SET007 Axioms: SET007+729.ax


%------------------------------------------------------------------------------
% File     : SET007+729 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Decompositions of Intervals and Simple Closed Curves
% 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    : borsuk_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   91 (   1 unit)
%            Number of atoms       :  605 (  79 equality)
%            Maximal formula depth :   24 (   9 average)
%            Number of connectives :  635 ( 121 ~  ;  14  |; 195  &)
%                                         (   4 <=>; 301 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   44 (   0 propositional; 1-4 arity)
%            Number of functors    :   43 (   8 constant; 0-4 arity)
%            Number of variables   :  271 (   0 singleton; 258 !;  13 ?)
%            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_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( v1_topreal2(A)
       => ( ~ v1_xboole_0(A)
          & ~ v1_realset1(A)
          & v1_topreal2(A)
          & v2_connsp_1(A,k15_euclid(np__2))
          & v6_compts_1(A,k15_euclid(np__2))
          & ~ v1_sppol_1(A)
          & ~ v2_sppol_1(A) ) ) ) )).

fof(rc1_borsuk_4,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)))
          & ~ v1_xboole_0(B)
          & v2_connsp_1(B,A)
          & v6_compts_1(B,A) ) ) )).

fof(rc2_borsuk_4,axiom,(
    ! [A] :
      ( ( ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & ~ v1_realset1(B) ) ) )).

fof(rc3_borsuk_4,axiom,(
    ! [A] :
      ( ~ v1_realset1(A)
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_realset1(B) ) ) )).

fof(fc1_borsuk_4,axiom,
    ( ~ v1_xboole_0(u1_struct_0(k5_topmetr))
    & v1_membered(u1_struct_0(k5_topmetr))
    & v2_membered(u1_struct_0(k5_topmetr)) )).

fof(t1_borsuk_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(A)) )
             => ~ ( r2_xboole_0(B,C)
                  & ! [D] :
                      ( m1_subset_1(D,A)
                     => ~ ( r2_hidden(D,C)
                          & r1_tarski(B,k4_xboole_0(C,k1_tarski(D))) ) ) ) ) ) ) )).

fof(t2_borsuk_4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ( v1_realset1(B)
          <=> ? [C] :
                ( m1_subset_1(C,A)
                & B = k1_tarski(C) ) ) ) ) )).

fof(t3_borsuk_4,axiom,(
    ! [A] :
      ( ~ v1_realset1(A)
     => ! [B] :
          ~ ! [C] :
              ( m1_subset_1(C,A)
             => C = B ) ) )).

fof(t4_borsuk_4,axiom,(
    ! [A] :
      ( ~ v1_realset1(A)
     => ! [B] :
          ( ( ~ v1_realset1(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C] :
            ? [D] :
              ( m1_subset_1(D,A)
              & r2_hidden(D,B)
              & D != C ) ) ) )).

fof(t5_borsuk_4,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v2_funct_1(A)
                & v2_funct_1(B)
                & k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_tarski(C)
                & k3_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k1_tarski(k1_funct_1(A,C)) )
             => v2_funct_1(k1_funct_4(A,B)) ) ) ) )).

fof(t6_borsuk_4,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v2_funct_1(A)
                & v2_funct_1(B)
                & k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_tarski(C)
                & k3_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k1_tarski(k1_funct_1(A,C))
                & k1_funct_1(A,C) = k1_funct_1(B,C) )
             => k2_funct_1(k1_funct_4(A,B)) = k1_funct_4(k2_funct_1(A),k2_funct_1(B)) ) ) ) )).

fof(t7_borsuk_4,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(k15_euclid(A)))
                 => ~ ( r1_topreal1(k15_euclid(A),C,D,B)
                      & v1_xboole_0(k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),C))) ) ) ) ) ) )).

fof(t8_borsuk_4,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)))
             => v1_jordan1(k3_topreal1(A,B,C),A) ) ) ) )).

