SET007 Axioms: SET007+629.ax


%------------------------------------------------------------------------------
% File     : SET007+629 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Asymptotic Notation. Part II: Examples and Problems
% 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    : asympt_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  127 (  14 unit)
%            Number of atoms       :  946 ( 168 equality)
%            Maximal formula depth :   26 (   8 average)
%            Number of connectives :  961 ( 142 ~  ;   8  |; 487  &)
%                                         (  13 <=>; 311 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   27 (   0 propositional; 1-3 arity)
%            Number of functors    :   81 (  29 constant; 0-4 arity)
%            Number of variables   :  268 (   0 singleton; 248 !;  20 ?)
%            Maximal term depth    :    7 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_asympt_1,axiom,(
    ! [A,B,C] :
      ( ( v2_xreal_0(A)
        & m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers)
        & m1_subset_1(C,k1_numbers) )
     => ( v1_relat_1(k1_asympt_1(A,B,C))
        & v1_funct_1(k1_asympt_1(A,B,C))
        & v1_funct_2(k1_asympt_1(A,B,C),k5_numbers,k1_numbers)
        & v1_seq_1(k1_asympt_1(A,B,C))
        & v2_asympt_0(k1_asympt_1(A,B,C))
        & v4_asympt_0(k1_asympt_1(A,B,C))
        & v5_asympt_0(k1_asympt_1(A,B,C)) ) ) )).

fof(fc2_asympt_1,axiom,
    ( v1_relat_1(k2_asympt_1)
    & v1_funct_1(k2_asympt_1)
    & v1_funct_2(k2_asympt_1,k5_numbers,k1_numbers)
    & v1_seq_1(k2_asympt_1)
    & v2_asympt_0(k2_asympt_1)
    & v4_asympt_0(k2_asympt_1)
    & v5_asympt_0(k2_asympt_1) )).

fof(fc3_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ( v1_relat_1(k3_asympt_1(A))
        & v1_funct_1(k3_asympt_1(A))
        & v1_funct_2(k3_asympt_1(A),k5_numbers,k1_numbers)
        & v1_seq_1(k3_asympt_1(A))
        & v2_asympt_0(k3_asympt_1(A))
        & v4_asympt_0(k3_asympt_1(A))
        & v5_asympt_0(k3_asympt_1(A)) ) ) )).

fof(fc4_asympt_1,axiom,
    ( v1_relat_1(k4_asympt_1(np__1))
    & v1_funct_1(k4_asympt_1(np__1))
    & v1_funct_2(k4_asympt_1(np__1),k5_numbers,k1_numbers)
    & v2_asympt_0(k4_asympt_1(np__1)) )).

fof(fc5_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ( v1_relat_1(k5_asympt_1(A))
        & v1_funct_1(k5_asympt_1(A))
        & v1_funct_2(k5_asympt_1(A),k5_numbers,k1_numbers)
        & v1_seq_1(k5_asympt_1(A))
        & v2_asympt_0(k5_asympt_1(A))
        & v4_asympt_0(k5_asympt_1(A))
        & v5_asympt_0(k5_asympt_1(A)) ) ) )).

fof(t1_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ~ ( k2_seq_1(k5_numbers,k1_numbers,A,np__0) = np__0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,np__0)
                   => k2_seq_1(k5_numbers,k1_numbers,A,C) = k3_real_1(k3_real_1(k5_real_1(k4_real_1(k2_nat_1(np__12,k3_series_1(C,np__3)),k6_power(np__2,C)),k4_real_1(np__5,k7_square_1(C))),k7_square_1(k6_power(np__2,C))),np__36) ) )
              & k2_seq_1(k5_numbers,k1_numbers,B,np__0) = np__0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,np__0)
                   => k2_seq_1(k5_numbers,k1_numbers,B,C) = k4_real_1(k3_series_1(C,np__3),k6_power(np__2,C)) ) )
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & v4_asympt_0(C)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,k5_numbers,k1_numbers)
                        & v4_asympt_0(D)
                        & m2_relset_1(D,k5_numbers,k1_numbers) )
                     => ~ ( C = A
                          & D = B
                          & r2_hidden(C,k5_asympt_0(D)) ) ) ) ) ) ) )).

fof(t2_asympt_1,axiom,(
    ! [A] :
      ( ( v1_asympt_0(A)
        & m1_subset_1(A,k1_numbers) )
     => ! [B] :
          ( ( v1_asympt_0(B)
            & m1_subset_1(B,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k1_numbers)
                    & m2_relset_1(D,k5_numbers,k1_numbers) )
                 => ~ ( ~ r1_xreal_0(A,np__1)
                      & ~ r1_xreal_0(B,np__1)
                      & k2_seq_1(k5_numbers,k1_numbers,C,np__0) = np__0
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ~ r1_xreal_0(E,np__0)
                           => k2_seq_1(k5_numbers,k1_numbers,C,E) = k6_power(A,E) ) )
                      & k2_seq_1(k5_numbers,k1_numbers,D,np__0) = np__0
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ~ r1_xreal_0(E,np__0)
                           => k2_seq_1(k5_numbers,k1_numbers,D,E) = k6_power(B,E) ) )
                      & ! [E] :
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,k5_numbers,k1_numbers)
                            & v4_asympt_0(E)
                            & m2_relset_1(E,k5_numbers,k1_numbers) )
                         => ! [F] :
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,k5_numbers,k1_numbers)
                                & v4_asympt_0(F)
                                & m2_relset_1(F,k5_numbers,k1_numbers) )
                             => ~ ( E = C
                                  & F = D
                                  & k5_asympt_0(E) = k5_asympt_0(F) ) ) ) ) ) ) ) ) )).

fof(d1_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k1_numbers)
                    & m2_relset_1(D,k5_numbers,k1_numbers) )
                 => ( D = k1_asympt_1(A,B,C)
                  <=> ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k2_seq_1(k5_numbers,k1_numbers,D,E) = k4_power(A,k3_real_1(k4_real_1(B,E),C)) ) ) ) ) ) ) )).

