SET007 Axioms: SET007+879.ax


%------------------------------------------------------------------------------
% File     : SET007+879 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Boundary and Derivative of a Set
% 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  101 (   0 unit)
%            Number of atoms       :  605 (  55 equality)
%            Maximal formula depth :   19 (   7 average)
%            Number of connectives :  586 (  82 ~  ;   0  |; 238  &)
%                                         (  31 <=>; 235 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   38 (   0 propositional; 1-3 arity)
%            Number of functors    :   27 (   6 constant; 0-3 arity)
%            Number of variables   :  232 (   0 singleton; 218 !;  14 ?)
%            Maximal term depth    :    5 (   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_1,axiom,(
    ! [A] :
      ( ( v6_group_1(A)
        & l1_struct_0(A) )
     => ( v1_finset_1(k2_pre_topc(A))
        & v1_card_4(k2_pre_topc(A)) ) ) )).

fof(cc1_topgen_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ( v6_group_1(A)
       => v1_orders_4(A) ) ) )).

fof(rc1_topgen_1,axiom,(
    ? [A] :
      ( l1_struct_0(A)
      & ~ v3_struct_0(A)
      & v1_orders_4(A) ) )).

fof(rc2_topgen_1,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v1_orders_4(A) ) )).

fof(fc2_topgen_1,axiom,(
    ! [A] :
      ( ( v1_orders_4(A)
        & l1_struct_0(A) )
     => v1_card_4(k2_pre_topc(A)) ) )).

fof(rc3_topgen_1,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v1_urysohn1(A)
      & v2_t_0topsp(A) ) )).

fof(fc3_topgen_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_urysohn1(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v4_pre_topc(k3_topgen_1(A,B),A) ) )).

fof(fc4_topgen_1,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v3_pre_topc(B,A)
        & v4_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_membered(k2_tops_1(A,B))
        & v2_membered(k2_tops_1(A,B))
        & v3_membered(k2_tops_1(A,B))
        & v4_membered(k2_tops_1(A,B))
        & v5_membered(k2_tops_1(A,B))
        & v1_xboole_0(k2_tops_1(A,B))
        & v3_pre_topc(k2_tops_1(A,B),A)
        & v4_pre_topc(k2_tops_1(A,B),A)
        & v2_tops_1(k2_tops_1(A,B),A)
        & v3_tops_1(k2_tops_1(A,B),A) ) ) )).

fof(rc4_topgen_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v3_pre_topc(B,A) ) ) )).

fof(rc5_topgen_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v4_pre_topc(B,A) ) ) )).

fof(fc5_topgen_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v1_tdlat_3(A)
        & l1_pre_topc(A)
        & ~ v3_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ~ v1_xboole_0(k2_tops_1(A,B)) ) )).

fof(fc6_topgen_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & ~ v1_tdlat_3(A)
        & l1_pre_topc(A)
        & ~ v4_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ~ v1_xboole_0(k2_tops_1(A,B)) ) )).

fof(cc2_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_topgen_1(B,A)
           => ( v4_pre_topc(B,A)
              & v2_topgen_1(B,A) ) ) ) ) )).

fof(cc3_topgen_1,axiom,(
    ! [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)
              & v2_topgen_1(B,A) )
           => v5_topgen_1(B,A) ) ) ) )).

fof(cc4_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => ( v4_pre_topc(B,A)
              & v2_topgen_1(B,A)
              & v5_topgen_1(B,A) ) ) ) ) )).

fof(rc6_topgen_1,axiom,(
    ! [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)
          & v2_topgen_1(B,A)
          & v5_topgen_1(B,A) ) ) )).

fof(cc5_topgen_1,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_xboole_0(B)
              & v6_topgen_1(B,A) )
           => ~ v2_topgen_1(B,A) ) ) ) )).

fof(cc6_topgen_1,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_xboole_0(B)
              & v2_topgen_1(B,A) )
           => ~ v6_topgen_1(B,A) ) ) ) )).

fof(cc7_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => v6_topgen_1(B,A) ) ) ) )).

