SET007 Axioms: SET007+832.ax


%------------------------------------------------------------------------------
% File     : SET007+832 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Algebraic Properties of Homotopies
% 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_6 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  159 (  23 unit)
%            Number of atoms       :  949 ( 116 equality)
%            Maximal formula depth :   23 (   7 average)
%            Number of connectives :  872 (  82 ~  ;   3  |; 405  &)
%                                         (  32 <=>; 350 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   47 (   1 propositional; 0-6 arity)
%            Number of functors    :   88 (  37 constant; 0-6 arity)
%            Number of variables   :  367 (   0 singleton; 338 !;  29 ?)
%            Maximal term depth    :    5 (   1 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_borsuk_6,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_monoid_0(k15_euclid(A))
        & v2_monoid_0(k15_euclid(A)) ) ) )).

fof(fc2_borsuk_6,axiom,
    ( ~ v3_struct_0(k22_borsuk_1)
    & v1_pre_topc(k22_borsuk_1)
    & v2_pre_topc(k22_borsuk_1)
    & v1_connsp_1(k22_borsuk_1)
    & v2_compts_1(k22_borsuk_1)
    & v3_compts_1(k22_borsuk_1)
    & v3_yellow_8(k22_borsuk_1)
    & v1_urysohn1(k22_borsuk_1)
    & v1_borsuk_2(k22_borsuk_1)
    & v2_t_0topsp(k22_borsuk_1)
    & v1_borsuk_6(k22_borsuk_1) )).

fof(rc1_borsuk_6,axiom,(
    ? [A] :
      ( l1_struct_0(A)
      & ~ v3_struct_0(A)
      & v1_borsuk_6(A) ) )).

fof(rc2_borsuk_6,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v1_borsuk_6(A) ) )).

fof(cc1_borsuk_6,axiom,(
    ! [A] :
      ( ( v1_borsuk_6(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) )).

fof(cc2_borsuk_6,axiom,(
    ! [A] :
      ( ( v1_borsuk_6(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => v1_borsuk_6(B) ) ) )).

fof(fc3_borsuk_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_6(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v1_borsuk_6(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) )
     => ( v1_xcmplx_0(k1_mcart_1(C))
        & v1_xreal_0(k1_mcart_1(C)) ) ) )).

fof(fc4_borsuk_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_6(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v1_borsuk_6(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) )
     => ( v1_xcmplx_0(k2_mcart_1(C))
        & v1_xreal_0(k2_mcart_1(C)) ) ) )).

fof(fc5_borsuk_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & m1_pre_topc(A,k6_borsuk_1(k5_topmetr,k5_topmetr))
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_xcmplx_0(k1_mcart_1(B))
        & v1_xreal_0(k1_mcart_1(B)) ) ) )).

fof(fc6_borsuk_6,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & m1_pre_topc(A,k6_borsuk_1(k5_topmetr,k5_topmetr))
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_xcmplx_0(k2_mcart_1(B))
        & v1_xreal_0(k2_mcart_1(B)) ) ) )).

fof(fc7_borsuk_6,axiom,
    ( ~ v3_struct_0(k3_topmetr)
    & v1_pre_topc(k3_topmetr)
    & v2_pre_topc(k3_topmetr)
    & v1_connsp_1(k3_topmetr)
    & v3_compts_1(k3_topmetr)
    & v1_urysohn1(k3_topmetr)
    & v1_borsuk_2(k3_topmetr)
    & v2_t_0topsp(k3_topmetr)
    & v1_borsuk_6(k3_topmetr) )).

fof(fc8_borsuk_6,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v1_funct_1(k1_pre_topc(A))
        & v1_xboole_0(k1_pre_topc(A))
        & v6_compts_1(k1_pre_topc(A),A)
        & v1_membered(k1_pre_topc(A))
        & v2_membered(k1_pre_topc(A))
        & v3_membered(k1_pre_topc(A))
        & v4_membered(k1_pre_topc(A))
        & v5_membered(k1_pre_topc(A)) ) ) )).

fof(rc3_borsuk_6,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_funct_1(B)
          & v1_xboole_0(B)
          & v6_compts_1(B,A)
          & v1_membered(B)
          & v2_membered(B)
          & v3_membered(B)
          & v4_membered(B)
          & v5_membered(B) ) ) )).

fof(fc9_borsuk_6,axiom,
    ( v1_relat_1(k3_borsuk_6)
    & v1_funct_1(k3_borsuk_6)
    & v1_funct_2(k3_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
    & v5_pre_topc(k3_borsuk_6,k5_topmetr,k5_topmetr) )).

fof(fc10_borsuk_6,axiom,
    ( v1_relat_1(k4_borsuk_6)
    & v1_funct_1(k4_borsuk_6)
    & v1_funct_2(k4_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
    & v5_pre_topc(k4_borsuk_6,k5_topmetr,k5_topmetr) )).

fof(fc11_borsuk_6,axiom,
    ( v1_relat_1(k5_borsuk_6)
    & v1_funct_1(k5_borsuk_6)
    & v1_funct_2(k5_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
    & v5_pre_topc(k5_borsuk_6,k5_topmetr,k5_topmetr) )).

fof(fc12_borsuk_6,axiom,
    ( ~ v1_xboole_0(k6_borsuk_6)
    & v4_pre_topc(k6_borsuk_6,k6_borsuk_1(k5_topmetr,k5_topmetr)) )).

fof(fc13_borsuk_6,axiom,
    ( ~ v1_xboole_0(k7_borsuk_6)
    & v4_pre_topc(k7_borsuk_6,k6_borsuk_1(k5_topmetr,k5_topmetr)) )).

fof(fc14_borsuk_6,axiom,
    ( ~ v1_xboole_0(k8_borsuk_6)
    & v4_pre_topc(k8_borsuk_6,k6_borsuk_1(k5_topmetr,k5_topmetr)) )).

