SET007 Axioms: SET007+923.ax


%------------------------------------------------------------------------------
% File     : SET007+923 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Differentiable Formulas of Special 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    : fdiff_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   25 (   0 unit)
%            Number of atoms       :  386 (  77 equality)
%            Maximal formula depth :   19 (  14 average)
%            Number of connectives :  384 (  23 ~  ;   0  |; 157  &)
%                                         (   0 <=>; 204 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   10 (   0 propositional; 1-3 arity)
%            Number of functors    :   33 (   9 constant; 0-6 arity)
%            Number of variables   :  128 (   0 singleton; 128 !;   0 ?)
%            Maximal term depth    :    7 (   2 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(t1_fdiff_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v3_rcomp_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,k1_numbers,k1_numbers) )
                 => ( ( r1_tarski(B,k1_relat_1(k2_rfunct_1(k1_numbers,k1_numbers,C,D)))
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => ( k2_seq_1(k1_numbers,k1_numbers,C,E) = k3_real_1(A,E)
                              & k2_seq_1(k1_numbers,k1_numbers,D,E) = k5_real_1(A,E)
                              & k2_seq_1(k1_numbers,k1_numbers,D,E) != np__0 ) ) ) )
                   => ( r2_fdiff_1(k2_rfunct_1(k1_numbers,k1_numbers,C,D),B)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k2_rfunct_1(k1_numbers,k1_numbers,C,D),B),E) = k6_real_1(k4_real_1(np__2,A),k7_square_1(k5_real_1(A,E))) ) ) ) ) ) ) ) ) )).

fof(t2_fdiff_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v3_rcomp_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,k1_numbers,k1_numbers) )
                 => ( ( r1_tarski(B,k1_relat_1(k2_rfunct_1(k1_numbers,k1_numbers,C,D)))
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => ( k2_seq_1(k1_numbers,k1_numbers,C,E) = k5_real_1(E,A)
                              & k2_seq_1(k1_numbers,k1_numbers,D,E) = k3_real_1(E,A)
                              & k2_seq_1(k1_numbers,k1_numbers,D,E) != np__0 ) ) ) )
                   => ( r2_fdiff_1(k2_rfunct_1(k1_numbers,k1_numbers,C,D),B)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k2_rfunct_1(k1_numbers,k1_numbers,C,D),B),E) = k6_real_1(k4_real_1(np__2,A),k7_square_1(k3_real_1(E,A))) ) ) ) ) ) ) ) ) )).

fof(t3_fdiff_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( ( v3_rcomp_1(C)
                & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,k1_numbers,k1_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,k1_numbers,k1_numbers) )
                     => ( ( r1_tarski(C,k1_relat_1(k2_rfunct_1(k1_numbers,k1_numbers,D,E)))
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,C)
                               => ( k2_seq_1(k1_numbers,k1_numbers,D,F) = k5_real_1(F,A)
                                  & k2_seq_1(k1_numbers,k1_numbers,E,F) = k5_real_1(F,B)
                                  & k2_seq_1(k1_numbers,k1_numbers,E,F) != np__0 ) ) ) )
                       => ( r2_fdiff_1(k2_rfunct_1(k1_numbers,k1_numbers,D,E),C)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,C)
                               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k2_rfunct_1(k1_numbers,k1_numbers,D,E),C),F) = k6_real_1(k5_real_1(A,B),k7_square_1(k5_real_1(F,B))) ) ) ) ) ) ) ) ) ) )).

fof(t4_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( r1_tarski(A,k1_relat_1(B))
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => ( k2_seq_1(k1_numbers,k1_numbers,B,C) = C
                      & k2_seq_1(k1_numbers,k1_numbers,B,C) != np__0 ) ) ) )
           => ( r2_fdiff_1(k4_rfunct_1(k1_numbers,k1_numbers,B),A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k4_rfunct_1(k1_numbers,k1_numbers,B),A),C) = k1_real_1(k6_real_1(np__1,k7_square_1(C))) ) ) ) ) ) ) )).

