SET007 Axioms: SET007+370.ax


%------------------------------------------------------------------------------
% File     : SET007+370 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Remarks on Special 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    : tops_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   90 (   0 unit)
%            Number of atoms       :  758 (  96 equality)
%            Maximal formula depth :   18 (  10 average)
%            Number of connectives :  762 (  94 ~  ;   4  |; 283  &)
%                                         (  27 <=>; 354 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   17 (   0 propositional; 1-2 arity)
%            Number of functors    :   13 (   1 constant; 0-3 arity)
%            Number of variables   :  286 (   0 singleton; 284 !;   2 ?)
%            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(t1_tops_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( B = k1_pre_topc(A)
             => k3_subset_1(u1_struct_0(A),B) = k2_pre_topc(A) )
            & ( k3_subset_1(u1_struct_0(A),B) = k2_pre_topc(A)
             => B = k1_pre_topc(A) )
            & ( B = k1_xboole_0
             => k3_subset_1(u1_struct_0(A),B) = u1_struct_0(A) )
            & ( k3_subset_1(u1_struct_0(A),B) = u1_struct_0(A)
             => B = k1_xboole_0 ) ) ) ) )).

fof(t2_tops_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( B = k2_pre_topc(A)
             => k3_subset_1(u1_struct_0(A),B) = k1_pre_topc(A) )
            & ( k3_subset_1(u1_struct_0(A),B) = k1_pre_topc(A)
             => B = k2_pre_topc(A) )
            & ( B = u1_struct_0(A)
             => k3_subset_1(u1_struct_0(A),B) = k1_xboole_0 )
            & ( k3_subset_1(u1_struct_0(A),B) = k1_xboole_0
             => B = u1_struct_0(A) ) ) ) ) )).

fof(t3_tops_3,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(k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k6_pre_topc(A,C)),k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C))) ) ) ) )).

fof(t4_tops_3,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(k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k1_tops_1(A,C))) ) ) ) )).

fof(t5_tops_3,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)))
             => ( v4_pre_topc(C,A)
               => r1_tarski(k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B)),k4_subset_1(u1_struct_0(A),C,k1_tops_1(A,B))) ) ) ) ) )).

fof(t6_tops_3,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)))
             => ( v4_pre_topc(C,A)
               => k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B)) = k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,k1_tops_1(A,B))) ) ) ) ) )).

fof(t7_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r1_xboole_0(B,k1_tops_1(A,k6_pre_topc(A,B)))
           => k1_tops_1(A,k6_pre_topc(A,B)) = k1_xboole_0 ) ) ) )).

fof(t8_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(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,k6_pre_topc(A,k1_tops_1(A,B))) = u1_struct_0(A)
           => k6_pre_topc(A,k1_tops_1(A,B)) = u1_struct_0(A) ) ) ) )).

fof(d1_tops_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_tops_1(B,A)
          <=> k1_tops_1(A,B) = k1_xboole_0 ) ) ) )).

fof(t9_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v2_tops_1(k1_pre_topc(A),A) ) )).

fof(t10_tops_3,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)))
         => ~ ( v2_tops_1(B,A)
              & B = u1_struct_0(A) ) ) ) )).

fof(t11_tops_3,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)))
             => ( ( v2_tops_1(B,A)
                  & r1_tarski(C,B) )
               => v2_tops_1(C,A) ) ) ) ) )).

fof(t12_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_tops_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( ( r1_tarski(k3_subset_1(u1_struct_0(A),B),C)
                    & v4_pre_topc(C,A) )
                 => C = u1_struct_0(A) ) ) ) ) ) )).

fof(t13_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_tops_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( C != k1_xboole_0
                    & v3_pre_topc(C,A)
                    & r1_xboole_0(k3_subset_1(u1_struct_0(A),B),C) ) ) ) ) ) )).

fof(t14_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_tops_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( v4_pre_topc(C,A)
                 => k1_tops_1(A,C) = k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B)) ) ) ) ) ) )).

fof(t15_tops_3,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)))
             => ( ( v2_tops_1(B,A)
                  | v2_tops_1(C,A) )
               => v2_tops_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(d2_tops_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tops_1(B,A)
          <=> k6_pre_topc(A,B) = u1_struct_0(A) ) ) ) )).

fof(t16_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v1_tops_1(k2_pre_topc(A),A) ) )).

fof(t17_tops_3,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_tops_1(B,A)
              & B = k1_xboole_0 ) ) ) )).

fof(t18_tops_3,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_tops_1(B,A)
          <=> v2_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t19_tops_3,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_tops_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( ( r1_tarski(B,C)
                    & v4_pre_topc(C,A) )
                 => C = u1_struct_0(A) ) ) ) ) ) )).

