SET007 Axioms: SET007+166.ax


%------------------------------------------------------------------------------
% File     : SET007+166 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Properties of Partial Functions from a Domain to the Real Numbers
% 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    : rfunct_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  151 (   5 unit)
%            Number of atoms       :  820 ( 112 equality)
%            Maximal formula depth :   20 (   8 average)
%            Number of connectives :  807 ( 138 ~  ;   3  |; 241  &)
%                                         (  21 <=>; 404 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   31 (   1 propositional; 0-4 arity)
%            Number of functors    :   93 (   6 constant; 0-6 arity)
%            Number of variables   :  476 (   0 singleton; 472 !;   4 ?)
%            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(rc1_rfunct_3,axiom,(
    ! [A,B] :
    ? [C] :
      ( m1_rfunct_3(C,A,B)
      & ~ v1_xboole_0(C) ) )).

fof(rc2_rfunct_3,axiom,(
    ! [A,B] :
    ? [C] :
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_finset_1(C) ) )).

fof(fc1_rfunct_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_finset_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => ( v1_relat_1(k19_rfunct_3(A,B))
        & v1_funct_1(k19_rfunct_3(A,B))
        & v1_finset_1(k19_rfunct_3(A,B))
        & v1_seq_1(k19_rfunct_3(A,B)) ) ) )).

fof(fc2_rfunct_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_finset_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => ( v1_relat_1(k20_rfunct_3(A,B))
        & v1_funct_1(k20_rfunct_3(A,B))
        & v1_finset_1(k20_rfunct_3(A,B))
        & v1_seq_1(k20_rfunct_3(A,B)) ) ) )).

fof(d1_rfunct_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k2_rfunct_3(A) = k2_square_1(A,np__0) ) )).

fof(d2_rfunct_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k3_rfunct_3(A) = k2_square_1(k4_xcmplx_0(A),np__0) ) )).

fof(t1_rfunct_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => A = k5_real_1(k2_rfunct_3(A),k3_rfunct_3(A)) ) )).

fof(t2_rfunct_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k18_complex1(A) = k3_real_1(k2_rfunct_3(A),k3_rfunct_3(A)) ) )).

fof(t3_rfunct_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k4_real_1(np__2,k2_rfunct_3(A)) = k2_xcmplx_0(A,k18_complex1(A)) ) )).

fof(t4_rfunct_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(np__0,A)
           => k2_rfunct_3(k3_xcmplx_0(A,B)) = k3_xcmplx_0(A,k2_rfunct_3(B)) ) ) ) )).

fof(t5_rfunct_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => r1_xreal_0(k2_rfunct_3(k2_xcmplx_0(A,B)),k3_real_1(k2_rfunct_3(A),k2_rfunct_3(B))) ) ) )).

fof(t6_rfunct_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( r1_xreal_0(np__0,k2_rfunct_3(A))
        & r1_xreal_0(np__0,k3_rfunct_3(A)) ) ) )).

fof(t7_rfunct_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,C)
                      & r1_xreal_0(B,D) )
                   => r1_xreal_0(k2_square_1(A,B),k2_square_1(C,D)) ) ) ) ) ) )).

fof(t8_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( C != np__0
                   => k11_relset_1(A,k1_numbers,B,k1_tarski(k7_xcmplx_0(D,C))) = k11_relset_1(A,k1_numbers,k13_seq_1(A,k1_numbers,B,C),k1_tarski(D)) ) ) ) ) ) )).

fof(t9_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => k11_relset_1(A,k1_numbers,k13_seq_1(A,k1_numbers,B,np__0),k2_setwiseo(k1_numbers,np__0)) = k4_relset_1(A,k1_numbers,B) ) ) )).

fof(t10_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( ~ r1_xreal_0(C,np__0)
               => k11_relset_1(A,k1_numbers,k21_seq_1(A,k1_numbers,B),k2_setwiseo(k1_numbers,C)) = k11_relset_1(A,k1_numbers,B,k3_setwiseo(k1_numbers,k1_real_1(C),C)) ) ) ) ) )).

fof(t11_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => k11_relset_1(A,k1_numbers,k21_seq_1(A,k1_numbers,B),k2_setwiseo(k1_numbers,np__0)) = k11_relset_1(A,k1_numbers,B,k2_setwiseo(k1_numbers,np__0)) ) ) )).

fof(t12_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( ~ r1_xreal_0(np__0,C)
               => k11_relset_1(A,k1_numbers,k21_seq_1(A,k1_numbers,B),k2_setwiseo(k1_numbers,C)) = k1_xboole_0 ) ) ) ) )).

fof(t13_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,B,k1_numbers) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ( E != np__0
                       => ( r1_rfinseq(C,D)
                        <=> r1_rfinseq(k13_seq_1(A,k1_numbers,C,E),k13_seq_1(B,k1_numbers,D,E)) ) ) ) ) ) ) ) )).

fof(t14_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,B,k1_numbers) )
                 => ( r1_rfinseq(C,D)
                  <=> r1_rfinseq(k16_seq_1(A,k1_numbers,C),k16_seq_1(B,k1_numbers,D)) ) ) ) ) ) )).