fof(t9_borsuk_4,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(np__0,D)
                      & r1_xreal_0(D,np__1) )
                   => ( r1_xreal_0(C,A)
                      | r1_xreal_0(A,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,D),B),k3_xcmplx_0(D,C))) ) ) ) ) ) ) )).

fof(t10_borsuk_4,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ! [C] :
          ( v1_xreal_0(C)
         => ~ ( r2_hidden(A,k1_rcomp_1(B,C))
              & ~ r2_hidden(A,k2_rcomp_1(B,C))
              & A != B
              & A != C ) ) ) )).

fof(t11_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xboole_0(k2_rcomp_1(A,B),k1_rcomp_1(C,D))
                      & r1_xreal_0(B,C) ) ) ) ) ) )).

fof(t12_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(B,C)
                   => r1_xboole_0(k1_rcomp_1(A,B),k2_rcomp_1(C,D)) ) ) ) ) ) )).

fof(t13_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(B,C)
                   => r1_xboole_0(k2_rcomp_1(A,B),k1_rcomp_1(C,D)) ) ) ) ) ) )).

fof(t14_borsuk_4,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_tarski(k1_rcomp_1(A,B),k1_rcomp_1(C,D)) )
                   => ( r1_xreal_0(C,A)
                      & r1_xreal_0(B,D) ) ) ) ) ) ) )).

fof(t15_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_tarski(k2_rcomp_1(A,B),k1_rcomp_1(C,D))
                   => ( r1_xreal_0(B,A)
                      | ( r1_xreal_0(C,A)
                        & r1_xreal_0(B,D) ) ) ) ) ) ) ) )).

fof(t16_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_tarski(k2_rcomp_1(A,B),k1_rcomp_1(C,D))
                   => ( r1_xreal_0(B,A)
                      | r1_tarski(k1_rcomp_1(A,B),k1_rcomp_1(C,D)) ) ) ) ) ) ) )).

fof(t17_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k2_rcomp_1(B,C)
               => ( r1_xreal_0(C,B)
                  | r1_tarski(k1_rcomp_1(B,C),u1_struct_0(k5_topmetr)) ) ) ) ) ) )).

fof(t18_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k2_rcomp_2(B,C)
               => ( r1_xreal_0(C,B)
                  | r1_tarski(k1_rcomp_1(B,C),u1_struct_0(k5_topmetr)) ) ) ) ) ) )).

fof(t19_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k1_rcomp_2(B,C)
               => ( r1_xreal_0(C,B)
                  | r1_tarski(k1_rcomp_1(B,C),u1_struct_0(k5_topmetr)) ) ) ) ) ) )).

fof(t20_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A != B
           => k7_pscomp_1(k2_rcomp_2(A,B)) = k1_rcomp_1(A,B) ) ) ) )).

fof(t21_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A != B
           => k7_pscomp_1(k1_rcomp_2(A,B)) = k1_rcomp_1(A,B) ) ) ) )).

fof(t22_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k2_rcomp_1(B,C)
               => ( r1_xreal_0(C,B)
                  | k6_pre_topc(k5_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) )).

fof(t23_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k2_rcomp_2(B,C)
               => ( r1_xreal_0(C,B)
                  | k6_pre_topc(k5_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) )).

fof(t24_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k1_rcomp_2(B,C)
               => ( r1_xreal_0(C,B)
                  | k6_pre_topc(k5_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) )).

fof(t25_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(B,A)
              & k1_rcomp_1(A,B) = k2_rcomp_2(A,B) ) ) ) )).

fof(t26_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xboole_0(k1_rcomp_2(A,B),k1_seq_4(B))
            & r1_xboole_0(k2_rcomp_2(A,B),k1_seq_4(A)) ) ) ) )).

fof(t27_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => k6_subset_1(k1_numbers,k1_rcomp_1(A,B),k1_seq_4(A)) = k2_rcomp_2(A,B) ) ) ) )).

fof(t28_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => k6_subset_1(k1_numbers,k1_rcomp_1(A,B),k1_seq_4(B)) = k1_rcomp_2(A,B) ) ) ) )).

