SET007 Axioms: SET007+113.ax


%------------------------------------------------------------------------------
% File     : SET007+113 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Limit of a Composition of Real Functions
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : limfunc4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   77 (   0 unit)
%            Number of atoms       : 1307 (  40 equality)
%            Maximal formula depth :   28 (  19 average)
%            Number of connectives : 1611 ( 381 ~  ;  45  |; 685  &)
%                                         (   0 <=>; 500 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   0 propositional; 1-3 arity)
%            Number of functors    :   21 (   3 constant; 0-6 arity)
%            Number of variables   :  473 (   0 singleton; 425 !;  48 ?)
%            Maximal term depth    :    5 (   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_limfunc4,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)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ! [D] :
                  ( r1_tarski(k1_rfunct_2(C),k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,A)),D))
                 => ( r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,A)))
                    & r1_tarski(k1_rfunct_2(C),D)
                    & r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,B))
                    & r1_tarski(k1_rfunct_2(C),k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),D))
                    & r1_tarski(k1_rfunct_2(k2_rfunct_2(B,C)),k4_relset_1(k1_numbers,k1_numbers,A)) ) ) ) ) ) )).

fof(t2_limfunc4,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)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ! [D] :
                  ( r1_tarski(k1_rfunct_2(C),k4_xboole_0(k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,A)),D))
                 => ( r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,A)))
                    & r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,B))
                    & r1_tarski(k1_rfunct_2(C),k4_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),D))
                    & r1_tarski(k1_rfunct_2(k2_rfunct_2(B,C)),k4_relset_1(k1_numbers,k1_numbers,A)) ) ) ) ) ) )).

fof(t3_limfunc4,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,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => v4_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) )).

fof(t4_limfunc4,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)
              & 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,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => v5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) )).

fof(t5_limfunc4,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)
              & v7_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => v4_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) )).

fof(t6_limfunc4,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)
              & v8_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => v5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) )).

fof(t7_limfunc4,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)
              & v4_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) )).

fof(t8_limfunc4,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)
              & v5_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => v8_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) )).

fof(t9_limfunc4,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)
              & 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,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) )).

fof(t10_limfunc4,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,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => v8_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) )).

