SET007 Axioms: SET007+875.ax


%------------------------------------------------------------------------------
% File     : SET007+875 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Properties of Rectangles on the Plane
% 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    : topreala [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   88 (   2 unit)
%            Number of atoms       :  674 (  32 equality)
%            Maximal formula depth :   17 (   9 average)
%            Number of connectives :  650 (  64 ~  ;  11  |; 275  &)
%                                         (   4 <=>; 296 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   48 (   0 propositional; 1-4 arity)
%            Number of functors    :   44 (   6 constant; 0-5 arity)
%            Number of variables   :  280 (   0 singleton; 278 !;   2 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ~ v1_xboole_0(k2_rcomp_1(A,k2_xcmplx_0(A,B))) ) )).

fof(fc2_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ~ v1_xboole_0(k1_rcomp_2(A,k2_xcmplx_0(A,B))) ) )).

fof(fc3_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ~ v1_xboole_0(k2_rcomp_2(A,k2_xcmplx_0(A,B))) ) )).

fof(fc4_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
        & v1_rcomp_1(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
        & v2_rcomp_1(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
        & v1_membered(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
        & v2_membered(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
        & v1_seq_4(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
        & v2_seq_4(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
        & v3_seq_4(k1_rcomp_1(A,k2_xcmplx_0(A,B))) ) ) )).

fof(fc5_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ~ v1_xboole_0(k2_rcomp_1(k6_xcmplx_0(A,B),A)) ) )).

fof(fc6_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ~ v1_xboole_0(k1_rcomp_2(k6_xcmplx_0(A,B),A)) ) )).

fof(fc7_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ~ v1_xboole_0(k2_rcomp_2(k6_xcmplx_0(A,B),A)) ) )).

fof(fc8_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k1_rcomp_1(k6_xcmplx_0(A,B),A))
        & v1_rcomp_1(k1_rcomp_1(k6_xcmplx_0(A,B),A))
        & v2_rcomp_1(k1_rcomp_1(k6_xcmplx_0(A,B),A))
        & v1_membered(k1_rcomp_1(k6_xcmplx_0(A,B),A))
        & v2_membered(k1_rcomp_1(k6_xcmplx_0(A,B),A))
        & v1_seq_4(k1_rcomp_1(k6_xcmplx_0(A,B),A))
        & v2_seq_4(k1_rcomp_1(k6_xcmplx_0(A,B),A))
        & v3_seq_4(k1_rcomp_1(k6_xcmplx_0(A,B),A)) ) ) )).

fof(fc9_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ~ v1_xboole_0(k2_rcomp_1(A,B)) ) )).

fof(fc10_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ~ v1_xboole_0(k1_rcomp_2(A,B)) ) )).

fof(fc11_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ~ v1_xboole_0(k2_rcomp_2(A,B)) ) )).

fof(fc12_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k1_rcomp_1(A,B))
        & v1_rcomp_1(k1_rcomp_1(A,B))
        & v2_rcomp_1(k1_rcomp_1(A,B))
        & v1_membered(k1_rcomp_1(A,B))
        & v2_membered(k1_rcomp_1(A,B))
        & v1_seq_4(k1_rcomp_1(A,B))
        & v2_seq_4(k1_rcomp_1(A,B))
        & v3_seq_4(k1_rcomp_1(A,B)) ) ) )).

fof(fc13_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ~ v1_xboole_0(k2_rcomp_1(A,B)) ) )).

fof(fc14_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ~ v1_xboole_0(k1_rcomp_2(A,B)) ) )).

fof(fc15_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ~ v1_xboole_0(k2_rcomp_2(A,B)) ) )).

fof(fc16_topreala,axiom,(
    ! [A,B] :
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k1_rcomp_1(A,B))
        & v1_rcomp_1(k1_rcomp_1(A,B))
        & v2_rcomp_1(k1_rcomp_1(A,B))
        & v1_membered(k1_rcomp_1(A,B))
        & v2_membered(k1_rcomp_1(A,B))
        & v1_seq_4(k1_rcomp_1(A,B))
        & v2_seq_4(k1_rcomp_1(A,B))
        & v3_seq_4(k1_rcomp_1(A,B)) ) ) )).

fof(rc1_topreala,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v1_monoid_0(A)
      & v2_monoid_0(A) ) )).

fof(cc1_topreala,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & v2_monoid_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_pre_topc(B,A)
         => ( v2_pre_topc(B)
            & v1_monoid_0(B)
            & v2_monoid_0(B) ) ) ) )).

