A)),u1_struct_0(A)) ) ) )).

fof(rc5_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
          & ~ v1_xboole_0(B)
          & v1_finsub_1(B)
          & v2_finsub_1(B)
          & v1_prob_1(B,u1_struct_0(A))
          & v1_measure1(B,u1_struct_0(A))
          & v3_topgen_4(B,u1_struct_0(A)) ) ) )).

fof(cc13_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_prob_1(B,u1_struct_0(A))
         => ( ~ v1_xboole_0(B)
            & v1_finsub_1(B)
            & v2_finsub_1(B)
            & v1_prob_1(B,u1_struct_0(A))
            & v3_topgen_4(B,u1_struct_0(A)) ) ) ) )).

fof(rc6_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_prob_1(B,u1_struct_0(A))
          & ~ v1_xboole_0(B)
          & v1_finsub_1(B)
          & v2_finsub_1(B)
          & v1_prob_1(B,u1_struct_0(A))
          & v1_topgen_4(B,A)
          & v2_topgen_4(B,A)
          & v3_topgen_4(B,u1_struct_0(A))
          & v4_topgen_4(B,u1_struct_0(A)) ) ) )).

fof(fc9_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_tops_2(k1_openlatt(A),A)
        & v1_topgen_4(k1_openlatt(A),A) ) ) )).

fof(cc14_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_topgen_4(B,A)
           => v8_topgen_4(B,A) ) ) ) )).

fof(cc15_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_topgen_4(B,A)
           => v8_topgen_4(B,A) ) ) ) )).

fof(d1_topgen_4,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => k1_topgen_4(A) = k1_pcomps_1(u1_struct_0(A)) ) )).

fof(t1_topgen_4,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_card_4(B)
      <=> v1_card_4(k7_setfam_1(A,B)) ) ) )).

fof(t3_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
          <=> r1_tarski(k3_topgen_1(A,B),B) ) ) ) )).

fof(t4_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_cantor_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v3_pre_topc(C,A)
                  & C != k1_xboole_0
                  & ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( r2_hidden(D,B)
                          & r1_tarski(D,C)
                          & D != k1_xboole_0 ) ) ) ) ) ) )).

fof(t5_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => r1_tarski(k5_topgen_1(A),k2_waybel23(A)) ) )).

fof(t6_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v7_topgen_1(A)
      <=> ? [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
            & v1_tops_1(B,A)
            & v1_card_4(B) ) ) ) )).

fof(t7_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v5_waybel23(A)
       => v7_topgen_1(A) ) ) )).

fof(t8_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(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_connsp_1(A,B,C)
               => k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C)) ) ) ) ) )).

fof(t9_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_pcomps_1(B,A)
           => r1_tarski(k2_tops_1(A,k5_setfam_1(u1_struct_0(A),B)),k5_setfam_1(u1_struct_0(A),k2_topgen_1(A,B))) ) ) ) )).

fof(t10_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ( v7_topgen_1(A)
      <=> r1_tarski(k1_card_1(k2_pre_topc(A)),k3_card_1(np__0)) ) ) )).

fof(t11_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ( v7_topgen_1(A)
      <=> v1_orders_4(A) ) ) )).

fof(d2_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_topgen_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( v3_pre_topc(C,A)
                 => r2_hidden(C,B) ) ) ) ) ) )).

fof(d3_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v2_topgen_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( v4_pre_topc(C,A)
                 => r2_hidden(C,B) ) ) ) ) ) )).

fof(d4_topgen_4,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v3_topgen_4(B,A)
      <=> ! [C] :
            ( ( v1_card_4(C)
              & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
           => ( r1_tarski(C,B)
             => r2_hidden(k5_setfam_1(A,C),B) ) ) ) ) )).

fof(t12_topgen_4,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v3_topgen_4(B,A)
       => r2_hidden(k1_xboole_0,B) ) ) )).

fof(t13_topgen_4,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( ~ v1_xboole_0(B)
          & v1_prob_1(B,A)
          & v1_measure1(B,A)
          & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
      <=> ( v1_prob_1(B,A)
          & v3_topgen_4(B,A) ) ) ) )).

fof(d5_topgen_4,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v4_topgen_4(B,A)
      <=> ! [C] :
            ( ( v1_card_4(C)
              & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
           => ( r1_tarski(C,B)
             => r2_hidden(k6_setfam_1(A,C),B) ) ) ) ) )).