fof(t20_tops_3,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_tops_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( v3_pre_topc(C,A)
                 => k6_pre_topc(A,C) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),C,B)) ) ) ) ) ) )).

fof(t21_tops_3,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)))
             => ( ( v1_tops_1(B,A)
                  | v1_tops_1(C,A) )
               => v1_tops_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(d3_tops_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tops_1(B,A)
          <=> k1_tops_1(A,k6_pre_topc(A,B)) = k1_xboole_0 ) ) ) )).

fof(t22_tops_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v3_tops_1(k1_pre_topc(A),A) ) )).

fof(t23_tops_3,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_tops_1(B,A)
              & B = u1_struct_0(A) ) ) ) )).

fof(t24_tops_3,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_tops_1(B,A)
           => v3_tops_1(k6_pre_topc(A,B),A) ) ) ) )).

fof(t25_tops_3,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_tops_1(B,A)
              & v1_tops_1(B,A) ) ) ) )).

fof(t26_tops_3,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_tops_1(B,A)
                  & r1_tarski(C,B) )
               => v3_tops_1(C,A) ) ) ) ) )).

fof(t27_tops_3,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_tops_1(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                & r1_tarski(B,C)
                & v4_pre_topc(C,A)
                & v2_tops_1(C,A) ) ) ) ) )).

fof(t28_tops_3,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_tops_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( C != k1_xboole_0
                    & v3_pre_topc(C,A)
                    & ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( r1_tarski(D,C)
                            & D != k1_xboole_0
                            & v3_pre_topc(D,A)
                            & r1_xboole_0(B,D) ) ) ) ) ) ) ) )).

fof(t29_tops_3,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_tops_1(B,A)
                  | v3_tops_1(C,A) )
               => v3_tops_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t30_tops_3,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_tops_1(B,A)
                  & v2_tops_1(C,A) )
               => v2_tops_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(d4_tops_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tops_3(B,A)
          <=> k6_pre_topc(A,k1_tops_1(A,B)) = k2_pre_topc(A) ) ) ) )).

fof(d5_tops_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tops_3(B,A)
          <=> k6_pre_topc(A,k1_tops_1(A,B)) = u1_struct_0(A) ) ) ) )).

fof(t31_tops_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v1_tops_3(k2_pre_topc(A),A) ) )).

fof(t32_tops_3,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_tops_3(B,A)
           => v1_tops_3(k1_tops_1(A,B),A) ) ) ) )).

fof(t33_tops_3,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_tops_3(B,A)
           => v1_tops_1(B,A) ) ) ) )).

fof(t34_tops_3,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_tops_3(B,A)
              & B = k1_xboole_0 ) ) ) )).

fof(t35_tops_3,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_tops_3(B,A)
          <=> v1_tops_1(k1_tops_1(A,B),A) ) ) ) )).

fof(t36_tops_3,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)
              & v1_tops_1(B,A) )
           => v1_tops_3(B,A) ) ) ) )).

fof(t37_tops_3,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_tops_3(B,A)
              & v2_tops_1(B,A) ) ) ) )).

fof(t38_tops_3,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)))
             => ( ( v1_tops_3(B,A)
                  & r1_tarski(B,C) )
               => v1_tops_3(C,A) ) ) ) ) )).

fof(t39_tops_3,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_tops_3(B,A)
          <=> v3_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t40_tops_3,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_tops_1(B,A)
          <=> v1_tops_3(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t41_tops_3,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_tops_3(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                & r1_tarski(C,B)
                & v3_pre_topc(C,A)
                & v1_tops_1(C,A) ) ) ) ) )).

fof(t42_tops_3,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_tops_3(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( C != u1_struct_0(A)
                    & v4_pre_topc(C,A)
                    & ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                       => ~ ( r1_tarski(C,D)
                            & D != u1_struct_0(A)
                            & v4_pre_topc(D,A)
                            & k4_subset_1(u1_struct_0(A),B,D) = u1_struct_0(A) ) ) ) ) ) ) ) )).

fof(t43_tops_3,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)))
             => ( ( v1_tops_3(B,A)
                  | v1_tops_3(C,A) )
               => v1_tops_3(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t44_tops_3,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)))
             => ( ( v1_tops_3(B,A)
                  & v1_tops_3(C,A) )
               => v1_tops_3(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t45_tops_3,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)))
             => ( ( v1_tops_3(B,A)
                  & v1_tops_1(C,A) )
               => v1_tops_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t46_tops_3,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)))
             => ( ( v1_tops_1(B,A)
                  & v3_tops_1(C,A) )
               => v1_tops_1(k6_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t47_tops_3,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)))
             => ( ( v1_tops_3(B,A)
                  & v2_tops_1(C,A) )
               => v1_tops_1(k6_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t48_tops_3,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)))
             => ( ( v1_tops_3(B,A)
                  & v3_tops_1(C,A) )
               => v1_tops_3(k6_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t49_tops_3,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_tops_3(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( v3_pre_topc(C,A)
                          & v1_tops_1(C,A)
                          & v3_tops_1(D,A)
                          & k4_subset_1(u1_struct_0(A),C,D) = B
                          & r1_xboole_0(C,D) ) ) ) ) ) ) )).