fof(cc2_topreala,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( v3_struct_0(A)
          & v2_pre_topc(A) )
       => ( v2_pre_topc(A)
          & v1_tdlat_3(A)
          & v2_tdlat_3(A) ) ) ) )).

fof(cc3_topreala,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & v1_tdlat_3(A)
        & l1_pre_topc(A)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ! [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v5_pre_topc(C,A,B) ) ) ) ) )).

fof(cc4_topreala,axiom,(
    ! [A,B] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & l1_pre_topc(B) )
     => ! [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_xboole_0(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v5_pre_topc(C,A,B) ) ) ) ) )).

fof(fc17_topreala,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B)
        & v1_xreal_0(C)
        & ~ v3_xreal_0(C)
        & v1_xreal_0(D)
        & ~ v3_xreal_0(D) )
     => ( ~ v3_struct_0(k1_topreala(A,C,B,D))
        & v2_pre_topc(k1_topreala(A,C,B,D))
        & v1_monoid_0(k1_topreala(A,C,B,D))
        & v2_monoid_0(k1_topreala(A,C,B,D)) ) ) )).

fof(t1_topreala,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k4_int_1(k2_xcmplx_0(B,A)) = k4_int_1(B) ) ) )).

fof(t2_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( r1_xreal_0(k2_xcmplx_0(k1_int_1(A),np__1),B)
              | k1_int_1(B) = k1_int_1(A) ) ) ) ) )).

fof(t3_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( r1_xreal_0(k2_xcmplx_0(k1_int_1(A),np__1),B)
              | r1_xreal_0(k4_int_1(A),k4_int_1(B)) ) ) ) ) )).

fof(t4_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(B,A)
              & ~ r1_xreal_0(k2_xcmplx_0(k1_int_1(A),np__1),B)
              & r1_xreal_0(k4_int_1(B),k4_int_1(A)) ) ) ) )).

fof(t5_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(k2_xcmplx_0(k1_int_1(B),np__1),A)
              & r1_xreal_0(A,k2_xcmplx_0(B,np__1)) )
           => k1_int_1(A) = k2_xcmplx_0(k1_int_1(B),np__1) ) ) ) )).

fof(t6_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(k2_xcmplx_0(k1_int_1(B),np__1),A)
              & ~ r1_xreal_0(k2_xcmplx_0(B,np__1),A)
              & r1_xreal_0(k4_int_1(B),k4_int_1(A)) ) ) ) )).

fof(t7_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(A,C)
                  & k4_int_1(B) = k4_int_1(C) )
               => ( r1_xreal_0(k2_xcmplx_0(A,np__1),B)
                  | r1_xreal_0(k2_xcmplx_0(A,np__1),C)
                  | B = C ) ) ) ) ) )).

fof(t8_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(A,B)
                   => ( r1_xreal_0(D,C)
                      | r1_tarski(k1_rcomp_1(B,C),k1_rcomp_2(A,D)) ) ) ) ) ) ) )).

fof(t9_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(C,D)
                   => ( r1_xreal_0(B,A)
                      | r1_tarski(k1_rcomp_1(B,C),k2_rcomp_2(A,D)) ) ) ) ) ) ) )).

fof(t10_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ~ r1_xreal_0(B,A)
                      & ~ r1_xreal_0(D,C)
                      & ~ r1_tarski(k1_rcomp_1(B,C),k2_rcomp_1(A,D)) ) ) ) ) ) )).

fof(t11_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_tarski(k1_rcomp_2(B,C),k1_rcomp_1(A,D)) ) ) ) ) ) )).

fof(t12_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_tarski(k1_rcomp_2(B,C),k1_rcomp_2(A,D)) ) ) ) ) ) )).

fof(t13_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(C,D)
                   => ( r1_xreal_0(B,A)
                      | r1_tarski(k1_rcomp_2(B,C),k2_rcomp_2(A,D)) ) ) ) ) ) ) )).

fof(t14_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(C,D)
                   => ( r1_xreal_0(B,A)
                      | r1_tarski(k1_rcomp_2(B,C),k2_rcomp_1(A,D)) ) ) ) ) ) ) )).

fof(t15_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_tarski(k2_rcomp_2(B,C),k1_rcomp_1(A,D)) ) ) ) ) ) )).

fof(t16_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(A,B)
                   => ( r1_xreal_0(D,C)
                      | r1_tarski(k2_rcomp_2(B,C),k1_rcomp_2(A,D)) ) ) ) ) ) ) )).

fof(t17_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_tarski(k2_rcomp_2(B,C),k2_rcomp_2(A,D)) ) ) ) ) ) )).

