SET007 Axioms: SET007+588.ax


%------------------------------------------------------------------------------
% File     : SET007+588 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Compactness of the Bounded Closed Subsets of cal E^2_T
% 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    : topreal6 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  120 (  10 unit)
%            Number of atoms       :  619 (  95 equality)
%            Maximal formula depth :   13 (   7 average)
%            Number of connectives :  576 (  77 ~  ;   9  |; 194  &)
%                                         (   7 <=>; 289 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   55 (   1 propositional; 0-3 arity)
%            Number of functors    :   79 (  10 constant; 0-5 arity)
%            Number of variables   :  245 (   0 singleton; 237 !;   8 ?)
%            Maximal term depth    :    8 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_topreal6,axiom,(
    ! [A,B] :
      ( ( l1_pre_topc(A)
        & v1_finset_1(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_pre_topc(k3_pre_topc(A,B))
        & v6_group_1(k3_pre_topc(A,B)) ) ) )).

fof(rc1_topreal6,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v2_compts_1(A)
      & v6_group_1(A)
      & v10_pscomp_1(A) ) )).

fof(cc1_topreal6,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => v2_connsp_1(B,A) ) ) ) )).

fof(cc2_topreal6,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_finset_1(B)
           => v6_compts_1(B,A) ) ) ) )).

fof(cc3_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( ( ~ v1_xboole_0(A)
          & v1_jordan1(A,np__2) )
       => v2_connsp_1(A,k15_euclid(np__2)) ) ) )).

fof(cc4_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( ~ v1_sppol_1(A)
       => ~ v1_xboole_0(A) ) ) )).

fof(cc5_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( ~ v2_sppol_1(A)
       => ~ v1_xboole_0(A) ) ) )).

fof(cc6_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v2_topreal4(A,k15_euclid(np__2))
       => ( v3_pre_topc(A,k15_euclid(np__2))
          & v2_connsp_1(A,k15_euclid(np__2)) ) ) ) )).

fof(cc7_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( ( v3_pre_topc(A,k15_euclid(np__2))
          & v2_connsp_1(A,k15_euclid(np__2)) )
       => v2_topreal4(A,k15_euclid(np__2)) ) ) )).

fof(cc8_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_xboole_0(A)
       => v1_sppol_1(A) ) ) )).

fof(cc9_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_xboole_0(A)
       => v2_sppol_1(A) ) ) )).

fof(rc2_topreal6,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
      & ~ v1_xboole_0(A)
      & v2_connsp_1(A,k15_euclid(np__2))
      & v1_jordan1(A,np__2) ) )).

fof(fc2_topreal6,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
        & m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
     => ( ~ v1_xboole_0(k1_topreal1(np__2,A,B))
        & v2_connsp_1(k1_topreal1(np__2,A,B),k15_euclid(np__2))
        & v1_jordan1(k1_topreal1(np__2,A,B),np__2)
        & v2_tops_1(k1_topreal1(np__2,A,B),k15_euclid(np__2)) ) ) )).

fof(fc3_topreal6,axiom,
    ( ~ v1_xboole_0(k2_topreal1)
    & v2_connsp_1(k2_topreal1,k15_euclid(np__2))
    & ~ v1_realset1(k2_topreal1)
    & ~ v1_sppol_1(k2_topreal1)
    & ~ v2_sppol_1(k2_topreal1)
    & v1_topreal4(k2_topreal1) )).

fof(cc10_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal2(A)
       => v2_connsp_1(A,k15_euclid(np__2)) ) ) )).

fof(fc4_topreal6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ~ v1_xboole_0(k7_pscomp_1(A))
        & v1_membered(k7_pscomp_1(A))
        & v2_membered(k7_pscomp_1(A))
        & v2_rcomp_1(k7_pscomp_1(A)) ) ) )).