fof(t14_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ( ( v2_topgen_4(B,A)
                & v1_prob_1(B,u1_struct_0(A)) )
             => ( v1_topgen_4(B,A)
                & v1_prob_1(B,u1_struct_0(A)) ) )
            & ( ( v1_topgen_4(B,A)
                & v1_prob_1(B,u1_struct_0(A)) )
             => ( v2_topgen_4(B,A)
                & v1_prob_1(B,u1_struct_0(A)) ) ) ) ) ) )).

fof(t15_topgen_4,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_prob_1(B,A)
       => B = k7_setfam_1(A,B) ) ) )).

fof(t16_topgen_4,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( ( r1_tarski(B,C)
              & v1_prob_1(C,A) )
           => r1_tarski(k7_setfam_1(A,B),C) ) ) ) )).

fof(t17_topgen_4,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( ( v4_topgen_4(B,A)
            & v1_prob_1(B,A) )
         => ( v3_topgen_4(B,A)
            & v1_prob_1(B,A) ) )
        & ( ( v3_topgen_4(B,A)
            & v1_prob_1(B,A) )
         => ( v4_topgen_4(B,A)
            & v1_prob_1(B,A) ) ) ) ) )).

fof(t18_topgen_4,axiom,(
    ! [A] :
      ( v1_xboole_0(k1_xboole_0)
      & m1_subset_1(k1_xboole_0,k1_zfmisc_1(k1_zfmisc_1(A))) ) )).

fof(t19_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( C = k1_tarski(B)
               => ( v3_pre_topc(B,A)
                <=> v1_tops_2(C,A) ) ) ) ) ) )).

fof(t20_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( C = k1_tarski(B)
               => ( v4_pre_topc(B,A)
                <=> v2_tops_2(C,A) ) ) ) ) ) )).

fof(t21_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( ( v2_tops_2(B,A)
                  & v2_tops_2(C,A) )
               => v2_tops_2(k2_topgen_4(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t22_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( ( v2_tops_2(B,A)
                  & v2_tops_2(C,A) )
               => v2_tops_2(k3_topgen_4(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t23_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( ( v1_tops_2(B,A)
                  & v1_tops_2(C,A) )
               => v1_tops_2(k2_topgen_4(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t24_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( ( v1_tops_2(B,A)
                  & v1_tops_2(C,A) )
               => v1_tops_2(k3_topgen_4(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t25_topgen_4,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => r1_tarski(k1_card_1(k2_topgen_4(A,B,C)),k1_card_1(k12_mcart_1(k1_zfmisc_1(A),k1_zfmisc_1(A),B,C))) ) ) )).

fof(t26_topgen_4,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => r1_tarski(k1_card_1(k3_topgen_4(A,B,C)),k1_card_1(k12_mcart_1(k1_zfmisc_1(A),k1_zfmisc_1(A),B,C))) ) ) )).

fof(t27_topgen_4,axiom,(
    ! [A,B] : r1_tarski(k3_tarski(k2_setfam_1(A,B)),k2_xboole_0(k3_tarski(A),k3_tarski(B))) )).

fof(t28_topgen_4,axiom,(
    ! [A,B] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & k2_xboole_0(k3_tarski(A),k3_tarski(B)) != k3_tarski(k2_setfam_1(A,B)) ) )).

fof(t29_topgen_4,axiom,(
    ! [A] : k2_setfam_1(k1_xboole_0,A) = k1_xboole_0 )).

fof(t30_topgen_4,axiom,(
    ! [A,B] :
      ~ ( k2_setfam_1(A,B) = k1_xboole_0
        & A != k1_xboole_0
        & B != k1_xboole_0 ) )).

fof(t31_topgen_4,axiom,(
    ! [A,B] :
      ~ ( k3_setfam_1(A,B) = k1_xboole_0
        & A != k1_xboole_0
        & B != k1_xboole_0 ) )).

fof(t32_topgen_4,axiom,(
    ! [A,B] : r1_tarski(k1_setfam_1(k2_setfam_1(A,B)),k2_xboole_0(k1_setfam_1(A),k1_setfam_1(B))) )).

fof(t33_topgen_4,axiom,(
    ! [A,B] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & k1_setfam_1(k2_setfam_1(A,B)) != k2_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) ) )).

fof(t34_topgen_4,axiom,(
    ! [A,B] :
      ~ ( A != k1_xboole_0
        & B != k1_xboole_0
        & k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) != k1_setfam_1(k3_setfam_1(A,B)) ) )).

fof(d6_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_topgen_4(B,A)
          <=> ? [C] :
                ( v2_tops_2(C,A)
                & v1_card_4(C)
                & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
                & B = k5_setfam_1(u1_struct_0(A),C) ) ) ) ) )).

