SET007 Axioms: SET007+357.ax


%------------------------------------------------------------------------------
% File     : SET007+357 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Algebra of Vector Functions
% 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    : vfunct_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   77 (   7 unit)
%            Number of atoms       : 1073 (  64 equality)
%            Maximal formula depth :   18 (  12 average)
%            Number of connectives : 1137 ( 141 ~  ;   0  |; 678  &)
%                                         (  11 <=>; 307 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   1 propositional; 0-4 arity)
%            Number of functors    :   35 (   3 constant; 0-4 arity)
%            Number of variables   :  324 (   0 singleton; 323 !;   1 ?)
%            Maximal term depth    :    6 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(d1_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => ( E = k1_vfunct_1(A,B,C,D)
                      <=> ( k4_relset_1(A,u1_struct_0(B),E) = k5_subset_1(A,k4_relset_1(A,u1_struct_0(B),C),k4_relset_1(A,u1_struct_0(B),D))
                          & ! [F] :
                              ( m1_subset_1(F,A)
                             => ( r2_hidden(F,k4_relset_1(A,u1_struct_0(B),E))
                               => k4_finseq_4(A,u1_struct_0(B),E,F) = k4_rlvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,F),k4_finseq_4(A,u1_struct_0(B),D,F)) ) ) ) ) ) ) ) ) ) )).

fof(d2_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => ( E = k2_vfunct_1(A,B,C,D)
                      <=> ( k4_relset_1(A,u1_struct_0(B),E) = k5_subset_1(A,k4_relset_1(A,u1_struct_0(B),C),k4_relset_1(A,u1_struct_0(B),D))
                          & ! [F] :
                              ( m1_subset_1(F,A)
                             => ( r2_hidden(F,k4_relset_1(A,u1_struct_0(B),E))
                               => k4_finseq_4(A,u1_struct_0(B),E,F) = k6_rlvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,F),k4_finseq_4(A,u1_struct_0(B),D,F)) ) ) ) ) ) ) ) ) ) )).

fof(d3_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => ( E = k3_vfunct_1(A,B,C,D)
                      <=> ( k4_relset_1(A,u1_struct_0(B),E) = k5_subset_1(A,k4_relset_1(A,k1_numbers,C),k4_relset_1(A,u1_struct_0(B),D))
                          & ! [F] :
                              ( m1_subset_1(F,A)
                             => ( r2_hidden(F,k4_relset_1(A,u1_struct_0(B),E))
                               => k4_finseq_4(A,u1_struct_0(B),E,F) = k3_rlvect_1(B,k4_finseq_4(A,u1_struct_0(B),D,F),k2_seq_1(A,k1_numbers,C,F)) ) ) ) ) ) ) ) ) ) )).

fof(d4_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => ( E = k4_vfunct_1(A,B,C,D)
                      <=> ( k4_relset_1(A,u1_struct_0(B),E) = k4_relset_1(A,u1_struct_0(B),C)
                          & ! [F] :
                              ( m1_subset_1(F,A)
                             => ( r2_hidden(F,k4_relset_1(A,u1_struct_0(B),E))
                               => k4_finseq_4(A,u1_struct_0(B),E,F) = k3_rlvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,F),D) ) ) ) ) ) ) ) ) ) )).

fof(d5_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k1_numbers) )
                 => ( D = k5_vfunct_1(A,B,C)
                  <=> ( k4_relset_1(A,k1_numbers,D) = k4_relset_1(A,u1_struct_0(B),C)
                      & ! [E] :
                          ( m1_subset_1(E,A)
                         => ( r2_hidden(E,k4_relset_1(A,k1_numbers,D))
                           => k2_seq_1(A,k1_numbers,D,E) = k1_normsp_1(B,k4_finseq_4(A,u1_struct_0(B),C,E)) ) ) ) ) ) ) ) ) )).

