SET007 Axioms: SET007+790.ax


%------------------------------------------------------------------------------
% File     : SET007+790 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Kuratowski Limit Operators
% 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    : kurato_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  116 (   3 unit)
%            Number of atoms       :  964 (  77 equality)
%            Maximal formula depth :   21 (  10 average)
%            Number of connectives :  925 (  77 ~  ;   4  |; 452  &)
%                                         (  24 <=>; 368 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   55 (   1 propositional; 0-3 arity)
%            Number of functors    :   59 (   8 constant; 0-6 arity)
%            Number of variables   :  403 (   0 singleton; 384 !;  19 ?)
%            Maximal term depth    :    6 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_kurato_2,axiom,(
    ! [A,B] :
      ( m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
     => ( ( v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A)) )
       => ( ~ v1_xboole_0(B)
          & v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
          & v1_partfun1(B,k5_numbers,k1_zfmisc_1(A)) ) ) ) )).

fof(rc1_kurato_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v2_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
          & v1_partfun1(B,k5_numbers,k1_zfmisc_1(A)) ) ) )).

fof(cc2_kurato_2,axiom,(
    ! [A,B] :
      ( m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
     => ( ( v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
          & v5_seqm_3(B) )
       => ( ~ v1_xboole_0(B)
          & v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
          & v1_partfun1(B,k5_numbers,k1_zfmisc_1(A))
          & v1_kurato_2(B,A)
          & v2_kurato_2(B,A)
          & v3_kurato_2(B,A) ) ) ) )).

fof(rc2_kurato_2,axiom,(
    ! [A] :
    ? [B] :
      ( m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
      & ~ v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
      & v1_partfun1(B,k5_numbers,k1_zfmisc_1(A))
      & v5_seqm_3(B)
      & v1_kurato_2(B,A)
      & v2_kurato_2(B,A)
      & v3_kurato_2(B,A) ) )).

fof(fc1_kurato_2,axiom,(
    ! [A] :
      ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
     => ( v4_pre_topc(k5_topreal1(np__2,A),k15_euclid(np__2))
        & v1_jordan2c(k5_topreal1(np__2,A),np__2)
        & v2_tops_1(k5_topreal1(np__2,A),k15_euclid(np__2))
        & v3_tops_1(k5_topreal1(np__2,A),k15_euclid(np__2))
        & v6_compts_1(k5_topreal1(np__2,A),k15_euclid(np__2)) ) ) )).

fof(fc2_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v7_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A) )
     => ( ~ v3_struct_0(k5_pcomps_1(A))
        & v1_pre_topc(k5_pcomps_1(A))
        & v2_pre_topc(k5_pcomps_1(A))
        & v1_frechet(k5_pcomps_1(A))
        & v3_compts_1(k5_pcomps_1(A)) ) ) )).

fof(fc3_kurato_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v3_struct_0(k15_euclid(A))
        & v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A))
        & v1_frechet(k15_euclid(A)) ) ) )).

fof(fc4_kurato_2,axiom,
    ( v1_relat_1(k6_relat_1(k5_numbers))
    & v1_funct_1(k6_relat_1(k5_numbers))
    & v1_seq_1(k6_relat_1(k5_numbers))
    & v1_relat_2(k6_relat_1(k5_numbers))
    & v3_relat_2(k6_relat_1(k5_numbers))
    & v4_relat_2(k6_relat_1(k5_numbers))
    & v8_relat_2(k6_relat_1(k5_numbers)) )).

fof(cc3_kurato_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
        & v5_seqm_3(B)
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
     => ! [C] :
          ( m1_kurato_2(C,A,B)
         => ( v1_relat_1(C)
            & v5_seqm_3(C) ) ) ) )).

fof(t1_kurato_2,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,k1_zfmisc_1(A))
     => ( r2_hidden(B,A)
       => ( r2_hidden(B,C)
          | r2_hidden(B,k3_subset_1(A,C)) ) ) ) )).

fof(t2_kurato_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( r2_hidden(B,k1_relat_1(A))
         => r1_tarski(k4_funct_6(A),k1_funct_1(A,B)) ) ) )).

fof(t3_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
            & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
         => ( B = C
          <=> ! [D] :
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => k1_prob_1(A,B,D) = k1_prob_1(A,C,D) ) ) ) ) )).