fof(t11_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r2_limfunc2(B,A)
                  & v4_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => r2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(t12_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r2_limfunc2(B,A)
                  & v5_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => r3_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(t13_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r3_limfunc2(B,A)
                  & v7_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => r2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(t14_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r3_limfunc2(B,A)
                  & v8_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => r3_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(t15_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r5_limfunc2(B,A)
                  & v4_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => r5_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(t16_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r5_limfunc2(B,A)
                  & v5_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => r6_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(t17_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r6_limfunc2(B,A)
                  & v7_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => r5_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(t18_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r6_limfunc2(B,A)
                  & v8_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => r6_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(t19_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc2(B,A)
                  & r2_limfunc2(C,k1_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
                                  & r1_xreal_0(k1_limfunc2(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
                  | r2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t20_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc2(B,A)
                  & r3_limfunc2(C,k1_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
                                  & r1_xreal_0(k1_limfunc2(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
                  | r3_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t21_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc2(B,A)
                  & r5_limfunc2(C,k1_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
                                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k1_limfunc2(B,A)) ) ) ) )
                  | r2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t22_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc2(B,A)
                  & r6_limfunc2(C,k1_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
                                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k1_limfunc2(B,A)) ) ) ) )
                  | r3_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t23_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r4_limfunc2(B,A)
                  & r5_limfunc2(C,k2_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
                                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k2_limfunc2(B,A)) ) ) ) )
                  | r5_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t24_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r4_limfunc2(B,A)
                  & r6_limfunc2(C,k2_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
                                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k2_limfunc2(B,A)) ) ) ) )
                  | r6_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t25_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r4_limfunc2(B,A)
                  & r2_limfunc2(C,k2_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
                                  & r1_xreal_0(k2_limfunc2(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
                  | r5_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t26_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r4_limfunc2(B,A)
                  & r3_limfunc2(C,k2_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
                                  & r1_xreal_0(k2_limfunc2(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
                  | r6_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t27_limfunc4,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)
              & r2_limfunc2(B,k5_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
                      & r1_xreal_0(k5_limfunc1(A),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) )
              | v4_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t28_limfunc4,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)
              & r3_limfunc2(B,k5_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
                      & r1_xreal_0(k5_limfunc1(A),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) )
              | v5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t29_limfunc4,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)
              & r5_limfunc2(B,k5_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
                      & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k5_limfunc1(A)) ) )
              | v4_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t30_limfunc4,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)
              & r6_limfunc2(B,k5_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
                      & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k5_limfunc1(A)) ) )
              | v5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t31_limfunc4,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)
              & r2_limfunc2(B,k6_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
                      & r1_xreal_0(k6_limfunc1(A),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) )
              | v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t32_limfunc4,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)
              & r3_limfunc2(B,k6_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
                      & r1_xreal_0(k6_limfunc1(A),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) )
              | v8_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t33_limfunc4,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)
              & r5_limfunc2(B,k6_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
                      & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k6_limfunc1(A)) ) )
              | v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t34_limfunc4,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)
              & r6_limfunc2(B,k6_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
                      & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k6_limfunc1(A)) ) )
              | v8_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t35_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r2_limfunc3(B,A)
                  & v4_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => r2_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(t36_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r2_limfunc3(B,A)
                  & v5_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => r3_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(t37_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r3_limfunc3(B,A)
                  & v7_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => r2_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(t38_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r3_limfunc3(B,A)
                  & v8_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => r3_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(t39_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc3(B,A)
                  & r2_limfunc3(C,k1_limfunc3(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
                                  & k2_seq_1(k1_numbers,k1_numbers,B,E) = k1_limfunc3(B,A) ) ) ) )
                  | r2_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t40_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc3(B,A)
                  & r3_limfunc3(C,k1_limfunc3(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
                                  & k2_seq_1(k1_numbers,k1_numbers,B,E) = k1_limfunc3(B,A) ) ) ) )
                  | r3_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t41_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc3(B,A)
                  & r5_limfunc2(C,k1_limfunc3(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
                                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k1_limfunc3(B,A)) ) ) ) )
                  | r2_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t42_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc3(B,A)
                  & r6_limfunc2(C,k1_limfunc3(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
                                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k1_limfunc3(B,A)) ) ) ) )
                  | r3_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t43_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r4_limfunc2(B,A)
                  & r2_limfunc3(C,k2_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
                                  & k2_seq_1(k1_numbers,k1_numbers,B,E) = k2_limfunc2(B,A) ) ) ) )
                  | r5_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t44_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r4_limfunc2(B,A)
                  & r3_limfunc3(C,k2_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
                                  & k2_seq_1(k1_numbers,k1_numbers,B,E) = k2_limfunc2(B,A) ) ) ) )
                  | r6_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t45_limfunc4,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)
              & r2_limfunc3(B,k5_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
                      & k2_seq_1(k1_numbers,k1_numbers,A,D) = k5_limfunc1(A) ) )
              | v4_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t46_limfunc4,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)
              & r3_limfunc3(B,k5_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
                      & k2_seq_1(k1_numbers,k1_numbers,A,D) = k5_limfunc1(A) ) )
              | v5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t47_limfunc4,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)
              & r2_limfunc3(B,k6_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
                      & k2_seq_1(k1_numbers,k1_numbers,A,D) = k6_limfunc1(A) ) )
              | v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t48_limfunc4,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)
              & r3_limfunc3(B,k6_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
                      & k2_seq_1(k1_numbers,k1_numbers,A,D) = k6_limfunc1(A) ) )
              | v8_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).

