SET007 Axioms: SET007+405.ax


%------------------------------------------------------------------------------
% File     : SET007+405 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Maximal Anti-Discrete Subspaces 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    : tex_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  160 (   2 unit)
%            Number of atoms       : 1097 (  72 equality)
%            Maximal formula depth :   15 (   8 average)
%            Number of connectives : 1199 ( 262 ~  ;  10  |; 486  &)
%                                         (  38 <=>; 403 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   35 (   1 propositional; 0-3 arity)
%            Number of functors    :   34 (   1 constant; 0-3 arity)
%            Number of variables   :  408 (   0 singleton; 394 !;  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_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v1_xboole_0(k6_pre_topc(A,B))
        & v4_pre_topc(k6_pre_topc(A,B),A) ) ) )).

fof(fc2_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_xboole_0(k6_pre_topc(A,B))
        & v3_pre_topc(k6_pre_topc(A,B),A)
        & v4_pre_topc(k6_pre_topc(A,B),A)
        & v2_tops_1(k6_pre_topc(A,B),A)
        & v3_tops_1(k6_pre_topc(A,B),A)
        & v1_tex_2(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A)))
        & v1_membered(k6_pre_topc(A,B))
        & v2_membered(k6_pre_topc(A,B))
        & v3_membered(k6_pre_topc(A,B))
        & v4_membered(k6_pre_topc(A,B))
        & v5_membered(k6_pre_topc(A,B)) ) ) )).

fof(fc3_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v1_xboole_0(k6_pre_topc(A,B))
        & v4_pre_topc(k6_pre_topc(A,B),A)
        & ~ v1_tex_2(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(fc4_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & ~ v1_realset1(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v1_xboole_0(k6_pre_topc(A,B))
        & ~ v1_realset1(k6_pre_topc(A,B))
        & v4_pre_topc(k6_pre_topc(A,B),A) ) ) )).

fof(fc5_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v1_xboole_0(k1_tops_1(A,B))
        & v3_pre_topc(k1_tops_1(A,B),A)
        & ~ v1_tex_2(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(fc6_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v3_pre_topc(k1_tops_1(A,B),A)
        & v1_tex_2(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(fc7_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_xboole_0(k1_tops_1(A,B))
        & v3_pre_topc(k1_tops_1(A,B),A)
        & v4_pre_topc(k1_tops_1(A,B),A)
        & v2_tops_1(k1_tops_1(A,B),A)
        & v3_tops_1(k1_tops_1(A,B),A)
        & v1_tex_2(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A)))
        & v1_membered(k1_tops_1(A,B))
        & v2_membered(k1_tops_1(A,B))
        & v3_membered(k1_tops_1(A,B))
        & v4_membered(k1_tops_1(A,B))
        & v5_membered(k1_tops_1(A,B)) ) ) )).

fof(fc8_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ~ v1_xboole_0(k1_tex_4(A,B)) ) )).

fof(fc9_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ~ v1_xboole_0(k2_tex_4(A,B)) ) )).

fof(fc10_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ~ v1_xboole_0(k3_tex_4(A,B)) ) )).

fof(fc11_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_xboole_0(k3_tex_4(A,B))
        & v2_tops_1(k3_tex_4(A,B),A)
        & v1_tex_2(k3_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A)))
        & v1_membered(k3_tex_4(A,B))
        & v2_membered(k3_tex_4(A,B))
        & v3_membered(k3_tex_4(A,B))
        & v4_membered(k3_tex_4(A,B))
        & v5_membered(k3_tex_4(A,B)) ) ) )).

fof(fc12_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v1_xboole_0(k3_tex_4(A,B))
        & ~ v1_tex_2(k3_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(fc13_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & ~ v1_realset1(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v1_xboole_0(k3_tex_4(A,B))
        & ~ v1_realset1(k3_tex_4(A,B)) ) ) )).

fof(cc1_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v4_tex_4(B,A)
           => ( v2_pre_topc(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B) ) ) ) ) )).

fof(cc2_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v2_tdlat_3(B)
           => ~ v4_tex_4(B,A) ) ) ) )).

fof(cc3_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v1_tsep_1(B,A)
              & v2_tdlat_3(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tex_4(B,A) ) ) ) ) )).

