SET007 Axioms: SET007+874.ax


%------------------------------------------------------------------------------
% File     : SET007+874 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Introduction to Real Linear Topological Spaces
% 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    : rltopsp1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  124 (   2 unit)
%            Number of atoms       : 1370 (  46 equality)
%            Maximal formula depth :   24 (  11 average)
%            Number of connectives : 1401 ( 155 ~  ;   0  |; 906  &)
%                                         (  19 <=>; 321 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   55 (   1 propositional; 0-3 arity)
%            Number of functors    :   50 (   3 constant; 0-5 arity)
%            Number of variables   :  368 (   0 singleton; 340 !;  28 ?)
%            Maximal term depth    :    4 (   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_rltopsp1,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_numbers)
      & ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) )).

fof(fc1_rltopsp1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A)
        & v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_xboole_0(k3_convex1(A,B))
        & v1_convex1(k3_convex1(A,B),A) ) ) )).

fof(fc2_rltopsp1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k1_rltopsp1(A,B,C))
        & v1_convex1(k1_rltopsp1(A,B,C),A) ) ) )).

fof(rc2_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
          & ~ v1_xboole_0(B)
          & v1_rltopsp1(B,A) ) ) )).

fof(rc3_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v2_rltopsp1(B,A) ) ) )).

fof(fc3_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ( v1_xboole_0(k1_pre_topc(A))
        & v1_membered(k1_pre_topc(A))
        & v2_membered(k1_pre_topc(A))
        & v3_membered(k1_pre_topc(A))
        & v4_membered(k1_pre_topc(A))
        & v5_membered(k1_pre_topc(A))
        & v3_rltopsp1(k1_pre_topc(A),A) ) ) )).

fof(rc4_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v3_rltopsp1(B,A) ) ) )).

fof(fc4_rltopsp1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A)
        & v3_rltopsp1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v3_rltopsp1(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => v3_rltopsp1(k6_rusub_4(A,B,C),A) ) )).

fof(cc1_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_rltopsp1(B,A)
           => v2_rltopsp1(B,A) ) ) ) )).

fof(fc5_rltopsp1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A)
        & v3_rltopsp1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_convex1(k3_convex1(A,B),A)
        & v2_rltopsp1(k3_convex1(A,B),A)
        & v3_rltopsp1(k3_convex1(A,B),A) ) ) )).

fof(rc5_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
          & ~ v1_xboole_0(B)
          & v4_rltopsp1(B,A) ) ) )).

fof(rc6_rltopsp1,axiom,(
    ? [A] :
      ( l1_rltopsp1(A)
      & v5_rltopsp1(A) ) )).

fof(fc6_rltopsp1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( ~ v3_struct_0(g1_rltopsp1(A,B,C,D,E))
        & v5_rltopsp1(g1_rltopsp1(A,B,C,D,E)) ) ) )).

fof(rc7_rltopsp1,axiom,(
    ? [A] :
      ( l1_rltopsp1(A)
      & ~ v3_struct_0(A)
      & v5_rltopsp1(A) ) )).

fof(rc8_rltopsp1,axiom,(
    ? [A] :
      ( l1_rltopsp1(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v7_rlvect_1(A)
      & v5_rltopsp1(A)
      & v6_rltopsp1(A)
      & v7_rltopsp1(A) ) )).

fof(fc7_rltopsp1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_relat_1(k3_rltopsp1(A,B))
        & v1_funct_1(k3_rltopsp1(A,B))
        & v1_funct_2(k3_rltopsp1(A,B),u1_struct_0(A),u1_struct_0(A))
        & v3_tops_2(k3_rltopsp1(A,B),A,A) ) ) )).

fof(fc8_rltopsp1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A)
        & v3_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,u1_struct_0(A)) )
     => v3_pre_topc(k5_rusub_4(A,B,C),A) ) )).

fof(fc9_rltopsp1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A)
        & v3_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => v3_pre_topc(k6_rusub_4(A,C,B),A) ) )).