fof(t4_kurato_2,axiom,(
    ! [A,B,C,D] :
      ~ ( ~ r1_xboole_0(A,B)
        & ~ r1_xboole_0(C,D)
        & r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) )).

fof(d1_kurato_2,axiom,(
    $true )).

fof(d2_kurato_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,A)
            & m2_relset_1(B,k5_numbers,A) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,A)
                    & m2_relset_1(D,k5_numbers,A) )
                 => ( D = k3_kurato_2(A,B,C)
                  <=> ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k8_funct_2(k5_numbers,A,D,E) = k8_funct_2(k5_numbers,A,B,k1_nat_1(E,C)) ) ) ) ) ) ) )).

fof(d3_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( C = k4_kurato_2(A,B)
          <=> ? [D] :
                ( v1_funct_1(D)
                & v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
                & m2_relset_1(D,k5_numbers,k1_zfmisc_1(A))
                & C = k1_kurato_2(A,D)
                & ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => k1_prob_1(A,D,E) = k2_kurato_2(A,k3_kurato_2(k1_zfmisc_1(A),B,E)) ) ) ) ) ) )).

fof(d4_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( C = k5_kurato_2(A,B)
          <=> ? [D] :
                ( v1_funct_1(D)
                & v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
                & m2_relset_1(D,k5_numbers,k1_zfmisc_1(A))
                & C = k2_kurato_2(A,D)
                & ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => k1_prob_1(A,D,E) = k1_kurato_2(A,k3_kurato_2(k1_zfmisc_1(A),B,E)) ) ) ) ) ) )).

fof(t5_kurato_2,axiom,(
    $true )).

fof(t6_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( r2_hidden(C,k2_kurato_2(A,B))
        <=> ! [D] :
              ( m2_subset_1(D,k1_numbers,k5_numbers)
             => r2_hidden(C,k1_prob_1(A,B,D)) ) ) ) )).

fof(t7_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( r2_hidden(C,k4_kurato_2(A,B))
        <=> ? [D] :
              ( m2_subset_1(D,k1_numbers,k5_numbers)
              & ! [E] :
                  ( m2_subset_1(E,k1_numbers,k5_numbers)
                 => r2_hidden(C,k1_prob_1(A,B,k1_nat_1(D,E))) ) ) ) ) )).

fof(t8_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( r2_hidden(C,k5_kurato_2(A,B))
        <=> ! [D] :
              ( m2_subset_1(D,k1_numbers,k5_numbers)
             => ? [E] :
                  ( m2_subset_1(E,k1_numbers,k5_numbers)
                  & r2_hidden(C,k1_prob_1(A,B,k1_nat_1(D,E))) ) ) ) ) )).

fof(t9_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => r1_tarski(k4_kurato_2(A,B),k5_kurato_2(A,B)) ) )).

fof(t10_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => r1_tarski(k2_kurato_2(A,B),k4_kurato_2(A,B)) ) )).

fof(t11_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => r1_tarski(k5_kurato_2(A,B),k1_kurato_2(A,B)) ) )).

fof(t12_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => k4_kurato_2(A,B) = k3_subset_1(A,k5_kurato_2(A,k3_prob_1(A,B))) ) )).

fof(t13_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
            & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
                & m2_relset_1(D,k5_numbers,k1_zfmisc_1(A)) )
             => ( ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => k1_prob_1(A,D,E) = k5_subset_1(A,k1_prob_1(A,B,E),k1_prob_1(A,C,E)) )
               => k4_kurato_2(A,D) = k5_subset_1(A,k4_kurato_2(A,B),k4_kurato_2(A,C)) ) ) ) ) )).

fof(t14_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
            & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
                & m2_relset_1(D,k5_numbers,k1_zfmisc_1(A)) )
             => ( ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => k1_prob_1(A,D,E) = k4_subset_1(A,k1_prob_1(A,B,E),k1_prob_1(A,C,E)) )
               => k5_kurato_2(A,D) = k4_subset_1(A,k5_kurato_2(A,B),k5_kurato_2(A,C)) ) ) ) ) )).

