SET007 Axioms: SET007+110.ax


%------------------------------------------------------------------------------
% File     : SET007+110 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Limit of a Real Function at Infinity
% 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    : limfunc1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  175 (  17 unit)
%            Number of atoms       : 1490 (  97 equality)
%            Maximal formula depth :   17 (   9 average)
%            Number of connectives : 1466 ( 151 ~  ;  73  |; 674  &)
%                                         (  21 <=>; 547 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   39 (   1 propositional; 0-3 arity)
%            Number of functors    :   53 (   5 constant; 0-4 arity)
%            Number of variables   :  482 (   0 singleton; 400 !;  82 ?)
%            Maximal term depth    :    4 (   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(t1_limfunc1,axiom,(
    $true )).

fof(t2_limfunc1,axiom,(
    $true )).

fof(t3_limfunc1,axiom,(
    $true )).

fof(t4_limfunc1,axiom,(
    $true )).

fof(t5_limfunc1,axiom,(
    $true )).

fof(t6_limfunc1,axiom,(
    $true )).

fof(t7_limfunc1,axiom,(
    $true )).

fof(t8_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => r1_tarski(k4_limfunc1(B),k4_limfunc1(A)) ) ) ) )).

fof(t9_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => r1_tarski(k3_limfunc1(B),k3_limfunc1(A)) ) ) ) )).

fof(t10_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => r1_tarski(k4_limfunc1(A),k3_limfunc1(A)) ) )).

fof(t11_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => r1_tarski(k2_rcomp_1(A,B),k4_limfunc1(A)) ) ) )).

fof(t12_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => r1_tarski(k1_rcomp_1(A,B),k3_limfunc1(A)) ) ) )).

fof(t13_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => r1_tarski(k12_prob_1(A),k12_prob_1(B)) ) ) ) )).

fof(t14_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => r1_tarski(k2_limfunc1(A),k2_limfunc1(B)) ) ) ) )).

fof(t15_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => r1_tarski(k12_prob_1(A),k2_limfunc1(A)) ) )).

fof(t16_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => r1_tarski(k2_rcomp_1(A,B),k12_prob_1(B)) ) ) )).

fof(t17_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => r1_tarski(k1_rcomp_1(A,B),k2_limfunc1(B)) ) ) )).

fof(t18_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k5_subset_1(k1_numbers,k12_prob_1(A),k4_limfunc1(B)) = k2_rcomp_1(B,A) ) ) )).

fof(t19_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k5_subset_1(k1_numbers,k2_limfunc1(A),k3_limfunc1(B)) = k1_rcomp_1(B,A) ) ) )).

fof(t20_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,B)
               => ( r1_tarski(k2_rcomp_1(B,C),k4_limfunc1(A))
                  & r1_tarski(k1_rcomp_1(B,C),k3_limfunc1(A)) ) ) ) ) ) )).

fof(t21_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ~ r1_xreal_0(B,A)
               => r1_tarski(k1_rcomp_1(B,C),k4_limfunc1(A)) ) ) ) ) )).

fof(t22_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,B)
               => ( r1_tarski(k2_rcomp_1(C,A),k12_prob_1(B))
                  & r1_tarski(k1_rcomp_1(C,A),k2_limfunc1(B)) ) ) ) ) ) )).

fof(t23_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ~ r1_xreal_0(B,A)
               => r1_tarski(k1_rcomp_1(C,A),k12_prob_1(B)) ) ) ) ) )).

fof(t24_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( k4_xboole_0(k1_numbers,k4_limfunc1(A)) = k2_limfunc1(A)
        & k4_xboole_0(k1_numbers,k3_limfunc1(A)) = k12_prob_1(A)
        & k4_xboole_0(k1_numbers,k12_prob_1(A)) = k3_limfunc1(A)
        & k4_xboole_0(k1_numbers,k2_limfunc1(A)) = k4_limfunc1(A) ) ) )).

fof(t25_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( k4_xboole_0(k1_numbers,k2_rcomp_1(A,B)) = k4_subset_1(k1_numbers,k2_limfunc1(A),k3_limfunc1(B))
            & k4_xboole_0(k1_numbers,k1_rcomp_1(A,B)) = k4_subset_1(k1_numbers,k12_prob_1(A),k4_limfunc1(B)) ) ) ) )).

fof(t26_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v3_seqm_3(A)
         => v2_seq_2(A) )
        & ( v4_seqm_3(A)
         => v1_seq_2(A) ) ) ) )).

fof(t27_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v2_relat_1(A)
          & v4_seq_2(A)
          & k2_seq_2(A) = np__0
          & v3_seqm_3(A) )
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ~ r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) )).

fof(t28_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v2_relat_1(A)
          & v4_seq_2(A)
          & k2_seq_2(A) = np__0
          & v4_seqm_3(A) )
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),np__0) ) ) ) )).

fof(t29_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ~ ( v4_seq_2(A)
          & ~ r1_xreal_0(k2_seq_2(A),np__0)
          & ! [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(k2_seq_1(k5_numbers,k1_numbers,A,C),np__0) ) ) ) ) )).

fof(t30_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ~ ( v4_seq_2(A)
          & ~ r1_xreal_0(k2_seq_2(A),np__0)
          & ! [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(k2_seq_1(k5_numbers,k1_numbers,A,C),k6_real_1(k2_seq_2(A),np__2)) ) ) ) ) )).

fof(d4_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_limfunc1(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ? [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ~ ( r1_xreal_0(C,D)
                        & r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,D),B) ) ) ) ) ) ) )).

fof(d5_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_limfunc1(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ? [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ~ ( r1_xreal_0(C,D)
                        & r1_xreal_0(B,k2_seq_1(k5_numbers,k1_numbers,A,D)) ) ) ) ) ) ) )).

fof(t31_limfunc1,axiom,(
    $true )).

fof(t32_limfunc1,axiom,(
    $true )).