fof(fc10_rltopsp1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A)
        & v4_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,u1_struct_0(A)) )
     => v4_pre_topc(k5_rusub_4(A,B,C),A) ) )).

fof(fc11_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ( v1_xboole_0(k1_pre_topc(A))
        & v3_pre_topc(k1_pre_topc(A),A)
        & v4_pre_topc(k1_pre_topc(A),A)
        & v2_tops_1(k1_pre_topc(A),A)
        & v3_tops_1(k1_pre_topc(A),A)
        & v1_membered(k1_pre_topc(A))
        & v2_membered(k1_pre_topc(A))
        & v3_membered(k1_pre_topc(A))
        & v4_membered(k1_pre_topc(A))
        & v5_membered(k1_pre_topc(A))
        & v2_rltopsp1(k1_pre_topc(A),A)
        & v3_rltopsp1(k1_pre_topc(A),A)
        & v9_rltopsp1(k1_pre_topc(A),A) ) ) )).

fof(rc9_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v9_rltopsp1(B,A) ) ) )).

fof(fc12_rltopsp1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_numbers) )
     => ( v1_relat_1(k4_rltopsp1(A,B))
        & v1_funct_1(k4_rltopsp1(A,B))
        & v1_funct_2(k4_rltopsp1(A,B),u1_struct_0(A),u1_struct_0(A))
        & v3_tops_2(k4_rltopsp1(A,B),A,A) ) ) )).

fof(fc13_rltopsp1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A)
        & v9_rltopsp1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_numbers) )
     => v9_rltopsp1(k1_convex1(A,B,C),A) ) )).

fof(cc2_rltopsp1,axiom,(
    ! [A] :
      ( l1_rltopsp1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_urysohn1(A)
          & v3_rlvect_1(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & v7_rlvect_1(A)
          & v6_rltopsp1(A)
          & v7_rltopsp1(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v3_compts_1(A)
          & v3_rlvect_1(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & v7_rlvect_1(A)
          & v6_rltopsp1(A)
          & v7_rltopsp1(A) ) ) ) )).

fof(fc14_rltopsp1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A)
        & v1_convex1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v4_pre_topc(k6_pre_topc(A,B),A)
        & v1_convex1(k6_pre_topc(A,B),A) ) ) )).

fof(fc15_rltopsp1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A)
        & v1_convex1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v3_pre_topc(k1_tops_1(A,B),A)
        & v1_convex1(k1_tops_1(A,B),A) ) ) )).

fof(fc16_rltopsp1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A)
        & v3_rltopsp1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v4_pre_topc(k6_pre_topc(A,B),A)
        & v2_rltopsp1(k6_pre_topc(A,B),A)
        & v3_rltopsp1(k6_pre_topc(A,B),A) ) ) )).

fof(fc17_rltopsp1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A)
        & v9_rltopsp1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v4_pre_topc(k6_pre_topc(A,B),A)
        & v9_rltopsp1(k6_pre_topc(A,B),A) ) ) )).

fof(t1_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( r2_hidden(C,B)
                   => r2_hidden(k3_rlvect_1(A,C,D),k1_convex1(A,B,D)) ) ) ) ) ) )).

fof(t2_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( r1_compts_1(A,C,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( r2_hidden(D,B)
                        & ! [E] :
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                           => ~ ( r2_hidden(D,E)
                                & r2_hidden(E,C) ) ) ) ) ) ) ) ) )).

fof(t3_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(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] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r2_hidden(D,B)
                          & r2_hidden(E,C) )
                       => r2_hidden(k2_rlvect_1(A,D,E),k6_rusub_4(A,B,C)) ) ) ) ) ) ) )).

fof(t5_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k5_rusub_4(A,B,k1_rlvect_1(A)) = B ) ) )).

fof(t6_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => k5_rusub_4(A,D,k2_rlvect_1(A,B,C)) = k5_rusub_4(A,k5_rusub_4(A,D,C),B) ) ) ) ) )).

fof(t7_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => k6_rusub_4(A,k5_rusub_4(A,C,B),D) = k5_rusub_4(A,k6_rusub_4(A,C,D),B) ) ) ) ) )).

