SET007 Axioms: SET007+309.ax


%------------------------------------------------------------------------------
% File     : SET007+309 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : A Borsuk Theorem on Homotopy Types
% 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  159 (  19 unit)
%            Number of atoms       : 1200 ( 101 equality)
%            Maximal formula depth :   23 (   9 average)
%            Number of connectives : 1271 ( 230 ~  ;   4  |; 613  &)
%                                         (  20 <=>; 404 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   39 (   1 propositional; 0-3 arity)
%            Number of functors    :   77 (   7 constant; 0-6 arity)
%            Number of variables   :  520 (   0 singleton; 489 !;  31 ?)
%            Maximal term depth    :    7 (   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(rc1_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_eqrel_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_setfam_1(B) ) ) )).

fof(fc1_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( ~ v1_xboole_0(k3_borsuk_1(A,B,C))
        & v1_relat_1(k3_borsuk_1(A,B,C))
        & v1_funct_1(k3_borsuk_1(A,B,C))
        & v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B))
        & v5_pre_topc(k3_borsuk_1(A,B,C),A,B)
        & v1_partfun1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) ) ) )).

fof(rc2_borsuk_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ? [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
          & v5_pre_topc(C,A,B)
          & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) )).

fof(fc2_borsuk_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ( ~ v3_struct_0(k6_borsuk_1(A,B))
        & v1_pre_topc(k6_borsuk_1(A,B))
        & v2_pre_topc(k6_borsuk_1(A,B)) ) ) )).

fof(fc3_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ( ~ v1_xboole_0(k15_borsuk_1(A))
        & v1_setfam_1(k15_borsuk_1(A)) ) ) )).

fof(fc4_borsuk_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & m1_eqrel_1(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k16_borsuk_1(A,B))
        & v1_pre_topc(k16_borsuk_1(A,B))
        & v2_pre_topc(k16_borsuk_1(A,B)) ) ) )).

fof(rc3_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_borsuk_1(B,A) ) ) )).

fof(rc4_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B)
          & v2_pre_topc(B)
          & v1_borsuk_1(B,A) ) ) )).

fof(rc5_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_borsuk_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_setfam_1(B)
          & v2_borsuk_1(B,A) ) ) )).

fof(fc5_borsuk_1,axiom,
    ( ~ v3_struct_0(k22_borsuk_1)
    & v1_pre_topc(k22_borsuk_1)
    & v2_pre_topc(k22_borsuk_1) )).

fof(t1_borsuk_1,axiom,(
    $true )).

fof(t2_borsuk_1,axiom,(
    $true )).

fof(t3_borsuk_1,axiom,(
    $true )).

fof(t4_borsuk_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k3_funct_2(A,A,k6_partfun1(A),B) = B ) )).

fof(t5_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(A,k10_relat_1(C,B))
       => r1_tarski(k9_relat_1(C,A),B) ) ) )).

fof(t6_borsuk_1,axiom,(
    ! [A,B,C] : r1_tarski(k9_relat_1(k2_funcop_1(A,B),C),k1_tarski(B)) )).

fof(t7_borsuk_1,axiom,(
    $true )).

fof(t8_borsuk_1,axiom,(
    $true )).

fof(t9_borsuk_1,axiom,(
    ! [A,B,C] :
      ( r1_tarski(A,k2_zfmisc_1(B,C))
     => k1_funct_1(k1_funct_3(k9_funct_3(B,C)),A) = k2_funct_2(k2_zfmisc_1(B,C),B,k9_funct_3(B,C),A) ) )).

fof(t10_borsuk_1,axiom,(
    ! [A,B,C] :
      ( r1_tarski(A,k2_zfmisc_1(B,C))
     => k1_funct_1(k1_funct_3(k10_funct_3(B,C)),A) = k2_funct_2(k2_zfmisc_1(B,C),C,k10_funct_3(B,C),A) ) )).

fof(t11_borsuk_1,axiom,(
    $true )).

fof(t12_borsuk_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,k1_zfmisc_1(A))
     => ! [D] :
          ( m1_subset_1(D,k1_zfmisc_1(B))
         => ( k12_mcart_1(A,B,C,D) != k1_xboole_0
           => ( k2_funct_2(k2_zfmisc_1(A,B),A,k9_funct_3(A,B),k12_mcart_1(A,B,C,D)) = C
              & k2_funct_2(k2_zfmisc_1(A,B),B,k10_funct_3(A,B),k12_mcart_1(A,B,C,D)) = D ) ) ) ) )).

fof(t13_borsuk_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,k1_zfmisc_1(A))
     => ! [D] :
          ( m1_subset_1(D,k1_zfmisc_1(B))
         => ( k12_mcart_1(A,B,C,D) != k1_xboole_0
           => ( k1_funct_1(k1_funct_3(k9_funct_3(A,B)),k12_mcart_1(A,B,C,D)) = C
              & k1_funct_1(k1_funct_3(k10_funct_3(A,B)),k12_mcart_1(A,B,C,D)) = D ) ) ) ) )).