fof(d6_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ( D = k6_vfunct_1(A,B,C)
                  <=> ( k4_relset_1(A,u1_struct_0(B),D) = k4_relset_1(A,u1_struct_0(B),C)
                      & ! [E] :
                          ( m1_subset_1(E,A)
                         => ( r2_hidden(E,k4_relset_1(A,u1_struct_0(B),D))
                           => k4_finseq_4(A,u1_struct_0(B),D,E) = k5_rlvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,E)) ) ) ) ) ) ) ) ) )).

fof(t1_vfunct_1,axiom,(
    $true )).

fof(t2_vfunct_1,axiom,(
    $true )).

fof(t3_vfunct_1,axiom,(
    $true )).

fof(t4_vfunct_1,axiom,(
    $true )).

fof(t5_vfunct_1,axiom,(
    $true )).

fof(t6_vfunct_1,axiom,(
    $true )).

fof(t7_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k1_numbers) )
                 => k6_subset_1(A,k4_relset_1(A,u1_struct_0(B),k3_vfunct_1(A,B,D,C)),k11_relset_1(A,u1_struct_0(B),k3_vfunct_1(A,B,D,C),k1_struct_0(B,k1_rlvect_1(B)))) = k5_subset_1(A,k6_subset_1(A,k4_relset_1(A,k1_numbers,D),k11_relset_1(A,k1_numbers,D,k1_tarski(np__0))),k6_subset_1(A,k4_relset_1(A,u1_struct_0(B),C),k11_relset_1(A,u1_struct_0(B),C,k1_struct_0(B,k1_rlvect_1(B))))) ) ) ) ) )).

fof(t8_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ( k11_relset_1(A,k1_numbers,k5_vfunct_1(A,B,C),k1_tarski(np__0)) = k11_relset_1(A,u1_struct_0(B),C,k1_struct_0(B,k1_rlvect_1(B)))
                & k11_relset_1(A,u1_struct_0(B),k6_vfunct_1(A,B,C),k1_struct_0(B,k1_rlvect_1(B))) = k11_relset_1(A,u1_struct_0(B),C,k1_struct_0(B,k1_rlvect_1(B))) ) ) ) ) )).

fof(t9_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( D != np__0
                   => k11_relset_1(A,u1_struct_0(B),k4_vfunct_1(A,B,C,D),k1_struct_0(B,k1_rlvect_1(B))) = k11_relset_1(A,u1_struct_0(B),C,k1_struct_0(B,k1_rlvect_1(B))) ) ) ) ) ) )).

fof(t10_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => k1_vfunct_1(A,B,C,D) = k1_vfunct_1(A,B,D,C) ) ) ) ) )).

fof(t11_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => k1_vfunct_1(A,B,k1_vfunct_1(A,B,C,D),E) = k1_vfunct_1(A,B,C,k1_vfunct_1(A,B,D,E)) ) ) ) ) ) )).

fof(t12_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k1_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => k3_vfunct_1(A,B,k8_seq_1(A,k1_numbers,C,D),E) = k3_vfunct_1(A,B,C,k3_vfunct_1(A,B,D,E)) ) ) ) ) ) )).

fof(t13_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k1_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k1_numbers) )
                     => k3_vfunct_1(A,B,k6_seq_1(A,k1_numbers,D,E),C) = k1_vfunct_1(A,B,k3_vfunct_1(A,B,D,C),k3_vfunct_1(A,B,E,C)) ) ) ) ) ) )).

fof(t14_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k1_numbers) )
                     => k3_vfunct_1(A,B,E,k1_vfunct_1(A,B,C,D)) = k1_vfunct_1(A,B,k3_vfunct_1(A,B,E,C),k3_vfunct_1(A,B,E,D)) ) ) ) ) ) )).

fof(t15_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k1_numbers) )
                     => k4_vfunct_1(A,B,k3_vfunct_1(A,B,E,C),D) = k3_vfunct_1(A,B,k13_seq_1(A,k1_numbers,E,D),C) ) ) ) ) ) )).