fof(t1_borsuk_6,axiom,(
    u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)) = k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(np__0,np__1),k1_rcomp_1(np__0,np__1)) )).

fof(t2_borsuk_6,axiom,(
    $true )).

fof(t3_borsuk_6,axiom,(
    $true )).

fof(t4_borsuk_6,axiom,(
    $true )).

fof(t5_borsuk_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,C)
                  & r1_xreal_0(C,B) )
               => r2_hidden(k7_xcmplx_0(k6_xcmplx_0(C,A),k6_xcmplx_0(B,A)),u1_struct_0(k4_topmetr(np__0,np__1))) ) ) ) ) )).

fof(t6_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ( r1_xreal_0(A,k6_real_1(np__1,np__2))
       => m1_subset_1(k3_xcmplx_0(np__2,A),u1_struct_0(k5_topmetr)) ) ) )).

fof(t7_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ( r1_xreal_0(k6_real_1(np__1,np__2),A)
       => m1_subset_1(k6_xcmplx_0(k3_xcmplx_0(np__2,A),np__1),u1_struct_0(k5_topmetr)) ) ) )).

fof(t8_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k5_topmetr))
         => m1_subset_1(k3_xcmplx_0(A,B),u1_struct_0(k5_topmetr)) ) ) )).

fof(t9_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => m1_subset_1(k3_xcmplx_0(k6_real_1(np__1,np__2),A),u1_struct_0(k5_topmetr)) ) )).

fof(t10_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ( r1_xreal_0(k6_real_1(np__1,np__2),A)
       => m1_subset_1(k6_xcmplx_0(A,k6_real_1(np__1,np__4)),u1_struct_0(k5_topmetr)) ) ) )).

fof(t11_borsuk_6,axiom,(
    $true )).

fof(t12_borsuk_6,axiom,(
    m1_borsuk_2(k7_grcat_1(k5_topmetr),k22_borsuk_1,k23_borsuk_1,k24_borsuk_1) )).

fof(t13_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,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(A,B)
                      & r1_xreal_0(C,D) )
                   => ( ~ v1_xboole_0(k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(A,B),k1_rcomp_1(C,D)))
                      & v6_compts_1(k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(A,B),k1_rcomp_1(C,D)),k6_borsuk_1(k5_topmetr,k5_topmetr))
                      & m1_subset_1(k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(A,B),k1_rcomp_1(C,D)),k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) ) ) ) ) ) ) )).

fof(d1_borsuk_6,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ( v1_borsuk_6(A)
      <=> v2_membered(u1_struct_0(A)) ) ) )).

fof(t18_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ( v1_borsuk_6(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => v1_xreal_0(B) ) ) ) )).

fof(t24_borsuk_6,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)) = k10_finseq_1(B,C) ) ) ) )).

fof(t31_borsuk_6,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(k6_borsuk_1(A,B)))
             => ( m1_subset_1(k1_mcart_1(C),u1_struct_0(A))
                & m1_subset_1(k2_mcart_1(C),u1_struct_0(B)) ) ) ) ) )).

fof(t32_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
         => ( ( A = k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(np__0,k6_real_1(np__1,np__2)),k1_rcomp_1(np__0,np__1))
              & B = k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(k6_real_1(np__1,np__2),np__1),k1_rcomp_1(np__0,np__1)) )
           => k2_xboole_0(k2_pre_topc(k3_pre_topc(k6_borsuk_1(k5_topmetr,k5_topmetr),A)),k2_pre_topc(k3_pre_topc(k6_borsuk_1(k5_topmetr,k5_topmetr),B))) = k2_pre_topc(k6_borsuk_1(k5_topmetr,k5_topmetr)) ) ) ) )).

fof(t33_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
         => ( ( A = k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(np__0,k6_real_1(np__1,np__2)),k1_rcomp_1(np__0,np__1))
              & B = k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(k6_real_1(np__1,np__2),np__1),k1_rcomp_1(np__0,np__1)) )
           => k3_xboole_0(k2_pre_topc(k3_pre_topc(k6_borsuk_1(k5_topmetr,k5_topmetr),A)),k2_pre_topc(k3_pre_topc(k6_borsuk_1(k5_topmetr,k5_topmetr),B))) = k2_zfmisc_1(k1_tarski(k6_real_1(np__1,np__2)),k1_rcomp_1(np__0,np__1)) ) ) ) )).

fof(t34_borsuk_6,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v1_xboole_0(k1_xboole_0)
        & v6_compts_1(k1_xboole_0,A)
        & m1_subset_1(k1_xboole_0,k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(t35_borsuk_6,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ~ r1_xreal_0(B,C)
               => ( v1_xboole_0(k1_rcomp_1(B,C))
                  & v6_compts_1(k1_rcomp_1(B,C),A)
                  & m1_subset_1(k1_rcomp_1(B,C),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) )).

fof(t36_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,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))
                 => ( v6_compts_1(k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(A,B),k1_rcomp_1(C,D)),k6_borsuk_1(k5_topmetr,k5_topmetr))
                    & m1_subset_1(k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(A,B),k1_rcomp_1(C,D)),k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) ) ) ) ) ) )).

fof(d2_borsuk_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => k1_borsuk_6(A,B,C,D) = k7_funct_2(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(np__0,np__1)),u1_struct_0(k4_topmetr(C,D)),k4_treal_1(A,B,k1_treal_1(np__0,np__1),k2_treal_1(np__0,np__1)),k3_treal_1(C,D,k1_treal_1(C,D),k2_treal_1(C,D))) ) ) ) ) )).

fof(t37_borsuk_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(B,A)
                      & ~ r1_xreal_0(D,C)
                      & ~ ( k1_funct_1(k1_borsuk_6(A,B,C,D),A) = C
                          & k1_funct_1(k1_borsuk_6(A,B,C,D),B) = D ) ) ) ) ) ) )).