fof(fc5_topreal6,axiom,(
    ! [A] :
      ( ( v2_seq_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( v1_membered(k7_pscomp_1(A))
        & v2_membered(k7_pscomp_1(A))
        & v2_seq_4(k7_pscomp_1(A))
        & v2_rcomp_1(k7_pscomp_1(A)) ) ) )).

fof(fc6_topreal6,axiom,(
    ! [A] :
      ( ( v1_seq_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( v1_membered(k7_pscomp_1(A))
        & v2_membered(k7_pscomp_1(A))
        & v1_seq_4(k7_pscomp_1(A))
        & v2_rcomp_1(k7_pscomp_1(A)) ) ) )).

fof(fc7_topreal6,axiom,
    ( ~ v3_struct_0(k3_topmetr)
    & v1_pre_topc(k3_topmetr)
    & v2_pre_topc(k3_topmetr)
    & v3_compts_1(k3_topmetr) )).

fof(cc11_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_finset_1(A)
       => ( v1_membered(A)
          & v2_membered(A)
          & v1_rcomp_1(A) ) ) ) )).

fof(fc8_topreal6,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k1_rcomp_1(A,B))
        & v2_membered(k1_rcomp_1(A,B))
        & v1_seq_4(k1_rcomp_1(A,B))
        & v2_seq_4(k1_rcomp_1(A,B))
        & v3_seq_4(k1_rcomp_1(A,B))
        & v1_rcomp_1(k1_rcomp_1(A,B))
        & v2_rcomp_1(k1_rcomp_1(A,B)) ) ) )).

fof(rc3_topreal6,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_card_4(A)
      & v1_membered(A)
      & v2_membered(A)
      & v1_seq_4(A)
      & v2_seq_4(A)
      & v3_seq_4(A)
      & v1_rcomp_1(A) ) )).

fof(t1_topreal6,axiom,(
    $true )).

fof(t2_topreal6,axiom,(
    $true )).

fof(t3_topreal6,axiom,(
    $true )).

fof(t4_topreal6,axiom,(
    $true )).

fof(t5_topreal6,axiom,(
    $true )).

fof(t6_topreal6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(np__0,A)
              & r1_xreal_0(np__0,B) )
           => r1_xreal_0(k8_square_1(k2_xcmplx_0(A,B)),k2_xcmplx_0(k8_square_1(A),k8_square_1(B))) ) ) ) )).

fof(t7_topreal6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(np__0,A)
              & r1_xreal_0(A,B) )
           => r1_xreal_0(k18_complex1(A),k18_complex1(B)) ) ) ) )).

fof(t8_topreal6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & r1_xreal_0(B,np__0) )
           => r1_xreal_0(k18_complex1(B),k18_complex1(A)) ) ) ) )).

fof(t9_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => k16_rvsum_1(k1_newton(np__0,A)) = np__1 ) )).

fof(t10_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => k16_rvsum_1(k1_newton(np__1,A)) = A ) )).

fof(t11_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => k16_rvsum_1(k1_newton(np__2,A)) = k4_real_1(A,A) ) )).

fof(t12_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k16_rvsum_1(k1_newton(k1_nat_1(B,np__1),A)) = k4_real_1(k16_rvsum_1(k1_newton(B,A)),A) ) ) )).

fof(t13_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( B != np__0
              & A = np__0 )
          <=> k16_rvsum_1(k1_newton(B,A)) = np__0 ) ) ) )).

fof(t14_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(B,C)
               => ( A = np__0
                  | k16_rvsum_1(k1_newton(k5_binarith(C,B),A)) = k6_real_1(k16_rvsum_1(k1_newton(C,A)),k16_rvsum_1(k1_newton(B,A))) ) ) ) ) ) )).

fof(t15_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_xreal_0(B,C)
               => ( A = np__0
                  | k3_newton(A,k5_binarith(C,B)) = k6_real_1(k3_newton(A,C),k3_newton(A,B)) ) ) ) ) ) )).