fof(t16_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k1_numbers) )
                     => k4_vfunct_1(A,B,k3_vfunct_1(A,B,E,C),D) = k3_vfunct_1(A,B,E,k4_vfunct_1(A,B,C,D)) ) ) ) ) ) )).

fof(t17_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k1_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k1_numbers) )
                     => k3_vfunct_1(A,B,k7_seq_1(A,k1_numbers,D,E),C) = k2_vfunct_1(A,B,k3_vfunct_1(A,B,D,C),k3_vfunct_1(A,B,E,C)) ) ) ) ) ) )).

fof(t18_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k1_numbers) )
                     => k2_vfunct_1(A,B,k3_vfunct_1(A,B,E,C),k3_vfunct_1(A,B,E,D)) = k3_vfunct_1(A,B,E,k2_vfunct_1(A,B,C,D)) ) ) ) ) ) )).

fof(t19_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => k4_vfunct_1(A,B,k1_vfunct_1(A,B,C,D),E) = k1_vfunct_1(A,B,k4_vfunct_1(A,B,C,E),k4_vfunct_1(A,B,D,E)) ) ) ) ) ) )).

fof(t20_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => k4_vfunct_1(A,B,C,k4_real_1(D,E)) = k4_vfunct_1(A,B,k4_vfunct_1(A,B,C,E),D) ) ) ) ) ) )).

fof(t21_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => k4_vfunct_1(A,B,k2_vfunct_1(A,B,C,D),E) = k2_vfunct_1(A,B,k4_vfunct_1(A,B,C,E),k4_vfunct_1(A,B,D,E)) ) ) ) ) ) )).

fof(t22_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => k2_vfunct_1(A,B,C,D) = k4_vfunct_1(A,B,k2_vfunct_1(A,B,D,C),k1_real_1(np__1)) ) ) ) ) )).

fof(t23_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => k2_vfunct_1(A,B,C,k1_vfunct_1(A,B,D,E)) = k2_vfunct_1(A,B,k2_vfunct_1(A,B,C,D),E) ) ) ) ) ) )).

fof(t24_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k4_vfunct_1(A,B,C,np__1) = C ) ) ) )).

fof(t25_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => k2_vfunct_1(A,B,C,k2_vfunct_1(A,B,D,E)) = k1_vfunct_1(A,B,k2_vfunct_1(A,B,C,D),E) ) ) ) ) ) )).

fof(t26_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => k1_vfunct_1(A,B,C,k2_vfunct_1(A,B,D,E)) = k2_vfunct_1(A,B,k1_vfunct_1(A,B,C,D),E) ) ) ) ) ) )).

fof(t27_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k1_numbers) )
                 => k5_vfunct_1(A,B,k3_vfunct_1(A,B,D,C)) = k8_seq_1(A,k1_numbers,k21_seq_1(A,k1_numbers,D),k5_vfunct_1(A,B,C)) ) ) ) ) )).

fof(t28_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => k5_vfunct_1(A,B,k4_vfunct_1(A,B,C,D)) = k13_seq_1(A,k1_numbers,k5_vfunct_1(A,B,C),k18_complex1(D)) ) ) ) ) )).

fof(t29_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k6_vfunct_1(A,B,C) = k4_vfunct_1(A,B,C,k1_real_1(np__1)) ) ) ) )).

fof(t30_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k6_vfunct_1(A,B,k6_vfunct_1(A,B,C)) = C ) ) ) )).

fof(t31_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => k2_vfunct_1(A,B,C,D) = k1_vfunct_1(A,B,C,k6_vfunct_1(A,B,D)) ) ) ) ) )).

fof(t32_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => k2_vfunct_1(A,B,C,k6_vfunct_1(A,B,D)) = k1_vfunct_1(A,B,C,D) ) ) ) ) )).

