SET007 Axioms: SET007+354.ax


%------------------------------------------------------------------------------
% File     : SET007+354 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Lattice of Domains of an Extremally Disconnected Space
% 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    : tdlat_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   86 (   2 unit)
%            Number of atoms       :  558 (  57 equality)
%            Maximal formula depth :   13 (   7 average)
%            Number of connectives :  542 (  70 ~  ;   0  |; 244  &)
%                                         (  27 <=>; 201 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   29 (   1 propositional; 0-2 arity)
%            Number of functors    :   34 (   1 constant; 0-3 arity)
%            Number of variables   :  152 (   0 singleton; 141 !;  11 ?)
%            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(rc1_tdlat_3,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v1_tdlat_3(A)
      & v2_tdlat_3(A) ) )).

fof(cc1_tdlat_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v1_tdlat_3(A)
       => v2_pre_topc(A) ) ) )).

fof(cc2_tdlat_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v2_tdlat_3(A)
       => v2_pre_topc(A) ) ) )).

fof(cc3_tdlat_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v1_tdlat_3(A)
       => v3_tdlat_3(A) ) ) )).

fof(cc4_tdlat_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v2_tdlat_3(A)
       => v3_tdlat_3(A) ) ) )).

fof(rc2_tdlat_3,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & v1_pre_topc(A)
      & v3_tdlat_3(A) ) )).

fof(rc3_tdlat_3,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v1_tdlat_3(A)
      & v2_tdlat_3(A)
      & v3_tdlat_3(A) ) )).

fof(cc5_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v2_pre_topc(B)
            & v1_borsuk_1(B,A)
            & v1_tsep_1(B,A)
            & v1_tdlat_3(B)
            & v3_tdlat_3(B) ) ) ) )).

fof(rc4_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_borsuk_1(B,A)
          & v1_tsep_1(B,A)
          & v1_tdlat_3(B)
          & v3_tdlat_3(B) ) ) )).

fof(cc6_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v2_pre_topc(B)
            & v2_tdlat_3(B)
            & v3_tdlat_3(B) ) ) ) )).

fof(rc5_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & v2_pre_topc(B)
          & v2_tdlat_3(B)
          & v3_tdlat_3(B) ) ) )).

fof(rc6_tdlat_3,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v3_tdlat_3(A) ) )).

fof(cc7_tdlat_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v1_tdlat_3(A) )
       => ( v2_pre_topc(A)
          & v3_tdlat_3(A) ) ) ) )).

fof(cc8_tdlat_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v2_tdlat_3(A) )
       => ( v2_pre_topc(A)
          & v3_tdlat_3(A) ) ) ) )).

fof(cc9_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v3_struct_0(B)
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v3_tdlat_3(B) ) ) ) ) )).

fof(cc10_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v1_tsep_1(B,A)
           => ( v2_pre_topc(B)
              & v1_borsuk_1(B,A) ) ) ) ) )).

fof(cc11_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v1_borsuk_1(B,A)
           => ( v2_pre_topc(B)
              & v1_tsep_1(B,A) ) ) ) ) )).

fof(rc7_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_tdlat_3(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v3_tdlat_3(B) ) ) )).

fof(rc8_tdlat_3,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v4_tdlat_3(A) ) )).

fof(rc9_tdlat_3,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v5_tdlat_3(A) ) )).

fof(cc12_tdlat_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v5_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v4_tdlat_3(A) ) ) ) )).

fof(cc13_tdlat_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v3_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v5_tdlat_3(A) ) ) ) )).

fof(cc14_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ( ~ v3_struct_0(B)
              & v1_tsep_1(B,A) )
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v4_tdlat_3(B) ) ) ) ) )).

fof(rc10_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v4_tdlat_3(B) ) ) )).

fof(cc15_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v5_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( ~ v3_struct_0(B)
           => ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & v4_tdlat_3(B)
              & v5_tdlat_3(B) ) ) ) ) )).