fof(t38_borsuk_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(C,D)
                   => ( r1_xreal_0(B,A)
                      | ( v1_funct_1(k1_borsuk_6(A,B,C,D))
                        & v1_funct_2(k1_borsuk_6(A,B,C,D),u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
                        & v5_pre_topc(k1_borsuk_6(A,B,C,D),k4_topmetr(A,B),k4_topmetr(C,D))
                        & m2_relset_1(k1_borsuk_6(A,B,C,D),u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) ) ) ) ) ) ) ) )).

fof(t39_borsuk_6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(C,D)
                   => ( r1_xreal_0(B,A)
                      | ! [E] :
                          ( v1_xreal_0(E)
                         => ( ( r1_xreal_0(A,E)
                              & r1_xreal_0(E,B) )
                           => k1_funct_1(k1_borsuk_6(A,B,C,D),E) = k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(D,C),k6_xcmplx_0(B,A)),k6_xcmplx_0(E,A)),C) ) ) ) ) ) ) ) ) )).

fof(t40_borsuk_6,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
        & m2_relset_1(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
            & m2_relset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
         => ~ ( v5_pre_topc(A,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr)
              & v5_pre_topc(B,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
                 => m1_subset_1(k3_xcmplx_0(k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),A,C),k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),B,C)),u1_struct_0(k5_topmetr)) )
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
                    & m2_relset_1(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
                 => ~ ( ! [D] :
                          ( m1_subset_1(D,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
                         => ! [E] :
                              ( v1_xreal_0(E)
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ( ( k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),A,D) = E
                                      & k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),B,D) = F )
                                   => k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),C,D) = k3_xcmplx_0(E,F) ) ) ) )
                      & v5_pre_topc(C,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr) ) ) ) ) ) )).

fof(t41_borsuk_6,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
        & m2_relset_1(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
            & m2_relset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
         => ~ ( v5_pre_topc(A,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr)
              & v5_pre_topc(B,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
                 => m1_subset_1(k2_xcmplx_0(k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),A,C),k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),B,C)),u1_struct_0(k5_topmetr)) )
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
                    & m2_relset_1(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
                 => ~ ( ! [D] :
                          ( m1_subset_1(D,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
                         => ! [E] :
                              ( v1_xreal_0(E)
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ( ( k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),A,D) = E
                                      & k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),B,D) = F )
                                   => k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),C,D) = k2_xcmplx_0(E,F) ) ) ) )
                      & v5_pre_topc(C,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr) ) ) ) ) ) )).

fof(t42_borsuk_6,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
        & m2_relset_1(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
            & m2_relset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
         => ~ ( v5_pre_topc(A,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr)
              & v5_pre_topc(B,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
                 => m1_subset_1(k6_xcmplx_0(k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),A,C),k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),B,C)),u1_struct_0(k5_topmetr)) )
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr))
                    & m2_relset_1(C,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr)) )
                 => ~ ( ! [D] :
                          ( m1_subset_1(D,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
                         => ! [E] :
                              ( v1_xreal_0(E)
                             => ! [F] :
                                  ( v1_xreal_0(F)
                                 => ( ( k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),A,D) = E
                                      & k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),B,D) = F )
                                   => k8_funct_2(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(k5_topmetr),C,D) = k6_xcmplx_0(E,F) ) ) ) )
                      & v5_pre_topc(C,k6_borsuk_1(k5_topmetr,k5_topmetr),k5_topmetr) ) ) ) ) ) )).

fof(t43_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ( v5_pre_topc(D,k5_topmetr,A)
                   => ( v1_funct_1(k5_relat_1(k3_treal_1(np__0,np__1,k2_treal_1(np__0,np__1),k1_treal_1(np__0,np__1)),D))
                      & v1_funct_2(k5_relat_1(k3_treal_1(np__0,np__1,k2_treal_1(np__0,np__1),k1_treal_1(np__0,np__1)),D),u1_struct_0(k5_topmetr),u1_struct_0(A))
                      & v5_pre_topc(k5_relat_1(k3_treal_1(np__0,np__1,k2_treal_1(np__0,np__1),k1_treal_1(np__0,np__1)),D),k5_topmetr,A)
                      & m2_relset_1(k5_relat_1(k3_treal_1(np__0,np__1,k2_treal_1(np__0,np__1),k1_treal_1(np__0,np__1)),D),u1_struct_0(k5_topmetr),u1_struct_0(A)) ) ) ) ) ) ) )).

fof(t44_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ( ( k1_funct_1(D,np__0) = B
                      & k1_funct_1(D,np__1) = C )
                   => ( k1_funct_1(k5_relat_1(k3_treal_1(np__0,np__1,k2_treal_1(np__0,np__1),k1_treal_1(np__0,np__1)),D),np__0) = C
                      & k1_funct_1(k5_relat_1(k3_treal_1(np__0,np__1,k2_treal_1(np__0,np__1),k1_treal_1(np__0,np__1)),D),np__1) = B ) ) ) ) ) ) )).

fof(t45_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ( ( v5_pre_topc(D,k5_topmetr,A)
                      & k1_funct_1(D,np__0) = B
                      & k1_funct_1(D,np__1) = C )
                   => ( v5_pre_topc(k2_borsuk_2(A,B,C,D),k5_topmetr,A)
                      & k1_funct_1(k2_borsuk_2(A,B,C,D),np__0) = C
                      & k1_funct_1(k2_borsuk_2(A,B,C,D),np__1) = B ) ) ) ) ) ) )).

fof(t46_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r1_borsuk_6(A,B,C)
                      & r1_borsuk_6(A,C,D) )
                   => r1_borsuk_6(A,B,D) ) ) ) ) ) )).

fof(t47_borsuk_6,axiom,(
    $true )).

fof(t48_borsuk_6,axiom,(
    $true )).

fof(t49_borsuk_6,axiom,(
    $true )).

fof(t50_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_borsuk_6(A,B,C)
               => ! [D] :
                    ( m1_borsuk_2(D,A,B,C)
                   => D = k2_borsuk_2(A,C,B,k2_borsuk_2(A,B,C,D)) ) ) ) ) ) )).