fof(t33_vfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(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)
                & m2_relset_1(D,B,u1_struct_0(C)) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & m2_relset_1(E,B,u1_struct_0(C)) )
                 => ( k2_partfun1(B,u1_struct_0(C),k1_vfunct_1(B,C,D,E),A) = k1_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A),k2_partfun1(B,u1_struct_0(C),E,A))
                    & k2_partfun1(B,u1_struct_0(C),k1_vfunct_1(B,C,D,E),A) = k1_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A),E)
                    & k2_partfun1(B,u1_struct_0(C),k1_vfunct_1(B,C,D,E),A) = k1_vfunct_1(B,C,D,k2_partfun1(B,u1_struct_0(C),E,A)) ) ) ) ) ) )).

fof(t34_vfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(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)
                & m2_relset_1(D,B,u1_struct_0(C)) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & m2_relset_1(E,B,k1_numbers) )
                 => ( k2_partfun1(B,u1_struct_0(C),k3_vfunct_1(B,C,E,D),A) = k3_vfunct_1(B,C,k2_partfun1(B,k1_numbers,E,A),k2_partfun1(B,u1_struct_0(C),D,A))
                    & k2_partfun1(B,u1_struct_0(C),k3_vfunct_1(B,C,E,D),A) = k3_vfunct_1(B,C,k2_partfun1(B,k1_numbers,E,A),D)
                    & k2_partfun1(B,u1_struct_0(C),k3_vfunct_1(B,C,E,D),A) = k3_vfunct_1(B,C,E,k2_partfun1(B,u1_struct_0(C),D,A)) ) ) ) ) ) )).

fof(t35_vfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(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)
                & m2_relset_1(D,B,u1_struct_0(C)) )
             => ( k2_partfun1(B,u1_struct_0(C),k6_vfunct_1(B,C,D),A) = k6_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A))
                & k2_partfun1(B,k1_numbers,k5_vfunct_1(B,C,D),A) = k5_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A)) ) ) ) ) )).

fof(t36_vfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(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)
                & m2_relset_1(D,B,u1_struct_0(C)) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & m2_relset_1(E,B,u1_struct_0(C)) )
                 => ( k2_partfun1(B,u1_struct_0(C),k2_vfunct_1(B,C,D,E),A) = k2_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A),k2_partfun1(B,u1_struct_0(C),E,A))
                    & k2_partfun1(B,u1_struct_0(C),k2_vfunct_1(B,C,D,E),A) = k2_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A),E)
                    & k2_partfun1(B,u1_struct_0(C),k2_vfunct_1(B,C,D,E),A) = k2_vfunct_1(B,C,D,k2_partfun1(B,u1_struct_0(C),E,A)) ) ) ) ) ) )).

fof(t37_vfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(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)
                & m2_relset_1(D,B,u1_struct_0(C)) )
             => ! [E] :
                  ( m1_subset_1(E,k1_numbers)
                 => k2_partfun1(B,u1_struct_0(C),k4_vfunct_1(B,C,D,E),A) = k4_vfunct_1(B,C,k2_partfun1(B,u1_struct_0(C),D,A),E) ) ) ) ) )).

fof(t38_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => ( ( ( v1_partfun1(C,A,u1_struct_0(B))
                        & v1_partfun1(D,A,u1_struct_0(B)) )
                     => v1_partfun1(k1_vfunct_1(A,B,C,D),A,u1_struct_0(B)) )
                    & ( v1_partfun1(k1_vfunct_1(A,B,C,D),A,u1_struct_0(B))
                     => ( v1_partfun1(C,A,u1_struct_0(B))
                        & v1_partfun1(D,A,u1_struct_0(B)) ) )
                    & ( ( v1_partfun1(C,A,u1_struct_0(B))
                        & v1_partfun1(D,A,u1_struct_0(B)) )
                     => v1_partfun1(k2_vfunct_1(A,B,C,D),A,u1_struct_0(B)) )
                    & ( v1_partfun1(k2_vfunct_1(A,B,C,D),A,u1_struct_0(B))
                     => ( v1_partfun1(C,A,u1_struct_0(B))
                        & v1_partfun1(D,A,u1_struct_0(B)) ) ) ) ) ) ) ) )).