fof(t16_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => k11_rvsum_1(k2_finseq_4(k1_numbers,A,B)) = k2_finseq_4(k1_numbers,k7_square_1(A),k7_square_1(B)) ) ) )).

fof(t17_topreal6,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m2_finseq_1(C,k1_numbers)
             => ( ( r2_hidden(A,k4_finseq_1(k3_euclid(C)))
                  & B = k2_seq_1(k5_numbers,k1_numbers,C,A) )
               => k2_seq_1(k5_numbers,k1_numbers,k3_euclid(C),A) = k18_complex1(B) ) ) ) ) )).

fof(t18_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => k3_euclid(k2_finseq_4(k1_numbers,A,B)) = k2_finseq_4(k1_numbers,k18_complex1(A),k18_complex1(B)) ) ) )).

fof(t19_topreal6,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) )
                   => k3_real_1(k18_complex1(k6_xcmplx_0(B,A)),k18_complex1(k6_xcmplx_0(D,C))) = k2_xcmplx_0(k6_xcmplx_0(B,A),k6_xcmplx_0(D,C)) ) ) ) ) ) )).

fof(t20_topreal6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(B,np__0)
           => r2_hidden(A,k2_rcomp_1(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B))) ) ) ) )).

fof(t21_topreal6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(np__0,B)
           => r2_hidden(A,k1_rcomp_1(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B))) ) ) ) )).

fof(t22_topreal6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(B,A)
           => ( k4_pscomp_1(k2_rcomp_1(A,B)) = A
              & k3_pscomp_1(k2_rcomp_1(A,B)) = B ) ) ) ) )).

fof(t23_topreal6,axiom,(
    $true )).

fof(t24_topreal6,axiom,(
    ! [A] :
      ( ( v3_seq_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => r1_tarski(A,k1_rcomp_1(k4_pscomp_1(A),k3_pscomp_1(A))) ) )).

fof(t25_topreal6,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( ( r1_t_0topsp(A,B)
              & v1_connsp_1(A) )
           => v1_connsp_1(B) ) ) ) )).

fof(t26_topreal6,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
         => ( ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v6_compts_1(C,A) ) )
           => v6_compts_1(k5_setfam_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t27_topreal6,axiom,(
    $true )).

fof(t28_topreal6,axiom,(
    $true )).

fof(t29_topreal6,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k4_card_3(k4_funct_4(E,F,A,C)),k4_card_3(k4_funct_4(E,F,B,D))) ) )).

fof(t30_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => m1_subset_1(k4_card_3(k5_funct_4(k1_zfmisc_1(k1_numbers),np__1,np__2,A,B)),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) )).

fof(t31_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ( k5_toprns_1(np__2,k23_euclid(np__0,A)) = k18_complex1(A)
        & k5_toprns_1(np__2,k23_euclid(A,np__0)) = k18_complex1(A) ) ) )).

fof(t32_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k14_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( ( A = k16_euclid(np__2)
              & A = B )
           => ( B = k2_finseq_4(k5_numbers,np__0,np__0)
              & k21_euclid(B) = np__0
              & k22_euclid(B) = np__0 ) ) ) ) )).

fof(t33_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k14_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( ( A = k16_euclid(np__2)
                  & B = C )
               => k4_metric_1(k14_euclid(np__2),A,B) = k5_toprns_1(np__2,C) ) ) ) ) )).

fof(t34_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => k18_euclid(A,np__2,B) = k23_euclid(k4_real_1(A,k21_euclid(B)),k4_real_1(A,k22_euclid(B))) ) ) )).

fof(t35_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( B = k17_euclid(np__2,k18_euclid(k5_real_1(np__1,A),np__2,C),k18_euclid(A,np__2,D))
                      & B != C
                      & r1_xreal_0(np__0,A)
                      & r1_xreal_0(A,np__0) ) ) ) ) ) )).