fof(fc7_topgen_1,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_membered(k2_tops_1(A,B))
        & v2_membered(k2_tops_1(A,B))
        & v3_membered(k2_tops_1(A,B))
        & v4_membered(k2_tops_1(A,B))
        & v5_membered(k2_tops_1(A,B))
        & v1_xboole_0(k2_tops_1(A,B))
        & v3_pre_topc(k2_tops_1(A,B),A)
        & v4_pre_topc(k2_tops_1(A,B),A)
        & v2_tops_1(k2_tops_1(A,B),A)
        & v3_tops_1(k2_tops_1(A,B),A)
        & v2_topgen_1(k2_tops_1(A,B),A)
        & v5_topgen_1(k2_tops_1(A,B),A)
        & v6_topgen_1(k2_tops_1(A,B),A) ) ) )).

fof(cc8_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
            & v4_pre_topc(B,A) ) ) ) )).

fof(fc8_topgen_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_membered(k3_topgen_1(A,B))
        & v2_membered(k3_topgen_1(A,B))
        & v3_membered(k3_topgen_1(A,B))
        & v4_membered(k3_topgen_1(A,B))
        & v5_membered(k3_topgen_1(A,B))
        & v1_xboole_0(k3_topgen_1(A,B))
        & v3_pre_topc(k3_topgen_1(A,B),A)
        & v4_pre_topc(k3_topgen_1(A,B),A)
        & v2_tops_1(k3_topgen_1(A,B),A)
        & v3_tops_1(k3_topgen_1(A,B),A)
        & v2_topgen_1(k3_topgen_1(A,B),A)
        & v5_topgen_1(k3_topgen_1(A,B),A)
        & v6_topgen_1(k3_topgen_1(A,B),A) ) ) )).

fof(cc9_topgen_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v1_orders_4(A) )
       => ( v2_pre_topc(A)
          & v7_topgen_1(A) ) ) ) )).

fof(t1_topgen_1,axiom,(
    ! [A] :
      ( l1_struct_0(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_xboole_0(B,k3_subset_1(u1_struct_0(A),C))
                    & k1_topgen_1(u1_struct_0(A),B,C) = k1_xboole_0 )
                & ~ ( k1_topgen_1(u1_struct_0(A),B,C) != k1_xboole_0
                    & r1_xboole_0(B,k3_subset_1(u1_struct_0(A),C)) ) ) ) ) ) )).

fof(t2_topgen_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ( v1_orders_4(A)
      <=> v1_card_4(k2_pre_topc(A)) ) ) )).

fof(t3_topgen_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ( v1_orders_4(A)
      <=> r1_tarski(k1_card_1(k2_pre_topc(A)),k3_card_1(np__0)) ) ) )).

fof(t4_topgen_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_subset_1(u1_struct_0(A),B,k2_pre_topc(A)) = k2_pre_topc(A) ) ) )).

fof(t5_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_tops_1(A,B) = k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))) ) ) )).

fof(d1_topgen_1,axiom,(
    ! [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))))
             => ( C = k2_topgen_1(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( r2_hidden(D,C)
                    <=> ? [E] :
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                          & D = k2_tops_1(A,E)
                          & r2_hidden(E,B) ) ) ) ) ) ) ) )).

fof(t6_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( B = k1_xboole_0
           => k2_topgen_1(A,B) = k1_xboole_0 ) ) ) )).

fof(t7_topgen_1,axiom,(
    ! [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(u1_struct_0(A)))
             => ( B = k1_tarski(C)
               => k2_topgen_1(A,B) = k1_tarski(k2_tops_1(A,C)) ) ) ) ) )).

fof(t8_topgen_1,axiom,(
    ! [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))))
             => ( r1_tarski(B,C)
               => r1_tarski(k2_topgen_1(A,B),k2_topgen_1(A,C)) ) ) ) ) )).

fof(t9_topgen_1,axiom,(
    ! [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))))
             => k2_topgen_1(A,k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C)) = k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),k2_topgen_1(A,B),k2_topgen_1(A,C)) ) ) ) )).

fof(t10_topgen_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k2_tops_1(A,B) = k1_topgen_1(u1_struct_0(A),k6_pre_topc(A,B),k1_tops_1(A,B)) ) ) )).