fof(cc4_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v1_tsep_1(B,A)
              & ~ v4_tex_4(B,A) )
           => ( ~ v3_struct_0(B)
              & ~ v3_realset2(B)
              & v2_pre_topc(B)
              & ~ v2_tdlat_3(B)
              & ~ v4_tex_4(B,A) ) ) ) ) )).

fof(cc5_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_tdlat_3(B)
              & ~ v4_tex_4(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & ~ v1_tsep_1(B,A)
              & v2_tex_2(B,A) ) ) ) ) )).

fof(cc6_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v1_borsuk_1(B,A)
              & v2_tdlat_3(B) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v2_tdlat_3(B)
              & v3_tdlat_3(B)
              & v4_tex_4(B,A) ) ) ) ) )).

fof(cc7_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v1_borsuk_1(B,A)
              & ~ v4_tex_4(B,A) )
           => ( ~ v3_struct_0(B)
              & ~ v3_realset2(B)
              & v2_pre_topc(B)
              & ~ v2_tdlat_3(B)
              & ~ v4_tex_4(B,A) ) ) ) ) )).

fof(cc8_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_tdlat_3(B)
              & ~ v4_tex_4(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & ~ v1_borsuk_1(B,A)
              & v2_tex_2(B,A) ) ) ) ) )).

fof(fc14_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k5_tex_4(A,B))
        & v1_pre_topc(k5_tex_4(A,B)) ) ) )).

fof(rc1_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v2_tdlat_3(B)
          & v3_tdlat_3(B)
          & v4_tex_4(B,A) ) ) )).

fof(fc15_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k5_tex_4(A,B))
        & v1_pre_topc(k5_tex_4(A,B))
        & v2_pre_topc(k5_tex_4(A,B))
        & v2_tdlat_3(k5_tex_4(A,B))
        & v3_tdlat_3(k5_tex_4(A,B))
        & v4_tex_4(k5_tex_4(A,B),A) ) ) )).

fof(fc16_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k6_tex_4(A,B))
        & v1_pre_topc(k6_tex_4(A,B)) ) ) )).

fof(rc2_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & ~ v2_tex_2(B,A) ) ) )).

fof(fc17_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & ~ v1_realset1(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k6_tex_4(A,B))
        & ~ v3_realset2(k6_tex_4(A,B))
        & v1_pre_topc(k6_tex_4(A,B)) ) ) )).

fof(fc18_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k6_tex_4(A,B))
        & v1_pre_topc(k6_tex_4(A,B))
        & ~ v2_tex_2(k6_tex_4(A,B),A) ) ) )).

fof(fc19_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k7_tex_4(A,B))
        & v1_pre_topc(k7_tex_4(A,B)) ) ) )).

fof(fc20_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & ~ v1_realset1(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k7_tex_4(A,B))
        & ~ v3_realset2(k7_tex_4(A,B))
        & v1_pre_topc(k7_tex_4(A,B)) ) ) )).

fof(fc21_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k7_tex_4(A,B))
        & v1_pre_topc(k7_tex_4(A,B))
        & ~ v2_tex_2(k7_tex_4(A,B),A) ) ) )).

fof(t3_tex_4,axiom,(
    $true )).

fof(d1_tex_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tex_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( ( v3_pre_topc(D,A)
                        & r2_hidden(C,D)
                        & r2_hidden(C,B) )
                     => r1_tarski(B,D) ) ) ) ) ) ) )).

fof(d2_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tex_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( ( v4_pre_topc(D,A)
                        & r2_hidden(C,D)
                        & r2_hidden(C,B) )
                     => r1_tarski(B,D) ) ) ) ) ) ) )).

fof(d3_tex_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tex_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( v3_pre_topc(C,A)
                    & ~ r1_xboole_0(B,C)
                    & ~ r1_tarski(B,C) ) ) ) ) ) )).

fof(d4_tex_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tex_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( v4_pre_topc(C,A)
                    & ~ r1_xboole_0(B,C)
                    & ~ r1_tarski(B,C) ) ) ) ) ) )).

fof(t5_tex_4,axiom,(
    $true )).

fof(t6_tex_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & C = D
                      & v1_tex_4(C,A) )
                   => v1_tex_4(D,B) ) ) ) ) ) )).

fof(t7_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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(C,B)
                  & v1_tex_4(B,A) )
               => v1_tex_4(C,A) ) ) ) ) )).

fof(t8_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v1_tex_4(k1_struct_0(A,B),A) ) ) )).

