SET007 Axioms: SET007+925.ax


%------------------------------------------------------------------------------
% File     : SET007+925 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Niemytzki Plane - an Example of Tychonoff Space Which Is Not T_4
% 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    : topgen_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  118 (  18 unit)
%            Number of atoms       :  838 (  91 equality)
%            Maximal formula depth :   22 (   8 average)
%            Number of connectives :  813 (  93 ~  ;  12  |; 365  &)
%                                         (  24 <=>; 319 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   51 (   0 propositional; 1-3 arity)
%            Number of functors    :   91 (  26 constant; 0-4 arity)
%            Number of variables   :  315 (   0 singleton; 288 !;  27 ?)
%            Maximal term depth    :    7 (   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(cc1_topgen_5,axiom,(
    ! [A,B] :
      ( v2_membered(B)
     => ! [C] :
          ( m1_relset_1(C,A,B)
         => v1_seq_1(C) ) ) )).

fof(cc2_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_finset_1(A)
       => ( v1_finset_1(A)
          & v1_membered(A)
          & v2_membered(A)
          & v1_seq_4(A)
          & v2_seq_4(A)
          & v3_seq_4(A) ) ) ) )).

fof(fc1_topgen_5,axiom,(
    ~ v1_xboole_0(k1_topgen_5) )).

fof(fc2_topgen_5,axiom,(
    ~ v1_xboole_0(k2_topgen_5) )).

fof(cc3_topgen_5,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( v2_pre_topc(A)
          & v1_topgen_5(A) )
       => ( v2_pre_topc(A)
          & v1_urysohn1(A)
          & v4_compts_1(A) ) ) ) )).

fof(cc4_topgen_5,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_urysohn1(A)
          & v5_compts_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_topgen_5(A) ) ) ) )).

fof(cc5_topgen_5,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_membered(B) )
     => ! [C] :
          ( m1_relset_1(C,A,B)
         => v1_seq_1(C) ) ) )).

fof(fc3_topgen_5,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k4_topgen_5(A,B))
        & v1_relat_1(k4_topgen_5(A,B))
        & v1_funct_1(k4_topgen_5(A,B))
        & v1_funct_2(k4_topgen_5(A,B),u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr))
        & v5_pre_topc(k4_topgen_5(A,B),k3_topgen_5,k5_topmetr)
        & v1_partfun1(k4_topgen_5(A,B),u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr))
        & v1_seq_1(k4_topgen_5(A,B)) ) ) )).

fof(fc4_topgen_5,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B)
        & v1_xreal_0(C)
        & v2_xreal_0(C) )
     => ( ~ v1_xboole_0(k5_topgen_5(A,B,C))
        & v1_relat_1(k5_topgen_5(A,B,C))
        & v1_funct_1(k5_topgen_5(A,B,C))
        & v1_funct_2(k5_topgen_5(A,B,C),u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr))
        & v5_pre_topc(k5_topgen_5(A,B,C),k3_topgen_5,k5_topmetr)
        & v1_partfun1(k5_topgen_5(A,B,C),u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr))
        & v1_seq_1(k5_topgen_5(A,B,C)) ) ) )).

fof(t1_topgen_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
           => ! [C] : k10_relat_1(k1_funct_4(A,B),C) = k2_xboole_0(k10_relat_1(A,C),k10_relat_1(B,C)) ) ) ) )).

fof(t2_topgen_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
           => ! [C] : k10_relat_1(k1_funct_4(A,B),C) = k2_xboole_0(k10_relat_1(A,C),k10_relat_1(B,C)) ) ) ) )).

fof(t3_topgen_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,k1_relat_1(C))
       => k1_funct_1(k10_funct_6(k3_cqc_lang(A,C)),B) = k3_cqc_lang(A,k1_funct_1(C,B)) ) ) )).

fof(t4_topgen_5,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k1_relat_1(k10_funct_6(B)))
      <=> ? [C,D] :
            ( v1_relat_1(D)
            & v1_funct_1(D)
            & r2_hidden(C,k1_relat_1(B))
            & D = k1_funct_1(B,C)
            & r2_hidden(A,k1_relat_1(D)) ) ) ) )).

fof(t5_topgen_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(A,k1_relat_1(k1_funct_1(k10_funct_6(C),B)))
      <=> ? [D] :
            ( v1_relat_1(D)
            & v1_funct_1(D)
            & r2_hidden(A,k1_relat_1(C))
            & D = k1_funct_1(C,A)
            & r2_hidden(B,k1_relat_1(D)) ) ) ) )).

fof(t6_topgen_5,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r2_hidden(A,k1_relat_1(C))
              & D = k1_funct_1(C,A)
              & r2_hidden(B,k1_relat_1(D)) )
           => k1_funct_1(k1_funct_1(k10_funct_6(C),B),A) = k1_funct_1(D,B) ) ) ) )).

fof(t7_topgen_5,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] :
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( D = k2_xboole_0(B,C)
               => k1_funct_1(k10_funct_6(D),A) = k2_xboole_0(k1_funct_1(k10_funct_6(B),A),k1_funct_1(k10_funct_6(C),A)) ) ) ) ) )).

fof(t8_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(C,D)
                   => ( r1_xreal_0(B,A)
                      | k5_subset_1(k1_numbers,k2_rcomp_1(A,C),k1_rcomp_1(B,D)) = k1_rcomp_2(B,C) ) ) ) ) ) ) )).

fof(t9_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(B,A)
                   => ( r1_xreal_0(C,D)
                      | k5_subset_1(k1_numbers,k2_rcomp_1(A,C),k1_rcomp_1(B,D)) = k2_rcomp_2(A,D) ) ) ) ) ) ) )).

fof(t10_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ( r1_xreal_0(C,B)
                      | k4_subset_1(k1_numbers,k1_rcomp_2(A,C),k2_rcomp_2(B,D)) = k1_rcomp_1(A,D) ) ) ) ) ) ) )).

fof(t11_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ( r1_xreal_0(C,B)
                      | k5_subset_1(k1_numbers,k1_rcomp_2(A,C),k2_rcomp_2(B,D)) = k2_rcomp_1(B,C) ) ) ) ) ) ) )).

fof(t12_topgen_5,axiom,(
    ! [A,B] :
      ( r2_tarski(k4_card_3(k10_finseq_1(A,B)),k2_zfmisc_1(A,B))
      & k1_card_1(k4_card_3(k10_finseq_1(A,B))) = k2_card_2(k1_card_1(A),k1_card_1(B)) ) )).

