SET007 Axioms: SET007+340.ax


%------------------------------------------------------------------------------
% File     : SET007+340 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Lattice of Domains of a Topological 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   74 (   0 unit)
%            Number of atoms       :  354 (  41 equality)
%            Maximal formula depth :   12 (   6 average)
%            Number of connectives :  289 (   9 ~  ;   2  |; 121  &)
%                                         (  11 <=>; 146 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   24 (   0 propositional; 1-3 arity)
%            Number of functors    :   29 (   0 constant; 1-6 arity)
%            Number of variables   :  142 (   0 singleton; 139 !;   3 ?)
%            Maximal term depth    :    8 (   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_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ~ v1_xboole_0(k1_tdlat_1(A)) ) )).

fof(fc2_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ~ v1_xboole_0(k5_tdlat_1(A)) ) )).

fof(fc3_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ~ v1_xboole_0(k9_tdlat_1(A)) ) )).

fof(t1_tdlat_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),B,C) = k2_pre_topc(A)
              <=> r1_tarski(k3_subset_1(u1_struct_0(A),B),C) ) ) ) ) )).

fof(t2_tdlat_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_xboole_0(B,C)
              <=> r1_tarski(C,k3_subset_1(u1_struct_0(A),B)) ) ) ) ) )).

fof(t3_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))),k6_pre_topc(A,B)) ) ) )).

fof(t4_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(k1_tops_1(A,B),k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))) ) ) )).

fof(t5_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_tops_1(A,k6_pre_topc(A,B)) = k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B)))) ) ) )).

fof(t6_tdlat_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) )
               => k4_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,B)),k6_pre_topc(A,k1_tops_1(A,C))) = k6_pre_topc(A,k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,C))) ) ) ) ) )).

fof(t7_tdlat_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) )
               => k5_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,B)),k1_tops_1(A,k6_pre_topc(A,C))) = k1_tops_1(A,k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C))) ) ) ) ) )).

fof(t8_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))) = k1_pre_topc(A) ) ) )).

fof(t9_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,k1_tops_1(A,k3_subset_1(u1_struct_0(A),B)))) = k2_pre_topc(A) ) ) )).

fof(t10_tdlat_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),k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,k4_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,C)),C)))),k4_subset_1(u1_struct_0(A),B,k4_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,C)),C))) = k4_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C))),k4_subset_1(u1_struct_0(A),B,C)) ) ) ) )).

fof(t11_tdlat_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),k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,B)),B),C))),k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,B)),B),C)) = k4_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C))),k4_subset_1(u1_struct_0(A),B,C)) ) ) ) )).

fof(t12_tdlat_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),k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,C)),C)))),k5_subset_1(u1_struct_0(A),B,k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,C)),C))) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))),k5_subset_1(u1_struct_0(A),B,C)) ) ) ) )).

fof(t13_tdlat_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),k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,B)),B),C))),k5_subset_1(u1_struct_0(A),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,B)),B),C)) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))),k5_subset_1(u1_struct_0(A),B,C)) ) ) ) )).

fof(t14_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v4_tops_1(k1_pre_topc(A),A) ) )).

fof(t15_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v4_tops_1(k2_pre_topc(A),A) ) )).

fof(t16_tdlat_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)
           => v4_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t17_tdlat_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_tops_1(B,A)
                  & v4_tops_1(C,A) )
               => ( v4_tops_1(k4_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C))),k4_subset_1(u1_struct_0(A),B,C)),A)
                  & v4_tops_1(k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))),k5_subset_1(u1_struct_0(A),B,C)),A) ) ) ) ) ) )).

fof(t18_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v5_tops_1(k1_pre_topc(A),A) ) )).

fof(t19_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v5_tops_1(k2_pre_topc(A),A) ) )).

fof(t20_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v6_tops_1(k1_pre_topc(A),A) ) )).

fof(t21_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v6_tops_1(k2_pre_topc(A),A) ) )).

fof(t22_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => v5_tops_1(k6_pre_topc(A,k1_tops_1(A,B)),A) ) ) )).

fof(t23_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => v6_tops_1(k1_tops_1(A,k6_pre_topc(A,B)),A) ) ) )).

fof(t24_tdlat_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)
           => v5_tops_1(k6_pre_topc(A,B),A) ) ) ) )).

fof(t25_tdlat_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)
           => v6_tops_1(k1_tops_1(A,B),A) ) ) ) )).

fof(t26_tdlat_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)
           => v5_tops_1(k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),A) ) ) ) )).