fof(t9_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => v1_tex_4(B,A) ) ) )).

fof(d5_tex_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v2_tex_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v1_tex_4(C,A) ) ) ) ) ) )).

fof(t10_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v2_tex_4(B,A)
           => ( k6_setfam_1(u1_struct_0(A),B) = k1_xboole_0
              | v1_tex_4(k5_setfam_1(u1_struct_0(A),B),A) ) ) ) ) )).

fof(t11_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v2_tex_4(B,A)
           => v1_tex_4(k6_setfam_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t12_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v2_tex_4(k1_tex_4(A,B),A) ) ) )).

fof(t13_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_struct_0(A,B) = k6_setfam_1(u1_struct_0(A),k1_tex_4(A,B)) ) ) )).

fof(t14_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_tarski(k1_struct_0(A,B),k5_setfam_1(u1_struct_0(A),k1_tex_4(A,B))) ) ) )).

fof(t15_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v1_tex_4(k5_setfam_1(u1_struct_0(A),k1_tex_4(A,B)),A) ) ) )).

fof(d7_tex_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tex_4(B,A)
          <=> ( v1_tex_4(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_tex_4(C,A)
                      & r1_tarski(B,C) )
                   => B = C ) ) ) ) ) ) )).

fof(t16_tex_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & C = D
                      & v3_tex_4(C,A) )
                   => v3_tex_4(D,B) ) ) ) ) ) )).

fof(t17_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ~ v3_tex_4(B,A) ) ) )).

fof(t18_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( ( v1_tex_4(B,A)
              & v3_pre_topc(B,A) )
           => v3_tex_4(B,A) ) ) ) )).

fof(t19_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( ( v1_tex_4(B,A)
              & v4_pre_topc(B,A) )
           => v3_tex_4(B,A) ) ) ) )).

fof(d8_tex_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_tex_4(A,B) = k5_setfam_1(u1_struct_0(A),k1_tex_4(A,B)) ) ) )).

fof(t20_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_tarski(k1_struct_0(A,B),k2_tex_4(A,B)) ) ) )).

fof(t21_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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))
             => ( ( v1_tex_4(B,A)
                  & r2_hidden(C,B) )
               => r1_tarski(B,k2_tex_4(A,C)) ) ) ) ) )).

fof(t22_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v3_tex_4(k2_tex_4(A,B),A) ) ) )).

fof(t23_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k2_tex_4(A,B))
              <=> k2_tex_4(A,C) = k2_tex_4(A,B) ) ) ) ) )).

fof(t24_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_subset_1(k2_tex_4(A,B),k2_tex_4(A,C))
                | k2_tex_4(A,B) = k2_tex_4(A,C) ) ) ) ) )).

fof(t25_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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))
             => ( ( v4_pre_topc(B,A)
                  & r2_hidden(C,B) )
               => r1_tarski(k2_tex_4(A,C),B) ) ) ) ) )).

fof(t26_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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))
             => ( ( v3_pre_topc(B,A)
                  & r2_hidden(C,B) )
               => r1_tarski(k2_tex_4(A,C),B) ) ) ) ) )).

fof(d9_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tex_4(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & r2_hidden(C,B)
                & B = k2_tex_4(A,C) ) ) ) ) )).

fof(t29_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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,B)
                  & v3_tex_4(B,A) )
               => B = k2_tex_4(A,C) ) ) ) ) )).

fof(d10_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v3_tex_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                 => B = k2_tex_4(A,C) ) ) ) ) ) )).

fof(t30_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_tex_4(A,B) = k3_tex_4(A,k1_struct_0(A,B)) ) ) )).

fof(t31_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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_xboole_0(k2_tex_4(A,C),k3_tex_4(A,B))
                  & r1_xboole_0(k2_tex_4(A,C),B) ) ) ) ) )).

fof(t32_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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_xboole_0(k2_tex_4(A,C),k3_tex_4(A,B))
               => r1_tarski(k2_tex_4(A,C),k3_tex_4(A,B)) ) ) ) ) )).

fof(t33_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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_tex_4(A,B),k3_tex_4(A,C)) ) ) ) ) )).

fof(t34_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(B,k3_tex_4(A,B)) ) ) )).

fof(t35_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_tex_4(A,B) = k3_tex_4(A,k3_tex_4(A,B)) ) ) )).