fof(t13_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k7_square_1(k5_toprns_1(np__2,k23_euclid(A,B))) = k2_xcmplx_0(k5_square_1(A),k5_square_1(B)) ) ) )).

fof(t14_topgen_5,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v4_pre_topc(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v4_pre_topc(D,A)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(B))
                        & v5_pre_topc(E,k3_pre_topc(A,C),B)
                        & m2_relset_1(E,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(B)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k3_pre_topc(A,D)),u1_struct_0(B))
                            & v5_pre_topc(F,k3_pre_topc(A,D),B)
                            & m2_relset_1(F,u1_struct_0(k3_pre_topc(A,D)),u1_struct_0(B)) )
                         => ( r1_partfun1(E,F)
                           => ( v1_funct_1(k1_funct_4(E,F))
                              & v1_funct_2(k1_funct_4(E,F),u1_struct_0(k3_pre_topc(A,k4_subset_1(u1_struct_0(A),C,D))),u1_struct_0(B))
                              & v5_pre_topc(k1_funct_4(E,F),k3_pre_topc(A,k4_subset_1(u1_struct_0(A),C,D)),B)
                              & m2_relset_1(k1_funct_4(E,F),u1_struct_0(k3_pre_topc(A,k4_subset_1(u1_struct_0(A),C,D))),u1_struct_0(B)) ) ) ) ) ) ) ) ) )).

fof(t15_topgen_5,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v4_pre_topc(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v4_pre_topc(D,A)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                 => ( r1_xboole_0(C,D)
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(B))
                          & v5_pre_topc(E,k3_pre_topc(A,C),B)
                          & m2_relset_1(E,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(B)) )
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,u1_struct_0(k3_pre_topc(A,D)),u1_struct_0(B))
                              & v5_pre_topc(F,k3_pre_topc(A,D),B)
                              & m2_relset_1(F,u1_struct_0(k3_pre_topc(A,D)),u1_struct_0(B)) )
                           => ( v1_funct_1(k1_funct_4(E,F))
                              & v1_funct_2(k1_funct_4(E,F),u1_struct_0(k3_pre_topc(A,k4_subset_1(u1_struct_0(A),C,D))),u1_struct_0(B))
                              & v5_pre_topc(k1_funct_4(E,F),k3_pre_topc(A,k4_subset_1(u1_struct_0(A),C,D)),B)
                              & m2_relset_1(k1_funct_4(E,F),u1_struct_0(k3_pre_topc(A,k4_subset_1(u1_struct_0(A),C,D))),u1_struct_0(B)) ) ) ) ) ) ) ) ) )).

fof(t16_topgen_5,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v3_pre_topc(C,A)
                & v4_pre_topc(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(B))
                    & v5_pre_topc(D,k3_pre_topc(A,C),B)
                    & m2_relset_1(D,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k3_pre_topc(A,k3_subset_1(u1_struct_0(A),C))),u1_struct_0(B))
                        & v5_pre_topc(E,k3_pre_topc(A,k3_subset_1(u1_struct_0(A),C)),B)
                        & m2_relset_1(E,u1_struct_0(k3_pre_topc(A,k3_subset_1(u1_struct_0(A),C))),u1_struct_0(B)) )
                     => ( v1_funct_1(k1_funct_4(D,E))
                        & v1_funct_2(k1_funct_4(D,E),u1_struct_0(A),u1_struct_0(B))
                        & v5_pre_topc(k1_funct_4(D,E),A,B)
                        & m2_relset_1(k1_funct_4(D,E),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) ) )).

fof(t17_topgen_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( ( v1_xreal_0(C)
                & v2_xreal_0(C) )
             => r2_hidden(B,k1_topreal9(A,B,C)) ) ) ) )).

fof(t18_topgen_5,axiom,(
    ! [A,B] :
      ( r2_hidden(k10_finseq_1(A,B),k1_topgen_5)
    <=> ( r2_hidden(A,k1_numbers)
        & B = np__0 ) ) )).

fof(t19_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r2_hidden(k23_euclid(A,B),k1_topgen_5)
          <=> B = np__0 ) ) ) )).

fof(t20_topgen_5,axiom,(
    k1_card_1(k1_topgen_5) = k3_topgen_3 )).

fof(t21_topgen_5,axiom,(
    ! [A,B] :
      ( r2_hidden(k10_finseq_1(A,B),k2_topgen_5)
    <=> ( r2_hidden(A,k1_numbers)
        & ? [C] :
            ( m1_subset_1(C,k1_numbers)
            & B = C
            & r1_xreal_0(np__0,C) ) ) ) )).

fof(t22_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r2_hidden(k23_euclid(A,B),k2_topgen_5)
          <=> r1_xreal_0(np__0,B) ) ) ) )).

fof(t23_topgen_5,axiom,(
    r1_tarski(k1_topgen_5,k2_topgen_5) )).

fof(t24_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ~ r1_xreal_0(C,np__0)
               => ( r1_tarski(k1_topreal9(np__2,k23_euclid(A,B),C),k2_topgen_5)
                <=> r1_xreal_0(C,B) ) ) ) ) ) )).

fof(t25_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( r1_xreal_0(np__0,B)
               => ( r1_xreal_0(C,np__0)
                  | ( r1_xboole_0(k1_topreal9(np__2,k23_euclid(A,B),C),k1_topgen_5)
                  <=> r1_xreal_0(C,B) ) ) ) ) ) ) )).

fof(t26_topgen_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( ( v1_xreal_0(D)
                    & v2_xreal_0(D) )
                 => ! [E] :
                      ( ( v1_xreal_0(E)
                        & v2_xreal_0(E) )
                     => ( r1_xreal_0(k5_toprns_1(A,k20_euclid(A,B,C)),k6_xcmplx_0(D,E))
                       => r1_tarski(k1_topreal9(A,C,E),k1_topreal9(A,B,D)) ) ) ) ) ) ) )).

fof(t27_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_xreal_0(B)
            & v2_xreal_0(B) )
         => ! [C] :
              ( ( v1_xreal_0(C)
                & v2_xreal_0(C) )
             => ( r1_xreal_0(B,C)
               => r1_tarski(k1_topreal9(np__2,k23_euclid(A,B),B),k1_topreal9(np__2,k23_euclid(A,C),C)) ) ) ) ) )).

fof(t28_topgen_5,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_topgen_2(C,A)
             => ! [D] :
                  ( m1_topgen_2(D,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)) ) ) ) ) ) )).