fof(t8_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(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] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_tarski(B,C)
                   => r1_tarski(k5_rusub_4(A,B,D),k5_rusub_4(A,C,D)) ) ) ) ) ) )).

fof(t9_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,B)
               => r2_hidden(k1_rlvect_1(A),k5_rusub_4(A,B,k5_rlvect_1(A,C))) ) ) ) ) )).

fof(t10_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(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] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r1_tarski(B,C)
                   => r1_tarski(k6_rusub_4(A,B,D),k6_rusub_4(A,C,D)) ) ) ) ) ) )).

fof(t11_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(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] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r1_tarski(B,D)
                          & r1_tarski(C,E) )
                       => r1_tarski(k6_rusub_4(A,B,C),k6_rusub_4(A,D,E)) ) ) ) ) ) ) )).

fof(t12_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v5_rlvect_1(A)
        & l1_rlvect_1(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)))
             => ( r2_hidden(k1_rlvect_1(A),C)
               => r1_tarski(B,k6_rusub_4(A,B,C)) ) ) ) ) )).

fof(t13_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => k1_convex1(A,k1_struct_0(A,k1_rlvect_1(A)),B) = k1_struct_0(A,k1_rlvect_1(A)) ) ) )).

fof(t14_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_numbers) )
             => ( r2_hidden(k1_rlvect_1(A),k1_convex1(A,B,C))
               => r2_hidden(k1_rlvect_1(A),B) ) ) ) ) )).

fof(t15_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_numbers) )
                 => k5_subset_1(u1_struct_0(A),k1_convex1(A,B,D),k1_convex1(A,C,D)) = k1_convex1(A,k5_subset_1(u1_struct_0(A),B,C),D) ) ) ) ) )).

fof(t16_rltopsp1,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_connsp_2(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r1_tarski(C,D)
                   => m1_connsp_2(D,A,B) ) ) ) ) ) )).

fof(d1_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_convex1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ( ( r1_xreal_0(np__0,E)
                            & r1_xreal_0(E,np__1)
                            & r2_hidden(C,B)
                            & r2_hidden(D,B) )
                         => r2_hidden(k4_rlvect_1(A,k3_rlvect_1(A,C,E),k3_rlvect_1(A,D,k5_real_1(np__1,E))),B) ) ) ) ) ) ) ) )).

fof(t17_rltopsp1,axiom,(
    $true )).

fof(t18_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( v1_convex1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => k3_convex1(A,B) = B ) ) )).

fof(t19_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => k1_convex1(A,k3_convex1(A,B),C) = k3_convex1(A,k1_convex1(A,B,C)) ) ) ) )).

fof(t20_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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)))
             => ( r1_tarski(B,C)
               => r1_tarski(k2_convex1(A,C),k2_convex1(A,B)) ) ) ) ) )).

fof(t21_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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)))
             => ( r1_tarski(B,C)
               => r1_tarski(k3_convex1(A,B),k3_convex1(A,C)) ) ) ) ) )).

fof(t22_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( v1_convex1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( ( r1_xreal_0(np__0,C)
                  & r1_xreal_0(C,np__1)
                  & r2_hidden(k1_rlvect_1(A),B) )
               => r1_tarski(k1_convex1(A,B,C),B) ) ) ) ) )).

fof(t23_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_convex1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => r1_tarski(k1_rltopsp1(A,C,D),B) ) ) ) ) ) ) )).

fof(d3_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_rltopsp1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v1_convex1(C,A) ) ) ) ) ) )).

fof(t24_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( v1_rltopsp1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
         => v1_convex1(k6_setfam_1(u1_struct_0(A),B),A) ) ) )).

fof(d4_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k2_rltopsp1(A,B) = k1_convex1(A,B,k1_real_1(np__1)) ) ) )).

fof(t25_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(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] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ~ r1_xboole_0(k5_rusub_4(A,B,D),C)
                  <=> r2_hidden(D,k7_rusub_4(A,C,k2_rltopsp1(A,B))) ) ) ) ) ) )).

