SET007 Axioms: SET007+779.ax


%------------------------------------------------------------------------------
% File     : SET007+779 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Subcontinua of a Real Line
% 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_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  150 (  19 unit)
%            Number of atoms       :  705 ( 155 equality)
%            Maximal formula depth :   30 (   7 average)
%            Number of connectives :  722 ( 167 ~  ;  22  |; 232  &)
%                                         (  12 <=>; 289 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   43 (   1 propositional; 0-7 arity)
%            Number of functors    :   56 (  16 constant; 0-7 arity)
%            Number of variables   :  318 (   0 singleton; 310 !;   8 ?)
%            Maximal term depth    :    6 (   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_5,axiom,
    ( ~ v3_struct_0(k3_topmetr)
    & v1_pre_topc(k3_topmetr)
    & v2_pre_topc(k3_topmetr)
    & v1_connsp_1(k3_topmetr)
    & v2_t_0topsp(k3_topmetr)
    & v3_compts_1(k3_topmetr)
    & v1_borsuk_2(k3_topmetr)
    & v1_urysohn1(k3_topmetr) )).

fof(rc1_borsuk_5,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v1_connsp_1(A) ) )).

fof(cc1_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_numbers)
     => ( v1_xreal_0(A)
        & v1_xcmplx_0(A)
        & v1_rat_1(A) ) ) )).

fof(cc2_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k8_metric_1))
     => ( v1_xreal_0(A)
        & v1_xcmplx_0(A) ) ) )).

fof(fc2_borsuk_5,axiom,
    ( v1_xreal_0(k7_power)
    & v1_xcmplx_0(k7_power)
    & ~ v1_rat_1(k7_power) )).

fof(rc2_borsuk_5,axiom,(
    ? [A] :
      ( v1_xreal_0(A)
      & v1_xcmplx_0(A)
      & ~ v1_rat_1(A) ) )).

fof(fc3_borsuk_5,axiom,
    ( ~ v1_xboole_0(k1_borsuk_5)
    & v1_membered(k1_borsuk_5)
    & v2_membered(k1_borsuk_5) )).

fof(cc3_borsuk_5,axiom,(
    ! [A] :
      ( ( v1_xreal_0(A)
        & ~ v1_rat_1(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & v1_xcmplx_0(A) ) ) )).

fof(fc4_borsuk_5,axiom,(
    ! [A] :
      ( ( v1_xreal_0(A)
        & ~ v1_rat_1(A) )
     => ( ~ v1_xboole_0(k3_int_1(A))
        & v1_xreal_0(k3_int_1(A))
        & v1_xcmplx_0(k3_int_1(A))
        & ~ v1_rat_1(k3_int_1(A)) ) ) )).

fof(fc5_borsuk_5,axiom,(
    ! [A] :
      ( ( v1_xreal_0(A)
        & ~ v1_rat_1(A) )
     => ( ~ v1_xboole_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & v1_xcmplx_0(k4_xcmplx_0(A))
        & ~ v1_rat_1(k4_xcmplx_0(A)) ) ) )).

fof(fc6_borsuk_5,axiom,(
    ! [A,B] :
      ( ( v1_rat_1(A)
        & v1_xreal_0(B)
        & ~ v1_rat_1(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & ~ v1_rat_1(k2_xcmplx_0(A,B)) ) ) )).

fof(fc7_borsuk_5,axiom,(
    ! [A,B] :
      ( ( v1_rat_1(A)
        & v1_xreal_0(B)
        & ~ v1_rat_1(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & ~ v1_rat_1(k2_xcmplx_0(B,A)) ) ) )).

fof(fc8_borsuk_5,axiom,(
    ! [A,B] :
      ( ( v1_rat_1(A)
        & v1_xreal_0(B)
        & ~ v1_rat_1(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & ~ v1_rat_1(k6_xcmplx_0(A,B)) ) ) )).

fof(fc9_borsuk_5,axiom,(
    ! [A,B] :
      ( ( v1_rat_1(A)
        & v1_xreal_0(B)
        & ~ v1_rat_1(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & ~ v1_rat_1(k6_xcmplx_0(B,A)) ) ) )).

