SET007 Axioms: SET007+825.ax


%------------------------------------------------------------------------------
% File     : SET007+825 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Complex Banach Space of Bounded Complex 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    : csspace4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   65 (   6 unit)
%            Number of atoms       :  791 (  67 equality)
%            Maximal formula depth :   21 (  11 average)
%            Number of connectives :  830 ( 104 ~  ;   0  |; 534  &)
%                                         (  18 <=>; 174 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   1 propositional; 0-3 arity)
%            Number of functors    :   49 (  11 constant; 0-5 arity)
%            Number of variables   :  181 (   0 singleton; 177 !;   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_csspace4,axiom,(
    ~ v1_xboole_0(k1_csspace4) )).

fof(fc2_csspace4,axiom,(
    v3_clvect_1(k1_csspace4,k7_csspace) )).

fof(fc3_csspace4,axiom,
    ( ~ v3_struct_0(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4)))
    & v3_rlvect_1(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4)))
    & v4_rlvect_1(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4)))
    & v5_rlvect_1(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4)))
    & v6_rlvect_1(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4)))
    & v1_clvect_1(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4)))
    & v2_clvect_1(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4))) )).

fof(fc4_csspace4,axiom,
    ( ~ v3_struct_0(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4))
    & v3_rlvect_1(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4))
    & v4_rlvect_1(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4))
    & v5_rlvect_1(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4))
    & v6_rlvect_1(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4))
    & v2_clvect_1(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4))
    & v4_clvect_1(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4)) )).

fof(fc5_csspace4,axiom,
    ( ~ v3_struct_0(k3_csspace4)
    & v3_rlvect_1(k3_csspace4)
    & v4_rlvect_1(k3_csspace4)
    & v5_rlvect_1(k3_csspace4)
    & v6_rlvect_1(k3_csspace4)
    & v2_clvect_1(k3_csspace4)
    & v5_clvect_1(k3_csspace4) )).

fof(rc1_csspace4,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_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_csspace4(C,A,B) ) ) )).

fof(fc6_csspace4,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ~ v1_xboole_0(k4_csspace4(A,B)) ) )).

fof(fc7_csspace4,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ( ~ v3_struct_0(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))))
        & v3_rlvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))))
        & v4_rlvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))))
        & v5_rlvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))))
        & v6_rlvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))))
        & v1_clvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))))
        & v2_clvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B)))) ) ) )).

fof(fc8_csspace4,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ( ~ v3_struct_0(k5_csspace4(A,B))
        & v3_rlvect_1(k5_csspace4(A,B))
        & v4_rlvect_1(k5_csspace4(A,B))
        & v5_rlvect_1(k5_csspace4(A,B))
        & v6_rlvect_1(k5_csspace4(A,B))
        & v1_clvect_1(k5_csspace4(A,B))
        & v2_clvect_1(k5_csspace4(A,B)) ) ) )).

fof(fc9_csspace4,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ( ~ v3_struct_0(k9_csspace4(A,B))
        & v3_rlvect_1(k9_csspace4(A,B))
        & v4_rlvect_1(k9_csspace4(A,B))
        & v5_rlvect_1(k9_csspace4(A,B))
        & v6_rlvect_1(k9_csspace4(A,B))
        & v2_clvect_1(k9_csspace4(A,B))
        & v5_clvect_1(k9_csspace4(A,B)) ) ) )).

fof(fc10_csspace4,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & v4_clopban1(B)
        & l2_clvect_1(B) )
     => ( ~ v3_struct_0(k9_csspace4(A,B))
        & v3_rlvect_1(k9_csspace4(A,B))
        & v4_rlvect_1(k9_csspace4(A,B))
        & v5_rlvect_1(k9_csspace4(A,B))
        & v6_rlvect_1(k9_csspace4(A,B))
        & v2_clvect_1(k9_csspace4(A,B))
        & v5_clvect_1(k9_csspace4(A,B))
        & v4_clopban1(k9_csspace4(A,B)) ) ) )).

fof(d1_csspace4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k7_csspace)))
     => ( A = k1_csspace4
      <=> ! [B] :
            ( r2_hidden(B,A)
          <=> ( r2_hidden(B,k1_csspace)
              & v1_comseq_2(k2_csspace(B)) ) ) ) ) )).