fof(t36_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                 => ~ ( B = k17_euclid(np__2,k18_euclid(k5_real_1(np__1,A),np__2,C),k18_euclid(A,np__2,D))
                      & B != D
                      & r1_xreal_0(A,np__1)
                      & r1_xreal_0(np__1,A) ) ) ) ) ) )).

fof(t37_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r2_hidden(A,k3_topreal1(np__2,B,C))
               => ( A = B
                  | A = C
                  | r1_xreal_0(k21_euclid(C),k21_euclid(B))
                  | ( ~ r1_xreal_0(k21_euclid(A),k21_euclid(B))
                    & ~ r1_xreal_0(k21_euclid(C),k21_euclid(A)) ) ) ) ) ) ) )).

fof(t38_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ( r2_hidden(A,k3_topreal1(np__2,B,C))
               => ( A = B
                  | A = C
                  | r1_xreal_0(k22_euclid(C),k22_euclid(B))
                  | ( ~ r1_xreal_0(k22_euclid(A),k22_euclid(B))
                    & ~ r1_xreal_0(k22_euclid(C),k22_euclid(A)) ) ) ) ) ) ) )).

fof(t39_topreal6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ? [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
              & ~ r1_xreal_0(k18_pscomp_1(A),k21_euclid(C))
              & B != C ) ) ) )).

fof(t40_topreal6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ? [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
              & ~ r1_xreal_0(k21_euclid(C),k20_pscomp_1(A))
              & B != C ) ) ) )).

fof(t41_topreal6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ? [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
              & ~ r1_xreal_0(k22_euclid(C),k19_pscomp_1(A))
              & B != C ) ) ) )).

fof(t42_topreal6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ? [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
              & ~ r1_xreal_0(k21_pscomp_1(A),k22_euclid(C))
              & B != C ) ) ) )).

fof(t43_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => r1_tarski(k3_topreal1(np__2,k24_pscomp_1(A),k25_pscomp_1(A)),k5_topreal1(np__2,k1_sprect_1(A))) ) )).

fof(t44_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => r1_tarski(k3_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)),k5_topreal1(np__2,k1_sprect_1(A))) ) )).

fof(t45_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => r1_tarski(k3_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)),k5_topreal1(np__2,k1_sprect_1(A))) ) )).

fof(t47_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k14_euclid(np__2)))
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( C = A
                      & r2_hidden(B,k9_metric_1(k14_euclid(np__2),C,D)) )
                   => ( ~ r1_xreal_0(k21_euclid(B),k6_xcmplx_0(k21_euclid(A),D))
                      & ~ r1_xreal_0(k2_xcmplx_0(k21_euclid(A),D),k21_euclid(B)) ) ) ) ) ) ) )).

fof(t48_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k14_euclid(np__2)))
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( C = A
                      & r2_hidden(B,k9_metric_1(k14_euclid(np__2),C,D)) )
                   => ( ~ r1_xreal_0(k22_euclid(B),k6_xcmplx_0(k22_euclid(A),D))
                      & ~ r1_xreal_0(k2_xcmplx_0(k22_euclid(A),D),k22_euclid(B)) ) ) ) ) ) ) )).

fof(t49_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(np__2)))
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = B
               => r1_tarski(k4_card_3(k5_funct_4(k1_zfmisc_1(k1_numbers),np__1,np__2,k2_rcomp_1(k6_xcmplx_0(k21_euclid(A),k7_xcmplx_0(C,k9_square_1(np__2))),k2_xcmplx_0(k21_euclid(A),k7_xcmplx_0(C,k9_square_1(np__2)))),k2_rcomp_1(k6_xcmplx_0(k22_euclid(A),k7_xcmplx_0(C,k9_square_1(np__2))),k2_xcmplx_0(k22_euclid(A),k7_xcmplx_0(C,k9_square_1(np__2)))))),k9_metric_1(k14_euclid(np__2),B,C)) ) ) ) ) )).