fof(t29_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(B,A)
                  & ~ r1_xreal_0(C,B)
                  & k5_subset_1(k1_numbers,k2_rcomp_2(A,B),k1_rcomp_2(B,C)) != k1_seq_4(B) ) ) ) ) )).

fof(t30_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( r1_xboole_0(k1_rcomp_2(A,B),k1_rcomp_1(B,C))
                & r1_xboole_0(k1_rcomp_1(A,B),k2_rcomp_2(B,C)) ) ) ) ) )).

fof(t31_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(B,C) )
               => k6_subset_1(k1_numbers,k1_rcomp_1(A,C),k1_seq_4(B)) = k4_subset_1(k1_numbers,k1_rcomp_2(A,B),k2_rcomp_2(B,C)) ) ) ) ) )).

fof(t32_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(B,C)
                  & A = k1_rcomp_1(B,C) )
               => ( r1_xreal_0(np__0,B)
                  & r1_xreal_0(C,np__1) ) ) ) ) ) )).

fof(t33_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( v1_xreal_0(E)
                     => ( ( A = k1_rcomp_2(C,D)
                          & B = k2_rcomp_2(D,E) )
                       => ( r1_xreal_0(D,C)
                          | r1_xreal_0(E,D)
                          | r1_connsp_1(k5_topmetr,A,B) ) ) ) ) ) ) ) )).

fof(t34_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => k1_rcomp_1(A,B) = k4_subset_1(k1_numbers,k1_rcomp_2(A,B),k1_seq_4(B)) ) ) ) )).

fof(t35_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => k1_rcomp_1(A,B) = k4_subset_1(k1_numbers,k1_seq_4(A),k2_rcomp_2(A,B)) ) ) ) )).

fof(t36_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ( r1_xreal_0(C,B)
                      | k1_rcomp_1(A,D) = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k1_rcomp_1(A,B),k2_rcomp_1(B,C)),k1_rcomp_1(C,D)) ) ) ) ) ) ) )).

fof(t37_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ( r1_xreal_0(C,B)
                      | k6_subset_1(k1_numbers,k1_rcomp_1(A,D),k4_subset_1(k1_numbers,k1_rcomp_1(A,B),k1_rcomp_1(C,D))) = k2_rcomp_1(B,C) ) ) ) ) ) ) )).

fof(t38_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(B,A)
                  & ~ r1_xreal_0(C,B)
                  & k4_subset_1(k1_numbers,k2_rcomp_2(A,B),k2_rcomp_1(B,C)) != k2_rcomp_1(A,C) ) ) ) ) )).

fof(t39_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(B,A)
                  & ~ r1_xreal_0(C,B)
                  & ~ r1_tarski(k1_rcomp_2(B,C),k2_rcomp_1(A,C)) ) ) ) ) )).

fof(t40_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(B,A)
                  & ~ r1_xreal_0(C,B)
                  & k4_subset_1(k1_numbers,k2_rcomp_2(A,B),k1_rcomp_2(B,C)) != k2_rcomp_1(A,C) ) ) ) ) )).

fof(t41_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(B,A)
                  & ~ r1_xreal_0(C,B)
                  & k6_subset_1(k1_numbers,k2_rcomp_1(A,C),k2_rcomp_2(A,B)) != k2_rcomp_1(B,C) ) ) ) ) )).

fof(t42_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(B,A)
                  & ~ r1_xreal_0(C,B)
                  & k6_subset_1(k1_numbers,k2_rcomp_1(A,C),k1_rcomp_2(B,C)) != k2_rcomp_1(A,B) ) ) ) ) )).

fof(t43_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k5_topmetr))
         => m1_subset_1(k1_rcomp_1(A,B),k1_zfmisc_1(u1_struct_0(k5_topmetr))) ) ) )).

fof(t44_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k5_topmetr))
         => m1_subset_1(k2_rcomp_1(A,B),k1_zfmisc_1(u1_struct_0(k5_topmetr))) ) ) )).