fof(d2_csspace4,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k1_csspace4,k1_numbers)
        & m2_relset_1(A,k1_csspace4,k1_numbers) )
     => ( A = k2_csspace4
      <=> ! [B] :
            ( r2_hidden(B,k1_csspace4)
           => k2_seq_1(k1_csspace4,k1_numbers,A,B) = k3_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,k2_csspace(B)))) ) ) ) )).

fof(t1_csspace4,axiom,(
    $true )).

fof(t2_csspace4,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( ( v1_comseq_2(A)
          & k3_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A))) = np__0 )
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k1_comseq_1(A,B) = k5_complex1 ) ) ) )).

fof(d3_csspace4,axiom,(
    k3_csspace4 = g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4) )).

fof(t3_csspace4,axiom,
    ( u1_struct_0(k3_csspace4) = k1_csspace4
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_csspace4))
      <=> ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k2_numbers)
          & m2_relset_1(A,k5_numbers,k2_numbers)
          & v1_comseq_2(k2_csspace(A)) ) )
    & k1_rlvect_1(k3_csspace4) = k6_csspace
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_csspace4))
       => A = k2_csspace(A) )
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_csspace4))
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k3_csspace4))
           => k2_rlvect_1(k3_csspace4,A,B) = k2_comseq_1(k5_numbers,k2_csspace(A),k2_csspace(B)) ) )
    & ! [A] :
        ( m1_subset_1(A,k2_numbers)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k3_csspace4))
           => k1_clvect_1(k3_csspace4,B,A) = k4_comseq_1(k5_numbers,k2_csspace(B),A) ) )
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_csspace4))
       => ( k5_rlvect_1(k3_csspace4,A) = k5_comseq_1(k5_numbers,k2_csspace(A))
          & k2_csspace(k5_rlvect_1(k3_csspace4,A)) = k5_comseq_1(k5_numbers,k2_csspace(A)) ) )
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_csspace4))
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k3_csspace4))
           => k6_rlvect_1(k3_csspace4,A,B) = k6_comseq_1(k5_numbers,k2_csspace(A),k2_csspace(B)) ) )
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_csspace4))
       => v1_comseq_2(k2_csspace(A)) )
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k3_csspace4))
       => k5_clvect_1(k3_csspace4,A) = k3_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,k2_csspace(A)))) ) )).

fof(t4_csspace4,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_csspace4))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_csspace4))
         => ! [C] :
              ( m1_subset_1(C,k2_numbers)
             => ( ( k5_clvect_1(k3_csspace4,A) = np__0
                 => A = k1_rlvect_1(k3_csspace4) )
                & ( A = k1_rlvect_1(k3_csspace4)
                 => k5_clvect_1(k3_csspace4,A) = np__0 )
                & r1_xreal_0(np__0,k5_clvect_1(k3_csspace4,A))
                & r1_xreal_0(k5_clvect_1(k3_csspace4,k2_rlvect_1(k3_csspace4,A,B)),k3_real_1(k5_clvect_1(k3_csspace4,A),k5_clvect_1(k3_csspace4,B)))
                & k5_clvect_1(k3_csspace4,k1_clvect_1(k3_csspace4,A,C)) = k4_real_1(k17_complex1(C),k5_clvect_1(k3_csspace4,A)) ) ) ) ) )).

fof(t5_csspace4,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,u1_struct_0(k3_csspace4))
        & m2_relset_1(A,k5_numbers,u1_struct_0(k3_csspace4)) )
     => ( v1_csspace3(A,k3_csspace4)
       => v6_clvect_1(A,k3_csspace4) ) ) )).

fof(t6_csspace4,axiom,
    ( ~ v3_struct_0(k3_csspace4)
    & v3_rlvect_1(k3_csspace4)
    & v4_rlvect_1(k3_csspace4)
    & v5_rlvect_1(k3_csspace4)
    & v6_rlvect_1(k3_csspace4)
    & v2_clvect_1(k3_csspace4)
    & v5_clvect_1(k3_csspace4)
    & v4_clopban1(k3_csspace4)
    & l2_clvect_1(k3_csspace4) )).

fof(d4_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_csspace4(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(k5_clvect_1(B,k8_funct_2(A,u1_struct_0(B),C,E)),D) ) ) ) ) ) ) )).

