SET007 Axioms: SET007+374.ax


%------------------------------------------------------------------------------
% File     : SET007+374 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Hahn-Banach Theorem
% 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    : hahnban [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   56 (   6 unit)
%            Number of atoms       :  668 (  60 equality)
%            Maximal formula depth :   27 (  11 average)
%            Number of connectives :  680 (  68 ~  ;   6  |; 366  &)
%                                         (   9 <=>; 231 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   34 (   1 propositional; 0-3 arity)
%            Number of functors    :   37 (   6 constant; 0-4 arity)
%            Number of variables   :  204 (   0 singleton; 195 !;   9 ?)
%            Maximal term depth    :    9 (   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_hahnban,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v6_ordinal1(B) ) ) )).

fof(cc1_hahnban,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_relset_1(B,u1_struct_0(A),k6_supinf_1)
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
              & v2_hahnban(B,A) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
              & v1_hahnban(B,A) ) ) ) ) )).

fof(cc2_hahnban,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_relset_1(B,u1_struct_0(A),k6_supinf_1)
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
              & v3_hahnban(B,A) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
              & v4_hahnban(B,A) ) ) ) ) )).

fof(cc3_hahnban,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_relset_1(B,u1_struct_0(A),k6_supinf_1)
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
              & v5_hahnban(B,A) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
              & v4_hahnban(B,A) ) ) ) ) )).

fof(cc4_hahnban,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_relset_1(B,u1_struct_0(A),k6_supinf_1)
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
              & v5_hahnban(B,A) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
              & v7_hahnban(B,A) ) ) ) ) )).

fof(cc5_hahnban,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_relset_1(B,u1_struct_0(A),k6_supinf_1)
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
              & v6_hahnban(B,A) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
              & v5_hahnban(B,A) ) ) ) ) )).

fof(cc6_hahnban,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_relset_1(B,u1_struct_0(A),k6_supinf_1)
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
              & v4_hahnban(B,A)
              & v7_hahnban(B,A) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
              & v5_hahnban(B,A) ) ) ) ) )).

fof(rc2_hahnban,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_relset_1(B,u1_struct_0(A),k6_supinf_1)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
          & v1_hahnban(B,A)
          & v2_hahnban(B,A)
          & v3_hahnban(B,A)
          & v4_hahnban(B,A)
          & v5_hahnban(B,A)
          & v6_hahnban(B,A)
          & v7_hahnban(B,A) ) ) )).

fof(t1_hahnban,axiom,(
    $true )).

fof(t2_hahnban,axiom,(
    $true )).

fof(t3_hahnban,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ~ ( A != k1_tarski(B)
            & ! [C] :
                ( m1_subset_1(C,A)
               => C = B ) ) ) )).

fof(t4_hahnban,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k4_rfunct_3(A,B))) )
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) )).

fof(t6_hahnban,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ( ! [B] :
            ( m1_subset_1(B,k3_supinf_1)
           => ( r2_hidden(B,A)
             => r1_supinf_1(B,k5_supinf_1) ) )
       => A = k11_supinf_1(k5_supinf_1) ) ) )).

fof(t7_hahnban,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ( ! [B] :
            ( m1_subset_1(B,k3_supinf_1)
           => ( r2_hidden(B,A)
             => r1_supinf_1(k4_supinf_1,B) ) )
       => A = k11_supinf_1(k4_supinf_1) ) ) )).

fof(t8_hahnban,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( ~ r1_supinf_1(k9_supinf_1(A),B)
              & ! [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                 => ~ ( r2_hidden(C,A)
                      & ~ r1_supinf_1(C,B) ) ) ) ) ) )).

fof(t9_hahnban,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( ~ r1_supinf_1(B,k10_supinf_1(A))
              & ! [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                 => ~ ( r2_hidden(C,A)
                      & ~ r1_supinf_1(B,C) ) ) ) ) ) )).

fof(t10_hahnban,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ( ! [C] :
                ( m1_subset_1(C,k3_supinf_1)
               => ! [D] :
                    ( m1_subset_1(D,k3_supinf_1)
                   => ( ( r2_hidden(C,A)
                        & r2_hidden(D,B) )
                     => r1_supinf_1(C,D) ) ) )
           => r1_supinf_1(k9_supinf_1(A),k10_supinf_1(B)) ) ) ) )).

