SET007 Axioms: SET007+207.ax


%------------------------------------------------------------------------------
% File     : SET007+207 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  145 (  30 unit)
%            Number of atoms       :  648 (  41 equality)
%            Maximal formula depth :   18 (   6 average)
%            Number of connectives :  516 (  13 ~  ;   0  |; 187  &)
%                                         (  24 <=>; 292 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   24 (   1 propositional; 0-2 arity)
%            Number of functors    :   12 (   1 constant; 0-3 arity)
%            Number of variables   :  262 (   0 singleton; 255 !;   7 ?)
%            Maximal term depth    :    6 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_xboole_0(k1_pre_topc(A))
        & v4_pre_topc(k1_pre_topc(A),A)
        & v1_membered(k1_pre_topc(A))
        & v2_membered(k1_pre_topc(A))
        & v3_membered(k1_pre_topc(A))
        & v4_membered(k1_pre_topc(A))
        & v5_membered(k1_pre_topc(A)) ) ) )).

fof(fc2_tops_1,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v4_pre_topc(k6_pre_topc(A,B),A) ) )).

fof(fc3_tops_1,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v4_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) )).

fof(rc1_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v3_pre_topc(B,A) ) ) )).

fof(fc4_tops_1,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v3_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) )).

fof(fc5_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v1_xboole_0(k1_tops_1(A,k1_pre_topc(A)))
        & v1_membered(k1_tops_1(A,k1_pre_topc(A)))
        & v2_membered(k1_tops_1(A,k1_pre_topc(A)))
        & v3_membered(k1_tops_1(A,k1_pre_topc(A)))
        & v4_membered(k1_tops_1(A,k1_pre_topc(A)))
        & v5_membered(k1_tops_1(A,k1_pre_topc(A))) ) ) )).

fof(fc6_tops_1,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v3_pre_topc(k1_tops_1(A,B),A) ) )).

fof(fc7_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_xboole_0(k1_pre_topc(A))
        & v3_pre_topc(k1_pre_topc(A),A)
        & v4_pre_topc(k1_pre_topc(A),A)
        & v1_membered(k1_pre_topc(A))
        & v2_membered(k1_pre_topc(A))
        & v3_membered(k1_pre_topc(A))
        & v4_membered(k1_pre_topc(A))
        & v5_membered(k1_pre_topc(A)) ) ) )).

fof(fc8_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v3_pre_topc(k2_pre_topc(A),A)
        & v4_pre_topc(k2_pre_topc(A),A) ) ) )).

fof(cc1_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => ( v3_pre_topc(B,A)
              & v4_pre_topc(B,A) ) ) ) ) )).

fof(rc2_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A) ) ) )).

fof(rc3_tops_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A) ) ) )).

fof(fc9_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => v1_tops_1(k2_pre_topc(A),A) ) )).

fof(cc2_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => v2_tops_1(B,A) ) ) ) )).

fof(rc4_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_xboole_0(B)
          & v1_membered(B)
          & v2_membered(B)
          & v3_membered(B)
          & v4_membered(B)
          & v5_membered(B)
          & v2_tops_1(B,A) ) ) )).

fof(fc10_tops_1,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & v2_tops_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_xboole_0(k1_tops_1(A,B))
        & 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))
        & v2_tops_1(k1_tops_1(A,B),A) ) ) )).

fof(cc3_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => v3_tops_1(B,A) ) ) ) )).

fof(rc5_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_xboole_0(B)
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A)
          & v1_membered(B)
          & v2_membered(B)
          & v3_membered(B)
          & v4_membered(B)
          & v5_membered(B)
          & v2_tops_1(B,A)
          & v3_tops_1(B,A) ) ) )).

fof(fc11_tops_1,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v3_tops_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v1_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) )).

fof(cc4_tops_1,axiom,(
    ! [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)
           => v2_tops_1(B,A) ) ) ) )).

fof(cc5_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v4_pre_topc(B,A)
              & v2_tops_1(B,A) )
           => ( v2_tops_1(B,A)
              & v3_tops_1(B,A) ) ) ) ) )).

fof(fc12_tops_1,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v3_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v2_tops_1(k2_tops_1(A,B),A)
        & v3_tops_1(k2_tops_1(A,B),A) ) ) )).

fof(fc13_tops_1,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v4_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v2_tops_1(k2_tops_1(A,B),A)
        & v3_tops_1(k2_tops_1(A,B),A) ) ) )).