fof(t7_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_csspace4(C,A,B) ) ) ) ) )).

fof(d5_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_clopban1(A,B))))
             => ( C = k4_csspace4(A,B)
              <=> ! [D] :
                    ( r2_hidden(D,C)
                  <=> ( v1_funct_1(D)
                      & v1_funct_2(D,A,u1_struct_0(B))
                      & v1_csspace4(D,A,B)
                      & m2_relset_1(D,A,u1_struct_0(B)) ) ) ) ) ) ) )).

fof(t8_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => v3_clvect_1(k4_csspace4(A,B),k3_clopban1(A,B)) ) ) )).

fof(t9_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => m1_clvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))),k3_clopban1(A,B)) ) ) )).

fof(d6_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => k5_csspace4(A,B) = g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))) ) ) )).

fof(t10_csspace4,axiom,(
    $true )).

fof(t11_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_csspace4(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k5_csspace4(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k5_csspace4(A,B)))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,u1_struct_0(B))
                            & v1_csspace4(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_csspace4(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_csspace4(H,A,B)
                                    & m2_relset_1(H,A,u1_struct_0(B)) )
                                 => ( ( F = C
                                      & G = D
                                      & H = E )
                                   => ( E = k4_rlvect_1(k5_csspace4(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(t12_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k5_csspace4(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k5_csspace4(A,B)))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(B))
                        & v1_csspace4(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_csspace4(F,A,B)
                            & m2_relset_1(F,A,u1_struct_0(B)) )
                         => ( ( E = C
                              & F = D )
                           => ! [G] :
                                ( m1_subset_1(G,k2_numbers)
                               => ( D = k1_clvect_1(k5_csspace4(A,B),C,G)
                                <=> ! [H] :
                                      ( m1_subset_1(H,A)
                                     => k8_funct_2(A,u1_struct_0(B),F,H) = k1_clvect_1(B,k8_funct_2(A,u1_struct_0(B),E,H),G) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => k1_rlvect_1(k5_csspace4(A,B)) = k2_funcop_1(A,k1_rlvect_1(B)) ) ) )).

fof(d7_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( r2_hidden(C,k4_csspace4(A,B))
             => k6_csspace4(A,B,C) = C ) ) ) )).

fof(t14_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & v1_csspace4(C,A,B)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ( ~ v1_xboole_0(k7_csspace4(A,B,C))
                & v1_seq_4(k7_csspace4(A,B,C)) ) ) ) ) )).

fof(t15_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_csspace4(C,A,B)
              <=> v1_seq_4(k7_csspace4(A,B,C)) ) ) ) ) )).

fof(t16_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ? [C] :
              ( v1_funct_1(C)
              & v1_funct_2(C,k4_csspace4(A,B),k1_numbers)
              & m2_relset_1(C,k4_csspace4(A,B),k1_numbers)
              & ! [D] :
                  ( r2_hidden(D,k4_csspace4(A,B))
                 => k2_seq_1(k4_csspace4(A,B),k1_numbers,C,D) = k3_pscomp_1(k7_csspace4(A,B,k6_csspace4(A,B,D))) ) ) ) ) )).

fof(d9_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k4_csspace4(A,B),k1_numbers)
                & m2_relset_1(C,k4_csspace4(A,B),k1_numbers) )
             => ( C = k8_csspace4(A,B)
              <=> ! [D] :
                    ( r2_hidden(D,k4_csspace4(A,B))
                   => k2_seq_1(k4_csspace4(A,B),k1_numbers,C,D) = k3_pscomp_1(k7_csspace4(A,B,k6_csspace4(A,B,D))) ) ) ) ) ) )).

fof(t17_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & v1_csspace4(C,A,B)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k6_csspace4(A,B,C) = C ) ) ) )).

fof(t18_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,u1_struct_0(B))
                & v1_csspace4(C,A,B)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k2_seq_1(k4_csspace4(A,B),k1_numbers,k8_csspace4(A,B),C) = k3_pscomp_1(k7_csspace4(A,B,C)) ) ) ) )).

fof(d10_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => k9_csspace4(A,B) = g2_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace4(A,B)) ) ) )).

fof(t19_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => k2_funcop_1(A,k1_rlvect_1(B)) = k1_rlvect_1(k9_csspace4(A,B)) ) ) )).