fof(d5_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_rltopsp1(B,A)
          <=> B = k2_rltopsp1(A,B) ) ) ) )).

fof(t26_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( v2_rltopsp1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,B)
               => r2_hidden(k5_rlvect_1(A,C),B) ) ) ) ) )).

fof(d6_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_rltopsp1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => ( r1_xreal_0(k18_complex1(C),np__1)
                 => r1_tarski(k1_convex1(A,B,C),B) ) ) ) ) ) )).

fof(t27_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => v3_rltopsp1(k1_struct_0(A,k1_rlvect_1(A)),A) ) )).

fof(t28_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v3_rltopsp1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => r2_hidden(k1_rlvect_1(A),B) ) ) )).

fof(t29_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( v3_rltopsp1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( k18_complex1(C) = np__1
               => k1_convex1(A,B,C) = B ) ) ) ) )).

fof(d7_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v4_rltopsp1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v3_rltopsp1(C,A) ) ) ) ) ) )).

fof(t30_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( v4_rltopsp1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
         => v3_rltopsp1(k5_setfam_1(u1_struct_0(A),B),A) ) ) )).

fof(t31_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( v4_rltopsp1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
         => v3_rltopsp1(k6_setfam_1(u1_struct_0(A),B),A) ) ) )).

fof(d8_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rltopsp1(A) )
     => ( v6_rltopsp1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ~ ( v3_pre_topc(D,A)
                        & r2_hidden(k2_rlvect_1(A,B,C),D)
                        & ! [E] :
                            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                           => ! [F] :
                                ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                               => ~ ( v3_pre_topc(E,A)
                                    & v3_pre_topc(F,A)
                                    & r2_hidden(B,E)
                                    & r2_hidden(C,F)
                                    & r1_tarski(k6_rusub_4(A,E,F),D) ) ) ) ) ) ) ) ) ) )).

fof(d9_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rltopsp1(A) )
     => ( v7_rltopsp1(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ~ ( v3_pre_topc(D,A)
                        & r2_hidden(k3_rlvect_1(A,C,B),D)
                        & ! [E] :
                            ( ( v2_xreal_0(E)
                              & m1_subset_1(E,k1_numbers) )
                           => ! [F] :
                                ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                               => ~ ( v3_pre_topc(F,A)
                                    & r2_hidden(C,F)
                                    & ! [G] :
                                        ( m1_subset_1(G,k1_numbers)
                                       => ( ~ r1_xreal_0(E,k18_complex1(k5_real_1(G,B)))
                                         => r1_tarski(k1_convex1(A,F,G),D) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t32_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_connsp_2(D,A,k4_rlvect_1(A,B,C))
                 => ? [E] :
                      ( m1_connsp_2(E,A,B)
                      & ? [F] :
                          ( m1_connsp_2(F,A,C)
                          & r1_tarski(k7_rusub_4(A,E,F),D) ) ) ) ) ) ) )).

fof(t33_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_connsp_2(D,A,k3_rlvect_1(A,C,B))
                 => ? [E] :
                      ( v2_xreal_0(E)
                      & m1_subset_1(E,k1_numbers)
                      & ? [F] :
                          ( m1_connsp_2(F,A,C)
                          & ! [G] :
                              ( m1_subset_1(G,k1_numbers)
                             => ( ~ r1_xreal_0(E,k18_complex1(k5_real_1(G,B)))
                               => r1_tarski(k1_convex1(A,F,G),D) ) ) ) ) ) ) ) ) )).

fof(d10_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( C = k3_rltopsp1(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) = k2_rlvect_1(A,B,D) ) ) ) ) ) )).

fof(t34_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k4_pre_topc(A,A,k3_rltopsp1(A,B),C) = k5_rusub_4(A,C,B) ) ) ) )).

fof(t35_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_relat_1(k3_rltopsp1(A,B)) = k2_pre_topc(A) ) ) )).