fof(t3_asympt_1,axiom,(
    ! [A] :
      ( ( v2_xreal_0(A)
        & m1_subset_1(A,k1_numbers) )
     => ! [B] :
          ( ( v2_xreal_0(B)
            & m1_subset_1(B,k1_numbers) )
         => ~ ( ~ r1_xreal_0(B,A)
              & r2_hidden(k1_asympt_1(B,np__1,np__0),k5_asympt_0(k1_asympt_1(A,np__1,np__0))) ) ) ) )).

fof(d2_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( A = k2_asympt_1
      <=> ( k2_seq_1(k5_numbers,k1_numbers,A,np__0) = np__0
          & ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(B,np__0)
               => k2_seq_1(k5_numbers,k1_numbers,A,B) = k6_power(np__2,B) ) ) ) ) ) )).

fof(d3_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( B = k3_asympt_1(A)
          <=> ( k2_seq_1(k5_numbers,k1_numbers,B,np__0) = np__0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,np__0)
                   => k2_seq_1(k5_numbers,k1_numbers,B,C) = k4_power(C,A) ) ) ) ) ) ) )).

fof(t4_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v2_asympt_0(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & v2_asympt_0(B)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( r1_tarski(k5_asympt_0(A),k5_asympt_0(B))
             => ( k5_asympt_0(A) = k5_asympt_0(B)
                | ( r2_hidden(A,k5_asympt_0(B))
                  & ~ r2_hidden(A,k6_asympt_0(B)) ) ) )
            & ( r2_hidden(A,k5_asympt_0(B))
             => ( r2_hidden(A,k6_asympt_0(B))
                | ( r1_tarski(k5_asympt_0(A),k5_asympt_0(B))
                  & k5_asympt_0(A) != k5_asympt_0(B) ) ) ) ) ) ) )).

fof(t5_asympt_1,axiom,
    ( r1_tarski(k5_asympt_0(k2_asympt_1),k5_asympt_0(k3_asympt_1(k6_real_1(np__1,np__2))))
    & k5_asympt_0(k2_asympt_1) != k5_asympt_0(k3_asympt_1(k6_real_1(np__1,np__2))) )).

fof(t6_asympt_1,axiom,
    ( r2_hidden(k3_asympt_1(k6_real_1(np__1,np__2)),k6_asympt_0(k2_asympt_1))
    & ~ r2_hidden(k2_asympt_1,k6_asympt_0(k3_asympt_1(k6_real_1(np__1,np__2)))) )).

fof(t7_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_seq_1(k5_numbers,k1_numbers,A,C) = k5_bhsp_4(k3_asympt_1(B),C) )
           => r2_hidden(A,k7_asympt_0(k3_asympt_1(k1_nat_1(B,np__1)))) ) ) ) )).

fof(t8_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ~ ( k2_seq_1(k5_numbers,k1_numbers,A,np__0) = np__0
          & ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(B,np__0)
               => k2_seq_1(k5_numbers,k1_numbers,A,B) = k4_power(B,k6_power(np__2,B)) ) )
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & v4_asympt_0(B)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ~ ( B = A
                  & ~ v7_asympt_0(B) ) ) ) ) )).

fof(d4_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => k4_asympt_1(A) = k2_pre_circ(k5_numbers,A) ) )).

fof(t9_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v2_asympt_0(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ? [B] :
          ( m1_fraenkel(B,k5_numbers,k1_numbers)
          & B = k6_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)),k3_asympt_1(np__1))
          & ~ ( r2_hidden(A,k14_asympt_0(B,k5_asympt_0(k4_asympt_1(np__1))))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( ~ r1_xreal_0(D,np__0)
                              & ! [F] :
                                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                                 => ( r1_xreal_0(C,F)
                                   => ( r1_xreal_0(np__1,k2_seq_1(k5_numbers,k1_numbers,A,F))
                                      & r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,F),k4_real_1(D,k2_seq_1(k5_numbers,k1_numbers,k3_asympt_1(E),F))) ) ) ) ) ) ) ) )
          & ( ? [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & ? [D] :
                    ( m1_subset_1(D,k1_numbers)
                    & ? [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                        & ~ r1_xreal_0(D,np__0)
                        & ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ( r1_xreal_0(C,F)
                             => ( r1_xreal_0(np__1,k2_seq_1(k5_numbers,k1_numbers,A,F))
                                & r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,F),k4_real_1(D,k2_seq_1(k5_numbers,k1_numbers,k3_asympt_1(E),F))) ) ) ) ) ) )
           => r2_hidden(A,k14_asympt_0(B,k5_asympt_0(k4_asympt_1(np__1)))) ) ) ) )).

fof(t10_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k2_seq_1(k5_numbers,k1_numbers,A,B) = k3_real_1(k5_real_1(k2_nat_1(np__3,k3_series_1(np__10,np__6)),k2_nat_1(k2_nat_1(np__18,k3_series_1(np__10,np__3)),B)),k4_real_1(np__27,k7_square_1(B))) )
       => r2_hidden(A,k5_asympt_0(k3_asympt_1(np__2))) ) ) )).

fof(t11_asympt_1,axiom,(
    r2_hidden(k3_asympt_1(np__2),k5_asympt_0(k3_asympt_1(np__3))) )).

fof(t12_asympt_1,axiom,(
    ~ r2_hidden(k3_asympt_1(np__2),k6_asympt_0(k3_asympt_1(np__3))) )).

fof(t13_asympt_1,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k1_numbers)
      & v4_asympt_0(A)
      & m2_relset_1(A,k5_numbers,k1_numbers)
      & A = k1_asympt_1(np__2,np__1,np__1)
      & r2_hidden(k1_asympt_1(np__2,np__1,np__0),k7_asympt_0(A)) ) )).