fof(t27_tdlat_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)
           => v6_tops_1(k1_tops_1(A,k3_subset_1(u1_struct_0(A),B)),A) ) ) ) )).

fof(t28_tdlat_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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v5_tops_1(B,A)
                      & v5_tops_1(C,A)
                      & v5_tops_1(D,A) )
                   => k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),C,D)))))) = k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))),D))) ) ) ) ) ) )).

fof(t29_tdlat_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)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v6_tops_1(B,A)
                      & v6_tops_1(C,A)
                      & v6_tops_1(D,A) )
                   => k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),C,D)))))) = k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C))),D))) ) ) ) ) ) )).

fof(d2_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k1_tdlat_1(A),k1_tdlat_1(A)),k1_tdlat_1(A))
            & m2_relset_1(B,k2_zfmisc_1(k1_tdlat_1(A),k1_tdlat_1(A)),k1_tdlat_1(A)) )
         => ( B = k2_tdlat_1(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A))
               => ! [D] :
                    ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A))
                   => k2_binop_1(k1_tdlat_1(A),k1_tdlat_1(A),k1_tdlat_1(A),B,C,D) = k4_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),C,D))),k4_subset_1(u1_struct_0(A),C,D)) ) ) ) ) ) )).

fof(d3_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k1_tdlat_1(A),k1_tdlat_1(A)),k1_tdlat_1(A))
            & m2_relset_1(B,k2_zfmisc_1(k1_tdlat_1(A),k1_tdlat_1(A)),k1_tdlat_1(A)) )
         => ( B = k3_tdlat_1(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A))
               => ! [D] :
                    ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A))
                   => k2_binop_1(k1_tdlat_1(A),k1_tdlat_1(A),k1_tdlat_1(A),B,C,D) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),C,D))),k5_subset_1(u1_struct_0(A),C,D)) ) ) ) ) ) )).

fof(t30_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(g3_lattices(k1_tdlat_1(A),k2_tdlat_1(A),k3_tdlat_1(A)))
        & v10_lattices(g3_lattices(k1_tdlat_1(A),k2_tdlat_1(A),k3_tdlat_1(A)))
        & v15_lattices(g3_lattices(k1_tdlat_1(A),k2_tdlat_1(A),k3_tdlat_1(A)))
        & v16_lattices(g3_lattices(k1_tdlat_1(A),k2_tdlat_1(A),k3_tdlat_1(A)))
        & l3_lattices(g3_lattices(k1_tdlat_1(A),k2_tdlat_1(A),k3_tdlat_1(A))) ) ) )).

fof(d4_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k4_tdlat_1(A) = g3_lattices(k1_tdlat_1(A),k2_tdlat_1(A),k3_tdlat_1(A)) ) )).

fof(t31_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => r1_tarski(k5_tdlat_1(A),k1_tdlat_1(A)) ) )).

fof(d6_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k5_tdlat_1(A),k5_tdlat_1(A)),k5_tdlat_1(A))
            & m2_relset_1(B,k2_zfmisc_1(k5_tdlat_1(A),k5_tdlat_1(A)),k5_tdlat_1(A)) )
         => ( B = k6_tdlat_1(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A))
               => ! [D] :
                    ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A))
                   => k2_binop_1(k5_tdlat_1(A),k5_tdlat_1(A),k5_tdlat_1(A),B,C,D) = k4_subset_1(u1_struct_0(A),C,D) ) ) ) ) ) )).

fof(t32_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A))
             => k2_binop_1(k5_tdlat_1(A),k5_tdlat_1(A),k5_tdlat_1(A),k6_tdlat_1(A),B,C) = k1_binop_1(k2_tdlat_1(A),B,C) ) ) ) )).

fof(d7_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k5_tdlat_1(A),k5_tdlat_1(A)),k5_tdlat_1(A))
            & m2_relset_1(B,k2_zfmisc_1(k5_tdlat_1(A),k5_tdlat_1(A)),k5_tdlat_1(A)) )
         => ( B = k7_tdlat_1(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A))
               => ! [D] :
                    ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A))
                   => k2_binop_1(k5_tdlat_1(A),k5_tdlat_1(A),k5_tdlat_1(A),B,C,D) = k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),C,D))) ) ) ) ) ) )).

fof(t33_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A))
             => k2_binop_1(k5_tdlat_1(A),k5_tdlat_1(A),k5_tdlat_1(A),k7_tdlat_1(A),B,C) = k1_binop_1(k3_tdlat_1(A),B,C) ) ) ) )).