fof(rc11_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v5_tdlat_3(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v4_tdlat_3(B)
          & v5_tdlat_3(B) ) ) )).

fof(t1_tdlat_3,axiom,(
    $true )).

fof(t2_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_pre_topc(A,B) = k3_subset_1(u1_struct_0(A),k1_tops_1(A,k3_subset_1(u1_struct_0(A),B))) ) ) )).

fof(t3_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)) = k3_subset_1(u1_struct_0(A),k1_tops_1(A,B)) ) ) )).

fof(t4_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_tops_1(A,k3_subset_1(u1_struct_0(A),B)) = k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)) ) ) )).

fof(t5_tdlat_3,axiom,(
    $true )).

fof(t6_tdlat_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)))
             => ( k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A)
               => ( ( v4_pre_topc(B,A)
                   => k4_subset_1(u1_struct_0(A),B,k1_tops_1(A,C)) = u1_struct_0(A) )
                  & ( v4_pre_topc(C,A)
                   => k4_subset_1(u1_struct_0(A),k1_tops_1(A,B),C) = u1_struct_0(A) ) ) ) ) ) ) )).

fof(t7_tdlat_3,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) )
          <=> k6_pre_topc(A,B) = k1_tops_1(A,B) ) ) ) )).

fof(t8_tdlat_3,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) )
           => k1_tops_1(A,k6_pre_topc(A,B)) = k6_pre_topc(A,k1_tops_1(A,B)) ) ) ) )).

fof(t9_tdlat_3,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)
              & r1_tarski(k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B))) )
           => ( v6_tops_1(B,A)
              & v5_tops_1(B,A) ) ) ) ) )).

fof(t10_tdlat_3,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)
              & r1_tarski(k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B))) )
           => ( v3_pre_topc(B,A)
              & v4_pre_topc(B,A) ) ) ) ) )).

fof(t11_tdlat_3,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,k6_pre_topc(A,B)) = k1_tops_1(A,B)
              & k6_pre_topc(A,B) = k6_pre_topc(A,k1_tops_1(A,B)) ) ) ) ) )).

fof(d1_tdlat_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v1_tdlat_3(A)
      <=> u1_pre_topc(A) = k1_pcomps_1(u1_struct_0(A)) ) ) )).

fof(d2_tdlat_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v2_tdlat_3(A)
      <=> u1_pre_topc(A) = k2_tarski(k1_xboole_0,u1_struct_0(A)) ) ) )).

fof(t12_tdlat_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( v1_tdlat_3(A)
          & v2_tdlat_3(A) )
       => k1_pcomps_1(u1_struct_0(A)) = k2_tarski(k1_xboole_0,u1_struct_0(A)) ) ) )).

fof(t13_tdlat_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( r2_hidden(k1_xboole_0,u1_pre_topc(A))
          & r2_hidden(u1_struct_0(A),u1_pre_topc(A))
          & k1_pcomps_1(u1_struct_0(A)) = k2_tarski(k1_xboole_0,u1_struct_0(A)) )
       => ( v1_tdlat_3(A)
          & v2_tdlat_3(A) ) ) ) )).

fof(t14_tdlat_3,axiom,(
    ! [A] :
      ( ( v1_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r2_hidden(k4_xboole_0(u1_struct_0(A),B),u1_pre_topc(A)) ) ) )).

fof(t15_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r2_hidden(B,u1_pre_topc(A))
           => r2_hidden(k4_xboole_0(u1_struct_0(A),B),u1_pre_topc(A)) ) ) ) )).

fof(t16_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( k1_pcomps_1(u1_struct_0(A)) = k2_tarski(k1_xboole_0,u1_struct_0(A))
       => ( v1_tdlat_3(A)
          & v2_tdlat_3(A) ) ) ) )).

fof(d3_tdlat_3,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v3_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( r2_hidden(B,u1_pre_topc(A))
             => r2_hidden(k4_xboole_0(u1_struct_0(A),B),u1_pre_topc(A)) ) ) ) ) )).