fof(t15_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
            & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
                & m2_relset_1(D,k5_numbers,k1_zfmisc_1(A)) )
             => ( ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => k1_prob_1(A,D,E) = k4_subset_1(A,k1_prob_1(A,B,E),k1_prob_1(A,C,E)) )
               => r1_tarski(k4_subset_1(A,k4_kurato_2(A,B),k4_kurato_2(A,C)),k4_kurato_2(A,D)) ) ) ) ) )).

fof(t16_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
            & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
                & m2_relset_1(D,k5_numbers,k1_zfmisc_1(A)) )
             => ( ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => k1_prob_1(A,D,E) = k5_subset_1(A,k1_prob_1(A,B,E),k1_prob_1(A,C,E)) )
               => r1_tarski(k5_kurato_2(A,D),k5_subset_1(A,k5_kurato_2(A,B),k5_kurato_2(A,C))) ) ) ) ) )).

fof(t17_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ! [D] :
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => k1_prob_1(A,B,D) = C )
           => k5_kurato_2(A,B) = C ) ) ) )).

fof(t18_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ! [D] :
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => k1_prob_1(A,B,D) = C )
           => k4_kurato_2(A,B) = C ) ) ) )).

fof(t19_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
            & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ( ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => k1_prob_1(A,C,E) = k7_subset_1(A,D,k1_prob_1(A,B,E)) )
               => r1_tarski(k7_subset_1(A,D,k4_kurato_2(A,B)),k5_kurato_2(A,C)) ) ) ) ) )).

fof(t20_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
            & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A)) )
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ( ! [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => k1_prob_1(A,C,E) = k7_subset_1(A,D,k1_prob_1(A,B,E)) )
               => r1_tarski(k7_subset_1(A,D,k5_kurato_2(A,B)),k5_kurato_2(A,C)) ) ) ) ) )).

fof(d5_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ( v1_kurato_2(B,A)
      <=> ! [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => r1_tarski(k1_prob_1(A,B,k1_nat_1(C,np__1)),k1_prob_1(A,B,C)) ) ) ) )).

fof(d6_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ( v2_kurato_2(B,A)
      <=> ! [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => r1_tarski(k1_prob_1(A,B,C),k1_prob_1(A,B,k1_nat_1(C,np__1))) ) ) ) )).

fof(t21_kurato_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => r1_tarski(k1_funct_1(A,k1_nat_1(B,np__1)),k1_funct_1(A,B)) )
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r1_xreal_0(B,C)
                 => r1_tarski(k1_funct_1(A,C),k1_funct_1(A,B)) ) ) ) ) ) )).

fof(t22_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ( v1_kurato_2(B,A)
       => ! [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => ! [D] :
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ( r1_xreal_0(D,C)
                 => r1_tarski(k1_prob_1(A,B,C),k1_prob_1(A,B,D)) ) ) ) ) ) )).

fof(t23_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ( v2_kurato_2(B,A)
       => ! [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => ! [D] :
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ( r1_xreal_0(D,C)
                 => r1_tarski(k1_prob_1(A,B,D),k1_prob_1(A,B,C)) ) ) ) ) ) )).

fof(t24_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( v1_kurato_2(B,A)
         => ( ! [D] :
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ? [E] :
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                    & ~ r1_xreal_0(E,D)
                    & ~ r2_hidden(C,k1_prob_1(A,B,E)) ) )
            | r2_hidden(C,k2_kurato_2(A,B)) ) ) ) )).

fof(t25_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ( v1_kurato_2(B,A)
       => k4_kurato_2(A,B) = k2_kurato_2(A,B) ) ) )).

fof(t26_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ( v2_kurato_2(B,A)
       => k5_kurato_2(A,B) = k1_kurato_2(A,B) ) ) )).

fof(d7_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ( v3_kurato_2(B,A)
      <=> k5_kurato_2(A,B) = k4_kurato_2(A,B) ) ) )).

fof(t27_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ( v5_seqm_3(B)
       => m1_subset_1(k1_yellow_6(B),k1_zfmisc_1(A)) ) ) )).

fof(d8_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ( v5_seqm_3(B)
      <=> ? [C] :
            ( m1_subset_1(C,k1_zfmisc_1(A))
            & ! [D] :
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => k1_prob_1(A,B,D) = C ) ) ) ) )).

fof(d9_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & v3_kurato_2(B,A)
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( C = k6_kurato_2(A,B)
          <=> ( C = k5_kurato_2(A,B)
              & C = k4_kurato_2(A,B) ) ) ) ) )).