fof(t5_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k18_sin_cos)))
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => ( k2_seq_1(k1_numbers,k1_numbers,B,C) = C
                      & k2_seq_1(k1_numbers,k1_numbers,B,C) != np__0 ) ) ) )
           => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k18_sin_cos),A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k18_sin_cos),A),C) = k1_real_1(k4_real_1(k6_real_1(np__1,k7_square_1(C)),k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,k6_real_1(np__1,C)))) ) ) ) ) ) ) )).

fof(t6_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k21_sin_cos)))
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => ( k2_seq_1(k1_numbers,k1_numbers,B,C) = C
                      & k2_seq_1(k1_numbers,k1_numbers,B,C) != np__0 ) ) ) )
           => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k21_sin_cos),A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k21_sin_cos),A),C) = k4_real_1(k6_real_1(np__1,k7_square_1(C)),k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k6_real_1(np__1,C))) ) ) ) ) ) ) )).

fof(t7_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k18_sin_cos))))
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => ( k2_seq_1(k1_numbers,k1_numbers,B,C) = C
                      & k2_seq_1(k1_numbers,k1_numbers,B,C) != np__0 ) ) ) )
           => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k18_sin_cos)),A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k18_sin_cos)),A),C) = k5_real_1(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k6_real_1(np__1,C)),k4_real_1(k6_real_1(np__1,C),k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,k6_real_1(np__1,C)))) ) ) ) ) ) ) )).

fof(t8_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k21_sin_cos))))
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => ( k2_seq_1(k1_numbers,k1_numbers,B,C) = C
                      & k2_seq_1(k1_numbers,k1_numbers,B,C) != np__0 ) ) ) )
           => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k21_sin_cos)),A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k21_sin_cos)),A),C) = k3_real_1(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,k6_real_1(np__1,C)),k4_real_1(k6_real_1(np__1,C),k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k6_real_1(np__1,C)))) ) ) ) ) ) ) )).

fof(t9_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k21_sin_cos))))
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => ( k2_seq_1(k1_numbers,k1_numbers,B,C) = C
                      & k2_seq_1(k1_numbers,k1_numbers,B,C) != np__0 ) ) ) )
           => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k21_sin_cos)),A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k21_sin_cos)),A),C) = k4_real_1(k6_real_1(np__1,k7_square_1(C)),k5_real_1(k7_square_1(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k6_real_1(np__1,C))),k7_square_1(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,k6_real_1(np__1,C))))) ) ) ) ) ) ) )).

fof(t10_fdiff_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v3_rcomp_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_tarski(B,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A)))))
                  & r1_xreal_0(np__1,A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,C,D) = k4_real_1(A,D) ) ) )
               => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A))),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A))),B),D) = k4_real_1(k4_real_1(A,k7_prepower(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,D),k5_real_1(A,np__1))),k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k4_real_1(k1_nat_1(A,np__1),D))) ) ) ) ) ) ) ) )).

fof(t11_fdiff_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v3_rcomp_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_tarski(B,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k21_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A)))))
                  & r1_xreal_0(np__1,A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,C,D) = k4_real_1(A,D) ) ) )
               => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k21_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A))),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k21_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A))),B),D) = k4_real_1(k4_real_1(A,k7_prepower(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,D),k5_real_1(A,np__1))),k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,k4_real_1(k1_nat_1(A,np__1),D))) ) ) ) ) ) ) ) )).

fof(t12_fdiff_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v3_rcomp_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_tarski(B,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k21_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k1_taylor_1(A)))))
                  & r1_xreal_0(np__1,A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,C,D) = k4_real_1(A,D) ) ) )
               => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k21_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k1_taylor_1(A))),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k21_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k1_taylor_1(A))),B),D) = k1_real_1(k4_real_1(k4_real_1(A,k7_prepower(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,D),k5_real_1(A,np__1))),k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k4_real_1(k1_nat_1(A,np__1),D)))) ) ) ) ) ) ) ) )).