fof(t49_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc3(B,A)
                  & r2_limfunc2(C,k1_limfunc3(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
                                  & r1_xreal_0(k1_limfunc3(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
                  | r2_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t50_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc3(B,A)
                  & r3_limfunc2(C,k1_limfunc3(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
                                  & r1_xreal_0(k1_limfunc3(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
                  | r3_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t51_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc2(B,A)
                  & r2_limfunc3(C,k1_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
                                  & k2_seq_1(k1_numbers,k1_numbers,B,E) = k1_limfunc2(B,A) ) ) ) )
                  | r2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t52_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc2(B,A)
                  & r3_limfunc3(C,k1_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
                                  & k2_seq_1(k1_numbers,k1_numbers,B,E) = k1_limfunc2(B,A) ) ) ) )
                  | r3_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t53_limfunc4,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)
              & 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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( v3_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
              & k5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k5_limfunc1(B) ) ) ) ) )).

fof(t54_limfunc4,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)
              & v6_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( v3_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
              & k5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k6_limfunc1(B) ) ) ) ) )).

fof(t55_limfunc4,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)
              & v3_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( v6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
              & k6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k5_limfunc1(B) ) ) ) ) )).

fof(t56_limfunc4,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)
              & 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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( v6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
              & k6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k6_limfunc1(B) ) ) ) ) )).

fof(t57_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r2_limfunc2(B,A)
                  & v3_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( r1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                  & k1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k5_limfunc1(C) ) ) ) ) ) )).

fof(t58_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r3_limfunc2(B,A)
                  & v6_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( r1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                  & k1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k6_limfunc1(C) ) ) ) ) ) )).

fof(t59_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r5_limfunc2(B,A)
                  & v3_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( r4_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                  & k2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k5_limfunc1(C) ) ) ) ) ) )).

fof(t60_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r6_limfunc2(B,A)
                  & v6_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( r4_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                  & k2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k6_limfunc1(C) ) ) ) ) ) )).

fof(t61_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc2(B,A)
                  & r1_limfunc2(C,k1_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
                                  & r1_xreal_0(k1_limfunc2(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
                  | ( r1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                    & k1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc2(C,k1_limfunc2(B,A)) ) ) ) ) ) ) )).

fof(t62_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r4_limfunc2(B,A)
                  & r4_limfunc2(C,k2_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
                                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k2_limfunc2(B,A)) ) ) ) )
                  | ( r4_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                    & k2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k2_limfunc2(C,k2_limfunc2(B,A)) ) ) ) ) ) ) )).

fof(t63_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc2(B,A)
                  & r4_limfunc2(C,k1_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
                                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k1_limfunc2(B,A)) ) ) ) )
                  | ( r1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                    & k1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k2_limfunc2(C,k1_limfunc2(B,A)) ) ) ) ) ) ) )).

fof(t64_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r4_limfunc2(B,A)
                  & r1_limfunc2(C,k2_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
                                  & r1_xreal_0(k2_limfunc2(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
                  | ( r4_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                    & k2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc2(C,k2_limfunc2(B,A)) ) ) ) ) ) ) )).

fof(t65_limfunc4,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)
              & r1_limfunc2(B,k5_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
                      & r1_xreal_0(k5_limfunc1(A),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) )
              | ( v3_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
                & k5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k1_limfunc2(B,k5_limfunc1(A)) ) ) ) ) ) )).

fof(t66_limfunc4,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)
              & r4_limfunc2(B,k5_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
                      & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k5_limfunc1(A)) ) )
              | ( v3_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
                & k5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k2_limfunc2(B,k5_limfunc1(A)) ) ) ) ) ) )).

fof(t67_limfunc4,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)
              & r1_limfunc2(B,k6_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
                      & r1_xreal_0(k6_limfunc1(A),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) )
              | ( v6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
                & k6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k1_limfunc2(B,k6_limfunc1(A)) ) ) ) ) ) )).

fof(t68_limfunc4,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)
              & r4_limfunc2(B,k6_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
                      & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k6_limfunc1(A)) ) )
              | ( v6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
                & k6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k2_limfunc2(B,k6_limfunc1(A)) ) ) ) ) ) )).

fof(t69_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r2_limfunc3(B,A)
                  & v3_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                  & k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k5_limfunc1(C) ) ) ) ) ) )).