fof(t36_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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,k3_tex_4(A,C))
               => r1_tarski(k3_tex_4(A,B),k3_tex_4(A,C)) ) ) ) ) )).

fof(t37_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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(C,k3_tex_4(A,B))
                  & r1_tarski(B,k3_tex_4(A,C)) )
              <=> k3_tex_4(A,B) = k3_tex_4(A,C) ) ) ) ) )).

fof(t38_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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_tex_4(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k3_tex_4(A,B),k3_tex_4(A,C)) ) ) ) )).

fof(t39_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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(k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),k3_tex_4(A,B),k3_tex_4(A,C))) ) ) ) )).

fof(t40_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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)))
             => ( ( v3_pre_topc(B,A)
                  & r1_tarski(C,B) )
               => r1_tarski(k3_tex_4(A,C),B) ) ) ) ) )).

fof(t42_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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)))
             => ( ( v4_pre_topc(B,A)
                  & r1_tarski(C,B) )
               => r1_tarski(k3_tex_4(A,C),B) ) ) ) ) )).

fof(d12_tex_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_tex_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                 => r1_tarski(B,k6_pre_topc(A,k1_struct_0(A,C))) ) ) ) ) ) )).

fof(d13_tex_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_tex_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                 => k6_pre_topc(A,B) = k6_pre_topc(A,k1_struct_0(A,C)) ) ) ) ) ) )).

fof(d14_tex_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_tex_4(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => k6_pre_topc(A,k1_struct_0(A,C)) = k6_pre_topc(A,k1_struct_0(A,D)) ) ) ) ) ) ) )).

fof(t44_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v1_tex_4(C,A)
                  & r1_tarski(k6_pre_topc(A,k1_struct_0(A,B)),C) )
               => C = k6_pre_topc(A,k1_struct_0(A,B)) ) ) ) ) )).

fof(t45_tex_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_tex_4(B,A)
              & v4_pre_topc(B,A) )
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                 => B = k6_pre_topc(A,k1_struct_0(A,C)) ) ) ) ) ) )).

fof(t46_tex_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_tex_4(B,A)
           => ( v3_pre_topc(B,A)
              | v2_tops_1(B,A) ) ) ) ) )).

fof(t47_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k6_pre_topc(A,k1_struct_0(A,B)) = k1_struct_0(A,B)
           => v3_tex_4(k1_struct_0(A,B),A) ) ) ) )).

fof(t50_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_tarski(k2_tex_4(A,B),k6_pre_topc(A,k1_struct_0(A,B))) ) ) )).

fof(t51_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k2_tex_4(A,B) = k2_tex_4(A,C)
              <=> k6_pre_topc(A,k1_struct_0(A,B)) = k6_pre_topc(A,k1_struct_0(A,C)) ) ) ) ) )).

fof(t52_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_subset_1(k2_tex_4(A,B),k2_tex_4(A,C))
              <=> k6_pre_topc(A,k1_struct_0(A,B)) != k6_pre_topc(A,k1_struct_0(A,C)) ) ) ) ) )).

fof(t55_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_subset_1(k4_tex_4(A,B),k4_tex_4(A,C))
              <=> ~ ( ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( v3_pre_topc(D,A)
                            & r1_tarski(k4_tex_4(A,B),D)
                            & r1_xboole_0(D,k4_tex_4(A,C)) ) )
                    & ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( v3_pre_topc(D,A)
                            & r1_xboole_0(D,k4_tex_4(A,B))
                            & r1_tarski(k4_tex_4(A,C),D) ) ) ) ) ) ) ) )).

fof(t56_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_subset_1(k4_tex_4(A,B),k4_tex_4(A,C))
              <=> ~ ( ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( v4_pre_topc(D,A)
                            & r1_tarski(k4_tex_4(A,B),D)
                            & r1_xboole_0(D,k4_tex_4(A,C)) ) )
                    & ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( v4_pre_topc(D,A)
                            & r1_xboole_0(D,k4_tex_4(A,B))
                            & r1_tarski(k4_tex_4(A,C),D) ) ) ) ) ) ) ) )).

fof(t58_tex_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)
           => k3_tex_4(A,B) = B ) ) ) )).

fof(t59_tex_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_tex_4(A,k1_tops_1(A,B)) = k1_tops_1(A,B) ) ) )).

fof(t61_tex_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(k3_tex_4(A,B),k6_pre_topc(A,B)) ) ) )).