fof(t11_hahnban,axiom,(
    $true )).

fof(t12_hahnban,axiom,(
    $true )).

fof(t13_hahnban,axiom,(
    ! [A,B,C] :
      ( ( v6_ordinal1(C)
        & m1_subset_1(C,k1_zfmisc_1(k4_rfunct_3(A,B))) )
     => r2_hidden(k3_tarski(C),k4_rfunct_3(A,B)) ) )).

fof(t14_hahnban,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => r1_tarski(u1_struct_0(B),u1_struct_0(k1_rlsub_2(A,B,C))) ) ) ) )).

fof(t15_hahnban,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( r1_rlsub_2(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( ( r1_rlvect_1(B,E)
                                & r1_rlvect_1(C,F)
                                & D = k4_rlvect_1(A,E,F) )
                             => k4_rlsub_2(A,D,B,C) = k1_domain_1(u1_struct_0(A),u1_struct_0(A),E,F) ) ) ) ) ) ) ) ) )).

fof(t16_hahnban,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( r1_rlsub_2(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( k4_rlsub_2(A,D,B,C) = k1_domain_1(u1_struct_0(A),u1_struct_0(A),E,F)
                             => D = k4_rlvect_1(A,E,F) ) ) ) ) ) ) ) ) )).

fof(t17_hahnban,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( r1_rlsub_2(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( k4_rlsub_2(A,D,B,C) = k1_domain_1(u1_struct_0(A),u1_struct_0(A),E,F)
                             => ( r1_rlvect_1(B,E)
                                & r1_rlvect_1(C,F) ) ) ) ) ) ) ) ) ) )).

fof(t18_hahnban,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( r1_rlsub_2(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( k4_rlsub_2(A,D,B,C) = k1_domain_1(u1_struct_0(A),u1_struct_0(A),E,F)
                             => k4_rlsub_2(A,D,C,B) = k1_domain_1(u1_struct_0(A),u1_struct_0(A),F,E) ) ) ) ) ) ) ) ) )).

fof(t19_hahnban,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( r1_rlsub_2(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_rlvect_1(B,D)
                     => k4_rlsub_2(A,D,B,C) = k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,k1_rlvect_1(A)) ) ) ) ) ) ) )).

fof(t20_hahnban,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ( r1_rlsub_2(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_rlvect_1(C,D)
                     => k4_rlsub_2(A,D,B,C) = k1_domain_1(u1_struct_0(A),u1_struct_0(A),k1_rlvect_1(A),D) ) ) ) ) ) ) )).

fof(t21_hahnban,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_rlvect_1(C,D)
                   => m1_subset_1(D,u1_struct_0(B)) ) ) ) ) ) )).

fof(t22_hahnban,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_rlsub_1(C,A)
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ! [E] :
                      ( m1_rlsub_1(E,D)
                     => ! [F] :
                          ( m1_rlsub_1(F,D)
                         => ( ( E = B
                              & F = C )
                           => k1_rlsub_2(D,E,F) = k1_rlsub_2(A,B,C) ) ) ) ) ) ) ) )).

fof(t23_hahnban,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_rlsub_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( C = D
                   => k1_rlvect_3(B,k6_domain_1(u1_struct_0(B),D)) = k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),C)) ) ) ) ) ) )).

fof(t24_hahnban,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_rlsub_1(C,A)
             => ( ~ r1_rlvect_1(C,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))))
                   => ! [E] :
                        ( m1_rlsub_1(E,k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))))
                       => ( ( B = D
                            & E = C )
                         => r1_rlsub_2(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),E,k1_rlvect_3(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),k6_domain_1(u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))),D))) ) ) ) ) ) ) ) )).

fof(t25_hahnban,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_rlsub_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))))
                 => ! [E] :
                      ( m1_rlsub_1(E,k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))))
                     => ( ( B = D
                          & C = E )
                       => ( r1_rlvect_1(C,B)
                          | k4_rlsub_2(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),D,E,k1_rlvect_3(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),k6_domain_1(u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))),D))) = k1_domain_1(u1_struct_0(E),u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))),k1_rlvect_1(E),D) ) ) ) ) ) ) ) )).