fof(rc3_borsuk_5,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_xreal_0(A)
      & v1_xcmplx_0(A)
      & v1_rat_1(A) ) )).

fof(fc10_borsuk_5,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_rat_1(A)
        & v1_xreal_0(B)
        & ~ v1_rat_1(B) )
     => ( ~ v1_xboole_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & v1_xcmplx_0(k3_xcmplx_0(A,B))
        & ~ v1_rat_1(k3_xcmplx_0(A,B)) ) ) )).

fof(fc11_borsuk_5,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_rat_1(A)
        & v1_xreal_0(B)
        & ~ v1_rat_1(B) )
     => ( ~ v1_xboole_0(k3_xcmplx_0(B,A))
        & v1_xreal_0(k3_xcmplx_0(B,A))
        & v1_xcmplx_0(k3_xcmplx_0(B,A))
        & ~ v1_rat_1(k3_xcmplx_0(B,A)) ) ) )).

fof(fc12_borsuk_5,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_rat_1(A)
        & v1_xreal_0(B)
        & ~ v1_rat_1(B) )
     => ( ~ v1_xboole_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & v1_xcmplx_0(k7_xcmplx_0(A,B))
        & ~ v1_rat_1(k7_xcmplx_0(A,B)) ) ) )).

fof(fc13_borsuk_5,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_rat_1(A)
        & v1_xreal_0(B)
        & ~ v1_rat_1(B) )
     => ( ~ v1_xboole_0(k7_xcmplx_0(B,A))
        & v1_xreal_0(k7_xcmplx_0(B,A))
        & v1_xcmplx_0(k7_xcmplx_0(B,A))
        & ~ v1_rat_1(k7_xcmplx_0(B,A)) ) ) )).

fof(fc14_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k4_limfunc1(A))
        & v1_membered(k4_limfunc1(A))
        & v2_membered(k4_limfunc1(A)) ) ) )).

fof(fc15_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k2_limfunc1(A))
        & v1_membered(k2_limfunc1(A))
        & v2_membered(k2_limfunc1(A)) ) ) )).

fof(fc16_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k12_prob_1(A))
        & v1_membered(k12_prob_1(A))
        & v2_membered(k12_prob_1(A)) ) ) )).

fof(fc17_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( ~ v1_xboole_0(k3_limfunc1(A))
        & v1_membered(k3_limfunc1(A))
        & v2_membered(k3_limfunc1(A)) ) ) )).

fof(fc18_borsuk_5,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_t_0topsp(k22_borsuk_1)
    & v2_compts_1(k22_borsuk_1)
    & v3_compts_1(k22_borsuk_1)
    & v3_yellow_8(k22_borsuk_1)
    & v1_borsuk_2(k22_borsuk_1)
    & v1_urysohn1(k22_borsuk_1) )).

fof(rc4_borsuk_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
          & v1_borsuk_5(B,A) ) ) )).

fof(rc5_borsuk_5,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
          & ~ v1_xboole_0(B)
          & v1_tops_2(B,A)
          & v2_tops_2(B,A) ) ) )).

fof(t1_borsuk_5,axiom,(
    $true )).

fof(t2_borsuk_5,axiom,(
    ! [A,B,C] :
      ~ ( r1_tarski(A,B)
        & r1_tarski(B,k2_xboole_0(A,k1_tarski(C)))
        & k2_xboole_0(A,k1_tarski(C)) != B
        & A != B ) )).

fof(t3_borsuk_5,axiom,(
    ! [A,B,C,D,E,F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_enumset1(A,C,F),k1_enumset1(B,D,E)) )).

fof(d1_borsuk_5,axiom,(
    ! [A,B,C,D,E,F] :
      ( r1_borsuk_5(A,B,C,D,E,F)
    <=> ( A != B
        & A != C
        & A != D
        & A != E
        & A != F
        & B != C
        & B != D
        & B != E
        & B != F
        & C != D
        & C != E
        & C != F
        & D != E
        & D != F
        & E != F ) ) )).

