SET007 Axioms: SET007+855.ax


%------------------------------------------------------------------------------
% File     : SET007+855 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Algebra of Complex Vector Valued 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_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   70 (   0 unit)
%            Number of atoms       : 1066 (  64 equality)
%            Maximal formula depth :   18 (  13 average)
%            Number of connectives : 1137 ( 141 ~  ;   0  |; 678  &)
%                                         (  11 <=>; 307 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   0 propositional; 1-4 arity)
%            Number of functors    :   39 (   5 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_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(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_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(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_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_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_2(A,B,C,D)
                      <=> ( k4_relset_1(A,u1_struct_0(B),E) = k5_subset_1(A,k4_relset_1(A,k2_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) = k1_clvect_1(B,k4_finseq_4(A,u1_struct_0(B),D,F),k4_finseq_4(A,k2_numbers,C,F)) ) ) ) ) ) ) ) ) ) )).

fof(d4_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => ( E = k4_vfunct_2(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) = k1_clvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,F),D) ) ) ) ) ) ) ) ) ) )).

fof(d5_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(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) = k5_clvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,E)) ) ) ) ) ) ) ) ) )).

fof(d6_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(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_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => k6_subset_1(A,k4_relset_1(A,u1_struct_0(B),k3_vfunct_2(A,B,C,D)),k11_relset_1(A,u1_struct_0(B),k3_vfunct_2(A,B,C,D),k1_struct_0(B,k1_rlvect_1(B)))) = k5_subset_1(A,k6_subset_1(A,k4_relset_1(A,k2_numbers,C),k11_relset_1(A,k2_numbers,C,k1_tarski(np__0))),k6_subset_1(A,k4_relset_1(A,u1_struct_0(B),D),k11_relset_1(A,u1_struct_0(B),D,k1_struct_0(B,k1_rlvect_1(B))))) ) ) ) ) )).

fof(t2_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ( k11_relset_1(A,k1_numbers,k5_vfunct_2(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_2(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(t3_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => ( D != k5_complex1
                   => k11_relset_1(A,u1_struct_0(B),k4_vfunct_2(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(t4_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(A,B,C,D) = k1_vfunct_2(A,B,D,C) ) ) ) ) )).

fof(t5_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(A,B,k1_vfunct_2(A,B,C,D),E) = k1_vfunct_2(A,B,C,k1_vfunct_2(A,B,D,E)) ) ) ) ) ) )).

fof(t6_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,u1_struct_0(B)) )
                     => k3_vfunct_2(A,B,k3_comseq_1(A,C,D),E) = k3_vfunct_2(A,B,C,k3_vfunct_2(A,B,D,E)) ) ) ) ) ) )).

fof(t7_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,k2_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k2_numbers) )
                     => k3_vfunct_2(A,B,k2_comseq_1(A,D,E),C) = k1_vfunct_2(A,B,k3_vfunct_2(A,B,D,C),k3_vfunct_2(A,B,E,C)) ) ) ) ) ) )).

fof(t8_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,k2_numbers) )
                     => k3_vfunct_2(A,B,E,k1_vfunct_2(A,B,C,D)) = k1_vfunct_2(A,B,k3_vfunct_2(A,B,E,C),k3_vfunct_2(A,B,E,D)) ) ) ) ) ) )).

fof(t9_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k2_numbers) )
                     => k4_vfunct_2(A,B,k3_vfunct_2(A,B,E,C),D) = k3_vfunct_2(A,B,k4_comseq_1(A,E,D),C) ) ) ) ) ) )).

fof(t10_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k2_numbers) )
                     => k4_vfunct_2(A,B,k3_vfunct_2(A,B,E,C),D) = k3_vfunct_2(A,B,E,k4_vfunct_2(A,B,C,D)) ) ) ) ) ) )).

fof(t11_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,k2_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k2_numbers) )
                     => k3_vfunct_2(A,B,k6_comseq_1(A,D,E),C) = k2_vfunct_2(A,B,k3_vfunct_2(A,B,D,C),k3_vfunct_2(A,B,E,C)) ) ) ) ) ) )).