fof(t29_topgen_5,axiom,
    ( v3_pre_topc(k1_topgen_1(u1_struct_0(k15_euclid(np__2)),k2_topgen_5,k1_topgen_5),k3_topgen_5)
    & m1_subset_1(k1_topgen_1(u1_struct_0(k15_euclid(np__2)),k2_topgen_5,k1_topgen_5),k1_zfmisc_1(u1_struct_0(k3_topgen_5))) )).

fof(t30_topgen_5,axiom,
    ( v4_pre_topc(k1_topgen_5,k3_topgen_5)
    & m1_subset_1(k1_topgen_5,k1_zfmisc_1(u1_struct_0(k3_topgen_5))) )).

fof(t31_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_xreal_0(B)
            & v2_xreal_0(B) )
         => ( v3_pre_topc(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k1_topreal9(np__2,k23_euclid(A,B),B),k1_struct_0(k15_euclid(np__2),k23_euclid(A,np__0))),k3_topgen_5)
            & m1_subset_1(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k1_topreal9(np__2,k23_euclid(A,B),B),k1_struct_0(k15_euclid(np__2),k23_euclid(A,np__0))),k1_zfmisc_1(u1_struct_0(k3_topgen_5))) ) ) ) )).

fof(t32_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_xreal_0(B)
            & v2_xreal_0(B) )
         => ! [C] :
              ( ( v1_xreal_0(C)
                & v2_xreal_0(C) )
             => ( v3_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_topreal9(np__2,k23_euclid(A,B),C),k2_topgen_5),k3_topgen_5)
                & m1_subset_1(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_topreal9(np__2,k23_euclid(A,B),C),k2_topgen_5),k1_zfmisc_1(u1_struct_0(k3_topgen_5))) ) ) ) ) )).

fof(t33_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_xreal_0(C)
                & v2_xreal_0(C) )
             => ( r1_xreal_0(C,B)
               => ( v3_pre_topc(k1_topreal9(np__2,k23_euclid(A,B),C),k3_topgen_5)
                  & m1_subset_1(k1_topreal9(np__2,k23_euclid(A,B),C),k1_zfmisc_1(u1_struct_0(k3_topgen_5))) ) ) ) ) ) )).

fof(t34_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_topgen_5))
     => ! [B] :
          ( ( v1_xreal_0(B)
            & v2_xreal_0(B) )
         => ? [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
              & ? [D] :
                  ( v3_pre_topc(D,k3_topgen_5)
                  & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_topgen_5)))
                  & r2_hidden(A,D)
                  & r2_hidden(C,D)
                  & ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                     => ~ ( r2_hidden(E,D)
                          & r1_xreal_0(B,k5_toprns_1(np__2,k20_euclid(np__2,E,C))) ) ) ) ) ) ) )).

fof(t35_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_xreal_0(C)
                & v2_xreal_0(C) )
             => ? [D] :
                  ( v1_rat_1(D)
                  & ? [E] :
                      ( v1_rat_1(E)
                      & r2_hidden(k23_euclid(D,E),k1_topreal9(np__2,k23_euclid(A,B),C))
                      & k23_euclid(D,E) != k23_euclid(A,B) ) ) ) ) ) )).

fof(t36_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topgen_5)))
     => ( A = k3_xboole_0(k1_topgen_1(u1_struct_0(k15_euclid(np__2)),k2_topgen_5,k1_topgen_5),k4_card_3(k10_finseq_1(k3_numbers,k3_numbers)))
       => ! [B] : k6_pre_topc(k3_topgen_5,k1_topgen_1(u1_struct_0(k3_topgen_5),A,k1_tarski(B))) = k2_pre_topc(k3_topgen_5) ) ) )).

fof(t37_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topgen_5)))
     => ( A = k1_topgen_1(u1_struct_0(k15_euclid(np__2)),k2_topgen_5,k1_topgen_5)
       => ! [B] : k6_pre_topc(k3_topgen_5,k1_topgen_1(u1_struct_0(k3_topgen_5),A,k1_tarski(B))) = k2_pre_topc(k3_topgen_5) ) ) )).

fof(t38_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topgen_5)))
     => ( A = k1_topgen_1(u1_struct_0(k15_euclid(np__2)),k2_topgen_5,k1_topgen_5)
       => k6_pre_topc(k3_topgen_5,A) = k2_pre_topc(k3_topgen_5) ) ) )).

fof(t39_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topgen_5)))
     => ( A = k1_topgen_5
       => ( k6_pre_topc(k3_topgen_5,A) = A
          & k1_tops_1(k3_topgen_5,A) = k1_xboole_0 ) ) ) )).

fof(t40_topgen_5,axiom,
    ( v1_tops_1(k3_xboole_0(k1_topgen_1(u1_struct_0(k15_euclid(np__2)),k2_topgen_5,k1_topgen_5),k4_card_3(k10_finseq_1(k3_numbers,k3_numbers))),k3_topgen_5)
    & m1_subset_1(k3_xboole_0(k1_topgen_1(u1_struct_0(k15_euclid(np__2)),k2_topgen_5,k1_topgen_5),k4_card_3(k10_finseq_1(k3_numbers,k3_numbers))),k1_zfmisc_1(u1_struct_0(k3_topgen_5))) )).

fof(t41_topgen_5,axiom,
    ( v2_topgen_1(k3_xboole_0(k1_topgen_1(u1_struct_0(k15_euclid(np__2)),k2_topgen_5,k1_topgen_5),k4_card_3(k10_finseq_1(k3_numbers,k3_numbers))),k3_topgen_5)
    & m1_subset_1(k3_xboole_0(k1_topgen_1(u1_struct_0(k15_euclid(np__2)),k2_topgen_5,k1_topgen_5),k4_card_3(k10_finseq_1(k3_numbers,k3_numbers))),k1_zfmisc_1(u1_struct_0(k3_topgen_5))) )).

fof(t42_topgen_5,axiom,
    ( v1_tops_1(k1_topgen_1(u1_struct_0(k15_euclid(np__2)),k2_topgen_5,k1_topgen_5),k3_topgen_5)
    & m1_subset_1(k1_topgen_1(u1_struct_0(k15_euclid(np__2)),k2_topgen_5,k1_topgen_5),k1_zfmisc_1(u1_struct_0(k3_topgen_5))) )).

fof(t43_topgen_5,axiom,
    ( v2_topgen_1(k1_topgen_1(u1_struct_0(k15_euclid(np__2)),k2_topgen_5,k1_topgen_5),k3_topgen_5)
    & m1_subset_1(k1_topgen_1(u1_struct_0(k15_euclid(np__2)),k2_topgen_5,k1_topgen_5),k1_zfmisc_1(u1_struct_0(k3_topgen_5))) )).