fof(t45_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( v1_integra1(k1_seq_4(A))
        & m1_subset_1(k1_seq_4(A),k1_zfmisc_1(k1_numbers)) ) ) )).

fof(t46_borsuk_4,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_connsp_1(A,k5_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k5_topmetr))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_topmetr))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k5_topmetr))
                 => ( ( r1_xreal_0(B,C)
                      & r1_xreal_0(C,D)
                      & r2_hidden(B,A)
                      & r2_hidden(D,A) )
                   => r2_hidden(C,A) ) ) ) ) ) )).

fof(t47_borsuk_4,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_connsp_1(A,k5_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r2_hidden(B,A)
                  & r2_hidden(C,A) )
               => r1_tarski(k1_rcomp_1(B,C),A) ) ) ) ) )).

fof(t48_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
             => ( C = k1_rcomp_1(A,B)
               => v4_pre_topc(C,k5_topmetr) ) ) ) ) )).

fof(t49_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k5_topmetr))
         => ( r1_xreal_0(A,B)
           => ( ~ v1_xboole_0(k1_rcomp_1(A,B))
              & v2_connsp_1(k1_rcomp_1(A,B),k5_topmetr)
              & v6_compts_1(k1_rcomp_1(A,B),k5_topmetr)
              & m1_subset_1(k1_rcomp_1(A,B),k1_zfmisc_1(u1_struct_0(k5_topmetr))) ) ) ) ) )).

fof(t50_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ( B = A
           => ( v1_seq_4(B)
              & v2_seq_4(B) ) ) ) ) )).

fof(t51_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r2_hidden(C,B)
                  & B = A )
               => ( r1_xreal_0(k4_pscomp_1(B),C)
                  & r1_xreal_0(C,k3_pscomp_1(B)) ) ) ) ) ) )).

fof(t52_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
         => ( A = B
           => ( v2_rcomp_1(A)
            <=> v4_pre_topc(B,k5_topmetr) ) ) ) ) )).

fof(t53_borsuk_4,axiom,(
    ! [A] :
      ( ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => r1_xreal_0(k4_pscomp_1(A),k3_pscomp_1(A)) ) )).

fof(t54_borsuk_4,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_connsp_1(A,k5_topmetr)
        & v6_compts_1(A,k5_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ( ( A = B
              & r1_tarski(k1_rcomp_1(k4_pscomp_1(B),k3_pscomp_1(B)),B) )
           => k1_rcomp_1(k4_pscomp_1(B),k3_pscomp_1(B)) = B ) ) ) )).

fof(t55_borsuk_4,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_connsp_1(A,k5_topmetr)
        & v6_compts_1(A,k5_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
     => ( v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) ) )).

fof(t56_borsuk_4,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_connsp_1(A,k5_topmetr)
        & v6_compts_1(A,k5_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
     => ? [B] :
          ( m1_subset_1(B,u1_struct_0(k5_topmetr))
          & ? [C] :
              ( m1_subset_1(C,u1_struct_0(k5_topmetr))
              & r1_xreal_0(B,C)
              & A = k1_rcomp_1(B,C) ) ) ) )).

fof(d1_borsuk_4,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_pre_topc(A)
        & m1_pre_topc(A,k5_topmetr) )
     => ( A = k1_borsuk_4
      <=> u1_struct_0(A) = k2_rcomp_1(np__0,np__1) ) ) )).

fof(t57_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
     => ( A = u1_struct_0(k1_borsuk_4)
       => k1_borsuk_4 = k3_pre_topc(k5_topmetr,A) ) ) )).

fof(t58_borsuk_4,axiom,(
    u1_struct_0(k1_borsuk_4) = k4_xboole_0(u1_struct_0(k5_topmetr),k2_tarski(np__0,np__1)) )).

fof(t59_borsuk_4,axiom,
    ( v1_tsep_1(k1_borsuk_4,k5_topmetr)
    & m1_pre_topc(k1_borsuk_4,k5_topmetr) )).