fof(d2_borsuk_5,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( r2_borsuk_5(A,B,C,D,E,F,G)
    <=> ( A != B
        & A != C
        & A != D
        & A != E
        & A != F
        & A != G
        & B != C
        & B != D
        & B != E
        & B != F
        & B != G
        & C != D
        & C != E
        & C != F
        & C != G
        & D != E
        & D != F
        & D != G
        & E != F
        & E != G
        & F != G ) ) )).

fof(t4_borsuk_5,axiom,(
    ! [A,B,C,D,E,F] :
      ( r1_borsuk_5(A,B,C,D,E,F)
     => k4_card_1(k4_enumset1(A,B,C,D,E,F)) = np__6 ) )).

fof(t5_borsuk_5,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( r2_borsuk_5(A,B,C,D,E,F,G)
     => k4_card_1(k5_enumset1(A,B,C,D,E,F,G)) = np__7 ) )).

fof(t6_borsuk_5,axiom,(
    ! [A,B,C,D,E,F] :
      ( r1_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F))
     => ( A != D
        & A != E
        & A != F
        & B != D
        & B != E
        & B != F
        & C != D
        & C != E
        & C != F ) ) )).

fof(t7_borsuk_5,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( r1_incproj(A,B,C)
        & r1_incproj(D,E,F)
        & r1_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F)) )
     => r1_borsuk_5(A,B,C,D,E,F) ) )).

fof(t8_borsuk_5,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( r1_borsuk_5(A,B,C,D,E,F)
        & r1_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_tarski(G)) )
     => r2_borsuk_5(A,B,C,D,E,F,G) ) )).

fof(t9_borsuk_5,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( r2_borsuk_5(A,B,C,D,E,F,G)
     => r2_borsuk_5(G,A,B,C,D,E,F) ) )).

fof(t10_borsuk_5,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( r2_borsuk_5(A,B,C,D,E,F,G)
     => r2_borsuk_5(A,B,E,C,F,G,D) ) )).

fof(t11_borsuk_5,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] :
                      ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(A))
                      & m2_relset_1(D,u1_struct_0(k5_topmetr),u1_struct_0(A))
                      & v5_pre_topc(D,k5_topmetr,A)
                      & k1_funct_1(D,np__0) = B
                      & k1_funct_1(D,np__1) = C )
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(A))
                        & m2_relset_1(D,u1_struct_0(k5_topmetr),u1_struct_0(A)) )
                     => ~ ( v5_pre_topc(D,k5_topmetr,A)
                          & k1_funct_1(D,np__0) = C
                          & k1_funct_1(D,np__1) = B ) ) ) ) ) ) )).

fof(t12_borsuk_5,axiom,(
    $true )).

fof(t13_borsuk_5,axiom,(
    k2_pre_topc(k3_topmetr) = k1_numbers )).

fof(t14_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r2_hidden(A,k4_limfunc1(B))
          <=> ~ r1_xreal_0(A,B) ) ) ) )).

fof(t15_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r2_hidden(A,k3_limfunc1(B))
          <=> r1_xreal_0(B,A) ) ) ) )).

fof(t16_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r2_hidden(A,k2_limfunc1(B))
          <=> r1_xreal_0(A,B) ) ) ) )).

fof(t17_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r2_hidden(A,k12_prob_1(B))
          <=> ~ r1_xreal_0(B,A) ) ) ) )).

fof(t18_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k4_xboole_0(k1_numbers,k1_seq_4(A)) = k4_subset_1(k1_numbers,k12_prob_1(A),k4_limfunc1(A)) ) )).

fof(t19_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(B,C)
                   => ( r1_xreal_0(B,A)
                      | r1_xboole_0(k1_rcomp_1(A,B),k2_rcomp_2(C,D)) ) ) ) ) ) ) )).

fof(t20_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(B,C)
                   => ( r1_xreal_0(B,A)
                      | r1_xboole_0(k1_rcomp_2(A,B),k1_rcomp_1(C,D)) ) ) ) ) ) ) )).