fof(t15_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,B,k1_numbers) )
                 => ( r1_rfinseq(C,D)
                   => r1_rfinseq(k21_seq_1(A,k1_numbers,C),k21_seq_1(B,k1_numbers,D)) ) ) ) ) ) )).

fof(d3_rfunct_3,axiom,(
    ! [A,B,C] :
      ( m1_rfunct_3(C,A,B)
    <=> ! [D] :
          ( m1_subset_1(D,C)
         => ( v1_funct_1(D)
            & m2_relset_1(D,A,B) ) ) ) )).

fof(d4_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k4_rfunct_3(A,k1_numbers),k4_rfunct_3(A,k1_numbers)),k4_rfunct_3(A,k1_numbers))
            & m2_relset_1(B,k2_zfmisc_1(k4_rfunct_3(A,k1_numbers),k4_rfunct_3(A,k1_numbers)),k4_rfunct_3(A,k1_numbers)) )
         => ( B = k14_rfunct_3(A)
          <=> ! [C] :
                ( m2_rfunct_3(C,A,k1_numbers,k4_rfunct_3(A,k1_numbers))
               => ! [D] :
                    ( m2_rfunct_3(D,A,k1_numbers,k4_rfunct_3(A,k1_numbers))
                   => k2_binop_1(k4_rfunct_3(A,k1_numbers),k4_rfunct_3(A,k1_numbers),k4_rfunct_3(A,k1_numbers),B,C,D) = k6_rfunct_3(A,k1_numbers,C,D) ) ) ) ) ) )).

fof(t16_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => v1_binop_1(k14_rfunct_3(A),k4_rfunct_3(A,k1_numbers)) ) )).

fof(t17_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => v2_binop_1(k14_rfunct_3(A),k4_rfunct_3(A,k1_numbers)) ) )).

fof(t18_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => r3_binop_1(k4_rfunct_3(A,k1_numbers),k5_rfunct_3(A,k1_numbers,k2_subset_1(A),np__0),k14_rfunct_3(A)) ) )).

fof(t19_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k3_binop_1(k4_rfunct_3(A,k1_numbers),k14_rfunct_3(A)) = k5_rfunct_3(A,k1_numbers,k2_subset_1(A),np__0) ) )).

fof(t20_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => v1_setwiseo(k14_rfunct_3(A),k4_rfunct_3(A,k1_numbers)) ) )).

fof(d5_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,k4_rfunct_3(A,k1_numbers))
         => k15_rfunct_3(A,B) = k2_finsop_1(k4_rfunct_3(A,k1_numbers),B,k14_rfunct_3(A)) ) ) )).

fof(t21_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k15_rfunct_3(A,k6_finseq_1(k4_rfunct_3(A,k1_numbers))) = k5_rfunct_3(A,k1_numbers,k2_subset_1(A),np__0) ) )).

fof(t22_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_rfunct_3(B,A,k1_numbers,k4_rfunct_3(A,k1_numbers))
         => k15_rfunct_3(A,k12_finseq_1(k4_rfunct_3(A,k1_numbers),B)) = B ) ) )).

fof(t23_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,k4_rfunct_3(A,k1_numbers))
         => ! [C] :
              ( m2_rfunct_3(C,A,k1_numbers,k4_rfunct_3(A,k1_numbers))
             => k15_rfunct_3(A,k8_finseq_1(k4_rfunct_3(A,k1_numbers),B,k12_finseq_1(k4_rfunct_3(A,k1_numbers),C))) = k6_rfunct_3(A,k1_numbers,k15_rfunct_3(A,B),C) ) ) ) )).

fof(t24_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,k4_rfunct_3(A,k1_numbers))
         => ! [C] :
              ( m2_finseq_1(C,k4_rfunct_3(A,k1_numbers))
             => k15_rfunct_3(A,k8_finseq_1(k4_rfunct_3(A,k1_numbers),B,C)) = k6_rfunct_3(A,k1_numbers,k15_rfunct_3(A,B),k15_rfunct_3(A,C)) ) ) ) )).

fof(t25_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,k4_rfunct_3(A,k1_numbers))
         => ! [C] :
              ( m2_rfunct_3(C,A,k1_numbers,k4_rfunct_3(A,k1_numbers))
             => k15_rfunct_3(A,k8_finseq_1(k4_rfunct_3(A,k1_numbers),k12_finseq_1(k4_rfunct_3(A,k1_numbers),C),B)) = k6_rfunct_3(A,k1_numbers,C,k15_rfunct_3(A,B)) ) ) ) )).

fof(t26_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_rfunct_3(B,A,k1_numbers,k4_rfunct_3(A,k1_numbers))
         => ! [C] :
              ( m2_rfunct_3(C,A,k1_numbers,k4_rfunct_3(A,k1_numbers))
             => k15_rfunct_3(A,k2_finseq_4(k4_rfunct_3(A,k1_numbers),B,C)) = k6_rfunct_3(A,k1_numbers,B,C) ) ) ) )).