fof(t12_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,k2_numbers) )
                     => k2_vfunct_2(A,B,k3_vfunct_2(A,B,E,C),k3_vfunct_2(A,B,E,D)) = k3_vfunct_2(A,B,E,k2_vfunct_2(A,B,C,D)) ) ) ) ) ) )).

fof(t13_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,k2_numbers)
                     => k4_vfunct_2(A,B,k1_vfunct_2(A,B,C,D),E) = k1_vfunct_2(A,B,k4_vfunct_2(A,B,C,E),k4_vfunct_2(A,B,D,E)) ) ) ) ) ) )).

fof(t14_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k2_numbers)
                     => k4_vfunct_2(A,B,C,k9_complex1(D,E)) = k4_vfunct_2(A,B,k4_vfunct_2(A,B,C,E),D) ) ) ) ) ) )).

fof(t15_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,k2_numbers)
                     => k4_vfunct_2(A,B,k2_vfunct_2(A,B,C,D),E) = k2_vfunct_2(A,B,k4_vfunct_2(A,B,C,E),k4_vfunct_2(A,B,D,E)) ) ) ) ) ) )).

fof(t16_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(A,B,C,D) = k4_vfunct_2(A,B,k2_vfunct_2(A,B,D,C),k10_complex1(k6_complex1)) ) ) ) ) )).

fof(t17_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(A,B,C,k1_vfunct_2(A,B,D,E)) = k2_vfunct_2(A,B,k2_vfunct_2(A,B,C,D),E) ) ) ) ) ) )).

fof(t18_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k4_vfunct_2(A,B,C,k6_complex1) = C ) ) ) )).

fof(t19_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(A,B,C,k2_vfunct_2(A,B,D,E)) = k1_vfunct_2(A,B,k2_vfunct_2(A,B,C,D),E) ) ) ) ) ) )).

fof(t20_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(A,B,C,k2_vfunct_2(A,B,D,E)) = k2_vfunct_2(A,B,k1_vfunct_2(A,B,C,D),E) ) ) ) ) ) )).

fof(t21_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,k2_numbers) )
                 => k5_vfunct_2(A,B,k3_vfunct_2(A,B,D,C)) = k8_seq_1(A,k1_numbers,k9_comseq_1(A,D),k5_vfunct_2(A,B,C)) ) ) ) ) )).

fof(t22_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => k5_vfunct_2(A,B,k4_vfunct_2(A,B,C,D)) = k13_seq_1(A,k1_numbers,k5_vfunct_2(A,B,C),k17_complex1(D)) ) ) ) ) )).

fof(t23_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k6_vfunct_2(A,B,C) = k4_vfunct_2(A,B,C,k10_complex1(k6_complex1)) ) ) ) )).

fof(t24_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => k6_vfunct_2(A,B,k6_vfunct_2(A,B,C)) = C ) ) ) )).

fof(t25_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(A,B,C,D) = k1_vfunct_2(A,B,C,k6_vfunct_2(A,B,D)) ) ) ) ) )).

fof(t26_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(A,B,C,k6_vfunct_2(A,B,D)) = k1_vfunct_2(A,B,C,D) ) ) ) ) )).

fof(t27_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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] :
                      ( k2_partfun1(A,u1_struct_0(B),k1_vfunct_2(A,B,C,D),E) = k1_vfunct_2(A,B,k2_partfun1(A,u1_struct_0(B),C,E),k2_partfun1(A,u1_struct_0(B),D,E))
                      & k2_partfun1(A,u1_struct_0(B),k1_vfunct_2(A,B,C,D),E) = k1_vfunct_2(A,B,k2_partfun1(A,u1_struct_0(B),C,E),D)
                      & k2_partfun1(A,u1_struct_0(B),k1_vfunct_2(A,B,C,D),E) = k1_vfunct_2(A,B,C,k2_partfun1(A,u1_struct_0(B),D,E)) ) ) ) ) ) )).