fof(t21_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( v1_xreal_0(E)
                     => ! [F] :
                          ( v1_xreal_0(F)
                         => ( ( r1_xreal_0(D,E)
                              & A = k1_rcomp_2(C,D)
                              & B = k2_rcomp_2(E,F) )
                           => ( r1_xreal_0(D,C)
                              | r1_xreal_0(F,E)
                              | r1_connsp_1(k3_topmetr,A,B) ) ) ) ) ) ) ) ) )).

fof(t22_borsuk_5,axiom,(
    $true )).

fof(t23_borsuk_5,axiom,(
    $true )).

fof(t24_borsuk_5,axiom,(
    $true )).

fof(t25_borsuk_5,axiom,(
    $true )).

fof(t26_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => r1_xboole_0(k2_limfunc1(A),k4_limfunc1(A)) ) )).

fof(t27_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => r1_xboole_0(k12_prob_1(A),k3_limfunc1(A)) ) )).

fof(t28_borsuk_5,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) )
               => k4_subset_1(k1_numbers,k1_rcomp_1(A,B),k3_limfunc1(C)) = k3_limfunc1(A) ) ) ) ) )).

fof(t29_borsuk_5,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) )
               => k4_subset_1(k1_numbers,k2_limfunc1(C),k1_rcomp_1(A,B)) = k2_limfunc1(B) ) ) ) ) )).

fof(t30_borsuk_5,axiom,(
    $true )).

fof(t31_borsuk_5,axiom,(
    $true )).

fof(t32_borsuk_5,axiom,(
    $true )).

fof(t33_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k8_metric_1))
         => ( r2_hidden(B,k6_pre_topc(k3_topmetr,A))
          <=> ! [C] :
                ( v1_xreal_0(C)
               => ~ ( ~ r1_xreal_0(C,np__0)
                    & r1_xboole_0(k9_metric_1(k8_metric_1,B,C),A) ) ) ) ) ) )).

fof(t34_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k8_metric_1))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k8_metric_1))
         => ( r1_xreal_0(A,B)
           => k4_metric_1(k8_metric_1,A,B) = k6_xcmplx_0(B,A) ) ) ) )).

fof(t35_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( A = k3_numbers
       => k6_pre_topc(k3_topmetr,A) = u1_struct_0(k3_topmetr) ) ) )).

fof(t36_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k2_rcomp_1(B,C)
               => ( B = C
                  | k6_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) )).

fof(d3_borsuk_5,axiom,(
    k1_borsuk_5 = k4_xboole_0(k1_numbers,k3_numbers) )).

fof(d4_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k2_borsuk_5(A,B) = k3_xboole_0(k3_numbers,k2_rcomp_1(A,B)) ) ) )).

fof(d5_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k3_borsuk_5(A,B) = k5_subset_1(k1_numbers,k1_borsuk_5,k2_rcomp_1(A,B)) ) ) )).

fof(t37_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( ~ v1_rat_1(A)
      <=> r2_hidden(A,k1_borsuk_5) ) ) )).

fof(t38_borsuk_5,axiom,(
    ! [A] :
      ( v1_rat_1(A)
     => ! [B] :
          ( ( v1_xreal_0(B)
            & ~ v1_rat_1(B) )
         => ~ v1_rat_1(k2_xcmplx_0(A,B)) ) ) )).

fof(t39_borsuk_5,axiom,(
    ! [A] :
      ( ( v1_xreal_0(A)
        & ~ v1_rat_1(A) )
     => ~ v1_rat_1(k4_xcmplx_0(A)) ) )).

fof(t40_borsuk_5,axiom,(
    ! [A] :
      ( v1_rat_1(A)
     => ! [B] :
          ( ( v1_xreal_0(B)
            & ~ v1_rat_1(B) )
         => ~ v1_rat_1(k6_xcmplx_0(A,B)) ) ) )).

fof(t41_borsuk_5,axiom,(
    ! [A] :
      ( v1_rat_1(A)
     => ! [B] :
          ( ( v1_xreal_0(B)
            & ~ v1_rat_1(B) )
         => ~ v1_rat_1(k6_xcmplx_0(B,A)) ) ) )).

