SET007 Axioms: SET007+911.ax


%------------------------------------------------------------------------------
% File     : SET007+911 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Several 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_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   57 (   0 unit)
%            Number of atoms       :  810 ( 134 equality)
%            Maximal formula depth :   24 (  14 average)
%            Number of connectives :  809 (  56 ~  ;   1  |; 309  &)
%                                         (   0 <=>; 443 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   10 (   0 propositional; 1-3 arity)
%            Number of functors    :   38 (  10 constant; 0-6 arity)
%            Number of variables   :  284 (   0 singleton; 284 !;   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_4,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) )
             => ( ( r1_tarski(B,k1_relat_1(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,B)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = k3_real_1(A,D)
                          & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,D),np__0) ) ) ) )
               => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k2_taylor_1(k8_power)),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k2_taylor_1(k8_power)),B),D) = k6_real_1(np__1,k3_real_1(A,D)) ) ) ) ) ) ) ) )).

fof(t2_fdiff_4,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) )
             => ( ( r1_tarski(B,k1_relat_1(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,B)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = k5_real_1(D,A)
                          & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,D),np__0) ) ) ) )
               => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k2_taylor_1(k8_power)),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k2_taylor_1(k8_power)),B),D) = k6_real_1(np__1,k5_real_1(D,A)) ) ) ) ) ) ) ) )).

fof(t3_fdiff_4,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) )
             => ( ( r1_tarski(B,k1_relat_1(k16_seq_1(k1_numbers,k1_numbers,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,B)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = k5_real_1(A,D)
                          & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,D),np__0) ) ) ) )
               => ( r2_fdiff_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k2_taylor_1(k8_power))),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k2_taylor_1(k8_power))),B),D) = k6_real_1(np__1,k5_real_1(A,D)) ) ) ) ) ) ) ) )).

fof(t4_fdiff_4,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(k7_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k13_seq_1(k1_numbers,k1_numbers,C,A))))
                      & 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,B)
                           => ( k2_seq_1(k1_numbers,k1_numbers,D,E) = k3_real_1(A,E)
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,D,E),np__0) ) ) ) )
                   => ( r2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k13_seq_1(k1_numbers,k1_numbers,C,A)),B)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k13_seq_1(k1_numbers,k1_numbers,C,A)),B),E) = k6_real_1(E,k3_real_1(A,E)) ) ) ) ) ) ) ) ) )).

fof(t5_fdiff_4,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(k7_seq_1(k1_numbers,k1_numbers,k13_seq_1(k1_numbers,k1_numbers,C,k4_real_1(np__2,A)),k1_partfun2(k1_numbers,B))))
                      & 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,B)
                           => ( k2_seq_1(k1_numbers,k1_numbers,D,E) = k3_real_1(A,E)
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,D,E),np__0) ) ) ) )
                   => ( r2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k13_seq_1(k1_numbers,k1_numbers,C,k4_real_1(np__2,A)),k1_partfun2(k1_numbers,B)),B)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k13_seq_1(k1_numbers,k1_numbers,C,k4_real_1(np__2,A)),k1_partfun2(k1_numbers,B)),B),E) = k6_real_1(k5_real_1(A,E),k3_real_1(A,E)) ) ) ) ) ) ) ) ) )).

fof(t6_fdiff_4,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(k7_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k13_seq_1(k1_numbers,k1_numbers,C,k4_real_1(np__2,A)))))
                      & 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,B)
                           => ( k2_seq_1(k1_numbers,k1_numbers,D,E) = k3_real_1(E,A)
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,D,E),np__0) ) ) ) )
                   => ( r2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k13_seq_1(k1_numbers,k1_numbers,C,k4_real_1(np__2,A))),B)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k13_seq_1(k1_numbers,k1_numbers,C,k4_real_1(np__2,A))),B),E) = k6_real_1(k5_real_1(E,A),k3_real_1(E,A)) ) ) ) ) ) ) ) ) )).

