SET007 Axioms: SET007+809.ax


%------------------------------------------------------------------------------
% File     : SET007+809 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Banach Algebra of Bounded Linear Operators
% 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_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   70 (   1 unit)
%            Number of atoms       :  964 (  77 equality)
%            Maximal formula depth :   27 (  12 average)
%            Number of connectives :  980 (  86 ~  ;   0  |; 761  &)
%                                         (   6 <=>; 127 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   42 (   0 propositional; 1-4 arity)
%            Number of functors    :   46 (   3 constant; 0-7 arity)
%            Number of variables   :  166 (   0 singleton; 156 !;  10 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_lopban_2,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) )
     => ( ~ v3_struct_0(k8_lopban_2(A))
        & v3_vectsp_1(k8_lopban_2(A)) ) ) )).

fof(fc2_lopban_2,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) )
     => ( ~ v3_struct_0(k8_lopban_2(A))
        & v2_group_1(k8_lopban_2(A))
        & v3_vectsp_1(k8_lopban_2(A))
        & v6_vectsp_1(k8_lopban_2(A))
        & v8_vectsp_1(k8_lopban_2(A)) ) ) )).

fof(fc3_lopban_2,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) )
     => ( ~ v3_struct_0(k8_lopban_2(A))
        & v3_rlvect_1(k8_lopban_2(A))
        & v4_rlvect_1(k8_lopban_2(A))
        & v5_rlvect_1(k8_lopban_2(A))
        & v6_rlvect_1(k8_lopban_2(A))
        & v2_group_1(k8_lopban_2(A))
        & v4_group_1(k8_lopban_2(A))
        & v3_vectsp_1(k8_lopban_2(A))
        & v4_vectsp_1(k8_lopban_2(A))
        & v5_vectsp_1(k8_lopban_2(A))
        & v6_vectsp_1(k8_lopban_2(A))
        & v7_vectsp_1(k8_lopban_2(A))
        & v8_vectsp_1(k8_lopban_2(A)) ) ) )).

fof(fc4_lopban_2,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) )
     => ( ~ v3_struct_0(k9_lopban_2(A))
        & v1_funcsdom(k9_lopban_2(A)) ) ) )).

fof(fc5_lopban_2,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) )
     => ( ~ v3_struct_0(k9_lopban_2(A))
        & v2_group_1(k9_lopban_2(A))
        & v6_vectsp_1(k9_lopban_2(A))
        & v8_vectsp_1(k9_lopban_2(A))
        & v1_funcsdom(k9_lopban_2(A)) ) ) )).

fof(fc6_lopban_2,axiom,
    ( ~ v3_struct_0(k3_rsspace3)
    & v3_rlvect_1(k3_rsspace3)
    & v4_rlvect_1(k3_rsspace3)
    & v5_rlvect_1(k3_rsspace3)
    & v6_rlvect_1(k3_rsspace3)
    & v7_rlvect_1(k3_rsspace3)
    & v2_normsp_1(k3_rsspace3)
    & v4_lopban_1(k3_rsspace3) )).

fof(fc7_lopban_2,axiom,
    ( ~ v3_struct_0(k3_rsspace3)
    & v3_rlvect_1(k3_rsspace3)
    & v4_rlvect_1(k3_rsspace3)
    & v5_rlvect_1(k3_rsspace3)
    & v6_rlvect_1(k3_rsspace3)
    & v7_rlvect_1(k3_rsspace3)
    & ~ v3_realset2(k3_rsspace3)
    & v2_normsp_1(k3_rsspace3)
    & v4_lopban_1(k3_rsspace3) )).

fof(rc1_lopban_2,axiom,(
    ? [A] :
      ( l1_normsp_1(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)
      & ~ v3_realset2(A)
      & v2_normsp_1(A)
      & v4_lopban_1(A) ) )).

fof(rc2_lopban_2,axiom,(
    ? [A] :
      ( l1_lopban_2(A)
      & v1_lopban_2(A) ) )).

fof(rc3_lopban_2,axiom,(
    ? [A] :
      ( l1_lopban_2(A)
      & ~ v3_struct_0(A) ) )).

fof(fc8_lopban_2,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) )
     => ( ~ v3_struct_0(k10_lopban_2(A))
        & v1_lopban_2(k10_lopban_2(A)) ) ) )).

