SET007 Axioms: SET007+842.ax


%------------------------------------------------------------------------------
% File     : SET007+842 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Differentiable Functions on Normed Linear Spaces
% 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    : ndiff_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   71 (   0 unit)
%            Number of atoms       : 1485 (  56 equality)
%            Maximal formula depth :   26 (  14 average)
%            Number of connectives : 1611 ( 197 ~  ;   3  |;1068  &)
%                                         (  18 <=>; 325 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   38 (   0 propositional; 1-4 arity)
%            Number of functors    :   50 (   4 constant; 0-4 arity)
%            Number of variables   :  306 (   0 singleton; 295 !;  11 ?)
%            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(rc1_ndiff_1,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)
        & ~ v3_realset2(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_ndiff_1(B,A) ) ) )).

fof(rc2_ndiff_1,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)
        & ~ v3_realset2(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))
          & v5_seqm_3(B) ) ) )).

fof(rc3_ndiff_1,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)
        & ~ v3_realset2(A)
        & l1_normsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & ~ v3_realset2(B)
        & l1_normsp_1(B) )
     => ? [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v3_ndiff_1(C,A,B) ) ) )).

fof(fc1_ndiff_1,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)
        & ~ v3_realset2(A)
        & l1_normsp_1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & v2_ndiff_1(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))
        & v2_ndiff_1(k3_lopban_3(A,B,C),A) ) ) )).

fof(fc2_ndiff_1,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)
        & ~ v3_realset2(A)
        & l1_normsp_1(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,u1_struct_0(A))
        & v5_seqm_3(B)
        & 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))
        & v5_seqm_3(k3_lopban_3(A,B,C)) ) ) )).

fof(t1_ndiff_1,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_nfcont_1(C,A,B)
             => ! [D] :
                  ( m1_nfcont_1(D,A,B)
                 => ? [E] :
                      ( m1_nfcont_1(E,A,B)
                      & r1_tarski(E,C)
                      & r1_tarski(E,D) ) ) ) ) ) )).

fof(t2_ndiff_1,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,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_nfcont_1(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( r2_hidden(C,B)
                    & ! [D] :
                        ( m1_nfcont_1(D,A,C)
                       => ~ r1_tarski(D,B) ) ) ) ) ) ) )).

fof(t4_ndiff_1,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,k1_zfmisc_1(u1_struct_0(A)))
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( r2_hidden(C,B)
                    & ! [D] :
                        ( m1_nfcont_1(D,A,C)
                       => ~ r1_tarski(D,B) ) ) )
           => v3_nfcont_1(B,A) ) ) ) )).

fof(t5_ndiff_1,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,k1_zfmisc_1(u1_struct_0(A)))
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( r2_hidden(C,B)
                    & ! [D] :
                        ( m1_nfcont_1(D,A,C)
                       => ~ r1_tarski(D,B) ) ) )
          <=> v3_nfcont_1(B,A) ) ) ) )).

fof(d1_ndiff_1,axiom,(
    ! [A] :
      ( l2_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)) )
         => ( v1_ndiff_1(B,A)
          <=> r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),B),k4_xboole_0(u1_struct_0(A),k1_tarski(k1_rlvect_1(A)))) ) ) ) )).

fof(t6_ndiff_1,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_ndiff_1(B,A)
          <=> ! [C] :
                ~ ( r2_hidden(C,k5_numbers)
                  & k1_funct_1(B,C) = k1_rlvect_1(A) ) ) ) ) )).

fof(t7_ndiff_1,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_ndiff_1(B,A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_normsp_1(A,B,C) != k1_rlvect_1(A) ) ) ) ) )).

fof(d2_ndiff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,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] :
                  ( ( 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 = k1_ndiff_1(A,B,C)
                  <=> ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k2_normsp_1(A,D,E) = k3_rlvect_1(A,k2_normsp_1(A,B,E),k2_seq_1(k5_numbers,k1_numbers,C,E)) ) ) ) ) ) ) )).

fof(d3_ndiff_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_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 = k2_ndiff_1(A,B,C)
                  <=> ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k2_normsp_1(A,D,E) = k3_rlvect_1(A,B,k2_seq_1(k5_numbers,k1_numbers,C,E)) ) ) ) ) ) ) )).