fof(t14_borsuk_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => ! [D] :
          ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B))))
         => ( ! [E] :
                ( r2_hidden(E,D)
               => ( r1_tarski(E,C)
                  & ? [F] :
                      ( m1_subset_1(F,k1_zfmisc_1(A))
                      & ? [G] :
                          ( m1_subset_1(G,k1_zfmisc_1(B))
                          & E = k12_mcart_1(A,B,F,G) ) ) ) )
           => r1_tarski(k2_zfmisc_1(k3_tarski(k9_relat_1(k1_funct_3(k9_funct_3(A,B)),D)),k1_setfam_1(k9_relat_1(k1_funct_3(k10_funct_3(A,B)),D))),C) ) ) ) )).

fof(t15_borsuk_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => ! [D] :
          ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B))))
         => ( ! [E] :
                ( r2_hidden(E,D)
               => ( r1_tarski(E,C)
                  & ? [F] :
                      ( m1_subset_1(F,k1_zfmisc_1(A))
                      & ? [G] :
                          ( m1_subset_1(G,k1_zfmisc_1(B))
                          & E = k12_mcart_1(A,B,F,G) ) ) ) )
           => r1_tarski(k2_zfmisc_1(k1_setfam_1(k9_relat_1(k1_funct_3(k9_funct_3(A,B)),D)),k3_tarski(k9_relat_1(k1_funct_3(k10_funct_3(A,B)),D))),C) ) ) ) )).

fof(t16_borsuk_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A)))
             => k5_setfam_1(B,k2_funct_2(k1_zfmisc_1(A),k1_zfmisc_1(B),k2_funct_3(A,B,C),D)) = k2_funct_2(A,B,C,k5_setfam_1(A,D)) ) ) ) )).

fof(t18_borsuk_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( k5_setfam_1(A,B) = A
       => ! [C] :
            ( m1_subset_1(C,k1_zfmisc_1(B))
           => ! [D] :
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( D = k3_tarski(C)
                 => r1_tarski(k3_subset_1(A,D),k3_tarski(k3_subset_1(B,C))) ) ) ) ) ) )).

fof(t19_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,C)
                        & m2_relset_1(E,A,C) )
                     => ~ ( ! [F] :
                              ( m1_subset_1(F,A)
                             => ! [G] :
                                  ( m1_subset_1(G,A)
                                 => ( k8_funct_2(A,B,D,F) = k8_funct_2(A,B,D,G)
                                   => k8_funct_2(A,C,E,F) = k8_funct_2(A,C,E,G) ) ) )
                          & ! [F] :
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,B,C)
                                & m2_relset_1(F,B,C) )
                             => k7_funct_2(A,B,C,D,F) != E ) ) ) ) ) ) ) )).

fof(t20_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,C)
                            & m2_relset_1(F,B,C) )
                         => r1_tarski(k3_funct_2(A,B,E,k6_domain_1(B,D)),k3_funct_2(A,C,k7_funct_2(A,B,C,E,F),k6_domain_1(C,k8_funct_2(B,C,F,D)))) ) ) ) ) ) ) )).

fof(t21_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( m1_subset_1(F,C)
                         => k8_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k1_domain_1(A,C,E,F)) = k1_domain_1(B,C,k8_funct_2(A,B,D,E),F) ) ) ) ) ) ) )).

fof(t22_borsuk_1,axiom,(
    $true )).

fof(t23_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(C))
                         => k2_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k12_mcart_1(A,C,E,F)) = k12_mcart_1(B,C,k2_funct_2(A,B,D,E),F) ) ) ) ) ) ) )).

fof(t24_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( m1_subset_1(F,C)
                         => k3_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k6_domain_1(k2_zfmisc_1(B,C),k1_domain_1(B,C,E,F))) = k12_mcart_1(A,C,k3_funct_2(A,B,D,k6_domain_1(B,E)),k6_domain_1(C,F)) ) ) ) ) ) ) )).

fof(t25_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(B))
             => m1_subset_1(k3_tarski(C),k1_zfmisc_1(A)) ) ) ) )).

fof(t26_borsuk_1,axiom,(
    ! [A,B] :
      ( m1_eqrel_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(B))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(B))
             => k3_tarski(k5_subset_1(B,C,D)) = k3_xboole_0(k3_tarski(C),k3_tarski(D)) ) ) ) )).

fof(t27_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_eqrel_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(B))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ( D = k3_tarski(C)
                   => k3_subset_1(A,D) = k3_tarski(k3_subset_1(B,C)) ) ) ) ) ) )).