fof(t39_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k1_numbers) )
                 => ( ( v1_partfun1(D,A,k1_numbers)
                      & v1_partfun1(C,A,u1_struct_0(B)) )
                  <=> v1_partfun1(k3_vfunct_1(A,B,D,C),A,u1_struct_0(B)) ) ) ) ) ) )).

fof(t40_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( v1_partfun1(C,A,u1_struct_0(B))
                  <=> v1_partfun1(k4_vfunct_1(A,B,C,D),A,u1_struct_0(B)) ) ) ) ) ) )).

fof(t41_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ( v1_partfun1(C,A,u1_struct_0(B))
              <=> v1_partfun1(k6_vfunct_1(A,B,C),A,u1_struct_0(B)) ) ) ) ) )).

fof(t42_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ( v1_partfun1(C,A,u1_struct_0(B))
              <=> v1_partfun1(k5_vfunct_1(A,B,C),A,k1_numbers) ) ) ) ) )).

fof(t43_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [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)
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,u1_struct_0(C)) )
                     => ( ( v1_partfun1(D,A,u1_struct_0(C))
                          & v1_partfun1(E,A,u1_struct_0(C)) )
                       => ( k4_finseq_4(A,u1_struct_0(C),k1_vfunct_1(A,C,D,E),B) = k4_rlvect_1(C,k4_finseq_4(A,u1_struct_0(C),D,B),k4_finseq_4(A,u1_struct_0(C),E,B))
                          & k4_finseq_4(A,u1_struct_0(C),k2_vfunct_1(A,C,D,E),B) = k6_rlvect_1(C,k4_finseq_4(A,u1_struct_0(C),D,B),k4_finseq_4(A,u1_struct_0(C),E,B)) ) ) ) ) ) ) ) )).

fof(t44_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [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)
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k1_numbers) )
                     => ( ( v1_partfun1(E,A,k1_numbers)
                          & v1_partfun1(D,A,u1_struct_0(C)) )
                       => k4_finseq_4(A,u1_struct_0(C),k3_vfunct_1(A,C,E,D),B) = k3_rlvect_1(C,k4_finseq_4(A,u1_struct_0(C),D,B),k2_seq_1(A,k1_numbers,E,B)) ) ) ) ) ) ) )).

fof(t45_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [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)
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ( v1_partfun1(D,A,u1_struct_0(C))
                       => k4_finseq_4(A,u1_struct_0(C),k4_vfunct_1(A,C,D,E),B) = k3_rlvect_1(C,k4_finseq_4(A,u1_struct_0(C),D,B),E) ) ) ) ) ) ) )).

fof(t46_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [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)
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ( v1_partfun1(D,A,u1_struct_0(C))
                   => ( k4_finseq_4(A,u1_struct_0(C),k6_vfunct_1(A,C,D),B) = k5_rlvect_1(C,k4_finseq_4(A,u1_struct_0(C),D,B))
                      & k2_seq_1(A,k1_numbers,k5_vfunct_1(A,C,D),B) = k1_normsp_1(C,k4_finseq_4(A,u1_struct_0(C),D,B)) ) ) ) ) ) ) )).

fof(d7_vfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & v2_normsp_1(B)
            & l1_normsp_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( r1_vfunct_1(A,B,C,D)
                <=> ? [E] :
                      ( m1_subset_1(E,k1_numbers)
                      & ! [F] :
                          ( m1_subset_1(F,A)
                         => ( r2_hidden(F,k3_xboole_0(D,k4_relset_1(A,u1_struct_0(B),C)))
                           => r1_xreal_0(k1_normsp_1(B,k4_finseq_4(A,u1_struct_0(B),C,F)),E) ) ) ) ) ) ) ) )).