fof(t8_ndiff_1,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] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k1_numbers)
                    & m2_relset_1(D,k5_numbers,k1_numbers) )
                 => k1_ndiff_1(A,B,k9_seq_1(C,D)) = k3_normsp_1(A,k1_ndiff_1(A,B,C),k1_ndiff_1(A,B,D)) ) ) ) ) )).

fof(t9_ndiff_1,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)) )
             => ! [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)) )
                 => k1_ndiff_1(A,k3_normsp_1(A,C,D),B) = k3_normsp_1(A,k1_ndiff_1(A,C,B),k1_ndiff_1(A,D,B)) ) ) ) ) )).

fof(t10_ndiff_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(B))
                & m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k1_numbers)
                    & m2_relset_1(D,k5_numbers,k1_numbers) )
                 => k6_normsp_1(B,k1_ndiff_1(B,C,D),A) = k1_ndiff_1(B,k6_normsp_1(B,C,A),D) ) ) ) ) )).

fof(t11_ndiff_1,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] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k1_numbers)
                    & m2_relset_1(D,k5_numbers,k1_numbers) )
                 => k1_ndiff_1(A,B,k10_seq_1(C,D)) = k4_normsp_1(A,k1_ndiff_1(A,B,C),k1_ndiff_1(A,B,D)) ) ) ) ) )).

fof(t12_ndiff_1,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)) )
             => ! [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)) )
                 => k1_ndiff_1(A,k4_normsp_1(A,C,D),B) = k4_normsp_1(A,k1_ndiff_1(A,C,B),k1_ndiff_1(A,D,B)) ) ) ) ) )).

fof(t13_ndiff_1,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)) )
             => ( ( v4_seq_2(B)
                  & v4_normsp_1(C,A) )
               => v4_normsp_1(k1_ndiff_1(A,C,B),A) ) ) ) ) )).

fof(t14_ndiff_1,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)) )
             => ( ( v4_seq_2(B)
                  & v4_normsp_1(C,A) )
               => k8_normsp_1(A,k1_ndiff_1(A,C,B)) = k3_rlvect_1(A,k8_normsp_1(A,C),k2_seq_2(B)) ) ) ) ) )).

fof(t15_ndiff_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(B))
                & m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,u1_struct_0(B))
                    & m2_relset_1(D,k5_numbers,u1_struct_0(B)) )
                 => k3_lopban_3(B,k3_normsp_1(B,C,D),A) = k3_normsp_1(B,k3_lopban_3(B,C,A),k3_lopban_3(B,D,A)) ) ) ) ) )).

fof(t16_ndiff_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(B))
                & m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,u1_struct_0(B))
                    & m2_relset_1(D,k5_numbers,u1_struct_0(B)) )
                 => k3_lopban_3(B,k4_normsp_1(B,C,D),A) = k4_normsp_1(B,k3_lopban_3(B,C,A),k3_lopban_3(B,D,A)) ) ) ) ) )).

fof(t17_ndiff_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(B))
                & m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
             => ( v1_ndiff_1(C,B)
               => v1_ndiff_1(k3_lopban_3(B,C,A),B) ) ) ) ) )).

fof(t18_ndiff_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(B))
                & m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
             => m1_bhsp_3(k3_lopban_3(B,C,A),B,C) ) ) ) )).

fof(t19_ndiff_1,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)) )
             => ( ( v5_seqm_3(B)
                  & m1_bhsp_3(C,A,B) )
               => v5_seqm_3(C) ) ) ) ) )).

fof(t20_ndiff_1,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)) )
             => ( ( v5_seqm_3(B)
                  & m1_bhsp_3(C,A,B) )
               => B = C ) ) ) ) )).

fof(d4_ndiff_1,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_ndiff_1(B,A)
          <=> ( v1_ndiff_1(B,A)
              & v4_normsp_1(B,A)
              & k8_normsp_1(A,B) = k1_rlvect_1(A) ) ) ) ) )).

fof(t21_ndiff_1,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)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k8_normsp_1(A,B) = k2_normsp_1(A,B,C) ) ) ) ) ) )).

fof(t22_ndiff_1,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,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k2_normsp_1(A,B,E) = k3_rlvect_1(A,C,k6_real_1(np__1,k3_real_1(E,D))) )
                   => ( r1_xreal_0(D,np__0)
                      | v4_normsp_1(B,A) ) ) ) ) ) ) )).