fof(d5_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( B = k5_asympt_1(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_seq_1(k5_numbers,k1_numbers,B,C) = k11_newton(k1_nat_1(C,A)) ) ) ) ) )).

fof(t14_asympt_1,axiom,(
    ~ r2_hidden(k5_asympt_1(np__0),k7_asympt_0(k5_asympt_1(np__1))) )).

fof(t15_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( r2_hidden(A,k5_asympt_0(k3_asympt_1(np__1)))
       => r2_hidden(k11_seq_1(A,A),k5_asympt_0(k3_asympt_1(np__2))) ) ) )).

fof(t16_asympt_1,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k1_numbers)
      & v4_asympt_0(A)
      & m2_relset_1(A,k5_numbers,k1_numbers)
      & A = k1_asympt_1(np__2,np__1,np__0)
      & r2_hidden(k3_asympt_0(k3_asympt_1(np__1),np__2),k5_asympt_0(k3_asympt_1(np__1)))
      & ~ r2_hidden(k1_asympt_1(np__2,np__2,np__0),k5_asympt_0(A)) ) )).

fof(t17_asympt_1,axiom,
    ( ~ r1_xreal_0(k6_real_1(np__159,np__100),k6_power(np__2,np__3))
   => ( r2_hidden(k3_asympt_1(k6_power(np__2,np__3)),k5_asympt_0(k3_asympt_1(k6_real_1(np__159,np__100))))
      & ~ r2_hidden(k3_asympt_1(k6_power(np__2,np__3)),k6_asympt_0(k3_asympt_1(k6_real_1(np__159,np__100))))
      & ~ r2_hidden(k3_asympt_1(k6_power(np__2,np__3)),k7_asympt_0(k3_asympt_1(k6_real_1(np__159,np__100)))) ) )).

fof(t18_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ~ ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k2_seq_1(k5_numbers,k1_numbers,A,C) = k4_nat_1(C,np__2) )
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k2_seq_1(k5_numbers,k1_numbers,B,C) = k4_nat_1(k1_nat_1(C,np__1),np__2) )
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & v2_asympt_0(C)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,k5_numbers,k1_numbers)
                        & v2_asympt_0(D)
                        & m2_relset_1(D,k5_numbers,k1_numbers) )
                     => ~ ( C = A
                          & D = B
                          & ~ r2_hidden(C,k5_asympt_0(D))
                          & ~ r2_hidden(D,k5_asympt_0(C)) ) ) ) ) ) ) )).

fof(t19_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v2_asympt_0(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & v2_asympt_0(B)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( k5_asympt_0(A) = k5_asympt_0(B)
          <=> r2_hidden(A,k7_asympt_0(B)) ) ) ) )).

fof(t20_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v2_asympt_0(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & v2_asympt_0(B)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( r2_hidden(A,k7_asympt_0(B))
          <=> k7_asympt_0(A) = k7_asympt_0(B) ) ) ) )).

fof(t21_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ~ ( ~ r1_xreal_0(A,np__0)
              & k2_seq_1(k5_numbers,k1_numbers,B,np__0) = np__0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,np__0)
                   => k2_seq_1(k5_numbers,k1_numbers,B,C) = k4_real_1(C,k6_power(np__2,C)) ) )
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & v4_asympt_0(C)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ~ ( C = B
                      & r1_tarski(k5_asympt_0(C),k5_asympt_0(k3_asympt_1(k3_real_1(np__1,A))))
                      & k5_asympt_0(C) != k5_asympt_0(k3_asympt_1(k3_real_1(np__1,A))) ) ) ) ) ) )).

fof(t22_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ~ ( ~ r1_xreal_0(A,np__0)
              & ~ r1_xreal_0(np__1,A)
              & k2_seq_1(k5_numbers,k1_numbers,B,np__0) = np__0
              & k2_seq_1(k5_numbers,k1_numbers,B,np__1) = np__0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,np__1)
                   => k2_seq_1(k5_numbers,k1_numbers,B,C) = k6_real_1(k3_series_1(C,np__2),k6_power(np__2,C)) ) )
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & v4_asympt_0(C)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ~ ( C = B
                      & r1_tarski(k5_asympt_0(k3_asympt_1(k3_real_1(np__1,A))),k5_asympt_0(C))
                      & k5_asympt_0(k3_asympt_1(k3_real_1(np__1,A))) != k5_asympt_0(C) ) ) ) ) ) )).

fof(t23_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ~ ( k2_seq_1(k5_numbers,k1_numbers,A,np__0) = np__0
          & k2_seq_1(k5_numbers,k1_numbers,A,np__1) = np__0
          & ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(B,np__1)
               => k2_seq_1(k5_numbers,k1_numbers,A,B) = k6_real_1(k3_series_1(B,np__2),k6_power(np__2,B)) ) )
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & v4_asympt_0(B)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ~ ( B = A
                  & r1_tarski(k5_asympt_0(B),k5_asympt_0(k3_asympt_1(np__8)))
                  & k5_asympt_0(B) != k5_asympt_0(k3_asympt_1(np__8)) ) ) ) ) )).

fof(t24_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ~ ( ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => k2_seq_1(k5_numbers,k1_numbers,A,B) = k4_power(k3_real_1(k5_real_1(k7_square_1(B),B),np__1),np__4) )
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & v4_asympt_0(B)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ~ ( B = A
                  & k5_asympt_0(k3_asympt_1(np__8)) = k5_asympt_0(B) ) ) ) ) )).

fof(t25_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ~ ( ~ r1_xreal_0(A,np__0)
          & ~ r1_xreal_0(np__1,A)
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & v4_asympt_0(B)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ~ ( B = k1_asympt_1(k3_real_1(np__1,A),np__1,np__0)
                  & r1_tarski(k5_asympt_0(k3_asympt_1(np__8)),k5_asympt_0(B))
                  & k5_asympt_0(k3_asympt_1(np__8)) != k5_asympt_0(B) ) ) ) ) )).