fof(t28_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & v3_kurato_2(B,A)
        & m2_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ! [C] :
          ( r2_hidden(C,k6_kurato_2(A,B))
        <=> ? [D] :
              ( m2_subset_1(D,k1_numbers,k5_numbers)
              & ! [E] :
                  ( m2_subset_1(E,k1_numbers,k5_numbers)
                 => r2_hidden(C,k1_prob_1(A,B,k1_nat_1(D,E))) ) ) ) ) )).

fof(t29_kurato_2,axiom,(
    $true )).

fof(t30_kurato_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(A)))
         => ! [C] :
              ( v1_xreal_0(C)
             => ( v3_pre_topc(k9_metric_1(k14_euclid(A),B,C),k15_euclid(A))
                & m1_subset_1(k9_metric_1(k14_euclid(A),B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ) ) ) )).

fof(t31_kurato_2,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] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k14_euclid(A)))
                     => ( ( B = D
                          & C = E )
                       => k4_metric_1(k14_euclid(A),D,E) = k5_toprns_1(A,k20_euclid(A,B,C)) ) ) ) ) ) ) )).

fof(t32_kurato_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( v1_xreal_0(E)
                     => ~ ( B = D
                          & r2_hidden(C,k9_metric_1(k14_euclid(A),B,E))
                          & r1_xreal_0(E,k5_toprns_1(A,k20_euclid(A,C,D))) ) ) ) ) ) ) )).

fof(t33_kurato_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( v1_xreal_0(E)
                     => ( B = D
                       => ( r1_xreal_0(E,k5_toprns_1(A,k20_euclid(A,C,D)))
                          | r2_hidden(C,k9_metric_1(k14_euclid(A),B,E)) ) ) ) ) ) ) ) )).

fof(t34_kurato_2,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ~ ( r2_hidden(B,k6_pre_topc(k15_euclid(A),C))
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,k5_numbers,u1_struct_0(k15_euclid(A)))
                        & m2_relset_1(D,k5_numbers,u1_struct_0(k15_euclid(A))) )
                     => ~ ( r1_tarski(k1_frechet(k15_euclid(A),D),C)
                          & v3_toprns_1(D,A)
                          & k7_toprns_1(A,D) = B ) ) ) ) ) ) )).

fof(t35_kurato_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( B = C
                   => ( r1_xreal_0(D,np__0)
                      | m1_connsp_2(k9_metric_1(k14_euclid(A),B,D),k15_euclid(A),C) ) ) ) ) ) ) )).

fof(t36_kurato_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
                 => ( C = D
                   => ( r2_hidden(C,k6_pre_topc(k15_euclid(A),B))
                    <=> ! [E] :
                          ( v1_xreal_0(E)
                         => ~ ( ~ r1_xreal_0(E,np__0)
                              & r1_xboole_0(k9_metric_1(k14_euclid(A),D,E),B) ) ) ) ) ) ) ) ) )).

fof(t37_kurato_2,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] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
                 => ~ ( D = B
                      & B != C
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => r2_hidden(C,k9_metric_1(k14_euclid(A),D,E)) ) ) ) ) ) ) )).

fof(t38_kurato_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
         => ( ~ v1_jordan2c(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => ~ ( ~ r1_xreal_0(C,np__0)
                    & ! [D] :
                        ( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
                       => ! [E] :
                            ( m1_subset_1(E,u1_struct_0(k14_euclid(A)))
                           => ~ ( r2_hidden(D,B)
                                & r2_hidden(E,B)
                                & ~ r1_xreal_0(k4_metric_1(k14_euclid(A),D,E),C) ) ) ) ) ) ) ) ) )).

fof(t39_kurato_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k14_euclid(A)))
                     => ~ ( ~ r1_xboole_0(k9_metric_1(k14_euclid(A),D,B),k9_metric_1(k14_euclid(A),E,C))
                          & r1_xreal_0(k2_xcmplx_0(B,C),k4_metric_1(k14_euclid(A),D,E)) ) ) ) ) ) ) )).