fof(t28_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v3_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,A,A)
            & m2_relset_1(B,A,A) )
         => ~ v1_xboole_0(k8_eqrel_1(A,B)) ) ) )).

fof(d1_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( C = k2_borsuk_1(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => r2_hidden(D,k8_funct_2(A,B,C,D)) ) ) ) ) ) )).

fof(t29_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(A),B)
                 => ( r2_hidden(C,D)
                   => D = k8_funct_2(A,B,k2_borsuk_1(A,B),C) ) ) ) ) ) )).

fof(t30_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(A),B)
             => C = k3_funct_2(A,B,k2_borsuk_1(A,B),k6_domain_1(B,C)) ) ) ) )).

fof(t31_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(B))
             => k3_funct_2(A,B,k2_borsuk_1(A,B),C) = k3_tarski(C) ) ) ) )).

fof(t32_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k1_zfmisc_1(A),B)
             => ? [D] :
                  ( m1_subset_1(D,A)
                  & k8_funct_2(A,B,k2_borsuk_1(A,B),D) = C ) ) ) ) )).

fof(t33_borsuk_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ( ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(A))
                   => ( r2_hidden(D,B)
                     => ( r1_xboole_0(D,C)
                        | r1_tarski(D,C) ) ) )
               => C = k3_funct_2(A,B,k2_borsuk_1(A,B),k2_funct_2(A,B,k2_borsuk_1(A,B),C)) ) ) ) ) )).

fof(t34_borsuk_1,axiom,(
    $true )).

fof(t35_borsuk_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_pre_topc(B,A)
         => r1_tarski(u1_struct_0(B),u1_struct_0(A)) ) ) )).

fof(d2_borsuk_1,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] :
              ( ( 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)) )
             => ( v5_pre_topc(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_connsp_2(E,B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D))
                       => ? [F] :
                            ( m1_connsp_2(F,A,D)
                            & r1_tarski(k4_pre_topc(A,B,C,F),E) ) ) ) ) ) ) ) )).

fof(d3_borsuk_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_struct_0(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k3_borsuk_1(A,B,C) = k1_borsuk_1(u1_struct_0(B),u1_struct_0(A),C) ) ) ) )).

fof(t36_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => v5_pre_topc(k3_borsuk_1(B,A,C),B,A) ) ) ) )).

fof(t37_borsuk_1,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_pre_topc(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => r1_tarski(k5_pre_topc(A,B,C,k1_tops_1(B,D)),k1_tops_1(A,k5_pre_topc(A,B,C,D))) ) ) ) ) )).

fof(t38_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
                    & v5_pre_topc(D,B,A)
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ! [E] :
                      ( m1_connsp_2(E,A,C)
                     => m2_connsp_2(k5_pre_topc(B,A,D,E),B,k5_pre_topc(B,A,D,k1_struct_0(A,C))) ) ) ) ) ) )).

fof(t39_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m2_connsp_2(D,A,C)
                 => ( r1_tarski(B,C)
                   => m2_connsp_2(D,A,B) ) ) ) ) ) )).

fof(t40_borsuk_1,axiom,(
    $true )).

fof(t41_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v6_compts_1(k1_struct_0(A,B),A) ) ) )).

fof(t42_borsuk_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( C = D
                   => ( v6_compts_1(C,A)
                    <=> v6_compts_1(D,B) ) ) ) ) ) ) )).

fof(d4_borsuk_1,axiom,(
    $true )).

fof(t43_borsuk_1,axiom,(
    $true )).

fof(t44_borsuk_1,axiom,(
    $true )).

fof(t45_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
             => ( v3_pre_topc(C,k6_borsuk_1(A,B))
              <=> ? [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))
                    & C = k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),D)
                    & ! [E] :
                        ~ ( r2_hidden(E,D)
                          & ! [F] :
                              ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                             => ! [G] :
                                  ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B)))
                                 => ~ ( E = k12_mcart_1(u1_struct_0(A),u1_struct_0(B),F,G)
                                      & v3_pre_topc(F,A)
                                      & v3_pre_topc(G,B) ) ) ) ) ) ) ) ) ) )).

fof(t46_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( v3_pre_topc(C,A)
                      & v3_pre_topc(D,B) )
                   => v3_pre_topc(k7_borsuk_1(A,B,C,D),k6_borsuk_1(A,B)) ) ) ) ) ) )).

fof(t47_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => k1_tops_1(k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)) = k7_borsuk_1(A,B,k1_tops_1(A,C),k1_tops_1(B,D)) ) ) ) ) )).

fof(t48_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_connsp_2(E,A,C)
                     => ! [F] :
                          ( m1_connsp_2(F,B,D)
                         => m1_connsp_2(k7_borsuk_1(A,B,E,F),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)) ) ) ) ) ) ) )).