fof(t51_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => D = k2_borsuk_2(A,C,B,k2_borsuk_2(A,B,C,D)) ) ) ) ) )).

fof(d3_borsuk_6,axiom,(
    $true )).

fof(d4_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_borsuk_2(E,A,B,C)
                     => ! [F] :
                          ( m1_borsuk_2(F,A,C,D)
                         => ! [G] :
                              ( m1_borsuk_2(G,A,B,D)
                             => ( G = k1_borsuk_2(A,B,C,D,E,F)
                              <=> ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(k5_topmetr))
                                   => ( ( r1_xreal_0(H,k6_real_1(np__1,np__2))
                                       => k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),G,H) = k1_funct_1(E,k3_xcmplx_0(np__2,H)) )
                                      & ( r1_xreal_0(k6_real_1(np__1,np__2),H)
                                       => k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),G,H) = k1_funct_1(F,k6_xcmplx_0(k3_xcmplx_0(np__2,H),np__1)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( m1_borsuk_2(E,A,C,B)
                     => ( E = k2_borsuk_2(A,B,C,D)
                      <=> ! [F] :
                            ( m1_subset_1(F,u1_struct_0(k5_topmetr))
                           => k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),E,F) = k1_funct_1(D,k6_xcmplx_0(np__1,F)) ) ) ) ) ) ) ) )).

fof(d6_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
                        & v5_pre_topc(E,k5_topmetr,k5_topmetr)
                        & m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
                     => ( ( k1_funct_1(E,np__0) = np__0
                          & k1_funct_1(E,np__1) = np__1
                          & r1_borsuk_6(A,B,C) )
                       => k2_borsuk_6(A,B,C,D,E) = k7_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),u1_struct_0(A),E,D) ) ) ) ) ) ) )).

fof(t52_borsuk_6,axiom,(
    $true )).

fof(t53_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
                        & v5_pre_topc(E,k5_topmetr,k5_topmetr)
                        & m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
                     => ( ( k1_funct_1(E,np__0) = np__0
                          & k1_funct_1(E,np__1) = np__1
                          & r1_borsuk_6(A,B,C) )
                       => r3_borsuk_2(A,B,C,k2_borsuk_6(A,B,C,D,E),D) ) ) ) ) ) ) )).

fof(t54_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
                        & v5_pre_topc(E,k5_topmetr,k5_topmetr)
                        & m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
                     => ( ( k1_funct_1(E,np__0) = np__0
                          & k1_funct_1(E,np__1) = np__1 )
                       => r4_borsuk_2(A,B,C,k2_borsuk_6(A,B,C,D,E),D) ) ) ) ) ) ) )).

fof(d7_borsuk_6,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
        & m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
     => ( A = k3_borsuk_6
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(k5_topmetr))
           => ( ( r1_xreal_0(B,k6_real_1(np__1,np__2))
               => k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k3_xcmplx_0(np__2,B) )
              & ( ~ r1_xreal_0(B,k6_real_1(np__1,np__2))
               => k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = np__1 ) ) ) ) ) )).

fof(t55_borsuk_6,axiom,
    ( k1_funct_1(k3_borsuk_6,np__0) = np__0
    & k1_funct_1(k3_borsuk_6,np__1) = np__1 )).

fof(d8_borsuk_6,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
        & m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
     => ( A = k4_borsuk_6
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(k5_topmetr))
           => ( ( r1_xreal_0(B,k6_real_1(np__1,np__2))
               => k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = np__0 )
              & ( ~ r1_xreal_0(B,k6_real_1(np__1,np__2))
               => k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k6_xcmplx_0(k3_xcmplx_0(np__2,B),np__1) ) ) ) ) ) )).

fof(t56_borsuk_6,axiom,
    ( k1_funct_1(k4_borsuk_6,np__0) = np__0
    & k1_funct_1(k4_borsuk_6,np__1) = np__1 )).

fof(d9_borsuk_6,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
        & m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
     => ( A = k5_borsuk_6
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(k5_topmetr))
           => ( ( r1_xreal_0(B,k6_real_1(np__1,np__2))
               => k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k3_xcmplx_0(k6_real_1(np__1,np__2),B) )
              & ( r1_xreal_0(B,k6_real_1(np__3,np__4))
               => ( r1_xreal_0(B,k6_real_1(np__1,np__2))
                  | k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k6_xcmplx_0(B,k6_real_1(np__1,np__4)) ) )
              & ( ~ r1_xreal_0(B,k6_real_1(np__3,np__4))
               => k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k6_xcmplx_0(k3_xcmplx_0(np__2,B),np__1) ) ) ) ) ) )).

fof(t57_borsuk_6,axiom,
    ( k1_funct_1(k5_borsuk_6,np__0) = np__0
    & k1_funct_1(k5_borsuk_6,np__1) = np__1 )).

fof(t58_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( ( v5_seqm_3(E)
                        & m1_borsuk_2(E,A,C,C) )
                     => ( r1_borsuk_6(A,B,C)
                       => k2_borsuk_6(A,B,C,D,k3_borsuk_6) = k1_borsuk_2(A,B,C,C,D,E) ) ) ) ) ) ) )).

fof(t59_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( ( v5_seqm_3(E)
                        & m1_borsuk_2(E,A,B,B) )
                     => ( r1_borsuk_6(A,B,C)
                       => k2_borsuk_6(A,B,C,D,k4_borsuk_6) = k1_borsuk_2(A,B,B,C,E,D) ) ) ) ) ) ) )).