fof(t26_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ~ ( k2_seq_1(k5_numbers,k1_numbers,A,np__0) = np__0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,np__0)
                   => k2_seq_1(k5_numbers,k1_numbers,A,C) = k4_power(C,k6_power(np__2,C)) ) )
              & k2_seq_1(k5_numbers,k1_numbers,B,np__0) = np__0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,np__0)
                   => k2_seq_1(k5_numbers,k1_numbers,B,C) = k4_power(C,k9_square_1(C)) ) )
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & v4_asympt_0(C)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,k5_numbers,k1_numbers)
                        & v4_asympt_0(D)
                        & m2_relset_1(D,k5_numbers,k1_numbers) )
                     => ~ ( C = A
                          & D = B
                          & r1_tarski(k5_asympt_0(C),k5_asympt_0(D))
                          & k5_asympt_0(C) != k5_asympt_0(D) ) ) ) ) ) ) )).

fof(t27_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ~ ( k2_seq_1(k5_numbers,k1_numbers,A,np__0) = np__0
          & ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(B,np__0)
               => k2_seq_1(k5_numbers,k1_numbers,A,B) = k4_power(B,k9_square_1(B)) ) )
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & v4_asympt_0(B)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & v4_asympt_0(C)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ~ ( B = A
                      & C = k1_asympt_1(np__2,np__1,np__0)
                      & r1_tarski(k5_asympt_0(B),k5_asympt_0(C))
                      & k5_asympt_0(B) != k5_asympt_0(C) ) ) ) ) ) )).

fof(t28_asympt_1,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k1_numbers)
      & v4_asympt_0(A)
      & m2_relset_1(A,k5_numbers,k1_numbers)
      & ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k1_numbers)
          & v4_asympt_0(B)
          & m2_relset_1(B,k5_numbers,k1_numbers)
          & A = k1_asympt_1(np__2,np__1,np__0)
          & B = k1_asympt_1(np__2,np__1,np__1)
          & k5_asympt_0(A) = k5_asympt_0(B) ) ) )).

fof(t29_asympt_1,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k1_numbers)
      & v4_asympt_0(A)
      & m2_relset_1(A,k5_numbers,k1_numbers)
      & ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k1_numbers)
          & v4_asympt_0(B)
          & m2_relset_1(B,k5_numbers,k1_numbers)
          & A = k1_asympt_1(np__2,np__1,np__0)
          & B = k1_asympt_1(np__2,np__2,np__0)
          & r1_tarski(k5_asympt_0(A),k5_asympt_0(B))
          & k5_asympt_0(A) != k5_asympt_0(B) ) ) )).

fof(t30_asympt_1,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k1_numbers)
      & v4_asympt_0(A)
      & m2_relset_1(A,k5_numbers,k1_numbers)
      & A = k1_asympt_1(np__2,np__2,np__0)
      & r1_tarski(k5_asympt_0(A),k5_asympt_0(k5_asympt_1(np__0)))
      & k5_asympt_0(A) != k5_asympt_0(k5_asympt_1(np__0)) ) )).

fof(t31_asympt_1,axiom,
    ( r1_tarski(k5_asympt_0(k5_asympt_1(np__0)),k5_asympt_0(k5_asympt_1(np__1)))
    & k5_asympt_0(k5_asympt_1(np__0)) != k5_asympt_0(k5_asympt_1(np__1)) )).

fof(t32_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ~ ( k2_seq_1(k5_numbers,k1_numbers,A,np__0) = np__0
          & ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(B,np__0)
               => k2_seq_1(k5_numbers,k1_numbers,A,B) = k3_series_1(B,B) ) )
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & v4_asympt_0(B)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ~ ( B = A
                  & r1_tarski(k5_asympt_0(k5_asympt_1(np__1)),k5_asympt_0(B))
                  & k5_asympt_0(k5_asympt_1(np__1)) != k5_asympt_0(B) ) ) ) ) )).

fof(t33_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(np__1,A)
       => ! [B] :
            ( ( v1_funct_1(B)
              & v1_funct_2(B,k5_numbers,k1_numbers)
              & m2_relset_1(B,k5_numbers,k1_numbers) )
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => k2_seq_1(k5_numbers,k1_numbers,B,D) = k5_bhsp_4(k3_asympt_1(C),D) )
                 => r1_xreal_0(k6_real_1(k3_series_1(A,k1_nat_1(C,np__1)),k1_nat_1(C,np__1)),k2_seq_1(k5_numbers,k1_numbers,B,A)) ) ) ) ) ) )).

fof(t34_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ~ ( k2_seq_1(k5_numbers,k1_numbers,B,np__0) = np__0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,np__0)
                   => k2_seq_1(k5_numbers,k1_numbers,B,C) = k4_real_1(C,k6_power(np__2,C)) ) )
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k2_seq_1(k5_numbers,k1_numbers,A,C) = k6_power(np__2,k11_newton(C)) )
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & v2_asympt_0(C)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ~ ( C = B
                      & r2_hidden(A,k7_asympt_0(C)) ) ) ) ) ) )).

fof(t35_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v2_asympt_0(A)
        & v6_asympt_0(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ~ ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( k4_nat_1(C,np__2) = np__0
                     => k2_seq_1(k5_numbers,k1_numbers,B,C) = np__1 )
                    & ( k4_nat_1(C,np__2) = np__1
                     => k2_seq_1(k5_numbers,k1_numbers,B,C) = C ) ) )
              & r2_hidden(B,k7_asympt_0(A)) ) ) ) )).