fof(t49_borsuk_1,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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ! [E] :
                      ( m2_connsp_2(E,A,C)
                     => ! [F] :
                          ( m2_connsp_2(F,B,D)
                         => m2_connsp_2(k7_borsuk_1(A,B,E,F),k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)) ) ) ) ) ) ) )).

fof(t50_borsuk_1,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)))
             => ? [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                  & ? [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                      & C = k8_borsuk_1(A,B,D,E) ) ) ) ) ) )).

fof(t51_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
             => v1_tops_2(k11_borsuk_1(A,B,C),k6_borsuk_1(A,B)) ) ) ) )).

fof(t52_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
                 => ( r1_tarski(C,D)
                   => r1_tarski(k11_borsuk_1(A,B,C),k11_borsuk_1(A,B,D)) ) ) ) ) ) )).

fof(t53_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
             => r1_tarski(k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C)),C) ) ) ) )).

fof(t54_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
             => ( v3_pre_topc(C,k6_borsuk_1(A,B))
               => C = k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C)) ) ) ) ) )).

fof(t55_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
             => k1_tops_1(k6_borsuk_1(A,B),C) = k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C)) ) ) ) )).

fof(d7_borsuk_1,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) )
         => k12_borsuk_1(A,B) = k2_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B))) ) ) )).

fof(d8_borsuk_1,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) )
         => k13_borsuk_1(A,B) = k2_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B))) ) ) )).

fof(t56_borsuk_1,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,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))
                 => ( ! [E] :
                        ( r2_hidden(E,D)
                       => ( r1_tarski(E,C)
                          & ? [F] :
                              ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                              & ? [G] :
                                  ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B)))
                                  & E = k7_borsuk_1(A,B,F,G) ) ) ) )
                   => r1_tarski(k7_borsuk_1(A,B,k5_setfam_1(u1_struct_0(A),k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),D)),k6_setfam_1(u1_struct_0(B),k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),D))),C) ) ) ) ) ) )).

fof(t57_borsuk_1,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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))
             => ! [D] :
                  ~ ( r2_hidden(D,k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),C))
                    & ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
                       => ~ ( r2_hidden(E,C)
                            & D = k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B)),E) ) ) ) ) ) ) )).

fof(t58_borsuk_1,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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))
             => ! [D] :
                  ~ ( r2_hidden(D,k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),C))
                    & ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
                       => ~ ( r2_hidden(E,C)
                            & D = k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),E) ) ) ) ) ) ) )).

fof(t59_borsuk_1,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,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
             => ( v3_pre_topc(C,k6_borsuk_1(A,B))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                       => ( ( D = k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B)),C)
                           => v3_pre_topc(D,A) )
                          & ( E = k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),C)
                           => v3_pre_topc(E,B) ) ) ) ) ) ) ) ) )).

fof(t60_borsuk_1,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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))
             => ( v1_tops_2(C,k6_borsuk_1(A,B))
               => ( v1_tops_2(k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C),A)
                  & v1_tops_2(k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C),B) ) ) ) ) ) )).

fof(t61_borsuk_1,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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))
             => ( ( k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C) = k1_xboole_0
                  | k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C) = k1_xboole_0 )
               => C = k1_xboole_0 ) ) ) ) )).

fof(t62_borsuk_1,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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
                     => ( r1_compts_1(k6_borsuk_1(A,B),C,k7_borsuk_1(A,B,D,E))
                       => ( ( E != k1_xboole_0
                           => r1_compts_1(A,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C),D) )
                          & ( D != k1_xboole_0
                           => r1_compts_1(B,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C),E) ) ) ) ) ) ) ) ) )).

fof(t63_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( r1_compts_1(A,C,D)
                      & ! [E] :
                          ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
                         => ~ ( r1_tarski(E,C)
                              & r1_compts_1(A,E,D)
                              & ! [F] :
                                  ~ ( r2_hidden(F,E)
                                    & r1_xboole_0(F,D) ) ) ) ) ) ) ) ) )).

fof(t64_borsuk_1,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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))
                 => ~ ( v1_finset_1(C)
                      & r1_tarski(C,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),D))
                      & ! [E] :
                          ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))
                         => ~ ( r1_tarski(E,D)
                              & v1_finset_1(E)
                              & C = k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),E) ) ) ) ) ) ) ) )).

fof(t65_borsuk_1,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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( k7_borsuk_1(A,B,C,D) != k1_xboole_0
                   => ( k8_funct_2(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)) = C
                      & k8_funct_2(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)) = D ) ) ) ) ) ) )).

fof(t66_borsuk_1,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) )
         => ( k1_funct_1(k12_borsuk_1(A,B),k1_xboole_0) = k1_xboole_0
            & k1_funct_1(k13_borsuk_1(A,B),k1_xboole_0) = k1_xboole_0 ) ) ) )).