fof(t42_borsuk_5,axiom,(
    ! [A] :
      ( v1_rat_1(A)
     => ! [B] :
          ( ( v1_xreal_0(B)
            & ~ v1_rat_1(B) )
         => ~ ( A != np__0
              & v1_rat_1(k3_xcmplx_0(A,B)) ) ) ) )).

fof(t43_borsuk_5,axiom,(
    ! [A] :
      ( v1_rat_1(A)
     => ! [B] :
          ( ( v1_xreal_0(B)
            & ~ v1_rat_1(B) )
         => ~ ( A != np__0
              & v1_rat_1(k7_xcmplx_0(B,A)) ) ) ) )).

fof(t44_borsuk_5,axiom,(
    ! [A] :
      ( v1_rat_1(A)
     => ! [B] :
          ( ( v1_xreal_0(B)
            & ~ v1_rat_1(B) )
         => ~ ( A != np__0
              & v1_rat_1(k7_xcmplx_0(A,B)) ) ) ) )).

fof(t45_borsuk_5,axiom,(
    ! [A] :
      ( ( v1_xreal_0(A)
        & ~ v1_rat_1(A) )
     => ~ v1_rat_1(k4_int_1(A)) ) )).

fof(t46_borsuk_5,axiom,(
    $true )).

fof(t47_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(B,A)
              & ! [C] :
                  ( v1_rat_1(C)
                 => ! [D] :
                      ( v1_rat_1(D)
                     => ~ ( ~ r1_xreal_0(C,A)
                          & ~ r1_xreal_0(D,C)
                          & ~ r1_xreal_0(B,D) ) ) ) ) ) ) )).

fof(t48_borsuk_5,axiom,(
    $true )).

fof(t49_borsuk_5,axiom,(
    $true )).

fof(t50_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(B,A)
              & ! [C] :
                  ( ( v1_xreal_0(C)
                    & ~ v1_rat_1(C) )
                 => ~ ( ~ r1_xreal_0(C,A)
                      & ~ r1_xreal_0(B,C) ) ) ) ) ) )).

fof(t51_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( A = k1_borsuk_5
       => k6_pre_topc(k3_topmetr,A) = u1_struct_0(k3_topmetr) ) ) )).

fof(t52_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ~ r1_xreal_0(B,A)
               => ( r2_hidden(C,k2_borsuk_5(A,B))
                <=> ( v1_rat_1(C)
                    & ~ r1_xreal_0(C,A)
                    & ~ r1_xreal_0(B,C) ) ) ) ) ) ) )).

fof(t53_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ~ r1_xreal_0(B,A)
               => ( r2_hidden(C,k3_borsuk_5(A,B))
                <=> ( ~ v1_rat_1(C)
                    & ~ r1_xreal_0(C,A)
                    & ~ r1_xreal_0(B,C) ) ) ) ) ) ) )).

fof(t54_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k2_borsuk_5(B,C)
               => ( r1_xreal_0(C,B)
                  | k6_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) )).

fof(t55_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k3_borsuk_5(B,C)
               => ( r1_xreal_0(C,B)
                  | k6_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) )).

fof(t56_borsuk_5,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v1_connsp_1(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v3_pre_topc(B,A)
            & v4_pre_topc(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( B = k1_xboole_0
            | B = k2_pre_topc(A) ) ) ) )).

fof(t57_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ~ ( v4_pre_topc(A,k3_topmetr)
          & v3_pre_topc(A,k3_topmetr)
          & A != k1_xboole_0
          & A != k1_numbers ) ) )).

fof(t58_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k1_rcomp_2(B,C)
               => ( B = C
                  | k6_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) )).

fof(t59_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k2_rcomp_2(B,C)
               => ( B = C
                  | k6_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) )).

fof(t60_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( A = k4_subset_1(k1_numbers,k1_rcomp_2(B,C),k2_rcomp_2(C,D))
                   => ( r1_xreal_0(C,B)
                      | r1_xreal_0(D,C)
                      | k6_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,D) ) ) ) ) ) ) )).

fof(t61_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A = k1_seq_4(B)
           => k6_pre_topc(k3_topmetr,A) = k1_seq_4(B) ) ) ) )).

