SET007 Axioms: SET007+806.ax


%------------------------------------------------------------------------------
% File     : SET007+806 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Banach Space of Bounded Real Sequences
% 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    : rsspace4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   60 (   6 unit)
%            Number of atoms       :  750 (  65 equality)
%            Maximal formula depth :   21 (  11 average)
%            Number of connectives :  793 ( 103 ~  ;   0  |; 511  &)
%                                         (  16 <=>; 163 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   32 (   1 propositional; 0-3 arity)
%            Number of functors    :   45 (   9 constant; 0-5 arity)
%            Number of variables   :  172 (   0 singleton; 168 !;   4 ?)
%            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_rsspace4,axiom,(
    ~ v1_xboole_0(k1_rsspace4) )).

fof(fc2_rsspace4,axiom,(
    v1_rlsub_1(k1_rsspace4,k7_rsspace) )).

fof(fc3_rsspace4,axiom,
    ( ~ v3_struct_0(g2_rlvect_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4)))
    & v2_rlvect_1(g2_rlvect_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4)))
    & v3_rlvect_1(g2_rlvect_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4)))
    & v4_rlvect_1(g2_rlvect_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4)))
    & v5_rlvect_1(g2_rlvect_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4)))
    & v6_rlvect_1(g2_rlvect_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4)))
    & v7_rlvect_1(g2_rlvect_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4))) )).

fof(fc4_rsspace4,axiom,
    ( ~ v3_struct_0(g1_normsp_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4),k2_rsspace4))
    & v3_rlvect_1(g1_normsp_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4),k2_rsspace4))
    & v4_rlvect_1(g1_normsp_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4),k2_rsspace4))
    & v5_rlvect_1(g1_normsp_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4),k2_rsspace4))
    & v6_rlvect_1(g1_normsp_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4),k2_rsspace4))
    & v7_rlvect_1(g1_normsp_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4),k2_rsspace4))
    & v1_normsp_1(g1_normsp_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4),k2_rsspace4)) )).

fof(fc5_rsspace4,axiom,
    ( ~ v3_struct_0(k3_rsspace4)
    & v3_rlvect_1(k3_rsspace4)
    & v4_rlvect_1(k3_rsspace4)
    & v5_rlvect_1(k3_rsspace4)
    & v6_rlvect_1(k3_rsspace4)
    & v7_rlvect_1(k3_rsspace4)
    & v2_normsp_1(k3_rsspace4) )).

fof(rc1_rsspace4,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ? [C] :
          ( m1_relset_1(C,A,u1_struct_0(B))
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,A,u1_struct_0(B))
          & v1_partfun1(C,A,u1_struct_0(B))
          & v1_rsspace4(C,A,B) ) ) )).

fof(fc6_rsspace4,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ~ v1_xboole_0(k4_rsspace4(A,B)) ) )).

fof(fc7_rsspace4,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ( ~ v3_struct_0(g2_rlvect_1(k4_rsspace4(A,B),k10_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B))))
        & v2_rlvect_1(g2_rlvect_1(k4_rsspace4(A,B),k10_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B))))
        & v3_rlvect_1(g2_rlvect_1(k4_rsspace4(A,B),k10_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B))))
        & v4_rlvect_1(g2_rlvect_1(k4_rsspace4(A,B),k10_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B))))
        & v5_rlvect_1(g2_rlvect_1(k4_rsspace4(A,B),k10_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B))))
        & v6_rlvect_1(g2_rlvect_1(k4_rsspace4(A,B),k10_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B))))
        & v7_rlvect_1(g2_rlvect_1(k4_rsspace4(A,B),k10_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)))) ) ) )).

fof(fc8_rsspace4,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ( ~ v3_struct_0(k5_rsspace4(A,B))
        & v2_rlvect_1(k5_rsspace4(A,B))
        & v3_rlvect_1(k5_rsspace4(A,B))
        & v4_rlvect_1(k5_rsspace4(A,B))
        & v5_rlvect_1(k5_rsspace4(A,B))
        & v6_rlvect_1(k5_rsspace4(A,B))
        & v7_rlvect_1(k5_rsspace4(A,B)) ) ) )).