fof(t7_fdiff_4,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(k6_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k13_seq_1(k1_numbers,k1_numbers,C,k4_real_1(np__2,A)))))
                      & 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,B)
                           => ( k2_seq_1(k1_numbers,k1_numbers,D,E) = k5_real_1(E,A)
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,D,E),np__0) ) ) ) )
                   => ( r2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k13_seq_1(k1_numbers,k1_numbers,C,k4_real_1(np__2,A))),B)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k13_seq_1(k1_numbers,k1_numbers,C,k4_real_1(np__2,A))),B),E) = k6_real_1(k3_real_1(E,A),k5_real_1(E,A)) ) ) ) ) ) ) ) ) )).

fof(t8_fdiff_4,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(k6_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k13_seq_1(k1_numbers,k1_numbers,D,k5_real_1(A,B)))))
                          & D = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,E,k2_taylor_1(k8_power))
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,C)
                               => ( k2_seq_1(k1_numbers,k1_numbers,E,F) = k3_real_1(F,B)
                                  & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,E,F),np__0) ) ) ) )
                       => ( r2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k13_seq_1(k1_numbers,k1_numbers,D,k5_real_1(A,B))),C)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,C)
                               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k13_seq_1(k1_numbers,k1_numbers,D,k5_real_1(A,B))),C),F) = k6_real_1(k3_real_1(F,A),k3_real_1(F,B)) ) ) ) ) ) ) ) ) ) )).

fof(t9_fdiff_4,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(k6_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k13_seq_1(k1_numbers,k1_numbers,D,k3_real_1(A,B)))))
                          & D = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,E,k2_taylor_1(k8_power))
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,C)
                               => ( k2_seq_1(k1_numbers,k1_numbers,E,F) = k5_real_1(F,B)
                                  & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,E,F),np__0) ) ) ) )
                       => ( r2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k13_seq_1(k1_numbers,k1_numbers,D,k3_real_1(A,B))),C)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,C)
                               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k13_seq_1(k1_numbers,k1_numbers,D,k3_real_1(A,B))),C),F) = k6_real_1(k3_real_1(F,A),k5_real_1(F,B)) ) ) ) ) ) ) ) ) ) )).

fof(t10_fdiff_4,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(k7_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k13_seq_1(k1_numbers,k1_numbers,D,k3_real_1(A,B)))))
                          & D = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,E,k2_taylor_1(k8_power))
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,C)
                               => ( k2_seq_1(k1_numbers,k1_numbers,E,F) = k3_real_1(F,B)
                                  & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,E,F),np__0) ) ) ) )
                       => ( r2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k13_seq_1(k1_numbers,k1_numbers,D,k3_real_1(A,B))),C)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,C)
                               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k13_seq_1(k1_numbers,k1_numbers,D,k3_real_1(A,B))),C),F) = k6_real_1(k5_real_1(F,A),k3_real_1(F,B)) ) ) ) ) ) ) ) ) ) )).

fof(t11_fdiff_4,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(k6_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k13_seq_1(k1_numbers,k1_numbers,D,k5_real_1(A,B)))))
                          & D = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,E,k2_taylor_1(k8_power))
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,C)
                               => ( k2_seq_1(k1_numbers,k1_numbers,E,F) = k5_real_1(F,A)
                                  & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,E,F),np__0) ) ) ) )
                       => ( r2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k13_seq_1(k1_numbers,k1_numbers,D,k5_real_1(A,B))),C)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,C)
                               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k13_seq_1(k1_numbers,k1_numbers,D,k5_real_1(A,B))),C),F) = k6_real_1(k5_real_1(F,B),k5_real_1(F,A)) ) ) ) ) ) ) ) ) ) )).