fof(t62_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
         => ( A = B
           => ( v3_rcomp_1(A)
            <=> v3_pre_topc(B,k3_topmetr) ) ) ) ) )).

fof(t63_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A = k4_limfunc1(B)
           => v3_pre_topc(A,k3_topmetr) ) ) ) )).

fof(t64_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A = k12_prob_1(B)
           => v3_pre_topc(A,k3_topmetr) ) ) ) )).

fof(t65_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A = k2_limfunc1(B)
           => v4_pre_topc(A,k3_topmetr) ) ) ) )).

fof(t66_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A = k3_limfunc1(B)
           => v4_pre_topc(A,k3_topmetr) ) ) ) )).

fof(t67_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k3_limfunc1(A) = k4_subset_1(k1_numbers,k1_seq_4(A),k4_limfunc1(A)) ) )).

fof(t68_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k2_limfunc1(A) = k4_subset_1(k1_numbers,k1_seq_4(A),k12_prob_1(A)) ) )).

fof(t69_borsuk_5,axiom,(
    $true )).

fof(t70_borsuk_5,axiom,(
    $true )).

fof(t71_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k4_limfunc1(A) != k1_numbers ) )).

fof(t72_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k3_limfunc1(A) != k1_numbers ) )).

fof(t73_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k2_limfunc1(A) != k1_numbers ) )).

fof(t74_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k12_prob_1(A) != k1_numbers ) )).

fof(t75_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A = k4_limfunc1(B)
           => k6_pre_topc(k3_topmetr,A) = k3_limfunc1(B) ) ) ) )).

fof(t76_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k7_pscomp_1(k4_limfunc1(A)) = k3_limfunc1(A) ) )).

fof(t77_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A = k12_prob_1(B)
           => k6_pre_topc(k3_topmetr,A) = k2_limfunc1(B) ) ) ) )).

fof(t78_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k7_pscomp_1(k12_prob_1(A)) = k2_limfunc1(A) ) )).

fof(t79_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( A = k12_prob_1(C)
                  & B = k4_limfunc1(C) )
               => r1_connsp_1(k3_topmetr,A,B) ) ) ) ) )).

fof(t80_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k4_subset_1(k1_numbers,k1_rcomp_2(B,C),k4_limfunc1(C))
               => ( r1_xreal_0(C,B)
                  | k6_pre_topc(k3_topmetr,A) = k3_limfunc1(B) ) ) ) ) ) )).

fof(t81_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k4_subset_1(k1_numbers,k2_rcomp_1(B,C),k4_limfunc1(C))
               => ( r1_xreal_0(C,B)
                  | k6_pre_topc(k3_topmetr,A) = k3_limfunc1(B) ) ) ) ) ) )).

fof(t82_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( A = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k2_borsuk_5(B,C),k2_rcomp_1(C,D)),k4_limfunc1(D))
                   => ( r1_xreal_0(C,B)
                      | r1_xreal_0(D,C)
                      | k6_pre_topc(k3_topmetr,A) = k3_limfunc1(B) ) ) ) ) ) ) )).

fof(t83_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => k3_subset_1(u1_struct_0(k3_topmetr),A) = k4_xboole_0(k1_numbers,A) ) )).

fof(t84_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(B,A)
           => r1_xboole_0(k3_borsuk_5(A,B),k2_borsuk_5(A,B)) ) ) ) )).

fof(t85_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k4_xboole_0(k1_numbers,k2_borsuk_5(A,B)) = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k2_limfunc1(A),k3_borsuk_5(A,B)),k3_limfunc1(B)) ) ) )).

fof(t86_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( r1_xreal_0(A,B)
                  & ~ r1_xreal_0(C,B)
                  & r2_hidden(A,k4_subset_1(k1_numbers,k2_rcomp_1(B,C),k4_limfunc1(C))) ) ) ) ) )).

fof(t87_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(B,A)
              & r2_hidden(B,k4_subset_1(k1_numbers,k2_rcomp_1(A,B),k4_limfunc1(B))) ) ) ) )).

