SET007 Axioms: SET007+813.ax


%------------------------------------------------------------------------------
% File     : SET007+813 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Series on Banach Algebra
% 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    : lopban_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   85 (   1 unit)
%            Number of atoms       : 1304 (  95 equality)
%            Maximal formula depth :   49 (  12 average)
%            Number of connectives : 1324 ( 105 ~  ;   6  |; 929  &)
%                                         (  16 <=>; 268 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   39 (   1 propositional; 0-3 arity)
%            Number of functors    :   47 (   5 constant; 0-4 arity)
%            Number of variables   :  277 (   0 singleton; 265 !;  12 ?)
%            Maximal term depth    :    6 (   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_lopban_3,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_relset_1(B,k5_numbers,u1_struct_0(A))
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,u1_struct_0(A))
          & v1_lopban_3(B,A) ) ) )).

fof(rc2_lopban_3,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_relset_1(B,k5_numbers,u1_struct_0(A))
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,u1_struct_0(A))
          & v2_lopban_3(B,A) ) ) )).

fof(fc1_lopban_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & v2_lopban_3(B,A)
        & m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
     => ( v1_relat_1(k7_normsp_1(A,B))
        & v1_funct_1(k7_normsp_1(A,B))
        & v1_funct_2(k7_normsp_1(A,B),k5_numbers,k1_numbers)
        & v1_series_1(k7_normsp_1(A,B)) ) ) )).

fof(cc1_lopban_3,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_relset_1(B,k5_numbers,u1_struct_0(A))
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,k5_numbers,u1_struct_0(A))
              & v1_lopban_3(B,A) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,k5_numbers,u1_struct_0(A))
              & v4_normsp_1(B,A) ) ) ) ) )).

fof(fc2_lopban_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & v1_lopban_3(B,A)
        & m1_relset_1(B,k5_numbers,u1_struct_0(A))
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,u1_struct_0(A))
        & v1_lopban_3(C,A)
        & m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
     => ( v1_relat_1(k3_normsp_1(A,B,C))
        & v1_funct_1(k3_normsp_1(A,B,C))
        & v1_funct_2(k3_normsp_1(A,B,C),k5_numbers,u1_struct_0(A))
        & v4_normsp_1(k3_normsp_1(A,B,C),A)
        & v1_lopban_3(k3_normsp_1(A,B,C),A) ) ) )).

fof(fc3_lopban_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & v1_lopban_3(B,A)
        & m1_relset_1(B,k5_numbers,u1_struct_0(A))
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,u1_struct_0(A))
        & v1_lopban_3(C,A)
        & m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
     => ( v1_relat_1(k4_normsp_1(A,B,C))
        & v1_funct_1(k4_normsp_1(A,B,C))
        & v1_funct_2(k4_normsp_1(A,B,C),k5_numbers,u1_struct_0(A))
        & v4_normsp_1(k4_normsp_1(A,B,C),A)
        & v1_lopban_3(k4_normsp_1(A,B,C),A) ) ) )).

fof(fc4_lopban_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A)
        & m1_subset_1(B,k1_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,u1_struct_0(A))
        & v1_lopban_3(C,A)
        & m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
     => ( v1_relat_1(k6_normsp_1(A,C,B))
        & v1_funct_1(k6_normsp_1(A,C,B))
        & v1_funct_2(k6_normsp_1(A,C,B),k5_numbers,u1_struct_0(A))
        & v4_normsp_1(k6_normsp_1(A,C,B),A)
        & v1_lopban_3(k6_normsp_1(A,C,B),A) ) ) )).

fof(fc5_lopban_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & v1_lopban_3(B,A)
        & m1_relset_1(B,k5_numbers,u1_struct_0(A))
        & m1_subset_1(C,k5_numbers) )
     => ( v1_relat_1(k3_lopban_3(A,B,C))
        & v1_funct_1(k3_lopban_3(A,B,C))
        & v1_funct_2(k3_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
        & v4_normsp_1(k3_lopban_3(A,B,C),A)
        & v1_lopban_3(k3_lopban_3(A,B,C),A) ) ) )).