fof(fc9_lopban_2,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) )
     => ( ~ v3_struct_0(k10_lopban_2(A))
        & v2_group_1(k10_lopban_2(A))
        & v6_vectsp_1(k10_lopban_2(A))
        & v8_vectsp_1(k10_lopban_2(A))
        & v1_lopban_2(k10_lopban_2(A)) ) ) )).

fof(rc4_lopban_2,axiom,(
    ? [A] :
      ( l1_lopban_2(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)
      & v4_group_1(A)
      & v2_funcsdom(A)
      & v2_normsp_1(A)
      & v1_lopban_2(A) ) )).

fof(fc10_lopban_2,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) )
     => ( ~ v3_struct_0(k10_lopban_2(A))
        & v3_rlvect_1(k10_lopban_2(A))
        & v4_rlvect_1(k10_lopban_2(A))
        & v5_rlvect_1(k10_lopban_2(A))
        & v6_rlvect_1(k10_lopban_2(A))
        & v7_rlvect_1(k10_lopban_2(A))
        & v2_group_1(k10_lopban_2(A))
        & v4_group_1(k10_lopban_2(A))
        & v6_vectsp_1(k10_lopban_2(A))
        & v8_vectsp_1(k10_lopban_2(A))
        & v2_funcsdom(k10_lopban_2(A))
        & v2_normsp_1(k10_lopban_2(A))
        & v1_lopban_2(k10_lopban_2(A)) ) ) )).

fof(cc1_lopban_2,axiom,(
    ! [A] :
      ( l1_lopban_2(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)
          & v4_group_1(A)
          & v2_funcsdom(A)
          & v2_normsp_1(A)
          & v5_lopban_2(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)
          & v4_group_1(A)
          & v5_vectsp_1(A)
          & v8_vectsp_1(A)
          & v2_funcsdom(A)
          & v2_normsp_1(A)
          & v4_lopban_1(A)
          & v2_lopban_2(A)
          & v3_lopban_2(A)
          & v4_lopban_2(A) ) ) ) )).

fof(cc2_lopban_2,axiom,(
    ! [A] :
      ( l1_lopban_2(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)
          & v4_group_1(A)
          & v5_vectsp_1(A)
          & v8_vectsp_1(A)
          & v2_funcsdom(A)
          & v2_normsp_1(A)
          & v4_lopban_1(A)
          & v2_lopban_2(A)
          & v3_lopban_2(A)
          & v4_lopban_2(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)
          & v4_group_1(A)
          & v2_funcsdom(A)
          & v2_normsp_1(A)
          & v5_lopban_2(A) ) ) ) )).

fof(fc11_lopban_2,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)
        & ~ v3_realset2(A)
        & v2_normsp_1(A)
        & v4_lopban_1(A)
        & l1_normsp_1(A) )
     => ( ~ v3_struct_0(k10_lopban_2(A))
        & v3_rlvect_1(k10_lopban_2(A))
        & v4_rlvect_1(k10_lopban_2(A))
        & v5_rlvect_1(k10_lopban_2(A))
        & v6_rlvect_1(k10_lopban_2(A))
        & v7_rlvect_1(k10_lopban_2(A))
        & v2_group_1(k10_lopban_2(A))
        & v4_group_1(k10_lopban_2(A))
        & v5_vectsp_1(k10_lopban_2(A))
        & v6_vectsp_1(k10_lopban_2(A))
        & v8_vectsp_1(k10_lopban_2(A))
        & v2_funcsdom(k10_lopban_2(A))
        & v2_normsp_1(k10_lopban_2(A))
        & v4_lopban_1(k10_lopban_2(A))
        & v1_lopban_2(k10_lopban_2(A))
        & v2_lopban_2(k10_lopban_2(A))
        & v3_lopban_2(k10_lopban_2(A))
        & v4_lopban_2(k10_lopban_2(A))
        & v5_lopban_2(k10_lopban_2(A)) ) ) )).

fof(rc5_lopban_2,axiom,(
    ? [A] :
      ( l1_lopban_2(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)
      & v4_group_1(A)
      & v5_vectsp_1(A)
      & v8_vectsp_1(A)
      & v2_funcsdom(A)
      & v2_normsp_1(A)
      & v4_lopban_1(A)
      & v2_lopban_2(A)
      & v3_lopban_2(A)
      & v4_lopban_2(A)
      & v5_lopban_2(A) ) )).