fof(fc9_rsspace4,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ( ~ v3_struct_0(k9_rsspace4(A,B))
        & v3_rlvect_1(k9_rsspace4(A,B))
        & v4_rlvect_1(k9_rsspace4(A,B))
        & v5_rlvect_1(k9_rsspace4(A,B))
        & v6_rlvect_1(k9_rsspace4(A,B))
        & v7_rlvect_1(k9_rsspace4(A,B))
        & v2_normsp_1(k9_rsspace4(A,B)) ) ) )).

fof(fc10_rsspace4,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & v4_lopban_1(B)
        & l1_normsp_1(B) )
     => ( ~ v3_struct_0(k9_rsspace4(A,B))
        & v3_rlvect_1(k9_rsspace4(A,B))
        & v4_rlvect_1(k9_rsspace4(A,B))
        & v5_rlvect_1(k9_rsspace4(A,B))
        & v6_rlvect_1(k9_rsspace4(A,B))
        & v7_rlvect_1(k9_rsspace4(A,B))
        & v2_normsp_1(k9_rsspace4(A,B))
        & v4_lopban_1(k9_rsspace4(A,B)) ) ) )).

fof(d1_rsspace4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k7_rsspace)))
     => ( A = k1_rsspace4
      <=> ! [B] :
            ( r2_hidden(B,A)
          <=> ( r2_hidden(B,k1_rsspace)
              & v3_seq_2(k2_rsspace(B)) ) ) ) ) )).

fof(d2_rsspace4,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k1_rsspace4,k1_numbers)
        & m2_relset_1(A,k1_rsspace4,k1_numbers) )
     => ( A = k2_rsspace4
      <=> ! [B] :
            ( r2_hidden(B,k1_rsspace4)
           => k2_seq_1(k1_rsspace4,k1_numbers,A,B) = k3_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,k22_seq_1(k2_rsspace(B)))) ) ) ) )).

fof(t1_rsspace4,axiom,(
    $true )).

fof(t2_rsspace4,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v3_seq_2(A)
          & k3_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,k22_seq_1(A))) = np__0 )
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k2_seq_1(k5_numbers,k1_numbers,A,B) = np__0 ) ) ) )).

fof(d3_rsspace4,axiom,(
    k3_rsspace4 = g1_normsp_1(k1_rsspace4,k10_rsspace(k7_rsspace,k1_rsspace4),k8_rsspace(k7_rsspace,k1_rsspace4),k9_rsspace(k7_rsspace,k1_rsspace4),k2_rsspace4) )).

fof(t3_rsspace4,axiom,
    ( u1_struct_0(k3_rsspace4) = k1_rsspace4
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_rsspace4))
      <=> ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k1_numbers)
          & m2_relset_1(A,k5_numbers,k1_numbers)
          & v3_seq_2(k2_rsspace(A)) ) )
    & k1_rlvect_1(k3_rsspace4) = k6_rsspace
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_rsspace4))
       => A = k2_rsspace(A) )
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_rsspace4))
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k3_rsspace4))
           => k2_rlvect_1(k3_rsspace4,A,B) = k9_seq_1(k2_rsspace(A),k2_rsspace(B)) ) )
    & ! [A] :
        ( m1_subset_1(A,k1_numbers)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k3_rsspace4))
           => k3_rlvect_1(k3_rsspace4,B,A) = k14_seq_1(k2_rsspace(B),A) ) )
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_rsspace4))
       => ( k5_rlvect_1(k3_rsspace4,A) = k17_seq_1(k2_rsspace(A))
          & k2_rsspace(k5_rlvect_1(k3_rsspace4,A)) = k17_seq_1(k2_rsspace(A)) ) )
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_rsspace4))
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k3_rsspace4))
           => k6_rlvect_1(k3_rsspace4,A,B) = k10_seq_1(k2_rsspace(A),k2_rsspace(B)) ) )
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_rsspace4))
       => v3_seq_2(k2_rsspace(A)) )
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_rsspace4))
       => k1_normsp_1(k3_rsspace4,A) = k3_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,k22_seq_1(k2_rsspace(A)))) ) )).