fof(t50_tops_3,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_tops_3(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( v3_pre_topc(C,A)
                          & v1_tops_1(C,A)
                          & v4_pre_topc(D,A)
                          & v2_tops_1(D,A)
                          & k4_subset_1(u1_struct_0(A),C,k5_subset_1(u1_struct_0(A),B,D)) = B
                          & r1_xboole_0(C,D)
                          & k4_subset_1(u1_struct_0(A),C,D) = u1_struct_0(A) ) ) ) ) ) ) )).

fof(t51_tops_3,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_tops_1(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( v4_pre_topc(C,A)
                          & v2_tops_1(C,A)
                          & v1_tops_3(D,A)
                          & k5_subset_1(u1_struct_0(A),C,D) = B
                          & k4_subset_1(u1_struct_0(A),C,D) = u1_struct_0(A) ) ) ) ) ) ) )).

fof(t52_tops_3,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_tops_1(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( v4_pre_topc(C,A)
                          & v2_tops_1(C,A)
                          & v3_pre_topc(D,A)
                          & v1_tops_1(D,A)
                          & k5_subset_1(u1_struct_0(A),C,k4_subset_1(u1_struct_0(A),B,D)) = B
                          & r1_xboole_0(C,D)
                          & k4_subset_1(u1_struct_0(A),C,D) = u1_struct_0(A) ) ) ) ) ) ) )).

fof(t53_tops_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( r1_tarski(D,C)
                   => r1_tarski(k6_pre_topc(B,D),k6_pre_topc(A,C)) ) ) ) ) ) )).

fof(t54_tops_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ( ( v4_pre_topc(C,A)
                          & r1_tarski(C,u1_struct_0(B))
                          & r1_tarski(D,C)
                          & D = E )
                       => k6_pre_topc(A,D) = k6_pre_topc(B,E) ) ) ) ) ) ) )).

fof(t55_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( C = D
                   => k6_pre_topc(A,C) = k6_pre_topc(B,D) ) ) ) ) ) )).

fof(t56_tops_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( r1_tarski(C,D)
                   => r1_tarski(k1_tops_1(A,C),k1_tops_1(B,D)) ) ) ) ) ) )).

fof(t57_tops_3,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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ( ( v3_pre_topc(C,A)
                          & r1_tarski(C,u1_struct_0(B))
                          & r1_tarski(D,C)
                          & D = E )
                       => k1_tops_1(A,D) = k1_tops_1(B,E) ) ) ) ) ) ) )).

fof(t58_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( C = D
                   => k1_tops_1(A,C) = k1_tops_1(B,D) ) ) ) ) ) )).

fof(t59_tops_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( r1_tarski(C,D)
                      & v1_tops_1(C,A) )
                   => v1_tops_1(D,B) ) ) ) ) ) )).

fof(t60_tops_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ( ( r1_tarski(C,u1_struct_0(B))
                          & r1_tarski(D,C)
                          & D = E )
                       => ( ( v1_tops_1(C,A)
                            & v1_tops_1(E,B) )
                        <=> v1_tops_1(D,A) ) ) ) ) ) ) ) )).

fof(t61_tops_3,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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( r1_tarski(C,D)
                      & v1_tops_3(C,A) )
                   => v1_tops_3(D,B) ) ) ) ) ) )).

fof(t62_tops_3,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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ( ( v3_pre_topc(C,A)
                          & r1_tarski(C,u1_struct_0(B))
                          & r1_tarski(D,C)
                          & D = E )
                       => ( ( v1_tops_1(C,A)
                            & v1_tops_3(E,B) )
                        <=> v1_tops_3(D,A) ) ) ) ) ) ) ) )).

fof(t63_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ( ( D = u1_struct_0(B)
                          & C = E )
                       => ( ( v1_tops_1(D,A)
                            & v1_tops_3(E,B) )
                        <=> v1_tops_3(C,A) ) ) ) ) ) ) ) )).

fof(t64_tops_3,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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ( ( r1_tarski(C,u1_struct_0(B))
                          & r1_tarski(D,C)
                          & D = E )
                       => ( ( v1_tops_3(C,A)
                            & v1_tops_3(E,B) )
                        <=> v1_tops_3(D,A) ) ) ) ) ) ) ) )).