fof(fc6_lopban_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & v2_lopban_3(B,A)
        & m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
     => ( v1_relat_1(k1_series_1(k7_normsp_1(A,B)))
        & v1_funct_1(k1_series_1(k7_normsp_1(A,B)))
        & v1_funct_2(k1_series_1(k7_normsp_1(A,B)),k5_numbers,k1_numbers)
        & v1_seq_2(k1_series_1(k7_normsp_1(A,B))) ) ) )).

fof(cc2_lopban_3,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)
        & v4_lopban_1(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( m1_relset_1(B,k5_numbers,u1_struct_0(A))
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,k5_numbers,u1_struct_0(A))
              & v2_lopban_3(B,A) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,k5_numbers,u1_struct_0(A))
              & v4_normsp_1(B,A)
              & v1_lopban_3(B,A) ) ) ) ) )).

fof(d1_lopban_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ( C = k1_lopban_3(A,B)
              <=> ( k2_normsp_1(A,C,np__0) = k2_normsp_1(A,B,np__0)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => k2_normsp_1(A,C,k1_nat_1(D,np__1)) = k2_rlvect_1(A,k2_normsp_1(A,C,D),k2_normsp_1(A,B,k1_nat_1(D,np__1))) ) ) ) ) ) ) )).

fof(t1_lopban_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_normsp_1(A,B,C) = k1_rlvect_1(A) )
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_normsp_1(A,k1_lopban_3(A,B),C) = k1_rlvect_1(A) ) ) ) ) )).

fof(d2_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v1_lopban_3(B,A)
          <=> v4_normsp_1(k1_lopban_3(A,B),A) ) ) ) )).

fof(d3_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => k2_lopban_3(A,B) = k8_normsp_1(A,k1_lopban_3(A,B)) ) ) )).

fof(d4_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v2_lopban_3(B,A)
          <=> v1_series_1(k7_normsp_1(A,B)) ) ) ) )).

fof(t2_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),C)) ) ) ) )).

fof(t3_lopban_3,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_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k1_normsp_1(A,k6_rlvect_1(A,B,C)) = k1_normsp_1(A,k4_rlvect_1(A,k6_rlvect_1(A,B,D),k6_rlvect_1(A,D,C))) ) ) ) ) )).

fof(t4_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v4_normsp_1(B,A)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => ~ ( ~ r1_xreal_0(C,np__0)
                    & ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ? [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                            & r1_xreal_0(D,E)
                            & r1_xreal_0(C,k1_normsp_1(A,k6_rlvect_1(A,k2_normsp_1(A,B,E),k2_normsp_1(A,B,D)))) ) ) ) ) ) ) ) )).

fof(t5_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v1_rsspace3(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => ~ ( ~ r1_xreal_0(C,np__0)
                    & ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ? [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                            & r1_xreal_0(D,E)
                            & r1_xreal_0(C,k1_normsp_1(A,k6_rlvect_1(A,k2_normsp_1(A,B,E),k2_normsp_1(A,B,D)))) ) ) ) ) ) ) ) )).

fof(t6_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_normsp_1(A,B,C) = k1_rlvect_1(A) )
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k7_normsp_1(A,B)),C) = np__0 ) ) ) ) )).

fof(d5_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v5_seqm_3(B)
          <=> ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k2_normsp_1(A,B,D) = C ) ) ) ) ) )).

fof(d6_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,u1_struct_0(A))
                    & m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
                 => ( D = k3_lopban_3(A,B,C)
                  <=> ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k2_normsp_1(A,D,E) = k2_normsp_1(A,B,k1_nat_1(E,C)) ) ) ) ) ) ) )).

fof(t7_lopban_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & v1_seqm_3(C)
                & v7_seqm_3(C)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => k2_normsp_1(A,k5_lopban_3(A,C,B),D) = k2_normsp_1(A,B,k2_seqm_3(C,D)) ) ) ) ) )).

fof(t8_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => k3_lopban_3(A,B,np__0) = B ) ) )).

fof(t9_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => k3_lopban_3(A,k3_lopban_3(A,B,C),D) = k3_lopban_3(A,k3_lopban_3(A,B,D),C) ) ) ) ) )).

fof(t10_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => k3_lopban_3(A,k3_lopban_3(A,B,C),D) = k3_lopban_3(A,B,k1_nat_1(C,D)) ) ) ) ) )).