fof(t18_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(A,B)
                   => ( r1_xreal_0(D,C)
                      | r1_tarski(k2_rcomp_2(B,C),k2_rcomp_1(A,D)) ) ) ) ) ) ) )).

fof(t19_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_tarski(k2_rcomp_1(B,C),k1_rcomp_1(A,D)) ) ) ) ) ) )).

fof(t20_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_tarski(k2_rcomp_1(B,C),k1_rcomp_2(A,D)) ) ) ) ) ) )).

fof(t21_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_tarski(k2_rcomp_1(B,C),k2_rcomp_2(A,D)) ) ) ) ) ) )).

fof(t22_topreala,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ( ( r2_hidden(B,k1_relat_1(A))
            & r2_hidden(k1_funct_1(A,B),k9_relat_1(A,C))
            & v2_funct_1(A) )
         => r2_hidden(B,C) ) ) )).

fof(t23_topreala,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( v4_ordinal2(B)
         => ~ ( r2_hidden(k2_xcmplx_0(B,np__1),k4_finseq_1(A))
              & ~ r2_hidden(B,k4_finseq_1(A))
              & B != np__0 ) ) ) )).

fof(t24_topreala,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_relat_1(E)
        & v1_funct_1(E) )
     => ( r2_hidden(E,k4_card_3(k4_funct_4(A,B,C,D)))
       => ( A = B
          | ( r2_hidden(k1_funct_1(E,A),C)
            & r2_hidden(k1_funct_1(E,B),D) ) ) ) ) )).

fof(t25_topreala,axiom,(
    ! [A,B] : k10_finseq_1(A,B) = k4_funct_4(np__1,np__2,A,B) )).

fof(t26_topreala,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( ( v3_pre_topc(E,A)
                        & m1_connsp_2(E,A,C) )
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
                         => ( ( C = D
                              & F = k3_xboole_0(E,k2_pre_topc(B)) )
                           => ( v3_pre_topc(F,B)
                              & m1_connsp_2(F,B,D) ) ) ) ) ) ) ) ) )).

fof(t27_topreala,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [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)) )
             => ( v1_xboole_0(C)
               => v5_pre_topc(C,A,B) ) ) ) ) )).

fof(t28_topreala,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) )
                 => ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) )).

fof(t29_topreala,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] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                        & v5_pre_topc(E,A,B)
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(k3_pre_topc(B,D)))
                            & m2_relset_1(F,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(k3_pre_topc(B,D))) )
                         => ( F = k2_partfun1(u1_struct_0(A),u1_struct_0(B),E,C)
                           => v5_pre_topc(F,k3_pre_topc(A,C),k3_pre_topc(B,D)) ) ) ) ) ) ) ) )).

fof(t30_topreala,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] :
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ( ( D = E
                          & v1_t_0topsp(D,A,B) )
                       => v1_t_0topsp(E,A,C) ) ) ) ) ) ) )).

fof(t31_topreala,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] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(k3_pre_topc(B,D)))
                            & m2_relset_1(F,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(k3_pre_topc(B,D))) )
                         => ( ( F = k2_partfun1(u1_struct_0(A),u1_struct_0(B),E,C)
                              & v2_funct_2(F,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(k3_pre_topc(B,D)))
                              & v1_t_0topsp(E,A,B)
                              & v2_funct_1(E) )
                           => v1_t_0topsp(F,k3_pre_topc(A,C),k3_pre_topc(B,D)) ) ) ) ) ) ) ) )).

fof(t32_topreala,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] :
              ( ( ~ v3_struct_0(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( ( v1_t_0topsp(D,A,B)
                          & v1_t_0topsp(E,B,C) )
                       => v1_t_0topsp(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) )).

fof(t33_topreala,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( v1_tsep_1(C,B)
                & m1_pre_topc(C,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                     => ( ( D = E
                          & v1_t_0topsp(E,A,C) )
                       => v1_t_0topsp(D,A,B) ) ) ) ) ) ) )).

fof(t34_topreala,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)) )
             => ( ( v2_funct_1(C)
                  & v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
               => ( v5_pre_topc(C,A,B)
                <=> v1_t_0topsp(k2_tops_2(A,B,C),B,A) ) ) ) ) ) )).

fof(t35_topreala,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)) )
             => ( ( v2_funct_1(C)
                  & v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
               => ( v1_t_0topsp(C,A,B)
                <=> v5_pre_topc(k2_tops_2(A,B,C),B,A) ) ) ) ) ) )).

fof(t36_topreala,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ( r1_t_0topsp(A,B)
          <=> r1_t_0topsp(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)),g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))) ) ) ) )).