fof(d7_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_topgen_4(B,A)
          <=> ? [C] :
                ( v1_tops_2(C,A)
                & v1_card_4(C)
                & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
                & B = k6_setfam_1(u1_struct_0(A),C) ) ) ) ) )).

fof(t35_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v5_topgen_4(k1_pre_topc(A),A) ) )).

fof(t36_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v6_topgen_4(k1_pre_topc(A),A) ) )).

fof(t37_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v5_topgen_4(k2_pre_topc(A),A) ) )).

fof(t38_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v6_topgen_4(k2_pre_topc(A),A) ) )).

fof(t39_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_topgen_4(B,A)
           => v6_topgen_4(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t40_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_topgen_4(B,A)
           => v5_topgen_4(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t41_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(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)))
             => ( ( v5_topgen_4(B,A)
                  & v5_topgen_4(C,A) )
               => v5_topgen_4(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t42_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(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)))
             => ( ( v5_topgen_4(B,A)
                  & v5_topgen_4(C,A) )
               => v5_topgen_4(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t43_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(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)))
             => ( ( v6_topgen_4(B,A)
                  & v6_topgen_4(C,A) )
               => v6_topgen_4(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t44_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(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)))
             => ( ( v6_topgen_4(B,A)
                  & v6_topgen_4(C,A) )
               => v6_topgen_4(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t45_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
           => v5_topgen_4(B,A) ) ) ) )).

fof(t46_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
           => v6_topgen_4(B,A) ) ) ) )).

fof(t47_topgen_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( A = k3_numbers
       => v5_topgen_4(A,k3_topmetr) ) ) )).

fof(d8_topgen_4,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v7_topgen_4(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => v4_pre_topc(k3_topgen_1(A,B),A) ) ) ) )).

fof(t48_topgen_4,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_urysohn1(A)
       => v7_topgen_4(A) ) ) )).

fof(t49_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v7_topgen_4(A)
       => v2_t_0topsp(A) ) ) )).

fof(t50_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r2_topgen_1(A,k2_pre_topc(A),B)
            | r1_topgen_1(A,k2_pre_topc(A),B) ) ) ) )).

fof(d9_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_topgen_4(A,B,C)
              <=> ! [D] :
                    ( m1_connsp_2(D,A,C)
                   => ~ v1_card_4(k5_subset_1(u1_struct_0(A),D,B)) ) ) ) ) ) )).

fof(t51_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(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))
                 => ( ( r1_topgen_4(A,B,D)
                      & r1_tarski(B,C) )
                   => r1_topgen_4(A,C,D) ) ) ) ) ) )).

fof(d10_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(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)))
             => ( C = k4_topgen_4(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,C)
                    <=> r1_topgen_4(A,B,D) ) ) ) ) ) ) )).

fof(t52_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_topgen_4(A,B,C)
               => r1_topgen_1(A,B,C) ) ) ) ) )).

fof(t53_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(k4_topgen_4(A,B),k3_topgen_1(A,B)) ) ) )).

fof(t54_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_topgen_4(A,B) = k6_pre_topc(A,k4_topgen_4(A,B)) ) ) )).

fof(t55_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(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(k4_topgen_4(A,B),k4_topgen_4(A,C)) ) ) ) ) )).

fof(t56_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(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))
                 => ~ ( r1_topgen_4(A,k4_subset_1(u1_struct_0(A),B,C),D)
                      & ~ r1_topgen_4(A,B,D)
                      & ~ r1_topgen_4(A,C,D) ) ) ) ) ) )).

fof(t57_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(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)))
             => k4_topgen_4(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k4_topgen_4(A,B),k4_topgen_4(A,C)) ) ) ) )).

fof(t58_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_card_4(B)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ r1_topgen_4(A,B,C) ) ) ) ) )).

fof(t59_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_card_4(B)
           => k4_topgen_4(A,B) = k1_xboole_0 ) ) ) )).

fof(t60_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ~ ( v5_waybel23(A)
          & ! [B] :
              ( m1_cantor_1(B,A)
             => ~ v1_card_4(B) ) ) ) )).

fof(t61_topgen_4,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ( ~ v1_xboole_0(k1_topgen_3(k5_numbers,A,B))
        & v1_card_4(k1_topgen_3(k5_numbers,A,B))
        & m1_subset_1(k1_topgen_3(k5_numbers,A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).