fof(t60_borsuk_4,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( r2_hidden(A,u1_struct_0(k1_borsuk_4))
      <=> ( ~ r1_xreal_0(A,np__0)
          & ~ r1_xreal_0(np__1,A) ) ) ) )).

fof(t61_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k5_topmetr))
         => ~ ( ~ r1_xreal_0(B,A)
              & B != np__1
              & ~ ( ~ v1_xboole_0(k2_rcomp_2(A,B))
                  & m1_subset_1(k2_rcomp_2(A,B),k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) ) ) ) ) )).

fof(t62_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k5_topmetr))
         => ~ ( ~ r1_xreal_0(B,A)
              & A != np__0
              & ~ ( ~ v1_xboole_0(k1_rcomp_2(A,B))
                  & m1_subset_1(k1_rcomp_2(A,B),k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) ) ) ) ) )).

fof(t63_borsuk_4,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_borsuk_3(k3_pre_topc(k15_euclid(np__2),k2_topreal1),k3_pre_topc(k15_euclid(np__2),A)) ) )).

fof(t64_borsuk_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(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(k15_euclid(A)))
                 => ( r1_topreal1(k15_euclid(A),C,D,B)
                   => r1_t_0topsp(k1_borsuk_4,k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k2_struct_0(k15_euclid(A),C,D)))) ) ) ) ) ) )).

fof(t65_borsuk_4,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(k15_euclid(A)))
                 => ( r1_topreal1(k15_euclid(A),C,D,B)
                   => r1_t_0topsp(k5_topmetr,k3_pre_topc(k15_euclid(A),B)) ) ) ) ) ) )).

fof(t66_borsuk_4,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)))
             => ( B != C
               => r1_borsuk_3(k5_topmetr,k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C))) ) ) ) ) )).

fof(t67_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k1_borsuk_4)))
     => ( ? [B] :
            ( m1_subset_1(B,u1_struct_0(k5_topmetr))
            & ? [C] :
                ( m1_subset_1(C,u1_struct_0(k5_topmetr))
                & ~ r1_xreal_0(C,B)
                & A = k1_rcomp_1(B,C) ) )
       => r1_t_0topsp(k5_topmetr,k3_pre_topc(k1_borsuk_4,A)) ) ) )).

fof(t68_borsuk_4,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(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k5_topmetr))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k5_topmetr))
                         => ~ ( r1_topreal1(k15_euclid(A),C,D,B)
                              & ~ r1_xreal_0(F,E)
                              & ! [G] :
                                  ( ( ~ v1_xboole_0(G)
                                    & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
                                 => ! [H] :
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,u1_struct_0(k3_pre_topc(k5_topmetr,G)),u1_struct_0(k3_pre_topc(k15_euclid(A),B)))
                                        & m2_relset_1(H,u1_struct_0(k3_pre_topc(k5_topmetr,G)),u1_struct_0(k3_pre_topc(k15_euclid(A),B))) )
                                     => ~ ( G = k1_rcomp_1(E,F)
                                          & v3_tops_2(H,k3_pre_topc(k5_topmetr,G),k3_pre_topc(k15_euclid(A),B))
                                          & k1_funct_1(H,E) = C
                                          & k1_funct_1(H,F) = D ) ) ) ) ) ) ) ) ) ) )).

fof(t69_borsuk_4,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v2_pre_topc(D)
                    & l1_pre_topc(D) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( v5_pre_topc(C,A,B)
                          & m1_pre_topc(D,B) )
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,u1_struct_0(k3_pre_topc(A,E)),u1_struct_0(D))
                              & m2_relset_1(F,u1_struct_0(k3_pre_topc(A,E)),u1_struct_0(D)) )
                           => ( F = k2_partfun1(u1_struct_0(A),u1_struct_0(B),C,E)
                             => v5_pre_topc(F,k3_pre_topc(A,E),D) ) ) ) ) ) ) ) ) )).