fof(t23_ndiff_1,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,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k2_normsp_1(A,B,E) = k3_rlvect_1(A,C,k6_real_1(np__1,k3_real_1(E,D))) )
                   => ( r1_xreal_0(D,np__0)
                      | k8_normsp_1(A,B) = k1_rlvect_1(A) ) ) ) ) ) ) )).

fof(t24_ndiff_1,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)
            & v1_fdiff_1(B)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( C != k1_rlvect_1(A)
               => v2_ndiff_1(k2_ndiff_1(A,C,B),A) ) ) ) ) )).

fof(t25_ndiff_1,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,k1_zfmisc_1(u1_struct_0(A)))
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                <=> r2_hidden(C,u1_struct_0(A)) ) )
          <=> B = u1_struct_0(A) ) ) ) )).

fof(d5_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v3_ndiff_1(C,A,B)
              <=> ( v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,k5_numbers,u1_struct_0(A))
                        & v2_ndiff_1(D,A)
                        & m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
                     => ( v4_normsp_1(k1_ndiff_1(B,k3_nfcont_1(A,B,C,D),k18_seq_1(k7_normsp_1(A,D))),B)
                        & k8_normsp_1(B,k1_ndiff_1(B,k3_nfcont_1(A,B,C,D),k18_seq_1(k7_normsp_1(A,D)))) = k1_rlvect_1(B) ) ) ) ) ) ) ) )).

fof(t26_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
               => ( v3_ndiff_1(C,A,B)
                <=> ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,np__0)
                                  & ! [F] :
                                      ( m1_subset_1(F,u1_struct_0(A))
                                     => ~ ( F != k1_rlvect_1(A)
                                          & ~ r1_xreal_0(E,k1_normsp_1(A,F))
                                          & r1_xreal_0(D,k4_real_1(k2_real_1(k1_normsp_1(A,F)),k1_normsp_1(B,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,F)))) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t27_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v3_ndiff_1(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,u1_struct_0(A))
                    & v2_ndiff_1(D,A)
                    & m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
                 => ( v4_normsp_1(k3_nfcont_1(A,B,C,D),B)
                    & k8_normsp_1(B,k3_nfcont_1(A,B,C,D)) = k1_rlvect_1(B) ) ) ) ) ) )).

fof(t28_ndiff_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u1_struct_0(B))
                & m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
             => r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(B),k3_lopban_3(B,C,A)),k5_relset_1(k5_numbers,u1_struct_0(B),C)) ) ) ) )).

fof(t29_ndiff_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [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)
            & ~ v3_realset2(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)
                & ~ v3_realset2(C)
                & l1_normsp_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k5_numbers,u1_struct_0(B))
                        & m2_relset_1(E,k5_numbers,u1_struct_0(B)) )
                     => ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(B),E),k4_relset_1(u1_struct_0(B),u1_struct_0(C),D))
                       => k3_lopban_3(C,k3_nfcont_1(B,C,D,E),A) = k3_nfcont_1(B,C,D,k3_lopban_3(B,E,A)) ) ) ) ) ) ) )).

fof(t30_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k5_numbers,u1_struct_0(A))
                        & m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
                     => ( ( v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
                          & v1_partfun1(D,u1_struct_0(A),u1_struct_0(B)) )
                       => ( k3_nfcont_1(A,B,k1_vfunct_1(u1_struct_0(A),B,C,D),E) = k3_normsp_1(B,k3_nfcont_1(A,B,C,E),k3_nfcont_1(A,B,D,E))
                          & k3_nfcont_1(A,B,k2_vfunct_1(u1_struct_0(A),B,C,D),E) = k4_normsp_1(B,k3_nfcont_1(A,B,C,E),k3_nfcont_1(A,B,D,E)) ) ) ) ) ) ) ) )).

fof(t31_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [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)) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ( v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
                       => k3_nfcont_1(A,B,k4_vfunct_1(u1_struct_0(A),B,C,E),D) = k6_normsp_1(B,k3_nfcont_1(A,B,C,D),E) ) ) ) ) ) ) )).