fof(t60_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_borsuk_2(F,A,B,C)
                         => ! [G] :
                              ( m1_borsuk_2(G,A,C,D)
                             => ! [H] :
                                  ( m1_borsuk_2(H,A,D,E)
                                 => ( ( r1_borsuk_6(A,B,C)
                                      & r1_borsuk_6(A,C,D)
                                      & r1_borsuk_6(A,D,E) )
                                   => k2_borsuk_6(A,B,E,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,F,G),H),k5_borsuk_6) = k1_borsuk_2(A,B,C,E,F,k1_borsuk_2(A,C,D,E,G,H)) ) ) ) ) ) ) ) ) ) )).

fof(d10_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
     => ( A = k6_borsuk_6
      <=> ! [B] :
            ( r2_hidden(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u1_struct_0(k5_topmetr))
                & ? [D] :
                    ( m1_subset_1(D,u1_struct_0(k5_topmetr))
                    & B = k8_borsuk_1(k5_topmetr,k5_topmetr,C,D)
                    & r1_xreal_0(D,k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,C))) ) ) ) ) ) )).

fof(d11_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
     => ( A = k7_borsuk_6
      <=> ! [B] :
            ( r2_hidden(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u1_struct_0(k5_topmetr))
                & ? [D] :
                    ( m1_subset_1(D,u1_struct_0(k5_topmetr))
                    & B = k8_borsuk_1(k5_topmetr,k5_topmetr,C,D)
                    & r1_xreal_0(k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,C)),D)
                    & r1_xreal_0(k6_xcmplx_0(k3_xcmplx_0(np__2,C),np__1),D) ) ) ) ) ) )).

fof(d12_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr))))
     => ( A = k8_borsuk_6
      <=> ! [B] :
            ( r2_hidden(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u1_struct_0(k5_topmetr))
                & ? [D] :
                    ( m1_subset_1(D,u1_struct_0(k5_topmetr))
                    & B = k8_borsuk_1(k5_topmetr,k5_topmetr,C,D)
                    & r1_xreal_0(D,k6_xcmplx_0(k3_xcmplx_0(np__2,C),np__1)) ) ) ) ) ) )).

fof(t64_borsuk_6,axiom,(
    k4_subset_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),k4_subset_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),k6_borsuk_6,k7_borsuk_6),k8_borsuk_6) = k12_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(np__0,np__1),k1_rcomp_1(np__0,np__1)) )).

fof(t67_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
     => ( r2_hidden(A,k6_borsuk_6)
       => r1_xreal_0(k1_mcart_1(A),k6_real_1(np__1,np__2)) ) ) )).

fof(t68_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
     => ( r2_hidden(A,k8_borsuk_6)
       => r1_xreal_0(k6_real_1(np__1,np__2),k1_mcart_1(A)) ) ) )).

fof(t69_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => r2_hidden(k4_tarski(np__0,A),k6_borsuk_6) ) )).

fof(t70_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(k4_tarski(np__0,A),k7_borsuk_6)
     => A = np__1 ) )).

fof(t71_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(k4_tarski(A,np__1),k8_borsuk_6)
     => A = np__1 ) )).

fof(t72_borsuk_6,axiom,(
    r2_hidden(k4_tarski(np__0,np__1),k7_borsuk_6) )).

fof(t73_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => r2_hidden(k4_tarski(A,np__1),k7_borsuk_6) ) )).

fof(t74_borsuk_6,axiom,
    ( r2_hidden(k4_tarski(k6_real_1(np__1,np__2),np__0),k8_borsuk_6)
    & r2_hidden(k4_tarski(np__1,np__1),k8_borsuk_6) )).

fof(t75_borsuk_6,axiom,(
    r2_hidden(k4_tarski(k6_real_1(np__1,np__2),np__0),k7_borsuk_6) )).

fof(t76_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => r2_hidden(k4_tarski(np__1,A),k8_borsuk_6) ) )).

fof(t77_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ( r1_xreal_0(k6_real_1(np__1,np__2),A)
       => r2_hidden(k4_tarski(A,np__0),k8_borsuk_6) ) ) )).

fof(t78_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ( r1_xreal_0(A,k6_real_1(np__1,np__2))
       => r2_hidden(k4_tarski(A,np__0),k6_borsuk_6) ) ) )).

fof(t79_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ( ~ r1_xreal_0(k6_real_1(np__1,np__2),A)
       => ( ~ r2_hidden(k4_tarski(A,np__0),k7_borsuk_6)
          & ~ r2_hidden(k4_tarski(A,np__0),k8_borsuk_6) ) ) ) )).

fof(t80_borsuk_6,axiom,(
    k5_subset_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),k6_borsuk_6,k8_borsuk_6) = k1_tarski(k4_tarski(k6_real_1(np__1,np__2),np__0)) )).

fof(t81_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_borsuk_2(F,A,B,C)
                         => ! [G] :
                              ( m1_borsuk_2(G,A,C,D)
                             => ! [H] :
                                  ( m1_borsuk_2(H,A,D,E)
                                 => ( ( r1_borsuk_6(A,B,C)
                                      & r1_borsuk_6(A,C,D)
                                      & r1_borsuk_6(A,D,E) )
                                   => r3_borsuk_2(A,B,E,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,F,G),H),k1_borsuk_2(A,B,C,E,F,k1_borsuk_2(A,C,D,E,G,H))) ) ) ) ) ) ) ) ) ) )).

fof(t82_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_borsuk_2(F,A,B,C)
                         => ! [G] :
                              ( m1_borsuk_2(G,A,C,D)
                             => ! [H] :
                                  ( m1_borsuk_2(H,A,D,E)
                                 => r4_borsuk_2(A,B,E,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,F,G),H),k1_borsuk_2(A,B,C,E,F,k1_borsuk_2(A,C,D,E,G,H))) ) ) ) ) ) ) ) ) )).