fof(t88_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(B,A)
           => k6_subset_1(k1_numbers,k3_limfunc1(A),k4_subset_1(k1_numbers,k2_rcomp_1(A,B),k4_limfunc1(B))) = k4_subset_1(k1_numbers,k1_seq_4(A),k1_seq_4(B)) ) ) ) )).

fof(t89_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( A = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k2_borsuk_5(np__2,np__4),k2_rcomp_1(np__4,np__5)),k4_limfunc1(np__5))
       => k3_subset_1(u1_struct_0(k3_topmetr),A) = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k2_limfunc1(np__2),k3_borsuk_5(np__2,np__4)),k1_seq_4(np__4)),k1_seq_4(np__5)) ) ) )).

fof(t90_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A = k1_seq_4(B)
           => k3_subset_1(u1_struct_0(k3_topmetr),A) = k4_subset_1(k1_numbers,k12_prob_1(B),k4_limfunc1(B)) ) ) ) )).

fof(t91_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(B,A)
           => k5_subset_1(k1_numbers,k4_limfunc1(A),k2_limfunc1(B)) = k2_rcomp_2(A,B) ) ) ) )).

fof(t92_borsuk_5,axiom,(
    k5_subset_1(k1_numbers,k4_subset_1(k1_numbers,k12_prob_1(np__1),k4_limfunc1(np__1)),k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k2_limfunc1(np__2),k3_borsuk_5(np__2,np__4)),k1_seq_4(np__4)),k1_seq_4(np__5))) = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k12_prob_1(np__1),k2_rcomp_2(np__1,np__2)),k3_borsuk_5(np__2,np__4)),k1_seq_4(np__4)),k1_seq_4(np__5)) )).

fof(t93_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => k6_subset_1(k1_numbers,k12_prob_1(B),k1_seq_4(A)) = k4_subset_1(k1_numbers,k12_prob_1(A),k2_rcomp_1(A,B)) ) ) ) )).

fof(t94_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => k6_subset_1(k1_numbers,k4_limfunc1(A),k1_seq_4(B)) = k4_subset_1(k1_numbers,k2_rcomp_1(A,B),k4_limfunc1(B)) ) ) ) )).

fof(t95_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(B,C)
                  & A = k4_subset_1(k1_numbers,k1_seq_4(B),k3_limfunc1(C)) )
               => k3_subset_1(u1_struct_0(k3_topmetr),A) = k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_1(B,C)) ) ) ) ) )).

fof(t96_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_1(B,C))
               => ( r1_xreal_0(C,B)
                  | k6_pre_topc(k3_topmetr,A) = k2_limfunc1(C) ) ) ) ) ) )).

fof(t97_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( A = k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_2(B,C))
               => ( r1_xreal_0(C,B)
                  | k6_pre_topc(k3_topmetr,A) = k2_limfunc1(C) ) ) ) ) ) )).

fof(t98_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A = k2_limfunc1(B)
           => k3_subset_1(u1_struct_0(k3_topmetr),A) = k4_limfunc1(B) ) ) ) )).

fof(t99_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ( A = k3_limfunc1(B)
           => k3_subset_1(u1_struct_0(k3_topmetr),A) = k12_prob_1(B) ) ) ) )).

fof(t100_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( A = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_2(B,C)),k3_borsuk_5(C,D)),k1_seq_4(D))
                   => ( r1_xreal_0(C,B)
                      | r1_xreal_0(D,C)
                      | k6_pre_topc(k3_topmetr,A) = k2_limfunc1(D) ) ) ) ) ) ) )).

fof(t101_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ! [E] :
                      ( v1_xreal_0(E)
                     => ( A = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_2(B,C)),k3_borsuk_5(C,D)),k1_seq_4(D)),k1_seq_4(E))
                       => ( r1_xreal_0(C,B)
                          | r1_xreal_0(D,C)
                          | k6_pre_topc(k3_topmetr,A) = k4_subset_1(k1_numbers,k2_limfunc1(D),k1_seq_4(E)) ) ) ) ) ) ) ) )).