fof(t28_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D,E] :
                  ( ( v1_funct_1(E)
                    & m2_relset_1(E,A,k2_numbers) )
                 => ( k2_partfun1(A,u1_struct_0(B),k3_vfunct_2(A,B,E,C),D) = k3_vfunct_2(A,B,k2_partfun1(A,k2_numbers,E,D),k2_partfun1(A,u1_struct_0(B),C,D))
                    & k2_partfun1(A,u1_struct_0(B),k3_vfunct_2(A,B,E,C),D) = k3_vfunct_2(A,B,k2_partfun1(A,k2_numbers,E,D),C)
                    & k2_partfun1(A,u1_struct_0(B),k3_vfunct_2(A,B,E,C),D) = k3_vfunct_2(A,B,E,k2_partfun1(A,u1_struct_0(B),C,D)) ) ) ) ) ) )).

fof(t29_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( k2_partfun1(A,u1_struct_0(B),k6_vfunct_2(A,B,C),D) = k6_vfunct_2(A,B,k2_partfun1(A,u1_struct_0(B),C,D))
                  & k2_partfun1(A,k1_numbers,k5_vfunct_2(A,B,C),D) = k5_vfunct_2(A,B,k2_partfun1(A,u1_struct_0(B),C,D)) ) ) ) ) )).

fof(t30_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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] :
                      ( k2_partfun1(A,u1_struct_0(B),k2_vfunct_2(A,B,C,D),E) = k2_vfunct_2(A,B,k2_partfun1(A,u1_struct_0(B),C,E),k2_partfun1(A,u1_struct_0(B),D,E))
                      & k2_partfun1(A,u1_struct_0(B),k2_vfunct_2(A,B,C,D),E) = k2_vfunct_2(A,B,k2_partfun1(A,u1_struct_0(B),C,E),D)
                      & k2_partfun1(A,u1_struct_0(B),k2_vfunct_2(A,B,C,D),E) = k2_vfunct_2(A,B,C,k2_partfun1(A,u1_struct_0(B),D,E)) ) ) ) ) ) )).

fof(t31_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => ! [E] : k2_partfun1(A,u1_struct_0(B),k4_vfunct_2(A,B,C,D),E) = k4_vfunct_2(A,B,k2_partfun1(A,u1_struct_0(B),C,E),D) ) ) ) ) )).

fof(t32_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(A,B,C,D),A,u1_struct_0(B)) )
                    & ( v1_partfun1(k1_vfunct_2(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_2(A,B,C,D),A,u1_struct_0(B)) )
                    & ( v1_partfun1(k2_vfunct_2(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(t33_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,k2_numbers) )
                 => ( ( v1_partfun1(D,A,k2_numbers)
                      & v1_partfun1(C,A,u1_struct_0(B)) )
                  <=> v1_partfun1(k3_vfunct_2(A,B,D,C),A,u1_struct_0(B)) ) ) ) ) ) )).

fof(t34_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => ( v1_partfun1(C,A,u1_struct_0(B))
                  <=> v1_partfun1(k4_vfunct_2(A,B,C,D),A,u1_struct_0(B)) ) ) ) ) ) )).

fof(t35_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(A,B,C),A,u1_struct_0(B)) ) ) ) ) )).

fof(t36_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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_2(A,B,C),A,k1_numbers) ) ) ) ) )).

fof(t37_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,A)
                     => ( ( v1_partfun1(C,A,u1_struct_0(B))
                          & v1_partfun1(D,A,u1_struct_0(B)) )
                       => ( k4_finseq_4(A,u1_struct_0(B),k1_vfunct_2(A,B,C,D),E) = k4_rlvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,E),k4_finseq_4(A,u1_struct_0(B),D,E))
                          & k4_finseq_4(A,u1_struct_0(B),k2_vfunct_2(A,B,C,D),E) = k6_rlvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,E),k4_finseq_4(A,u1_struct_0(B),D,E)) ) ) ) ) ) ) ) )).

fof(t38_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,k2_numbers) )
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ( ( v1_partfun1(D,A,k2_numbers)
                          & v1_partfun1(C,A,u1_struct_0(B)) )
                       => k4_finseq_4(A,u1_struct_0(B),k3_vfunct_2(A,B,D,C),E) = k1_clvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,E),k4_finseq_4(A,k2_numbers,D,E)) ) ) ) ) ) ) )).