fof(t62_tex_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)
           => k3_tex_4(A,B) = B ) ) ) )).

fof(t63_tex_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_tex_4(A,k6_pre_topc(A,B)) = k6_pre_topc(A,B) ) ) )).

fof(t64_tex_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)))
         => k6_pre_topc(A,k3_tex_4(A,B)) = k6_pre_topc(A,B) ) ) )).

fof(t65_tex_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)))
             => ( k3_tex_4(A,B) = k3_tex_4(A,C)
               => k6_pre_topc(A,B) = k6_pre_topc(A,C) ) ) ) ) )).

fof(t66_tex_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)))
             => ( ( v4_pre_topc(B,A)
                  | v4_pre_topc(C,A) )
               => k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k3_tex_4(A,B),k3_tex_4(A,C)) ) ) ) ) )).

fof(t67_tex_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)))
             => ( ( v3_pre_topc(B,A)
                  | v3_pre_topc(C,A) )
               => k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k3_tex_4(A,B),k3_tex_4(A,C)) ) ) ) ) )).

fof(t68_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( C = u1_struct_0(B)
                  & v2_tdlat_3(B) )
               => v1_tex_4(C,A) ) ) ) ) )).

fof(t69_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v2_pre_topc(B)
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( ( C = u1_struct_0(B)
                    & v1_tex_4(C,A) )
                 => v2_tdlat_3(B) ) ) ) ) ) )).

fof(t70_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ( ! [C] :
                ( ( v1_tsep_1(C,A)
                  & m1_pre_topc(C,A) )
               => ( r1_tsep_1(A,B,C)
                  | m1_pre_topc(B,C) ) )
           => v2_tdlat_3(B) ) ) ) )).

fof(t71_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ( ! [C] :
                ( ( v1_borsuk_1(C,A)
                  & m1_pre_topc(C,A) )
               => ( r1_tsep_1(A,B,C)
                  | m1_pre_topc(B,C) ) )
           => v2_tdlat_3(B) ) ) ) )).

fof(t72_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_tdlat_3(B)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( v1_tsep_1(C,A)
                & m1_pre_topc(C,A) )
             => ( r1_tsep_1(A,B,C)
                | m1_pre_topc(B,C) ) ) ) ) )).

fof(t73_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_tdlat_3(B)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( v1_borsuk_1(C,A)
                & m1_pre_topc(C,A) )
             => ( r1_tsep_1(A,B,C)
                | m1_pre_topc(B,C) ) ) ) ) )).

fof(d16_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v4_tex_4(B,A)
          <=> ( v2_tdlat_3(B)
              & ! [C] :
                  ( m1_pre_topc(C,A)
                 => ( ( v2_tdlat_3(C)
                      & r1_tarski(u1_struct_0(B),u1_struct_0(C)) )
                   => u1_struct_0(B) = u1_struct_0(C) ) ) ) ) ) ) )).

fof(t74_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = u1_struct_0(B)
               => ( v4_tex_4(B,A)
                <=> v3_tex_4(C,A) ) ) ) ) ) )).

fof(d17_tex_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_pre_topc(C)
                & m1_pre_topc(C,A) )
             => ( C = k5_tex_4(A,B)
              <=> u1_struct_0(C) = k2_tex_4(A,B) ) ) ) ) )).

fof(t75_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => m1_pre_topc(k1_tex_2(A,B),k5_tex_4(A,B)) ) ) )).

fof(t76_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( m1_subset_1(C,u1_struct_0(k5_tex_4(A,B)))
              <=> g1_pre_topc(u1_struct_0(k5_tex_4(A,C)),u1_pre_topc(k5_tex_4(A,C))) = g1_pre_topc(u1_struct_0(k5_tex_4(A,B)),u1_pre_topc(k5_tex_4(A,B))) ) ) ) ) )).

fof(t77_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_subset_1(u1_struct_0(k5_tex_4(A,B)),u1_struct_0(k5_tex_4(A,C)))
                | g1_pre_topc(u1_struct_0(k5_tex_4(A,B)),u1_pre_topc(k5_tex_4(A,B))) = g1_pre_topc(u1_struct_0(k5_tex_4(A,C)),u1_pre_topc(k5_tex_4(A,C))) ) ) ) ) )).