fof(t20_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(B))
                    & v1_csspace4(D,A,B)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ( D = C
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => r1_xreal_0(k5_clvect_1(B,k8_funct_2(A,u1_struct_0(B),D,E)),k5_clvect_1(k9_csspace4(A,B),C)) ) ) ) ) ) ) )).

fof(t21_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
             => r1_xreal_0(np__0,k5_clvect_1(k9_csspace4(A,B),C)) ) ) ) )).

fof(t22_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
             => ( C = k1_rlvect_1(k9_csspace4(A,B))
               => np__0 = k5_clvect_1(k9_csspace4(A,B),C) ) ) ) ) )).

fof(t23_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_csspace4(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k9_csspace4(A,B)))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,u1_struct_0(B))
                            & v1_csspace4(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_csspace4(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_csspace4(H,A,B)
                                    & m2_relset_1(H,A,u1_struct_0(B)) )
                                 => ( ( F = C
                                      & G = D
                                      & H = E )
                                   => ( E = k2_rlvect_1(k9_csspace4(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(t24_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_csspace4(A,B)))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(B))
                        & v1_csspace4(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_csspace4(F,A,B)
                            & m2_relset_1(F,A,u1_struct_0(B)) )
                         => ( ( E = C
                              & F = D )
                           => ! [G] :
                                ( m1_subset_1(G,k2_numbers)
                               => ( D = k1_clvect_1(k9_csspace4(A,B),C,G)
                                <=> ! [H] :
                                      ( m1_subset_1(H,A)
                                     => k8_funct_2(A,u1_struct_0(B),F,H) = k1_clvect_1(B,k8_funct_2(A,u1_struct_0(B),E,H),G) ) ) ) ) ) ) ) ) ) ) )).

fof(t25_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_csspace4(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,k2_numbers)
                     => ( ( k5_clvect_1(k9_csspace4(A,B),C) = np__0
                         => C = k1_rlvect_1(k9_csspace4(A,B)) )
                        & ( C = k1_rlvect_1(k9_csspace4(A,B))
                         => k5_clvect_1(k9_csspace4(A,B),C) = np__0 )
                        & k5_clvect_1(k9_csspace4(A,B),k1_clvect_1(k9_csspace4(A,B),C,E)) = k4_real_1(k17_complex1(E),k5_clvect_1(k9_csspace4(A,B),C))
                        & r1_xreal_0(k5_clvect_1(k9_csspace4(A,B),k2_rlvect_1(k9_csspace4(A,B),C,D)),k3_real_1(k5_clvect_1(k9_csspace4(A,B),C),k5_clvect_1(k9_csspace4(A,B),D))) ) ) ) ) ) ) )).

fof(t26_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => v5_clvect_1(k9_csspace4(A,B)) ) ) )).

fof(t27_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ( ~ v3_struct_0(k9_csspace4(A,B))
            & v3_rlvect_1(k9_csspace4(A,B))
            & v4_rlvect_1(k9_csspace4(A,B))
            & v5_rlvect_1(k9_csspace4(A,B))
            & v6_rlvect_1(k9_csspace4(A,B))
            & v2_clvect_1(k9_csspace4(A,B))
            & v5_clvect_1(k9_csspace4(A,B))
            & l2_clvect_1(k9_csspace4(A,B)) ) ) ) )).

fof(t28_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_csspace4(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k9_csspace4(A,B)))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,u1_struct_0(B))
                            & v1_csspace4(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_csspace4(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_csspace4(H,A,B)
                                    & m2_relset_1(H,A,u1_struct_0(B)) )
                                 => ( ( F = C
                                      & G = D
                                      & H = E )
                                   => ( E = k6_rlvect_1(k9_csspace4(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(t29_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ( v4_clopban1(B)
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k5_numbers,u1_struct_0(k9_csspace4(A,B)))
                  & m2_relset_1(C,k5_numbers,u1_struct_0(k9_csspace4(A,B))) )
               => ( v1_csspace3(C,k9_csspace4(A,B))
                 => v6_clvect_1(C,k9_csspace4(A,B)) ) ) ) ) ) )).