fof(d6_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v2_xreal_0(B)
            & m1_subset_1(B,k1_numbers) )
         => ! [C] :
              ( ( v2_xreal_0(C)
                & m1_subset_1(C,k1_numbers) )
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( ( A = np__0
                     => ( D = k7_asympt_1(A,B,C)
                      <=> D = np__0 ) )
                    & ( A != np__0
                     => ( D = k7_asympt_1(A,B,C)
                      <=> ? [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                            & ? [F] :
                                ( v1_funct_1(F)
                                & v1_funct_2(F,k5_numbers,k3_finseq_2(k1_numbers))
                                & m2_relset_1(F,k5_numbers,k3_finseq_2(k1_numbers))
                                & k1_nat_1(E,np__1) = A
                                & D = k4_finseq_4(k5_numbers,k1_numbers,k6_asympt_1(F,E),A)
                                & k6_asympt_1(F,np__0) = k12_finseq_1(k1_numbers,B)
                                & ! [G] :
                                    ( m2_subset_1(G,k1_numbers,k5_numbers)
                                   => ? [H] :
                                        ( m2_subset_1(H,k1_numbers,k5_numbers)
                                        & H = k2_int_1(k6_real_1(k1_nat_1(k1_nat_1(G,np__1),np__1),np__2))
                                        & k6_asympt_1(F,k1_nat_1(G,np__1)) = k8_finseq_1(k1_numbers,k6_asympt_1(F,G),k12_finseq_1(k1_numbers,k3_real_1(k4_real_1(np__4,k4_finseq_4(k5_numbers,k1_numbers,k6_asympt_1(F,G),H)),k4_real_1(C,k1_nat_1(k1_nat_1(G,np__1),np__1))))) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d7_asympt_1,axiom,(
    ! [A] :
      ( ( v2_xreal_0(A)
        & m1_subset_1(A,k1_numbers) )
     => ! [B] :
          ( ( v2_xreal_0(B)
            & m1_subset_1(B,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( C = k8_asympt_1(A,B)
              <=> ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k2_seq_1(k5_numbers,k1_numbers,C,D) = k7_asympt_1(D,A,B) ) ) ) ) ) )).

fof(t36_asympt_1,axiom,(
    ! [A] :
      ( ( v2_xreal_0(A)
        & m1_subset_1(A,k1_numbers) )
     => ! [B] :
          ( ( v2_xreal_0(B)
            & m1_subset_1(B,k1_numbers) )
         => v6_asympt_0(k8_asympt_1(A,B)) ) ) )).

fof(t37_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( ( r2_hidden(B,k9_asympt_1)
               => k2_seq_1(k5_numbers,k1_numbers,A,B) = B )
              & ( ~ r2_hidden(B,k9_asympt_1)
               => k2_seq_1(k5_numbers,k1_numbers,A,B) = k3_series_1(np__2,B) ) ) )
       => ( r2_hidden(A,k10_asympt_0(k3_asympt_1(np__1),k9_asympt_1))
          & ~ r2_hidden(A,k7_asympt_0(k3_asympt_1(np__1)))
          & v7_asympt_0(k3_asympt_1(np__1))
          & ~ v6_asympt_0(A) ) ) ) )).

fof(t38_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ~ ( k2_seq_1(k5_numbers,k1_numbers,A,np__0) = np__0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,np__0)
                   => k2_seq_1(k5_numbers,k1_numbers,A,C) = k3_power(C,k3_power(np__2,k1_int_1(k6_power(np__2,C)))) ) )
              & k2_seq_1(k5_numbers,k1_numbers,B,np__0) = np__0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,np__0)
                   => k2_seq_1(k5_numbers,k1_numbers,B,C) = k3_series_1(C,C) ) )
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & v4_asympt_0(C)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ~ ( C = B
                      & r2_hidden(A,k10_asympt_0(C,k9_asympt_1))
                      & ~ r2_hidden(A,k7_asympt_0(C))
                      & v6_asympt_0(A)
                      & v6_asympt_0(C)
                      & ~ r2_asympt_0(C,np__2) ) ) ) ) ) )).

fof(t39_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ~ ( ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ( r2_hidden(B,k9_asympt_1)
                 => k2_seq_1(k5_numbers,k1_numbers,A,B) = B )
                & ( ~ r2_hidden(B,k9_asympt_1)
                 => k2_seq_1(k5_numbers,k1_numbers,A,B) = k3_series_1(B,np__2) ) ) )
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & v4_asympt_0(B)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ~ ( B = A
                  & r2_hidden(k3_asympt_1(np__1),k10_asympt_0(B,k9_asympt_1))
                  & ~ r2_hidden(k3_asympt_1(np__1),k7_asympt_0(B))
                  & r2_hidden(k11_asympt_0(B,np__2),k5_asympt_0(B))
                  & v6_asympt_0(k3_asympt_1(np__1))
                  & ~ v6_asympt_0(B) ) ) ) ) )).

fof(d9_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( A != np__0
             => ( B = k10_asympt_1(A)
              <=> ? [C] :
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                    & r1_xreal_0(k11_newton(C),A)
                    & ~ r1_xreal_0(k11_newton(k1_nat_1(C,np__1)),A)
                    & B = k11_newton(C) ) ) )
            & ( A = np__0
             => ( B = k10_asympt_1(A)
              <=> B = np__0 ) ) ) ) ) )).

fof(t40_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ~ ( ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => k2_seq_1(k5_numbers,k1_numbers,A,B) = k10_asympt_1(B) )
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & v4_asympt_0(B)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ~ ( B = A
                  & v6_asympt_0(A)
                  & ! [C] :
                      ( m2_subset_1(C,k1_numbers,k5_numbers)
                     => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,k3_asympt_1(np__1),C)) )
                  & ~ v7_asympt_0(B) ) ) ) ) )).

fof(t41_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v2_asympt_0(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( A = k10_seq_1(k3_asympt_1(np__1),k4_asympt_1(np__1))
       => k12_asympt_0(k5_numbers,k7_asympt_0(A),k7_asympt_0(k3_asympt_1(np__1))) = k7_asympt_0(k3_asympt_1(np__1)) ) ) )).