fof(t33_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ~ ( ( v1_limfunc1(A)
            | v2_limfunc1(A) )
          & ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ? [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                  & r1_xreal_0(B,C)
                  & ~ v2_relat_1(k1_seqm_3(A,C)) ) ) ) ) )).

fof(t34_limfunc1,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) )
         => ( ( v1_limfunc1(k1_seqm_3(B,A))
             => v1_limfunc1(B) )
            & ( v2_limfunc1(k1_seqm_3(B,A))
             => v2_limfunc1(B) ) ) ) ) )).

fof(t35_limfunc1,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) )
         => ( ( v1_limfunc1(A)
              & v1_limfunc1(B) )
           => v1_limfunc1(k9_seq_1(A,B)) ) ) ) )).

fof(t36_limfunc1,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) )
         => ( ( v1_limfunc1(A)
              & v2_seq_2(B) )
           => v1_limfunc1(k9_seq_1(A,B)) ) ) ) )).

fof(t37_limfunc1,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) )
         => ( ( v1_limfunc1(A)
              & v1_limfunc1(B) )
           => v1_limfunc1(k11_seq_1(A,B)) ) ) ) )).

fof(t38_limfunc1,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) )
         => ( ( v2_limfunc1(A)
              & v2_limfunc1(B) )
           => v2_limfunc1(k9_seq_1(A,B)) ) ) ) )).

fof(t39_limfunc1,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) )
         => ( ( v2_limfunc1(A)
              & v1_seq_2(B) )
           => v2_limfunc1(k9_seq_1(A,B)) ) ) ) )).

fof(t40_limfunc1,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)
         => ( ( v1_limfunc1(A)
             => ( r1_xreal_0(B,np__0)
                | v1_limfunc1(k14_seq_1(A,B)) ) )
            & ( v1_limfunc1(A)
             => ( r1_xreal_0(np__0,B)
                | v2_limfunc1(k14_seq_1(A,B)) ) )
            & ( ( v1_limfunc1(A)
                & B = np__0 )
             => ( k1_rfunct_2(k14_seq_1(A,B)) = k1_tarski(np__0)
                & v5_seqm_3(k14_seq_1(A,B)) ) ) ) ) ) )).

fof(t41_limfunc1,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)
         => ( ( v2_limfunc1(A)
             => ( r1_xreal_0(B,np__0)
                | v2_limfunc1(k14_seq_1(A,B)) ) )
            & ( v2_limfunc1(A)
             => ( r1_xreal_0(np__0,B)
                | v1_limfunc1(k14_seq_1(A,B)) ) )
            & ( ( v2_limfunc1(A)
                & B = np__0 )
             => ( k1_rfunct_2(k14_seq_1(A,B)) = k1_tarski(np__0)
                & v5_seqm_3(k14_seq_1(A,B)) ) ) ) ) ) )).

fof(t42_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v1_limfunc1(A)
         => v2_limfunc1(k17_seq_1(A)) )
        & ( v2_limfunc1(A)
         => v1_limfunc1(k17_seq_1(A)) ) ) ) )).

fof(t43_limfunc1,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) )
         => ( ( v2_seq_2(A)
              & v2_limfunc1(B) )
           => v1_limfunc1(k10_seq_1(A,B)) ) ) ) )).

fof(t44_limfunc1,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) )
         => ( ( v1_seq_2(A)
              & v1_limfunc1(B) )
           => v2_limfunc1(k10_seq_1(A,B)) ) ) ) )).

fof(t45_limfunc1,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) )
         => ( ( v1_limfunc1(A)
              & v4_seq_2(B) )
           => v1_limfunc1(k9_seq_1(A,B)) ) ) ) )).

fof(t46_limfunc1,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) )
         => ( ( v2_limfunc1(A)
              & v4_seq_2(B) )
           => v2_limfunc1(k9_seq_1(A,B)) ) ) ) )).

fof(t47_limfunc1,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) = B )
       => v1_limfunc1(A) ) ) )).

fof(t48_limfunc1,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) = k1_real_1(B) )
       => v2_limfunc1(A) ) ) )).

fof(t49_limfunc1,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) )
         => ( v1_limfunc1(A)
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => r1_xreal_0(C,k2_seq_1(k5_numbers,k1_numbers,B,D)) ) ) )
              | v1_limfunc1(k11_seq_1(A,B)) ) ) ) ) )).

fof(t50_limfunc1,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) )
         => ( v2_limfunc1(A)
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => r1_xreal_0(C,k2_seq_1(k5_numbers,k1_numbers,B,D)) ) ) )
              | v2_limfunc1(k11_seq_1(A,B)) ) ) ) ) )).

fof(t51_limfunc1,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) )
         => ( ( v2_limfunc1(A)
              & v2_limfunc1(B) )
           => v1_limfunc1(k11_seq_1(A,B)) ) ) ) )).

fof(t52_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v1_limfunc1(A)
          | v2_limfunc1(A) )
       => v1_limfunc1(k22_seq_1(A)) ) ) )).

fof(t53_limfunc1,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) )
         => ( ( v1_limfunc1(A)
              & m1_seqm_3(B,A) )
           => v1_limfunc1(B) ) ) ) )).

fof(t54_limfunc1,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) )
         => ( ( v2_limfunc1(A)
              & m1_seqm_3(B,A) )
           => v2_limfunc1(B) ) ) ) )).

fof(t55_limfunc1,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) )
         => ( ( v1_limfunc1(A)
              & v4_seq_2(B) )
           => ( r1_xreal_0(k2_seq_2(B),np__0)
              | v1_limfunc1(k11_seq_1(A,B)) ) ) ) ) )).

fof(t56_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v3_seqm_3(A)
       => ( v1_seq_2(A)
          | v1_limfunc1(A) ) ) ) )).

fof(t57_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v4_seqm_3(A)
       => ( v2_seq_2(A)
          | v2_limfunc1(A) ) ) ) )).