fof(t1_lopban_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_rlvect_1(C)
                & l2_rlvect_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v1_lopban_1(D,A,B)
                    & v2_lopban_1(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & v1_lopban_1(E,B,C)
                        & v2_lopban_1(E,B,C)
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( v1_funct_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E))
                        & v1_funct_2(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C))
                        & v1_lopban_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
                        & v2_lopban_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
                        & m2_relset_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C)) ) ) ) ) ) ) )).

fof(t2_lopban_2,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] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_rlvect_1(C)
                & v2_normsp_1(C)
                & l1_normsp_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v1_lopban_1(D,A,B)
                    & v2_lopban_1(D,A,B)
                    & v3_lopban_1(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & v1_lopban_1(E,B,C)
                        & v2_lopban_1(E,B,C)
                        & v3_lopban_1(E,B,C)
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( v1_funct_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E))
                        & v1_funct_2(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C))
                        & v1_lopban_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
                        & v2_lopban_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
                        & v3_lopban_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
                        & m2_relset_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C))
                        & ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r1_xreal_0(k1_normsp_1(C,k8_funct_2(u1_struct_0(A),u1_struct_0(C),k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),F)),k4_real_1(k4_real_1(k2_seq_1(k10_lopban_1(B,C),k1_numbers,k15_lopban_1(B,C),E),k2_seq_1(k10_lopban_1(A,B),k1_numbers,k15_lopban_1(A,B),D)),k1_normsp_1(A,F)))
                              & r1_xreal_0(k2_seq_1(k10_lopban_1(A,C),k1_numbers,k15_lopban_1(A,C),k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)),k4_real_1(k2_seq_1(k10_lopban_1(B,C),k1_numbers,k15_lopban_1(B,C),E),k2_seq_1(k10_lopban_1(A,B),k1_numbers,k15_lopban_1(A,B),D))) ) ) ) ) ) ) ) ) )).

fof(d1_lopban_2,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_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
         => ! [C] :
              ( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
             => k3_lopban_2(A,B,C) = k2_binop_1(k10_lopban_1(A,A),k10_lopban_1(A,A),k10_lopban_1(A,A),k8_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),B,C) ) ) ) )).

fof(d2_lopban_2,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_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
         => ! [C] :
              ( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
             => k4_lopban_2(A,B,C) = k2_lopban_2(A,k13_lopban_1(A,A,B),k13_lopban_1(A,A,C)) ) ) ) )).

fof(d3_lopban_2,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_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => k5_lopban_2(A,B,C) = k2_binop_1(k1_numbers,k10_lopban_1(A,A),k10_lopban_1(A,A),k9_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),C,B) ) ) ) )).

fof(d4_lopban_2,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,k2_zfmisc_1(k10_lopban_1(A,A),k10_lopban_1(A,A)),k10_lopban_1(A,A))
            & m2_relset_1(B,k2_zfmisc_1(k10_lopban_1(A,A),k10_lopban_1(A,A)),k10_lopban_1(A,A)) )
         => ( B = k6_lopban_2(A)
          <=> ! [C] :
                ( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
               => ! [D] :
                    ( m1_struct_0(D,k8_lopban_1(A,A),k10_lopban_1(A,A))
                   => k2_binop_1(k10_lopban_1(A,A),k10_lopban_1(A,A),k10_lopban_1(A,A),B,C,D) = k4_lopban_2(A,D,C) ) ) ) ) ) )).

fof(t3_lopban_2,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(k6_partfun1(u1_struct_0(A)))
        & v1_funct_2(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A))
        & v1_lopban_1(k6_partfun1(u1_struct_0(A)),A,A)
        & v2_lopban_1(k6_partfun1(u1_struct_0(A)),A,A)
        & v3_lopban_1(k6_partfun1(u1_struct_0(A)),A,A)
        & m2_relset_1(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(d5_lopban_2,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) )
     => k7_lopban_2(A) = k6_partfun1(u1_struct_0(A)) ) )).

fof(t4_lopban_2,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,u1_struct_0(A),u1_struct_0(A))
            & v1_lopban_1(B,A,A)
            & v2_lopban_1(B,A,A)
            & v3_lopban_1(B,A,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v1_lopban_1(C,A,A)
                & v2_lopban_1(C,A,A)
                & v3_lopban_1(C,A,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v1_lopban_1(D,A,A)
                    & v2_lopban_1(D,A,A)
                    & v3_lopban_1(D,A,A)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ( D = k2_lopban_2(A,C,B)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,E) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,E)) ) ) ) ) ) ) )).