fof(t4_rsspace4,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_rsspace4))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_rsspace4))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( ( k1_normsp_1(k3_rsspace4,A) = np__0
                 => A = k1_rlvect_1(k3_rsspace4) )
                & ( A = k1_rlvect_1(k3_rsspace4)
                 => k1_normsp_1(k3_rsspace4,A) = np__0 )
                & r1_xreal_0(np__0,k1_normsp_1(k3_rsspace4,A))
                & r1_xreal_0(k1_normsp_1(k3_rsspace4,k2_rlvect_1(k3_rsspace4,A,B)),k3_real_1(k1_normsp_1(k3_rsspace4,A),k1_normsp_1(k3_rsspace4,B)))
                & k1_normsp_1(k3_rsspace4,k3_rlvect_1(k3_rsspace4,A,C)) = k4_real_1(k18_complex1(C),k1_normsp_1(k3_rsspace4,A)) ) ) ) ) )).

fof(t5_rsspace4,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,u1_struct_0(k3_rsspace4))
        & m2_relset_1(A,k5_numbers,u1_struct_0(k3_rsspace4)) )
     => ( v1_rsspace3(A,k3_rsspace4)
       => v4_normsp_1(A,k3_rsspace4) ) ) )).

fof(d4_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ( v1_rsspace4(C,A,B)
              <=> ? [D] :
                    ( m1_subset_1(D,k1_numbers)
                    & r1_xreal_0(np__0,D)
                    & ! [E] :
                        ( m1_subset_1(E,A)
                       => r1_xreal_0(k1_normsp_1(B,k8_funct_2(A,u1_struct_0(B),C,E)),D) ) ) ) ) ) ) )).

fof(t6_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ( ! [D] :
                    ( m1_subset_1(D,A)
                   => k8_funct_2(A,u1_struct_0(B),C,D) = k1_rlvect_1(B) )
               => v1_rsspace4(C,A,B) ) ) ) ) )).

fof(d5_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_lopban_1(A,B))))
             => ( C = k4_rsspace4(A,B)
              <=> ! [D] :
                    ( r2_hidden(D,C)
                  <=> ( v1_funct_1(D)
                      & v1_funct_2(D,A,u1_struct_0(B))
                      & v1_rsspace4(D,A,B)
                      & m2_relset_1(D,A,u1_struct_0(B)) ) ) ) ) ) ) )).

fof(t7_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => v1_rlsub_1(k4_rsspace4(A,B),k5_lopban_1(A,B)) ) ) )).

fof(t8_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => m1_rlsub_1(g2_rlvect_1(k4_rsspace4(A,B),k10_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B))),k5_lopban_1(A,B)) ) ) )).

fof(d6_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => k5_rsspace4(A,B) = g2_rlvect_1(k4_rsspace4(A,B),k10_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B))) ) ) )).

fof(t9_rsspace4,axiom,(
    $true )).

fof(t10_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_rsspace4(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k5_rsspace4(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k5_rsspace4(A,B)))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,u1_struct_0(B))
                            & v1_rsspace4(F,A,B)
                            & m2_relset_1(F,A,u1_struct_0(B)) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,A,u1_struct_0(B))
                                & v1_rsspace4(G,A,B)
                                & m2_relset_1(G,A,u1_struct_0(B)) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,A,u1_struct_0(B))
                                    & v1_rsspace4(H,A,B)
                                    & m2_relset_1(H,A,u1_struct_0(B)) )
                                 => ( ( F = C
                                      & G = D
                                      & H = E )
                                   => ( E = k4_rlvect_1(k5_rsspace4(A,B),C,D)
                                    <=> ! [I] :
                                          ( m1_subset_1(I,A)
                                         => k8_funct_2(A,u1_struct_0(B),H,I) = k4_rlvect_1(B,k8_funct_2(A,u1_struct_0(B),F,I),k8_funct_2(A,u1_struct_0(B),G,I)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t11_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_rsspace4(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k5_rsspace4(A,B)))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(B))
                        & v1_rsspace4(E,A,B)
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,u1_struct_0(B))
                            & v1_rsspace4(F,A,B)
                            & m2_relset_1(F,A,u1_struct_0(B)) )
                         => ( ( E = C
                              & F = D )
                           => ! [G] :
                                ( m1_subset_1(G,k1_numbers)
                               => ( D = k3_rlvect_1(k5_rsspace4(A,B),C,G)
                                <=> ! [H] :
                                      ( m1_subset_1(H,A)
                                     => k8_funct_2(A,u1_struct_0(B),F,H) = k3_rlvect_1(B,k8_funct_2(A,u1_struct_0(B),E,H),G) ) ) ) ) ) ) ) ) ) ) )).