fof(t40_kurato_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k14_euclid(A)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k14_euclid(A)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k14_euclid(A)))
                             => ~ ( ~ r1_xboole_0(k9_metric_1(k14_euclid(A),E,B),k9_metric_1(k14_euclid(A),G,D))
                                  & ~ r1_xboole_0(k9_metric_1(k14_euclid(A),G,D),k9_metric_1(k14_euclid(A),F,C))
                                  & r1_xreal_0(k2_xcmplx_0(k2_xcmplx_0(B,C),k3_xcmplx_0(np__2,D)),k4_metric_1(k14_euclid(A),E,F)) ) ) ) ) ) ) ) ) )).

fof(t41_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
                     => ( m2_connsp_2(E,k6_borsuk_1(A,B),k7_borsuk_1(A,B,k1_struct_0(A,C),k1_struct_0(B,D)))
                      <=> m1_connsp_2(E,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)) ) ) ) ) ) ) )).

fof(t42_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & v7_seqm_3(C)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( v1_funct_1(k1_partfun1(k5_numbers,k1_numbers,k5_numbers,k1_zfmisc_1(u1_struct_0(A)),C,B))
                & v1_funct_2(k1_partfun1(k5_numbers,k1_numbers,k5_numbers,k1_zfmisc_1(u1_struct_0(A)),C,B),k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
                & m2_relset_1(k1_partfun1(k5_numbers,k1_numbers,k5_numbers,k1_zfmisc_1(u1_struct_0(A)),C,B),k5_numbers,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).

fof(t43_kurato_2,axiom,
    ( v1_funct_1(k6_partfun1(k5_numbers))
    & v1_funct_2(k6_partfun1(k5_numbers),k5_numbers,k1_numbers)
    & v1_seqm_3(k6_partfun1(k5_numbers))
    & v7_seqm_3(k6_partfun1(k5_numbers))
    & m2_relset_1(k6_partfun1(k5_numbers),k5_numbers,k1_numbers) )).

fof(d10_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
             => ( m1_kurato_2(C,A,B)
              <=> ? [D] :
                    ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k1_numbers)
                    & v1_seqm_3(D)
                    & v7_seqm_3(D)
                    & m2_relset_1(D,k5_numbers,k1_numbers)
                    & C = k1_partfun1(k5_numbers,k1_numbers,k5_numbers,k1_zfmisc_1(u1_struct_0(A)),D,B) ) ) ) ) ) )).

fof(t44_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => m1_kurato_2(B,A,B) ) ) )).

fof(t45_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_kurato_2(C,A,B)
             => r1_tarski(k1_pscomp_1(k5_numbers,k1_zfmisc_1(u1_struct_0(A)),C),k1_pscomp_1(k5_numbers,k1_zfmisc_1(u1_struct_0(A)),B)) ) ) ) )).

fof(t46_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_kurato_2(C,A,B)
             => ! [D] :
                  ( m1_kurato_2(D,A,C)
                 => m1_kurato_2(D,A,B) ) ) ) ) )).

fof(t47_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( m1_kurato_2(C,A,B)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => k7_kurato_2(u1_struct_0(A),B,E) = D ) )
                   => C = B ) ) ) ) ) )).

fof(t48_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & v5_seqm_3(B)
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_kurato_2(C,A,B)
             => B = C ) ) ) )).

fof(t49_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_kurato_2(C,A,B)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ? [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                      & r1_xreal_0(D,E)
                      & k7_kurato_2(u1_struct_0(A),C,D) = k7_kurato_2(u1_struct_0(A),B,E) ) ) ) ) ) )).

fof(d11_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = k8_kurato_2(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,C)
                    <=> ! [E] :
                          ( m1_connsp_2(E,A,D)
                         => ? [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                              & ! [G] :
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ~ ( ~ r1_xreal_0(G,F)
                                      & r1_xboole_0(k7_kurato_2(u1_struct_0(A),B,G),E) ) ) ) ) ) ) ) ) ) ) )).

fof(t50_kurato_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
                 => ( C = D
                   => ( r2_hidden(C,k8_kurato_2(k15_euclid(A),B))
                    <=> ! [E] :
                          ( v1_xreal_0(E)
                         => ~ ( ~ r1_xreal_0(E,np__0)
                              & ! [F] :
                                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                                 => ? [G] :
                                      ( m2_subset_1(G,k1_numbers,k5_numbers)
                                      & ~ r1_xreal_0(G,F)
                                      & r1_xboole_0(k7_kurato_2(u1_struct_0(k15_euclid(A)),B,G),k9_metric_1(k14_euclid(A),D,E)) ) ) ) ) ) ) ) ) ) ) )).