fof(t26_hahnban,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_rlsub_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))))
                 => ! [E] :
                      ( m1_rlsub_1(E,k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))))
                     => ( ( B = D
                          & C = E )
                       => ( r1_rlvect_1(C,B)
                          | ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))))
                             => ( r1_rlvect_1(C,F)
                               => k4_rlsub_2(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),F,E,k1_rlvect_3(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),k6_domain_1(u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))),D))) = k1_domain_1(u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))),u1_struct_0(A),F,k1_rlvect_1(A)) ) ) ) ) ) ) ) ) ) )).

fof(t27_hahnban,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_rlsub_1(C,A)
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ? [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                      & ? [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                          & k4_rlsub_2(A,B,C,D) = k1_domain_1(u1_struct_0(A),u1_struct_0(A),E,F) ) ) ) ) ) ) )).

fof(t28_hahnban,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_rlsub_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))))
                 => ! [E] :
                      ( m1_rlsub_1(E,k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))))
                     => ( ( B = D
                          & C = E )
                       => ( r1_rlvect_1(C,B)
                          | ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))))
                             => ? [G] :
                                  ( m1_subset_1(G,u1_struct_0(C))
                                  & ? [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                      & k4_rlsub_2(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),F,E,k1_rlvect_3(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),k6_domain_1(u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))),D))) = k1_domain_1(u1_struct_0(C),u1_struct_0(A),G,k3_rlvect_1(A,B,H)) ) ) ) ) ) ) ) ) ) ) )).

fof(t29_hahnban,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_rlsub_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))))
                 => ! [E] :
                      ( m1_rlsub_1(E,k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))))
                     => ( ( B = D
                          & C = E )
                       => ( r1_rlvect_1(C,B)
                          | ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))))
                                 => ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(C))
                                     => ! [I] :
                                          ( m1_subset_1(I,u1_struct_0(C))
                                         => ! [J] :
                                              ( m1_subset_1(J,k1_numbers)
                                             => ! [K] :
                                                  ( m1_subset_1(K,k1_numbers)
                                                 => ( ( k4_rlsub_2(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),F,E,k1_rlvect_3(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),k6_domain_1(u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))),D))) = k1_domain_1(u1_struct_0(C),u1_struct_0(A),H,k3_rlvect_1(A,B,J))
                                                      & k4_rlsub_2(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),G,E,k1_rlvect_3(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),k6_domain_1(u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))),D))) = k1_domain_1(u1_struct_0(C),u1_struct_0(A),I,k3_rlvect_1(A,B,K)) )
                                                   => k4_rlsub_2(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),k4_rlvect_1(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),F,G),E,k1_rlvect_3(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),k6_domain_1(u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))),D))) = k1_domain_1(u1_struct_0(C),u1_struct_0(A),k4_rlvect_1(C,H,I),k3_rlvect_1(A,B,k3_real_1(J,K))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t30_hahnban,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_rlsub_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))))
                 => ! [E] :
                      ( m1_rlsub_1(E,k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))))
                     => ( ( B = D
                          & C = E )
                       => ( r1_rlvect_1(C,B)
                          | ! [F] :
                              ( m1_subset_1(F,u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(C))
                                 => ! [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                     => ! [I] :
                                          ( m1_subset_1(I,k1_numbers)
                                         => ( k4_rlsub_2(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),F,E,k1_rlvect_3(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),k6_domain_1(u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))),D))) = k1_domain_1(u1_struct_0(C),u1_struct_0(A),G,k3_rlvect_1(A,B,I))
                                           => k4_rlsub_2(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),k3_rlvect_1(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),F,H),E,k1_rlvect_3(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B))),k6_domain_1(u1_struct_0(k1_rlsub_2(A,C,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)))),D))) = k1_domain_1(u1_struct_0(C),u1_struct_0(A),k3_rlvect_1(C,G,H),k3_rlvect_1(A,B,k4_real_1(H,I))) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d1_hahnban,axiom,(
    $true )).

fof(d2_hahnban,axiom,(
    $true )).

fof(d3_hahnban,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_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
            & m2_relset_1(B,u1_struct_0(A),k6_supinf_1) )
         => ( v1_hahnban(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r1_xreal_0(k8_funct_2(u1_struct_0(A),k6_supinf_1,B,k4_rlvect_1(A,C,D)),k3_real_1(k8_funct_2(u1_struct_0(A),k6_supinf_1,B,C),k8_funct_2(u1_struct_0(A),k6_supinf_1,B,D))) ) ) ) ) ) )).