fof(t65_tops_3,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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( r1_tarski(C,D)
                      & v2_tops_1(D,B) )
                   => v2_tops_1(C,A) ) ) ) ) ) )).

fof(t66_tops_3,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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ( ( v3_pre_topc(C,A)
                          & r1_tarski(C,u1_struct_0(B))
                          & r1_tarski(D,C)
                          & D = E
                          & v2_tops_1(D,A) )
                       => v2_tops_1(E,B) ) ) ) ) ) ) )).

fof(t67_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( C = D
                   => ( v2_tops_1(C,A)
                    <=> v2_tops_1(D,B) ) ) ) ) ) ) )).

fof(t68_tops_3,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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( r1_tarski(C,D)
                      & v3_tops_1(D,B) )
                   => v3_tops_1(C,A) ) ) ) ) ) )).

fof(t69_tops_3,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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ( ( v3_pre_topc(C,A)
                          & r1_tarski(C,u1_struct_0(B))
                          & r1_tarski(D,C)
                          & D = E
                          & v3_tops_1(D,A) )
                       => v3_tops_1(E,B) ) ) ) ) ) ) )).

fof(t70_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( C = D
                   => ( v3_tops_1(C,A)
                    <=> v3_tops_1(D,B) ) ) ) ) ) ) )).

fof(t71_tops_3,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_struct_0(B)
         => ( u1_struct_0(A) = u1_struct_0(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)))
                   => ( C = D
                    <=> k3_subset_1(u1_struct_0(A),C) = k3_subset_1(u1_struct_0(B),D) ) ) ) ) ) ) )).

fof(t72_tops_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ( ( u1_struct_0(A) = u1_struct_0(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)))
                     => ( C = D
                       => ( v3_pre_topc(C,A)
                        <=> v3_pre_topc(D,B) ) ) ) ) )
           => g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) )).

fof(t73_tops_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ( ( u1_struct_0(A) = u1_struct_0(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)))
                     => ( C = D
                       => ( v4_pre_topc(C,A)
                        <=> v4_pre_topc(D,B) ) ) ) ) )
           => g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) )).

fof(t74_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( ( u1_struct_0(A) = u1_struct_0(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)))
                     => ( C = D
                       => k1_tops_1(A,C) = k1_tops_1(B,D) ) ) ) )
           => g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) )).

fof(t75_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( ( u1_struct_0(A) = u1_struct_0(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)))
                     => ( C = D
                       => k6_pre_topc(A,C) = k6_pre_topc(B,D) ) ) ) )
           => g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) )).

fof(t76_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(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)))
                 => ( ( C = D
                      & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & v3_pre_topc(C,A) )
                   => v3_pre_topc(D,B) ) ) ) ) ) )).

fof(t77_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(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)))
                 => ( ( C = D
                      & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) )
                   => k1_tops_1(A,C) = k1_tops_1(B,D) ) ) ) ) ) )).

fof(t78_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(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)))
                 => ( ( r1_tarski(C,D)
                      & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) )
                   => r1_tarski(k1_tops_1(A,C),k1_tops_1(B,D)) ) ) ) ) ) )).

fof(t79_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(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)))
                 => ( ( C = D
                      & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & v4_pre_topc(C,A) )
                   => v4_pre_topc(D,B) ) ) ) ) ) )).

fof(t80_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(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)))
                 => ( ( C = D
                      & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) )
                   => k6_pre_topc(A,C) = k6_pre_topc(B,D) ) ) ) ) ) )).

fof(t81_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(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)))
                 => ( ( r1_tarski(C,D)
                      & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) )
                   => r1_tarski(k6_pre_topc(A,C),k6_pre_topc(B,D)) ) ) ) ) ) )).

fof(t82_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(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)))
                 => ( ( r1_tarski(D,C)
                      & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & v2_tops_1(C,A) )
                   => v2_tops_1(D,B) ) ) ) ) ) )).

fof(t83_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(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)))
                 => ( ( r1_tarski(C,D)
                      & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & v1_tops_1(C,A) )
                   => v1_tops_1(D,B) ) ) ) ) ) )).

fof(t84_tops_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(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)))
                 => ( ( r1_tarski(D,C)
                      & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & v3_tops_1(C,A) )
                   => v3_tops_1(D,B) ) ) ) ) ) )).

fof(t85_tops_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(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)))
                 => ( ( r1_tarski(C,D)
                      & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & v1_tops_3(C,A) )
                   => v1_tops_3(D,B) ) ) ) ) ) )).
%------------------------------------------------------------------------------