fof(t37_topreala,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)) )
             => ( ( v2_funct_1(C)
                  & v2_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                  & v5_pre_topc(C,A,B)
                  & v1_t_0topsp(C,A,B) )
               => v3_tops_2(C,A,B) ) ) ) ) )).

fof(t38_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( B = k2_funcop_1(k1_numbers,A)
           => r2_fcont_1(B,k1_numbers) ) ) ) )).

fof(t39_topreala,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( k4_relset_1(k1_numbers,k1_numbers,A) = k4_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_relset_1(k1_numbers,k1_numbers,C))
                  & v3_rcomp_1(k4_relset_1(k1_numbers,k1_numbers,B))
                  & v3_rcomp_1(k4_relset_1(k1_numbers,k1_numbers,C))
                  & r2_fcont_1(B,k4_relset_1(k1_numbers,k1_numbers,B))
                  & r2_fcont_1(C,k4_relset_1(k1_numbers,k1_numbers,C))
                  & ! [D] :
                      ( r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,B))
                     => k2_seq_1(k1_numbers,k1_numbers,A,D) = k2_seq_1(k1_numbers,k1_numbers,B,D) )
                  & ! [D] :
                      ( r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,C))
                     => k2_seq_1(k1_numbers,k1_numbers,A,D) = k2_seq_1(k1_numbers,k1_numbers,C,D) ) )
               => r2_fcont_1(A,k4_relset_1(k1_numbers,k1_numbers,A)) ) ) ) ) )).

fof(t40_topreala,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_topalg_2))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_topalg_2)))
             => ( ( C = B
                  & m1_rcomp_1(B,A) )
               => m1_connsp_2(C,k3_topalg_2,A) ) ) ) ) )).

fof(t41_topreala,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_topalg_2))
     => ! [B] :
          ( m1_connsp_2(B,k3_topalg_2,A)
         => ? [C] :
              ( m1_rcomp_1(C,A)
              & r1_tarski(C,B) ) ) ) )).

fof(t42_topreala,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k3_topalg_2),u1_struct_0(k3_topalg_2))
        & m2_relset_1(A,u1_struct_0(k3_topalg_2),u1_struct_0(k3_topalg_2)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k3_topalg_2))
             => ( ( A = B
                  & r1_fcont_1(B,C) )
               => r1_tmap_1(k3_topalg_2,k3_topalg_2,A,C) ) ) ) ) )).

fof(t43_topreala,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k3_topalg_2),u1_struct_0(k3_topalg_2))
        & m2_relset_1(A,u1_struct_0(k3_topalg_2),u1_struct_0(k3_topalg_2)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_numbers,k1_numbers)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( A = B
              & r2_fcont_1(B,k1_numbers) )
           => v5_pre_topc(A,k3_topalg_2,k3_topalg_2) ) ) ) )).

fof(t44_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ( v4_pre_topc(k1_rcomp_1(B,C),k4_topmetr(A,D))
                      & m1_subset_1(k1_rcomp_1(B,C),k1_zfmisc_1(u1_struct_0(k4_topmetr(A,D)))) ) ) ) ) ) ) )).

fof(t45_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ( v3_pre_topc(k2_rcomp_1(B,C),k4_topmetr(A,D))
                      & m1_subset_1(k2_rcomp_1(B,C),k1_zfmisc_1(u1_struct_0(k4_topmetr(A,D)))) ) ) ) ) ) ) )).

fof(t46_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(A,C) )
               => ( v3_pre_topc(k2_rcomp_2(C,B),k4_topmetr(A,B))
                  & m1_subset_1(k2_rcomp_2(C,B),k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) ) ) ) ) ) )).

fof(t47_topreala,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) )
               => ( v3_pre_topc(k1_rcomp_2(A,C),k4_topmetr(A,B))
                  & m1_subset_1(k1_rcomp_2(A,C),k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) ) ) ) ) ) )).

fof(t48_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))) = k2_zfmisc_1(k1_rcomp_1(A,B),k1_rcomp_1(C,D)) ) ) ) ) ) )).

fof(t49_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k23_euclid(A,B) = k4_funct_4(np__1,np__2,A,B) ) ) )).

fof(t50_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( k1_funct_1(k23_euclid(A,B),np__1) = A
            & k1_funct_1(k23_euclid(A,B),np__2) = B ) ) ) )).

fof(t51_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => k2_jgraph_6(A,B,C,D) = k4_card_3(k4_funct_4(np__1,np__2,k1_rcomp_1(A,B),k1_rcomp_1(C,D))) ) ) ) ) )).