fof(t11_topgen_1,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))
             => ( r2_hidden(C,k2_tops_1(A,B))
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( ( v3_pre_topc(D,A)
                        & r2_hidden(C,D) )
                     => ( ~ r1_xboole_0(B,D)
                        & k1_topgen_1(u1_struct_0(A),D,B) != k1_xboole_0 ) ) ) ) ) ) ) )).

fof(t12_topgen_1,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))
             => ( r2_hidden(C,k2_tops_1(A,B))
              <=> ! [D] :
                    ( m1_yellow_8(D,A,C)
                   => ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ( r2_hidden(E,D)
                         => ( ~ r1_xboole_0(B,E)
                            & k1_topgen_1(u1_struct_0(A),E,B) != k1_xboole_0 ) ) ) ) ) ) ) ) )).

fof(t13_topgen_1,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))
             => ( r2_hidden(C,k2_tops_1(A,B))
              <=> ? [D] :
                    ( m1_yellow_8(D,A,C)
                    & ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ( r2_hidden(E,D)
                         => ( ~ r1_xboole_0(B,E)
                            & k1_topgen_1(u1_struct_0(A),E,B) != k1_xboole_0 ) ) ) ) ) ) ) ) )).

fof(t14_topgen_1,axiom,(
    ! [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(k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k2_tops_1(A,C)),k5_subset_1(u1_struct_0(A),k2_tops_1(A,B),k6_pre_topc(A,C)))) ) ) ) )).

fof(t15_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => u1_struct_0(A) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k1_tops_1(A,B),k2_tops_1(A,B)),k1_tops_1(A,k3_subset_1(u1_struct_0(A),B))) ) ) )).

fof(t16_topgen_1,axiom,(
    ! [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)
              & v4_pre_topc(B,A) )
          <=> k2_tops_1(A,B) = k1_xboole_0 ) ) ) )).

fof(d2_topgen_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( r1_topgen_1(A,B,C)
            <=> r2_hidden(C,k6_pre_topc(A,k1_topgen_1(u1_struct_0(A),B,k1_tarski(C)))) ) ) ) )).

fof(t17_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( r1_topgen_1(A,B,C)
             => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).

fof(d3_topgen_1,axiom,(
    ! [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 = k3_topgen_1(A,B)
              <=> ! [D] :
                    ( r2_hidden(D,u1_struct_0(A))
                   => ( r2_hidden(D,C)
                    <=> r1_topgen_1(A,B,D) ) ) ) ) ) ) )).

fof(t18_topgen_1,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] :
              ( r2_hidden(C,k3_topgen_1(A,B))
            <=> r1_topgen_1(A,B,C) ) ) ) )).

fof(t19_topgen_1,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))
             => ( r2_hidden(C,k3_topgen_1(A,B))
              <=> ! [D] :
                    ( ( v3_pre_topc(D,A)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => ~ ( r2_hidden(C,D)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(E,k5_subset_1(u1_struct_0(A),B,D))
                                & C != E ) ) ) ) ) ) ) ) )).

fof(t20_topgen_1,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))
             => ( r2_hidden(C,k3_topgen_1(A,B))
              <=> ! [D] :
                    ( m1_yellow_8(D,A,C)
                   => ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( r2_hidden(E,D)
                            & ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ~ ( r2_hidden(F,k5_subset_1(u1_struct_0(A),B,E))
                                    & C != F ) ) ) ) ) ) ) ) ) )).

fof(t21_topgen_1,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))
             => ( r2_hidden(C,k3_topgen_1(A,B))
              <=> ? [D] :
                    ( m1_yellow_8(D,A,C)
                    & ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( r2_hidden(E,D)
                            & ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ~ ( r2_hidden(F,k5_subset_1(u1_struct_0(A),B,E))
                                    & C != F ) ) ) ) ) ) ) ) ) )).

fof(d4_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( r2_topgen_1(A,B,C)
            <=> ( r2_hidden(C,B)
                & ~ r1_topgen_1(A,B,C) ) ) ) ) )).

fof(t22_topgen_1,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] :
              ( r2_hidden(C,k1_topgen_1(u1_struct_0(A),B,k3_topgen_1(A,B)))
            <=> r2_topgen_1(A,B,C) ) ) ) )).