fof(t12_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => k1_rlvect_1(k5_rsspace4(A,B)) = k2_funcop_1(A,k1_rlvect_1(B)) ) ) )).

fof(d7_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( r2_hidden(C,k4_rsspace4(A,B))
             => k6_rsspace4(A,B,C) = C ) ) ) )).

fof(t13_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & v1_rsspace4(C,A,B)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ( ~ v1_xboole_0(k7_rsspace4(A,B,C))
                & v1_seq_4(k7_rsspace4(A,B,C)) ) ) ) ) )).

fof(t14_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ( v1_rsspace4(C,A,B)
              <=> v1_seq_4(k7_rsspace4(A,B,C)) ) ) ) ) )).

fof(t15_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ? [C] :
              ( v1_funct_1(C)
              & v1_funct_2(C,k4_rsspace4(A,B),k1_numbers)
              & m2_relset_1(C,k4_rsspace4(A,B),k1_numbers)
              & ! [D] :
                  ( r2_hidden(D,k4_rsspace4(A,B))
                 => k2_seq_1(k4_rsspace4(A,B),k1_numbers,C,D) = k3_pscomp_1(k7_rsspace4(A,B,k6_rsspace4(A,B,D))) ) ) ) ) )).

fof(d9_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k4_rsspace4(A,B),k1_numbers)
                & m2_relset_1(C,k4_rsspace4(A,B),k1_numbers) )
             => ( C = k8_rsspace4(A,B)
              <=> ! [D] :
                    ( r2_hidden(D,k4_rsspace4(A,B))
                   => k2_seq_1(k4_rsspace4(A,B),k1_numbers,C,D) = k3_pscomp_1(k7_rsspace4(A,B,k6_rsspace4(A,B,D))) ) ) ) ) ) )).

fof(t16_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & v1_rsspace4(C,A,B)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k6_rsspace4(A,B,C) = C ) ) ) )).

fof(t17_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & v1_rsspace4(C,A,B)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k2_seq_1(k4_rsspace4(A,B),k1_numbers,k8_rsspace4(A,B),C) = k3_pscomp_1(k7_rsspace4(A,B,C)) ) ) ) )).

fof(d10_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => k9_rsspace4(A,B) = g1_normsp_1(k4_rsspace4(A,B),k10_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace4(A,B)) ) ) )).

fof(t18_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => k2_funcop_1(A,k1_rlvect_1(B)) = k1_rlvect_1(k9_rsspace4(A,B)) ) ) )).

fof(t19_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B)))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(B))
                    & v1_rsspace4(D,A,B)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ( D = C
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => r1_xreal_0(k1_normsp_1(B,k8_funct_2(A,u1_struct_0(B),D,E)),k1_normsp_1(k9_rsspace4(A,B),C)) ) ) ) ) ) ) )).

fof(t20_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B)))
             => r1_xreal_0(np__0,k1_normsp_1(k9_rsspace4(A,B),C)) ) ) ) )).

fof(t21_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B)))
             => ( C = k1_rlvect_1(k9_rsspace4(A,B))
               => np__0 = k1_normsp_1(k9_rsspace4(A,B),C) ) ) ) ) )).