fof(t11_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ( ( m1_bhsp_3(C,A,B)
                  & v4_normsp_1(B,A) )
               => v4_normsp_1(C,A) ) ) ) ) )).

fof(t12_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ( ( m1_bhsp_3(C,A,B)
                  & v4_normsp_1(B,A) )
               => k8_normsp_1(A,C) = k8_normsp_1(A,B) ) ) ) ) )).

fof(t13_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => m1_bhsp_3(k3_lopban_3(A,B,C),A,B) ) ) ) )).

fof(t14_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( v4_normsp_1(B,A)
                   => ( v4_normsp_1(k3_lopban_3(A,B,D),A)
                      & k8_normsp_1(A,k3_lopban_3(A,B,D)) = k8_normsp_1(A,B) ) ) ) ) ) ) )).

fof(t15_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ( v4_normsp_1(B,A)
               => ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => B != k3_lopban_3(A,C,D) )
                  | v4_normsp_1(C,A) ) ) ) ) ) )).

fof(t16_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ( v4_normsp_1(B,A)
               => ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => B != k3_lopban_3(A,C,D) )
                  | k8_normsp_1(A,C) = k8_normsp_1(A,B) ) ) ) ) ) )).

fof(t17_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v5_seqm_3(B)
           => v4_normsp_1(B,A) ) ) ) )).

fof(t18_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_normsp_1(A,B,C) = k1_rlvect_1(A) )
           => v2_lopban_3(B,A) ) ) ) )).

fof(t19_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v1_lopban_3(B,A)
           => ( v4_normsp_1(B,A)
              & k8_normsp_1(A,B) = k1_rlvect_1(A) ) ) ) ) )).

fof(t20_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => k3_normsp_1(A,k1_lopban_3(A,B),k1_lopban_3(A,C)) = k1_lopban_3(A,k3_normsp_1(A,B,C)) ) ) ) )).

fof(t21_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => k4_normsp_1(A,k1_lopban_3(A,B),k1_lopban_3(A,C)) = k1_lopban_3(A,k4_normsp_1(A,B,C)) ) ) ) )).

fof(t22_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ( ( v1_lopban_3(B,A)
                  & v1_lopban_3(C,A) )
               => ( v1_lopban_3(k3_normsp_1(A,B,C),A)
                  & k2_lopban_3(A,k3_normsp_1(A,B,C)) = k4_rlvect_1(A,k2_lopban_3(A,B),k2_lopban_3(A,C)) ) ) ) ) ) )).

fof(t23_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ( ( v1_lopban_3(B,A)
                  & v1_lopban_3(C,A) )
               => ( v1_lopban_3(k4_normsp_1(A,B,C),A)
                  & k2_lopban_3(A,k4_normsp_1(A,B,C)) = k6_rlvect_1(A,k2_lopban_3(A,B),k2_lopban_3(A,C)) ) ) ) ) ) )).

fof(t24_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => k1_lopban_3(A,k6_normsp_1(A,B,C)) = k6_normsp_1(A,k1_lopban_3(A,B),C) ) ) ) )).

fof(t25_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & v1_lopban_3(B,A)
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( v1_lopban_3(k6_normsp_1(A,B,C),A)
                & k2_lopban_3(A,k6_normsp_1(A,B,C)) = k3_rlvect_1(A,k2_lopban_3(A,B),C) ) ) ) ) )).

fof(t26_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k2_normsp_1(A,C,D) = k2_normsp_1(A,B,np__0) )
               => k1_lopban_3(A,k3_lopban_3(A,B,np__1)) = k4_normsp_1(A,k3_lopban_3(A,k1_lopban_3(A,B),np__1),C) ) ) ) ) )).

fof(t27_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v1_lopban_3(B,A)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => v1_lopban_3(k3_lopban_3(A,B,C),A) ) ) ) ) )).

fof(t28_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v1_seq_2(k1_series_1(k7_normsp_1(A,B)))
          <=> v2_lopban_3(B,A) ) ) ) )).

fof(t29_lopban_3,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)
        & v4_lopban_1(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v1_lopban_3(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => ~ ( ~ r1_xreal_0(C,np__0)
                    & ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ? [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                            & r1_xreal_0(D,E)
                            & r1_xreal_0(C,k1_normsp_1(A,k6_rlvect_1(A,k2_normsp_1(A,k1_lopban_3(A,B),E),k2_normsp_1(A,k1_lopban_3(A,B),D)))) ) ) ) ) ) ) ) )).