fof(cc6_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v3_pre_topc(B,A)
              & v3_tops_1(B,A) )
           => ( v1_xboole_0(B)
              & v3_pre_topc(B,A)
              & v4_pre_topc(B,A)
              & v1_membered(B)
              & v2_membered(B)
              & v3_membered(B)
              & v4_membered(B)
              & v5_membered(B)
              & v2_tops_1(B,A)
              & v3_tops_1(B,A) ) ) ) ) )).

fof(t1_tops_1,axiom,(
    $true )).

fof(t2_tops_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_subset_1(u1_struct_0(A),B,k2_pre_topc(A)) = k2_pre_topc(A) ) ) )).

fof(t3_tops_1,axiom,(
    $true )).

fof(t4_tops_1,axiom,(
    $true )).

fof(t5_tops_1,axiom,(
    $true )).

fof(t6_tops_1,axiom,(
    $true )).

fof(t7_tops_1,axiom,(
    $true )).

fof(t8_tops_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => k3_subset_1(u1_struct_0(A),k2_pre_topc(A)) = k1_pre_topc(A) ) )).

fof(t9_tops_1,axiom,(
    $true )).

fof(t10_tops_1,axiom,(
    $true )).

fof(t11_tops_1,axiom,(
    $true )).

fof(t12_tops_1,axiom,(
    $true )).

fof(t13_tops_1,axiom,(
    $true )).

fof(t14_tops_1,axiom,(
    $true )).

fof(t15_tops_1,axiom,(
    $true )).

fof(t16_tops_1,axiom,(
    $true )).

fof(t17_tops_1,axiom,(
    $true )).

fof(t18_tops_1,axiom,(
    $true )).

fof(t19_tops_1,axiom,(
    $true )).

fof(t20_tops_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(B,C)
              <=> r1_xboole_0(B,k3_subset_1(u1_struct_0(A),C)) ) ) ) ) )).

fof(t21_tops_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( k3_subset_1(u1_struct_0(A),B) = k3_subset_1(u1_struct_0(A),C)
               => B = C ) ) ) ) )).

fof(t22_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v4_pre_topc(k1_pre_topc(A),A) ) )).

fof(t23_tops_1,axiom,(
    $true )).

fof(t24_tops_1,axiom,(
    $true )).

fof(t25_tops_1,axiom,(
    $true )).

fof(t26_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_pre_topc(A,k6_pre_topc(A,B)) = k6_pre_topc(A,B) ) ) )).

fof(t27_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => k6_pre_topc(A,k2_pre_topc(A)) = k2_pre_topc(A) ) )).

fof(t28_tops_1,axiom,(
    $true )).

fof(t29_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
          <=> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t30_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
          <=> v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t31_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v4_pre_topc(B,A)
                  & r1_tarski(C,B) )
               => r1_tarski(k6_pre_topc(A,C),B) ) ) ) ) )).

fof(t32_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)),k6_pre_topc(A,k6_subset_1(u1_struct_0(A),B,C))) ) ) ) )).

fof(t33_tops_1,axiom,(
    $true )).

fof(t34_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v4_pre_topc(B,A)
                  & v4_pre_topc(C,A) )
               => k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)) ) ) ) ) )).

fof(t35_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v4_pre_topc(B,A)
                  & v4_pre_topc(C,A) )
               => v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t36_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v4_pre_topc(B,A)
                  & v4_pre_topc(C,A) )
               => v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t37_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v3_pre_topc(B,A)
                  & v3_pre_topc(C,A) )
               => v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t38_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v3_pre_topc(B,A)
                  & v3_pre_topc(C,A) )
               => v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t39_tops_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k6_pre_topc(A,B))
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ~ ( v3_pre_topc(D,A)
                        & r2_hidden(C,D)
                        & r1_xboole_0(B,D) ) ) ) ) ) ) )).

fof(t40_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( v3_pre_topc(B,A)
               => r1_tarski(k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)),k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C))) ) ) ) ) )).

fof(t41_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( v3_pre_topc(B,A)
               => k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C))) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) ) ) ) ) )).

fof(d1_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_tops_1(A,B) = k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))) ) ) )).

fof(t42_tops_1,axiom,(
    $true )).

fof(t43_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k1_tops_1(A,k2_pre_topc(A)) = k2_pre_topc(A) ) )).

fof(t44_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(k1_tops_1(A,B),B) ) ) )).

fof(t45_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_tops_1(A,k1_tops_1(A,B)) = k1_tops_1(A,B) ) ) )).

fof(t46_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)) = k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)) ) ) ) )).