fof(t22_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_rsspace4(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k9_rsspace4(A,B)))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,u1_struct_0(B))
                            & v1_rsspace4(F,A,B)
                            & m2_relset_1(F,A,u1_struct_0(B)) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,A,u1_struct_0(B))
                                & v1_rsspace4(G,A,B)
                                & m2_relset_1(G,A,u1_struct_0(B)) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,A,u1_struct_0(B))
                                    & v1_rsspace4(H,A,B)
                                    & m2_relset_1(H,A,u1_struct_0(B)) )
                                 => ( ( F = C
                                      & G = D
                                      & H = E )
                                   => ( E = k2_rlvect_1(k9_rsspace4(A,B),C,D)
                                    <=> ! [I] :
                                          ( m1_subset_1(I,A)
                                         => k8_funct_2(A,u1_struct_0(B),H,I) = k4_rlvect_1(B,k8_funct_2(A,u1_struct_0(B),F,I),k8_funct_2(A,u1_struct_0(B),G,I)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t23_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_rsspace4(A,B)))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(B))
                        & v1_rsspace4(E,A,B)
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,u1_struct_0(B))
                            & v1_rsspace4(F,A,B)
                            & m2_relset_1(F,A,u1_struct_0(B)) )
                         => ( ( E = C
                              & F = D )
                           => ! [G] :
                                ( m1_subset_1(G,k1_numbers)
                               => ( D = k3_rlvect_1(k9_rsspace4(A,B),C,G)
                                <=> ! [H] :
                                      ( m1_subset_1(H,A)
                                     => k8_funct_2(A,u1_struct_0(B),F,H) = k3_rlvect_1(B,k8_funct_2(A,u1_struct_0(B),E,H),G) ) ) ) ) ) ) ) ) ) ) )).

fof(t24_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_rsspace4(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ( ( k1_normsp_1(k9_rsspace4(A,B),C) = np__0
                         => C = k1_rlvect_1(k9_rsspace4(A,B)) )
                        & ( C = k1_rlvect_1(k9_rsspace4(A,B))
                         => k1_normsp_1(k9_rsspace4(A,B),C) = np__0 )
                        & k1_normsp_1(k9_rsspace4(A,B),k3_rlvect_1(k9_rsspace4(A,B),C,E)) = k4_real_1(k18_complex1(E),k1_normsp_1(k9_rsspace4(A,B),C))
                        & r1_xreal_0(k1_normsp_1(k9_rsspace4(A,B),k2_rlvect_1(k9_rsspace4(A,B),C,D)),k3_real_1(k1_normsp_1(k9_rsspace4(A,B),C),k1_normsp_1(k9_rsspace4(A,B),D))) ) ) ) ) ) ) )).

fof(t25_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => v2_normsp_1(k9_rsspace4(A,B)) ) ) )).

fof(t26_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ( ~ v3_struct_0(k9_rsspace4(A,B))
            & v3_rlvect_1(k9_rsspace4(A,B))
            & v4_rlvect_1(k9_rsspace4(A,B))
            & v5_rlvect_1(k9_rsspace4(A,B))
            & v6_rlvect_1(k9_rsspace4(A,B))
            & v7_rlvect_1(k9_rsspace4(A,B))
            & v2_normsp_1(k9_rsspace4(A,B))
            & l1_normsp_1(k9_rsspace4(A,B)) ) ) ) )).

fof(t27_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_rsspace4(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k9_rsspace4(A,B)))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,u1_struct_0(B))
                            & v1_rsspace4(F,A,B)
                            & m2_relset_1(F,A,u1_struct_0(B)) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,A,u1_struct_0(B))
                                & v1_rsspace4(G,A,B)
                                & m2_relset_1(G,A,u1_struct_0(B)) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,A,u1_struct_0(B))
                                    & v1_rsspace4(H,A,B)
                                    & m2_relset_1(H,A,u1_struct_0(B)) )
                                 => ( ( F = C
                                      & G = D
                                      & H = E )
                                   => ( E = k6_rlvect_1(k9_rsspace4(A,B),C,D)
                                    <=> ! [I] :
                                          ( m1_subset_1(I,A)
                                         => k8_funct_2(A,u1_struct_0(B),H,I) = k6_rlvect_1(B,k8_funct_2(A,u1_struct_0(B),F,I),k8_funct_2(A,u1_struct_0(B),G,I)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t28_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ( v4_lopban_1(B)
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k5_numbers,u1_struct_0(k9_rsspace4(A,B)))
                  & m2_relset_1(C,k5_numbers,u1_struct_0(k9_rsspace4(A,B))) )
               => ( v1_rsspace3(C,k9_rsspace4(A,B))
                 => v4_normsp_1(C,k9_rsspace4(A,B)) ) ) ) ) ) )).