fof(t44_topgen_5,axiom,
    ( v3_tops_1(k1_topgen_5,k3_topgen_5)
    & m1_subset_1(k1_topgen_5,k1_zfmisc_1(u1_struct_0(k3_topgen_5))) )).

fof(t45_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topgen_5)))
     => ( A = k1_topgen_5
       => v1_xboole_0(k3_topgen_1(k3_topgen_5,A)) ) ) )).

fof(t46_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_topgen_5))
     => ( v4_pre_topc(A,k3_topgen_5)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topgen_5))) ) ) )).

fof(t47_topgen_5,axiom,
    ( v1_tops_1(k3_numbers,k2_topgen_3)
    & m1_subset_1(k3_numbers,k1_zfmisc_1(u1_struct_0(k2_topgen_3))) )).

fof(t48_topgen_5,axiom,(
    v7_topgen_1(k2_topgen_3) )).

fof(t49_topgen_5,axiom,(
    v7_topgen_1(k3_topgen_5) )).

fof(t50_topgen_5,axiom,(
    v1_urysohn1(k3_topgen_5) )).

fof(t51_topgen_5,axiom,(
    ~ v5_compts_1(k3_topgen_5) )).

fof(d4_topgen_5,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_topgen_5(A)
      <=> ( v1_urysohn1(A)
          & ! [B] :
              ( ( v4_pre_topc(B,A)
                & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ~ ( r2_hidden(C,k3_subset_1(u1_struct_0(A),B))
                      & ! [D] :
                          ( ( v1_funct_1(D)
                            & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k5_topmetr))
                            & v5_pre_topc(D,A,k5_topmetr)
                            & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k5_topmetr)) )
                         => ~ ( k2_seq_1(u1_struct_0(A),u1_struct_0(k5_topmetr),D,C) = np__0
                              & r1_tarski(k4_pre_topc(A,k5_topmetr,D,B),k1_seq_4(np__1)) ) ) ) ) ) ) ) ) )).

fof(t52_topgen_5,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v1_urysohn1(A)
        & l1_pre_topc(A) )
     => ( v1_topgen_5(A)
       => ! [B] :
            ( m2_cantor_1(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ~ ( r2_hidden(C,D)
                        & r2_hidden(D,B)
                        & ! [E] :
                            ( ( v1_funct_1(E)
                              & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k5_topmetr))
                              & v5_pre_topc(E,A,k5_topmetr)
                              & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k5_topmetr)) )
                           => ~ ( k2_seq_1(u1_struct_0(A),u1_struct_0(k5_topmetr),E,C) = np__0
                                & r1_tarski(k4_pre_topc(A,k5_topmetr,E,k3_subset_1(u1_struct_0(A),D)),k1_seq_4(np__1)) ) ) ) ) ) ) ) ) )).

fof(t53_topgen_5,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,k3_topmetr) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_pre_topc(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v5_pre_topc(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r2_hidden(F,E)
                            <=> r1_xreal_0(k2_seq_1(u1_struct_0(A),u1_struct_0(B),C,F),k2_seq_1(u1_struct_0(A),u1_struct_0(B),D,F)) ) )
                       => v4_pre_topc(E,A) ) ) ) ) ) ) )).

fof(t54_topgen_5,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,k3_topmetr) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_pre_topc(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v5_pre_topc(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ? [E] :
                      ( v1_funct_1(E)
                      & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                      & v5_pre_topc(E,A,B)
                      & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B))
                      & ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => k2_seq_1(u1_struct_0(A),u1_struct_0(B),E,F) = k4_square_1(k2_seq_1(u1_struct_0(A),u1_struct_0(B),C,F),k2_seq_1(u1_struct_0(A),u1_struct_0(B),D,F)) ) ) ) ) ) ) )).

fof(t55_topgen_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,k3_topmetr) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_finset_1(C) )
             => ! [D] :
                  ( ( v1_funcop_1(D)
                    & m1_pboole(D,C) )
                 => ~ ( ! [E] :
                          ( r2_hidden(E,C)
                         => ( v1_funct_1(k1_funct_1(D,E))
                            & v1_funct_2(k1_funct_1(D,E),u1_struct_0(A),u1_struct_0(B))
                            & v5_pre_topc(k1_funct_1(D,E),A,B)
                            & m2_relset_1(k1_funct_1(D,E),u1_struct_0(A),u1_struct_0(B)) ) )
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                            & v5_pre_topc(E,A,B)
                            & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                         => ? [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                              & ? [G] :
                                  ( ~ v1_xboole_0(G)
                                  & v1_finset_1(G)
                                  & m1_subset_1(G,k1_zfmisc_1(k1_numbers))
                                  & G = k2_relat_1(k1_funct_1(k10_funct_6(D),F))
                                  & k2_seq_1(u1_struct_0(A),u1_struct_0(B),E,F) != k2_seq_4(G) ) ) ) ) ) ) ) ) )).

fof(t56_topgen_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_urysohn1(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m2_cantor_1(B,A)
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ~ ( r2_hidden(C,D)
                        & r2_hidden(D,B)
                        & ! [E] :
                            ( ( v1_funct_1(E)
                              & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k5_topmetr))
                              & v5_pre_topc(E,A,k5_topmetr)
                              & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k5_topmetr)) )
                           => ~ ( k2_seq_1(u1_struct_0(A),u1_struct_0(k5_topmetr),E,C) = np__0
                                & r1_tarski(k4_pre_topc(A,k5_topmetr,E,k3_subset_1(u1_struct_0(A),D)),k1_seq_4(np__1)) ) ) ) ) )
           => v1_topgen_5(A) ) ) ) )).

fof(t57_topgen_5,axiom,(
    v1_urysohn1(k2_topgen_3) )).

fof(t58_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( v4_pre_topc(k12_prob_1(A),k2_topgen_3)
        & m1_subset_1(k12_prob_1(A),k1_zfmisc_1(u1_struct_0(k2_topgen_3))) ) ) )).

fof(t59_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( v4_pre_topc(k2_limfunc1(A),k2_topgen_3)
        & m1_subset_1(k2_limfunc1(A),k1_zfmisc_1(u1_struct_0(k2_topgen_3))) ) ) )).

fof(t60_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( v4_pre_topc(k3_limfunc1(A),k2_topgen_3)
        & m1_subset_1(k3_limfunc1(A),k1_zfmisc_1(u1_struct_0(k2_topgen_3))) ) ) )).