fof(t12_fdiff_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( ( v3_rcomp_1(D)
                    & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,k1_numbers,k1_numbers) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & m2_relset_1(F,k1_numbers,k1_numbers) )
                         => ( ( r1_tarski(D,k1_relat_1(k6_seq_1(k1_numbers,k1_numbers,E,k13_seq_1(k1_numbers,k1_numbers,F,A))))
                              & ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ( r2_hidden(G,D)
                                   => k2_seq_1(k1_numbers,k1_numbers,E,G) = k3_real_1(B,k4_real_1(C,G)) ) )
                              & F = k1_taylor_1(np__2) )
                           => ( r2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,E,k13_seq_1(k1_numbers,k1_numbers,F,A)),D)
                              & ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ( r2_hidden(G,D)
                                   => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,E,k13_seq_1(k1_numbers,k1_numbers,F,A)),D),G) = k3_real_1(C,k4_real_1(k4_real_1(np__2,A),G)) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_fdiff_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( ( v3_rcomp_1(D)
                    & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,k1_numbers,k1_numbers) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & m2_relset_1(F,k1_numbers,k1_numbers) )
                         => ( ( r1_tarski(D,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,E,k13_seq_1(k1_numbers,k1_numbers,F,A)),k2_taylor_1(k8_power))))
                              & F = k1_taylor_1(np__2)
                              & ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ( r2_hidden(G,D)
                                   => ( k2_seq_1(k1_numbers,k1_numbers,E,G) = k3_real_1(B,k4_real_1(C,G))
                                      & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,E,k13_seq_1(k1_numbers,k1_numbers,F,A)),G),np__0) ) ) ) )
                           => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,E,k13_seq_1(k1_numbers,k1_numbers,F,A)),k2_taylor_1(k8_power)),D)
                              & ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ( r2_hidden(G,D)
                                   => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,E,k13_seq_1(k1_numbers,k1_numbers,F,A)),k2_taylor_1(k8_power)),D),G) = k6_real_1(k3_real_1(C,k4_real_1(k4_real_1(np__2,A),G)),k3_real_1(k3_real_1(B,k4_real_1(C,G)),k4_real_1(A,k3_prepower(G,np__2)))) ) ) ) ) ) ) ) ) ) ) )).

fof(t14_fdiff_4,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) )
             => ( ( r1_tarski(B,k1_relat_1(C))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = k3_real_1(A,D)
                          & k2_seq_1(k1_numbers,k1_numbers,C,D) != np__0 ) ) ) )
               => ( r2_fdiff_1(k4_rfunct_1(k1_numbers,k1_numbers,C),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k4_rfunct_1(k1_numbers,k1_numbers,C),B),D) = k1_real_1(k6_real_1(np__1,k7_square_1(k3_real_1(A,D)))) ) ) ) ) ) ) ) )).

fof(t15_fdiff_4,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) )
             => ( ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,C),k1_real_1(np__1))))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = k3_real_1(A,D)
                          & k2_seq_1(k1_numbers,k1_numbers,C,D) != np__0 ) ) ) )
               => ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,C),k1_real_1(np__1)),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,C),k1_real_1(np__1)),B),D) = k6_real_1(np__1,k7_square_1(k3_real_1(A,D))) ) ) ) ) ) ) ) )).

fof(t16_fdiff_4,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) )
             => ( ( r1_tarski(B,k1_relat_1(C))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = k5_real_1(A,D)
                          & k2_seq_1(k1_numbers,k1_numbers,C,D) != np__0 ) ) ) )
               => ( r2_fdiff_1(k4_rfunct_1(k1_numbers,k1_numbers,C),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k4_rfunct_1(k1_numbers,k1_numbers,C),B),D) = k6_real_1(np__1,k7_square_1(k5_real_1(A,D))) ) ) ) ) ) ) ) )).

fof(t17_fdiff_4,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(k6_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) = k7_square_1(A) ) )
                      & D = k1_taylor_1(np__2) )
                   => ( r2_fdiff_1(k6_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(k6_seq_1(k1_numbers,k1_numbers,C,D),B),E) = k4_real_1(np__2,E) ) ) ) ) ) ) ) ) )).