fof(t13_fdiff_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v3_rcomp_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_tarski(B,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k1_taylor_1(A)))))
                  & r1_xreal_0(np__1,A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,C,D) = k4_real_1(A,D) ) ) )
               => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k1_taylor_1(A))),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k1_taylor_1(A))),B),D) = k4_real_1(k4_real_1(A,k7_prepower(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,D),k5_real_1(A,np__1))),k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,k4_real_1(k1_nat_1(A,np__1),D))) ) ) ) ) ) ) ) )).

fof(t14_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k18_sin_cos)))
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => ( k2_seq_1(k1_numbers,k1_numbers,B,C) = C
                      & k2_seq_1(k1_numbers,k1_numbers,B,C) != np__0 ) ) ) )
           => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k18_sin_cos),A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k18_sin_cos),A),C) = k5_real_1(k4_real_1(k6_real_1(np__1,C),k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,C)),k4_real_1(k6_real_1(np__1,k7_square_1(C)),k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,C))) ) ) ) ) ) ) )).

fof(t15_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k21_sin_cos)))
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => ( k2_seq_1(k1_numbers,k1_numbers,B,C) = C
                      & k2_seq_1(k1_numbers,k1_numbers,B,C) != np__0 ) ) ) )
           => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k21_sin_cos),A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k21_sin_cos),A),C) = k5_real_1(k1_real_1(k4_real_1(k6_real_1(np__1,C),k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,C))),k4_real_1(k6_real_1(np__1,k7_square_1(C)),k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,C))) ) ) ) ) ) ) )).

fof(t16_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( r1_tarski(A,k1_relat_1(k6_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_taylor_1(k6_real_1(np__1,np__2))))))
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => ( k2_seq_1(k1_numbers,k1_numbers,B,C) = C
                      & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,C),np__0) ) ) ) )
           => ( r2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_taylor_1(k6_real_1(np__1,np__2)))),A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_taylor_1(k6_real_1(np__1,np__2)))),A),C) = k3_real_1(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,C),k4_real_1(k6_real_1(np__1,np__2),k13_prepower(C,k1_real_1(k6_real_1(np__1,np__2))))) ) ) ) ) ) ) )).

fof(t17_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,C),k18_sin_cos))))
                  & B = k1_taylor_1(np__2)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,A)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = D
                          & k2_seq_1(k1_numbers,k1_numbers,C,D) != np__0 ) ) ) )
               => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,C),k18_sin_cos)),A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,A)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,C),k18_sin_cos)),A),D) = k5_real_1(k4_real_1(k4_real_1(np__2,D),k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k6_real_1(np__1,D))),k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,k6_real_1(np__1,D))) ) ) ) ) ) ) ) )).

fof(t18_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,C),k21_sin_cos))))
                  & B = k1_taylor_1(np__2)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,A)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = D
                          & k2_seq_1(k1_numbers,k1_numbers,C,D) != np__0 ) ) ) )
               => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,C),k21_sin_cos)),A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,A)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,C),k21_sin_cos)),A),D) = k3_real_1(k4_real_1(k4_real_1(np__2,D),k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,k6_real_1(np__1,D))),k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k6_real_1(np__1,D))) ) ) ) ) ) ) ) )).

fof(t19_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power))))
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => ( k2_seq_1(k1_numbers,k1_numbers,B,C) = C
                      & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,C),np__0) ) ) ) )
           => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),A),C) = k6_real_1(np__1,C) ) ) ) ) ) ) )).

fof(t20_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),B)))
                  & B = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k2_taylor_1(k8_power))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,A)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = D
                          & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,D),np__0) ) ) ) )
               => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),B),A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,A)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),B),A),D) = k3_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k2_taylor_1(k8_power),D)) ) ) ) ) ) ) ) )).