fof(t70_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r3_limfunc3(B,A)
                  & v6_limfunc1(C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                  & k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k6_limfunc1(C) ) ) ) ) ) )).

fof(t71_limfunc4,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)
              & r1_limfunc3(B,k5_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k4_limfunc1(C)))
                      & k2_seq_1(k1_numbers,k1_numbers,A,D) = k5_limfunc1(A) ) )
              | ( v3_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
                & k5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k1_limfunc3(B,k5_limfunc1(A)) ) ) ) ) ) )).

fof(t72_limfunc4,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)
              & r1_limfunc3(B,k6_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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) )
           => ( ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ? [D] :
                      ( m1_subset_1(D,k1_numbers)
                      & r2_hidden(D,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,A),k12_prob_1(C)))
                      & k2_seq_1(k1_numbers,k1_numbers,A,D) = k6_limfunc1(A) ) )
              | ( v6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))
                & k6_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) = k1_limfunc3(B,k6_limfunc1(A)) ) ) ) ) ) )).

fof(t73_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc3(B,A)
                  & r1_limfunc2(C,k1_limfunc3(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
                                  & r1_xreal_0(k1_limfunc3(B,A),k2_seq_1(k1_numbers,k1_numbers,B,E)) ) ) ) )
                  | ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                    & k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc2(C,k1_limfunc3(B,A)) ) ) ) ) ) ) )).

fof(t74_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc2(B,A)
                  & r1_limfunc3(C,k1_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(A,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,D)
                                  & ~ r1_xreal_0(A,E)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(k5_real_1(A,D),A)))
                                  & k2_seq_1(k1_numbers,k1_numbers,B,E) = k1_limfunc2(B,A) ) ) ) )
                  | ( r1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                    & k1_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc3(C,k1_limfunc2(B,A)) ) ) ) ) ) ) )).

fof(t75_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc3(B,A)
                  & r4_limfunc2(C,k1_limfunc3(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
                                  & r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,E),k1_limfunc3(B,A)) ) ) ) )
                  | ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                    & k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k2_limfunc2(C,k1_limfunc3(B,A)) ) ) ) ) ) ) )).

fof(t76_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,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) )
             => ( ( r4_limfunc2(B,A)
                  & r1_limfunc3(C,k2_limfunc2(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,A)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(D,E)
                                  & ~ r1_xreal_0(E,A)
                                  & r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_rcomp_1(A,k3_real_1(A,D))))
                                  & k2_seq_1(k1_numbers,k1_numbers,B,E) = k2_limfunc2(B,A) ) ) ) )
                  | ( r4_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                    & k2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc3(C,k2_limfunc2(B,A)) ) ) ) ) ) ) )).

fof(t77_limfunc4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_limfunc3(B,A)
                  & r1_limfunc3(C,k1_limfunc3(B,A))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(A,D)
                              & ~ r1_xreal_0(E,A)
                              & ! [F] :
                                  ( m1_subset_1(F,k1_numbers)
                                 => ! [G] :
                                      ( m1_subset_1(G,k1_numbers)
                                     => ~ ( ~ r1_xreal_0(F,D)
                                          & ~ r1_xreal_0(A,F)
                                          & r2_hidden(F,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C)))
                                          & ~ r1_xreal_0(E,G)
                                          & ~ r1_xreal_0(G,A)
                                          & r2_hidden(G,k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) ) ) ) ) ) )
               => ( ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ~ ( ~ r1_xreal_0(D,np__0)
                          & ! [E] :
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( r2_hidden(E,k3_xboole_0(k4_relset_1(k1_numbers,k1_numbers,B),k2_xboole_0(k2_rcomp_1(k5_real_1(A,D),A),k2_rcomp_1(A,k3_real_1(A,D)))))
                                  & k2_seq_1(k1_numbers,k1_numbers,B,E) = k1_limfunc3(B,A) ) ) ) )
                  | ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A)
                    & k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc3(C,k1_limfunc3(B,A)) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------