fof(t18_fdiff_4,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,k6_seq_1(k1_numbers,k1_numbers,C,D),k2_taylor_1(k8_power))))
                      & D = k1_taylor_1(np__2)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => ( k2_seq_1(k1_numbers,k1_numbers,C,E) = k7_square_1(A)
                              & ~ 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,k6_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,k6_seq_1(k1_numbers,k1_numbers,C,D),k2_taylor_1(k8_power)),B),E) = k6_real_1(k4_real_1(np__2,E),k3_real_1(k7_square_1(A),k3_prepower(E,np__2))) ) ) ) ) ) ) ) ) )).

fof(t19_fdiff_4,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(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,C,D),k2_taylor_1(k8_power)))))
                      & D = k1_taylor_1(np__2)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => ( k2_seq_1(k1_numbers,k1_numbers,C,E) = k7_square_1(A)
                              & ~ 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(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,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(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,C,D),k2_taylor_1(k8_power))),B),E) = k6_real_1(k4_real_1(np__2,E),k5_real_1(k7_square_1(A),k3_prepower(E,np__2))) ) ) ) ) ) ) ) ) )).

fof(t20_fdiff_4,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(k6_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__3) )
                   => ( r2_fdiff_1(k6_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(k6_seq_1(k1_numbers,k1_numbers,C,D),B),E) = k4_real_1(np__3,k3_prepower(E,np__2)) ) ) ) ) ) ) ) ) )).

fof(t21_fdiff_4,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,k6_seq_1(k1_numbers,k1_numbers,C,D),k2_taylor_1(k8_power))))
                      & D = k1_taylor_1(np__3)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,B)
                           => ( k2_seq_1(k1_numbers,k1_numbers,C,E) = A
                              & ~ 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,k6_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,k6_seq_1(k1_numbers,k1_numbers,C,D),k2_taylor_1(k8_power)),B),E) = k6_real_1(k4_real_1(np__3,k3_prepower(E,np__2)),k3_real_1(A,k3_prepower(E,np__3))) ) ) ) ) ) ) ) ) )).

fof(t22_fdiff_4,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,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) = k3_real_1(A,E)
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,E),np__0)
                              & k2_seq_1(k1_numbers,k1_numbers,D,E) = k5_real_1(A,E)
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,D,E),np__0) ) ) ) )
                   => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_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,C,D),k2_taylor_1(k8_power)),B),E) = k6_real_1(k4_real_1(np__2,A),k5_real_1(k7_square_1(A),k7_square_1(E))) ) ) ) ) ) ) ) ) )).

fof(t23_fdiff_4,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,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) = k5_real_1(E,A)
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,E),np__0)
                              & k2_seq_1(k1_numbers,k1_numbers,D,E) = k3_real_1(E,A)
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,D,E),np__0) ) ) ) )
                   => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_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,C,D),k2_taylor_1(k8_power)),B),E) = k6_real_1(k4_real_1(np__2,A),k5_real_1(k7_square_1(E),k7_square_1(A))) ) ) ) ) ) ) ) ) )).

fof(t24_fdiff_4,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(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,D,E),k2_taylor_1(k8_power))))
                          & ! [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)
                                  & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,D,F),np__0)
                                  & k2_seq_1(k1_numbers,k1_numbers,E,F) = k5_real_1(F,B)
                                  & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,E,F),np__0) ) ) ) )
                       => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,D,E),k2_taylor_1(k8_power)),C)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,C)
                               => 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,D,E),k2_taylor_1(k8_power)),C),F) = k6_real_1(k5_real_1(A,B),k4_real_1(k5_real_1(F,A),k5_real_1(F,B))) ) ) ) ) ) ) ) ) ) )).