fof(t23_topgen_1,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_1(A,B,C)
              <=> ! [D] :
                    ( ( v3_pre_topc(D,A)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => ~ ( r2_hidden(C,D)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( E != C
                                & r2_hidden(E,B)
                                & r2_hidden(E,D) ) ) ) ) ) ) ) ) )).

fof(t24_topgen_1,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))
             => ( r2_topgen_1(A,B,C)
              <=> ? [D] :
                    ( v3_pre_topc(D,A)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                    & k5_subset_1(u1_struct_0(A),D,B) = k1_struct_0(A,C) ) ) ) ) ) )).

fof(d5_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_topgen_1(B,A)
          <=> r2_topgen_1(A,k2_pre_topc(A),B) ) ) ) )).

fof(t25_topgen_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_topgen_1(B,A)
          <=> v3_pre_topc(k1_struct_0(A,B),A) ) ) ) )).

fof(d6_topgen_1,axiom,(
    ! [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))))
             => ( C = k4_topgen_1(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( r2_hidden(D,C)
                    <=> ? [E] :
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                          & D = k3_topgen_1(A,E)
                          & r2_hidden(E,B) ) ) ) ) ) ) ) )).

fof(t26_topgen_1,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))))
         => ( B = k1_xboole_0
           => k4_topgen_1(A,B) = k1_xboole_0 ) ) ) )).

fof(t27_topgen_1,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)
               => k4_topgen_1(A,C) = k1_tarski(k3_topgen_1(A,B)) ) ) ) ) )).

fof(t28_topgen_1,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))))
             => ( r1_tarski(B,C)
               => r1_tarski(k4_topgen_1(A,B),k4_topgen_1(A,C)) ) ) ) ) )).

fof(t29_topgen_1,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))))
             => k4_topgen_1(A,k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C)) = k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),k4_topgen_1(A,B),k4_topgen_1(A,C)) ) ) ) )).

fof(t30_topgen_1,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(k3_topgen_1(A,B),k6_pre_topc(A,B)) ) ) )).

fof(t31_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_pre_topc(A,B) = k4_subset_1(u1_struct_0(A),B,k3_topgen_1(A,B)) ) ) )).

fof(t32_topgen_1,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(k3_topgen_1(A,B),k3_topgen_1(A,C)) ) ) ) ) )).

fof(t33_topgen_1,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)))
             => k3_topgen_1(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k3_topgen_1(A,B),k3_topgen_1(A,C)) ) ) ) )).

fof(t34_topgen_1,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_urysohn1(A)
           => r1_tarski(k3_topgen_1(A,k3_topgen_1(A,B)),k3_topgen_1(A,B)) ) ) ) )).

fof(t35_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_urysohn1(A)
           => k6_pre_topc(A,k3_topgen_1(A,B)) = k3_topgen_1(A,B) ) ) ) )).

fof(t36_topgen_1,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))))
         => r1_tarski(k5_setfam_1(u1_struct_0(A),k4_topgen_1(A,B)),k3_topgen_1(A,k5_setfam_1(u1_struct_0(A),B))) ) ) )).

fof(t37_topgen_1,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] :
                  ( ( r1_tarski(B,C)
                    & r1_topgen_1(A,B,D) )
                 => r1_topgen_1(A,C,D) ) ) ) ) )).

fof(d7_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_topgen_1(B,A)
          <=> r1_tarski(B,k3_topgen_1(A,B)) ) ) ) )).

fof(d8_topgen_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v3_topgen_1(A)
      <=> v2_topgen_1(k2_pre_topc(A),A) ) ) )).

fof(t38_topgen_1,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_urysohn1(A)
              & v2_topgen_1(B,A) )
           => v2_topgen_1(k6_pre_topc(A,B),A) ) ) ) )).

fof(d9_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v4_topgen_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v2_topgen_1(C,A) ) ) ) ) ) )).

fof(t39_topgen_1,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))))
         => ( v4_topgen_1(B,A)
           => r1_tarski(k5_setfam_1(u1_struct_0(A),B),k5_setfam_1(u1_struct_0(A),k4_topgen_1(A,B))) ) ) ) )).