fof(t51_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => k6_pre_topc(A,k8_kurato_2(A,B)) = k8_kurato_2(A,B) ) ) )).

fof(t52_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => v4_pre_topc(k8_kurato_2(A,B),A) ) ) )).

fof(t53_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
             => ( m1_kurato_2(B,A,C)
               => r1_tarski(k8_kurato_2(A,C),k8_kurato_2(A,B)) ) ) ) ) )).

fof(t54_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => r1_tarski(k7_kurato_2(u1_struct_0(A),B,D),k7_kurato_2(u1_struct_0(A),C,D)) )
               => r1_tarski(k8_kurato_2(A,B),k8_kurato_2(A,C)) ) ) ) ) )).

fof(t55_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
                    & m2_relset_1(D,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
                 => ( ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k7_kurato_2(u1_struct_0(A),D,E) = k4_subset_1(u1_struct_0(A),k7_kurato_2(u1_struct_0(A),B,E),k7_kurato_2(u1_struct_0(A),C,E)) )
                   => r1_tarski(k4_subset_1(u1_struct_0(A),k8_kurato_2(A,B),k8_kurato_2(A,C)),k8_kurato_2(A,D)) ) ) ) ) ) )).

fof(t56_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
                    & m2_relset_1(D,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
                 => ( ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k7_kurato_2(u1_struct_0(A),D,E) = k5_subset_1(u1_struct_0(A),k7_kurato_2(u1_struct_0(A),B,E),k7_kurato_2(u1_struct_0(A),C,E)) )
                   => r1_tarski(k8_kurato_2(A,D),k5_subset_1(u1_struct_0(A),k8_kurato_2(A,B),k8_kurato_2(A,C))) ) ) ) ) ) )).

fof(t57_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k7_kurato_2(u1_struct_0(A),C,D) = k6_pre_topc(A,k7_kurato_2(u1_struct_0(A),B,D)) )
               => k8_kurato_2(A,C) = k8_kurato_2(A,B) ) ) ) ) )).

fof(t58_kurato_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ( ? [D] :
                    ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,u1_struct_0(k15_euclid(A)))
                    & m2_relset_1(D,k5_numbers,u1_struct_0(k15_euclid(A)))
                    & v3_toprns_1(D,A)
                    & ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => r2_hidden(k2_normsp_1(k15_euclid(A),D,E),k7_kurato_2(u1_struct_0(k15_euclid(A)),B,E)) )
                    & C = k7_toprns_1(A,D) )
               => r2_hidden(C,k8_kurato_2(k15_euclid(A),B)) ) ) ) ) )).

fof(t59_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => r1_tarski(k7_kurato_2(u1_struct_0(A),C,D),B) )
               => r1_tarski(k8_kurato_2(A,C),k6_pre_topc(A,B)) ) ) ) ) )).

fof(t60_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k7_kurato_2(u1_struct_0(A),B,D) = C )
               => k8_kurato_2(A,B) = k6_pre_topc(A,C) ) ) ) ) )).

fof(t61_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v4_pre_topc(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k7_kurato_2(u1_struct_0(A),B,D) = C )
               => k8_kurato_2(A,B) = C ) ) ) ) )).

fof(t62_kurato_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( ( v1_jordan2c(C,A)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(A)),B,D),C) ) )
               => v1_jordan2c(k8_kurato_2(k15_euclid(A),B),A) ) ) ) ) )).

fof(t63_kurato_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( ( v1_jordan2c(B,np__2)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,C),B) ) )
           => v6_compts_1(k8_kurato_2(k15_euclid(np__2),A),k15_euclid(np__2)) ) ) ) )).

fof(t64_kurato_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A)))))
                    & m2_relset_1(D,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))))) )
                 => ( ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k7_kurato_2(u1_struct_0(k6_borsuk_1(k15_euclid(A),k15_euclid(A))),D,E) = k7_borsuk_1(k15_euclid(A),k15_euclid(A),k7_kurato_2(u1_struct_0(k15_euclid(A)),B,E),k7_kurato_2(u1_struct_0(k15_euclid(A)),C,E)) )
                   => k7_borsuk_1(k15_euclid(A),k15_euclid(A),k8_kurato_2(k15_euclid(A),B),k8_kurato_2(k15_euclid(A),C)) = k8_kurato_2(k6_borsuk_1(k15_euclid(A),k15_euclid(A)),D) ) ) ) ) ) )).