fof(t83_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_borsuk_2(E,A,B,C)
                     => ! [F] :
                          ( m1_borsuk_2(F,A,B,C)
                         => ! [G] :
                              ( m1_borsuk_2(G,A,C,D)
                             => ! [H] :
                                  ( m1_borsuk_2(H,A,C,D)
                                 => ( ( r1_borsuk_6(A,B,C)
                                      & r1_borsuk_6(A,C,D)
                                      & r3_borsuk_2(A,B,C,E,F)
                                      & r3_borsuk_2(A,C,D,G,H) )
                                   => r3_borsuk_2(A,B,D,k1_borsuk_2(A,B,C,D,E,G),k1_borsuk_2(A,B,C,D,F,H)) ) ) ) ) ) ) ) ) ) )).

fof(t84_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_borsuk_2(E,A,B,C)
                     => ! [F] :
                          ( m1_borsuk_2(F,A,B,C)
                         => ! [G] :
                              ( m1_borsuk_2(G,A,C,D)
                             => ! [H] :
                                  ( m1_borsuk_2(H,A,C,D)
                                 => ( ( r4_borsuk_2(A,B,C,E,F)
                                      & r4_borsuk_2(A,C,D,G,H) )
                                   => r4_borsuk_2(A,B,D,k1_borsuk_2(A,B,C,D,E,G),k1_borsuk_2(A,B,C,D,F,H)) ) ) ) ) ) ) ) ) ) )).

fof(t85_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( m1_borsuk_2(E,A,B,C)
                     => ( ( r1_borsuk_6(A,B,C)
                          & r3_borsuk_2(A,B,C,D,E) )
                       => r3_borsuk_2(A,C,B,k2_borsuk_2(A,B,C,D),k2_borsuk_2(A,B,C,E)) ) ) ) ) ) ) )).

fof(t86_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( m1_borsuk_2(E,A,B,C)
                     => ( r4_borsuk_2(A,B,C,D,E)
                       => r4_borsuk_2(A,C,B,k2_borsuk_2(A,B,C,D),k2_borsuk_2(A,B,C,E)) ) ) ) ) ) ) )).

fof(t87_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( m1_borsuk_2(E,A,B,C)
                     => ! [F] :
                          ( m1_borsuk_2(F,A,B,C)
                         => ( ( r3_borsuk_2(A,B,C,D,E)
                              & r3_borsuk_2(A,B,C,E,F) )
                           => r3_borsuk_2(A,B,C,D,F) ) ) ) ) ) ) ) )).

fof(t88_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( ( v5_seqm_3(E)
                        & m1_borsuk_2(E,A,C,C) )
                     => ( r1_borsuk_6(A,B,C)
                       => r3_borsuk_2(A,B,C,k1_borsuk_2(A,B,C,C,D,E),D) ) ) ) ) ) ) )).

fof(t89_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( ( v5_seqm_3(E)
                        & m1_borsuk_2(E,A,C,C) )
                     => r4_borsuk_2(A,B,C,k1_borsuk_2(A,B,C,C,D,E),D) ) ) ) ) ) )).

fof(t90_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( ( v5_seqm_3(E)
                        & m1_borsuk_2(E,A,B,B) )
                     => ( r1_borsuk_6(A,B,C)
                       => r3_borsuk_2(A,B,C,k1_borsuk_2(A,B,B,C,E,D),D) ) ) ) ) ) ) )).

fof(t91_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( ( v5_seqm_3(E)
                        & m1_borsuk_2(E,A,B,B) )
                     => r4_borsuk_2(A,B,C,k1_borsuk_2(A,B,B,C,E,D),D) ) ) ) ) ) )).

fof(t92_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( ( v5_seqm_3(E)
                        & m1_borsuk_2(E,A,B,B) )
                     => ( r1_borsuk_6(A,B,C)
                       => r3_borsuk_2(A,B,B,k1_borsuk_2(A,B,C,B,D,k2_borsuk_2(A,B,C,D)),E) ) ) ) ) ) ) )).

fof(t93_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( ( v5_seqm_3(E)
                        & m1_borsuk_2(E,A,B,B) )
                     => r4_borsuk_2(A,B,B,k1_borsuk_2(A,B,C,B,D,k2_borsuk_2(A,B,C,D)),E) ) ) ) ) ) )).

fof(t94_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( ( v5_seqm_3(E)
                        & m1_borsuk_2(E,A,C,C) )
                     => ( r1_borsuk_6(A,B,C)
                       => r3_borsuk_2(A,C,C,k1_borsuk_2(A,C,B,C,k2_borsuk_2(A,B,C,D),D),E) ) ) ) ) ) ) )).

fof(t95_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v1_borsuk_2(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( ( v5_seqm_3(E)
                        & m1_borsuk_2(E,A,C,C) )
                     => r4_borsuk_2(A,C,C,k1_borsuk_2(A,C,B,C,k2_borsuk_2(A,B,C,D),D),E) ) ) ) ) ) )).

fof(t96_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v5_seqm_3(C)
                & m1_borsuk_2(C,A,B,B) )
             => ! [D] :
                  ( ( v5_seqm_3(D)
                    & m1_borsuk_2(D,A,B,B) )
                 => r3_borsuk_2(A,B,B,C,D) ) ) ) ) )).