fof(t58_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_seqm_3(A)
       => ( v1_seq_2(A)
          | v1_limfunc1(A) ) ) ) )).

fof(t59_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v2_seqm_3(A)
       => ( v2_seq_2(A)
          | v2_limfunc1(A) ) ) ) )).

fof(t60_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ~ ( v6_seqm_3(A)
          & ~ v4_seq_2(A)
          & ~ v1_limfunc1(A)
          & ~ v2_limfunc1(A) ) ) )).

fof(t61_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v1_limfunc1(A)
          | v2_limfunc1(A) )
       => ( v4_seq_2(k18_seq_1(A))
          & k2_seq_2(k18_seq_1(A)) = np__0 ) ) ) )).

fof(t62_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v2_relat_1(A)
          & v4_seq_2(A)
          & k2_seq_2(A) = np__0 )
       => ( ! [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(k2_seq_1(k5_numbers,k1_numbers,A,C),np__0) ) )
          | v1_limfunc1(k18_seq_1(A)) ) ) ) )).

fof(t63_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v2_relat_1(A)
          & v4_seq_2(A)
          & k2_seq_2(A) = np__0 )
       => ( ! [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(np__0,k2_seq_1(k5_numbers,k1_numbers,A,C)) ) )
          | v2_limfunc1(k18_seq_1(A)) ) ) ) )).

fof(t64_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v2_relat_1(A)
          & v4_seq_2(A)
          & k2_seq_2(A) = np__0
          & v3_seqm_3(A) )
       => v2_limfunc1(k18_seq_1(A)) ) ) )).

fof(t65_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v2_relat_1(A)
          & v4_seq_2(A)
          & k2_seq_2(A) = np__0
          & v4_seqm_3(A) )
       => v1_limfunc1(k18_seq_1(A)) ) ) )).

fof(t66_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v2_relat_1(A)
          & v4_seq_2(A)
          & k2_seq_2(A) = np__0
          & v1_seqm_3(A) )
       => v2_limfunc1(k18_seq_1(A)) ) ) )).

fof(t67_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v2_relat_1(A)
          & v4_seq_2(A)
          & k2_seq_2(A) = np__0
          & v2_seqm_3(A) )
       => v1_limfunc1(k18_seq_1(A)) ) ) )).

fof(t68_limfunc1,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) )
         => ( ( v3_seq_2(A)
              & v2_relat_1(B) )
           => ( ( ~ v1_limfunc1(B)
                & ~ v2_limfunc1(B) )
              | ( v4_seq_2(k19_seq_1(A,B))
                & k2_seq_2(k19_seq_1(A,B)) = np__0 ) ) ) ) ) )).

fof(t69_limfunc1,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) )
         => ( ( v1_limfunc1(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,B,C)) ) )
           => v1_limfunc1(B) ) ) ) )).

fof(t70_limfunc1,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) )
         => ( ( v2_limfunc1(A)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,C),k2_seq_1(k5_numbers,k1_numbers,A,C)) ) )
           => v2_limfunc1(B) ) ) ) )).

fof(d6_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v3_limfunc1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(C,B)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
          & ? [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) )
                 => ( ( v1_limfunc1(C)
                      & r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,A)) )
                   => ( v4_seq_2(k2_rfunct_2(A,C))
                      & k2_seq_2(k2_rfunct_2(A,C)) = B ) ) ) ) ) ) ) )).

fof(d7_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v4_limfunc1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(C,B)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ( ( v1_limfunc1(B)
                  & r1_tarski(k1_rfunct_2(B),k4_relset_1(k1_numbers,k1_numbers,A)) )
               => v1_limfunc1(k2_rfunct_2(A,B)) ) ) ) ) ) )).

fof(d8_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v5_limfunc1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(C,B)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ( ( v1_limfunc1(B)
                  & r1_tarski(k1_rfunct_2(B),k4_relset_1(k1_numbers,k1_numbers,A)) )
               => v2_limfunc1(k2_rfunct_2(A,B)) ) ) ) ) ) )).

fof(d9_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v6_limfunc1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(B,C)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
          & ? [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) )
                 => ( ( v2_limfunc1(C)
                      & r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,A)) )
                   => ( v4_seq_2(k2_rfunct_2(A,C))
                      & k2_seq_2(k2_rfunct_2(A,C)) = B ) ) ) ) ) ) ) )).

fof(d10_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v7_limfunc1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(B,C)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ( ( v2_limfunc1(B)
                  & r1_tarski(k1_rfunct_2(B),k4_relset_1(k1_numbers,k1_numbers,A)) )
               => v1_limfunc1(k2_rfunct_2(A,B)) ) ) ) ) ) )).

fof(d11_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v8_limfunc1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(B,C)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k1_numbers)
                & m2_relset_1(B,k5_numbers,k1_numbers) )
             => ( ( v2_limfunc1(B)
                  & r1_tarski(k1_rfunct_2(B),k4_relset_1(k1_numbers,k1_numbers,A)) )
               => v2_limfunc1(k2_rfunct_2(A,B)) ) ) ) ) ) )).

fof(t71_limfunc1,axiom,(
    $true )).

fof(t72_limfunc1,axiom,(
    $true )).

fof(t73_limfunc1,axiom,(
    $true )).

fof(t74_limfunc1,axiom,(
    $true )).

fof(t75_limfunc1,axiom,(
    $true )).

fof(t76_limfunc1,axiom,(
    $true )).

fof(t77_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v3_limfunc1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(C,B)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
          & ? [B] :
              ( m1_subset_1(B,k1_numbers)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => ? [E] :
                              ( m1_subset_1(E,k1_numbers)
                              & ~ r1_xreal_0(E,D)
                              & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,A))
                              & r1_xreal_0(C,k18_complex1(k5_real_1(k2_seq_1(k1_numbers,k1_numbers,A,E),B))) ) ) ) ) ) ) ) ) )).