fof(t27_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_rfunct_3(B,A,k1_numbers,k4_rfunct_3(A,k1_numbers))
         => ! [C] :
              ( m2_rfunct_3(C,A,k1_numbers,k4_rfunct_3(A,k1_numbers))
             => ! [D] :
                  ( m2_rfunct_3(D,A,k1_numbers,k4_rfunct_3(A,k1_numbers))
                 => k15_rfunct_3(A,k3_finseq_4(k4_rfunct_3(A,k1_numbers),B,C,D)) = k6_rfunct_3(A,k1_numbers,k6_rfunct_3(A,k1_numbers,B,C),D) ) ) ) ) )).

fof(t28_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,k4_rfunct_3(A,k1_numbers))
         => ! [C] :
              ( m2_finseq_1(C,k4_rfunct_3(A,k1_numbers))
             => ( r1_rfinseq(B,C)
               => k15_rfunct_3(A,B) = k15_rfunct_3(A,C) ) ) ) ) )).

fof(d6_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( m2_finseq_1(C,k4_rfunct_3(A,k1_numbers))
             => ( C = k16_rfunct_3(A,B)
              <=> ( k3_finseq_1(C) = k3_finseq_1(B)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(C))
                       => k1_funct_1(C,D) = k5_rfunct_1(k1_funct_1(B,D),A) ) ) ) ) ) ) ) )).

fof(d7_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,k4_rfunct_3(A,k1_numbers))
         => ! [C] :
              ( m2_finseq_1(C,k1_numbers)
             => ! [D] :
                  ( m2_finseq_1(D,k4_rfunct_3(A,k1_numbers))
                 => ( D = k17_rfunct_3(A,B,C)
                  <=> ( k3_finseq_1(D) = k1_rfunct_3(k3_finseq_1(C),k3_finseq_1(B))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r2_hidden(E,k4_finseq_1(D))
                           => ! [F] :
                                ( ( v1_funct_1(F)
                                  & m2_relset_1(F,A,k1_numbers) )
                               => ! [G] :
                                    ( m1_subset_1(G,k1_numbers)
                                   => ( ( G = k2_seq_1(k5_numbers,k1_numbers,C,E)
                                        & F = k1_funct_1(B,E) )
                                     => k1_funct_1(D,E) = k13_seq_1(A,k1_numbers,F,G) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d8_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,k4_rfunct_3(A,k1_numbers))
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_finseq_1(D,k1_numbers)
                 => ( D = k18_rfunct_3(A,B,C)
                  <=> ( k3_finseq_1(D) = k3_finseq_1(B)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( m2_rfunct_3(F,A,k1_numbers,k4_rfunct_3(A,k1_numbers))
                             => ( ( r2_hidden(E,k4_finseq_1(D))
                                  & k1_funct_1(B,E) = F )
                               => k2_seq_1(k5_numbers,k1_numbers,D,E) = k2_seq_1(A,k1_numbers,F,C) ) ) ) ) ) ) ) ) ) )).

fof(d9_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,k4_rfunct_3(A,B))
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ( r1_rfunct_3(A,B,C,D)
                  <=> ! [E] :
                        ( m2_rfunct_3(E,A,B,k4_rfunct_3(A,B))
                       => ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ( ( r2_hidden(F,k4_finseq_1(C))
                                & k1_funct_1(C,F) = E )
                             => r2_hidden(D,k4_relset_1(A,B,E)) ) ) ) ) ) ) ) ) )).

fof(t29_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,k4_rfunct_3(A,B))
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_rfunct_3(A,B,C,D)
                       => ( E = np__0
                          | r1_rfunct_3(A,B,k16_finseq_1(k4_rfunct_3(A,B),C,E),D) ) ) ) ) ) ) ) )).

fof(t30_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,k4_rfunct_3(A,B))
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_rfunct_3(A,B,C,D)
                       => r1_rfunct_3(A,B,k1_rfinseq(k4_rfunct_3(A,B),C,E),D) ) ) ) ) ) ) )).

fof(t31_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,k4_rfunct_3(A,k1_numbers))
             => ( k3_finseq_1(C) != np__0
               => ( r1_rfunct_3(A,k1_numbers,C,B)
                <=> r2_hidden(B,k4_relset_1(A,k1_numbers,k15_rfunct_3(A,C))) ) ) ) ) ) )).

fof(t32_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,k4_rfunct_3(A,k1_numbers))
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => k18_rfunct_3(A,k16_finseq_1(k4_rfunct_3(A,k1_numbers),B,D),C) = k16_finseq_1(k1_numbers,k18_rfunct_3(A,B,C),D) ) ) ) ) )).

fof(t33_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => r1_rfunct_3(A,k1_numbers,k16_rfunct_3(A,B),C) ) ) ) )).

fof(t34_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,k4_rfunct_3(A,k1_numbers))
             => ! [D] :
                  ( m2_finseq_1(D,k1_numbers)
                 => ( r1_rfunct_3(A,k1_numbers,C,B)
                   => r1_rfunct_3(A,k1_numbers,k17_rfunct_3(A,C,D),B) ) ) ) ) ) )).

fof(t35_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( m2_finseq_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => r1_rfunct_3(A,k1_numbers,k17_rfunct_3(A,k16_rfunct_3(A,B),C),D) ) ) ) ) )).