fof(t102_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(B,C)
                  & A = k4_subset_1(k1_numbers,k2_limfunc1(B),k1_seq_4(C)) )
               => k3_subset_1(u1_struct_0(k3_topmetr),A) = k4_subset_1(k1_numbers,k2_rcomp_1(B,C),k4_limfunc1(C)) ) ) ) ) )).

fof(t103_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k4_subset_1(k1_numbers,k3_limfunc1(A),k1_seq_4(B)) != k1_numbers ) ) )).

fof(t104_borsuk_5,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k4_subset_1(k1_numbers,k2_limfunc1(A),k1_seq_4(B)) != k1_numbers ) ) )).

fof(t105_borsuk_5,axiom,(
    ! [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)))
             => ~ ( B != C
                  & k3_subset_1(u1_struct_0(A),B) = k3_subset_1(u1_struct_0(A),C) ) ) ) ) )).

fof(t106_borsuk_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
     => ( k1_numbers = k3_subset_1(u1_struct_0(k3_topmetr),A)
       => A = k1_xboole_0 ) ) )).

fof(t107_borsuk_5,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k3_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ( B = A
           => ( v1_seq_4(B)
              & v2_seq_4(B) ) ) ) ) )).

fof(t108_borsuk_5,axiom,(
    ! [A] :
      ( ( v6_compts_1(A,k3_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r2_hidden(C,B)
                  & B = A )
               => ( r1_xreal_0(k4_pscomp_1(B),C)
                  & r1_xreal_0(C,k3_pscomp_1(B)) ) ) ) ) ) )).

fof(t109_borsuk_5,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_connsp_1(A,k3_topmetr)
        & v6_compts_1(A,k3_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ( ( A = B
              & r1_tarski(k1_rcomp_1(k4_pscomp_1(B),k3_pscomp_1(B)),B) )
           => k1_rcomp_1(k4_pscomp_1(B),k3_pscomp_1(B)) = B ) ) ) )).

fof(t110_borsuk_5,axiom,(
    ! [A] :
      ( ( v2_connsp_1(A,k3_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(B,C)
                      & r1_xreal_0(C,D)
                      & r2_hidden(B,A)
                      & r2_hidden(D,A) )
                   => r2_hidden(C,A) ) ) ) ) ) )).

fof(t111_borsuk_5,axiom,(
    ! [A] :
      ( ( v2_connsp_1(A,k3_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r2_hidden(B,A)
                  & r2_hidden(C,A) )
               => r1_tarski(k1_rcomp_1(B,C),A) ) ) ) ) )).

fof(t112_borsuk_5,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_connsp_1(A,k3_topmetr)
        & v6_compts_1(A,k3_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
     => ( ~ v1_xboole_0(A)
        & v1_integra1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) ) )).

fof(t113_borsuk_5,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_connsp_1(A,k3_topmetr)
        & v6_compts_1(A,k3_topmetr)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )
     => ? [B] :
          ( v1_xreal_0(B)
          & ? [C] :
              ( v1_xreal_0(C)
              & r1_xreal_0(B,C)
              & A = k1_rcomp_1(B,C) ) ) ) )).

fof(d6_borsuk_5,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_borsuk_5(B,A)
          <=> ~ r2_hidden(u1_struct_0(A),B) ) ) ) )).

fof(t114_borsuk_5,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( ( v1_borsuk_5(B,A)
                  & r1_tarski(C,B) )
               => v1_borsuk_5(C,A) ) ) ) ) )).

fof(t115_borsuk_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_borsuk_5(B,A)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
         => ! [C] :
              ( ( v1_borsuk_5(C,A)
                & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
             => v1_borsuk_5(k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A) ) ) ) )).

fof(dt_k1_borsuk_5,axiom,(
    m1_subset_1(k1_borsuk_5,k1_zfmisc_1(k1_numbers)) )).

fof(dt_k2_borsuk_5,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k2_borsuk_5(A,B),k1_zfmisc_1(k1_numbers)) ) )).

fof(dt_k3_borsuk_5,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k3_borsuk_5(A,B),k1_zfmisc_1(k1_numbers)) ) )).
%------------------------------------------------------------------------------