fof(t30_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(C,D)
                   => r1_xreal_0(k1_normsp_1(A,k6_rlvect_1(A,k2_normsp_1(A,k1_lopban_3(A,B),D),k2_normsp_1(A,k1_lopban_3(A,B),C))),k18_complex1(k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k7_normsp_1(A,B)),D),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k7_normsp_1(A,B)),C)))) ) ) ) ) ) )).

fof(t31_lopban_3,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)
        & v4_lopban_1(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ( v2_lopban_3(B,A)
           => v1_lopban_3(B,A) ) ) ) )).

fof(t32_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ( v1_series_1(B)
               => ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ? [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                          & r1_xreal_0(D,E)
                          & ~ r1_xreal_0(k1_normsp_1(A,k2_normsp_1(A,C,E)),k2_seq_1(k5_numbers,k1_numbers,B,E)) ) )
                  | v2_lopban_3(C,A) ) ) ) ) ) )).

fof(t33_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ( ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D))
                        & r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D),k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,C),D)) ) )
                  & v2_lopban_3(C,A) )
               => ( v2_lopban_3(B,A)
                  & r1_xreal_0(k2_series_1(k7_normsp_1(A,B)),k2_series_1(k7_normsp_1(A,C))) ) ) ) ) ) )).

fof(t34_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ~ ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),C),np__0) )
              & ? [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(C,D)
                       => r1_xreal_0(np__1,k6_real_1(k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),k1_nat_1(D,np__1)),k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D))) ) ) )
              & v2_lopban_3(B,A) ) ) ) )).

fof(t35_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => k2_seq_1(k5_numbers,k1_numbers,C,D) = k2_power(D,k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D)) )
                  & v4_seq_2(C) )
               => ( r1_xreal_0(np__1,k2_seq_2(C))
                  | v2_lopban_3(B,A) ) ) ) ) ) )).

fof(t36_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ~ ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => k2_seq_1(k5_numbers,k1_numbers,C,D) = k2_power(D,k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D)) )
                  & ? [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(D,E)
                           => r1_xreal_0(np__1,k2_seq_1(k5_numbers,k1_numbers,C,E)) ) ) )
                  & v1_series_1(k7_normsp_1(A,B)) ) ) ) ) )).

fof(t37_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ~ ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => k2_seq_1(k5_numbers,k1_numbers,C,D) = k2_power(D,k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D)) )
                  & v4_seq_2(C)
                  & ~ r1_xreal_0(k2_seq_2(C),np__1)
                  & v2_lopban_3(B,A) ) ) ) ) )).

fof(t38_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( ( v4_seqm_3(k7_normsp_1(A,B))
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => k2_seq_1(k5_numbers,k1_numbers,C,D) = k4_real_1(k4_power(np__2,D),k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),k4_power(np__2,D))) ) )
               => ( v2_lopban_3(B,A)
                <=> v1_series_1(C) ) ) ) ) ) )).

fof(t39_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_xreal_0(np__1,D)
                     => k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D) = k6_real_1(np__1,k4_power(D,C)) ) )
               => ( r1_xreal_0(C,np__1)
                  | v2_lopban_3(B,A) ) ) ) ) ) )).

fof(t40_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ~ ( r1_xreal_0(C,np__1)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(np__1,D)
                       => k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D) = k6_real_1(np__1,k4_power(D,C)) ) )
                  & v2_lopban_3(B,A) ) ) ) ) )).

fof(t41_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( k2_normsp_1(A,B,D) != k1_rlvect_1(A)
                        & k2_seq_1(k5_numbers,k1_numbers,C,D) = k6_real_1(k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),k1_nat_1(D,np__1)),k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D)) ) )
                  & v4_seq_2(C) )
               => ( r1_xreal_0(np__1,k2_seq_2(C))
                  | v2_lopban_3(B,A) ) ) ) ) ) )).

fof(t42_lopban_3,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ~ ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k2_normsp_1(A,B,C) != k1_rlvect_1(A) )
              & ? [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(C,D)
                       => r1_xreal_0(np__1,k6_real_1(k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),k1_nat_1(D,np__1)),k2_seq_1(k5_numbers,k1_numbers,k7_normsp_1(A,B),D))) ) ) )
              & v2_lopban_3(B,A) ) ) ) )).