fof(t61_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( v4_pre_topc(k1_rcomp_2(A,B),k2_topgen_3)
            & m1_subset_1(k1_rcomp_2(A,B),k1_zfmisc_1(u1_struct_0(k2_topgen_3))) ) ) ) )).

fof(t62_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_rat_1(B)
         => ~ ( ~ r1_xreal_0(B,A)
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(k2_topgen_3),u1_struct_0(k5_topmetr))
                    & v5_pre_topc(C,k2_topgen_3,k5_topmetr)
                    & m2_relset_1(C,u1_struct_0(k2_topgen_3),u1_struct_0(k5_topmetr)) )
                 => ~ ! [D] :
                        ( m1_subset_1(D,u1_struct_0(k2_topgen_3))
                       => ( ( r2_hidden(D,k1_rcomp_2(A,B))
                           => k2_seq_1(u1_struct_0(k2_topgen_3),u1_struct_0(k5_topmetr),C,D) = np__0 )
                          & ( ~ r2_hidden(D,k1_rcomp_2(A,B))
                           => k2_seq_1(u1_struct_0(k2_topgen_3),u1_struct_0(k5_topmetr),C,D) = np__1 ) ) ) ) ) ) ) )).

fof(t63_topgen_5,axiom,(
    v1_topgen_5(k2_topgen_3) )).

fof(d5_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_xreal_0(B)
            & v2_xreal_0(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr))
                & m2_relset_1(C,u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr)) )
             => ( C = k4_topgen_5(A,B)
              <=> ( k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),C,k23_euclid(A,np__0)) = np__0
                  & ! [D] :
                      ( v1_xreal_0(D)
                     => ! [E] :
                          ( ( v1_xreal_0(E)
                            & ~ v3_xreal_0(E) )
                         => ( ~ ( ~ ( D = A
                                    & E = np__0 )
                                & ~ r2_hidden(k23_euclid(D,E),k1_topreal9(np__2,k23_euclid(A,B),B))
                                & k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),C,k23_euclid(D,E)) != np__1 )
                            & ( r2_hidden(k23_euclid(D,E),k1_topreal9(np__2,k23_euclid(A,B),B))
                             => k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),C,k23_euclid(D,E)) = k7_xcmplx_0(k7_square_1(k5_toprns_1(np__2,k20_euclid(np__2,k23_euclid(A,np__0),k23_euclid(D,E)))),k3_xcmplx_0(k3_xcmplx_0(np__2,B),E)) ) ) ) ) ) ) ) ) ) )).

fof(t64_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( r1_xreal_0(np__0,k22_euclid(A))
       => ! [B] :
            ( v1_xreal_0(B)
           => ! [C] :
                ( ( v1_xreal_0(C)
                  & v2_xreal_0(C) )
               => ( k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k4_topgen_5(B,C),A) = np__0
                 => A = k23_euclid(B,np__0) ) ) ) ) ) )).

fof(t65_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_xreal_0(C)
                & v2_xreal_0(C) )
             => ( A != B
               => k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k4_topgen_5(A,C),k23_euclid(B,np__0)) = np__1 ) ) ) ) )).

fof(t66_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_xreal_0(C)
                & v2_xreal_0(C) )
             => ! [D] :
                  ( ( v1_xreal_0(D)
                    & v2_xreal_0(D) )
                 => ( ( r1_xreal_0(C,np__1)
                      & k5_toprns_1(np__2,k20_euclid(np__2,A,k23_euclid(B,k3_xcmplx_0(D,C)))) = k3_xcmplx_0(D,C) )
                   => ( k22_euclid(A) = np__0
                      | k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k4_topgen_5(B,D),A) = C ) ) ) ) ) ) )).

fof(t67_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( ( v1_xreal_0(D)
                    & v2_xreal_0(D) )
                 => ~ ( r1_xreal_0(np__0,C)
                      & r1_xreal_0(C,np__1)
                      & ~ r1_xreal_0(k3_xcmplx_0(D,C),k5_toprns_1(np__2,k20_euclid(np__2,A,k23_euclid(B,k3_xcmplx_0(D,C)))))
                      & r1_xreal_0(C,k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k4_topgen_5(B,D),A)) ) ) ) ) ) )).

fof(t68_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( r1_xreal_0(np__0,k22_euclid(A))
       => ! [B] :
            ( v1_xreal_0(B)
           => ! [C] :
                ( v1_xreal_0(C)
               => ! [D] :
                    ( ( v1_xreal_0(D)
                      & v2_xreal_0(D) )
                   => ~ ( r1_xreal_0(np__0,C)
                        & ~ r1_xreal_0(np__1,C)
                        & ~ r1_xreal_0(k5_toprns_1(np__2,k20_euclid(np__2,A,k23_euclid(B,k3_xcmplx_0(D,C)))),k3_xcmplx_0(D,C))
                        & r1_xreal_0(k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k4_topgen_5(B,D),A),C) ) ) ) ) ) ) )).

fof(t69_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( r1_xreal_0(np__0,k22_euclid(A))
       => ! [B] :
            ( v1_xreal_0(B)
           => ! [C] :
                ( v1_xreal_0(C)
               => ! [D] :
                    ( v1_xreal_0(D)
                   => ! [E] :
                        ( ( v1_xreal_0(E)
                          & v2_xreal_0(E) )
                       => ~ ( r1_xreal_0(np__0,C)
                            & r1_xreal_0(D,np__1)
                            & r2_hidden(k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k4_topgen_5(B,E),A),k2_rcomp_1(C,D))
                            & ! [F] :
                                ( ( v1_xreal_0(F)
                                  & v2_xreal_0(F) )
                               => ~ ( r1_xreal_0(F,k22_euclid(A))
                                    & r1_tarski(k1_topreal9(np__2,A,F),k5_pre_topc(k3_topgen_5,k5_topmetr,k4_topgen_5(B,E),k2_rcomp_1(C,D))) ) ) ) ) ) ) ) ) ) )).

fof(t70_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_xreal_0(B)
            & v2_xreal_0(B) )
         => ! [C] :
              ( ( v1_xreal_0(C)
                & v2_xreal_0(C) )
             => r1_tarski(k1_topreal9(np__2,k23_euclid(A,k3_xcmplx_0(C,B)),k3_xcmplx_0(C,B)),k5_pre_topc(k3_topgen_5,k5_topmetr,k4_topgen_5(A,C),k2_rcomp_1(np__0,B))) ) ) ) )).