fof(t21_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,k1_numbers,k1_numbers) )
                 => ( ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,B,C)))
                      & B = k1_taylor_1(np__2)
                      & C = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k2_taylor_1(k8_power))
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,A)
                           => ( k2_seq_1(k1_numbers,k1_numbers,D,E) = E
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,D,E),np__0) ) ) ) )
                   => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,B,C),A)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,A)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,B,C),A),E) = k3_real_1(E,k4_real_1(k4_real_1(np__2,E),k2_seq_1(k1_numbers,k1_numbers,k2_taylor_1(k8_power),E))) ) ) ) ) ) ) ) ) )).

fof(t22_fdiff_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v3_rcomp_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,k1_numbers,k1_numbers) )
                 => ( ( r1_tarski(B,k1_relat_1(k2_rfunct_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,D),k7_seq_1(k1_numbers,k1_numbers,C,D))))
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => k2_seq_1(k1_numbers,k1_numbers,C,E) = A ) )
                      & D = k1_taylor_1(np__2)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( r2_hidden(E,B)
                              & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,C,D),E),np__0) ) ) )
                   => ( r2_fdiff_1(k2_rfunct_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,D),k7_seq_1(k1_numbers,k1_numbers,C,D)),B)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k2_rfunct_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,D),k7_seq_1(k1_numbers,k1_numbers,C,D)),B),E) = k6_real_1(k4_real_1(k4_real_1(np__4,A),E),k3_prepower(k5_real_1(A,k3_prepower(E,np__2)),np__2)) ) ) ) ) ) ) ) ) )).

fof(t23_fdiff_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v3_rcomp_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,k1_numbers,k1_numbers) )
                 => ( ( r1_tarski(B,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,D),k7_seq_1(k1_numbers,k1_numbers,C,D)),k2_taylor_1(k8_power))))
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => k2_seq_1(k1_numbers,k1_numbers,C,E) = A ) )
                      & D = k1_taylor_1(np__2)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( r2_hidden(E,B)
                              & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,C,D),E),np__0) ) )
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( r2_hidden(E,B)
                              & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,D),E),np__0) ) ) )
                   => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,D),k7_seq_1(k1_numbers,k1_numbers,C,D)),k2_taylor_1(k8_power)),B)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,D),k7_seq_1(k1_numbers,k1_numbers,C,D)),k2_taylor_1(k8_power)),B),E) = k6_real_1(k4_real_1(k4_real_1(np__4,A),E),k5_real_1(k3_prepower(A,np__2),k3_prepower(E,np__4))) ) ) ) ) ) ) ) ) )).

fof(t24_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,k1_numbers,k1_numbers) )
                 => ( ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),C)))
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,A)
                           => k2_seq_1(k1_numbers,k1_numbers,B,E) = E ) )
                      & C = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k2_taylor_1(k8_power))
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,A)
                           => ( k2_seq_1(k1_numbers,k1_numbers,D,E) = E
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,D,E),np__0) ) ) ) )
                   => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),C),A)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,A)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),C),A),E) = k4_real_1(k6_real_1(np__1,k7_square_1(E)),k5_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k2_taylor_1(k8_power),E))) ) ) ) ) ) ) ) ) )).

fof(t25_fdiff_5,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_tarski(A,k1_relat_1(k4_rfunct_1(k1_numbers,k1_numbers,B)))
                  & B = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k2_taylor_1(k8_power))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,A)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = D
                          & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,D),np__0) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( r2_hidden(D,A)
                          & k2_seq_1(k1_numbers,k1_numbers,B,D) = np__0 ) ) )
               => ( r2_fdiff_1(k4_rfunct_1(k1_numbers,k1_numbers,B),A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,A)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k4_rfunct_1(k1_numbers,k1_numbers,B),A),D) = k1_real_1(k6_real_1(np__1,k4_real_1(D,k7_square_1(k2_seq_1(k1_numbers,k1_numbers,k2_taylor_1(k8_power),D))))) ) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------