fof(t67_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( v6_compts_1(D,B)
                   => ! [E] :
                        ( m2_connsp_2(E,k6_borsuk_1(B,A),k7_borsuk_1(B,A,D,k1_struct_0(A,C)))
                       => ? [F] :
                            ( m2_connsp_2(F,B,D)
                            & ? [G] :
                                ( m1_connsp_2(G,A,C)
                                & r1_tarski(k10_borsuk_1(B,A,D,C,F,G),E) ) ) ) ) ) ) ) ) )).

fof(d9_borsuk_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => k15_borsuk_1(A) = k8_eqrel_1(u1_struct_0(A),k6_partfun1(u1_struct_0(A))) ) )).

fof(t68_borsuk_1,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)))
         => ~ ( r2_hidden(B,k15_borsuk_1(A))
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => B != k1_struct_0(A,C) ) ) ) ) )).

fof(t69_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(B))
             => ( r2_hidden(k3_tarski(C),u1_pre_topc(A))
              <=> r2_hidden(C,u1_pre_topc(k16_borsuk_1(A,B))) ) ) ) ) )).

fof(d11_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,u1_struct_0(A)) )
         => k17_borsuk_1(A,B) = k2_borsuk_1(u1_struct_0(A),B) ) ) )).

fof(t70_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_hidden(C,k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)),k17_borsuk_1(A,B),C)) ) ) ) )).

fof(t71_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k16_borsuk_1(A,B)))
             => ? [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                  & k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)),k17_borsuk_1(A,B),D) = C ) ) ) ) )).

fof(t72_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,u1_struct_0(A)) )
         => k2_relat_1(k17_borsuk_1(A,B)) = u1_struct_0(k16_borsuk_1(A,B)) ) ) )).

fof(t73_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_eqrel_1(C,u1_struct_0(B)) )
             => r1_tarski(C,k18_borsuk_1(A,B,C)) ) ) ) )).

fof(t74_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_eqrel_1(C,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( r2_hidden(D,k18_borsuk_1(A,B,C))
                      & ~ r2_hidden(D,C)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( ~ r2_hidden(E,k2_pre_topc(B))
                              & D = k1_struct_0(A,E) ) ) ) ) ) ) ) )).

fof(t75_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_eqrel_1(C,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ~ r2_hidden(D,u1_struct_0(B))
                   => r2_hidden(k1_struct_0(A,D),k18_borsuk_1(A,B,C)) ) ) ) ) ) )).

fof(t76_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_eqrel_1(C,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_hidden(D,u1_struct_0(B))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D) = k1_funct_1(k17_borsuk_1(B,C),D) ) ) ) ) ) )).

fof(t77_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_eqrel_1(C,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ~ r2_hidden(D,u1_struct_0(B))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D) = k1_struct_0(A,D) ) ) ) ) ) )).

fof(t78_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_eqrel_1(C,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D) = k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),E)
                       => ( r2_hidden(D,u1_struct_0(B))
                          | D = E ) ) ) ) ) ) ) )).

fof(t79_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_eqrel_1(C,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D),u1_struct_0(k16_borsuk_1(B,C)))
                   => r2_hidden(D,u1_struct_0(B)) ) ) ) ) ) )).

fof(t80_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_eqrel_1(C,u1_struct_0(B)) )
             => ! [D] :
                  ( r2_hidden(D,u1_struct_0(B))
                 => r2_hidden(k1_funct_1(k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D),u1_struct_0(k16_borsuk_1(B,C))) ) ) ) ) )).

fof(d13_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,u1_struct_0(A)) )
         => ( m1_borsuk_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => ! [D] :
                      ( m2_connsp_2(D,A,C)
                     => ? [E] :
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                          & v3_pre_topc(E,A)
                          & r1_tarski(C,E)
                          & r1_tarski(E,D)
                          & ! [F] :
                              ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                             => ( r2_hidden(F,B)
                               => ( r1_xboole_0(F,E)
                                  | r1_tarski(F,E) ) ) ) ) ) ) ) ) ) ) )).

fof(t81_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_borsuk_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k16_borsuk_1(A,B)))
             => ! [D] :
                  ( m2_connsp_2(D,A,k5_pre_topc(A,k16_borsuk_1(A,B),k17_borsuk_1(A,B),k1_struct_0(k16_borsuk_1(A,B),C)))
                 => m1_connsp_2(k4_pre_topc(A,k16_borsuk_1(A,B),k17_borsuk_1(A,B),D),k16_borsuk_1(A,B),C) ) ) ) ) )).

fof(t82_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => m1_borsuk_1(k15_borsuk_1(A),A) ) )).

fof(d14_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v1_borsuk_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( C = u1_struct_0(B)
                 => v4_pre_topc(C,A) ) ) ) ) ) )).

fof(d15_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_borsuk_1(B,A)
         => ( v2_borsuk_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v6_compts_1(C,A) ) ) ) ) ) )).