fof(t42_asympt_1,axiom,(
    ? [A] :
      ( m1_fraenkel(A,k5_numbers,k1_numbers)
      & A = k6_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)),k3_asympt_1(np__1))
      & ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k3_asympt_1(k1_real_1(np__1)),B),k2_seq_1(k5_numbers,k1_numbers,k3_asympt_1(np__1),B)) )
      & ~ r2_hidden(k3_asympt_1(k1_real_1(np__1)),k14_asympt_0(A,k5_asympt_0(k4_asympt_1(np__1)))) ) )).

fof(t43_asympt_1,axiom,(
    ! [A] :
      ( ( ~ v3_xreal_0(A)
        & m1_subset_1(A,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & v2_asympt_0(B)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & v2_asympt_0(C)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( r2_hidden(B,k5_asympt_0(k2_asympt_0(C,A)))
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ~ ( ~ r1_xreal_0(D,np__0)
                              & ! [F] :
                                  ( m2_subset_1(F,k1_numbers,k5_numbers)
                                 => ( r1_xreal_0(E,F)
                                   => r1_xreal_0(D,k2_seq_1(k5_numbers,k1_numbers,C,F)) ) ) ) ) )
                  | r2_hidden(B,k5_asympt_0(C)) ) ) ) ) ) )).

fof(t44_asympt_1,axiom,(
    k3_series_1(np__2,np__2) = np__4 )).

fof(t45_asympt_1,axiom,(
    k3_series_1(np__2,np__3) = np__8 )).

fof(t46_asympt_1,axiom,(
    k3_series_1(np__2,np__4) = np__16 )).

fof(t47_asympt_1,axiom,(
    k3_series_1(np__2,np__5) = np__32 )).

fof(t48_asympt_1,axiom,(
    k3_series_1(np__2,np__6) = np__64 )).

fof(t49_asympt_1,axiom,(
    k3_series_1(np__2,np__12) = np__4096 )).

fof(t50_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__3,A)
          & r1_xreal_0(k7_square_1(A),k1_nat_1(k2_nat_1(np__2,A),np__1)) ) ) )).

fof(t51_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__10,A)
          & r1_xreal_0(k4_power(np__2,k5_real_1(A,np__1)),k7_square_1(k2_nat_1(np__2,A))) ) ) )).

fof(t52_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__9,A)
          & r1_xreal_0(k2_nat_1(np__2,k3_series_1(A,np__6)),k3_series_1(k1_nat_1(A,np__1),np__6)) ) ) )).

fof(t53_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__30,A)
          & r1_xreal_0(k3_series_1(np__2,A),k3_series_1(A,np__6)) ) ) )).

fof(t54_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ~ ( ~ r1_xreal_0(A,np__9)
          & r1_xreal_0(k4_power(np__2,A),k7_square_1(k4_real_1(np__2,A))) ) ) )).

fof(t55_asympt_1,axiom,(
    ? [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
      & ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r1_xreal_0(A,B)
              & r1_xreal_0(k5_real_1(k9_square_1(B),k6_power(np__2,B)),np__1) ) ) ) )).

fof(t56_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ~ ( ~ r1_xreal_0(A,np__0)
                  & ~ r1_xreal_0(C,np__0)
                  & C != np__1
                  & k4_power(A,B) != k4_power(C,k4_real_1(B,k6_power(C,A))) ) ) ) ) )).

fof(t57_asympt_1,axiom,(
    k11_newton(k1_nat_1(np__4,np__1)) = np__120 )).

fof(t58_asympt_1,axiom,(
    k3_series_1(np__5,np__5) = np__3125 )).

fof(t59_asympt_1,axiom,(
    k3_series_1(np__4,np__4) = np__256 )).

fof(t60_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ r1_xreal_0(k3_real_1(k5_real_1(k7_square_1(A),A),np__1),np__0) ) )).

fof(t61_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__2,A)
          & r1_xreal_0(k11_newton(A),np__1) ) ) )).

fof(t62_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(B,A)
           => r1_xreal_0(k11_newton(B),k11_newton(A)) ) ) ) )).

fof(t63_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__1,A)
          & ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ~ ( r1_xreal_0(k11_newton(B),A)
                  & ~ r1_xreal_0(k11_newton(k1_nat_1(B,np__1)),A)
                  & ! [C] :
                      ( m2_subset_1(C,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(k11_newton(C),A)
                       => ( r1_xreal_0(k11_newton(k1_nat_1(C,np__1)),A)
                          | C = B ) ) ) ) ) ) ) )).

fof(t64_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__2,A)
          & r1_xreal_0(A,k2_int_1(k6_real_1(A,np__2))) ) ) )).

fof(t65_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__3,A)
          & r1_xreal_0(k11_newton(A),A) ) ) )).

fof(t66_asympt_1,axiom,(
    v4_asympt_0(k10_seq_1(k3_asympt_1(np__1),k4_asympt_1(np__1))) )).

fof(t67_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__2,A)
          & r1_xreal_0(k3_series_1(np__2,A),k1_nat_1(A,np__1)) ) ) )).

fof(t68_asympt_1,axiom,(
    ! [A] :
      ( ( v1_asympt_0(A)
        & m1_subset_1(A,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( k2_seq_1(k5_numbers,k1_numbers,B,np__0) = np__0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,np__0)
                   => k2_seq_1(k5_numbers,k1_numbers,B,C) = k6_power(A,C) ) ) )
           => ( r1_xreal_0(A,np__1)
              | v4_asympt_0(B) ) ) ) ) )).

fof(t69_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v2_asympt_0(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & v2_asympt_0(B)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( r2_hidden(A,k5_asympt_0(B))
              & r2_hidden(B,k5_asympt_0(A)) )
          <=> k5_asympt_0(A) = k5_asympt_0(B) ) ) ) )).

fof(t70_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(np__0,C) )
               => ( r1_xreal_0(A,np__0)
                  | r1_xreal_0(k4_power(A,C),k4_power(B,C)) ) ) ) ) ) )).

fof(t71_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__4,A)
          & r1_xreal_0(k3_series_1(np__2,A),k1_nat_1(k2_nat_1(np__2,A),np__3)) ) ) )).