fof(t36_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,k4_rfunct_3(A,k1_numbers))
             => ( r1_rfunct_3(A,k1_numbers,C,B)
               => k2_seq_1(A,k1_numbers,k15_rfunct_3(A,C),B) = k15_rvsum_1(k18_rfunct_3(A,C,B)) ) ) ) ) )).

fof(d10_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ( C = k19_rfunct_3(A,B)
              <=> ( k4_relset_1(A,k1_numbers,C) = k4_relset_1(A,k1_numbers,B)
                  & ! [D] :
                      ( m1_subset_1(D,A)
                     => ( r2_hidden(D,k4_relset_1(A,k1_numbers,C))
                       => k2_seq_1(A,k1_numbers,C,D) = k2_rfunct_3(k2_seq_1(A,k1_numbers,B,D)) ) ) ) ) ) ) ) )).

fof(d11_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ( C = k20_rfunct_3(A,B)
              <=> ( k4_relset_1(A,k1_numbers,C) = k4_relset_1(A,k1_numbers,B)
                  & ! [D] :
                      ( m1_subset_1(D,A)
                     => ( r2_hidden(D,k4_relset_1(A,k1_numbers,C))
                       => k2_seq_1(A,k1_numbers,C,D) = k3_rfunct_3(k2_seq_1(A,k1_numbers,B,D)) ) ) ) ) ) ) ) )).

fof(t37_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( B = k7_seq_1(A,k1_numbers,k19_rfunct_3(A,B),k20_rfunct_3(A,B))
            & k21_seq_1(A,k1_numbers,B) = k6_seq_1(A,k1_numbers,k19_rfunct_3(A,B),k20_rfunct_3(A,B))
            & k13_seq_1(A,k1_numbers,k19_rfunct_3(A,B),np__2) = k6_seq_1(A,k1_numbers,B,k21_seq_1(A,k1_numbers,B)) ) ) ) )).

fof(t38_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( ~ r1_xreal_0(C,np__0)
               => k11_relset_1(A,k1_numbers,B,k2_setwiseo(k1_numbers,C)) = k11_relset_1(A,k1_numbers,k19_rfunct_3(A,B),k2_setwiseo(k1_numbers,C)) ) ) ) ) )).

fof(t39_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => k11_relset_1(A,k1_numbers,B,k2_limfunc1(np__0)) = k11_relset_1(A,k1_numbers,k19_rfunct_3(A,B),k2_setwiseo(k1_numbers,np__0)) ) ) )).

fof(t40_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ( r2_hidden(C,k4_relset_1(A,k1_numbers,B))
               => r1_xreal_0(np__0,k2_seq_1(A,k1_numbers,k19_rfunct_3(A,B),C)) ) ) ) ) )).

fof(t41_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( ~ r1_xreal_0(C,np__0)
               => k11_relset_1(A,k1_numbers,B,k2_setwiseo(k1_numbers,k1_real_1(C))) = k11_relset_1(A,k1_numbers,k20_rfunct_3(A,B),k2_setwiseo(k1_numbers,C)) ) ) ) ) )).

fof(t42_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => k11_relset_1(A,k1_numbers,B,k3_limfunc1(np__0)) = k11_relset_1(A,k1_numbers,k20_rfunct_3(A,B),k2_setwiseo(k1_numbers,np__0)) ) ) )).

fof(t43_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ( r2_hidden(C,k4_relset_1(A,k1_numbers,B))
               => r1_xreal_0(np__0,k2_seq_1(A,k1_numbers,k20_rfunct_3(A,B),C)) ) ) ) ) )).

fof(t44_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,B,k1_numbers) )
                 => ( r1_rfinseq(C,D)
                   => r1_rfinseq(k19_rfunct_3(A,C),k19_rfunct_3(B,D)) ) ) ) ) ) )).

fof(t45_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,B,k1_numbers) )
                 => ( r1_rfinseq(C,D)
                   => r1_rfinseq(k20_rfunct_3(A,C),k20_rfunct_3(B,D)) ) ) ) ) ) )).

fof(t46_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_finset_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_finset_1(D)
                    & m2_relset_1(D,B,k1_numbers) )
                 => ( ( r1_rfinseq(k19_rfunct_3(A,C),k19_rfunct_3(B,D))
                      & r1_rfinseq(k20_rfunct_3(A,C),k20_rfunct_3(B,D)) )
                   => r1_rfinseq(C,D) ) ) ) ) ) )).

fof(t47_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] : k2_partfun1(A,k1_numbers,k19_rfunct_3(A,B),C) = k19_rfunct_3(A,k2_partfun1(A,k1_numbers,B,C)) ) ) )).

fof(t48_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] : k2_partfun1(A,k1_numbers,k20_rfunct_3(A,B),C) = k20_rfunct_3(A,k2_partfun1(A,k1_numbers,B,C)) ) ) )).

fof(t49_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( ! [C] :
                ( m1_subset_1(C,A)
               => ( r2_hidden(C,k4_relset_1(A,k1_numbers,B))
                 => r1_xreal_0(np__0,k2_seq_1(A,k1_numbers,B,C)) ) )
           => k19_rfunct_3(A,B) = B ) ) ) )).