fof(d16_borsuk_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( A = k22_borsuk_1
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(k8_metric_1))))
           => ( B = k1_rcomp_1(np__0,np__1)
             => A = k3_pre_topc(k5_pcomps_1(k8_metric_1),B) ) ) ) ) )).

fof(t83_borsuk_1,axiom,(
    u1_struct_0(k22_borsuk_1) = k1_rcomp_1(np__0,np__1) )).

fof(d17_borsuk_1,axiom,(
    k23_borsuk_1 = np__0 )).

fof(d18_borsuk_1,axiom,(
    k24_borsuk_1 = np__1 )).

fof(d19_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [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)) )
             => ( v3_borsuk_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,u1_struct_0(B))
                     => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) = D ) ) ) ) ) ) )).

fof(d20_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ( r1_borsuk_1(A,B)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_pre_topc(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
                & v3_borsuk_1(C,A,B) ) ) ) ) )).

fof(d21_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ( r2_borsuk_1(A,B)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A))
                & v5_pre_topc(C,k6_borsuk_1(A,k22_borsuk_1),A)
                & m2_relset_1(C,u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A))
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,k23_borsuk_1)) = D
                      & r2_hidden(k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,k24_borsuk_1)),u1_struct_0(B))
                      & ( r2_hidden(D,u1_struct_0(B))
                       => ! [E] :
                            ( m1_subset_1(E,u1_struct_0(k22_borsuk_1))
                           => k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,E)) = D ) ) ) ) ) ) ) ) )).

fof(t84_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_borsuk_1(B,A)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( v2_borsuk_1(C,B)
                & m1_borsuk_1(C,B) )
             => ( r1_borsuk_1(A,B)
               => r1_borsuk_1(k16_borsuk_1(A,k20_borsuk_1(A,B,C)),k21_borsuk_1(A,B,C)) ) ) ) ) )).

fof(t85_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_borsuk_1(B,A)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( v2_borsuk_1(C,B)
                & m1_borsuk_1(C,B) )
             => ( r2_borsuk_1(A,B)
               => r2_borsuk_1(k16_borsuk_1(A,k20_borsuk_1(A,B,C)),k21_borsuk_1(A,B,C)) ) ) ) ) )).

fof(dt_m1_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_borsuk_1(B,A)
         => ( ~ v1_xboole_0(B)
            & m1_eqrel_1(B,u1_struct_0(A)) ) ) ) )).

fof(existence_m1_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : m1_borsuk_1(B,A) ) )).

fof(dt_k1_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => ( v1_funct_1(k1_borsuk_1(A,B,C))
        & v1_funct_2(k1_borsuk_1(A,B,C),B,A)
        & m2_relset_1(k1_borsuk_1(A,B,C),B,A) ) ) )).

fof(redefinition_k1_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => k1_borsuk_1(A,B,C) = k2_funcop_1(B,C) ) )).

fof(dt_k2_borsuk_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_eqrel_1(B,A) )
     => ( v1_funct_1(k2_borsuk_1(A,B))
        & v1_funct_2(k2_borsuk_1(A,B),A,B)
        & m2_relset_1(k2_borsuk_1(A,B),A,B) ) ) )).

fof(dt_k3_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( v1_funct_1(k3_borsuk_1(A,B,C))
        & v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B))
        & m2_relset_1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) ) ) )).

fof(dt_k4_borsuk_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
        & v5_pre_topc(D,A,B)
        & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
        & v5_pre_topc(E,B,C)
        & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
     => ( v1_funct_1(k4_borsuk_1(A,B,C,D,E))
        & v1_funct_2(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C))
        & v5_pre_topc(k4_borsuk_1(A,B,C,D,E),A,C)
        & m2_relset_1(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) ) ) )).

fof(redefinition_k4_borsuk_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
        & v5_pre_topc(D,A,B)
        & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B))
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
        & v5_pre_topc(E,B,C)
        & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
     => k4_borsuk_1(A,B,C,D,E) = k5_relat_1(D,E) ) )).

fof(dt_k5_borsuk_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
        & v5_pre_topc(D,A,B)
        & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B))
        & m1_connsp_2(E,B,C) )
     => m2_connsp_2(k5_borsuk_1(A,B,C,D,E),A,k5_pre_topc(A,B,D,k1_struct_0(B,C))) ) )).

fof(redefinition_k5_borsuk_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
        & v5_pre_topc(D,A,B)
        & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B))
        & m1_connsp_2(E,B,C) )
     => k5_borsuk_1(A,B,C,D,E) = k10_relat_1(D,E) ) )).

fof(dt_k6_borsuk_1,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ( v1_pre_topc(k6_borsuk_1(A,B))
        & v2_pre_topc(k6_borsuk_1(A,B))
        & l1_pre_topc(k6_borsuk_1(A,B)) ) ) )).