fof(t78_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v6_limfunc1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(B,C)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
          & ? [B] :
              ( m1_subset_1(B,k1_numbers)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => ? [E] :
                              ( m1_subset_1(E,k1_numbers)
                              & ~ r1_xreal_0(D,E)
                              & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,A))
                              & r1_xreal_0(C,k18_complex1(k5_real_1(k2_seq_1(k1_numbers,k1_numbers,A,E),B))) ) ) ) ) ) ) ) ) )).

fof(t79_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v4_limfunc1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(C,B)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,C)
                          & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,A))
                          & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),B) ) ) ) ) ) ) ) )).

fof(t80_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v5_limfunc1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(C,B)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,C)
                          & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,A))
                          & r1_xreal_0(B,k2_seq_1(k1_numbers,k1_numbers,A,D)) ) ) ) ) ) ) ) )).

fof(t81_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v7_limfunc1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(B,C)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(C,D)
                          & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,A))
                          & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),B) ) ) ) ) ) ) ) )).

fof(t82_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v8_limfunc1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(B,C)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(C,D)
                          & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,A))
                          & r1_xreal_0(B,k2_seq_1(k1_numbers,k1_numbers,A,D)) ) ) ) ) ) ) ) )).

fof(t83_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v4_limfunc1(A)
              & v4_limfunc1(B)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(D,C)
                      & r2_hidden(D,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_relset_1(k1_numbers,k1_numbers,B))) ) ) )
           => ( v4_limfunc1(k6_seq_1(k1_numbers,k1_numbers,A,B))
              & v4_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t84_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v5_limfunc1(A)
              & v5_limfunc1(B)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(D,C)
                      & r2_hidden(D,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_relset_1(k1_numbers,k1_numbers,B))) ) ) )
           => ( v5_limfunc1(k6_seq_1(k1_numbers,k1_numbers,A,B))
              & v4_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t85_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v7_limfunc1(A)
              & v7_limfunc1(B)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(C,D)
                      & r2_hidden(D,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_relset_1(k1_numbers,k1_numbers,B))) ) ) )
           => ( v7_limfunc1(k6_seq_1(k1_numbers,k1_numbers,A,B))
              & v7_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t86_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v8_limfunc1(A)
              & v8_limfunc1(B)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(C,D)
                      & r2_hidden(D,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_relset_1(k1_numbers,k1_numbers,B))) ) ) )
           => ( v8_limfunc1(k6_seq_1(k1_numbers,k1_numbers,A,B))
              & v7_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t87_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v4_limfunc1(A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(D,C)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ r2_rfunct_1(B,k4_limfunc1(C)) )
              | v4_limfunc1(k6_seq_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t88_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v4_limfunc1(A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(D,C)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(C,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ( r2_hidden(E,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_limfunc1(D)))
                               => r1_xreal_0(C,k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) ) )
              | v4_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t89_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v7_limfunc1(A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(C,D)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ r2_rfunct_1(B,k12_prob_1(C)) )
              | v7_limfunc1(k6_seq_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t90_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v7_limfunc1(A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(C,D)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(C,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ( r2_hidden(E,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k12_prob_1(D)))
                               => r1_xreal_0(C,k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) ) )
              | v7_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t91_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( ( v4_limfunc1(A)
             => ( r1_xreal_0(B,np__0)
                | v4_limfunc1(k13_seq_1(k1_numbers,k1_numbers,A,B)) ) )
            & ( v4_limfunc1(A)
             => ( r1_xreal_0(np__0,B)
                | v5_limfunc1(k13_seq_1(k1_numbers,k1_numbers,A,B)) ) )
            & ( v5_limfunc1(A)
             => ( r1_xreal_0(B,np__0)
                | v5_limfunc1(k13_seq_1(k1_numbers,k1_numbers,A,B)) ) )
            & ( v5_limfunc1(A)
             => ( r1_xreal_0(np__0,B)
                | v4_limfunc1(k13_seq_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) ) )).

fof(t92_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( ( v7_limfunc1(A)
             => ( r1_xreal_0(B,np__0)
                | v7_limfunc1(k13_seq_1(k1_numbers,k1_numbers,A,B)) ) )
            & ( v7_limfunc1(A)
             => ( r1_xreal_0(np__0,B)
                | v8_limfunc1(k13_seq_1(k1_numbers,k1_numbers,A,B)) ) )
            & ( v8_limfunc1(A)
             => ( r1_xreal_0(B,np__0)
                | v8_limfunc1(k13_seq_1(k1_numbers,k1_numbers,A,B)) ) )
            & ( v8_limfunc1(A)
             => ( r1_xreal_0(np__0,B)
                | v7_limfunc1(k13_seq_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) ) )).

fof(t93_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v4_limfunc1(A)
          | v5_limfunc1(A) )
       => v4_limfunc1(k21_seq_1(k1_numbers,k1_numbers,A)) ) ) )).

fof(t94_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v7_limfunc1(A)
          | v8_limfunc1(A) )
       => v7_limfunc1(k21_seq_1(k1_numbers,k1_numbers,A)) ) ) )).

fof(t95_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ? [C] :
                ( m1_subset_1(C,k1_numbers)
                & ~ r1_xreal_0(C,B)
                & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ ( r3_rfunct_2(A,k4_limfunc1(B))
                  & ~ r1_rfunct_1(A,k4_limfunc1(B)) ) )
          | v4_limfunc1(A) ) ) ) )).

fof(t96_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ? [C] :
                ( m1_subset_1(C,k1_numbers)
                & ~ r1_xreal_0(C,B)
                & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ ( r1_rfunct_2(A,k4_limfunc1(B))
                  & ~ r1_rfunct_1(A,k4_limfunc1(B)) ) )
          | v4_limfunc1(A) ) ) ) )).