fof(t17_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => v3_pre_topc(B,A) ) ) ) )).

fof(t18_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => v4_pre_topc(B,A) ) ) ) )).

fof(t19_tdlat_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,u1_struct_0(A))
               => ( B = k1_tarski(C)
                 => v3_pre_topc(B,A) ) ) )
       => v1_tdlat_3(A) ) ) )).

fof(t20_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ~ ( v3_pre_topc(B,A)
                & B != k1_xboole_0
                & B != u1_struct_0(A) ) ) ) ) )).

fof(t21_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ~ ( v4_pre_topc(B,A)
                & B != k1_xboole_0
                & B != u1_struct_0(A) ) ) ) ) )).

fof(t22_tdlat_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,u1_struct_0(A))
               => ( B = k1_tarski(C)
                 => k6_pre_topc(A,B) = u1_struct_0(A) ) ) )
       => v2_tdlat_3(A) ) ) )).

fof(t23_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v3_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v3_pre_topc(B,A)
             => v4_pre_topc(B,A) ) ) ) ) )).

fof(t24_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v3_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v4_pre_topc(B,A)
             => v3_pre_topc(B,A) ) ) ) ) )).

fof(t25_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v3_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v3_pre_topc(B,A)
             => k6_pre_topc(A,B) = B ) ) ) ) )).

fof(t26_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v3_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v4_pre_topc(B,A)
             => k1_tops_1(A,B) = B ) ) ) ) )).

fof(t27_tdlat_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,u1_struct_0(A))
               => ( B = k1_tarski(C)
                 => v3_pre_topc(k6_pre_topc(A,B),A) ) ) )
       => v3_tdlat_3(A) ) ) )).

fof(t28_tdlat_3,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_tdlat_3(A)
      <=> ( v3_tdlat_3(A)
          & ! [B] :
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( B = k1_tarski(C)
                   => v4_pre_topc(B,A) ) ) ) ) ) ) )).

fof(d4_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v3_pre_topc(B,A)
             => v3_pre_topc(k6_pre_topc(A,B),A) ) ) ) ) )).

fof(t29_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v4_pre_topc(B,A)
             => v4_pre_topc(k1_tops_1(A,B),A) ) ) ) ) )).

fof(t30_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(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)
                    & r1_xboole_0(B,C) )
                 => r1_xboole_0(k6_pre_topc(A,B),k6_pre_topc(A,C)) ) ) ) ) ) )).

fof(t31_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(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)
                    & k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A) )
                 => k4_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)) = u1_struct_0(A) ) ) ) ) ) )).

fof(t32_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v3_pre_topc(B,A)
             => k6_pre_topc(A,B) = k1_tops_1(A,k6_pre_topc(A,B)) ) ) ) ) )).

fof(t33_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v4_pre_topc(B,A)
             => k1_tops_1(A,B) = k6_pre_topc(A,k1_tops_1(A,B)) ) ) ) ) )).

fof(t34_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v4_tops_1(B,A)
             => ( v4_pre_topc(B,A)
                & v3_pre_topc(B,A) ) ) ) ) ) )).

fof(t35_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v4_tops_1(B,A)
             => ( v5_tops_1(B,A)
                & v6_tops_1(B,A) ) ) ) ) ) )).

fof(t36_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v4_tops_1(B,A)
             => k1_tops_1(A,k6_pre_topc(A,B)) = k6_pre_topc(A,k1_tops_1(A,B)) ) ) ) ) )).

fof(t37_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( v4_tops_1(B,A)
             => k1_tops_1(A,B) = k6_pre_topc(A,B) ) ) ) ) )).

fof(t38_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ( ( v6_tops_1(B,A)
               => v5_tops_1(B,A) )
              & ( v5_tops_1(B,A)
               => v6_tops_1(B,A) ) ) ) ) ) )).