fof(t50_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(np__2)))
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = B
               => r1_tarski(k9_metric_1(k14_euclid(np__2),B,C),k4_card_3(k5_funct_4(k1_zfmisc_1(k1_numbers),np__1,np__2,k2_rcomp_1(k6_xcmplx_0(k21_euclid(A),C),k2_xcmplx_0(k21_euclid(A),C)),k2_rcomp_1(k6_xcmplx_0(k22_euclid(A),C),k2_xcmplx_0(k22_euclid(A),C))))) ) ) ) ) )).

fof(t51_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( C = k9_metric_1(k14_euclid(np__2),B,D)
                      & A = B )
                   => k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,C) = k2_rcomp_1(k6_xcmplx_0(k21_euclid(A),D),k2_xcmplx_0(k21_euclid(A),D)) ) ) ) ) ) )).

fof(t52_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( C = k9_metric_1(k14_euclid(np__2),B,D)
                      & A = B )
                   => k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,C) = k2_rcomp_1(k6_xcmplx_0(k22_euclid(A),D),k2_xcmplx_0(k22_euclid(A),D)) ) ) ) ) ) )).

fof(t53_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(np__2)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( C = k9_metric_1(k14_euclid(np__2),B,D)
                      & A = B )
                   => k18_pscomp_1(C) = k6_xcmplx_0(k21_euclid(A),D) ) ) ) ) ) )).

fof(t54_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(np__2)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( C = k9_metric_1(k14_euclid(np__2),B,D)
                      & A = B )
                   => k20_pscomp_1(C) = k2_xcmplx_0(k21_euclid(A),D) ) ) ) ) ) )).

fof(t55_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(np__2)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( C = k9_metric_1(k14_euclid(np__2),B,D)
                      & A = B )
                   => k21_pscomp_1(C) = k6_xcmplx_0(k22_euclid(A),D) ) ) ) ) ) )).

fof(t56_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(np__2)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( C = k9_metric_1(k14_euclid(np__2),B,D)
                      & A = B )
                   => k19_pscomp_1(C) = k2_xcmplx_0(k22_euclid(A),D) ) ) ) ) ) )).

fof(t57_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k14_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( B = k9_metric_1(k14_euclid(np__2),A,C)
                  & v1_sppol_1(B) ) ) ) ) )).

fof(t58_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k14_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( B = k9_metric_1(k14_euclid(np__2),A,C)
                  & v2_sppol_1(B) ) ) ) ) )).

fof(t59_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k14_euclid(np__2)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
             => ~ ( r2_hidden(C,k9_metric_1(k14_euclid(np__2),B,A))
                  & r2_hidden(k23_euclid(k5_real_1(k21_euclid(C),k4_real_1(np__2,A)),k22_euclid(C)),k9_metric_1(k14_euclid(np__2),B,A)) ) ) ) ) )).

fof(t60_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k14_euclid(np__2)))
             => ( C = k16_euclid(np__2)
               => ( r1_xreal_0(A,np__0)
                  | r1_tarski(B,k9_metric_1(k14_euclid(np__2),C,k3_real_1(k3_real_1(k3_real_1(k3_real_1(k18_complex1(k20_pscomp_1(B)),k18_complex1(k19_pscomp_1(B))),k18_complex1(k18_pscomp_1(B))),k18_complex1(k21_pscomp_1(B))),A))) ) ) ) ) ) )).

fof(t61_topreal6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_metric_1(B)
            & v8_metric_1(B)
            & v9_metric_1(B)
            & l1_metric_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ( ~ r1_xreal_0(np__0,A)
               => k11_metric_1(B,C,A) = k1_xboole_0 ) ) ) ) )).

fof(t62_topreal6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v7_metric_1(A)
        & l1_metric_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k11_metric_1(A,B,np__0) = k1_struct_0(A,B) ) ) )).

fof(t63_topreal6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v6_metric_1(B)
            & v8_metric_1(B)
            & v9_metric_1(B)
            & l1_metric_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ( ~ r1_xreal_0(np__0,A)
               => k10_metric_1(B,C,A) = k1_xboole_0 ) ) ) ) )).