fof(t50_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ( ! [C] :
                ( m1_subset_1(C,A)
               => ( r2_hidden(C,k4_relset_1(A,k1_numbers,B))
                 => r1_xreal_0(k2_seq_1(A,k1_numbers,B,C),np__0) ) )
           => k20_rfunct_3(A,B) = k16_seq_1(A,k1_numbers,B) ) ) ) )).

fof(d12_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k1_numbers) )
                 => ( D = k21_rfunct_3(A,B,C)
                  <=> ( k4_relset_1(A,k1_numbers,D) = k4_relset_1(A,k1_numbers,B)
                      & ! [E] :
                          ( m1_subset_1(E,A)
                         => ( r2_hidden(E,k4_relset_1(A,k1_numbers,D))
                           => k2_seq_1(A,k1_numbers,D,E) = k5_real_1(k2_seq_1(A,k1_numbers,B,E),C) ) ) ) ) ) ) ) ) )).

fof(t51_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => k21_rfunct_3(A,B,np__0) = B ) ) )).

fof(t52_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] : k21_rfunct_3(A,k2_partfun1(A,k1_numbers,B,D),C) = k2_partfun1(A,k1_numbers,k21_rfunct_3(A,B,C),D) ) ) ) )).

fof(t53_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => k11_relset_1(A,k1_numbers,B,k2_setwiseo(k1_numbers,k3_real_1(D,C))) = k11_relset_1(A,k1_numbers,k21_rfunct_3(A,B,C),k2_setwiseo(k1_numbers,D)) ) ) ) ) )).

fof(t54_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,B,k1_numbers) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ( r1_rfinseq(C,D)
                      <=> r1_rfinseq(k21_rfunct_3(A,C,E),k21_rfunct_3(B,D,E)) ) ) ) ) ) ) )).

fof(d13_rfunct_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( r2_rfunct_3(A,B)
        <=> ( r1_tarski(B,k4_relset_1(k1_numbers,k1_numbers,A))
            & ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => ( ( r1_xreal_0(np__0,C)
                    & r1_xreal_0(C,np__1) )
                 => ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( ( r2_hidden(D,B)
                              & r2_hidden(E,B)
                              & r2_hidden(k3_real_1(k4_real_1(C,D),k4_real_1(k5_real_1(np__1,C),E)),B) )
                           => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,k3_real_1(k4_real_1(C,D),k4_real_1(k5_real_1(np__1,C),E))),k3_real_1(k4_real_1(C,k2_seq_1(k1_numbers,k1_numbers,A,D)),k4_real_1(k5_real_1(np__1,C),k2_seq_1(k1_numbers,k1_numbers,A,E)))) ) ) ) ) ) ) ) ) )).

fof(t55_rfunct_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( r2_rfunct_3(C,k1_rcomp_1(A,B))
              <=> ( r1_tarski(k1_rcomp_1(A,B),k4_relset_1(k1_numbers,k1_numbers,C))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( ( r1_xreal_0(np__0,D)
                          & r1_xreal_0(D,np__1) )
                       => ! [E] :
                            ( m1_subset_1(E,k1_numbers)
                           => ! [F] :
                                ( m1_subset_1(F,k1_numbers)
                               => ( ( r2_hidden(E,k1_rcomp_1(A,B))
                                    & r2_hidden(F,k1_rcomp_1(A,B)) )
                                 => r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,k3_real_1(k4_real_1(D,E),k4_real_1(k5_real_1(np__1,D),F))),k3_real_1(k4_real_1(D,k2_seq_1(k1_numbers,k1_numbers,C,E)),k4_real_1(k5_real_1(np__1,D),k2_seq_1(k1_numbers,k1_numbers,C,F)))) ) ) ) ) ) ) ) ) ) ) )).

fof(t56_rfunct_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( r2_rfunct_3(C,k1_rcomp_1(A,B))
              <=> ( r1_tarski(k1_rcomp_1(A,B),k4_relset_1(k1_numbers,k1_numbers,C))
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ( ( r2_hidden(D,k1_rcomp_1(A,B))
                                  & r2_hidden(E,k1_rcomp_1(A,B))
                                  & r2_hidden(F,k1_rcomp_1(A,B)) )
                               => ( r1_xreal_0(E,D)
                                  | r1_xreal_0(F,E)
                                  | r1_xreal_0(k6_real_1(k5_real_1(k2_seq_1(k1_numbers,k1_numbers,C,D),k2_seq_1(k1_numbers,k1_numbers,C,E)),k5_real_1(D,E)),k6_real_1(k5_real_1(k2_seq_1(k1_numbers,k1_numbers,C,E),k2_seq_1(k1_numbers,k1_numbers,C,F)),k5_real_1(E,F))) ) ) ) ) ) ) ) ) ) ) )).

fof(t57_rfunct_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B,C] :
          ( ( r2_rfunct_3(A,B)
            & r1_tarski(C,B) )
         => r2_rfunct_3(A,C) ) ) )).

fof(t58_rfunct_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B,C] :
          ( m1_subset_1(C,k1_numbers)
         => ( r2_rfunct_3(A,B)
          <=> r2_rfunct_3(k21_rfunct_3(k1_numbers,A,C),B) ) ) ) )).