fof(t71_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_xreal_0(B)
            & v2_xreal_0(B) )
         => ! [C] :
              ( ( v1_xreal_0(C)
                & v2_xreal_0(C) )
             => r1_tarski(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k1_topreal9(np__2,k23_euclid(A,k3_xcmplx_0(C,B)),k3_xcmplx_0(C,B)),k1_struct_0(k15_euclid(np__2),k23_euclid(A,np__0))),k5_pre_topc(k3_topgen_5,k5_topmetr,k4_topgen_5(A,C),k1_rcomp_2(np__0,B))) ) ) ) )).

fof(t72_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( r1_xreal_0(np__0,k22_euclid(A))
       => ! [B] :
            ( v1_xreal_0(B)
           => ! [C] :
                ( v1_xreal_0(C)
               => ! [D] :
                    ( ( v1_xreal_0(D)
                      & v2_xreal_0(D) )
                   => ( r1_xreal_0(C,np__1)
                     => ( r1_xreal_0(k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k4_topgen_5(B,D),A),np__0)
                        | r1_xreal_0(C,k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k4_topgen_5(B,D),A))
                        | r2_hidden(A,k1_topreal9(np__2,k23_euclid(B,k3_xcmplx_0(D,C)),k3_xcmplx_0(D,C))) ) ) ) ) ) ) ) )).

fof(t73_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ~ r1_xreal_0(k22_euclid(A),np__0)
       => ! [B] :
            ( v1_xreal_0(B)
           => ! [C] :
                ( v1_xreal_0(C)
               => ! [D] :
                    ( ( v1_xreal_0(D)
                      & v2_xreal_0(D) )
                   => ~ ( r1_xreal_0(np__0,C)
                        & ~ r1_xreal_0(k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k4_topgen_5(B,D),A),C)
                        & ! [E] :
                            ( ( v1_xreal_0(E)
                              & v2_xreal_0(E) )
                           => ~ ( r1_xreal_0(E,k22_euclid(A))
                                & r1_tarski(k1_topreal9(np__2,A,E),k5_pre_topc(k3_topgen_5,k5_topmetr,k4_topgen_5(B,D),k2_rcomp_2(C,np__1))) ) ) ) ) ) ) ) ) )).

fof(t74_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( k22_euclid(A) = np__0
       => ! [B] :
            ( v1_xreal_0(B)
           => ! [C] :
                ( ( v1_xreal_0(C)
                  & v2_xreal_0(C) )
               => ~ ( k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k4_topgen_5(B,C),A) = np__1
                    & ! [D] :
                        ( ( v1_xreal_0(D)
                          & v2_xreal_0(D) )
                       => ~ r1_tarski(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k1_topreal9(np__2,k23_euclid(k21_euclid(A),D),D),k1_struct_0(k15_euclid(np__2),A)),k5_pre_topc(k3_topgen_5,k5_topmetr,k4_topgen_5(B,C),k1_seq_4(np__1))) ) ) ) ) ) ) )).

fof(t77_topgen_5,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] :
                  ( ( r2_hidden(B,D)
                    & r2_hidden(C,D)
                    & m1_cantor_1(k2_xboole_0(D,k1_tarski(k4_subset_1(u1_struct_0(A),B,C))),A) )
                 => m1_cantor_1(D,A) ) ) ) ) )).

fof(t79_topgen_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k5_topmetr))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k5_topmetr)) )
         => ( v5_pre_topc(B,A,k5_topmetr)
          <=> ! [C] :
                ( v1_xreal_0(C)
               => ! [D] :
                    ( v1_xreal_0(D)
                   => ( ( r1_xreal_0(np__0,C)
                        & r1_xreal_0(D,np__1) )
                     => ( r1_xreal_0(np__1,C)
                        | r1_xreal_0(D,np__0)
                        | ( v3_pre_topc(k5_pre_topc(A,k5_topmetr,B,k1_rcomp_2(np__0,D)),A)
                          & v3_pre_topc(k5_pre_topc(A,k5_topmetr,B,k2_rcomp_2(C,np__1)),A) ) ) ) ) ) ) ) ) )).

fof(t80_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topgen_5)))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( ( v1_xreal_0(C)
                & v2_xreal_0(C) )
             => ~ ( A = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k1_topreal9(np__2,k23_euclid(B,C),C),k1_struct_0(k15_euclid(np__2),k23_euclid(B,np__0)))
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr))
                        & v5_pre_topc(D,k3_topgen_5,k5_topmetr)
                        & m2_relset_1(D,u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr)) )
                     => ~ ( k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),D,k23_euclid(B,np__0)) = np__0
                          & ! [E] :
                              ( v1_xreal_0(E)
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ( ( r2_hidden(k23_euclid(E,F),k3_subset_1(u1_struct_0(k3_topgen_5),A))
                                     => k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),D,k23_euclid(E,F)) = np__1 )
                                    & ( r2_hidden(k23_euclid(E,F),k1_topgen_1(u1_struct_0(k3_topgen_5),A,k1_struct_0(k15_euclid(np__2),k23_euclid(B,np__0))))
                                     => k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),D,k23_euclid(E,F)) = k7_xcmplx_0(k7_square_1(k5_toprns_1(np__2,k20_euclid(np__2,k23_euclid(B,np__0),k23_euclid(E,F)))),k3_xcmplx_0(k3_xcmplx_0(np__2,C),F)) ) ) ) ) ) ) ) ) ) ) )).

fof(d6_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_xreal_0(C)
                & v2_xreal_0(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr))
                    & m2_relset_1(D,u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr)) )
                 => ( D = k5_topgen_5(A,B,C)
                  <=> ! [E] :
                        ( v1_xreal_0(E)
                       => ! [F] :
                            ( ( v1_xreal_0(F)
                              & ~ v3_xreal_0(F) )
                           => ( ( ~ r2_hidden(k23_euclid(E,F),k1_topreal9(np__2,k23_euclid(A,B),C))
                               => k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),D,k23_euclid(E,F)) = np__1 )
                              & ( r2_hidden(k23_euclid(E,F),k1_topreal9(np__2,k23_euclid(A,B),C))
                               => k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),D,k23_euclid(E,F)) = k7_xcmplx_0(k5_toprns_1(np__2,k20_euclid(np__2,k23_euclid(A,B),k23_euclid(E,F))),C) ) ) ) ) ) ) ) ) ) )).