fof(dt_k7_borsuk_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => m1_subset_1(k7_borsuk_1(A,B,C,D),k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) ) )).

fof(redefinition_k7_borsuk_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => k7_borsuk_1(A,B,C,D) = k2_zfmisc_1(C,D) ) )).

fof(dt_k8_borsuk_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => m1_subset_1(k8_borsuk_1(A,B,C,D),u1_struct_0(k6_borsuk_1(A,B))) ) )).

fof(redefinition_k8_borsuk_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => k8_borsuk_1(A,B,C,D) = k4_tarski(C,D) ) )).

fof(dt_k9_borsuk_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B))
        & m1_connsp_2(E,A,C)
        & m1_connsp_2(F,B,D) )
     => m1_connsp_2(k9_borsuk_1(A,B,C,D,E,F),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)) ) )).

fof(redefinition_k9_borsuk_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B))
        & m1_connsp_2(E,A,C)
        & m1_connsp_2(F,B,D) )
     => k9_borsuk_1(A,B,C,D,E,F) = k2_zfmisc_1(E,F) ) )).

fof(dt_k10_borsuk_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(D,u1_struct_0(B))
        & m2_connsp_2(E,A,C)
        & m1_connsp_2(F,B,D) )
     => m2_connsp_2(k10_borsuk_1(A,B,C,D,E,F),k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,k1_struct_0(B,D))) ) )).

fof(redefinition_k10_borsuk_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(D,u1_struct_0(B))
        & m2_connsp_2(E,A,C)
        & m1_connsp_2(F,B,D) )
     => k10_borsuk_1(A,B,C,D,E,F) = k2_zfmisc_1(E,F) ) )).

fof(dt_k11_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) )
     => m1_subset_1(k11_borsuk_1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) ) )).

fof(dt_k12_borsuk_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ( v1_funct_1(k12_borsuk_1(A,B))
        & v1_funct_2(k12_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)))
        & m2_relset_1(k12_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A))) ) ) )).

fof(dt_k13_borsuk_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ( v1_funct_1(k13_borsuk_1(A,B))
        & v1_funct_2(k13_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)))
        & m2_relset_1(k13_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B))) ) ) )).

fof(dt_k14_borsuk_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B))
        & m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B))
        & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => m1_subset_1(k14_borsuk_1(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ) )).

fof(redefinition_k14_borsuk_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B))
        & m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B))
        & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => k14_borsuk_1(A,B,C,D) = k9_relat_1(C,D) ) )).

fof(dt_k15_borsuk_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => m1_eqrel_1(k15_borsuk_1(A),u1_struct_0(A)) ) )).

fof(dt_k16_borsuk_1,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_eqrel_1(B,u1_struct_0(A)) )
     => ( v1_pre_topc(k16_borsuk_1(A,B))
        & v2_pre_topc(k16_borsuk_1(A,B))
        & l1_pre_topc(k16_borsuk_1(A,B)) ) ) )).

fof(dt_k17_borsuk_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & m1_eqrel_1(B,u1_struct_0(A)) )
     => ( v1_funct_1(k17_borsuk_1(A,B))
        & v1_funct_2(k17_borsuk_1(A,B),u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)))
        & v5_pre_topc(k17_borsuk_1(A,B),A,k16_borsuk_1(A,B))
        & m2_relset_1(k17_borsuk_1(A,B),u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B))) ) ) )).

fof(dt_k18_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & m1_pre_topc(B,A)
        & ~ v1_xboole_0(C)
        & m1_eqrel_1(C,u1_struct_0(B)) )
     => ( ~ v1_xboole_0(k18_borsuk_1(A,B,C))
        & m1_eqrel_1(k18_borsuk_1(A,B,C),u1_struct_0(A)) ) ) )).

fof(dt_k19_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v1_borsuk_1(B,A)
        & m1_pre_topc(B,A)
        & m1_borsuk_1(C,B) )
     => m1_borsuk_1(k19_borsuk_1(A,B,C),A) ) )).

fof(redefinition_k19_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v1_borsuk_1(B,A)
        & m1_pre_topc(B,A)
        & m1_borsuk_1(C,B) )
     => k19_borsuk_1(A,B,C) = k18_borsuk_1(A,B,C) ) )).

fof(dt_k20_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v1_borsuk_1(B,A)
        & m1_pre_topc(B,A)
        & v2_borsuk_1(C,B)
        & m1_borsuk_1(C,B) )
     => ( v2_borsuk_1(k20_borsuk_1(A,B,C),A)
        & m1_borsuk_1(k20_borsuk_1(A,B,C),A) ) ) )).

fof(redefinition_k20_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v1_borsuk_1(B,A)
        & m1_pre_topc(B,A)
        & v2_borsuk_1(C,B)
        & m1_borsuk_1(C,B) )
     => k20_borsuk_1(A,B,C) = k18_borsuk_1(A,B,C) ) )).