fof(t5_lopban_2,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,u1_struct_0(A),u1_struct_0(A))
            & v1_lopban_1(B,A,A)
            & v2_lopban_1(B,A,A)
            & v3_lopban_1(B,A,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v1_lopban_1(C,A,A)
                & v2_lopban_1(C,A,A)
                & v3_lopban_1(C,A,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v1_lopban_1(D,A,A)
                    & v2_lopban_1(D,A,A)
                    & v3_lopban_1(D,A,A)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => k2_lopban_2(A,k2_lopban_2(A,D,C),B) = k2_lopban_2(A,D,k2_lopban_2(A,C,B)) ) ) ) ) )).

fof(t6_lopban_2,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,u1_struct_0(A),u1_struct_0(A))
            & v1_lopban_1(B,A,A)
            & v2_lopban_1(B,A,A)
            & v3_lopban_1(B,A,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_partfun1(u1_struct_0(A)),B) = B
            & k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,k6_partfun1(u1_struct_0(A))) = B ) ) ) )).

fof(t7_lopban_2,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_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
         => ! [C] :
              ( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
             => ! [D] :
                  ( m1_struct_0(D,k8_lopban_1(A,A),k10_lopban_1(A,A))
                 => k4_lopban_2(A,k4_lopban_2(A,D,C),B) = k4_lopban_2(A,D,k4_lopban_2(A,C,B)) ) ) ) ) )).

fof(t8_lopban_2,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_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
         => ( k4_lopban_2(A,k7_lopban_2(A),B) = B
            & k4_lopban_2(A,B,k7_lopban_2(A)) = B ) ) ) )).

fof(t9_lopban_2,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_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
         => ! [C] :
              ( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
             => ! [D] :
                  ( m1_struct_0(D,k8_lopban_1(A,A),k10_lopban_1(A,A))
                 => k4_lopban_2(A,k3_lopban_2(A,C,D),B) = k3_lopban_2(A,k4_lopban_2(A,C,B),k4_lopban_2(A,D,B)) ) ) ) ) )).

fof(t10_lopban_2,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_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
         => ! [C] :
              ( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
             => ! [D] :
                  ( m1_struct_0(D,k8_lopban_1(A,A),k10_lopban_1(A,A))
                 => k4_lopban_2(A,B,k3_lopban_2(A,C,D)) = k3_lopban_2(A,k4_lopban_2(A,B,C),k4_lopban_2(A,B,D)) ) ) ) ) )).

fof(t11_lopban_2,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_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
         => ! [C] :
              ( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => k5_lopban_2(A,k4_lopban_2(A,C,B),k4_real_1(D,E)) = k4_lopban_2(A,k5_lopban_2(A,C,E),k5_lopban_2(A,B,D)) ) ) ) ) ) )).

fof(t12_lopban_2,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_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
         => ! [C] :
              ( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => k5_lopban_2(A,k4_lopban_2(A,C,B),D) = k4_lopban_2(A,C,k5_lopban_2(A,B,D)) ) ) ) ) )).

fof(d6_lopban_2,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) )
     => k8_lopban_2(A) = g3_vectsp_1(k10_lopban_1(A,A),k8_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k6_lopban_2(A),k7_lopban_2(A),k10_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A))) ) )).