fof(t65_kurato_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_tarski(k4_kurato_2(u1_struct_0(k15_euclid(np__2)),A),k8_kurato_2(k15_euclid(np__2),A)) ) )).

fof(t66_kurato_2,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k2_tops_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jordan2c(np__2,k5_topreal1(np__2,k1_jordan9(A,B))))) = k5_topreal1(np__2,k1_jordan9(A,B)) ) ) )).

fof(d12_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = k9_kurato_2(A,B)
              <=> ! [D] :
                    ( r2_hidden(D,C)
                  <=> ? [E] :
                        ( m1_kurato_2(E,A,B)
                        & r2_hidden(D,k8_kurato_2(A,E)) ) ) ) ) ) ) )).

fof(t67_kurato_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(k15_euclid(A)))
            & m2_relset_1(B,k5_numbers,u1_struct_0(k15_euclid(A))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k14_euclid(A)))
                 => ( C = D
                   => ( r1_frechet2(k15_euclid(A),B,C)
                    <=> ! [E] :
                          ( v1_xreal_0(E)
                         => ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ~ ( ~ r1_xreal_0(E,np__0)
                                  & ! [G] :
                                      ( m2_subset_1(G,k1_numbers,k5_numbers)
                                     => ~ ( r1_xreal_0(F,G)
                                          & r2_hidden(k2_normsp_1(k15_euclid(A),B,G),k9_metric_1(k14_euclid(A),D,E)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t68_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => r1_tarski(k8_kurato_2(A,B),k9_kurato_2(A,B)) ) ) )).

fof(t69_kurato_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ~ ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,D),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,D)) )
                  & m1_kurato_2(C,k15_euclid(np__2),A)
                  & ! [D] :
                      ( m1_kurato_2(D,k15_euclid(np__2),B)
                     => ~ ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),C,E),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),D,E)) ) ) ) ) ) ) )).

fof(t70_kurato_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ~ ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,D),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,D)) )
                  & m1_kurato_2(C,k15_euclid(np__2),B)
                  & ! [D] :
                      ( m1_kurato_2(D,k15_euclid(np__2),A)
                     => ~ ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),D,E),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),C,E)) ) ) ) ) ) ) )).

fof(t71_kurato_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r1_tarski(k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,C),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,C)) )
           => r1_tarski(k9_kurato_2(k15_euclid(np__2),A),k9_kurato_2(k15_euclid(np__2),B)) ) ) ) )).

fof(t72_kurato_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k7_kurato_2(u1_struct_0(k15_euclid(np__2)),C,D) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,D),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,D)) )
               => r1_tarski(k4_subset_1(u1_struct_0(k15_euclid(np__2)),k9_kurato_2(k15_euclid(np__2),A),k9_kurato_2(k15_euclid(np__2),B)),k9_kurato_2(k15_euclid(np__2),C)) ) ) ) ) )).

fof(t73_kurato_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k7_kurato_2(u1_struct_0(k15_euclid(np__2)),C,D) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,D),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,D)) )
               => r1_tarski(k9_kurato_2(k15_euclid(np__2),C),k5_subset_1(u1_struct_0(k15_euclid(np__2)),k9_kurato_2(k15_euclid(np__2),A),k9_kurato_2(k15_euclid(np__2),B))) ) ) ) ) )).

fof(t74_kurato_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)))))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)))))
                    & m2_relset_1(D,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))))) )
                 => ~ ( ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => k7_kurato_2(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),C,E) = k7_borsuk_1(k15_euclid(np__2),k15_euclid(np__2),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,E),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,E)) )
                      & m1_kurato_2(D,k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)),C)
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                            & m2_relset_1(E,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                         => ! [F] :
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                                & m2_relset_1(F,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
                             => ~ ( m1_kurato_2(E,k15_euclid(np__2),A)
                                  & m1_kurato_2(F,k15_euclid(np__2),B)
                                  & ! [G] :
                                      ( m2_subset_1(G,k1_numbers,k5_numbers)
                                     => k7_kurato_2(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),D,G) = k7_borsuk_1(k15_euclid(np__2),k15_euclid(np__2),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),E,G),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),F,G)) ) ) ) ) ) ) ) ) ) )).