fof(t43_lopban_3,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)
        & v4_group_1(A)
        & v2_funcsdom(A)
        & v5_lopban_2(A)
        & l1_lopban_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ( k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B)
                            & k4_rlvect_1(A,k4_rlvect_1(A,B,C),D) = k4_rlvect_1(A,B,k4_rlvect_1(A,C,D))
                            & k4_rlvect_1(A,B,k1_rlvect_1(A)) = B
                            & ? [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                                & k4_rlvect_1(A,B,G) = k1_rlvect_1(A) )
                            & k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D))
                            & k3_rlvect_1(A,B,np__1) = B
                            & k3_rlvect_1(A,B,np__0) = k1_rlvect_1(A)
                            & k3_rlvect_1(A,k1_rlvect_1(A),E) = k1_rlvect_1(A)
                            & k3_rlvect_1(A,B,k1_real_1(np__1)) = k5_rlvect_1(A,B)
                            & k1_group_1(A,B,k2_group_1(A)) = B
                            & k1_group_1(A,k2_group_1(A),B) = B
                            & k1_group_1(A,B,k4_rlvect_1(A,C,D)) = k4_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D))
                            & k1_group_1(A,k4_rlvect_1(A,C,D),B) = k4_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B))
                            & k3_rlvect_1(A,k1_group_1(A,B,C),E) = k1_group_1(A,k3_rlvect_1(A,B,E),C)
                            & k3_rlvect_1(A,k4_rlvect_1(A,B,C),E) = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,E))
                            & k3_rlvect_1(A,B,k3_real_1(E,F)) = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,B,F))
                            & k3_rlvect_1(A,B,k4_real_1(E,F)) = k3_rlvect_1(A,k3_rlvect_1(A,B,F),E)
                            & k3_rlvect_1(A,k1_group_1(A,B,C),k4_real_1(E,F)) = k1_group_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F))
                            & k3_rlvect_1(A,k1_group_1(A,B,C),E) = k1_group_1(A,B,k3_rlvect_1(A,C,E))
                            & k1_group_1(A,k1_rlvect_1(A),B) = k1_rlvect_1(A)
                            & k1_group_1(A,B,k1_rlvect_1(A)) = k1_rlvect_1(A)
                            & k1_group_1(A,B,k6_rlvect_1(A,C,D)) = k6_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D))
                            & k1_group_1(A,k6_rlvect_1(A,C,D),B) = k6_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B))
                            & k6_rlvect_1(A,k4_rlvect_1(A,B,C),D) = k4_rlvect_1(A,B,k6_rlvect_1(A,C,D))
                            & k4_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,B,k6_rlvect_1(A,C,D))
                            & k6_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,B,k4_rlvect_1(A,C,D))
                            & k4_rlvect_1(A,B,C) = k4_rlvect_1(A,k6_rlvect_1(A,B,D),k4_rlvect_1(A,D,C))
                            & k6_rlvect_1(A,B,C) = k4_rlvect_1(A,k6_rlvect_1(A,B,D),k6_rlvect_1(A,D,C))
                            & B = k4_rlvect_1(A,k6_rlvect_1(A,B,C),C)
                            & B = k6_rlvect_1(A,C,k6_rlvect_1(A,C,B))
                            & ( k1_normsp_1(A,B) = np__0
                             => B = k1_rlvect_1(A) )
                            & ( B = k1_rlvect_1(A)
                             => k1_normsp_1(A,B) = np__0 )
                            & k1_normsp_1(A,k3_rlvect_1(A,B,E)) = k4_real_1(k18_complex1(E),k1_normsp_1(A,B))
                            & r1_xreal_0(k1_normsp_1(A,k4_rlvect_1(A,B,C)),k3_real_1(k1_normsp_1(A,B),k1_normsp_1(A,C)))
                            & r1_xreal_0(k1_normsp_1(A,k1_group_1(A,B,C)),k4_real_1(k1_normsp_1(A,B),k1_normsp_1(A,C)))
                            & k1_normsp_1(A,k2_group_1(A)) = np__1
                            & v4_lopban_1(A) ) ) ) ) ) ) ) )).

fof(d7_lopban_3,axiom,(
    $true )).