fof(t64_topreal6,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) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k10_metric_1(A,B,np__0) = k1_struct_0(A,B) ) ) )).

fof(t65_topreal6,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) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
                 => ( D = k10_metric_1(A,B,C)
                   => v4_pre_topc(D,k5_pcomps_1(A)) ) ) ) ) ) )).

fof(t66_topreal6,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( C = k10_metric_1(k14_euclid(A),B,D)
                   => v4_pre_topc(C,k15_euclid(A)) ) ) ) ) ) )).

fof(t67_topreal6,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) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( v1_xreal_0(C)
             => v6_tbsp_1(k10_metric_1(A,B,C),A) ) ) ) )).

fof(t68_topreal6,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) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
                 => ( D = k11_metric_1(A,B,C)
                   => v4_pre_topc(D,k5_pcomps_1(A)) ) ) ) ) ) )).

fof(t69_topreal6,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( C = k11_metric_1(k14_euclid(A),B,D)
                   => v4_pre_topc(C,k15_euclid(A)) ) ) ) ) ) )).

fof(t70_topreal6,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) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( v1_xreal_0(C)
             => v6_tbsp_1(k11_metric_1(A,B,C),A) ) ) ) )).

fof(t71_topreal6,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)
           => v1_jordan2c(k6_pre_topc(k15_euclid(A),B),A) ) ) ) )).

fof(t72_topreal6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_metric_1(A) )
     => ( v5_tbsp_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => v6_tbsp_1(B,A) ) ) ) )).

fof(t73_topreal6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(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)))
             => ~ ( u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C)
                  & ~ v5_tbsp_1(A)
                  & v6_tbsp_1(B,A)
                  & v6_tbsp_1(C,A) ) ) ) ) )).

fof(t74_topreal6,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ~ ( r1_xreal_0(np__1,A)
                  & u1_struct_0(k15_euclid(A)) = k4_subset_1(u1_struct_0(k15_euclid(A)),B,C)
                  & v1_jordan2c(B,A)
                  & v1_jordan2c(C,A) ) ) ) ) )).

fof(t75_topreal6,axiom,(
    $true )).

fof(t76_topreal6,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
             => ( ( v1_jordan2c(B,A)
                  & v1_jordan2c(C,A) )
               => v1_jordan2c(k4_subset_1(u1_struct_0(k15_euclid(A)),B,C),A) ) ) ) ) )).

fof(t77_topreal6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_seq_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => k4_pscomp_1(A) = k4_pscomp_1(k7_pscomp_1(A)) ) )).

fof(t78_topreal6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_seq_4(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => k3_pscomp_1(A) = k3_pscomp_1(k7_pscomp_1(A)) ) )).

fof(t79_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
         => ( A = B
           => ( v2_rcomp_1(A)
            <=> v4_pre_topc(B,k3_topmetr) ) ) ) ) )).

fof(t80_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
         => ( A = B
           => k7_pscomp_1(A) = k6_pre_topc(k3_topmetr,B) ) ) ) )).

fof(t81_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
         => ( A = B
           => ( v1_rcomp_1(A)
            <=> v6_compts_1(B,k3_topmetr) ) ) ) ) )).

fof(t82_topreal6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A != B
          <=> k7_pscomp_1(k2_rcomp_1(A,B)) = k1_rcomp_1(A,B) ) ) ) )).

fof(t83_topreal6,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
             => ( B = C
               => ( v9_pscomp_1(B,A)
                <=> v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) )).

fof(t84_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)),u1_struct_0(k15_euclid(np__2)))
                & m2_relset_1(C,u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)),u1_struct_0(k15_euclid(np__2))) )
             => ( ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => k1_funct_1(C,k4_tarski(D,E)) = k2_finseq_4(k1_numbers,D,E) ) )
               => k4_pre_topc(k6_borsuk_1(k3_topmetr,k3_topmetr),k15_euclid(np__2),C,k2_zfmisc_1(A,B)) = k4_card_3(k5_funct_4(k1_zfmisc_1(k1_numbers),np__1,np__2,A,B)) ) ) ) ) )).