fof(dt_k21_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v1_borsuk_1(B,A)
        & m1_pre_topc(B,A)
        & v2_borsuk_1(C,B)
        & m1_borsuk_1(C,B) )
     => ( v1_pre_topc(k21_borsuk_1(A,B,C))
        & v1_borsuk_1(k21_borsuk_1(A,B,C),k16_borsuk_1(A,k20_borsuk_1(A,B,C)))
        & m1_pre_topc(k21_borsuk_1(A,B,C),k16_borsuk_1(A,k20_borsuk_1(A,B,C))) ) ) )).

fof(redefinition_k21_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v1_borsuk_1(B,A)
        & m1_pre_topc(B,A)
        & v2_borsuk_1(C,B)
        & m1_borsuk_1(C,B) )
     => k21_borsuk_1(A,B,C) = k16_borsuk_1(B,C) ) )).

fof(dt_k22_borsuk_1,axiom,(
    l1_pre_topc(k22_borsuk_1) )).

fof(dt_k23_borsuk_1,axiom,(
    m1_subset_1(k23_borsuk_1,u1_struct_0(k22_borsuk_1)) )).

fof(dt_k24_borsuk_1,axiom,(
    m1_subset_1(k24_borsuk_1,u1_struct_0(k22_borsuk_1)) )).

fof(t17_borsuk_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k3_tarski(k5_setfam_1(A,B)) = k3_tarski(a_2_0_borsuk_1(A,B)) ) )).

fof(d5_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v1_pre_topc(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ( C = k6_borsuk_1(A,B)
              <=> ( u1_struct_0(C) = k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))
                  & u1_pre_topc(C) = a_3_0_borsuk_1(A,B,C) ) ) ) ) ) )).

fof(d6_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))
             => k11_borsuk_1(A,B,C) = a_3_1_borsuk_1(A,B,C) ) ) ) )).

fof(d10_borsuk_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_eqrel_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_pre_topc(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ( C = k16_borsuk_1(A,B)
              <=> ( u1_struct_0(C) = B
                  & u1_pre_topc(C) = a_2_2_borsuk_1(A,B) ) ) ) ) ) )).

fof(d12_borsuk_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_eqrel_1(C,u1_struct_0(B)) )
             => k18_borsuk_1(A,B,C) = k2_xboole_0(C,a_2_3_borsuk_1(A,B)) ) ) ) )).

fof(fraenkel_a_2_0_borsuk_1,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B)))
     => ( r2_hidden(A,a_2_0_borsuk_1(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(B))
            & A = k3_tarski(D)
            & r2_hidden(D,C) ) ) ) )).

fof(fraenkel_a_3_0_borsuk_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_pre_topc(B)
        & l1_pre_topc(B)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & v1_pre_topc(D)
        & v2_pre_topc(D)
        & l1_pre_topc(D) )
     => ( r2_hidden(A,a_3_0_borsuk_1(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(D))))
            & A = k5_setfam_1(u1_struct_0(D),E)
            & r1_tarski(E,a_2_1_borsuk_1(B,C)) ) ) ) )).

fof(fraenkel_a_2_1_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( v2_pre_topc(B)
        & l1_pre_topc(B)
        & v2_pre_topc(C)
        & l1_pre_topc(C) )
     => ( r2_hidden(A,a_2_1_borsuk_1(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
            & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
            & A = k12_mcart_1(u1_struct_0(B),u1_struct_0(C),D,E)
            & r2_hidden(D,u1_pre_topc(B))
            & r2_hidden(E,u1_pre_topc(C)) ) ) ) )).

fof(fraenkel_a_3_1_borsuk_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_pre_topc(B)
        & l1_pre_topc(B)
        & v2_pre_topc(C)
        & l1_pre_topc(C)
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(B,C)))) )
     => ( r2_hidden(A,a_3_1_borsuk_1(B,C,D))
      <=> ? [E,F] :
            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
            & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C)))
            & A = k7_borsuk_1(B,C,E,F)
            & r1_tarski(k7_borsuk_1(B,C,E,F),D)
            & v3_pre_topc(E,B)
            & v3_pre_topc(F,C) ) ) ) )).

fof(fraenkel_a_2_2_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_eqrel_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_2_borsuk_1(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_zfmisc_1(C))
            & A = D
            & r2_hidden(k3_tarski(D),u1_pre_topc(B)) ) ) ) )).

fof(fraenkel_a_2_3_borsuk_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & ~ v3_struct_0(C)
        & m1_pre_topc(C,B) )
     => ( r2_hidden(A,a_2_3_borsuk_1(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = k1_struct_0(B,D)
            & ~ r2_hidden(D,u1_struct_0(C)) ) ) ) )).
%------------------------------------------------------------------------------