fof(t75_kurato_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)))))
                & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))))) )
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k7_kurato_2(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),C,D) = k7_borsuk_1(k15_euclid(np__2),k15_euclid(np__2),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,D),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,D)) )
               => r1_tarski(k9_kurato_2(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)),C),k7_borsuk_1(k15_euclid(np__2),k15_euclid(np__2),k9_kurato_2(k15_euclid(np__2),A),k9_kurato_2(k15_euclid(np__2),B))) ) ) ) ) )).

fof(t76_kurato_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k7_kurato_2(u1_struct_0(A),B,D) = C )
               => k8_kurato_2(A,B) = k9_kurato_2(A,B) ) ) ) ) )).

fof(t77_kurato_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,C) = B )
           => k9_kurato_2(k15_euclid(np__2),A) = k6_pre_topc(k15_euclid(np__2),B) ) ) ) )).

fof(t78_kurato_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
        & m2_relset_1(A,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
            & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k7_kurato_2(u1_struct_0(k15_euclid(np__2)),B,C) = k6_pre_topc(k15_euclid(np__2),k7_kurato_2(u1_struct_0(k15_euclid(np__2)),A,C)) )
           => k9_kurato_2(k15_euclid(np__2),B) = k9_kurato_2(k15_euclid(np__2),A) ) ) ) )).

fof(s1_kurato_2,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k1_zfmisc_1(f1_s1_kurato_2))
      & m2_relset_1(A,k5_numbers,k1_zfmisc_1(f1_s1_kurato_2))
      & ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k1_prob_1(f1_s1_kurato_2,A,B) = f2_s1_kurato_2(B) ) ) )).

fof(s2_kurato_2,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ? [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & r1_xreal_0(A,B)
            & p1_s2_kurato_2(k7_kurato_2(u1_struct_0(f1_s2_kurato_2),f2_s2_kurato_2,B)) ) )
   => ? [A] :
        ( m1_kurato_2(A,f1_s2_kurato_2,f2_s2_kurato_2)
        & ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => p1_s2_kurato_2(k7_kurato_2(u1_struct_0(f1_s2_kurato_2),A,B)) ) ) )).

fof(dt_m1_kurato_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
     => ! [C] :
          ( m1_kurato_2(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(C,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(existence_m1_kurato_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
     => ? [C] : m1_kurato_2(C,A,B) ) )).

fof(redefinition_v4_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => ( v4_kurato_2(B,A)
      <=> v5_seqm_3(B) ) ) )).

fof(dt_k1_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => m1_subset_1(k1_kurato_2(A,B),k1_zfmisc_1(A)) ) )).

fof(redefinition_k1_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => k1_kurato_2(A,B) = k3_card_3(B) ) )).

fof(dt_k2_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => m1_subset_1(k2_kurato_2(A,B),k1_zfmisc_1(A)) ) )).

fof(redefinition_k2_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => k2_kurato_2(A,B) = k4_funct_6(B) ) )).

fof(dt_k3_kurato_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,A)
        & m1_relset_1(B,k5_numbers,A)
        & m1_subset_1(C,k5_numbers) )
     => ( v1_funct_1(k3_kurato_2(A,B,C))
        & v1_funct_2(k3_kurato_2(A,B,C),k5_numbers,A)
        & m2_relset_1(k3_kurato_2(A,B,C),k5_numbers,A) ) ) )).

fof(dt_k4_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_kurato_2(A,B),k1_zfmisc_1(A)) ) )).

fof(dt_k5_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_kurato_2(A,B),k1_zfmisc_1(A)) ) )).

fof(dt_k6_kurato_2,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & v3_kurato_2(B,A)
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) )
     => m1_subset_1(k6_kurato_2(A,B),k1_zfmisc_1(A)) ) )).

fof(dt_k7_kurato_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
        & m1_subset_1(C,k5_numbers) )
     => m1_subset_1(k7_kurato_2(A,B,C),k1_zfmisc_1(A)) ) )).

fof(redefinition_k7_kurato_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A))
        & m1_subset_1(C,k5_numbers) )
     => k7_kurato_2(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k8_kurato_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k8_kurato_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k9_kurato_2,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A)))
        & m1_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k9_kurato_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
%------------------------------------------------------------------------------