fof(t32_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( r1_nfcont_1(B,A,C,D)
                  <=> ( r2_hidden(D,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,k5_numbers,u1_struct_0(B))
                            & m2_relset_1(E,k5_numbers,u1_struct_0(B)) )
                         => ( ( r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(B),E),k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
                              & v4_normsp_1(E,B)
                              & k8_normsp_1(B,E) = D
                              & ! [F] :
                                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                                 => k2_normsp_1(B,E,F) != D ) )
                           => ( v4_normsp_1(k3_nfcont_1(B,A,C,E),A)
                              & k4_finseq_4(u1_struct_0(B),u1_struct_0(A),C,D) = k8_normsp_1(A,k3_nfcont_1(B,A,C,E)) ) ) ) ) ) ) ) ) ) )).

fof(t33_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v3_ndiff_1(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v3_ndiff_1(D,B,A)
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ( v1_funct_1(k1_vfunct_1(u1_struct_0(B),A,C,D))
                    & v3_ndiff_1(k1_vfunct_1(u1_struct_0(B),A,C,D),B,A)
                    & m2_relset_1(k1_vfunct_1(u1_struct_0(B),A,C,D),u1_struct_0(B),u1_struct_0(A))
                    & v1_funct_1(k2_vfunct_1(u1_struct_0(B),A,C,D))
                    & v3_ndiff_1(k2_vfunct_1(u1_struct_0(B),A,C,D),B,A)
                    & m2_relset_1(k2_vfunct_1(u1_struct_0(B),A,C,D),u1_struct_0(B),u1_struct_0(A)) ) ) ) ) ) )).

fof(t34_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v3_ndiff_1(D,B,A)
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ( v1_funct_1(k4_vfunct_1(u1_struct_0(B),A,D,C))
                    & v3_ndiff_1(k4_vfunct_1(u1_struct_0(B),A,D,C),B,A)
                    & m2_relset_1(k4_vfunct_1(u1_struct_0(B),A,D,C),u1_struct_0(B),u1_struct_0(A)) ) ) ) ) ) )).

fof(d6_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_ndiff_1(A,B,C,D)
                  <=> ? [E] :
                        ( m1_nfcont_1(E,A,D)
                        & r1_tarski(E,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
                        & ? [F] :
                            ( m1_subset_1(F,u1_struct_0(k16_lopban_1(A,B)))
                            & ? [G] :
                                ( v1_funct_1(G)
                                & v3_ndiff_1(G,A,B)
                                & m2_relset_1(G,u1_struct_0(A),u1_struct_0(B))
                                & ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ( r2_hidden(H,E)
                                     => k6_rlvect_1(B,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,H),k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,D)) = k4_rlvect_1(B,k17_lopban_1(A,B,F,k6_rlvect_1(A,H,D)),k4_finseq_4(u1_struct_0(A),u1_struct_0(B),G,k6_rlvect_1(A,H,D))) ) ) ) ) ) ) ) ) ) ) )).

fof(d7_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_ndiff_1(A,B,C,D)
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(k16_lopban_1(A,B)))
                       => ( E = k3_ndiff_1(A,B,C,D)
                        <=> ? [F] :
                              ( m1_nfcont_1(F,A,D)
                              & r1_tarski(F,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
                              & ? [G] :
                                  ( v1_funct_1(G)
                                  & v3_ndiff_1(G,A,B)
                                  & m2_relset_1(G,u1_struct_0(A),u1_struct_0(B))
                                  & ! [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                     => ( r2_hidden(H,F)
                                       => k6_rlvect_1(B,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,H),k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,D)) = k4_rlvect_1(B,k17_lopban_1(A,B,E,k6_rlvect_1(A,H,D)),k4_finseq_4(u1_struct_0(A),u1_struct_0(B),G,k6_rlvect_1(A,H,D))) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d8_ndiff_1,axiom,(
    ! [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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(C)
            & l1_normsp_1(C) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
             => ( r2_ndiff_1(A,B,C,D)
              <=> ( r1_tarski(A,k4_relset_1(u1_struct_0(B),u1_struct_0(C),D))
                  & ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( r2_hidden(E,A)
                       => r1_ndiff_1(B,C,k2_partfun1(u1_struct_0(B),u1_struct_0(C),D,A),E) ) ) ) ) ) ) ) )).

fof(t35_ndiff_1,axiom,(
    ! [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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(C)
            & l1_normsp_1(C) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
             => ( r2_ndiff_1(A,B,C,D)
               => m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) )).

fof(t36_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( v3_nfcont_1(D,A)
                   => ( r2_ndiff_1(D,A,B,C)
                    <=> ( r1_tarski(D,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ( r2_hidden(E,D)
                             => r1_ndiff_1(A,B,C,E) ) ) ) ) ) ) ) ) ) )).