fof(t47_vfunct_1,axiom,(
    $true )).

fof(t48_vfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & v3_rlvect_1(D)
            & v4_rlvect_1(D)
            & v5_rlvect_1(D)
            & v6_rlvect_1(D)
            & v7_rlvect_1(D)
            & v2_normsp_1(D)
            & l1_normsp_1(D) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,u1_struct_0(D)) )
             => ( ( r1_tarski(A,B)
                  & r1_vfunct_1(C,D,E,B) )
               => r1_vfunct_1(C,D,E,A) ) ) ) ) )).

fof(t49_vfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(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)
                & m2_relset_1(D,B,u1_struct_0(C)) )
             => ( r1_xboole_0(A,k4_relset_1(B,u1_struct_0(C),D))
               => r1_vfunct_1(B,C,D,A) ) ) ) ) )).

fof(t50_vfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(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)
                & m2_relset_1(D,B,u1_struct_0(C)) )
             => r1_vfunct_1(B,C,k4_vfunct_1(B,C,D,np__0),A) ) ) ) )).

fof(t51_vfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(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)
                & m2_relset_1(D,B,u1_struct_0(C)) )
             => ! [E] :
                  ( m1_subset_1(E,k1_numbers)
                 => ( r1_vfunct_1(B,C,D,A)
                   => r1_vfunct_1(B,C,k4_vfunct_1(B,C,D,E),A) ) ) ) ) ) )).

fof(t52_vfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(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)
                & m2_relset_1(D,B,u1_struct_0(C)) )
             => ( r1_vfunct_1(B,C,D,A)
               => ( r3_rfunct_1(k5_vfunct_1(B,C,D),A)
                  & r1_vfunct_1(B,C,k6_vfunct_1(B,C,D),A) ) ) ) ) ) )).

fof(t53_vfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & v3_rlvect_1(D)
            & v4_rlvect_1(D)
            & v5_rlvect_1(D)
            & v6_rlvect_1(D)
            & v7_rlvect_1(D)
            & v2_normsp_1(D)
            & l1_normsp_1(D) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,u1_struct_0(D)) )
             => ! [F] :
                  ( ( v1_funct_1(F)
                    & m2_relset_1(F,C,u1_struct_0(D)) )
                 => ( ( r1_vfunct_1(C,D,E,A)
                      & r1_vfunct_1(C,D,F,B) )
                   => r1_vfunct_1(C,D,k1_vfunct_1(C,D,E,F),k3_xboole_0(A,B)) ) ) ) ) ) )).

fof(t54_vfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & v3_rlvect_1(D)
            & v4_rlvect_1(D)
            & v5_rlvect_1(D)
            & v6_rlvect_1(D)
            & v7_rlvect_1(D)
            & v2_normsp_1(D)
            & l1_normsp_1(D) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,u1_struct_0(D)) )
             => ! [F] :
                  ( ( v1_funct_1(F)
                    & m2_relset_1(F,C,k1_numbers) )
                 => ( ( r3_rfunct_1(F,A)
                      & r1_vfunct_1(C,D,E,B) )
                   => r1_vfunct_1(C,D,k3_vfunct_1(C,D,F,E),k3_xboole_0(A,B)) ) ) ) ) ) )).

fof(t55_vfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & v3_rlvect_1(D)
            & v4_rlvect_1(D)
            & v5_rlvect_1(D)
            & v6_rlvect_1(D)
            & v7_rlvect_1(D)
            & v2_normsp_1(D)
            & l1_normsp_1(D) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,u1_struct_0(D)) )
             => ! [F] :
                  ( ( v1_funct_1(F)
                    & m2_relset_1(F,C,u1_struct_0(D)) )
                 => ( ( r1_vfunct_1(C,D,E,A)
                      & r1_vfunct_1(C,D,F,B) )
                   => r1_vfunct_1(C,D,k2_vfunct_1(C,D,E,F),k3_xboole_0(A,B)) ) ) ) ) ) )).