fof(t29_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & v4_lopban_1(B)
            & l1_normsp_1(B) )
         => ( ~ v3_struct_0(k9_rsspace4(A,B))
            & v3_rlvect_1(k9_rsspace4(A,B))
            & v4_rlvect_1(k9_rsspace4(A,B))
            & v5_rlvect_1(k9_rsspace4(A,B))
            & v6_rlvect_1(k9_rsspace4(A,B))
            & v7_rlvect_1(k9_rsspace4(A,B))
            & v2_normsp_1(k9_rsspace4(A,B))
            & v4_lopban_1(k9_rsspace4(A,B))
            & l1_normsp_1(k9_rsspace4(A,B)) ) ) ) )).

fof(dt_k1_rsspace4,axiom,(
    m1_subset_1(k1_rsspace4,k1_zfmisc_1(u1_struct_0(k7_rsspace))) )).

fof(dt_k2_rsspace4,axiom,
    ( v1_funct_1(k2_rsspace4)
    & v1_funct_2(k2_rsspace4,k1_rsspace4,k1_numbers)
    & m2_relset_1(k2_rsspace4,k1_rsspace4,k1_numbers) )).

fof(dt_k3_rsspace4,axiom,
    ( ~ v3_struct_0(k3_rsspace4)
    & l1_normsp_1(k3_rsspace4) )).

fof(dt_k4_rsspace4,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => m1_subset_1(k4_rsspace4(A,B),k1_zfmisc_1(u1_struct_0(k5_lopban_1(A,B)))) ) )).

fof(dt_k5_rsspace4,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ( ~ v3_struct_0(k5_rsspace4(A,B))
        & v3_rlvect_1(k5_rsspace4(A,B))
        & v4_rlvect_1(k5_rsspace4(A,B))
        & v5_rlvect_1(k5_rsspace4(A,B))
        & v6_rlvect_1(k5_rsspace4(A,B))
        & v7_rlvect_1(k5_rsspace4(A,B))
        & l2_rlvect_1(k5_rsspace4(A,B)) ) ) )).

fof(dt_k6_rsspace4,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ( v1_funct_1(k6_rsspace4(A,B,C))
        & v1_funct_2(k6_rsspace4(A,B,C),A,u1_struct_0(B))
        & v1_rsspace4(k6_rsspace4(A,B,C),A,B)
        & m2_relset_1(k6_rsspace4(A,B,C),A,u1_struct_0(B)) ) ) )).

fof(dt_k7_rsspace4,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => ( ~ v1_xboole_0(k7_rsspace4(A,B,C))
        & m1_subset_1(k7_rsspace4(A,B,C),k1_zfmisc_1(k1_numbers)) ) ) )).

fof(dt_k8_rsspace4,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ( v1_funct_1(k8_rsspace4(A,B))
        & v1_funct_2(k8_rsspace4(A,B),k4_rsspace4(A,B),k1_numbers)
        & m2_relset_1(k8_rsspace4(A,B),k4_rsspace4(A,B),k1_numbers) ) ) )).

fof(dt_k9_rsspace4,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B) )
     => ( ~ v3_struct_0(k9_rsspace4(A,B))
        & l1_normsp_1(k9_rsspace4(A,B)) ) ) )).

fof(d8_rsspace4,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k7_rsspace4(A,B,C) = a_3_0_rsspace4(A,B,C) ) ) ) )).

fof(fraenkel_a_3_0_rsspace4,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v7_rlvect_1(C)
        & v2_normsp_1(C)
        & l1_normsp_1(C)
        & v1_funct_1(D)
        & v1_funct_2(D,B,u1_struct_0(C))
        & m2_relset_1(D,B,u1_struct_0(C)) )
     => ( r2_hidden(A,a_3_0_rsspace4(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,B)
            & A = k1_normsp_1(C,k8_funct_2(B,u1_struct_0(C),D,E)) ) ) ) )).
%------------------------------------------------------------------------------