fof(t59_rfunct_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B,C] :
          ( m1_subset_1(C,k1_numbers)
         => ( ~ r1_xreal_0(C,np__0)
           => ( r2_rfunct_3(A,B)
            <=> r2_rfunct_3(k13_seq_1(k1_numbers,k1_numbers,A,C),B) ) ) ) ) )).

fof(t60_rfunct_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( r1_tarski(B,k4_relset_1(k1_numbers,k1_numbers,A))
         => r2_rfunct_3(k13_seq_1(k1_numbers,k1_numbers,A,np__0),B) ) ) )).

fof(t61_rfunct_3,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] :
              ( ( r2_rfunct_3(A,C)
                & r2_rfunct_3(B,C) )
             => r2_rfunct_3(k6_seq_1(k1_numbers,k1_numbers,A,B),C) ) ) ) )).

fof(t62_rfunct_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B,C] :
          ( m1_subset_1(C,k1_numbers)
         => ( r2_rfunct_3(A,B)
           => r2_rfunct_3(k19_rfunct_3(k1_numbers,k21_rfunct_3(k1_numbers,A,C)),B) ) ) ) )).

fof(t63_rfunct_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( r2_rfunct_3(A,B)
         => r2_rfunct_3(k19_rfunct_3(k1_numbers,A),B) ) ) )).

fof(t64_rfunct_3,axiom,(
    r2_rfunct_3(k1_partfun2(k1_numbers,k2_subset_1(k1_numbers)),k1_numbers) )).

fof(t65_rfunct_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => r2_rfunct_3(k19_rfunct_3(k1_numbers,k21_rfunct_3(k1_numbers,k1_partfun2(k1_numbers,k2_subset_1(k1_numbers)),A)),k1_numbers) ) )).

fof(d14_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C)))
             => ! [D] :
                  ( ( v1_rfinseq(D)
                    & m2_finseq_1(D,k1_numbers) )
                 => ( D = k22_rfunct_3(A,B,C)
                  <=> r1_rfinseq(k2_partfun1(A,k1_numbers,B,C),D) ) ) ) ) ) )).

fof(t66_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C)))
             => k22_rfunct_3(A,B,k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C))) = k22_rfunct_3(A,B,C) ) ) ) )).

fof(t67_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C)))
             => k22_rfunct_3(A,k2_partfun1(A,k1_numbers,B,C),C) = k22_rfunct_3(A,B,C) ) ) ) )).

fof(t68_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C,D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,A,k1_numbers) )
             => ( ( v1_finset_1(C)
                  & r2_hidden(B,k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,D,C))) )
               => r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(A,D,k4_xboole_0(C,k2_setwiseo(A,B))),k12_finseq_1(k1_numbers,k2_seq_1(A,k1_numbers,D,B))),k2_partfun1(A,k1_numbers,D,C)) ) ) ) ) )).

fof(t69_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C,D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,A,k1_numbers) )
             => ( ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,D,C)))
                  & r2_hidden(B,k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,D,C))) )
               => r1_rfinseq(k8_finseq_1(k1_numbers,k22_rfunct_3(A,D,k4_xboole_0(C,k2_setwiseo(A,B))),k12_finseq_1(k1_numbers,k2_seq_1(A,k1_numbers,D,B))),k2_partfun1(A,k1_numbers,D,C)) ) ) ) ) )).

fof(t70_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C,D] :
              ( v1_finset_1(D)
             => ( D = k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C))
               => k3_finseq_1(k22_rfunct_3(A,B,C)) = k4_card_1(D) ) ) ) ) )).

fof(t71_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => k22_rfunct_3(A,B,k1_xboole_0) = k6_finseq_1(k1_numbers) ) ) )).

fof(t72_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ( r2_hidden(C,k4_relset_1(A,k1_numbers,B))
               => k22_rfunct_3(A,B,k2_setwiseo(A,C)) = k12_finseq_1(k1_numbers,k2_seq_1(A,k1_numbers,B,C)) ) ) ) ) )).

fof(t73_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C,D] :
              ( m1_subset_1(D,A)
             => ( ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C)))
                  & r2_hidden(D,k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C)))
                  & k2_seq_1(k5_numbers,k1_numbers,k22_rfunct_3(A,B,C),k3_finseq_1(k22_rfunct_3(A,B,C))) = k2_seq_1(A,k1_numbers,B,D) )
               => k22_rfunct_3(A,B,C) = k8_finseq_1(k1_numbers,k22_rfunct_3(A,B,k4_xboole_0(C,k2_setwiseo(A,D))),k12_finseq_1(k1_numbers,k2_seq_1(A,k1_numbers,B,D))) ) ) ) ) )).

fof(t74_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C,D] :
              ( ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C)))
                & r1_tarski(D,C)
                & ! [E] :
                    ( m1_subset_1(E,A)
                   => ! [F] :
                        ( m1_subset_1(F,A)
                       => ( ( r2_hidden(E,k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,D)))
                            & r2_hidden(F,k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k4_xboole_0(C,D)))) )
                         => r1_xreal_0(k2_seq_1(A,k1_numbers,B,F),k2_seq_1(A,k1_numbers,B,E)) ) ) ) )
             => k22_rfunct_3(A,B,C) = k8_finseq_1(k1_numbers,k22_rfunct_3(A,B,D),k22_rfunct_3(A,B,k4_xboole_0(C,D))) ) ) ) )).