fof(t56_vfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & v3_rlvect_1(D)
            & v4_rlvect_1(D)
            & v5_rlvect_1(D)
            & v6_rlvect_1(D)
            & v7_rlvect_1(D)
            & v2_normsp_1(D)
            & l1_normsp_1(D) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,u1_struct_0(D)) )
             => ( ( r1_vfunct_1(C,D,E,A)
                  & r1_vfunct_1(C,D,E,B) )
               => r1_vfunct_1(C,D,E,k2_xboole_0(A,B)) ) ) ) ) )).

fof(t57_vfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & v3_rlvect_1(D)
            & v4_rlvect_1(D)
            & v5_rlvect_1(D)
            & v6_rlvect_1(D)
            & v7_rlvect_1(D)
            & v2_normsp_1(D)
            & l1_normsp_1(D) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,u1_struct_0(D)) )
             => ! [F] :
                  ( ( v1_funct_1(F)
                    & m2_relset_1(F,C,u1_struct_0(D)) )
                 => ( ( r1_partfun2(C,u1_struct_0(D),E,A)
                      & r1_partfun2(C,u1_struct_0(D),F,B) )
                   => ( r1_partfun2(C,u1_struct_0(D),k1_vfunct_1(C,D,E,F),k3_xboole_0(A,B))
                      & r1_partfun2(C,u1_struct_0(D),k2_vfunct_1(C,D,E,F),k3_xboole_0(A,B)) ) ) ) ) ) ) )).

fof(t58_vfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & v3_rlvect_1(D)
            & v4_rlvect_1(D)
            & v5_rlvect_1(D)
            & v6_rlvect_1(D)
            & v7_rlvect_1(D)
            & v2_normsp_1(D)
            & l1_normsp_1(D) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,u1_struct_0(D)) )
             => ! [F] :
                  ( ( v1_funct_1(F)
                    & m2_relset_1(F,C,k1_numbers) )
                 => ( ( r1_partfun2(C,k1_numbers,F,A)
                      & r1_partfun2(C,u1_struct_0(D),E,B) )
                   => r1_partfun2(C,u1_struct_0(D),k3_vfunct_1(C,D,F,E),k3_xboole_0(A,B)) ) ) ) ) ) )).

fof(t59_vfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(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)
                & m2_relset_1(D,B,u1_struct_0(C)) )
             => ! [E] :
                  ( m1_subset_1(E,k1_numbers)
                 => ( r1_partfun2(B,u1_struct_0(C),D,A)
                   => r1_partfun2(B,u1_struct_0(C),k4_vfunct_1(B,C,D,E),A) ) ) ) ) ) )).

fof(t60_vfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(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)
                & m2_relset_1(D,B,u1_struct_0(C)) )
             => ( r1_partfun2(B,u1_struct_0(C),D,A)
               => ( r1_partfun2(B,k1_numbers,k5_vfunct_1(B,C,D),A)
                  & r1_partfun2(B,u1_struct_0(C),k6_vfunct_1(B,C,D),A) ) ) ) ) ) )).

fof(t61_vfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(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)
                & m2_relset_1(D,B,u1_struct_0(C)) )
             => ( r1_partfun2(B,u1_struct_0(C),D,A)
               => r1_vfunct_1(B,C,D,A) ) ) ) ) )).

fof(t62_vfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(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)
                & m2_relset_1(D,B,u1_struct_0(C)) )
             => ( r1_partfun2(B,u1_struct_0(C),D,A)
               => ( ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => r1_vfunct_1(B,C,k4_vfunct_1(B,C,D,E),A) )
                  & r1_vfunct_1(B,C,k6_vfunct_1(B,C,D),A)
                  & r3_rfunct_1(k5_vfunct_1(B,C,D),A) ) ) ) ) ) )).