fof(d8_lopban_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v4_lopban_3(B,A)
          <=> ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & k1_group_1(A,B,C) = k2_group_1(A)
                & k1_group_1(A,C,B) = k2_group_1(A) ) ) ) ) )).

fof(d9_lopban_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_lopban_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,u1_struct_0(A))
                    & m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
                 => ( D = k6_lopban_3(A,B,C)
                  <=> ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k2_normsp_1(A,D,E) = k1_group_1(A,C,k2_normsp_1(A,B,E)) ) ) ) ) ) ) )).

fof(d10_lopban_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_lopban_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,u1_struct_0(A))
                    & m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
                 => ( D = k7_lopban_3(A,B,C)
                  <=> ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k2_normsp_1(A,D,E) = k1_group_1(A,k2_normsp_1(A,B,E),C) ) ) ) ) ) ) )).

fof(d11_lopban_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_lopban_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u1_struct_0(A))
            & m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,u1_struct_0(A))
                    & m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
                 => ( D = k8_lopban_3(A,B,C)
                  <=> ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k2_normsp_1(A,D,E) = k1_group_1(A,k2_normsp_1(A,B,E),k2_normsp_1(A,C,E)) ) ) ) ) ) ) )).

fof(d12_lopban_3,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)
        & v4_group_1(A)
        & v2_funcsdom(A)
        & v5_lopban_2(A)
        & l1_lopban_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v4_lopban_3(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( C = k9_lopban_3(A,B)
                <=> ( k1_group_1(A,B,C) = k2_group_1(A)
                    & k1_group_1(A,C,B) = k2_group_1(A) ) ) ) ) ) ) )).

fof(d13_lopban_3,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)
        & v4_group_1(A)
        & v2_funcsdom(A)
        & v5_lopban_2(A)
        & l1_lopban_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(A))
                & m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
             => ( C = k10_lopban_3(A,B)
              <=> ( k2_normsp_1(A,C,np__0) = k2_group_1(A)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => k2_normsp_1(A,C,k1_nat_1(D,np__1)) = k1_group_1(A,k2_normsp_1(A,C,D),B) ) ) ) ) ) ) )).

fof(d14_lopban_3,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)
        & v4_group_1(A)
        & v2_funcsdom(A)
        & v5_lopban_2(A)
        & l1_lopban_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => k11_lopban_3(A,B,C) = k2_normsp_1(A,k10_lopban_3(A,B),C) ) ) ) )).

fof(t44_lopban_3,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)
        & v4_group_1(A)
        & v2_funcsdom(A)
        & v5_lopban_2(A)
        & l1_lopban_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k11_lopban_3(A,B,np__0) = k2_group_1(A) ) ) )).

fof(t45_lopban_3,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)
        & v4_group_1(A)
        & v2_funcsdom(A)
        & v5_lopban_2(A)
        & l1_lopban_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ~ r1_xreal_0(np__1,k1_normsp_1(A,B))
           => ( v1_lopban_3(k10_lopban_3(A,B),A)
              & v2_lopban_3(k10_lopban_3(A,B),A) ) ) ) ) )).

fof(t46_lopban_3,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)
        & v4_group_1(A)
        & v2_funcsdom(A)
        & v5_lopban_2(A)
        & l1_lopban_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ~ r1_xreal_0(np__1,k1_normsp_1(A,k6_rlvect_1(A,k2_group_1(A),B)))
           => ( v1_lopban_3(k10_lopban_3(A,k6_rlvect_1(A,k2_group_1(A),B)),A)
              & v2_lopban_3(k10_lopban_3(A,k6_rlvect_1(A,k2_group_1(A),B)),A) ) ) ) ) )).

fof(t47_lopban_3,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)
        & v4_group_1(A)
        & v2_funcsdom(A)
        & v5_lopban_2(A)
        & l1_lopban_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ~ r1_xreal_0(np__1,k1_normsp_1(A,k6_rlvect_1(A,k2_group_1(A),B)))
           => ( v4_lopban_3(B,A)
              & k9_lopban_3(A,B) = k2_lopban_3(A,k10_lopban_3(A,k6_rlvect_1(A,k2_group_1(A),B))) ) ) ) ) )).