fof(t36_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_tops_2(A,A,k3_rltopsp1(A,B)) = k3_rltopsp1(A,k5_rlvect_1(A,B)) ) ) )).

fof(t37_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(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] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r1_tarski(k7_rusub_4(A,B,C),D)
                   => r1_tarski(k7_rusub_4(A,k1_tops_1(A,B),k1_tops_1(A,C)),k1_tops_1(A,D)) ) ) ) ) ) )).

fof(t38_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k5_rusub_4(A,k1_tops_1(A,C),B) = k1_tops_1(A,k5_rusub_4(A,C,B)) ) ) ) )).

fof(t39_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k5_rusub_4(A,k6_pre_topc(A,C),B) = k6_pre_topc(A,k5_rusub_4(A,C,B)) ) ) ) )).

fof(t40_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_connsp_2(D,A,B)
                 => m1_connsp_2(k5_rusub_4(A,D,C),A,k4_rlvect_1(A,C,B)) ) ) ) ) )).

fof(t41_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_connsp_2(C,A,B)
             => m1_connsp_2(k5_rusub_4(A,C,k5_rlvect_1(A,B)),A,k1_rlvect_1(A)) ) ) ) )).

fof(d11_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rltopsp1(A) )
     => ( v8_rltopsp1(A)
      <=> ? [B] :
            ( m1_yellow13(B,A,k1_rlvect_1(A))
            & v1_rltopsp1(B,A) ) ) ) )).

fof(d12_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v9_rltopsp1(B,A)
          <=> ! [C] :
                ( m1_connsp_2(C,A,k1_rlvect_1(A))
               => ? [D] :
                    ( m1_subset_1(D,k1_numbers)
                    & ~ r1_xreal_0(D,np__0)
                    & ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ( ~ r1_xreal_0(E,D)
                         => r1_tarski(B,k1_convex1(A,C,E)) ) ) ) ) ) ) ) )).

fof(t42_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( ( v9_rltopsp1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v9_rltopsp1(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => v9_rltopsp1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) )).

fof(t43_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( ( v9_rltopsp1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(C,B)
               => v9_rltopsp1(C,A) ) ) ) ) )).

fof(d13_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( C = k4_rltopsp1(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) = k3_rlvect_1(A,D,B) ) ) ) ) ) )).

fof(t47_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_numbers) )
             => k4_pre_topc(A,A,k4_rltopsp1(A,C),B) = k1_convex1(A,B,C) ) ) ) )).

fof(t48_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_numbers) )
         => k2_relat_1(k4_rltopsp1(A,B)) = k2_pre_topc(A) ) ) )).

fof(t49_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_numbers) )
         => k2_tops_2(A,A,k4_rltopsp1(A,B)) = k4_rltopsp1(A,k2_real_1(B)) ) ) )).

fof(t50_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( ( v3_pre_topc(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_numbers) )
             => v3_pre_topc(k1_convex1(A,B,C),A) ) ) ) )).

fof(t51_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( ( v4_pre_topc(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_numbers) )
             => v4_pre_topc(k1_convex1(A,B,C),A) ) ) ) )).

fof(t52_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_numbers) )
             => k1_convex1(A,k1_tops_1(A,B),C) = k1_tops_1(A,k1_convex1(A,B,C)) ) ) ) )).

fof(t53_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_numbers) )
             => k1_convex1(A,k6_pre_topc(A,B),C) = k6_pre_topc(A,k1_convex1(A,B,C)) ) ) ) )).

fof(t54_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_urysohn1(A)
           => k1_convex1(A,k6_pre_topc(A,B),np__0) = k6_pre_topc(A,k1_convex1(A,B,np__0)) ) ) ) )).

fof(t55_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_connsp_2(C,A,B)
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_numbers) )
                 => m1_connsp_2(k1_convex1(A,C,D),A,k3_rlvect_1(A,B,D)) ) ) ) ) )).

fof(t56_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_connsp_2(B,A,k1_rlvect_1(A))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_numbers) )
             => m1_connsp_2(k1_convex1(A,B,C),A,k1_rlvect_1(A)) ) ) ) )).