fof(t37_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_ndiff_1(D,A,B,C)
                   => v3_nfcont_1(D,A) ) ) ) ) ) )).

fof(d9_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( r2_ndiff_1(D,A,B,C)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B))) )
                     => ( E = k4_ndiff_1(A,B,C,D)
                      <=> ( k4_relset_1(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),E) = D
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ( r2_hidden(F,D)
                               => k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),E,F) = k3_ndiff_1(A,B,C,F) ) ) ) ) ) ) ) ) ) )).

fof(t38_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v3_nfcont_1(D,A)
                      & r1_tarski(D,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C)) )
                   => ( ! [E] :
                          ( m1_subset_1(E,u1_struct_0(B))
                         => k5_relset_1(u1_struct_0(A),u1_struct_0(B),C) != k1_struct_0(B,E) )
                      | ( r2_ndiff_1(D,A,B,C)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ( r2_hidden(E,D)
                             => k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),k4_ndiff_1(A,B,C,D),E) = k1_rlvect_1(k16_lopban_1(A,B)) ) ) ) ) ) ) ) ) ) )).

fof(t39_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_nfcont_1(E,A,D)
                     => ( ( r1_ndiff_1(A,B,C,D)
                          & r1_tarski(E,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C)) )
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,k5_numbers,u1_struct_0(A))
                              & v2_ndiff_1(F,A)
                              & m2_relset_1(F,k5_numbers,u1_struct_0(A)) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,k5_numbers,u1_struct_0(A))
                                  & v5_seqm_3(G)
                                  & m2_relset_1(G,k5_numbers,u1_struct_0(A)) )
                               => ( ( k5_relset_1(k5_numbers,u1_struct_0(A),G) = k1_struct_0(A,D)
                                    & r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),k3_normsp_1(A,F,G)),E) )
                                 => ( v4_normsp_1(k4_normsp_1(B,k3_nfcont_1(A,B,C,k3_normsp_1(A,F,G)),k3_nfcont_1(A,B,C,G)),B)
                                    & k8_normsp_1(B,k4_normsp_1(B,k3_nfcont_1(A,B,C,k3_normsp_1(A,F,G)),k3_nfcont_1(A,B,C,G))) = k1_rlvect_1(B) ) ) ) ) ) ) ) ) ) ) )).

fof(t40_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( ( r1_ndiff_1(B,A,C,E)
                          & r1_ndiff_1(B,A,D,E) )
                       => ( r1_ndiff_1(B,A,k1_vfunct_1(u1_struct_0(B),A,C,D),E)
                          & k3_ndiff_1(B,A,k1_vfunct_1(u1_struct_0(B),A,C,D),E) = k4_rlvect_1(k16_lopban_1(B,A),k3_ndiff_1(B,A,C,E),k3_ndiff_1(B,A,D,E)) ) ) ) ) ) ) ) )).

fof(t41_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( ( r1_ndiff_1(B,A,C,E)
                          & r1_ndiff_1(B,A,D,E) )
                       => ( r1_ndiff_1(B,A,k2_vfunct_1(u1_struct_0(B),A,C,D),E)
                          & k3_ndiff_1(B,A,k2_vfunct_1(u1_struct_0(B),A,C,D),E) = k6_rlvect_1(k16_lopban_1(B,A),k3_ndiff_1(B,A,C,E),k3_ndiff_1(B,A,D,E)) ) ) ) ) ) ) ) )).

fof(t42_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( r1_ndiff_1(B,A,D,E)
                       => ( r1_ndiff_1(B,A,k4_vfunct_1(u1_struct_0(B),A,D,C),E)
                          & k3_ndiff_1(B,A,k4_vfunct_1(u1_struct_0(B),A,D,C),E) = k3_rlvect_1(k16_lopban_1(B,A),k3_ndiff_1(B,A,D,E),C) ) ) ) ) ) ) ) )).

fof(t43_ndiff_1,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)
        & ~ v3_realset2(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v3_nfcont_1(C,A)
                  & r1_tarski(C,k4_relset_1(u1_struct_0(A),u1_struct_0(A),B))
                  & k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C) = k1_partfun2(u1_struct_0(A),C) )
               => ( r2_ndiff_1(C,A,A,B)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_hidden(D,C)
                       => k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,A)),k4_ndiff_1(A,A,B,C),D) = k6_partfun1(u1_struct_0(A)) ) ) ) ) ) ) ) )).