fof(t97_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ? [C] :
                ( m1_subset_1(C,k1_numbers)
                & ~ r1_xreal_0(C,B)
                & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ ( r4_rfunct_2(A,k4_limfunc1(B))
                  & ~ r2_rfunct_1(A,k4_limfunc1(B)) ) )
          | v5_limfunc1(A) ) ) ) )).

fof(t98_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ? [C] :
                ( m1_subset_1(C,k1_numbers)
                & ~ r1_xreal_0(C,B)
                & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ ( r2_rfunct_2(A,k4_limfunc1(B))
                  & ~ r2_rfunct_1(A,k4_limfunc1(B)) ) )
          | v5_limfunc1(A) ) ) ) )).

fof(t99_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ? [C] :
                ( m1_subset_1(C,k1_numbers)
                & ~ r1_xreal_0(B,C)
                & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ ( r4_rfunct_2(A,k12_prob_1(B))
                  & ~ r1_rfunct_1(A,k12_prob_1(B)) ) )
          | v7_limfunc1(A) ) ) ) )).

fof(t100_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ? [C] :
                ( m1_subset_1(C,k1_numbers)
                & ~ r1_xreal_0(B,C)
                & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ ( r2_rfunct_2(A,k12_prob_1(B))
                  & ~ r1_rfunct_1(A,k12_prob_1(B)) ) )
          | v7_limfunc1(A) ) ) ) )).

fof(t101_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ? [C] :
                ( m1_subset_1(C,k1_numbers)
                & ~ r1_xreal_0(B,C)
                & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ ( r3_rfunct_2(A,k12_prob_1(B))
                  & ~ r2_rfunct_1(A,k12_prob_1(B)) ) )
          | v8_limfunc1(A) ) ) ) )).

fof(t102_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ? [C] :
                ( m1_subset_1(C,k1_numbers)
                & ~ r1_xreal_0(B,C)
                & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ ( r1_rfunct_2(A,k12_prob_1(B))
                  & ~ r2_rfunct_1(A,k12_prob_1(B)) ) )
          | v8_limfunc1(A) ) ) ) )).

fof(t103_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v4_limfunc1(A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(D,C)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,B)) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_limfunc1(C)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => ( r2_hidden(D,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_limfunc1(C)))
                           => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k2_seq_1(k1_numbers,k1_numbers,B,D)) ) ) ) )
              | v4_limfunc1(B) ) ) ) ) )).

fof(t104_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v5_limfunc1(A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(D,C)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,B)) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_limfunc1(C)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => ( r2_hidden(D,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_limfunc1(C)))
                           => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,D),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) ) ) )
              | v5_limfunc1(B) ) ) ) ) )).

fof(t105_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v7_limfunc1(A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(C,D)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,B)) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k12_prob_1(C)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => ( r2_hidden(D,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k12_prob_1(C)))
                           => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k2_seq_1(k1_numbers,k1_numbers,B,D)) ) ) ) )
              | v7_limfunc1(B) ) ) ) ) )).

fof(t106_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v8_limfunc1(A)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(C,D)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,B)) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k12_prob_1(C)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => ( r2_hidden(D,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k12_prob_1(C)))
                           => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,D),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) ) ) )
              | v8_limfunc1(B) ) ) ) ) )).

fof(t107_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( v4_limfunc1(A)
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( r1_tarski(k4_limfunc1(C),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_relset_1(k1_numbers,k1_numbers,A)))
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => ( r2_hidden(D,k4_limfunc1(C))
                           => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k2_seq_1(k1_numbers,k1_numbers,B,D)) ) ) ) )
              | v4_limfunc1(B) ) ) ) ) )).

fof(t108_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( v5_limfunc1(A)
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( r1_tarski(k4_limfunc1(C),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_relset_1(k1_numbers,k1_numbers,A)))
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => ( r2_hidden(D,k4_limfunc1(C))
                           => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,D),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) ) ) )
              | v5_limfunc1(B) ) ) ) ) )).

fof(t109_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( v7_limfunc1(A)
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( r1_tarski(k12_prob_1(C),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_relset_1(k1_numbers,k1_numbers,A)))
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => ( r2_hidden(D,k12_prob_1(C))
                           => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k2_seq_1(k1_numbers,k1_numbers,B,D)) ) ) ) )
              | v7_limfunc1(B) ) ) ) ) )).

fof(t110_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( v8_limfunc1(A)
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( r1_tarski(k12_prob_1(C),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_relset_1(k1_numbers,k1_numbers,A)))
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => ( r2_hidden(D,k12_prob_1(C))
                           => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,D),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) ) ) )
              | v8_limfunc1(B) ) ) ) ) )).

fof(d12_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v3_limfunc1(A)
       => ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ( B = k5_limfunc1(A)
            <=> ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ( ( v1_limfunc1(C)
                      & r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,A)) )
                   => ( v4_seq_2(k2_rfunct_2(A,C))
                      & k2_seq_2(k2_rfunct_2(A,C)) = B ) ) ) ) ) ) ) )).

fof(d13_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v6_limfunc1(A)
       => ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ( B = k6_limfunc1(A)
            <=> ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ( ( v2_limfunc1(C)
                      & r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,A)) )
                   => ( v4_seq_2(k2_rfunct_2(A,C))
                      & k2_seq_2(k2_rfunct_2(A,C)) = B ) ) ) ) ) ) ) )).

fof(t111_limfunc1,axiom,(
    $true )).

fof(t112_limfunc1,axiom,(
    $true )).

fof(t113_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( v6_limfunc1(A)
           => ( k6_limfunc1(A) = B
            <=> ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => ? [E] :
                              ( m1_subset_1(E,k1_numbers)
                              & ~ r1_xreal_0(D,E)
                              & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,A))
                              & r1_xreal_0(C,k18_complex1(k5_real_1(k2_seq_1(k1_numbers,k1_numbers,A,E),B))) ) ) ) ) ) ) ) ) )).