fof(t72_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__6,A)
          & r1_xreal_0(k3_series_1(np__2,A),k7_square_1(k1_nat_1(A,np__1))) ) ) )).

fof(t73_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ~ ( ~ r1_xreal_0(A,np__6)
          & r1_xreal_0(k4_power(np__2,A),k7_square_1(A)) ) ) )).

fof(t74_asympt_1,axiom,(
    ! [A] :
      ( ( v2_xreal_0(A)
        & m1_subset_1(A,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( k2_seq_1(k5_numbers,k1_numbers,B,np__0) = np__0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,np__0)
                   => k2_seq_1(k5_numbers,k1_numbers,B,C) = k6_power(np__2,k4_power(C,A)) ) ) )
           => ( v4_seq_2(k19_seq_1(B,k3_asympt_1(A)))
              & k2_seq_2(k19_seq_1(B,k3_asympt_1(A))) = np__0 ) ) ) ) )).

fof(t75_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ( ~ r1_xreal_0(A,np__0)
       => ( v4_seq_2(k19_seq_1(k2_asympt_1,k3_asympt_1(A)))
          & k2_seq_2(k19_seq_1(k2_asympt_1,k3_asympt_1(A))) = np__0 ) ) ) )).

fof(t76_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r1_xreal_0(C,B)
                 => r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,A,C)) ) )
           => r1_xreal_0(np__0,k5_bhsp_4(A,B)) ) ) ) )).

fof(t77_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_xreal_0(D,C)
                     => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,D),k2_seq_1(k5_numbers,k1_numbers,B,D)) ) )
               => r1_xreal_0(k5_bhsp_4(A,C),k5_bhsp_4(B,C)) ) ) ) ) )).

fof(t78_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( ( k2_seq_1(k5_numbers,k1_numbers,A,np__0) = np__0
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(C,np__0)
                   => k2_seq_1(k5_numbers,k1_numbers,A,C) = B ) ) )
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k5_bhsp_4(A,C) = k4_real_1(B,C) ) ) ) ) )).

fof(t79_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => k3_real_1(k6_bhsp_4(A,B,C),k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1))) = k6_bhsp_4(A,k1_nat_1(B,np__1),C) ) ) ) )).

fof(t80_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(k1_nat_1(C,np__1),D)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ( r1_xreal_0(k1_nat_1(C,np__1),E)
                              & r1_xreal_0(E,D) )
                           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,E),k2_seq_1(k5_numbers,k1_numbers,B,E)) ) ) )
                   => r1_xreal_0(k6_bhsp_4(A,D,C),k6_bhsp_4(B,D,C)) ) ) ) ) ) )).

fof(t81_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => r1_xreal_0(k2_int_1(k6_real_1(A,np__2)),A) ) )).

fof(t82_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( k2_seq_1(k5_numbers,k1_numbers,A,np__0) = np__0
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( ~ r1_xreal_0(D,np__0)
                       => k2_seq_1(k5_numbers,k1_numbers,A,D) = B ) ) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k6_bhsp_4(A,C,D) = k4_real_1(B,k5_real_1(C,D)) ) ) ) ) ) )).

fof(t83_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( ( v4_seq_2(A)
                      & k2_seq_2(A) = D
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(C,E)
                           => k2_seq_1(k5_numbers,k1_numbers,A,E) = k2_seq_1(k5_numbers,k1_numbers,B,E) ) ) )
                   => ( v4_seq_2(B)
                      & k2_seq_2(B) = D ) ) ) ) ) ) )).

fof(t84_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(np__1,A)
       => r1_xreal_0(k3_real_1(k5_real_1(k7_square_1(A),A),np__1),k7_square_1(A)) ) ) )).

fof(t85_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(np__1,A)
       => r1_xreal_0(k7_square_1(A),k4_real_1(np__2,k3_real_1(k5_real_1(k7_square_1(A),A),np__1))) ) ) )).

fof(t86_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ~ ( ~ r1_xreal_0(A,np__0)
          & ~ r1_xreal_0(np__1,A)
          & ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ? [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                  & r1_xreal_0(B,C)
                  & r1_xreal_0(k5_real_1(k4_real_1(C,k6_power(np__2,k3_real_1(np__1,A))),k4_real_1(np__8,k6_power(np__2,C))),k4_real_1(np__8,k6_power(np__2,C))) ) ) ) ) )).

fof(t87_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__10,A)
          & r1_xreal_0(k6_real_1(np__1,k4_power(np__2,k5_real_1(A,np__9))),k6_real_1(k3_series_1(np__2,k2_nat_1(np__2,A)),k11_newton(A))) ) ) )).

fof(t88_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(np__3,A)
       => r1_xreal_0(k5_real_1(A,np__1),k4_real_1(np__2,k5_real_1(A,np__2))) ) ) )).

fof(t89_asympt_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( r1_xreal_0(np__0,A)
       => k3_power(A,k6_real_1(np__1,np__2)) = k8_square_1(A) ) ) )).

fof(t90_asympt_1,axiom,(
    ? [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
      & ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r1_xreal_0(A,B)
              & r1_xreal_0(k5_real_1(B,k4_real_1(k9_square_1(B),k6_power(np__2,B))),k6_real_1(B,np__2)) ) ) ) )).

fof(t91_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k2_seq_1(k5_numbers,k1_numbers,A,B) = k4_power(k3_real_1(np__1,k6_real_1(np__1,k1_nat_1(B,np__1))),k1_nat_1(B,np__1)) )
       => v3_seqm_3(A) ) ) )).

fof(t92_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(np__1,A)
       => r1_xreal_0(k4_power(k6_real_1(k1_nat_1(A,np__1),A),A),k4_power(k6_real_1(k1_nat_1(A,np__2),k1_nat_1(A,np__1)),k1_nat_1(A,np__1))) ) ) )).