fof(t70_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k5_topmetr))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_topmetr))
             => ( A = k2_rcomp_1(B,C)
               => v3_pre_topc(A,k5_topmetr) ) ) ) ) )).

fof(t71_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k1_borsuk_4)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k5_topmetr))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_topmetr))
             => ( A = k2_rcomp_1(B,C)
               => v3_pre_topc(A,k1_borsuk_4) ) ) ) ) )).

fof(t72_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k1_borsuk_4)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k5_topmetr))
         => ( A = k2_rcomp_2(np__0,B)
           => v4_pre_topc(A,k1_borsuk_4) ) ) ) )).

fof(t73_borsuk_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k1_borsuk_4)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k5_topmetr))
         => ( A = k1_rcomp_2(B,np__1)
           => v4_pre_topc(A,k1_borsuk_4) ) ) ) )).

fof(t74_borsuk_4,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(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k5_topmetr))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k5_topmetr))
                         => ~ ( r1_topreal1(k15_euclid(A),C,D,B)
                              & ~ r1_xreal_0(F,E)
                              & F != np__1
                              & ! [G] :
                                  ( ( ~ v1_xboole_0(G)
                                    & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) )
                                 => ! [H] :
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,u1_struct_0(k3_pre_topc(k1_borsuk_4,G)),u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),C)))))
                                        & m2_relset_1(H,u1_struct_0(k3_pre_topc(k1_borsuk_4,G)),u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),C))))) )
                                     => ~ ( G = k2_rcomp_2(E,F)
                                          & v3_tops_2(H,k3_pre_topc(k1_borsuk_4,G),k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),C))))
                                          & k1_funct_1(H,F) = D ) ) ) ) ) ) ) ) ) ) )).

fof(t75_borsuk_4,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(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k5_topmetr))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k5_topmetr))
                         => ~ ( r1_topreal1(k15_euclid(A),C,D,B)
                              & ~ r1_xreal_0(F,E)
                              & E != np__0
                              & ! [G] :
                                  ( ( ~ v1_xboole_0(G)
                                    & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) )
                                 => ! [H] :
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,u1_struct_0(k3_pre_topc(k1_borsuk_4,G)),u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),D)))))
                                        & m2_relset_1(H,u1_struct_0(k3_pre_topc(k1_borsuk_4,G)),u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),D))))) )
                                     => ~ ( G = k1_rcomp_2(E,F)
                                          & v3_tops_2(H,k3_pre_topc(k1_borsuk_4,G),k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),D))))
                                          & k1_funct_1(H,E) = C ) ) ) ) ) ) ) ) ) ) )).

fof(t76_borsuk_4,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))))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                     => ( ( r1_topreal1(k15_euclid(A),D,E,B)
                          & r1_topreal1(k15_euclid(A),E,D,C)
                          & k5_subset_1(u1_struct_0(k15_euclid(A)),B,C) = k2_struct_0(k15_euclid(A),D,E) )
                       => ( D = E
                          | r1_t_0topsp(k1_borsuk_4,k3_pre_topc(k15_euclid(A),k4_subset_1(u1_struct_0(k15_euclid(A)),k6_subset_1(u1_struct_0(k15_euclid(A)),B,k1_struct_0(k15_euclid(A),D)),k6_subset_1(u1_struct_0(k15_euclid(A)),C,k1_struct_0(k15_euclid(A),D))))) ) ) ) ) ) ) ) )).

fof(t77_borsuk_4,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)))
         => ( r2_hidden(B,A)
           => r1_t_0topsp(k3_pre_topc(k15_euclid(np__2),k6_subset_1(u1_struct_0(k15_euclid(np__2)),A,k1_struct_0(k15_euclid(np__2),B))),k1_borsuk_4) ) ) ) )).