fof(t114_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( v3_limfunc1(A)
           => ( k5_limfunc1(A) = B
            <=> ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => ? [E] :
                              ( m1_subset_1(E,k1_numbers)
                              & ~ r1_xreal_0(E,D)
                              & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,A))
                              & r1_xreal_0(C,k18_complex1(k5_real_1(k2_seq_1(k1_numbers,k1_numbers,A,E),B))) ) ) ) ) ) ) ) ) )).

fof(t115_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( v3_limfunc1(A)
           => ( v3_limfunc1(k13_seq_1(k1_numbers,k1_numbers,A,B))
              & k5_limfunc1(k13_seq_1(k1_numbers,k1_numbers,A,B)) = k4_real_1(B,k5_limfunc1(A)) ) ) ) ) )).

fof(t116_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v3_limfunc1(A)
       => ( v3_limfunc1(k16_seq_1(k1_numbers,k1_numbers,A))
          & k5_limfunc1(k16_seq_1(k1_numbers,k1_numbers,A)) = k1_real_1(k5_limfunc1(A)) ) ) ) )).

fof(t117_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v3_limfunc1(A)
              & v3_limfunc1(B)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(D,C)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( v3_limfunc1(k6_seq_1(k1_numbers,k1_numbers,A,B))
              & k5_limfunc1(k6_seq_1(k1_numbers,k1_numbers,A,B)) = k3_real_1(k5_limfunc1(A),k5_limfunc1(B)) ) ) ) ) )).

fof(t118_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v3_limfunc1(A)
              & v3_limfunc1(B)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(D,C)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( v3_limfunc1(k7_seq_1(k1_numbers,k1_numbers,A,B))
              & k5_limfunc1(k7_seq_1(k1_numbers,k1_numbers,A,B)) = k5_real_1(k5_limfunc1(A),k5_limfunc1(B)) ) ) ) ) )).

fof(t119_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v3_limfunc1(A)
          & k11_relset_1(k1_numbers,k1_numbers,A,k1_tarski(np__0)) = k1_xboole_0 )
       => ( k5_limfunc1(A) = np__0
          | ( v3_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A))
            & k5_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) = k2_real_1(k5_limfunc1(A)) ) ) ) ) )).

fof(t120_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v3_limfunc1(A)
       => ( v3_limfunc1(k21_seq_1(k1_numbers,k1_numbers,A))
          & k5_limfunc1(k21_seq_1(k1_numbers,k1_numbers,A)) = k18_complex1(k5_limfunc1(A)) ) ) ) )).

fof(t121_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v3_limfunc1(A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(C,B)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A))
                  & k2_seq_1(k1_numbers,k1_numbers,A,C) != np__0 ) ) )
       => ( k5_limfunc1(A) = np__0
          | ( v3_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A))
            & k5_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) = k2_real_1(k5_limfunc1(A)) ) ) ) ) )).

fof(t122_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v3_limfunc1(A)
              & v3_limfunc1(B)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(D,C)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( v3_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B))
              & k5_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B)) = k4_real_1(k5_limfunc1(A),k5_limfunc1(B)) ) ) ) ) )).

fof(t123_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v3_limfunc1(A)
              & v3_limfunc1(B)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(D,C)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( k5_limfunc1(B) = np__0
              | ( v3_limfunc1(k2_rfunct_1(k1_numbers,k1_numbers,A,B))
                & k5_limfunc1(k2_rfunct_1(k1_numbers,k1_numbers,A,B)) = k6_real_1(k5_limfunc1(A),k5_limfunc1(B)) ) ) ) ) ) )).

fof(t124_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( v6_limfunc1(A)
           => ( v6_limfunc1(k13_seq_1(k1_numbers,k1_numbers,A,B))
              & k6_limfunc1(k13_seq_1(k1_numbers,k1_numbers,A,B)) = k4_real_1(B,k6_limfunc1(A)) ) ) ) ) )).

fof(t125_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v6_limfunc1(A)
       => ( v6_limfunc1(k16_seq_1(k1_numbers,k1_numbers,A))
          & k6_limfunc1(k16_seq_1(k1_numbers,k1_numbers,A)) = k1_real_1(k6_limfunc1(A)) ) ) ) )).

fof(t126_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v6_limfunc1(A)
              & v6_limfunc1(B)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(C,D)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( v6_limfunc1(k6_seq_1(k1_numbers,k1_numbers,A,B))
              & k6_limfunc1(k6_seq_1(k1_numbers,k1_numbers,A,B)) = k3_real_1(k6_limfunc1(A),k6_limfunc1(B)) ) ) ) ) )).

fof(t127_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v6_limfunc1(A)
              & v6_limfunc1(B)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(C,D)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( v6_limfunc1(k7_seq_1(k1_numbers,k1_numbers,A,B))
              & k6_limfunc1(k7_seq_1(k1_numbers,k1_numbers,A,B)) = k5_real_1(k6_limfunc1(A),k6_limfunc1(B)) ) ) ) ) )).

fof(t128_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v6_limfunc1(A)
          & k11_relset_1(k1_numbers,k1_numbers,A,k1_tarski(np__0)) = k1_xboole_0 )
       => ( k6_limfunc1(A) = np__0
          | ( v6_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A))
            & k6_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) = k2_real_1(k6_limfunc1(A)) ) ) ) ) )).

fof(t129_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v6_limfunc1(A)
       => ( v6_limfunc1(k21_seq_1(k1_numbers,k1_numbers,A))
          & k6_limfunc1(k21_seq_1(k1_numbers,k1_numbers,A)) = k18_complex1(k6_limfunc1(A)) ) ) ) )).

fof(t130_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v6_limfunc1(A)
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(B,C)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A))
                  & k2_seq_1(k1_numbers,k1_numbers,A,C) != np__0 ) ) )
       => ( k6_limfunc1(A) = np__0
          | ( v6_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A))
            & k6_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) = k2_real_1(k6_limfunc1(A)) ) ) ) ) )).