fof(t40_topgen_1,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))))
         => ( v4_topgen_1(B,A)
           => v2_topgen_1(k5_setfam_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t41_topgen_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k2_tops_1(A,k1_pre_topc(A)) = k1_xboole_0 ) )).

fof(d10_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_topgen_1(B,A)
          <=> ( v4_pre_topc(B,A)
              & v2_topgen_1(B,A) ) ) ) ) )).

fof(t42_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k3_topgen_1(A,k1_pre_topc(A)) = k1_pre_topc(A) ) )).

fof(t43_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_topgen_1(B,A)
          <=> k3_topgen_1(A,B) = B ) ) ) )).

fof(t44_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v5_topgen_1(k1_pre_topc(A),A) ) )).

fof(d11_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_topgen_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( ~ v1_xboole_0(C)
                    & r1_tarski(C,B)
                    & v2_topgen_1(C,A) ) ) ) ) ) )).

fof(t45_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v6_topgen_1(k1_pre_topc(A),A) ) )).

fof(t46_topgen_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ~ ( v1_urysohn1(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_subset_1(u1_struct_0(A),B,C) = k2_pre_topc(A)
                      & r1_xboole_0(B,C)
                      & v5_topgen_1(B,A)
                      & v6_topgen_1(C,A) ) ) ) ) ) )).

fof(t47_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_topgen_1(A,B) = k1_xboole_0 ) ) )).

fof(t48_topgen_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tops_1(B,A)
           => B = k2_pre_topc(A) ) ) ) )).

fof(d12_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( v1_card_1(B)
         => ( B = k5_topgen_1(A)
          <=> ( ? [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                  & v1_tops_1(C,A)
                  & B = k1_card_1(C) )
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ( v1_tops_1(C,A)
                   => r1_tarski(B,k1_card_1(C)) ) ) ) ) ) ) )).

fof(d13_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v7_topgen_1(A)
      <=> r1_tarski(k5_topgen_1(A),k3_card_1(np__0)) ) ) )).

fof(t49_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v1_orders_4(A)
        & l1_pre_topc(A) )
     => v7_topgen_1(A) ) )).

fof(t50_topgen_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( A = k3_numbers
       => k3_subset_1(u1_struct_0(k3_topmetr),A) = k1_borsuk_5 ) ) )).

fof(t51_topgen_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( A = k1_borsuk_5
       => k3_subset_1(u1_struct_0(k3_topmetr),A) = k3_numbers ) ) )).

fof(t52_topgen_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( A = k3_numbers
       => k1_tops_1(k3_topmetr,A) = k1_xboole_0 ) ) )).

fof(t53_topgen_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( A = k1_borsuk_5
       => k1_tops_1(k3_topmetr,A) = k1_xboole_0 ) ) )).

fof(t54_topgen_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( A = k3_numbers
       => v1_tops_1(A,k3_topmetr) ) ) )).

fof(t55_topgen_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( A = k1_borsuk_5
       => v1_tops_1(A,k3_topmetr) ) ) )).

fof(t56_topgen_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( A = k3_numbers
       => v2_tops_1(A,k3_topmetr) ) ) )).

fof(t57_topgen_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( A = k1_borsuk_5
       => v2_tops_1(A,k3_topmetr) ) ) )).

fof(t58_topgen_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ~ ( A = k1_numbers
          & v2_tops_1(A,k3_topmetr) ) ) )).

fof(t59_topgen_1,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
      & ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
          & v2_tops_1(A,k3_topmetr)
          & v2_tops_1(B,k3_topmetr)
          & ~ v2_tops_1(k4_subset_1(u1_struct_0(k3_topmetr),A,B),k3_topmetr) ) ) )).

fof(dt_k1_topgen_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => m1_subset_1(k1_topgen_1(A,B,C),k1_zfmisc_1(A)) ) )).

fof(redefinition_k1_topgen_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k1_topgen_1(A,B,C) = k4_xboole_0(B,C) ) )).

fof(dt_k2_topgen_1,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
     => m1_subset_1(k2_topgen_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k3_topgen_1,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k3_topgen_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k4_topgen_1,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
     => m1_subset_1(k4_topgen_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k5_topgen_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v1_card_1(k5_topgen_1(A)) ) )).
%------------------------------------------------------------------------------