fof(t57_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_connsp_2(B,A,k1_rlvect_1(A))
         => ? [C] :
              ( v3_pre_topc(C,A)
              & m1_connsp_2(C,A,k1_rlvect_1(A))
              & v2_rltopsp1(C,A)
              & r1_tarski(k7_rusub_4(A,C,C),B) ) ) ) )).

fof(t58_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( ( v6_compts_1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v4_pre_topc(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ~ ( r1_xboole_0(B,C)
                  & ! [D] :
                      ( m1_connsp_2(D,A,k1_rlvect_1(A))
                     => ~ r1_xboole_0(k7_rusub_4(A,B,D),k7_rusub_4(A,C,D)) ) ) ) ) ) )).

fof(t59_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_yellow13(B,A,k1_rlvect_1(A))
         => ! [C] :
              ( m1_connsp_2(C,A,k1_rlvect_1(A))
             => ? [D] :
                  ( m1_connsp_2(D,A,k1_rlvect_1(A))
                  & r2_hidden(D,B)
                  & r1_tarski(k6_pre_topc(A,D),C) ) ) ) ) )).

fof(t60_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_connsp_2(B,A,k1_rlvect_1(A))
         => ? [C] :
              ( m1_connsp_2(C,A,k1_rlvect_1(A))
              & r1_tarski(k6_pre_topc(A,C),B) ) ) ) )).

fof(t62_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(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)))
             => r1_tarski(k7_rusub_4(A,k1_tops_1(A,B),k1_tops_1(A,C)),k1_tops_1(A,k7_rusub_4(A,B,C))) ) ) ) )).

fof(t63_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(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)))
             => r1_tarski(k7_rusub_4(A,k6_pre_topc(A,B),k6_pre_topc(A,C)),k6_pre_topc(A,k7_rusub_4(A,B,C))) ) ) ) )).

fof(t64_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( ( v3_rltopsp1(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( r2_hidden(k1_rlvect_1(A),k1_tops_1(A,B))
           => v3_rltopsp1(k1_tops_1(A,B),A) ) ) ) )).

fof(t65_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_connsp_2(B,A,k1_rlvect_1(A))
         => ? [C] :
              ( m1_connsp_2(C,A,k1_rlvect_1(A))
              & v3_rltopsp1(C,A)
              & r1_tarski(C,B) ) ) ) )).

fof(t66_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_connsp_2(B,A,k1_rlvect_1(A))
         => ~ ( v1_convex1(B,A)
              & ! [C] :
                  ( m1_connsp_2(C,A,k1_rlvect_1(A))
                 => ~ ( v3_rltopsp1(C,A)
                      & v1_convex1(C,A)
                      & r1_tarski(C,B) ) ) ) ) ) )).

fof(t67_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ? [B] :
          ( m1_yellow13(B,A,k1_rlvect_1(A))
          & v4_rltopsp1(B,A) ) ) )).

fof(t68_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ~ ( v8_rltopsp1(A)
          & ! [B] :
              ( m1_yellow13(B,A,k1_rlvect_1(A))
             => ~ v1_rltopsp1(B,A) ) ) ) )).

fof(dt_l1_rltopsp1,axiom,(
    ! [A] :
      ( l1_rltopsp1(A)
     => ( l2_rlvect_1(A)
        & l1_pre_topc(A) ) ) )).

fof(existence_l1_rltopsp1,axiom,(
    ? [A] : l1_rltopsp1(A) )).

fof(abstractness_v5_rltopsp1,axiom,(
    ! [A] :
      ( l1_rltopsp1(A)
     => ( v5_rltopsp1(A)
       => A = g1_rltopsp1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_pre_topc(A)) ) ) )).