fof(t13_lopban_2,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(k8_lopban_2(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k8_lopban_2(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k8_lopban_2(A)))
                 => ( k2_rlvect_1(k8_lopban_2(A),B,C) = k2_rlvect_1(k8_lopban_2(A),C,B)
                    & k2_rlvect_1(k8_lopban_2(A),k2_rlvect_1(k8_lopban_2(A),B,C),D) = k2_rlvect_1(k8_lopban_2(A),B,k2_rlvect_1(k8_lopban_2(A),C,D))
                    & k2_rlvect_1(k8_lopban_2(A),B,k1_rlvect_1(k8_lopban_2(A))) = B
                    & ? [E] :
                        ( m1_subset_1(E,u1_struct_0(k8_lopban_2(A)))
                        & k2_rlvect_1(k8_lopban_2(A),B,E) = k1_rlvect_1(k8_lopban_2(A)) )
                    & k1_group_1(k8_lopban_2(A),k1_group_1(k8_lopban_2(A),B,C),D) = k1_group_1(k8_lopban_2(A),B,k1_group_1(k8_lopban_2(A),C,D))
                    & k1_group_1(k8_lopban_2(A),B,k2_group_1(k8_lopban_2(A))) = B
                    & k1_group_1(k8_lopban_2(A),k2_group_1(k8_lopban_2(A)),B) = B
                    & k1_group_1(k8_lopban_2(A),B,k2_rlvect_1(k8_lopban_2(A),C,D)) = k2_rlvect_1(k8_lopban_2(A),k1_group_1(k8_lopban_2(A),B,C),k1_group_1(k8_lopban_2(A),B,D))
                    & k1_group_1(k8_lopban_2(A),k2_rlvect_1(k8_lopban_2(A),C,D),B) = k2_rlvect_1(k8_lopban_2(A),k1_group_1(k8_lopban_2(A),C,B),k1_group_1(k8_lopban_2(A),D,B)) ) ) ) ) ) )).

fof(t14_lopban_2,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) )
     => ( ~ v3_struct_0(k8_lopban_2(A))
        & v3_rlvect_1(k8_lopban_2(A))
        & v4_rlvect_1(k8_lopban_2(A))
        & v5_rlvect_1(k8_lopban_2(A))
        & v6_rlvect_1(k8_lopban_2(A))
        & v4_group_1(k8_lopban_2(A))
        & v6_vectsp_1(k8_lopban_2(A))
        & v7_vectsp_1(k8_lopban_2(A))
        & v8_vectsp_1(k8_lopban_2(A))
        & l3_vectsp_1(k8_lopban_2(A)) ) ) )).

fof(d7_lopban_2,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) )
     => k9_lopban_2(A) = g1_funcsdom(k10_lopban_1(A,A),k6_lopban_2(A),k8_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k9_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k7_lopban_2(A),k10_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A))) ) )).

fof(t15_lopban_2,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(k9_lopban_2(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k9_lopban_2(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k9_lopban_2(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ( k2_rlvect_1(k9_lopban_2(A),B,C) = k2_rlvect_1(k9_lopban_2(A),C,B)
                            & k2_rlvect_1(k9_lopban_2(A),k2_rlvect_1(k9_lopban_2(A),B,C),D) = k2_rlvect_1(k9_lopban_2(A),B,k2_rlvect_1(k9_lopban_2(A),C,D))
                            & k2_rlvect_1(k9_lopban_2(A),B,k1_rlvect_1(k9_lopban_2(A))) = B
                            & ? [G] :
                                ( m1_subset_1(G,u1_struct_0(k9_lopban_2(A)))
                                & k2_rlvect_1(k9_lopban_2(A),B,G) = k1_rlvect_1(k9_lopban_2(A)) )
                            & k1_group_1(k9_lopban_2(A),k1_group_1(k9_lopban_2(A),B,C),D) = k1_group_1(k9_lopban_2(A),B,k1_group_1(k9_lopban_2(A),C,D))
                            & k1_group_1(k9_lopban_2(A),B,k2_group_1(k9_lopban_2(A))) = B
                            & k1_group_1(k9_lopban_2(A),k2_group_1(k9_lopban_2(A)),B) = B
                            & k1_group_1(k9_lopban_2(A),B,k2_rlvect_1(k9_lopban_2(A),C,D)) = k2_rlvect_1(k9_lopban_2(A),k1_group_1(k9_lopban_2(A),B,C),k1_group_1(k9_lopban_2(A),B,D))
                            & k1_group_1(k9_lopban_2(A),k2_rlvect_1(k9_lopban_2(A),C,D),B) = k2_rlvect_1(k9_lopban_2(A),k1_group_1(k9_lopban_2(A),C,B),k1_group_1(k9_lopban_2(A),D,B))
                            & k3_rlvect_1(k9_lopban_2(A),k1_group_1(k9_lopban_2(A),B,C),E) = k1_group_1(k9_lopban_2(A),k3_rlvect_1(k9_lopban_2(A),B,E),C)
                            & k3_rlvect_1(k9_lopban_2(A),k2_rlvect_1(k9_lopban_2(A),B,C),E) = k2_rlvect_1(k9_lopban_2(A),k3_rlvect_1(k9_lopban_2(A),B,E),k3_rlvect_1(k9_lopban_2(A),C,E))
                            & k3_rlvect_1(k9_lopban_2(A),B,k3_real_1(E,F)) = k2_rlvect_1(k9_lopban_2(A),k3_rlvect_1(k9_lopban_2(A),B,E),k3_rlvect_1(k9_lopban_2(A),B,F))
                            & k3_rlvect_1(k9_lopban_2(A),B,k4_real_1(E,F)) = k3_rlvect_1(k9_lopban_2(A),k3_rlvect_1(k9_lopban_2(A),B,F),E)
                            & k3_rlvect_1(k9_lopban_2(A),k1_group_1(k9_lopban_2(A),B,C),k4_real_1(E,F)) = k1_group_1(k9_lopban_2(A),k3_rlvect_1(k9_lopban_2(A),B,E),k3_rlvect_1(k9_lopban_2(A),C,F)) ) ) ) ) ) ) ) )).