fof(t25_fdiff_4,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) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & m2_relset_1(F,k1_numbers,k1_numbers) )
                         => ( ( r1_tarski(C,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,D,k6_real_1(np__1,k5_real_1(A,B)))))
                              & D = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,E,F),k2_taylor_1(k8_power))
                              & ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ( r2_hidden(G,C)
                                   => ( k2_seq_1(k1_numbers,k1_numbers,E,G) = k5_real_1(G,A)
                                      & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,E,G),np__0)
                                      & k2_seq_1(k1_numbers,k1_numbers,F,G) = k5_real_1(G,B)
                                      & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,F,G),np__0)
                                      & k5_real_1(A,B) != np__0 ) ) ) )
                           => ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,D,k6_real_1(np__1,k5_real_1(A,B))),C)
                              & ! [G] :
                                  ( m1_subset_1(G,k1_numbers)
                                 => ( r2_hidden(G,C)
                                   => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,D,k6_real_1(np__1,k5_real_1(A,B))),C),G) = k6_real_1(np__1,k4_real_1(k5_real_1(G,A),k5_real_1(G,B))) ) ) ) ) ) ) ) ) ) ) )).

fof(t26_fdiff_4,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,C,D),k2_taylor_1(k8_power))))
                      & D = k1_taylor_1(np__2)
                      & ! [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)
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,E),np__0)
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,D,E),np__0)
                              & E != np__0 ) ) ) )
                   => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_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,C,D),k2_taylor_1(k8_power)),B),E) = k6_real_1(k5_real_1(k4_real_1(np__2,A),E),k4_real_1(E,k5_real_1(E,A))) ) ) ) ) ) ) ) ) )).

fof(t27_fdiff_4,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) )
             => ( ( r1_tarski(B,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__3,np__2)))))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = k3_real_1(A,D)
                          & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,D),np__0) ) ) ) )
               => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__3,np__2))),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__3,np__2))),B),D) = k4_real_1(k6_real_1(np__3,np__2),k13_prepower(k3_real_1(A,D),k6_real_1(np__1,np__2))) ) ) ) ) ) ) ) )).

fof(t28_fdiff_4,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) )
             => ( ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__3,np__2))),k6_real_1(np__2,np__3))))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = k3_real_1(A,D)
                          & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,D),np__0) ) ) ) )
               => ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__3,np__2))),k6_real_1(np__2,np__3)),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__3,np__2))),k6_real_1(np__2,np__3)),B),D) = k13_prepower(k3_real_1(A,D),k6_real_1(np__1,np__2)) ) ) ) ) ) ) ) )).

fof(t29_fdiff_4,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) )
             => ( ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__3,np__2))),k1_real_1(k6_real_1(np__2,np__3)))))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = k5_real_1(A,D)
                          & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,D),np__0) ) ) ) )
               => ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__3,np__2))),k1_real_1(k6_real_1(np__2,np__3))),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__3,np__2))),k1_real_1(k6_real_1(np__2,np__3))),B),D) = k13_prepower(k5_real_1(A,D),k6_real_1(np__1,np__2)) ) ) ) ) ) ) ) )).

fof(t30_fdiff_4,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) )
             => ( ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__1,np__2))),np__2)))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = k3_real_1(A,D)
                          & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,D),np__0) ) ) ) )
               => ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__1,np__2))),np__2),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__1,np__2))),np__2),B),D) = k13_prepower(k3_real_1(A,D),k1_real_1(k6_real_1(np__1,np__2))) ) ) ) ) ) ) ) )).

fof(t31_fdiff_4,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) )
             => ( ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__1,np__2))),k1_real_1(np__2))))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => ( k2_seq_1(k1_numbers,k1_numbers,C,D) = k5_real_1(A,D)
                          & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,D),np__0) ) ) ) )
               => ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__1,np__2))),k1_real_1(np__2)),B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( r2_hidden(D,B)
                       => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__1,np__2))),k1_real_1(np__2)),B),D) = k13_prepower(k5_real_1(A,D),k1_real_1(k6_real_1(np__1,np__2))) ) ) ) ) ) ) ) )).