fof(t78_borsuk_4,axiom,(
    ! [A] :
      ( ( v1_topreal2(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)))
             => ( ( r2_hidden(B,A)
                  & r2_hidden(C,A) )
               => r1_t_0topsp(k3_pre_topc(k15_euclid(np__2),k6_subset_1(u1_struct_0(k15_euclid(np__2)),A,k1_struct_0(k15_euclid(np__2),B))),k3_pre_topc(k15_euclid(np__2),k6_subset_1(u1_struct_0(k15_euclid(np__2)),A,k1_struct_0(k15_euclid(np__2),C)))) ) ) ) ) )).

fof(t79_borsuk_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(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(k1_borsuk_4)))
             => ~ ( ? [D] :
                      ( m1_subset_1(D,u1_struct_0(k5_topmetr))
                      & ? [E] :
                          ( m1_subset_1(E,u1_struct_0(k5_topmetr))
                          & ~ r1_xreal_0(E,D)
                          & C = k1_rcomp_1(D,E) ) )
                  & r1_t_0topsp(k3_pre_topc(k1_borsuk_4,C),k3_pre_topc(k15_euclid(A),B))
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
                         => ~ r1_topreal1(k15_euclid(A),D,E,B) ) ) ) ) ) ) )).

fof(t80_borsuk_4,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k1_borsuk_4))
            & m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),u1_struct_0(k1_borsuk_4)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
             => ~ ( v3_tops_2(B,k3_pre_topc(k15_euclid(np__2),A),k1_borsuk_4)
                  & r1_tarski(C,A)
                  & ? [D] :
                      ( m1_subset_1(D,u1_struct_0(k5_topmetr))
                      & ? [E] :
                          ( m1_subset_1(E,u1_struct_0(k5_topmetr))
                          & ~ r1_xreal_0(E,D)
                          & k4_pre_topc(k3_pre_topc(k15_euclid(np__2),A),k1_borsuk_4,B,C) = k1_rcomp_1(D,E) ) )
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
                         => ~ r1_topreal1(k15_euclid(np__2),D,E,C) ) ) ) ) ) ) )).

fof(t81_borsuk_4,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v2_connsp_1(B,k15_euclid(np__2))
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ~ ( r1_tarski(B,A)
              & B != A
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                     => ~ r1_topreal1(k15_euclid(np__2),C,D,B) ) )
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => B != k1_struct_0(k15_euclid(np__2),C) ) ) ) ) )).

fof(t82_borsuk_4,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k5_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
     => ~ ( r1_tarski(A,k2_rcomp_1(np__0,np__1))
          & ! [B] :
              ( ( v1_integra1(B)
                & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
             => ~ ( r1_tarski(A,B)
                  & r1_tarski(B,k2_rcomp_1(np__0,np__1))
                  & k3_seq_4(A) = k4_pscomp_1(B)
                  & k2_seq_4(A) = k3_pscomp_1(B) ) ) ) ) )).

fof(t83_borsuk_4,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k5_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )
     => ~ ( r1_tarski(A,k2_rcomp_1(np__0,np__1))
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(k5_topmetr))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k5_topmetr))
                 => ~ ( r1_xreal_0(B,C)
                      & r1_tarski(A,k1_rcomp_1(B,C))
                      & r1_tarski(k1_rcomp_1(B,C),k2_rcomp_1(np__0,np__1)) ) ) ) ) ) )).

fof(t84_borsuk_4,axiom,(
    ! [A] :
      ( ( v1_topreal2(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ! [B] :
          ( ( v4_pre_topc(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ~ ( r1_tarski(B,A)
              & B != A
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
                     => ! [E] :
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
                         => ~ ( r1_topreal1(k15_euclid(np__2),C,D,E)
                              & r1_tarski(B,E)
                              & r1_tarski(E,A) ) ) ) ) ) ) ) )).

fof(dt_k1_borsuk_4,axiom,
    ( ~ v3_struct_0(k1_borsuk_4)
    & v1_pre_topc(k1_borsuk_4)
    & m1_pre_topc(k1_borsuk_4,k5_topmetr) )).
%------------------------------------------------------------------------------