fof(t131_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v6_limfunc1(A)
              & v6_limfunc1(B)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(C,D)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( v6_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B))
              & k6_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B)) = k4_real_1(k6_limfunc1(A),k6_limfunc1(B)) ) ) ) ) )).

fof(t132_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v6_limfunc1(A)
              & v6_limfunc1(B)
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(C,D)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( k6_limfunc1(B) = np__0
              | ( v6_limfunc1(k2_rfunct_1(k1_numbers,k1_numbers,A,B))
                & k6_limfunc1(k2_rfunct_1(k1_numbers,k1_numbers,A,B)) = k6_real_1(k6_limfunc1(A),k6_limfunc1(B)) ) ) ) ) ) )).

fof(t133_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v3_limfunc1(A)
              & k5_limfunc1(A) = np__0
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(D,C)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ r3_rfunct_1(B,k4_limfunc1(C)) )
              | ( v3_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B))
                & k5_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B)) = np__0 ) ) ) ) ) )).

fof(t134_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v6_limfunc1(A)
              & k6_limfunc1(A) = np__0
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & ~ r1_xreal_0(C,D)
                      & r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ r3_rfunct_1(B,k12_prob_1(C)) )
              | ( v6_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B))
                & k6_limfunc1(k8_seq_1(k1_numbers,k1_numbers,A,B)) = np__0 ) ) ) ) ) )).

fof(t135_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,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) )
             => ( ( v3_limfunc1(A)
                  & v3_limfunc1(B)
                  & k5_limfunc1(A) = k5_limfunc1(B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ? [E] :
                          ( m1_subset_1(E,k1_numbers)
                          & ~ r1_xreal_0(E,D)
                          & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,C)) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ( ( r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(D)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_limfunc1(D)))
                              & r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,C),k4_limfunc1(D)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(D))) )
                            | ( r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_limfunc1(D)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(D)))
                              & r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,C),k4_limfunc1(D)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_limfunc1(D))) ) )
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ( r2_hidden(E,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,C),k4_limfunc1(D)))
                               => ( r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,E),k2_seq_1(k1_numbers,k1_numbers,C,E))
                                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,E),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) ) )
                  | ( v3_limfunc1(C)
                    & k5_limfunc1(C) = k5_limfunc1(A) ) ) ) ) ) ) )).

fof(t136_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,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) )
             => ( ( v3_limfunc1(A)
                  & v3_limfunc1(B)
                  & k5_limfunc1(A) = k5_limfunc1(B) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( r1_tarski(k4_limfunc1(D),k5_subset_1(k1_numbers,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_relset_1(k1_numbers,k1_numbers,B)),k4_relset_1(k1_numbers,k1_numbers,C)))
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ( r2_hidden(E,k4_limfunc1(D))
                               => ( r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,E),k2_seq_1(k1_numbers,k1_numbers,C,E))
                                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,E),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) ) )
                  | ( v3_limfunc1(C)
                    & k5_limfunc1(C) = k5_limfunc1(A) ) ) ) ) ) ) )).

fof(t137_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,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) )
             => ( ( v6_limfunc1(A)
                  & v6_limfunc1(B)
                  & k6_limfunc1(A) = k6_limfunc1(B)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ? [E] :
                          ( m1_subset_1(E,k1_numbers)
                          & ~ r1_xreal_0(D,E)
                          & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,C)) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ( ( r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(D)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k12_prob_1(D)))
                              & r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,C),k12_prob_1(D)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(D))) )
                            | ( r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k12_prob_1(D)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(D)))
                              & r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,C),k12_prob_1(D)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k12_prob_1(D))) ) )
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ( r2_hidden(E,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,C),k12_prob_1(D)))
                               => ( r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,E),k2_seq_1(k1_numbers,k1_numbers,C,E))
                                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,E),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) ) )
                  | ( v6_limfunc1(C)
                    & k6_limfunc1(C) = k6_limfunc1(A) ) ) ) ) ) ) )).

fof(t138_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,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) )
             => ( ( v6_limfunc1(A)
                  & v6_limfunc1(B)
                  & k6_limfunc1(A) = k6_limfunc1(B) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( r1_tarski(k12_prob_1(D),k5_subset_1(k1_numbers,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_relset_1(k1_numbers,k1_numbers,B)),k4_relset_1(k1_numbers,k1_numbers,C)))
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ( r2_hidden(E,k12_prob_1(D))
                               => ( r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,E),k2_seq_1(k1_numbers,k1_numbers,C,E))
                                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,E),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) ) )
                  | ( v6_limfunc1(C)
                    & k6_limfunc1(C) = k6_limfunc1(A) ) ) ) ) ) ) )).

fof(t139_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v3_limfunc1(A)
              & v3_limfunc1(B) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( ~ ( r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_limfunc1(C)))
                        & ! [D] :
                            ( m1_subset_1(D,k1_numbers)
                           => ( r2_hidden(D,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
                             => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k2_seq_1(k1_numbers,k1_numbers,B,D)) ) ) )
                    & ~ ( r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_limfunc1(C)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
                        & ! [D] :
                            ( m1_subset_1(D,k1_numbers)
                           => ( r2_hidden(D,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_limfunc1(C)))
                             => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k2_seq_1(k1_numbers,k1_numbers,B,D)) ) ) ) ) )
              | r1_xreal_0(k5_limfunc1(A),k5_limfunc1(B)) ) ) ) ) )).