fof(t85_topreal6,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)),u1_struct_0(k15_euclid(np__2)))
        & m2_relset_1(A,u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)),u1_struct_0(k15_euclid(np__2))) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => k1_funct_1(A,k4_tarski(B,C)) = k2_finseq_4(k1_numbers,B,C) ) )
       => v3_tops_2(A,k6_borsuk_1(k3_topmetr,k3_topmetr),k15_euclid(np__2)) ) ) )).

fof(t86_topreal6,axiom,(
    r1_t_0topsp(k6_borsuk_1(k3_topmetr,k3_topmetr),k15_euclid(np__2)) )).

fof(t87_topreal6,axiom,(
    ! [A] :
      ( ( v1_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_rcomp_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ( v6_compts_1(k4_card_3(k5_funct_4(k1_zfmisc_1(k1_numbers),np__1,np__2,A,B)),k15_euclid(np__2))
            & m1_subset_1(k4_card_3(k5_funct_4(k1_zfmisc_1(k1_numbers),np__1,np__2,A,B)),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) ) )).

fof(t88_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( ( v1_jordan2c(A,np__2)
          & v4_pre_topc(A,k15_euclid(np__2)) )
       => v6_compts_1(A,k15_euclid(np__2)) ) ) )).

fof(t89_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_jordan2c(A,np__2)
       => ! [B] :
            ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(k15_euclid(np__2)),k1_numbers)
              & v9_pscomp_1(B,k15_euclid(np__2))
              & m2_relset_1(B,u1_struct_0(k15_euclid(np__2)),k1_numbers) )
           => r1_tarski(k7_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,B,A)),k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,B,k6_pre_topc(k15_euclid(np__2),A))) ) ) ) )).

fof(t90_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => r1_tarski(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k6_pre_topc(k15_euclid(np__2),A)),k7_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A))) ) )).

fof(t91_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => r1_tarski(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k6_pre_topc(k15_euclid(np__2),A)),k7_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,A))) ) )).

fof(t92_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_jordan2c(A,np__2)
       => k7_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A)) = k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k6_pre_topc(k15_euclid(np__2),A)) ) ) )).

fof(t93_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_jordan2c(A,np__2)
       => k7_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,A)) = k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k6_pre_topc(k15_euclid(np__2),A)) ) ) )).

fof(t94_topreal6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( v1_jordan2c(A,np__2)
       => k18_pscomp_1(A) = k18_pscomp_1(k6_pre_topc(k15_euclid(np__2),A)) ) ) )).

fof(t95_topreal6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( v1_jordan2c(A,np__2)
       => k20_pscomp_1(A) = k20_pscomp_1(k6_pre_topc(k15_euclid(np__2),A)) ) ) )).

fof(t96_topreal6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( v1_jordan2c(A,np__2)
       => k19_pscomp_1(A) = k19_pscomp_1(k6_pre_topc(k15_euclid(np__2),A)) ) ) )).

fof(t97_topreal6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( v1_jordan2c(A,np__2)
       => k21_pscomp_1(A) = k21_pscomp_1(k6_pre_topc(k15_euclid(np__2),A)) ) ) )).

fof(t46_topreal6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( ~ v1_xboole_0(a_1_0_topreal6(A))
        & v2_connsp_1(a_1_0_topreal6(A),k15_euclid(np__2))
        & v1_jordan1(a_1_0_topreal6(A),np__2)
        & m1_subset_1(a_1_0_topreal6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ) )).

fof(fraenkel_a_1_0_topreal6,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( r2_hidden(A,a_1_0_topreal6(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
            & A = C
            & ~ r1_xreal_0(k18_pscomp_1(B),k21_euclid(C)) ) ) ) )).
%------------------------------------------------------------------------------