fof(d13_borsuk_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_borsuk_2(D,A,B,C)
                 => ! [E] :
                      ( m1_borsuk_2(E,A,B,C)
                     => ( r3_borsuk_2(A,B,C,D,E)
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A))
                              & m2_relset_1(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A)) )
                           => ( m1_borsuk_6(F,A,B,C,D,E)
                            <=> ( v5_pre_topc(F,k6_borsuk_1(k5_topmetr,k5_topmetr),A)
                                & ! [G] :
                                    ( m1_subset_1(G,u1_struct_0(k5_topmetr))
                                   => ( k1_binop_1(F,G,np__0) = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),D,G)
                                      & k1_binop_1(F,G,np__1) = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),E,G)
                                      & ! [H] :
                                          ( m1_subset_1(H,u1_struct_0(k5_topmetr))
                                         => ( k1_binop_1(F,np__0,H) = B
                                            & k1_binop_1(F,np__1,H) = C ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(s1_borsuk_6,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s1_borsuk_6)
         => ( ~ ( p1_s1_borsuk_6(A)
                & p2_s1_borsuk_6(A) )
            & ~ ( p1_s1_borsuk_6(A)
                & p3_s1_borsuk_6(A) )
            & ~ ( p2_s1_borsuk_6(A)
                & p3_s1_borsuk_6(A) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s1_borsuk_6)
         => ~ ( ~ p1_s1_borsuk_6(A)
              & ~ p2_s1_borsuk_6(A)
              & ~ p3_s1_borsuk_6(A) ) ) )
   => ? [A] :
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = f1_s1_borsuk_6
        & ! [B] :
            ( m1_subset_1(B,f1_s1_borsuk_6)
           => ( ( p1_s1_borsuk_6(B)
               => k1_funct_1(A,B) = f2_s1_borsuk_6(B) )
              & ( p2_s1_borsuk_6(B)
               => k1_funct_1(A,B) = f3_s1_borsuk_6(B) )
              & ( p3_s1_borsuk_6(B)
               => k1_funct_1(A,B) = f4_s1_borsuk_6(B) ) ) ) ) )).

fof(dt_m1_borsuk_6,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_borsuk_2(D,A,B,C)
        & m1_borsuk_2(E,A,B,C) )
     => ! [F] :
          ( m1_borsuk_6(F,A,B,C,D,E)
         => ( v1_funct_1(F)
            & v1_funct_2(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A))
            & m2_relset_1(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A)) ) ) ) )).

fof(existence_m1_borsuk_6,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_borsuk_2(D,A,B,C)
        & m1_borsuk_2(E,A,B,C) )
     => ? [F] : m1_borsuk_6(F,A,B,C,D,E) ) )).

fof(symmetry_r1_borsuk_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r1_borsuk_6(A,B,C)
       => r1_borsuk_6(A,C,B) ) ) )).

fof(reflexivity_r1_borsuk_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r1_borsuk_6(A,B,B) ) )).

fof(redefinition_r1_borsuk_6,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r1_borsuk_6(A,B,C)
      <=> r1_borsuk_2(A,B,C) ) ) )).

fof(dt_k1_borsuk_6,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => ( v1_funct_1(k1_borsuk_6(A,B,C,D))
        & v1_funct_2(k1_borsuk_6(A,B,C,D),u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D)))
        & m2_relset_1(k1_borsuk_6(A,B,C,D),u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(C,D))) ) ) )).

fof(dt_k2_borsuk_6,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_borsuk_2(D,A,B,C)
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
        & v5_pre_topc(E,k5_topmetr,k5_topmetr)
        & m1_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )
     => m1_borsuk_2(k2_borsuk_6(A,B,C,D,E),A,B,C) ) )).

fof(dt_k3_borsuk_6,axiom,
    ( v1_funct_1(k3_borsuk_6)
    & v1_funct_2(k3_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
    & m2_relset_1(k3_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )).

fof(dt_k4_borsuk_6,axiom,
    ( v1_funct_1(k4_borsuk_6)
    & v1_funct_2(k4_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
    & m2_relset_1(k4_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )).

fof(dt_k5_borsuk_6,axiom,
    ( v1_funct_1(k5_borsuk_6)
    & v1_funct_2(k5_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr))
    & m2_relset_1(k5_borsuk_6,u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )).

fof(dt_k6_borsuk_6,axiom,(
    m1_subset_1(k6_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) )).

fof(dt_k7_borsuk_6,axiom,(
    m1_subset_1(k7_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) )).

fof(dt_k8_borsuk_6,axiom,(
    m1_subset_1(k8_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) )).

fof(t14_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,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))))
         => ( ( A = a_0_0_borsuk_6
              & B = a_0_1_borsuk_6 )
           => k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k2_jgraph_2(np__1,np__0,k6_real_1(np__1,np__2),k6_real_1(np__1,np__2)),A) = B ) ) ) )).

fof(t15_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,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))))
         => ( ( A = a_0_2_borsuk_6
              & B = a_0_3_borsuk_6 )
           => k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k2_jgraph_2(np__1,np__0,k6_real_1(np__1,np__2),k6_real_1(np__1,np__2)),A) = B ) ) ) )).

fof(t16_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,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))))
         => ( ( A = a_0_4_borsuk_6
              & B = a_0_5_borsuk_6 )
           => k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k2_jgraph_2(np__1,np__0,k6_real_1(np__1,np__2),k1_real_1(k6_real_1(np__1,np__2))),A) = B ) ) ) )).

fof(t17_borsuk_6,axiom,(
    ! [A] :
      ( m1_subset_1(A,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))))
         => ( ( A = a_0_6_borsuk_6
              & B = a_0_7_borsuk_6 )
           => k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),k2_jgraph_2(np__1,np__0,k6_real_1(np__1,np__2),k1_real_1(k6_real_1(np__1,np__2))),A) = B ) ) ) )).

fof(t19_borsuk_6,axiom,
    ( v4_pre_topc(a_0_0_borsuk_6,k15_euclid(np__2))
    & m1_subset_1(a_0_0_borsuk_6,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )).

fof(t20_borsuk_6,axiom,
    ( v4_pre_topc(a_0_2_borsuk_6,k15_euclid(np__2))
    & m1_subset_1(a_0_2_borsuk_6,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )).

fof(t21_borsuk_6,axiom,
    ( v4_pre_topc(a_0_6_borsuk_6,k15_euclid(np__2))
    & m1_subset_1(a_0_6_borsuk_6,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )).

fof(t22_borsuk_6,axiom,
    ( v4_pre_topc(a_0_4_borsuk_6,k15_euclid(np__2))
    & m1_subset_1(a_0_4_borsuk_6,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )).

fof(t23_borsuk_6,axiom,
    ( v4_pre_topc(a_0_8_borsuk_6,k15_euclid(np__2))
    & m1_subset_1(a_0_8_borsuk_6,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )).