fof(t16_lopban_2,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) )
     => ( ~ v3_struct_0(k9_lopban_2(A))
        & v3_rlvect_1(k9_lopban_2(A))
        & v4_rlvect_1(k9_lopban_2(A))
        & v5_rlvect_1(k9_lopban_2(A))
        & v6_rlvect_1(k9_lopban_2(A))
        & v4_group_1(k9_lopban_2(A))
        & v2_funcsdom(k9_lopban_2(A))
        & l1_funcsdom(k9_lopban_2(A)) ) ) )).

fof(t17_lopban_2,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)
        & ~ v3_realset2(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A) )
     => ? [B] :
          ( m1_subset_1(B,u1_struct_0(A))
          & k1_normsp_1(A,B) = np__1 ) ) )).

fof(t18_lopban_2,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)
        & ~ v3_realset2(A)
        & v2_normsp_1(A)
        & l1_normsp_1(A) )
     => k2_seq_1(k10_lopban_1(A,A),k1_numbers,k15_lopban_1(A,A),k6_partfun1(u1_struct_0(A))) = np__1 ) )).

fof(d8_lopban_2,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) )
     => k10_lopban_2(A) = g1_lopban_2(k10_lopban_1(A,A),k6_lopban_2(A),k8_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k9_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k7_lopban_2(A),k10_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k15_lopban_1(A,A)) ) )).

fof(t19_lopban_2,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(k10_lopban_2(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k10_lopban_2(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k10_lopban_2(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ( k2_rlvect_1(k10_lopban_2(A),B,C) = k2_rlvect_1(k10_lopban_2(A),C,B)
                            & k2_rlvect_1(k10_lopban_2(A),k2_rlvect_1(k10_lopban_2(A),B,C),D) = k2_rlvect_1(k10_lopban_2(A),B,k2_rlvect_1(k10_lopban_2(A),C,D))
                            & k2_rlvect_1(k10_lopban_2(A),B,k1_rlvect_1(k10_lopban_2(A))) = B
                            & ? [G] :
                                ( m1_subset_1(G,u1_struct_0(k10_lopban_2(A)))
                                & k2_rlvect_1(k10_lopban_2(A),B,G) = k1_rlvect_1(k10_lopban_2(A)) )
                            & k1_group_1(k10_lopban_2(A),k1_group_1(k10_lopban_2(A),B,C),D) = k1_group_1(k10_lopban_2(A),B,k1_group_1(k10_lopban_2(A),C,D))
                            & k1_group_1(k10_lopban_2(A),B,k2_group_1(k10_lopban_2(A))) = B
                            & k1_group_1(k10_lopban_2(A),k2_group_1(k10_lopban_2(A)),B) = B
                            & k1_group_1(k10_lopban_2(A),B,k2_rlvect_1(k10_lopban_2(A),C,D)) = k2_rlvect_1(k10_lopban_2(A),k1_group_1(k10_lopban_2(A),B,C),k1_group_1(k10_lopban_2(A),B,D))
                            & k1_group_1(k10_lopban_2(A),k2_rlvect_1(k10_lopban_2(A),C,D),B) = k2_rlvect_1(k10_lopban_2(A),k1_group_1(k10_lopban_2(A),C,B),k1_group_1(k10_lopban_2(A),D,B))
                            & k3_rlvect_1(k10_lopban_2(A),k1_group_1(k10_lopban_2(A),B,C),E) = k1_group_1(k10_lopban_2(A),k3_rlvect_1(k10_lopban_2(A),B,E),C)
                            & k3_rlvect_1(k10_lopban_2(A),k1_group_1(k10_lopban_2(A),B,C),k4_real_1(E,F)) = k1_group_1(k10_lopban_2(A),k3_rlvect_1(k10_lopban_2(A),B,E),k3_rlvect_1(k10_lopban_2(A),C,F))
                            & k3_rlvect_1(k10_lopban_2(A),k2_rlvect_1(k10_lopban_2(A),B,C),E) = k2_rlvect_1(k10_lopban_2(A),k3_rlvect_1(k10_lopban_2(A),B,E),k3_rlvect_1(k10_lopban_2(A),C,E))
                            & k3_rlvect_1(k10_lopban_2(A),B,k3_real_1(E,F)) = k2_rlvect_1(k10_lopban_2(A),k3_rlvect_1(k10_lopban_2(A),B,E),k3_rlvect_1(k10_lopban_2(A),B,F))
                            & k3_rlvect_1(k10_lopban_2(A),B,k4_real_1(E,F)) = k3_rlvect_1(k10_lopban_2(A),k3_rlvect_1(k10_lopban_2(A),B,F),E)
                            & k3_rlvect_1(k10_lopban_2(A),B,np__1) = B ) ) ) ) ) ) ) )).