fof(t93_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => r1_xreal_0(k6_real_1(k8_newton(A,k1_nat_1(B,np__1)),k1_nat_1(B,np__1)),k8_newton(A,B)) ) ) ) )).

fof(t94_asympt_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k2_seq_1(k5_numbers,k1_numbers,A,B) = k6_power(np__2,k11_newton(B)) )
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k2_seq_1(k5_numbers,k1_numbers,A,B) = k5_bhsp_4(k2_asympt_1,B) ) ) ) )).

fof(t95_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(np__4,A)
       => r1_xreal_0(k2_nat_1(np__2,A),k4_real_1(A,k6_power(np__2,A))) ) ) )).

fof(t96_asympt_1,axiom,(
    ! [A] :
      ( ( v2_xreal_0(A)
        & m1_subset_1(A,k1_numbers) )
     => ! [B] :
          ( ( v2_xreal_0(B)
            & m1_subset_1(B,k1_numbers) )
         => ( k7_asympt_1(np__0,A,B) = np__0
            & k7_asympt_1(np__1,A,B) = A
            & ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ~ ( r1_xreal_0(np__2,C)
                    & ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ~ ( D = k2_int_1(k6_real_1(C,np__2))
                            & k7_asympt_1(C,A,B) = k3_real_1(k4_real_1(np__4,k7_asympt_1(D,A,B)),k4_real_1(B,C)) ) ) ) ) ) ) ) )).

fof(t97_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__2,A)
          & r1_xreal_0(k7_square_1(A),k1_nat_1(A,np__1)) ) ) )).

fof(t98_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__1,A)
          & r1_xreal_0(k5_real_1(k3_series_1(np__2,k1_nat_1(A,np__1)),k3_series_1(np__2,A)),np__1) ) ) )).

fof(t99_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( r1_xreal_0(np__2,A)
          & r2_hidden(k5_real_1(k3_series_1(np__2,A),np__1),k9_asympt_1) ) ) )).

fof(t100_asympt_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(np__1,B)
              & r1_xreal_0(k11_newton(A),B) )
           => ( r1_xreal_0(k11_newton(k1_nat_1(A,np__1)),B)
              | k10_asympt_1(B) = k11_newton(A) ) ) ) ) )).

fof(t101_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(np__1,C) )
               => ( r1_xreal_0(A,np__1)
                  | r1_xreal_0(k6_power(B,C),k6_power(A,C)) ) ) ) ) ) )).

fof(dt_k1_asympt_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers)
        & m1_subset_1(C,k1_numbers) )
     => ( v1_funct_1(k1_asympt_1(A,B,C))
        & v1_funct_2(k1_asympt_1(A,B,C),k5_numbers,k1_numbers)
        & m2_relset_1(k1_asympt_1(A,B,C),k5_numbers,k1_numbers) ) ) )).

fof(dt_k2_asympt_1,axiom,
    ( v1_funct_1(k2_asympt_1)
    & v1_funct_2(k2_asympt_1,k5_numbers,k1_numbers)
    & m2_relset_1(k2_asympt_1,k5_numbers,k1_numbers) )).

fof(dt_k3_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ( v1_funct_1(k3_asympt_1(A))
        & v1_funct_2(k3_asympt_1(A),k5_numbers,k1_numbers)
        & m2_relset_1(k3_asympt_1(A),k5_numbers,k1_numbers) ) ) )).

fof(dt_k4_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ( v1_funct_1(k4_asympt_1(A))
        & v1_funct_2(k4_asympt_1(A),k5_numbers,k1_numbers)
        & m2_relset_1(k4_asympt_1(A),k5_numbers,k1_numbers) ) ) )).

fof(dt_k5_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ( v1_funct_1(k5_asympt_1(A))
        & v1_funct_2(k5_asympt_1(A),k5_numbers,k1_numbers)
        & m2_relset_1(k5_asympt_1(A),k5_numbers,k1_numbers) ) ) )).

fof(dt_k6_asympt_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_finseq_2(k1_numbers))
        & m1_relset_1(A,k5_numbers,k3_finseq_2(k1_numbers))
        & m1_subset_1(B,k5_numbers) )
     => m2_finseq_1(k6_asympt_1(A,B),k1_numbers) ) )).

fof(redefinition_k6_asympt_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_finseq_2(k1_numbers))
        & m1_relset_1(A,k5_numbers,k3_finseq_2(k1_numbers))
        & m1_subset_1(B,k5_numbers) )
     => k6_asympt_1(A,B) = k1_funct_1(A,B) ) )).

fof(dt_k7_asympt_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k5_numbers)
        & v2_xreal_0(B)
        & m1_subset_1(B,k1_numbers)
        & v2_xreal_0(C)
        & m1_subset_1(C,k1_numbers) )
     => m1_subset_1(k7_asympt_1(A,B,C),k1_numbers) ) )).

fof(dt_k8_asympt_1,axiom,(
    ! [A,B] :
      ( ( v2_xreal_0(A)
        & m1_subset_1(A,k1_numbers)
        & v2_xreal_0(B)
        & m1_subset_1(B,k1_numbers) )
     => ( v1_funct_1(k8_asympt_1(A,B))
        & v1_funct_2(k8_asympt_1(A,B),k5_numbers,k1_numbers)
        & m2_relset_1(k8_asympt_1(A,B),k5_numbers,k1_numbers) ) ) )).

fof(dt_k9_asympt_1,axiom,
    ( ~ v1_xboole_0(k9_asympt_1)
    & m1_subset_1(k9_asympt_1,k1_zfmisc_1(k5_numbers)) )).

fof(dt_k10_asympt_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m2_subset_1(k10_asympt_1(A),k1_numbers,k5_numbers) ) )).

fof(d8_asympt_1,axiom,(
    k9_asympt_1 = a_0_0_asympt_1 )).

fof(fraenkel_a_0_0_asympt_1,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_asympt_1)
    <=> ? [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = k3_series_1(np__2,B) ) ) )).
%------------------------------------------------------------------------------