fof(t47_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => k1_tops_1(A,k1_pre_topc(A)) = k1_pre_topc(A) ) )).

fof(t48_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(B,C)
               => r1_tarski(k1_tops_1(A,B),k1_tops_1(A,C)) ) ) ) ) )).

fof(t49_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k4_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)),k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,C))) ) ) ) )).

fof(t50_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k1_tops_1(A,k6_subset_1(u1_struct_0(A),B,C)),k6_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C))) ) ) ) )).

fof(t51_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => v3_pre_topc(k1_tops_1(A,B),A) ) ) )).

fof(t52_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v3_pre_topc(k1_pre_topc(A),A) ) )).

fof(t53_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v3_pre_topc(k2_pre_topc(A),A) ) )).

fof(t54_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B,C] :
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
         => ( r2_hidden(B,k1_tops_1(A,C))
          <=> ? [D] :
                ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                & v3_pre_topc(D,A)
                & r1_tarski(D,C)
                & r2_hidden(B,D) ) ) ) ) )).

fof(t55_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(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)))
                 => ( ( v3_pre_topc(D,B)
                     => k1_tops_1(B,D) = D )
                    & ( k1_tops_1(A,C) = C
                     => v3_pre_topc(C,A) ) ) ) ) ) ) )).

fof(t56_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v3_pre_topc(B,A)
                  & r1_tarski(B,C) )
               => r1_tarski(B,k1_tops_1(A,C)) ) ) ) ) )).

fof(t57_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
          <=> ! [C] :
                ( r2_hidden(C,B)
              <=> ? [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                    & v3_pre_topc(D,A)
                    & r1_tarski(D,B)
                    & r2_hidden(C,D) ) ) ) ) ) )).

fof(t58_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_pre_topc(A,k1_tops_1(A,B)) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))) ) ) )).

fof(t59_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
           => k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))) = k6_pre_topc(A,B) ) ) ) )).

fof(d2_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k2_tops_1(A,B) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))) ) ) )).

fof(t60_tops_1,axiom,(
    $true )).

fof(t61_tops_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k2_tops_1(A,B))
              <=> ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( ( v3_pre_topc(D,A)
                        & r2_hidden(C,D) )
                     => ( ~ r1_xboole_0(B,D)
                        & ~ r1_xboole_0(k3_subset_1(u1_struct_0(A),B),D) ) ) ) ) ) ) ) )).

fof(t62_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k2_tops_1(A,B) = k2_tops_1(A,k3_subset_1(u1_struct_0(A),B)) ) ) )).

fof(t63_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(k2_tops_1(A,B),k6_pre_topc(A,B)) ) ) )).

fof(t64_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k2_tops_1(A,B) = k4_subset_1(u1_struct_0(A),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),B),k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B)) ) ) )).

fof(t65_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_pre_topc(A,B) = k4_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)) ) ) )).

fof(t66_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))) ) ) ) )).

fof(t67_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => r1_tarski(k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))) ) ) ) )).

fof(t68_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(k2_tops_1(A,k2_tops_1(A,B)),k2_tops_1(A,B)) ) ) )).

fof(t69_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
           => r1_tarski(k2_tops_1(A,B),B) ) ) ) )).

fof(t70_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C)) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))),k5_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))) ) ) ) )).

fof(t71_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(k2_tops_1(A,k1_tops_1(A,B)),k2_tops_1(A,B)) ) ) )).

fof(t72_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(k2_tops_1(A,k6_pre_topc(A,B)),k2_tops_1(A,B)) ) ) )).

fof(t73_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_xboole_0(k1_tops_1(A,B),k2_tops_1(A,B)) ) ) )).

fof(t74_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_tops_1(A,B) = k6_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)) ) ) )).

fof(t75_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k2_tops_1(A,k2_tops_1(A,k2_tops_1(A,B))) = k2_tops_1(A,k2_tops_1(A,B)) ) ) )).

fof(t76_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
          <=> k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B) ) ) ) )).

fof(t77_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
          <=> k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),B,k1_tops_1(A,B)) ) ) ) )).

fof(d3_tops_1,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) = k2_pre_topc(A) ) ) ) )).

fof(t78_tops_1,axiom,(
    $true )).

fof(t79_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v1_tops_1(B,A)
                  & r1_tarski(B,C) )
               => v1_tops_1(C,A) ) ) ) ) )).

fof(t80_tops_1,axiom,(
    ! [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)))
               => ~ ( C != k1_xboole_0
                    & v3_pre_topc(C,A)
                    & r1_xboole_0(B,C) ) ) ) ) ) )).