fof(t81_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( r1_xreal_0(np__0,k22_euclid(A))
       => ! [B] :
            ( v1_xreal_0(B)
           => ! [C] :
                ( ( v1_xreal_0(C)
                  & ~ v3_xreal_0(C) )
               => ! [D] :
                    ( ( v1_xreal_0(D)
                      & v2_xreal_0(D) )
                   => ( k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k5_topgen_5(B,C,D),A) = np__0
                    <=> A = k23_euclid(B,C) ) ) ) ) ) ) )).

fof(t82_topgen_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_xreal_0(B)
            & ~ v3_xreal_0(B) )
         => ! [C] :
              ( ( v1_xreal_0(C)
                & v2_xreal_0(C) )
             => ! [D] :
                  ( ( v1_xreal_0(D)
                    & v2_xreal_0(D) )
                 => ( r1_xreal_0(D,np__1)
                   => k5_pre_topc(k3_topgen_5,k5_topmetr,k5_topgen_5(A,B,C),k1_rcomp_2(np__0,D)) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_topreal9(np__2,k23_euclid(A,B),k3_xcmplx_0(C,D)),k2_topgen_5) ) ) ) ) ) )).

fof(t83_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( ~ r1_xreal_0(k22_euclid(A),np__0)
       => ! [B] :
            ( v1_xreal_0(B)
           => ! [C] :
                ( ( v1_xreal_0(C)
                  & ~ v3_xreal_0(C) )
               => ! [D] :
                    ( ( v1_xreal_0(D)
                      & v2_xreal_0(D) )
                   => ! [E] :
                        ( ( v1_xreal_0(E)
                          & v2_xreal_0(E) )
                       => ( ~ r1_xreal_0(k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k5_topgen_5(B,D,E),A),C)
                         => ( ~ r1_xreal_0(k5_toprns_1(np__2,k20_euclid(np__2,k23_euclid(B,D),A)),k3_xcmplx_0(E,C))
                            & r1_tarski(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_topreal9(np__2,A,k6_xcmplx_0(k5_toprns_1(np__2,k20_euclid(np__2,k23_euclid(B,D),A)),k3_xcmplx_0(E,C))),k2_topgen_5),k5_pre_topc(k3_topgen_5,k5_topmetr,k5_topgen_5(B,D,E),k2_rcomp_2(C,np__1))) ) ) ) ) ) ) ) ) )).

fof(t84_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( k22_euclid(A) = np__0
       => ! [B] :
            ( v1_xreal_0(B)
           => ! [C] :
                ( ( v1_xreal_0(C)
                  & ~ v3_xreal_0(C) )
               => ! [D] :
                    ( ( v1_xreal_0(D)
                      & v2_xreal_0(D) )
                   => ! [E] :
                        ( ( v1_xreal_0(E)
                          & v2_xreal_0(E) )
                       => ( ~ r1_xreal_0(k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k5_topgen_5(B,D,E),A),C)
                         => ( ~ r1_xreal_0(k5_toprns_1(np__2,k20_euclid(np__2,k23_euclid(B,D),A)),k3_xcmplx_0(E,C))
                            & ? [F] :
                                ( v1_xreal_0(F)
                                & v2_xreal_0(F)
                                & F = k7_xcmplx_0(k6_xcmplx_0(k5_toprns_1(np__2,k20_euclid(np__2,k23_euclid(B,D),A)),k3_xcmplx_0(E,C)),np__2)
                                & r1_tarski(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k1_topreal9(np__2,k23_euclid(k21_euclid(A),F),F),k1_struct_0(k15_euclid(np__2),A)),k5_pre_topc(k3_topgen_5,k5_topmetr,k5_topgen_5(B,D,E),k2_rcomp_2(C,np__1))) ) ) ) ) ) ) ) ) ) )).

fof(t85_topgen_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topgen_5)))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( ( v1_xreal_0(D)
                    & v2_xreal_0(D) )
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & A = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_topreal9(np__2,k23_euclid(B,C),D),k2_topgen_5)
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr))
                            & v5_pre_topc(E,k3_topgen_5,k5_topmetr)
                            & m2_relset_1(E,u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr)) )
                         => ~ ( k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),E,k23_euclid(B,C)) = np__0
                              & ! [F] :
                                  ( v1_xreal_0(F)
                                 => ! [G] :
                                      ( v1_xreal_0(G)
                                     => ( ( r2_hidden(k23_euclid(F,G),k3_subset_1(u1_struct_0(k3_topgen_5),A))
                                         => k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),E,k23_euclid(F,G)) = np__1 )
                                        & ( r2_hidden(k23_euclid(F,G),A)
                                         => k2_seq_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),E,k23_euclid(F,G)) = k7_xcmplx_0(k5_toprns_1(np__2,k20_euclid(np__2,k23_euclid(B,C),k23_euclid(F,G))),D) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t86_topgen_5,axiom,(
    v1_urysohn1(k3_topgen_5) )).

fof(t87_topgen_5,axiom,(
    v1_topgen_5(k3_topgen_5) )).

fof(s1_topgen_5,axiom,
    ( ( r1_tarski(f3_s1_topgen_5,f1_s1_topgen_5)
      & ! [A] :
          ( m1_subset_1(A,f1_s1_topgen_5)
         => ( r2_hidden(A,f3_s1_topgen_5)
           => ( ( p1_s1_topgen_5(A)
               => r2_hidden(f4_s1_topgen_5(A),f2_s1_topgen_5) )
              & ( ~ p1_s1_topgen_5(A)
               => r2_hidden(f5_s1_topgen_5(A),f2_s1_topgen_5) ) ) ) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f3_s1_topgen_5,f2_s1_topgen_5)
        & m2_relset_1(A,f3_s1_topgen_5,f2_s1_topgen_5)
        & ! [B] :
            ( m1_subset_1(B,f1_s1_topgen_5)
           => ( r2_hidden(B,f3_s1_topgen_5)
             => ( ( p1_s1_topgen_5(B)
                 => k1_funct_1(A,B) = f4_s1_topgen_5(B) )
                & ( ~ p1_s1_topgen_5(B)
                 => k1_funct_1(A,B) = f5_s1_topgen_5(B) ) ) ) ) ) )).