fof(t32_fdiff_4,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) )
                 => ( ( r1_tarski(C,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k3_taylor_1(k6_real_1(np__3,np__2))),k6_real_1(np__2,k4_real_1(np__3,A)))))
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,C)
                           => ( k2_seq_1(k1_numbers,k1_numbers,D,E) = k3_real_1(B,k4_real_1(A,E))
                              & A != np__0
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,D,E),np__0) ) ) ) )
                   => ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k3_taylor_1(k6_real_1(np__3,np__2))),k6_real_1(np__2,k4_real_1(np__3,A))),C)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,C)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k3_taylor_1(k6_real_1(np__3,np__2))),k6_real_1(np__2,k4_real_1(np__3,A))),C),E) = k13_prepower(k3_real_1(B,k4_real_1(A,E)),k6_real_1(np__1,np__2)) ) ) ) ) ) ) ) ) )).

fof(t33_fdiff_4,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) )
                 => ( ( r1_tarski(C,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k3_taylor_1(k6_real_1(np__3,np__2))),k1_real_1(k6_real_1(np__2,k4_real_1(np__3,A))))))
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,C)
                           => ( k2_seq_1(k1_numbers,k1_numbers,D,E) = k5_real_1(B,k4_real_1(A,E))
                              & A != np__0
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,D,E),np__0) ) ) ) )
                   => ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k3_taylor_1(k6_real_1(np__3,np__2))),k1_real_1(k6_real_1(np__2,k4_real_1(np__3,A)))),C)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,C)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k3_taylor_1(k6_real_1(np__3,np__2))),k1_real_1(k6_real_1(np__2,k4_real_1(np__3,A)))),C),E) = k13_prepower(k5_real_1(B,k4_real_1(A,E)),k6_real_1(np__1,np__2)) ) ) ) ) ) ) ) ) )).

fof(t34_fdiff_4,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) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,k1_numbers,k1_numbers) )
                     => ( ( r1_tarski(B,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__1,np__2)))))
                          & C = k6_seq_1(k1_numbers,k1_numbers,D,E)
                          & E = k1_taylor_1(np__2)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,B)
                               => ( k2_seq_1(k1_numbers,k1_numbers,D,F) = k7_square_1(A)
                                  & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,F),np__0) ) ) ) )
                       => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__1,np__2))),B)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,B)
                               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__1,np__2))),B),F) = k4_real_1(F,k13_prepower(k3_real_1(k7_square_1(A),k3_prepower(F,np__2)),k1_real_1(k6_real_1(np__1,np__2)))) ) ) ) ) ) ) ) ) ) )).

fof(t35_fdiff_4,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) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,k1_numbers,k1_numbers) )
                     => ( ( r1_tarski(B,k1_relat_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__1,np__2))))))
                          & C = k7_seq_1(k1_numbers,k1_numbers,D,E)
                          & E = k1_taylor_1(np__2)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,B)
                               => ( k2_seq_1(k1_numbers,k1_numbers,D,F) = k7_square_1(A)
                                  & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,F),np__0) ) ) ) )
                       => ( r2_fdiff_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__1,np__2)))),B)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( r2_hidden(F,B)
                               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1(k6_real_1(np__1,np__2)))),B),F) = k4_real_1(F,k13_prepower(k5_real_1(k7_square_1(A),k3_prepower(F,np__2)),k1_real_1(k6_real_1(np__1,np__2)))) ) ) ) ) ) ) ) ) ) )).

fof(t36_fdiff_4,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(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_taylor_1(k6_real_1(np__1,np__2))),np__2)))
                      & B = k6_seq_1(k1_numbers,k1_numbers,C,D)
                      & D = k1_taylor_1(np__2)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,A)
                           => ( k2_seq_1(k1_numbers,k1_numbers,C,E) = E
                              & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),np__0) ) ) ) )
                   => ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_taylor_1(k6_real_1(np__1,np__2))),np__2),A)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,A)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_taylor_1(k6_real_1(np__1,np__2))),np__2),A),E) = k4_real_1(k3_real_1(k4_real_1(np__2,E),np__1),k13_prepower(k3_real_1(k3_prepower(E,np__2),E),k1_real_1(k6_real_1(np__1,np__2)))) ) ) ) ) ) ) ) ) )).