fof(dt_k1_rltopsp1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_rltopsp1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k2_rltopsp1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l2_rlvect_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k2_rltopsp1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k3_rltopsp1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_rltopsp1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_funct_1(k3_rltopsp1(A,B))
        & v1_funct_2(k3_rltopsp1(A,B),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k3_rltopsp1(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(dt_k4_rltopsp1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_rltopsp1(A)
        & m1_subset_1(B,k1_numbers) )
     => ( v1_funct_1(k4_rltopsp1(A,B))
        & v1_funct_2(k4_rltopsp1(A,B),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k4_rltopsp1(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(dt_g1_rltopsp1,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( v5_rltopsp1(g1_rltopsp1(A,B,C,D,E))
        & l1_rltopsp1(g1_rltopsp1(A,B,C,D,E)) ) ) )).

fof(free_g1_rltopsp1,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [F,G,H,I,J] :
          ( g1_rltopsp1(A,B,C,D,E) = g1_rltopsp1(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) )).

fof(t4_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(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] :
                  ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
                 => ( D = a_3_0_rltopsp1(A,B,C)
                   => k6_rusub_4(A,B,C) = k5_setfam_1(u1_struct_0(A),D) ) ) ) ) ) )).

fof(d2_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_rltopsp1(A,B,C) = a_3_1_rltopsp1(A,B,C) ) ) ) )).

fof(t44_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ( v1_finset_1(B)
              & B = a_1_0_rltopsp1(A) )
           => v9_rltopsp1(k5_setfam_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t45_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( B = a_1_1_rltopsp1(A)
           => m1_yellow13(B,A,k1_rlvect_1(A)) ) ) ) )).

fof(t46_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_yellow13(B,A,k1_rlvect_1(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
             => ( C = a_2_0_rltopsp1(A,B)
               => m2_yellow13(C,A) ) ) ) ) )).

fof(t61_rltopsp1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v6_rltopsp1(A)
        & v7_rltopsp1(A)
        & l1_rltopsp1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_pre_topc(A,B) = k1_setfam_1(a_2_1_rltopsp1(A,B)) ) ) )).

fof(fraenkel_a_3_0_rltopsp1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & l1_rlvect_1(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_3_0_rltopsp1(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k5_rusub_4(B,D,E)
            & r2_hidden(E,C) ) ) ) )).

fof(fraenkel_a_3_1_rltopsp1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & l2_rlvect_1(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_1_rltopsp1(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,k1_numbers)
            & A = k4_rlvect_1(B,k3_rlvect_1(B,C,k5_real_1(np__1,E)),k3_rlvect_1(B,D,E))
            & r1_xreal_0(np__0,E)
            & r1_xreal_0(E,np__1) ) ) ) )).

fof(fraenkel_a_1_0_rltopsp1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v6_rltopsp1(B)
        & v7_rltopsp1(B)
        & l1_rltopsp1(B) )
     => ( r2_hidden(A,a_1_0_rltopsp1(B))
      <=> ? [C] :
            ( v9_rltopsp1(C,B)
            & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
            & A = C ) ) ) )).

fof(fraenkel_a_1_1_rltopsp1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v6_rltopsp1(B)
        & v7_rltopsp1(B)
        & l1_rltopsp1(B) )
     => ( r2_hidden(A,a_1_1_rltopsp1(B))
      <=> ? [C] :
            ( m1_connsp_2(C,B,k1_rlvect_1(B))
            & A = C ) ) ) )).

fof(fraenkel_a_2_0_rltopsp1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v6_rltopsp1(B)
        & v7_rltopsp1(B)
        & l1_rltopsp1(B)
        & m1_yellow13(C,B,k1_rlvect_1(B)) )
     => ( r2_hidden(A,a_2_0_rltopsp1(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,u1_struct_0(B))
            & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
            & A = k5_rusub_4(B,E,D)
            & r2_hidden(E,C) ) ) ) )).

fof(fraenkel_a_2_1_rltopsp1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v6_rltopsp1(B)
        & v7_rltopsp1(B)
        & l1_rltopsp1(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_1_rltopsp1(B,C))
      <=> ? [D] :
            ( m1_connsp_2(D,B,k1_rlvect_1(B))
            & A = k7_rusub_4(B,C,D) ) ) ) )).
%------------------------------------------------------------------------------