fof(t44_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( v3_nfcont_1(C,A)
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                       => ( ( r1_tarski(C,k4_relset_1(u1_struct_0(A),u1_struct_0(B),k1_vfunct_1(u1_struct_0(A),B,D,E)))
                            & r2_ndiff_1(C,A,B,D)
                            & r2_ndiff_1(C,A,B,E) )
                         => ( r2_ndiff_1(C,A,B,k1_vfunct_1(u1_struct_0(A),B,D,E))
                            & ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ( r2_hidden(F,C)
                                 => k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),k4_ndiff_1(A,B,k1_vfunct_1(u1_struct_0(A),B,D,E),C),F) = k4_rlvect_1(k16_lopban_1(A,B),k3_ndiff_1(A,B,D,F),k3_ndiff_1(A,B,E,F)) ) ) ) ) ) ) ) ) ) ) )).

fof(t45_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( v3_nfcont_1(C,A)
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                       => ( ( r1_tarski(C,k4_relset_1(u1_struct_0(A),u1_struct_0(B),k2_vfunct_1(u1_struct_0(A),B,D,E)))
                            & r2_ndiff_1(C,A,B,D)
                            & r2_ndiff_1(C,A,B,E) )
                         => ( r2_ndiff_1(C,A,B,k2_vfunct_1(u1_struct_0(A),B,D,E))
                            & ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ( r2_hidden(F,C)
                                 => k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),k4_ndiff_1(A,B,k2_vfunct_1(u1_struct_0(A),B,D,E),C),F) = k6_rlvect_1(k16_lopban_1(A,B),k3_ndiff_1(A,B,D,F),k3_ndiff_1(A,B,E,F)) ) ) ) ) ) ) ) ) ) ) )).

fof(t46_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( v3_nfcont_1(C,A)
               => ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                       => ( ( r1_tarski(C,k4_relset_1(u1_struct_0(A),u1_struct_0(B),k4_vfunct_1(u1_struct_0(A),B,E,D)))
                            & r2_ndiff_1(C,A,B,E) )
                         => ( r2_ndiff_1(C,A,B,k4_vfunct_1(u1_struct_0(A),B,E,D))
                            & ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ( r2_hidden(F,C)
                                 => k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),k4_ndiff_1(A,B,k4_vfunct_1(u1_struct_0(A),B,E,D),C),F) = k3_rlvect_1(k16_lopban_1(A,B),k3_ndiff_1(A,B,E,F),D) ) ) ) ) ) ) ) ) ) ) )).

fof(t47_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v3_nfcont_1(D,A)
                      & r1_tarski(D,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
                      & r1_partfun2(u1_struct_0(A),u1_struct_0(B),C,D) )
                   => ( r2_ndiff_1(D,A,B,C)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( r2_hidden(E,D)
                           => k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B)),k4_ndiff_1(A,B,C,D),E) = k1_rlvect_1(k16_lopban_1(A,B)) ) ) ) ) ) ) ) ) )).

fof(t48_ndiff_1,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)
        & ~ v3_realset2(A)
        & l1_normsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( v3_nfcont_1(E,A)
                          & r1_tarski(E,k4_relset_1(u1_struct_0(A),u1_struct_0(A),B))
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ( r2_hidden(F,E)
                               => k4_finseq_4(u1_struct_0(A),u1_struct_0(A),B,F) = k4_rlvect_1(A,k3_rlvect_1(A,F,C),D) ) ) )
                       => ( r2_ndiff_1(E,A,A,B)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ( r2_hidden(F,E)
                               => k4_finseq_4(u1_struct_0(A),u1_struct_0(k16_lopban_1(A,A)),k4_ndiff_1(A,A,B,E),F) = k5_lopban_2(A,k7_lopban_2(A),C) ) ) ) ) ) ) ) ) ) )).

fof(t49_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( r1_ndiff_1(B,A,C,D)
                   => r1_nfcont_1(B,A,C,D) ) ) ) ) ) )).

fof(t50_ndiff_1,axiom,(
    ! [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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(C)
            & l1_normsp_1(C) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
             => ( r2_ndiff_1(A,B,C,D)
               => r3_nfcont_1(B,C,D,A) ) ) ) ) )).