fof(d4_hahnban,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_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
            & m2_relset_1(B,u1_struct_0(A),k6_supinf_1) )
         => ( v2_hahnban(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),k6_supinf_1,B,k4_rlvect_1(A,C,D)) = k3_real_1(k8_funct_2(u1_struct_0(A),k6_supinf_1,B,C),k8_funct_2(u1_struct_0(A),k6_supinf_1,B,D)) ) ) ) ) ) )).

fof(d5_hahnban,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_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
            & m2_relset_1(B,u1_struct_0(A),k6_supinf_1) )
         => ( v3_hahnban(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => k8_funct_2(u1_struct_0(A),k6_supinf_1,B,k3_rlvect_1(A,C,D)) = k4_real_1(D,k8_funct_2(u1_struct_0(A),k6_supinf_1,B,C)) ) ) ) ) ) )).

fof(d6_hahnban,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_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
            & m2_relset_1(B,u1_struct_0(A),k6_supinf_1) )
         => ( v4_hahnban(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => ( ~ r1_xreal_0(D,np__0)
                     => k8_funct_2(u1_struct_0(A),k6_supinf_1,B,k3_rlvect_1(A,C,D)) = k4_real_1(D,k8_funct_2(u1_struct_0(A),k6_supinf_1,B,C)) ) ) ) ) ) ) )).

fof(d7_hahnban,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_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
            & m2_relset_1(B,u1_struct_0(A),k6_supinf_1) )
         => ( v5_hahnban(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => ( r1_xreal_0(np__0,D)
                     => k8_funct_2(u1_struct_0(A),k6_supinf_1,B,k3_rlvect_1(A,C,D)) = k4_real_1(D,k8_funct_2(u1_struct_0(A),k6_supinf_1,B,C)) ) ) ) ) ) ) )).

fof(d8_hahnban,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_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
            & m2_relset_1(B,u1_struct_0(A),k6_supinf_1) )
         => ( v6_hahnban(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => k8_funct_2(u1_struct_0(A),k6_supinf_1,B,k3_rlvect_1(A,C,D)) = k4_real_1(k18_complex1(D),k8_funct_2(u1_struct_0(A),k6_supinf_1,B,C)) ) ) ) ) ) )).

fof(d9_hahnban,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_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
            & m2_relset_1(B,u1_struct_0(A),k6_supinf_1) )
         => ( v7_hahnban(B,A)
          <=> k8_funct_2(u1_struct_0(A),k6_supinf_1,B,k1_rlvect_1(A)) = np__0 ) ) ) )).

fof(t31_hahnban,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_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
            & v3_hahnban(B,A)
            & m2_relset_1(B,u1_struct_0(A),k6_supinf_1) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k8_funct_2(u1_struct_0(A),k6_supinf_1,B,k5_rlvect_1(A,C)) = k1_real_1(k8_funct_2(u1_struct_0(A),k6_supinf_1,B,C)) ) ) ) )).

fof(t32_hahnban,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_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
            & v2_hahnban(B,A)
            & v3_hahnban(B,A)
            & m2_relset_1(B,u1_struct_0(A),k6_supinf_1) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k8_funct_2(u1_struct_0(A),k6_supinf_1,B,k6_rlvect_1(A,C,D)) = k5_real_1(k8_funct_2(u1_struct_0(A),k6_supinf_1,B,C),k8_funct_2(u1_struct_0(A),k6_supinf_1,B,D)) ) ) ) ) )).

fof(t33_hahnban,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_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
            & v2_hahnban(B,A)
            & m2_relset_1(B,u1_struct_0(A),k6_supinf_1) )
         => k8_funct_2(u1_struct_0(A),k6_supinf_1,B,k1_rlvect_1(A)) = np__0 ) ) )).

fof(t34_hahnban,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_rlsub_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),k6_supinf_1)
                & v2_hahnban(C,B)
                & v3_hahnban(C,B)
                & m2_relset_1(C,u1_struct_0(B),k6_supinf_1) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),D)))))
                     => ( D = E
                       => ( r1_rlvect_1(B,D)
                          | ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ? [G] :
                                  ( v1_funct_1(G)
                                  & v1_funct_2(G,u1_struct_0(k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),D)))),k6_supinf_1)
                                  & v2_hahnban(G,k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),D))))
                                  & v3_hahnban(G,k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),D))))
                                  & m2_relset_1(G,u1_struct_0(k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),D)))),k6_supinf_1)
                                  & k2_partfun1(u1_struct_0(k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),D)))),k6_supinf_1,G,u1_struct_0(B)) = C
                                  & k8_funct_2(u1_struct_0(k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),D)))),k6_supinf_1,G,E) = F ) ) ) ) ) ) ) ) ) )).