fof(t78_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_borsuk_1(B,A)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( m1_subset_1(C,u1_struct_0(B))
               => m1_pre_topc(k5_tex_4(A,C),B) ) ) ) ) )).

fof(t79_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_tsep_1(B,A)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( m1_subset_1(C,u1_struct_0(B))
               => m1_pre_topc(k5_tex_4(A,C),B) ) ) ) ) )).

fof(t80_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k6_pre_topc(A,k1_struct_0(A,B)) = k1_struct_0(A,B)
           => v4_tex_4(k1_tex_2(A,B),A) ) ) ) )).

fof(d18_tex_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( v1_pre_topc(C)
                & m1_pre_topc(C,A) )
             => ( C = k6_tex_4(A,B)
              <=> u1_struct_0(C) = B ) ) ) ) )).

fof(t81_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_tex_4(A,B)))) ) ) )).

fof(t82_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
               => m1_pre_topc(k6_tex_4(A,C),B) ) ) ) ) )).

fof(d19_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( v1_pre_topc(C)
                & m1_pre_topc(C,A) )
             => ( C = k7_tex_4(A,B)
              <=> u1_struct_0(C) = k3_tex_4(A,B) ) ) ) ) )).

fof(t83_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_tex_4(A,B)))) ) ) )).

fof(t84_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => m1_pre_topc(k6_tex_4(A,B),k7_tex_4(A,B)) ) ) )).

fof(t85_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => g1_pre_topc(u1_struct_0(k5_tex_4(A,B)),u1_pre_topc(k5_tex_4(A,B))) = g1_pre_topc(u1_struct_0(k7_tex_4(A,k1_struct_0(A,B))),u1_pre_topc(k7_tex_4(A,k1_struct_0(A,B)))) ) ) )).

fof(t86_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( r1_tarski(B,C)
               => m1_pre_topc(k7_tex_4(A,B),k7_tex_4(A,C)) ) ) ) ) )).

fof(t87_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => g1_pre_topc(u1_struct_0(k7_tex_4(A,B)),u1_pre_topc(k7_tex_4(A,B))) = g1_pre_topc(u1_struct_0(k7_tex_4(A,k3_tex_4(A,B))),u1_pre_topc(k7_tex_4(A,k3_tex_4(A,B)))) ) ) )).

fof(t88_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_tex_4(A,C))))
               => m1_pre_topc(k7_tex_4(A,B),k7_tex_4(A,C)) ) ) ) ) )).

fof(t89_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_tex_4(A,B))))
                  & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_tex_4(A,C)))) )
              <=> g1_pre_topc(u1_struct_0(k7_tex_4(A,B)),u1_pre_topc(k7_tex_4(A,B))) = g1_pre_topc(u1_struct_0(k7_tex_4(A,C)),u1_pre_topc(k7_tex_4(A,C))) ) ) ) ) )).

fof(t90_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_tsep_1(B,A)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
               => m1_pre_topc(k7_tex_4(A,C),B) ) ) ) ) )).

fof(t91_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_borsuk_1(B,A)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
               => m1_pre_topc(k7_tex_4(A,C),B) ) ) ) ) )).

fof(dt_k1_tex_4,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_tex_4(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k2_tex_4,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k2_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k3_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k3_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k4_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k4_tex_4(A,B))
        & m1_subset_1(k4_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(redefinition_k4_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => k4_tex_4(A,B) = k2_tex_4(A,B) ) )).

fof(dt_k5_tex_4,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_pre_topc(k5_tex_4(A,B))
        & m1_pre_topc(k5_tex_4(A,B),A) ) ) )).

fof(dt_k6_tex_4,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_pre_topc(k6_tex_4(A,B))
        & m1_pre_topc(k6_tex_4(A,B),A) ) ) )).

fof(dt_k7_tex_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_pre_topc(k7_tex_4(A,B))
        & m1_pre_topc(k7_tex_4(A,B),A) ) ) )).

fof(t1_tex_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)))
         => k6_pre_topc(A,B) = k1_setfam_1(a_2_0_tex_4(A,B)) ) ) )).

fof(t2_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_pre_topc(A,k1_struct_0(A,B)) = k1_setfam_1(a_2_1_tex_4(A,B)) ) ) )).

fof(t4_tex_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)))
         => k1_tops_1(A,B) = k3_tarski(a_2_2_tex_4(A,B)) ) ) )).