fof(t52_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r2_hidden(k23_euclid(A,C),k2_jgraph_6(A,B,C,D)) ) ) ) ) ) )).

fof(d1_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => k1_topreala(A,B,C,D) = k3_pre_topc(k15_euclid(np__2),k2_jgraph_6(A,B,C,D)) ) ) ) ) )).

fof(t53_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => u1_struct_0(k1_topreala(A,B,C,D)) = k2_jgraph_6(A,B,C,D) ) ) ) ) )).

fof(t54_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D)
                      & v3_struct_0(k1_topreala(A,B,C,D)) ) ) ) ) ) )).

fof(d2_topreala,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2)))
        & m2_relset_1(A,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2))) )
     => ( A = k2_topreala
      <=> ! [B] :
            ( v1_xreal_0(B)
           => ! [C] :
                ( v1_xreal_0(C)
               => k1_funct_1(A,k4_tarski(B,C)) = k10_finseq_1(B,C) ) ) ) ) )).

fof(t55_topreala,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => k4_pre_topc(k6_borsuk_1(k3_topalg_2,k3_topalg_2),k15_euclid(np__2),k2_topreala,k2_zfmisc_1(A,B)) = k4_card_3(k4_funct_4(np__1,np__2,A,B)) ) ) )).

fof(t56_topreala,axiom,(
    v3_tops_2(k2_topreala,k6_borsuk_1(k3_topalg_2,k3_topalg_2),k15_euclid(np__2)) )).

fof(t57_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ( v1_funct_1(k2_partfun1(u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2)),k2_topreala,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D)))))
                      & v1_funct_2(k2_partfun1(u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2)),k2_topreala,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D)))),u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))),u1_struct_0(k1_topreala(A,B,C,D)))
                      & m2_relset_1(k2_partfun1(u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2)),k2_topreala,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D)))),u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))),u1_struct_0(k1_topreala(A,B,C,D))) ) ) ) ) ) ) )).

fof(t58_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))),u1_struct_0(k1_topreala(A,B,C,D)))
                          & m2_relset_1(E,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))),u1_struct_0(k1_topreala(A,B,C,D))) )
                       => ( E = k2_partfun1(u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2)),k2_topreala,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))))
                         => v3_tops_2(E,k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D)),k1_topreala(A,B,C,D)) ) ) ) ) ) ) ) )).

fof(t59_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_t_0topsp(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D)),k1_topreala(A,B,C,D)) ) ) ) ) ) )).

fof(t60_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))
                       => ! [F] :
                            ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_topmetr(C,D))))
                           => m1_subset_1(k4_card_3(k4_funct_4(np__1,np__2,E,F)),k1_zfmisc_1(u1_struct_0(k1_topreala(A,B,C,D)))) ) ) ) ) ) ) ) )).

fof(t61_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ! [E] :
                        ( ( v3_pre_topc(E,k4_topmetr(A,B))
                          & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) )
                       => ! [F] :
                            ( ( v3_pre_topc(F,k4_topmetr(C,D))
                              & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_topmetr(C,D)))) )
                           => ( v3_pre_topc(k4_card_3(k4_funct_4(np__1,np__2,E,F)),k1_topreala(A,B,C,D))
                              & m1_subset_1(k4_card_3(k4_funct_4(np__1,np__2,E,F)),k1_zfmisc_1(u1_struct_0(k1_topreala(A,B,C,D)))) ) ) ) ) ) ) ) ) )).

fof(t62_topreala,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => ! [E] :
                        ( ( v4_pre_topc(E,k4_topmetr(A,B))
                          & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) )
                       => ! [F] :
                            ( ( v4_pre_topc(F,k4_topmetr(C,D))
                              & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_topmetr(C,D)))) )
                           => ( v4_pre_topc(k4_card_3(k4_funct_4(np__1,np__2,E,F)),k1_topreala(A,B,C,D))
                              & m1_subset_1(k4_card_3(k4_funct_4(np__1,np__2,E,F)),k1_zfmisc_1(u1_struct_0(k1_topreala(A,B,C,D)))) ) ) ) ) ) ) ) ) )).

fof(dt_k1_topreala,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => m1_pre_topc(k1_topreala(A,B,C,D),k15_euclid(np__2)) ) )).

fof(dt_k2_topreala,axiom,
    ( v1_funct_1(k2_topreala)
    & v1_funct_2(k2_topreala,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2)))
    & m2_relset_1(k2_topreala,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2))) )).
%------------------------------------------------------------------------------