fof(t62_topgen_4,axiom,(
    ! [A,B] :
      ( m1_prob_1(B,A)
    <=> ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).

fof(t63_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( ( v1_topgen_4(B,A)
                  & r1_tarski(B,C) )
               => v1_topgen_4(C,A) ) ) ) ) )).

fof(t64_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( ( v2_topgen_4(B,A)
                  & r1_tarski(B,C) )
               => v2_topgen_4(C,A) ) ) ) ) )).

fof(t65_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_topgen_4(k11_prob_1(u1_struct_0(A),k1_topgen_4(A)),A)
        & v1_prob_1(k11_prob_1(u1_struct_0(A),k1_topgen_4(A)),u1_struct_0(A))
        & v3_topgen_4(k11_prob_1(u1_struct_0(A),k1_topgen_4(A)),u1_struct_0(A)) ) ) )).

fof(t66_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ( v1_prob_1(B,u1_struct_0(A))
              & v3_topgen_4(B,u1_struct_0(A)) )
           => m1_prob_1(B,u1_struct_0(A)) ) ) ) )).

fof(t67_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ? [C] :
              ( v1_prob_1(C,u1_struct_0(A))
              & v1_topgen_4(C,A)
              & v3_topgen_4(C,u1_struct_0(A))
              & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
              & r1_tarski(B,C)
              & ! [D] :
                  ( ( v1_prob_1(D,u1_struct_0(A))
                    & v1_topgen_4(D,A)
                    & v3_topgen_4(D,u1_struct_0(A))
                    & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
                 => ( r1_tarski(B,D)
                   => r1_tarski(C,D) ) ) ) ) ) )).

fof(d11_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_prob_1(B,u1_struct_0(A))
            & v1_topgen_4(B,A)
            & v3_topgen_4(B,u1_struct_0(A))
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
         => ( B = k5_topgen_4(A)
          <=> ! [C] :
                ( ( v1_prob_1(C,u1_struct_0(A))
                  & v1_topgen_4(C,A)
                  & v3_topgen_4(C,u1_struct_0(A))
                  & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
               => r1_tarski(B,C) ) ) ) ) )).

fof(t68_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_tops_2(B,A)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
         => r1_tarski(B,k5_topgen_4(A)) ) ) )).

fof(t69_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_tops_2(B,A)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
         => r1_tarski(B,k5_topgen_4(A)) ) ) )).

fof(t70_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k5_topgen_4(A) = k11_prob_1(u1_struct_0(A),k1_openlatt(A)) ) )).

fof(d12_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v8_topgen_4(B,A)
          <=> r2_hidden(B,k5_topgen_4(A)) ) ) ) )).

fof(dt_k1_topgen_4,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => m1_subset_1(k1_topgen_4(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k2_topgen_4,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => m1_subset_1(k2_topgen_4(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) )).

fof(commutativity_k2_topgen_4,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => k2_topgen_4(A,B,C) = k2_topgen_4(A,C,B) ) )).

fof(redefinition_k2_topgen_4,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => k2_topgen_4(A,B,C) = k3_setfam_1(B,C) ) )).

fof(dt_k3_topgen_4,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => m1_subset_1(k3_topgen_4(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) )).

fof(commutativity_k3_topgen_4,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => k3_topgen_4(A,B,C) = k3_topgen_4(A,C,B) ) )).

fof(redefinition_k3_topgen_4,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => k3_topgen_4(A,B,C) = k2_setfam_1(B,C) ) )).

fof(dt_k4_topgen_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k4_topgen_4(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k5_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_prob_1(k5_topgen_4(A),u1_struct_0(A))
        & v1_topgen_4(k5_topgen_4(A),A)
        & v3_topgen_4(k5_topgen_4(A),u1_struct_0(A))
        & m1_subset_1(k5_topgen_4(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) )).

fof(t2_topgen_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_topgen_1(A,B) = a_2_0_topgen_4(A,B) ) ) )).

fof(s1_topgen_4,axiom,(
    v1_card_4(a_0_0_topgen_4) )).

fof(fraenkel_a_2_0_topgen_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_0_topgen_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r2_hidden(D,k6_pre_topc(B,k1_topgen_1(u1_struct_0(B),C,k1_struct_0(B,D)))) ) ) ) )).

fof(fraenkel_a_0_0_topgen_4,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_topgen_4)
    <=> ? [B] :
          ( m1_subset_1(B,k3_numbers)
          & A = k1_tarski(B)
          & p1_s1_topgen_4(B) ) ) )).
%------------------------------------------------------------------------------