fof(t20_lopban_2,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) )
     => ( v2_normsp_1(k10_lopban_2(A))
        & v3_rlvect_1(k10_lopban_2(A))
        & v4_rlvect_1(k10_lopban_2(A))
        & v5_rlvect_1(k10_lopban_2(A))
        & v6_rlvect_1(k10_lopban_2(A))
        & v4_group_1(k10_lopban_2(A))
        & v2_funcsdom(k10_lopban_2(A))
        & v7_rlvect_1(k10_lopban_2(A)) ) ) )).

fof(d9_lopban_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_lopban_2(A) )
     => ( v2_lopban_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => 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))) ) ) ) ) )).

fof(d10_lopban_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_lopban_2(A) )
     => ( v3_lopban_2(A)
      <=> k1_normsp_1(A,k2_group_1(A)) = np__1 ) ) )).

fof(d11_lopban_2,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_lopban_2(A) )
     => ( v4_lopban_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k3_rlvect_1(A,k1_group_1(A,C,D),B) = k1_group_1(A,C,k3_rlvect_1(A,D,B)) ) ) ) ) ) )).

fof(d12_lopban_2,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)
        & v4_group_1(A)
        & v2_funcsdom(A)
        & v2_normsp_1(A)
        & l1_lopban_2(A) )
     => ( v5_lopban_2(A)
      <=> ( v2_lopban_2(A)
          & v3_lopban_2(A)
          & v4_lopban_2(A)
          & v8_vectsp_1(A)
          & v5_vectsp_1(A)
          & v4_lopban_1(A) ) ) ) )).

fof(t21_lopban_2,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) )
     => k2_group_1(k8_lopban_2(A)) = k7_lopban_2(A) ) )).

fof(t22_lopban_2,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) )
     => k2_group_1(k9_lopban_2(A)) = k7_lopban_2(A) ) )).

fof(t23_lopban_2,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) )
     => k2_group_1(k10_lopban_2(A)) = k7_lopban_2(A) ) )).

fof(dt_l1_lopban_2,axiom,(
    ! [A] :
      ( l1_lopban_2(A)
     => ( l1_funcsdom(A)
        & l1_normsp_1(A) ) ) )).

fof(existence_l1_lopban_2,axiom,(
    ? [A] : l1_lopban_2(A) )).

fof(abstractness_v1_lopban_2,axiom,(
    ! [A] :
      ( l1_lopban_2(A)
     => ( v1_lopban_2(A)
       => A = g1_lopban_2(u1_struct_0(A),u1_group_1(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_vectsp_1(A),u2_struct_0(A),u1_normsp_1(A)) ) ) )).

fof(dt_k1_lopban_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,A))
        & m1_subset_1(C,k1_fraenkel(A,A)) )
     => m2_fraenkel(k1_lopban_2(A,B,C),A,A,k1_fraenkel(A,A)) ) )).