fof(t37_fdiff_4,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) )
                 => ( ( r1_tarski(C,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k18_sin_cos)))
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,C)
                           => k2_seq_1(k1_numbers,k1_numbers,D,E) = k3_real_1(k4_real_1(A,E),B) ) ) )
                   => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k18_sin_cos),C)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,C)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k18_sin_cos),C),E) = k4_real_1(A,k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,k3_real_1(k4_real_1(A,E),B))) ) ) ) ) ) ) ) ) )).

fof(t38_fdiff_4,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) )
                 => ( ( r1_tarski(C,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k21_sin_cos)))
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,C)
                           => k2_seq_1(k1_numbers,k1_numbers,D,E) = k3_real_1(k4_real_1(A,E),B) ) ) )
                   => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k21_sin_cos),C)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( r2_hidden(E,C)
                           => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k21_sin_cos),C),E) = k1_real_1(k4_real_1(A,k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k3_real_1(k4_real_1(A,E),B)))) ) ) ) ) ) ) ) ) )).

fof(t39_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ~ ( r2_hidden(B,A)
                & k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B) = np__0 ) )
       => ( r2_fdiff_1(k4_rfunct_1(k1_numbers,k1_numbers,k21_sin_cos),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k4_rfunct_1(k1_numbers,k1_numbers,k21_sin_cos),A),B) = k6_real_1(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B),k7_square_1(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B))) ) ) ) ) ) )).

fof(t40_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ~ ( r2_hidden(B,A)
                & k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B) = np__0 ) )
       => ( r2_fdiff_1(k4_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k4_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos),A),B) = k1_real_1(k6_real_1(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B),k7_square_1(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B)))) ) ) ) ) ) )).

fof(t41_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k21_sin_cos)))
       => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k21_sin_cos),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k21_sin_cos),A),B) = k23_sin_cos(k4_real_1(np__2,B)) ) ) ) ) ) )).

fof(t42_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k2_taylor_1(k8_power))))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ ( r2_hidden(B,A)
                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B),np__0) ) ) )
       => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k2_taylor_1(k8_power)),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k2_taylor_1(k8_power)),A),B) = k1_real_1(k1_sin_cos4(B)) ) ) ) ) ) )).

fof(t43_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k2_taylor_1(k8_power))))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ ( r2_hidden(B,A)
                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B),np__0) ) ) )
       => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k2_taylor_1(k8_power)),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k2_taylor_1(k8_power)),A),B) = k2_sin_cos4(B) ) ) ) ) ) )).

fof(t44_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k16_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),k21_sin_cos)))
       => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k16_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),k21_sin_cos),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k16_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),k21_sin_cos),A),B) = k3_real_1(k1_real_1(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B)),k4_real_1(B,k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B))) ) ) ) ) ) )).

fof(t45_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k18_sin_cos)))
       => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k18_sin_cos),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k18_sin_cos),A),B) = k3_real_1(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B),k4_real_1(B,k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B))) ) ) ) ) ) )).

fof(t46_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( r1_tarski(A,k1_relat_1(k6_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k16_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),k21_sin_cos),k18_sin_cos)))
       => ( r2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k16_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),k21_sin_cos),k18_sin_cos),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k16_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),k21_sin_cos),k18_sin_cos),A),B) = k4_real_1(B,k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B)) ) ) ) ) ) )).

fof(t47_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( r1_tarski(A,k1_relat_1(k6_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k18_sin_cos),k21_sin_cos)))
       => ( r2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k18_sin_cos),k21_sin_cos),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k18_sin_cos),k21_sin_cos),A),B) = k4_real_1(B,k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B)) ) ) ) ) ) )).

fof(t48_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ( r1_tarski(A,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k3_taylor_1(k6_real_1(np__1,np__2))),np__2)))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ ( r2_hidden(B,A)
                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B),np__0) ) ) )
       => ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k3_taylor_1(k6_real_1(np__1,np__2))),np__2),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k3_taylor_1(k6_real_1(np__1,np__2))),np__2),A),B) = k4_real_1(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B),k13_prepower(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B),k1_real_1(k6_real_1(np__1,np__2)))) ) ) ) ) ) )).