fof(redefinition_v3_lopban_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
     => ( v3_lopban_3(B,A)
      <=> v5_seqm_3(B) ) ) )).

fof(dt_k1_lopban_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_normsp_1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
     => ( v1_funct_1(k1_lopban_3(A,B))
        & v1_funct_2(k1_lopban_3(A,B),k5_numbers,u1_struct_0(A))
        & m2_relset_1(k1_lopban_3(A,B),k5_numbers,u1_struct_0(A)) ) ) )).

fof(dt_k2_lopban_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
     => m1_subset_1(k2_lopban_3(A,B),u1_struct_0(A)) ) )).

fof(dt_k3_lopban_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & m1_relset_1(B,k5_numbers,u1_struct_0(A))
        & m1_subset_1(C,k5_numbers) )
     => ( v1_funct_1(k3_lopban_3(A,B,C))
        & v1_funct_2(k3_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
        & m2_relset_1(k3_lopban_3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) )).

fof(dt_k4_lopban_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_numbers)
        & v1_seqm_3(B)
        & v7_seqm_3(B)
        & m1_relset_1(B,k5_numbers,k1_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,u1_struct_0(A))
        & m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
     => ( v1_funct_1(k4_lopban_3(A,B,C))
        & v1_funct_2(k4_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
        & m2_relset_1(k4_lopban_3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) )).

fof(redefinition_k4_lopban_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_numbers)
        & v1_seqm_3(B)
        & v7_seqm_3(B)
        & m1_relset_1(B,k5_numbers,k1_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,u1_struct_0(A))
        & m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
     => k4_lopban_3(A,B,C) = k5_relat_1(B,C) ) )).

fof(dt_k5_lopban_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_numbers)
        & v1_seqm_3(B)
        & v7_seqm_3(B)
        & m1_relset_1(B,k5_numbers,k1_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,u1_struct_0(A))
        & m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
     => ( v1_funct_1(k5_lopban_3(A,B,C))
        & v1_funct_2(k5_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
        & m2_relset_1(k5_lopban_3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) )).

fof(redefinition_k5_lopban_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_numbers)
        & v1_seqm_3(B)
        & v7_seqm_3(B)
        & m1_relset_1(B,k5_numbers,k1_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,u1_struct_0(A))
        & m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
     => k5_lopban_3(A,B,C) = k5_relat_1(B,C) ) )).

fof(dt_k6_lopban_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_lopban_2(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & m1_relset_1(B,k5_numbers,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( v1_funct_1(k6_lopban_3(A,B,C))
        & v1_funct_2(k6_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
        & m2_relset_1(k6_lopban_3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) )).

fof(dt_k7_lopban_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_lopban_2(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & m1_relset_1(B,k5_numbers,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( v1_funct_1(k7_lopban_3(A,B,C))
        & v1_funct_2(k7_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
        & m2_relset_1(k7_lopban_3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) )).

fof(dt_k8_lopban_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_lopban_2(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & m1_relset_1(B,k5_numbers,u1_struct_0(A))
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,u1_struct_0(A))
        & m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
     => ( v1_funct_1(k8_lopban_3(A,B,C))
        & v1_funct_2(k8_lopban_3(A,B,C),k5_numbers,u1_struct_0(A))
        & m2_relset_1(k8_lopban_3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) )).

fof(dt_k9_lopban_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & v4_group_1(A)
        & v2_funcsdom(A)
        & v5_lopban_2(A)
        & l1_lopban_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k9_lopban_3(A,B),u1_struct_0(A)) ) )).

fof(dt_k10_lopban_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & v4_group_1(A)
        & v2_funcsdom(A)
        & v5_lopban_2(A)
        & l1_lopban_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ( v1_funct_1(k10_lopban_3(A,B))
        & v1_funct_2(k10_lopban_3(A,B),k5_numbers,u1_struct_0(A))
        & m2_relset_1(k10_lopban_3(A,B),k5_numbers,u1_struct_0(A)) ) ) )).

fof(dt_k11_lopban_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & v2_normsp_1(A)
        & v4_group_1(A)
        & v2_funcsdom(A)
        & v5_lopban_2(A)
        & l1_lopban_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,k5_numbers) )
     => m1_subset_1(k11_lopban_3(A,B,C),u1_struct_0(A)) ) )).
%------------------------------------------------------------------------------