fof(t34_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(g3_lattices(k5_tdlat_1(A),k6_tdlat_1(A),k7_tdlat_1(A)))
        & v10_lattices(g3_lattices(k5_tdlat_1(A),k6_tdlat_1(A),k7_tdlat_1(A)))
        & v17_lattices(g3_lattices(k5_tdlat_1(A),k6_tdlat_1(A),k7_tdlat_1(A)))
        & l3_lattices(g3_lattices(k5_tdlat_1(A),k6_tdlat_1(A),k7_tdlat_1(A))) ) ) )).

fof(d8_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k8_tdlat_1(A) = g3_lattices(k5_tdlat_1(A),k6_tdlat_1(A),k7_tdlat_1(A)) ) )).

fof(t35_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => r1_tarski(k9_tdlat_1(A),k1_tdlat_1(A)) ) )).

fof(d10_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k9_tdlat_1(A),k9_tdlat_1(A)),k9_tdlat_1(A))
            & m2_relset_1(B,k2_zfmisc_1(k9_tdlat_1(A),k9_tdlat_1(A)),k9_tdlat_1(A)) )
         => ( B = k10_tdlat_1(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A))
               => ! [D] :
                    ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A))
                   => k2_binop_1(k9_tdlat_1(A),k9_tdlat_1(A),k9_tdlat_1(A),B,C,D) = k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),C,D))) ) ) ) ) ) )).

fof(t36_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A))
             => k2_binop_1(k9_tdlat_1(A),k9_tdlat_1(A),k9_tdlat_1(A),k10_tdlat_1(A),B,C) = k1_binop_1(k2_tdlat_1(A),B,C) ) ) ) )).

fof(d11_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k9_tdlat_1(A),k9_tdlat_1(A)),k9_tdlat_1(A))
            & m2_relset_1(B,k2_zfmisc_1(k9_tdlat_1(A),k9_tdlat_1(A)),k9_tdlat_1(A)) )
         => ( B = k11_tdlat_1(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A))
               => ! [D] :
                    ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A))
                   => k2_binop_1(k9_tdlat_1(A),k9_tdlat_1(A),k9_tdlat_1(A),B,C,D) = k5_subset_1(u1_struct_0(A),C,D) ) ) ) ) ) )).

fof(t37_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A))
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A))
             => k2_binop_1(k9_tdlat_1(A),k9_tdlat_1(A),k9_tdlat_1(A),k11_tdlat_1(A),B,C) = k1_binop_1(k3_tdlat_1(A),B,C) ) ) ) )).

fof(t38_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(g3_lattices(k9_tdlat_1(A),k10_tdlat_1(A),k11_tdlat_1(A)))
        & v10_lattices(g3_lattices(k9_tdlat_1(A),k10_tdlat_1(A),k11_tdlat_1(A)))
        & v17_lattices(g3_lattices(k9_tdlat_1(A),k10_tdlat_1(A),k11_tdlat_1(A)))
        & l3_lattices(g3_lattices(k9_tdlat_1(A),k10_tdlat_1(A),k11_tdlat_1(A))) ) ) )).

fof(d12_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k12_tdlat_1(A) = g3_lattices(k9_tdlat_1(A),k10_tdlat_1(A),k11_tdlat_1(A)) ) )).

fof(t39_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k6_tdlat_1(A) = k1_realset1(k2_tdlat_1(A),k5_tdlat_1(A)) ) )).

fof(t40_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k7_tdlat_1(A) = k1_realset1(k3_tdlat_1(A),k5_tdlat_1(A)) ) )).

fof(t41_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => m2_nat_lat(k8_tdlat_1(A),k4_tdlat_1(A)) ) )).

fof(t42_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k10_tdlat_1(A) = k1_realset1(k2_tdlat_1(A),k9_tdlat_1(A)) ) )).

fof(t43_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k11_tdlat_1(A) = k1_realset1(k3_tdlat_1(A),k9_tdlat_1(A)) ) )).

fof(t44_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => m2_nat_lat(k12_tdlat_1(A),k4_tdlat_1(A)) ) )).

fof(dt_k1_tdlat_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => m1_subset_1(k1_tdlat_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k2_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_funct_1(k2_tdlat_1(A))
        & v1_funct_2(k2_tdlat_1(A),k2_zfmisc_1(k1_tdlat_1(A),k1_tdlat_1(A)),k1_tdlat_1(A))
        & m2_relset_1(k2_tdlat_1(A),k2_zfmisc_1(k1_tdlat_1(A),k1_tdlat_1(A)),k1_tdlat_1(A)) ) ) )).