fof(redefinition_k1_lopban_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,A))
        & m1_subset_1(C,k1_fraenkel(A,A)) )
     => k1_lopban_2(A,B,C) = k5_relat_1(B,C) ) )).

fof(dt_k2_lopban_2,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,u1_struct_0(A),u1_struct_0(A))
        & v1_lopban_1(B,A,A)
        & v2_lopban_1(B,A,A)
        & v3_lopban_1(B,A,A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
        & v1_lopban_1(C,A,A)
        & v2_lopban_1(C,A,A)
        & v3_lopban_1(C,A,A)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
     => ( v1_funct_1(k2_lopban_2(A,B,C))
        & v1_funct_2(k2_lopban_2(A,B,C),u1_struct_0(A),u1_struct_0(A))
        & v1_lopban_1(k2_lopban_2(A,B,C),A,A)
        & v2_lopban_1(k2_lopban_2(A,B,C),A,A)
        & v3_lopban_1(k2_lopban_2(A,B,C),A,A)
        & m2_relset_1(k2_lopban_2(A,B,C),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(redefinition_k2_lopban_2,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,u1_struct_0(A),u1_struct_0(A))
        & v1_lopban_1(B,A,A)
        & v2_lopban_1(B,A,A)
        & v3_lopban_1(B,A,A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
        & v1_lopban_1(C,A,A)
        & v2_lopban_1(C,A,A)
        & v3_lopban_1(C,A,A)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
     => k2_lopban_2(A,B,C) = k5_relat_1(B,C) ) )).

fof(dt_k3_lopban_2,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,k10_lopban_1(A,A))
        & m1_subset_1(C,k10_lopban_1(A,A)) )
     => m1_struct_0(k3_lopban_2(A,B,C),k8_lopban_1(A,A),k10_lopban_1(A,A)) ) )).

fof(dt_k4_lopban_2,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,k10_lopban_1(A,A))
        & m1_subset_1(C,k10_lopban_1(A,A)) )
     => m1_struct_0(k4_lopban_2(A,B,C),k8_lopban_1(A,A),k10_lopban_1(A,A)) ) )).

fof(dt_k5_lopban_2,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,k10_lopban_1(A,A))
        & m1_subset_1(C,k1_numbers) )
     => m1_struct_0(k5_lopban_2(A,B,C),k8_lopban_1(A,A),k10_lopban_1(A,A)) ) )).

fof(dt_k6_lopban_2,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(k6_lopban_2(A))
        & v1_funct_2(k6_lopban_2(A),k2_zfmisc_1(k10_lopban_1(A,A),k10_lopban_1(A,A)),k10_lopban_1(A,A))
        & m2_relset_1(k6_lopban_2(A),k2_zfmisc_1(k10_lopban_1(A,A),k10_lopban_1(A,A)),k10_lopban_1(A,A)) ) ) )).

fof(dt_k7_lopban_2,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) )
     => m1_struct_0(k7_lopban_2(A),k8_lopban_1(A,A),k10_lopban_1(A,A)) ) )).

fof(dt_k8_lopban_2,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) )
     => l3_vectsp_1(k8_lopban_2(A)) ) )).

fof(dt_k9_lopban_2,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) )
     => l1_funcsdom(k9_lopban_2(A)) ) )).

fof(dt_k10_lopban_2,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) )
     => l1_lopban_2(k10_lopban_2(A)) ) )).

fof(dt_g1_lopban_2,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_subset_1(E,A)
        & m1_subset_1(F,A)
        & v1_funct_1(G)
        & v1_funct_2(G,A,k1_numbers)
        & m1_relset_1(G,A,k1_numbers) )
     => ( v1_lopban_2(g1_lopban_2(A,B,C,D,E,F,G))
        & l1_lopban_2(g1_lopban_2(A,B,C,D,E,F,G)) ) ) )).

fof(free_g1_lopban_2,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A)
        & m1_subset_1(E,A)
        & m1_subset_1(F,A)
        & v1_funct_1(G)
        & v1_funct_2(G,A,k1_numbers)
        & m1_relset_1(G,A,k1_numbers) )
     => ! [H,I,J,K,L,M,N] :
          ( g1_lopban_2(A,B,C,D,E,F,G) = g1_lopban_2(H,I,J,K,L,M,N)
         => ( A = H
            & B = I
            & C = J
            & D = K
            & E = L
            & F = M
            & G = N ) ) ) )).
%------------------------------------------------------------------------------