fof(t39_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ( v1_partfun1(C,A,u1_struct_0(B))
                       => k4_finseq_4(A,u1_struct_0(B),k4_vfunct_2(A,B,C,D),E) = k1_clvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,E),D) ) ) ) ) ) ) )).

fof(t40_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ( v1_partfun1(C,A,u1_struct_0(B))
                   => ( k4_finseq_4(A,u1_struct_0(B),k6_vfunct_2(A,B,C),D) = k5_rlvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,D))
                      & k2_seq_1(A,k1_numbers,k5_vfunct_2(A,B,C),D) = k5_clvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,D)) ) ) ) ) ) ) )).

fof(d7_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( r1_vfunct_2(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(k5_clvect_1(B,k4_finseq_4(A,u1_struct_0(B),C,F)),E) ) ) ) ) ) ) ) )).

fof(t41_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D,E] :
                  ( ( r1_tarski(D,E)
                    & r1_vfunct_2(A,B,C,E) )
                 => r1_vfunct_2(A,B,C,D) ) ) ) ) )).

fof(t42_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( r1_xboole_0(D,k4_relset_1(A,u1_struct_0(B),C))
                 => r1_vfunct_2(A,B,C,D) ) ) ) ) )).

fof(t43_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] : r1_vfunct_2(A,B,k4_vfunct_2(A,B,C,k5_complex1),D) ) ) ) )).

fof(t44_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => ! [E] :
                      ( r1_vfunct_2(A,B,C,E)
                     => r1_vfunct_2(A,B,k4_vfunct_2(A,B,C,D),E) ) ) ) ) ) )).

fof(t45_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( r1_vfunct_2(A,B,C,D)
                 => ( r3_rfunct_1(k5_vfunct_2(A,B,C),D)
                    & r1_vfunct_2(A,B,k6_vfunct_2(A,B,C),D) ) ) ) ) ) )).

fof(t46_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,F] :
                      ( ( r1_vfunct_2(A,B,C,E)
                        & r1_vfunct_2(A,B,D,F) )
                     => r1_vfunct_2(A,B,k1_vfunct_2(A,B,C,D),k3_xboole_0(E,F)) ) ) ) ) ) )).

fof(t47_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D,E,F] :
                  ( ( v1_funct_1(F)
                    & m2_relset_1(F,A,k2_numbers) )
                 => ( ( r1_cfunct_1(A,F,D)
                      & r1_vfunct_2(A,B,C,E) )
                   => r1_vfunct_2(A,B,k3_vfunct_2(A,B,F,C),k3_xboole_0(D,E)) ) ) ) ) ) )).

fof(t48_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,F] :
                      ( ( r1_vfunct_2(A,B,C,E)
                        & r1_vfunct_2(A,B,D,F) )
                     => r1_vfunct_2(A,B,k2_vfunct_2(A,B,C,D),k3_xboole_0(E,F)) ) ) ) ) ) )).

fof(t49_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D,E] :
                  ( ( r1_vfunct_2(A,B,C,D)
                    & r1_vfunct_2(A,B,C,E) )
                 => r1_vfunct_2(A,B,C,k2_xboole_0(D,E)) ) ) ) ) )).

fof(t50_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,F] :
                      ( ( r1_partfun2(A,u1_struct_0(B),C,E)
                        & r1_partfun2(A,u1_struct_0(B),D,F) )
                     => ( r1_partfun2(A,u1_struct_0(B),k1_vfunct_2(A,B,C,D),k3_xboole_0(E,F))
                        & r1_partfun2(A,u1_struct_0(B),k2_vfunct_2(A,B,C,D),k3_xboole_0(E,F)) ) ) ) ) ) ) )).

fof(t51_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D,E,F] :
                  ( ( v1_funct_1(F)
                    & m2_relset_1(F,A,k2_numbers) )
                 => ( ( r1_partfun2(A,k2_numbers,F,D)
                      & r1_partfun2(A,u1_struct_0(B),C,E) )
                   => r1_partfun2(A,u1_struct_0(B),k3_vfunct_2(A,B,F,C),k3_xboole_0(D,E)) ) ) ) ) ) )).