fof(t63_vfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & v3_rlvect_1(D)
            & v4_rlvect_1(D)
            & v5_rlvect_1(D)
            & v6_rlvect_1(D)
            & v7_rlvect_1(D)
            & v2_normsp_1(D)
            & l1_normsp_1(D) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,u1_struct_0(D)) )
             => ! [F] :
                  ( ( v1_funct_1(F)
                    & m2_relset_1(F,C,u1_struct_0(D)) )
                 => ( ( r1_vfunct_1(C,D,E,A)
                      & r1_partfun2(C,u1_struct_0(D),F,B) )
                   => r1_vfunct_1(C,D,k1_vfunct_1(C,D,E,F),k3_xboole_0(A,B)) ) ) ) ) ) )).

fof(t64_vfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & v3_rlvect_1(D)
            & v4_rlvect_1(D)
            & v5_rlvect_1(D)
            & v6_rlvect_1(D)
            & v7_rlvect_1(D)
            & v2_normsp_1(D)
            & l1_normsp_1(D) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,u1_struct_0(D)) )
             => ! [F] :
                  ( ( v1_funct_1(F)
                    & m2_relset_1(F,C,u1_struct_0(D)) )
                 => ( ( r1_vfunct_1(C,D,E,A)
                      & r1_partfun2(C,u1_struct_0(D),F,B) )
                   => ( r1_vfunct_1(C,D,k2_vfunct_1(C,D,E,F),k3_xboole_0(A,B))
                      & r1_vfunct_1(C,D,k2_vfunct_1(C,D,F,E),k3_xboole_0(A,B)) ) ) ) ) ) ) )).

fof(dt_k1_vfunct_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(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)
        & l1_normsp_1(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,u1_struct_0(B))
        & v1_funct_1(D)
        & m1_relset_1(D,A,u1_struct_0(B)) )
     => ( v1_funct_1(k1_vfunct_1(A,B,C,D))
        & m2_relset_1(k1_vfunct_1(A,B,C,D),A,u1_struct_0(B)) ) ) )).

fof(dt_k2_vfunct_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(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)
        & l1_normsp_1(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,u1_struct_0(B))
        & v1_funct_1(D)
        & m1_relset_1(D,A,u1_struct_0(B)) )
     => ( v1_funct_1(k2_vfunct_1(A,B,C,D))
        & m2_relset_1(k2_vfunct_1(A,B,C,D),A,u1_struct_0(B)) ) ) )).

fof(dt_k3_vfunct_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(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)
        & l1_normsp_1(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,k1_numbers)
        & v1_funct_1(D)
        & m1_relset_1(D,A,u1_struct_0(B)) )
     => ( v1_funct_1(k3_vfunct_1(A,B,C,D))
        & m2_relset_1(k3_vfunct_1(A,B,C,D),A,u1_struct_0(B)) ) ) )).

fof(dt_k4_vfunct_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(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)
        & l1_normsp_1(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,u1_struct_0(B))
        & m1_subset_1(D,k1_numbers) )
     => ( v1_funct_1(k4_vfunct_1(A,B,C,D))
        & m2_relset_1(k4_vfunct_1(A,B,C,D),A,u1_struct_0(B)) ) ) )).

fof(dt_k5_vfunct_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => ( v1_funct_1(k5_vfunct_1(A,B,C))
        & m2_relset_1(k5_vfunct_1(A,B,C),A,k1_numbers) ) ) )).

fof(dt_k6_vfunct_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & v2_normsp_1(B)
        & l1_normsp_1(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => ( v1_funct_1(k6_vfunct_1(A,B,C))
        & m2_relset_1(k6_vfunct_1(A,B,C),A,u1_struct_0(B)) ) ) )).
%------------------------------------------------------------------------------