fof(d5_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v5_tdlat_3(A)
      <=> ! [B] :
            ( ( ~ v3_struct_0(B)
              & m1_pre_topc(B,A) )
           => v4_tdlat_3(B) ) ) ) )).

fof(t39_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(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)
                  & v1_tops_1(C,A) )
               => v4_tdlat_3(B) ) ) ) ) )).

fof(t40_tdlat_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) )
           => v4_tdlat_3(B) )
       => v5_tdlat_3(A) ) ) )).

fof(t41_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(A)
        & l1_pre_topc(A) )
     => k1_tdlat_1(A) = k5_tdlat_1(A) ) )).

fof(t42_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(A)
        & l1_pre_topc(A) )
     => ( k2_tdlat_1(A) = k6_tdlat_1(A)
        & k3_tdlat_1(A) = k7_tdlat_1(A) ) ) )).

fof(t43_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(A)
        & l1_pre_topc(A) )
     => k4_tdlat_1(A) = k8_tdlat_1(A) ) )).

fof(t44_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(A)
        & l1_pre_topc(A) )
     => k1_tdlat_1(A) = k9_tdlat_1(A) ) )).

fof(t45_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(A)
        & l1_pre_topc(A) )
     => ( k2_tdlat_1(A) = k10_tdlat_1(A)
        & k3_tdlat_1(A) = k11_tdlat_1(A) ) ) )).

fof(t46_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(A)
        & l1_pre_topc(A) )
     => k4_tdlat_1(A) = k12_tdlat_1(A) ) )).

fof(t47_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_tdlat_1(A))
         => ! [C] :
              ( m1_subset_1(C,k1_tdlat_1(A))
             => ( k1_binop_1(k2_tdlat_1(A),B,C) = k2_xboole_0(B,C)
                & k1_binop_1(k3_tdlat_1(A),B,C) = k3_xboole_0(B,C) ) ) ) ) )).

fof(t48_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k4_tdlat_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k4_tdlat_1(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_tdlat_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_tdlat_1(A))
                     => ( ( B = D
                          & C = E )
                       => ( k3_lattices(k4_tdlat_1(A),B,C) = k2_xboole_0(D,E)
                          & k4_lattices(k4_tdlat_1(A),B,C) = k3_xboole_0(D,E) ) ) ) ) ) ) ) )).

fof(t49_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_tdlat_2(B,A)
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_tdlat_1(A))))
               => ( C = B
                 => k15_lattice3(k4_tdlat_1(A),C) = k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)) ) ) ) ) ) )).

fof(t50_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v4_tdlat_3(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_tdlat_2(B,A)
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_tdlat_1(A))))
               => ( C = B
                 => ( ( C != k1_xboole_0
                     => k16_lattice3(k4_tdlat_1(A),C) = k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)) )
                    & ( C = k1_xboole_0
                     => k16_lattice3(k4_tdlat_1(A),C) = k2_pre_topc(A) ) ) ) ) ) ) ) )).

fof(t51_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(A)
      <=> ( ~ v3_struct_0(k4_tdlat_1(A))
          & v10_lattices(k4_tdlat_1(A))
          & v12_lattices(k4_tdlat_1(A))
          & l3_lattices(k4_tdlat_1(A)) ) ) ) )).

fof(t52_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( k4_tdlat_1(A) = k8_tdlat_1(A)
       => v4_tdlat_3(A) ) ) )).

fof(t53_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( k4_tdlat_1(A) = k12_tdlat_1(A)
       => v4_tdlat_3(A) ) ) )).

fof(t54_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( k8_tdlat_1(A) = k12_tdlat_1(A)
       => v4_tdlat_3(A) ) ) )).

fof(t55_tdlat_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v4_tdlat_3(A)
      <=> ( ~ v3_struct_0(k4_tdlat_1(A))
          & v10_lattices(k4_tdlat_1(A))
          & v17_lattices(k4_tdlat_1(A))
          & l3_lattices(k4_tdlat_1(A)) ) ) ) )).
%------------------------------------------------------------------------------