fof(d6_tex_4,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_tex_4(A,B) = a_2_3_tex_4(A,B) ) ) )).

fof(t27_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( a_2_4_tex_4(A,B) != k1_xboole_0
           => r1_tarski(k2_tex_4(A,B),k1_setfam_1(a_2_4_tex_4(A,B))) ) ) ) )).

fof(t28_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( a_2_5_tex_4(A,B) != k1_xboole_0
           => r1_tarski(k2_tex_4(A,B),k1_setfam_1(a_2_5_tex_4(A,B))) ) ) ) )).

fof(d11_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k3_tex_4(A,B) = k3_tarski(a_2_6_tex_4(A,B)) ) ) )).

fof(t41_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( a_2_7_tex_4(A,B) != k1_xboole_0
           => r1_tarski(k3_tex_4(A,B),k1_setfam_1(a_2_7_tex_4(A,B))) ) ) ) )).

fof(t43_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( a_2_8_tex_4(A,B) != k1_xboole_0
           => r1_tarski(k3_tex_4(A,B),k1_setfam_1(a_2_8_tex_4(A,B))) ) ) ) )).

fof(t48_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_tarski(k2_tex_4(A,B),k1_setfam_1(a_2_9_tex_4(A,B))) ) ) )).

fof(t49_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_tarski(k2_tex_4(A,B),k1_setfam_1(a_2_1_tex_4(A,B))) ) ) )).

fof(d15_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_tex_4(A,B) = k3_xboole_0(k6_pre_topc(A,k1_struct_0(A,B)),k1_setfam_1(a_2_9_tex_4(A,B))) ) ) )).

fof(t53_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_tarski(k6_pre_topc(A,k1_struct_0(A,B)),k6_pre_topc(A,k1_struct_0(A,C)))
              <=> r1_tarski(k1_setfam_1(a_2_9_tex_4(A,C)),k1_setfam_1(a_2_9_tex_4(A,B))) ) ) ) ) )).

fof(t54_tex_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_tarski(k6_pre_topc(A,k1_struct_0(A,B)),k6_pre_topc(A,k1_struct_0(A,C)))
              <=> r1_tarski(k4_tex_4(A,C),k1_setfam_1(a_2_9_tex_4(A,B))) ) ) ) ) )).

fof(t57_tex_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(k3_tex_4(A,B),k1_setfam_1(a_2_10_tex_4(A,B))) ) ) )).

fof(t60_tex_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(k3_tex_4(A,B),k1_setfam_1(a_2_0_tex_4(A,B))) ) ) )).

fof(fraenkel_a_2_0_tex_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_tex_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & v4_pre_topc(D,B)
            & r1_tarski(C,D) ) ) ) )).

fof(fraenkel_a_2_1_tex_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_1_tex_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & v4_pre_topc(D,B)
            & r2_hidden(C,D) ) ) ) )).

fof(fraenkel_a_2_2_tex_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_2_tex_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & v3_pre_topc(D,B)
            & r1_tarski(D,C) ) ) ) )).

fof(fraenkel_a_2_3_tex_4,axiom,(
    ! [A,B,C] :
      ( ( l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_3_tex_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & v1_tex_4(D,B)
            & r2_hidden(C,D) ) ) ) )).

fof(fraenkel_a_2_4_tex_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_4_tex_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & v4_pre_topc(D,B)
            & r2_hidden(C,D) ) ) ) )).

fof(fraenkel_a_2_5_tex_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_5_tex_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & v3_pre_topc(D,B)
            & r2_hidden(C,D) ) ) ) )).

fof(fraenkel_a_2_6_tex_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_6_tex_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = k2_tex_4(B,D)
            & r2_hidden(D,C) ) ) ) )).

fof(fraenkel_a_2_7_tex_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_7_tex_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & v3_pre_topc(D,B)
            & r1_tarski(C,D) ) ) ) )).

fof(fraenkel_a_2_8_tex_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_8_tex_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & v4_pre_topc(D,B)
            & r1_tarski(C,D) ) ) ) )).

fof(fraenkel_a_2_9_tex_4,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_9_tex_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & v3_pre_topc(D,B)
            & r2_hidden(C,D) ) ) ) )).

fof(fraenkel_a_2_10_tex_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_10_tex_4(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & A = D
            & v3_pre_topc(D,B)
            & r1_tarski(C,D) ) ) ) )).
%------------------------------------------------------------------------------