fof(t140_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( v6_limfunc1(A)
              & v6_limfunc1(B) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ( ~ ( r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k12_prob_1(C)))
                        & ! [D] :
                            ( m1_subset_1(D,k1_numbers)
                           => ( r2_hidden(D,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
                             => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k2_seq_1(k1_numbers,k1_numbers,B,D)) ) ) )
                    & ~ ( r1_tarski(k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k12_prob_1(C)),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
                        & ! [D] :
                            ( m1_subset_1(D,k1_numbers)
                           => ( r2_hidden(D,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k12_prob_1(C)))
                             => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k2_seq_1(k1_numbers,k1_numbers,B,D)) ) ) ) ) )
              | r1_xreal_0(k6_limfunc1(A),k6_limfunc1(B)) ) ) ) ) )).

fof(t141_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ? [C] :
                ( m1_subset_1(C,k1_numbers)
                & ~ r1_xreal_0(C,B)
                & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A))
                & k2_seq_1(k1_numbers,k1_numbers,A,C) != np__0 ) )
       => ( ( ~ v4_limfunc1(A)
            & ~ v5_limfunc1(A) )
          | ( v3_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A))
            & k5_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) = np__0 ) ) ) ) )).

fof(t142_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ? [C] :
                ( m1_subset_1(C,k1_numbers)
                & ~ r1_xreal_0(B,C)
                & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A))
                & k2_seq_1(k1_numbers,k1_numbers,A,C) != np__0 ) )
       => ( ( ~ v7_limfunc1(A)
            & ~ v8_limfunc1(A) )
          | ( v6_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A))
            & k6_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) = np__0 ) ) ) ) )).

fof(t143_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v3_limfunc1(A)
          & k5_limfunc1(A) = np__0
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(C,B)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A))
                  & k2_seq_1(k1_numbers,k1_numbers,A,C) != np__0 ) ) )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & r2_hidden(C,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(B)))
                  & ~ r1_xreal_0(np__0,k2_seq_1(k1_numbers,k1_numbers,A,C)) ) )
          | v4_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).

fof(t144_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v3_limfunc1(A)
          & k5_limfunc1(A) = np__0
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(C,B)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A))
                  & k2_seq_1(k1_numbers,k1_numbers,A,C) != np__0 ) ) )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & r2_hidden(C,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(B)))
                  & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,C),np__0) ) )
          | v5_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).

fof(t145_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v6_limfunc1(A)
          & k6_limfunc1(A) = np__0
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(B,C)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A))
                  & k2_seq_1(k1_numbers,k1_numbers,A,C) != np__0 ) ) )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & r2_hidden(C,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(B)))
                  & ~ r1_xreal_0(np__0,k2_seq_1(k1_numbers,k1_numbers,A,C)) ) )
          | v7_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).

fof(t146_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v6_limfunc1(A)
          & k6_limfunc1(A) = np__0
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(B,C)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A))
                  & k2_seq_1(k1_numbers,k1_numbers,A,C) != np__0 ) ) )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & r2_hidden(C,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(B)))
                  & ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,C),np__0) ) )
          | v8_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).

fof(t147_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v3_limfunc1(A)
          & k5_limfunc1(A) = np__0 )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & r2_hidden(C,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(B)))
                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,C),np__0) ) )
          | v4_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).

fof(t148_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v3_limfunc1(A)
          & k5_limfunc1(A) = np__0 )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & r2_hidden(C,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(B)))
                  & r1_xreal_0(np__0,k2_seq_1(k1_numbers,k1_numbers,A,C)) ) )
          | v5_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).

fof(t149_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v6_limfunc1(A)
          & k6_limfunc1(A) = np__0 )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & r2_hidden(C,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(B)))
                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,C),np__0) ) )
          | v7_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).

fof(t150_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v6_limfunc1(A)
          & k6_limfunc1(A) = np__0 )
       => ( ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ? [C] :
                  ( m1_subset_1(C,k1_numbers)
                  & r2_hidden(C,k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(B)))
                  & r1_xreal_0(np__0,k2_seq_1(k1_numbers,k1_numbers,A,C)) ) )
          | v8_limfunc1(k4_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).

fof(dt_k1_limfunc1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_limfunc1(A,B),k1_numbers,k5_numbers) ) )).

fof(commutativity_k1_limfunc1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_limfunc1(A,B) = k1_limfunc1(B,A) ) )).

fof(idempotence_k1_limfunc1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_limfunc1(A,A) = A ) )).

fof(redefinition_k1_limfunc1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_limfunc1(A,B) = k2_square_1(A,B) ) )).

fof(dt_k2_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => m1_subset_1(k2_limfunc1(A),k1_zfmisc_1(k1_numbers)) ) )).

fof(dt_k3_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => m1_subset_1(k3_limfunc1(A),k1_zfmisc_1(k1_numbers)) ) )).

fof(dt_k4_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => m1_subset_1(k4_limfunc1(A),k1_zfmisc_1(k1_numbers)) ) )).

fof(dt_k5_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m1_relset_1(A,k1_numbers,k1_numbers) )
     => m1_subset_1(k5_limfunc1(A),k1_numbers) ) )).

fof(dt_k6_limfunc1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m1_relset_1(A,k1_numbers,k1_numbers) )
     => m1_subset_1(k6_limfunc1(A),k1_numbers) ) )).

fof(d1_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k2_limfunc1(A) = a_1_0_limfunc1(A) ) )).

fof(d2_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k3_limfunc1(A) = a_1_1_limfunc1(A) ) )).

fof(d3_limfunc1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k4_limfunc1(A) = a_1_2_limfunc1(A) ) )).

fof(fraenkel_a_1_0_limfunc1,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_0_limfunc1(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_numbers)
            & A = C
            & r1_xreal_0(C,B) ) ) ) )).

fof(fraenkel_a_1_1_limfunc1,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_1_limfunc1(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_numbers)
            & A = C
            & r1_xreal_0(B,C) ) ) ) )).

fof(fraenkel_a_1_2_limfunc1,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ( r2_hidden(A,a_1_2_limfunc1(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_numbers)
            & A = C
            & ~ r1_xreal_0(C,B) ) ) ) )).
%------------------------------------------------------------------------------