fof(t51_ndiff_1,axiom,(
    ! [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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(C)
            & l1_normsp_1(C) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
             => ! [E] :
                  ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C)))
                 => ( ( v3_nfcont_1(E,C)
                      & r2_ndiff_1(A,C,B,D)
                      & r1_tarski(E,A) )
                   => r2_ndiff_1(E,C,B,D) ) ) ) ) ) )).

fof(t52_ndiff_1,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)
        & ~ v3_realset2(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)
            & ~ v3_realset2(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ~ ( r1_ndiff_1(B,A,C,D)
                      & ! [E] :
                          ( m1_nfcont_1(E,B,D)
                         => ~ ( r1_tarski(E,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
                              & ? [F] :
                                  ( v1_funct_1(F)
                                  & v3_ndiff_1(F,B,A)
                                  & m2_relset_1(F,u1_struct_0(B),u1_struct_0(A))
                                  & k4_finseq_4(u1_struct_0(B),u1_struct_0(A),F,k1_rlvect_1(B)) = k1_rlvect_1(A)
                                  & r1_nfcont_1(B,A,F,k1_rlvect_1(B))
                                  & ! [G] :
                                      ( m1_subset_1(G,u1_struct_0(B))
                                     => ( r2_hidden(G,E)
                                       => k6_rlvect_1(A,k4_finseq_4(u1_struct_0(B),u1_struct_0(A),C,G),k4_finseq_4(u1_struct_0(B),u1_struct_0(A),C,D)) = k4_rlvect_1(A,k17_lopban_1(B,A,k3_ndiff_1(B,A,C,D),k6_rlvect_1(B,G,D)),k4_finseq_4(u1_struct_0(B),u1_struct_0(A),F,k6_rlvect_1(B,G,D))) ) ) ) ) ) ) ) ) ) ) )).

fof(dt_k1_ndiff_1,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)
        & l2_rlvect_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(C)
        & v1_funct_2(C,k5_numbers,k1_numbers)
        & m1_relset_1(C,k5_numbers,k1_numbers) )
     => ( v1_funct_1(k1_ndiff_1(A,B,C))
        & v1_funct_2(k1_ndiff_1(A,B,C),k5_numbers,u1_struct_0(A))
        & m2_relset_1(k1_ndiff_1(A,B,C),k5_numbers,u1_struct_0(A)) ) ) )).

fof(dt_k2_ndiff_1,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)
        & l2_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,k1_numbers)
        & m1_relset_1(C,k5_numbers,k1_numbers) )
     => ( v1_funct_1(k2_ndiff_1(A,B,C))
        & v1_funct_2(k2_ndiff_1(A,B,C),k5_numbers,u1_struct_0(A))
        & m2_relset_1(k2_ndiff_1(A,B,C),k5_numbers,u1_struct_0(A)) ) ) )).

fof(dt_k3_ndiff_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ 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)
        & ~ v3_realset2(A)
        & l1_normsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & ~ v3_realset2(B)
        & l1_normsp_1(B)
        & v1_funct_1(C)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
        & m1_subset_1(D,u1_struct_0(A)) )
     => m1_subset_1(k3_ndiff_1(A,B,C,D),u1_struct_0(k16_lopban_1(A,B))) ) )).

fof(dt_k4_ndiff_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ 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)
        & ~ v3_realset2(A)
        & l1_normsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & ~ v3_realset2(B)
        & l1_normsp_1(B)
        & v1_funct_1(C)
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ( v1_funct_1(k4_ndiff_1(A,B,C,D))
        & m2_relset_1(k4_ndiff_1(A,B,C,D),u1_struct_0(A),u1_struct_0(k16_lopban_1(A,B))) ) ) )).

fof(t3_ndiff_1,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,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_nfcont_1(B,A)
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( r2_hidden(C,B)
                    & ! [D] :
                        ( m1_subset_1(D,k1_numbers)
                       => ~ ( ~ r1_xreal_0(D,np__0)
                            & r1_tarski(a_3_0_ndiff_1(A,C,D),B) ) ) ) ) ) ) ) )).

fof(fraenkel_a_3_0_ndiff_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_subset_1(D,k1_numbers) )
     => ( r2_hidden(A,a_3_0_ndiff_1(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = E
            & ~ r1_xreal_0(D,k1_normsp_1(B,k6_rlvect_1(B,E,C))) ) ) ) )).
%------------------------------------------------------------------------------