fof(t30_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & v4_clopban1(B)
            & l2_clvect_1(B) )
         => ( ~ v3_struct_0(k9_csspace4(A,B))
            & v3_rlvect_1(k9_csspace4(A,B))
            & v4_rlvect_1(k9_csspace4(A,B))
            & v5_rlvect_1(k9_csspace4(A,B))
            & v6_rlvect_1(k9_csspace4(A,B))
            & v2_clvect_1(k9_csspace4(A,B))
            & v5_clvect_1(k9_csspace4(A,B))
            & v4_clopban1(k9_csspace4(A,B))
            & l2_clvect_1(k9_csspace4(A,B)) ) ) ) )).

fof(t31_csspace4,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( ( v1_comseq_2(A)
              & v1_comseq_2(B) )
           => v1_comseq_2(k2_comseq_1(k5_numbers,A,B)) ) ) ) )).

fof(t32_csspace4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( v1_comseq_2(B)
           => v1_comseq_2(k4_comseq_1(k5_numbers,B,A)) ) ) ) )).

fof(t33_csspace4,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_comseq_2(A)
      <=> v3_seq_2(k9_comseq_1(k5_numbers,A)) ) ) )).

fof(t34_csspace4,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k2_numbers)
                & m2_relset_1(C,k5_numbers,k2_numbers) )
             => ( A = k6_comseq_1(k5_numbers,B,C)
              <=> ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k1_comseq_1(A,D) = k11_complex1(k1_comseq_1(B,D),k1_comseq_1(C,D)) ) ) ) ) ) )).

fof(dt_k1_csspace4,axiom,(
    m1_subset_1(k1_csspace4,k1_zfmisc_1(u1_struct_0(k7_csspace))) )).

fof(dt_k2_csspace4,axiom,
    ( v1_funct_1(k2_csspace4)
    & v1_funct_2(k2_csspace4,k1_csspace4,k1_numbers)
    & m2_relset_1(k2_csspace4,k1_csspace4,k1_numbers) )).

fof(dt_k3_csspace4,axiom,
    ( ~ v3_struct_0(k3_csspace4)
    & l2_clvect_1(k3_csspace4) )).

fof(dt_k4_csspace4,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => m1_subset_1(k4_csspace4(A,B),k1_zfmisc_1(u1_struct_0(k3_clopban1(A,B)))) ) )).

fof(dt_k5_csspace4,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ( ~ v3_struct_0(k5_csspace4(A,B))
        & v3_rlvect_1(k5_csspace4(A,B))
        & v4_rlvect_1(k5_csspace4(A,B))
        & v5_rlvect_1(k5_csspace4(A,B))
        & v6_rlvect_1(k5_csspace4(A,B))
        & v2_clvect_1(k5_csspace4(A,B))
        & l1_clvect_1(k5_csspace4(A,B)) ) ) )).

fof(dt_k6_csspace4,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ( v1_funct_1(k6_csspace4(A,B,C))
        & v1_funct_2(k6_csspace4(A,B,C),A,u1_struct_0(B))
        & v1_csspace4(k6_csspace4(A,B,C),A,B)
        & m2_relset_1(k6_csspace4(A,B,C),A,u1_struct_0(B)) ) ) )).

fof(dt_k7_csspace4,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_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_csspace4(A,B,C))
        & m1_subset_1(k7_csspace4(A,B,C),k1_zfmisc_1(k1_numbers)) ) ) )).

fof(dt_k8_csspace4,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ( v1_funct_1(k8_csspace4(A,B))
        & v1_funct_2(k8_csspace4(A,B),k4_csspace4(A,B),k1_numbers)
        & m2_relset_1(k8_csspace4(A,B),k4_csspace4(A,B),k1_numbers) ) ) )).

fof(dt_k9_csspace4,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B) )
     => ( ~ v3_struct_0(k9_csspace4(A,B))
        & l2_clvect_1(k9_csspace4(A,B)) ) ) )).

fof(d8_csspace4,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_csspace4(A,B,C) = a_3_0_csspace4(A,B,C) ) ) ) )).

fof(fraenkel_a_3_0_csspace4,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)
        & v2_clvect_1(C)
        & v5_clvect_1(C)
        & l2_clvect_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_csspace4(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,B)
            & A = k5_clvect_1(C,k8_funct_2(B,u1_struct_0(C),D,E)) ) ) ) )).
%------------------------------------------------------------------------------