fof(t75_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D,E] :
                  ( m1_subset_1(E,A)
                 => ( ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,D)))
                      & r2_hidden(E,k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,D))) )
                   => ( k2_seq_1(k5_numbers,k1_numbers,k22_rfunct_3(A,k21_rfunct_3(A,B,C),D),k3_finseq_1(k22_rfunct_3(A,k21_rfunct_3(A,B,C),D))) = k2_seq_1(A,k1_numbers,k21_rfunct_3(A,B,C),E)
                    <=> k2_seq_1(k5_numbers,k1_numbers,k22_rfunct_3(A,B,D),k3_finseq_1(k22_rfunct_3(A,B,D))) = k2_seq_1(A,k1_numbers,B,E) ) ) ) ) ) ) )).

fof(t76_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ! [D,E] :
                  ( v1_finset_1(E)
                 => ( E = k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,D))
                   => k22_rfunct_3(A,k21_rfunct_3(A,B,C),D) = k7_rvsum_1(k22_rfunct_3(A,B,D),k4_finseqop(k1_numbers,k4_card_1(E),C)) ) ) ) ) ) )).

fof(t77_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C)))
                & ! [D] :
                    ( m1_subset_1(D,A)
                   => ( r2_hidden(D,k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C)))
                     => r1_xreal_0(np__0,k2_seq_1(A,k1_numbers,B,D)) ) ) )
             => k22_rfunct_3(A,k19_rfunct_3(A,B),C) = k22_rfunct_3(A,B,C) ) ) ) )).

fof(t78_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C,D] :
              ( m1_subset_1(D,k1_numbers)
             => ! [E] :
                  ( v1_finset_1(E)
                 => ( ( E = k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C))
                      & k5_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C)) = k2_setwiseo(k1_numbers,D) )
                   => k22_rfunct_3(A,B,C) = k4_finseqop(k1_numbers,k4_card_1(E),D) ) ) ) ) ) )).

fof(t79_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C,D] :
              ( ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_xboole_0(C,D))))
                & r1_xboole_0(C,D) )
             => r1_rfinseq(k22_rfunct_3(A,B,k2_xboole_0(C,D)),k8_finseq_1(k1_numbers,k22_rfunct_3(A,B,C),k22_rfunct_3(A,B,D))) ) ) ) )).

fof(d15_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] : k24_rfunct_3(A,B,C) = k15_rvsum_1(k22_rfunct_3(A,B,C)) ) ) )).

fof(t80_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C,D] :
              ( m1_subset_1(D,k1_numbers)
             => ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C)))
               => k24_rfunct_3(A,k13_seq_1(A,k1_numbers,B,D),C) = k4_real_1(D,k24_rfunct_3(A,B,C)) ) ) ) ) )).

fof(t81_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D,E] :
                  ( v1_finset_1(E)
                 => ( ( E = k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,D))
                      & k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,D)) = k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,C,D)) )
                   => k24_rfunct_3(A,k6_seq_1(A,k1_numbers,B,C),D) = k3_real_1(k24_rfunct_3(A,B,D),k24_rfunct_3(A,C,D)) ) ) ) ) ) )).

fof(t82_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k1_numbers) )
             => ! [D] :
                  ( ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,D)))
                    & k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,D)) = k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,C,D)) )
                 => k24_rfunct_3(A,k7_seq_1(A,k1_numbers,B,C),D) = k5_real_1(k24_rfunct_3(A,B,D),k24_rfunct_3(A,C,D)) ) ) ) ) )).

fof(t83_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C,D] :
              ( m1_subset_1(D,k1_numbers)
             => ! [E] :
                  ( v1_finset_1(E)
                 => ( E = k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C))
                   => k24_rfunct_3(A,k21_rfunct_3(A,B,D),C) = k5_real_1(k24_rfunct_3(A,B,C),k4_real_1(D,k4_card_1(E))) ) ) ) ) ) )).

fof(t84_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => k24_rfunct_3(A,B,k1_xboole_0) = np__0 ) ) )).

fof(t85_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ( r2_hidden(C,k4_relset_1(A,k1_numbers,B))
               => k24_rfunct_3(A,B,k2_setwiseo(A,C)) = k2_seq_1(A,k1_numbers,B,C) ) ) ) ) )).

fof(t86_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C,D] :
              ( ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_xboole_0(C,D))))
                & r1_xboole_0(C,D) )
             => k24_rfunct_3(A,B,k2_xboole_0(C,D)) = k3_real_1(k24_rfunct_3(A,B,C),k24_rfunct_3(A,B,D)) ) ) ) )).

fof(t87_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) )
         => ! [C,D] :
              ( ( v1_finset_1(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k2_xboole_0(C,D))))
                & r1_xboole_0(k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,C)),k4_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,D))) )
             => k24_rfunct_3(A,B,k2_xboole_0(C,D)) = k3_real_1(k24_rfunct_3(A,B,C),k24_rfunct_3(A,B,D)) ) ) ) )).