fof(t25_borsuk_6,axiom,
    ( v4_pre_topc(a_0_9_borsuk_6,k6_borsuk_1(k3_topmetr,k3_topmetr))
    & m1_subset_1(a_0_9_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)))) )).

fof(t26_borsuk_6,axiom,
    ( v4_pre_topc(a_0_10_borsuk_6,k6_borsuk_1(k3_topmetr,k3_topmetr))
    & m1_subset_1(a_0_10_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)))) )).

fof(t27_borsuk_6,axiom,
    ( v4_pre_topc(a_0_11_borsuk_6,k6_borsuk_1(k3_topmetr,k3_topmetr))
    & m1_subset_1(a_0_11_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)))) )).

fof(t28_borsuk_6,axiom,
    ( ~ v1_xboole_0(a_0_12_borsuk_6)
    & v4_pre_topc(a_0_12_borsuk_6,k6_borsuk_1(k5_topmetr,k5_topmetr))
    & m1_subset_1(a_0_12_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) )).

fof(t29_borsuk_6,axiom,
    ( ~ v1_xboole_0(a_0_13_borsuk_6)
    & v4_pre_topc(a_0_13_borsuk_6,k6_borsuk_1(k5_topmetr,k5_topmetr))
    & m1_subset_1(a_0_13_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) )).

fof(t30_borsuk_6,axiom,
    ( ~ v1_xboole_0(a_0_14_borsuk_6)
    & v4_pre_topc(a_0_14_borsuk_6,k6_borsuk_1(k5_topmetr,k5_topmetr))
    & m1_subset_1(a_0_14_borsuk_6,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))) )).

fof(t61_borsuk_6,axiom,(
    k6_borsuk_6 = a_0_12_borsuk_6 )).

fof(t62_borsuk_6,axiom,(
    k7_borsuk_6 = a_0_13_borsuk_6 )).

fof(t63_borsuk_6,axiom,(
    k8_borsuk_6 = a_0_14_borsuk_6 )).

fof(t65_borsuk_6,axiom,(
    k5_subset_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),k6_borsuk_6,k7_borsuk_6) = a_0_15_borsuk_6 )).

fof(t66_borsuk_6,axiom,(
    k5_subset_1(u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),k8_borsuk_6,k7_borsuk_6) = a_0_16_borsuk_6 )).

fof(fraenkel_a_0_0_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k22_euclid(B),k5_real_1(k4_real_1(np__2,k21_euclid(B)),np__1)) ) ) )).

fof(fraenkel_a_0_1_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_1_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k22_euclid(B),k21_euclid(B)) ) ) )).

fof(fraenkel_a_0_2_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_2_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k5_real_1(k4_real_1(np__2,k21_euclid(B)),np__1),k22_euclid(B)) ) ) )).

fof(fraenkel_a_0_3_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_3_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k21_euclid(B),k22_euclid(B)) ) ) )).

fof(fraenkel_a_0_4_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_4_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k5_real_1(np__1,k4_real_1(np__2,k21_euclid(B))),k22_euclid(B)) ) ) )).

fof(fraenkel_a_0_5_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_5_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k1_real_1(k21_euclid(B)),k22_euclid(B)) ) ) )).

fof(fraenkel_a_0_6_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_6_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k22_euclid(B),k5_real_1(np__1,k4_real_1(np__2,k21_euclid(B)))) ) ) )).

fof(fraenkel_a_0_7_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_7_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k22_euclid(B),k1_real_1(k21_euclid(B))) ) ) )).

fof(fraenkel_a_0_8_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_8_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
          & A = B
          & r1_xreal_0(k5_real_1(np__1,k4_real_1(np__2,k21_euclid(B))),k22_euclid(B))
          & r1_xreal_0(k5_real_1(k4_real_1(np__2,k21_euclid(B)),np__1),k22_euclid(B)) ) ) )).

fof(fraenkel_a_0_9_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_9_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)))
          & A = B
          & r1_xreal_0(k2_mcart_1(B),k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,k1_mcart_1(B)))) ) ) )).

fof(fraenkel_a_0_10_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_10_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)))
          & A = B
          & r1_xreal_0(k2_mcart_1(B),k6_xcmplx_0(k3_xcmplx_0(np__2,k1_mcart_1(B)),np__1)) ) ) )).

fof(fraenkel_a_0_11_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_11_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k3_topmetr,k3_topmetr)))
          & A = B
          & r1_xreal_0(k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,k1_mcart_1(B))),k2_mcart_1(B))
          & r1_xreal_0(k6_xcmplx_0(k3_xcmplx_0(np__2,k1_mcart_1(B)),np__1),k2_mcart_1(B)) ) ) )).

fof(fraenkel_a_0_12_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_12_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
          & A = B
          & r1_xreal_0(k2_mcart_1(B),k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,k1_mcart_1(B)))) ) ) )).

fof(fraenkel_a_0_13_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_13_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
          & A = B
          & r1_xreal_0(k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,k1_mcart_1(B))),k2_mcart_1(B))
          & r1_xreal_0(k6_xcmplx_0(k3_xcmplx_0(np__2,k1_mcart_1(B)),np__1),k2_mcart_1(B)) ) ) )).

fof(fraenkel_a_0_14_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_14_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
          & A = B
          & r1_xreal_0(k2_mcart_1(B),k6_xcmplx_0(k3_xcmplx_0(np__2,k1_mcart_1(B)),np__1)) ) ) )).

fof(fraenkel_a_0_15_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_15_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
          & A = B
          & k2_mcart_1(B) = k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,k1_mcart_1(B))) ) ) )).

fof(fraenkel_a_0_16_borsuk_6,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_16_borsuk_6)
    <=> ? [B] :
          ( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)))
          & A = B
          & k2_mcart_1(B) = k6_xcmplx_0(k3_xcmplx_0(np__2,k1_mcart_1(B)),np__1) ) ) )).
%------------------------------------------------------------------------------