fof(dt_k3_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_funct_1(k3_tdlat_1(A))
        & v1_funct_2(k3_tdlat_1(A),k2_zfmisc_1(k1_tdlat_1(A),k1_tdlat_1(A)),k1_tdlat_1(A))
        & m2_relset_1(k3_tdlat_1(A),k2_zfmisc_1(k1_tdlat_1(A),k1_tdlat_1(A)),k1_tdlat_1(A)) ) ) )).

fof(dt_k4_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k4_tdlat_1(A))
        & v10_lattices(k4_tdlat_1(A))
        & v15_lattices(k4_tdlat_1(A))
        & v16_lattices(k4_tdlat_1(A))
        & l3_lattices(k4_tdlat_1(A)) ) ) )).

fof(dt_k5_tdlat_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => m1_subset_1(k5_tdlat_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k6_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_funct_1(k6_tdlat_1(A))
        & v1_funct_2(k6_tdlat_1(A),k2_zfmisc_1(k5_tdlat_1(A),k5_tdlat_1(A)),k5_tdlat_1(A))
        & m2_relset_1(k6_tdlat_1(A),k2_zfmisc_1(k5_tdlat_1(A),k5_tdlat_1(A)),k5_tdlat_1(A)) ) ) )).

fof(dt_k7_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_funct_1(k7_tdlat_1(A))
        & v1_funct_2(k7_tdlat_1(A),k2_zfmisc_1(k5_tdlat_1(A),k5_tdlat_1(A)),k5_tdlat_1(A))
        & m2_relset_1(k7_tdlat_1(A),k2_zfmisc_1(k5_tdlat_1(A),k5_tdlat_1(A)),k5_tdlat_1(A)) ) ) )).

fof(dt_k8_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k8_tdlat_1(A))
        & v10_lattices(k8_tdlat_1(A))
        & v17_lattices(k8_tdlat_1(A))
        & l3_lattices(k8_tdlat_1(A)) ) ) )).

fof(dt_k9_tdlat_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => m1_subset_1(k9_tdlat_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k10_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_funct_1(k10_tdlat_1(A))
        & v1_funct_2(k10_tdlat_1(A),k2_zfmisc_1(k9_tdlat_1(A),k9_tdlat_1(A)),k9_tdlat_1(A))
        & m2_relset_1(k10_tdlat_1(A),k2_zfmisc_1(k9_tdlat_1(A),k9_tdlat_1(A)),k9_tdlat_1(A)) ) ) )).

fof(dt_k11_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_funct_1(k11_tdlat_1(A))
        & v1_funct_2(k11_tdlat_1(A),k2_zfmisc_1(k9_tdlat_1(A),k9_tdlat_1(A)),k9_tdlat_1(A))
        & m2_relset_1(k11_tdlat_1(A),k2_zfmisc_1(k9_tdlat_1(A),k9_tdlat_1(A)),k9_tdlat_1(A)) ) ) )).

fof(dt_k12_tdlat_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k12_tdlat_1(A))
        & v10_lattices(k12_tdlat_1(A))
        & v17_lattices(k12_tdlat_1(A))
        & l3_lattices(k12_tdlat_1(A)) ) ) )).

fof(d1_tdlat_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => k1_tdlat_1(A) = a_1_0_tdlat_1(A) ) )).

fof(d5_tdlat_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => k5_tdlat_1(A) = a_1_1_tdlat_1(A) ) )).

fof(d9_tdlat_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => k9_tdlat_1(A) = a_1_2_tdlat_1(A) ) )).

fof(fraenkel_a_1_0_tdlat_1,axiom,(
    ! [A,B] :
      ( l1_pre_topc(B)
     => ( r2_hidden(A,a_1_0_tdlat_1(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & A = C
            & v4_tops_1(C,B) ) ) ) )).

fof(fraenkel_a_1_1_tdlat_1,axiom,(
    ! [A,B] :
      ( l1_pre_topc(B)
     => ( r2_hidden(A,a_1_1_tdlat_1(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & A = C
            & v5_tops_1(C,B) ) ) ) )).

fof(fraenkel_a_1_2_tdlat_1,axiom,(
    ! [A,B] :
      ( l1_pre_topc(B)
     => ( r2_hidden(A,a_1_2_tdlat_1(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & A = C
            & v6_tops_1(C,B) ) ) ) )).
%------------------------------------------------------------------------------