fof(t35_hahnban,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_rlsub_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),k6_supinf_1)
                & v1_hahnban(C,A)
                & v4_hahnban(C,A)
                & m2_relset_1(C,u1_struct_0(A),k6_supinf_1) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),k6_supinf_1)
                    & v2_hahnban(D,B)
                    & v3_hahnban(D,B)
                    & m2_relset_1(D,u1_struct_0(B),k6_supinf_1) )
                 => ~ ( ! [E] :
                          ( m1_subset_1(E,u1_struct_0(B))
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ( E = F
                               => r1_xreal_0(k8_funct_2(u1_struct_0(B),k6_supinf_1,D,E),k8_funct_2(u1_struct_0(A),k6_supinf_1,C,F)) ) ) )
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(A),k6_supinf_1)
                            & v2_hahnban(E,A)
                            & v3_hahnban(E,A)
                            & m2_relset_1(E,u1_struct_0(A),k6_supinf_1) )
                         => ~ ( k2_partfun1(u1_struct_0(A),k6_supinf_1,E,u1_struct_0(B)) = D
                              & ! [F] :
                                  ( m1_subset_1(F,u1_struct_0(A))
                                 => r1_xreal_0(k8_funct_2(u1_struct_0(A),k6_supinf_1,E,F),k8_funct_2(u1_struct_0(A),k6_supinf_1,C,F)) ) ) ) ) ) ) ) ) )).

fof(t36_hahnban,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)
        & v2_normsp_1(A)
        & l1_normsp_1(A) )
     => ( v1_funct_1(u1_normsp_1(A))
        & v1_funct_2(u1_normsp_1(A),u1_struct_0(A),k6_supinf_1)
        & v1_hahnban(u1_normsp_1(A),A)
        & v6_hahnban(u1_normsp_1(A),A)
        & m2_relset_1(u1_normsp_1(A),u1_struct_0(A),k6_supinf_1) ) ) )).

fof(t37_hahnban,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)
        & v2_normsp_1(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( m1_rlsub_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),k6_supinf_1)
                & v2_hahnban(C,B)
                & v3_hahnban(C,B)
                & m2_relset_1(C,u1_struct_0(B),k6_supinf_1) )
             => ~ ( ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( D = E
                           => r1_xreal_0(k8_funct_2(u1_struct_0(B),k6_supinf_1,C,D),k1_normsp_1(A,E)) ) ) )
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),k6_supinf_1)
                        & v2_hahnban(D,A)
                        & v3_hahnban(D,A)
                        & m2_relset_1(D,u1_struct_0(A),k6_supinf_1) )
                     => ~ ( k2_partfun1(u1_struct_0(A),k6_supinf_1,D,u1_struct_0(B)) = C
                          & ! [E] :
                              ( m1_subset_1(E,u1_struct_0(A))
                             => r1_xreal_0(k8_funct_2(u1_struct_0(A),k6_supinf_1,D,E),k1_normsp_1(A,E)) ) ) ) ) ) ) ) )).

fof(t5_hahnban,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k3_tarski(A)
           => ( k1_relat_1(B) = k3_tarski(a_1_0_hahnban(A))
              & k2_relat_1(B) = k3_tarski(a_1_1_hahnban(A)) ) ) ) ) )).

fof(fraenkel_a_1_0_hahnban,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_fraenkel(B) )
     => ( r2_hidden(A,a_1_0_hahnban(B))
      <=> ? [C] :
            ( m1_subset_1(C,B)
            & A = k1_relat_1(C) ) ) ) )).

fof(fraenkel_a_1_1_hahnban,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_fraenkel(B) )
     => ( r2_hidden(A,a_1_1_hahnban(B))
      <=> ? [C] :
            ( m1_subset_1(C,B)
            & A = k2_relat_1(C) ) ) ) )).
%------------------------------------------------------------------------------