fof(t81_tops_1,axiom,(
    ! [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(t82_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v1_tops_1(B,A)
                  & v1_tops_1(C,A)
                  & v3_pre_topc(C,A) )
               => v1_tops_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(d4_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_tops_1(B,A)
          <=> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t83_tops_1,axiom,(
    $true )).

fof(t84_tops_1,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(t85_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v2_tops_1(B,A)
                  & v2_tops_1(C,A)
                  & v4_pre_topc(C,A) )
               => v2_tops_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t86_tops_1,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(C,B)
                    & v3_pre_topc(C,A) )
                 => C = k1_xboole_0 ) ) ) ) ) )).

fof(t87_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
           => ( v2_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(t88_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_tops_1(B,A)
          <=> r1_tarski(B,k2_tops_1(A,B)) ) ) ) )).

fof(d5_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tops_1(B,A)
          <=> v2_tops_1(k6_pre_topc(A,B),A) ) ) ) )).

fof(t89_tops_1,axiom,(
    $true )).

fof(t90_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v3_tops_1(B,A)
                  & v3_tops_1(C,A) )
               => v3_tops_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t91_tops_1,axiom,(
    ! [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(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t92_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tops_1(B,A)
           => v2_tops_1(B,A) ) ) ) )).

fof(t93_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v2_tops_1(B,A)
              & v4_pre_topc(B,A) )
           => v3_tops_1(B,A) ) ) ) )).

fof(t94_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
           => ( v3_tops_1(B,A)
            <=> B = k2_tops_1(A,B) ) ) ) ) )).

fof(t95_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
           => v3_tops_1(k2_tops_1(A,B),A) ) ) ) )).

fof(t96_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
           => v3_tops_1(k2_tops_1(A,B),A) ) ) ) )).

fof(t97_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v3_pre_topc(B,A)
              & v3_tops_1(B,A) )
           => B = k1_xboole_0 ) ) ) )).

fof(d6_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
          <=> ( r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B)
              & r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) ) )).

fof(d7_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_tops_1(B,A)
          <=> B = k6_pre_topc(A,k1_tops_1(A,B)) ) ) ) )).

fof(d8_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(B,A)
          <=> B = k1_tops_1(A,k6_pre_topc(A,B)) ) ) ) )).

fof(t98_tops_1,axiom,(
    $true )).

fof(t99_tops_1,axiom,(
    $true )).

fof(t100_tops_1,axiom,(
    $true )).

fof(t101_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(B,A)
          <=> v5_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t102_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_tops_1(B,A)
           => k2_tops_1(A,k1_tops_1(A,B)) = k2_tops_1(A,B) ) ) ) )).

fof(t103_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_tops_1(B,A)
           => r1_tarski(k2_tops_1(A,B),k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) )).

fof(t104_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(B,A)
           => ( k2_tops_1(A,B) = k2_tops_1(A,k6_pre_topc(A,B))
              & k2_tops_1(A,k6_pre_topc(A,B)) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B) ) ) ) ) )).

fof(t105_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v3_pre_topc(B,A)
              & v4_pre_topc(B,A) )
           => ( v5_tops_1(B,A)
            <=> v6_tops_1(B,A) ) ) ) ) )).

fof(t106_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(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)))
                 => ( ( ( v4_pre_topc(D,B)
                        & v4_tops_1(D,B) )
                     => v5_tops_1(D,B) )
                    & ( v5_tops_1(C,A)
                     => ( v4_pre_topc(C,A)
                        & v4_tops_1(C,A) ) ) ) ) ) ) ) )).

fof(t107_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(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)))
                 => ( ( ( v3_pre_topc(D,B)
                        & v4_tops_1(D,B) )
                     => v6_tops_1(D,B) )
                    & ( v6_tops_1(C,A)
                     => ( v3_pre_topc(C,A)
                        & v4_tops_1(C,A) ) ) ) ) ) ) ) )).

fof(t108_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v5_tops_1(B,A)
                  & v5_tops_1(C,A) )
               => v5_tops_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t109_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v6_tops_1(B,A)
                  & v6_tops_1(C,A) )
               => v6_tops_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t110_tops_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
           => k1_tops_1(A,k2_tops_1(A,B)) = k1_xboole_0 ) ) ) )).

fof(t111_tops_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
           => ( v4_tops_1(k1_tops_1(A,B),A)
              & v4_tops_1(k6_pre_topc(A,B),A) ) ) ) ) )).

fof(dt_k1_tops_1,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k2_tops_1,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k2_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
%------------------------------------------------------------------------------