fof(s2_topgen_5,axiom,
    ( ( r1_tarski(f3_s2_topgen_5,f1_s2_topgen_5)
      & ! [A] :
          ( m1_subset_1(A,f1_s2_topgen_5)
         => ( r2_hidden(A,f3_s2_topgen_5)
           => ( ( p1_s2_topgen_5(A)
               => r2_hidden(f4_s2_topgen_5(A),f2_s2_topgen_5) )
              & ( p2_s2_topgen_5(A)
               => ( p1_s2_topgen_5(A)
                  | r2_hidden(f5_s2_topgen_5(A),f2_s2_topgen_5) ) )
              & ~ ( ~ p1_s2_topgen_5(A)
                  & ~ p2_s2_topgen_5(A)
                  & ~ r2_hidden(f6_s2_topgen_5(A),f2_s2_topgen_5) ) ) ) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f3_s2_topgen_5,f2_s2_topgen_5)
        & m2_relset_1(A,f3_s2_topgen_5,f2_s2_topgen_5)
        & ! [B] :
            ( m1_subset_1(B,f1_s2_topgen_5)
           => ( r2_hidden(B,f3_s2_topgen_5)
             => ( ( p1_s2_topgen_5(B)
                 => k1_funct_1(A,B) = f4_s2_topgen_5(B) )
                & ( p2_s2_topgen_5(B)
                 => ( p1_s2_topgen_5(B)
                    | k1_funct_1(A,B) = f5_s2_topgen_5(B) ) )
                & ~ ( ~ p1_s2_topgen_5(B)
                    & ~ p2_s2_topgen_5(B)
                    & k1_funct_1(A,B) != f6_s2_topgen_5(B) ) ) ) ) ) )).

fof(dt_k1_topgen_5,axiom,(
    m1_subset_1(k1_topgen_5,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )).

fof(dt_k2_topgen_5,axiom,(
    m1_subset_1(k2_topgen_5,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )).

fof(dt_k3_topgen_5,axiom,
    ( ~ v3_struct_0(k3_topgen_5)
    & v1_pre_topc(k3_topgen_5)
    & v2_pre_topc(k3_topgen_5)
    & l1_pre_topc(k3_topgen_5) )).

fof(dt_k4_topgen_5,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ( v1_funct_1(k4_topgen_5(A,B))
        & v1_funct_2(k4_topgen_5(A,B),u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr))
        & m2_relset_1(k4_topgen_5(A,B),u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr)) ) ) )).

fof(dt_k5_topgen_5,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v2_xreal_0(C) )
     => ( v1_funct_1(k5_topgen_5(A,B,C))
        & v1_funct_2(k5_topgen_5(A,B,C),u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr))
        & m2_relset_1(k5_topgen_5(A,B,C),u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr)) ) ) )).

fof(d1_topgen_5,axiom,(
    k1_topgen_5 = a_0_0_topgen_5 )).

fof(d2_topgen_5,axiom,(
    k2_topgen_5 = a_0_1_topgen_5 )).

fof(d3_topgen_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_pre_topc(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( A = k3_topgen_5
      <=> ( u1_struct_0(A) = k2_topgen_5
          & ? [B] :
              ( m1_topgen_2(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => k1_funct_1(B,k23_euclid(C,np__0)) = a_1_0_topgen_5(C) )
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( ~ r1_xreal_0(D,np__0)
                       => k1_funct_1(B,k23_euclid(C,D)) = a_2_0_topgen_5(C,D) ) ) ) ) ) ) ) )).

fof(t75_topgen_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( m1_cantor_1(C,A)
             => m1_cantor_1(a_3_0_topgen_5(A,B,C),B) ) ) ) )).

fof(t76_topgen_5,axiom,(
    m1_cantor_1(a_0_2_topgen_5,k3_topmetr) )).

fof(t78_topgen_5,axiom,(
    m1_cantor_1(k2_xboole_0(k2_xboole_0(a_0_3_topgen_5,a_0_4_topgen_5),a_0_5_topgen_5),k5_topmetr) )).

fof(fraenkel_a_0_0_topgen_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_topgen_5)
    <=> ? [B] :
          ( m1_subset_1(B,k1_numbers)
          & A = k23_euclid(B,np__0) ) ) )).

fof(fraenkel_a_0_1_topgen_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_1_topgen_5)
    <=> ? [B,C] :
          ( m1_subset_1(B,k1_numbers)
          & m1_subset_1(C,k1_numbers)
          & A = k23_euclid(B,C)
          & r1_xreal_0(np__0,C) ) ) )).

fof(fraenkel_a_1_0_topgen_5,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_numbers)
     => ( r2_hidden(A,a_1_0_topgen_5(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_numbers)
            & A = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k1_topreal9(np__2,k23_euclid(B,C),C),k1_struct_0(k15_euclid(np__2),k23_euclid(B,np__0)))
            & ~ r1_xreal_0(C,np__0) ) ) ) )).

fof(fraenkel_a_2_0_topgen_5,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_numbers)
        & m1_subset_1(C,k1_numbers) )
     => ( r2_hidden(A,a_2_0_topgen_5(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_numbers)
            & A = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_topreal9(np__2,k23_euclid(B,C),D),k2_topgen_5)
            & ~ r1_xreal_0(D,np__0) ) ) ) )).

fof(fraenkel_a_3_0_topgen_5,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_pre_topc(C,B)
        & m1_cantor_1(D,B) )
     => ( r2_hidden(A,a_3_0_topgen_5(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
            & A = k3_xboole_0(E,k2_pre_topc(C))
            & r2_hidden(E,D)
            & ~ r1_xboole_0(E,k2_pre_topc(C)) ) ) ) )).

fof(fraenkel_a_0_2_topgen_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_2_topgen_5)
    <=> ? [B,C] :
          ( m1_subset_1(B,k1_numbers)
          & m1_subset_1(C,k1_numbers)
          & A = k2_rcomp_1(B,C)
          & ~ r1_xreal_0(C,B) ) ) )).

fof(fraenkel_a_0_3_topgen_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_3_topgen_5)
    <=> ? [B] :
          ( m1_subset_1(B,k1_numbers)
          & A = k1_rcomp_2(np__0,B)
          & ~ r1_xreal_0(B,np__0)
          & r1_xreal_0(B,np__1) ) ) )).

fof(fraenkel_a_0_4_topgen_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_4_topgen_5)
    <=> ? [B] :
          ( m1_subset_1(B,k1_numbers)
          & A = k2_rcomp_2(B,np__1)
          & r1_xreal_0(np__0,B)
          & ~ r1_xreal_0(np__1,B) ) ) )).

fof(fraenkel_a_0_5_topgen_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_5_topgen_5)
    <=> ? [B,C] :
          ( m1_subset_1(B,k1_numbers)
          & m1_subset_1(C,k1_numbers)
          & A = k2_rcomp_1(B,C)
          & r1_xreal_0(np__0,B)
          & ~ r1_xreal_0(C,B)
          & r1_xreal_0(C,np__1) ) ) )).
%------------------------------------------------------------------------------