fof(t49_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( r1_tarski(A,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2))))
       => ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2)),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2)),A),B) = k4_real_1(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B),k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B)) ) ) ) ) ) )).

fof(t50_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ( r1_tarski(A,k1_relat_1(k6_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2)))))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => ( ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B),np__0)
                  & ~ r1_xreal_0(np__1,k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B)) ) ) ) )
       => ( r2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2))),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2))),A),B) = k6_real_1(k3_prepower(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B),np__3),k5_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B))) ) ) ) ) ) )).

fof(t51_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ( r1_tarski(A,k1_relat_1(k7_seq_1(k1_numbers,k1_numbers,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2)),k21_sin_cos)))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => ( ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B),np__0)
                  & ~ r1_xreal_0(np__1,k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B)) ) ) ) )
       => ( r2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2)),k21_sin_cos),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2)),k21_sin_cos),A),B) = k6_real_1(k3_prepower(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B),np__3),k5_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B))) ) ) ) ) ) )).

fof(t52_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ( r1_tarski(A,k1_relat_1(k7_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2)))))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => ( ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B),np__0)
                  & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B),k1_real_1(np__1)) ) ) ) )
       => ( r2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2))),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2))),A),B) = k6_real_1(k3_prepower(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B),np__3),k3_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B))) ) ) ) ) ) )).

fof(t53_fdiff_4,axiom,(
    ! [A] :
      ( ( v3_rcomp_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ( r1_tarski(A,k1_relat_1(k7_seq_1(k1_numbers,k1_numbers,k16_seq_1(k1_numbers,k1_numbers,k21_sin_cos),k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2)))))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => ( ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B),np__0)
                  & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B),k1_real_1(np__1)) ) ) ) )
       => ( r2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k16_seq_1(k1_numbers,k1_numbers,k21_sin_cos),k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2))),A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ( r2_hidden(B,A)
               => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k16_seq_1(k1_numbers,k1_numbers,k21_sin_cos),k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__2)),k6_real_1(np__1,np__2))),A),B) = k6_real_1(k3_prepower(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,B),np__3),k3_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,B))) ) ) ) ) ) )).

fof(t54_fdiff_4,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v3_rcomp_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A)),k6_real_1(np__1,A))))
           => ( r1_xreal_0(A,np__0)
              | ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A)),k6_real_1(np__1,A)),B)
                & ! [C] :
                    ( m1_subset_1(C,k1_numbers)
                   => ( r2_hidden(C,B)
                     => k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A)),k6_real_1(np__1,A)),B),C) = k4_real_1(k7_prepower(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,C),k5_real_1(A,np__1)),k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,C)) ) ) ) ) ) ) ) )).

fof(t55_fdiff_4,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,k26_sin_cos,B)))
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( r2_hidden(C,A)
                   => k2_seq_1(k1_numbers,k1_numbers,B,C) = k5_real_1(C,np__1) ) ) )
           => ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),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,k26_sin_cos,B),A),C) = k4_real_1(C,k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C)) ) ) ) ) ) ) )).

fof(t56_fdiff_4,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,k2_rfunct_1(k1_numbers,k1_numbers,k26_sin_cos,k6_seq_1(k1_numbers,k1_numbers,k26_sin_cos,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) = np__1 ) ) )
           => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k26_sin_cos,k6_seq_1(k1_numbers,k1_numbers,k26_sin_cos,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,k2_rfunct_1(k1_numbers,k1_numbers,k26_sin_cos,k6_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B)),k2_taylor_1(k8_power)),A),C) = k6_real_1(np__1,k3_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C),np__1)) ) ) ) ) ) ) )).

fof(t57_fdiff_4,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,k2_rfunct_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k26_sin_cos),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) = np__1
                      & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),C),np__0) ) ) ) )
           => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k26_sin_cos),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,k2_rfunct_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k26_sin_cos),k2_taylor_1(k8_power)),A),C) = k6_real_1(np__1,k5_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C),np__1)) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------