fof(t52_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => ! [E] :
                      ( r1_partfun2(A,u1_struct_0(B),C,E)
                     => r1_partfun2(A,u1_struct_0(B),k4_vfunct_2(A,B,C,D),E) ) ) ) ) ) )).

fof(t53_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( r1_partfun2(A,u1_struct_0(B),C,D)
                 => ( r1_partfun2(A,k1_numbers,k5_vfunct_2(A,B,C),D)
                    & r1_partfun2(A,u1_struct_0(B),k6_vfunct_2(A,B,C),D) ) ) ) ) ) )).

fof(t54_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( r1_partfun2(A,u1_struct_0(B),C,D)
                 => r1_vfunct_2(A,B,C,D) ) ) ) ) )).

fof(t55_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,u1_struct_0(B)) )
             => ! [D] :
                  ( r1_partfun2(A,u1_struct_0(B),C,D)
                 => ( ! [E] :
                        ( m1_subset_1(E,k2_numbers)
                       => r1_vfunct_2(A,B,k4_vfunct_2(A,B,C,E),D) )
                    & r1_vfunct_2(A,B,k6_vfunct_2(A,B,C),D)
                    & r3_rfunct_1(k5_vfunct_2(A,B,C),D) ) ) ) ) ) )).

fof(t56_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,F] :
                      ( ( r1_vfunct_2(A,B,C,E)
                        & r1_partfun2(A,u1_struct_0(B),D,F) )
                     => r1_vfunct_2(A,B,k1_vfunct_2(A,B,C,D),k3_xboole_0(E,F)) ) ) ) ) ) )).

fof(t57_vfunct_2,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)
            & v2_clvect_1(B)
            & v5_clvect_1(B)
            & l2_clvect_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,F] :
                      ( ( r1_vfunct_2(A,B,C,E)
                        & r1_partfun2(A,u1_struct_0(B),D,F) )
                     => ( r1_vfunct_2(A,B,k2_vfunct_2(A,B,C,D),k3_xboole_0(E,F))
                        & r1_vfunct_2(A,B,k2_vfunct_2(A,B,D,C),k3_xboole_0(E,F)) ) ) ) ) ) ) )).

fof(dt_k1_vfunct_2,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_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_2(A,B,C,D))
        & m2_relset_1(k1_vfunct_2(A,B,C,D),A,u1_struct_0(B)) ) ) )).

fof(dt_k2_vfunct_2,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_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_2(A,B,C,D))
        & m2_relset_1(k2_vfunct_2(A,B,C,D),A,u1_struct_0(B)) ) ) )).

fof(dt_k3_vfunct_2,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,k2_numbers)
        & v1_funct_1(D)
        & m1_relset_1(D,A,u1_struct_0(B)) )
     => ( v1_funct_1(k3_vfunct_2(A,B,C,D))
        & m2_relset_1(k3_vfunct_2(A,B,C,D),A,u1_struct_0(B)) ) ) )).

fof(dt_k4_vfunct_2,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,u1_struct_0(B))
        & m1_subset_1(D,k2_numbers) )
     => ( v1_funct_1(k4_vfunct_2(A,B,C,D))
        & m2_relset_1(k4_vfunct_2(A,B,C,D),A,u1_struct_0(B)) ) ) )).

fof(dt_k5_vfunct_2,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => ( v1_funct_1(k5_vfunct_2(A,B,C))
        & m2_relset_1(k5_vfunct_2(A,B,C),A,k1_numbers) ) ) )).

fof(dt_k6_vfunct_2,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)
        & v2_clvect_1(B)
        & v5_clvect_1(B)
        & l2_clvect_1(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => ( v1_funct_1(k6_vfunct_2(A,B,C))
        & m2_relset_1(k6_vfunct_2(A,B,C),A,u1_struct_0(B)) ) ) )).
%------------------------------------------------------------------------------