fof(dt_m1_rfunct_3,axiom,(
    $true )).

fof(existence_m1_rfunct_3,axiom,(
    ! [A,B] :
    ? [C] : m1_rfunct_3(C,A,B) )).

fof(dt_m2_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(C)
        & m1_rfunct_3(C,A,B) )
     => ! [D] :
          ( m2_rfunct_3(D,A,B,C)
         => ( v1_funct_1(D)
            & m2_relset_1(D,A,B) ) ) ) )).

fof(existence_m2_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(C)
        & m1_rfunct_3(C,A,B) )
     => ? [D] : m2_rfunct_3(D,A,B,C) ) )).

fof(redefinition_m2_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(C)
        & m1_rfunct_3(C,A,B) )
     => ! [D] :
          ( m2_rfunct_3(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) )).

fof(dt_k1_rfunct_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_rfunct_3(A,B),k1_numbers,k5_numbers) ) )).

fof(commutativity_k1_rfunct_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_rfunct_3(A,B) = k1_rfunct_3(B,A) ) )).

fof(idempotence_k1_rfunct_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_rfunct_3(A,A) = A ) )).

fof(redefinition_k1_rfunct_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_rfunct_3(A,B) = k1_square_1(A,B) ) )).

fof(dt_k2_rfunct_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => m1_subset_1(k2_rfunct_3(A),k1_numbers) ) )).

fof(dt_k3_rfunct_3,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => m1_subset_1(k3_rfunct_3(A),k1_numbers) ) )).

fof(dt_k4_rfunct_3,axiom,(
    ! [A,B] : m1_rfunct_3(k4_rfunct_3(A,B),A,B) )).

fof(redefinition_k4_rfunct_3,axiom,(
    ! [A,B] : k4_rfunct_3(A,B) = k4_partfun1(A,B) )).

fof(dt_k5_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k1_zfmisc_1(A))
        & m1_subset_1(D,B) )
     => m2_rfunct_3(k5_rfunct_3(A,B,C,D),A,B,k4_rfunct_3(A,B)) ) )).

fof(redefinition_k5_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k1_zfmisc_1(A))
        & m1_subset_1(D,B) )
     => k5_rfunct_3(A,B,C,D) = k2_funcop_1(C,D) ) )).

fof(dt_k6_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B))
        & m1_subset_1(D,k4_rfunct_3(A,B)) )
     => m2_rfunct_3(k6_rfunct_3(A,B,C,D),A,k1_numbers,k4_rfunct_3(A,k1_numbers)) ) )).

fof(commutativity_k6_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B))
        & m1_subset_1(D,k4_rfunct_3(A,B)) )
     => k6_rfunct_3(A,B,C,D) = k6_rfunct_3(A,B,D,C) ) )).

fof(redefinition_k6_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B))
        & m1_subset_1(D,k4_rfunct_3(A,B)) )
     => k6_rfunct_3(A,B,C,D) = k3_seq_1(C,D) ) )).

fof(dt_k7_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B))
        & m1_subset_1(D,k4_rfunct_3(A,B)) )
     => m2_rfunct_3(k7_rfunct_3(A,B,C,D),A,k1_numbers,k4_rfunct_3(A,k1_numbers)) ) )).

fof(redefinition_k7_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B))
        & m1_subset_1(D,k4_rfunct_3(A,B)) )
     => k7_rfunct_3(A,B,C,D) = k4_seq_1(C,D) ) )).

fof(dt_k8_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B))
        & m1_subset_1(D,k4_rfunct_3(A,B)) )
     => m2_rfunct_3(k8_rfunct_3(A,B,C,D),A,k1_numbers,k4_rfunct_3(A,k1_numbers)) ) )).

fof(commutativity_k8_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B))
        & m1_subset_1(D,k4_rfunct_3(A,B)) )
     => k8_rfunct_3(A,B,C,D) = k8_rfunct_3(A,B,D,C) ) )).

fof(redefinition_k8_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B))
        & m1_subset_1(D,k4_rfunct_3(A,B)) )
     => k8_rfunct_3(A,B,C,D) = k5_seq_1(C,D) ) )).

fof(dt_k9_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B))
        & m1_subset_1(D,k4_rfunct_3(A,B)) )
     => m2_rfunct_3(k9_rfunct_3(A,B,C,D),A,k1_numbers,k4_rfunct_3(A,k1_numbers)) ) )).

fof(redefinition_k9_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B))
        & m1_subset_1(D,k4_rfunct_3(A,B)) )
     => k9_rfunct_3(A,B,C,D) = k1_rfunct_1(C,D) ) )).

fof(dt_k10_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B)) )
     => m2_rfunct_3(k10_rfunct_3(A,B,C),A,k1_numbers,k4_rfunct_3(A,k1_numbers)) ) )).

fof(redefinition_k10_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B)) )
     => k10_rfunct_3(A,B,C) = k20_seq_1(C) ) )).

fof(dt_k11_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B)) )
     => m2_rfunct_3(k11_rfunct_3(A,B,C),A,k1_numbers,k4_rfunct_3(A,k1_numbers)) ) )).

fof(redefinition_k11_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B)) )
     => k11_rfunct_3(A,B,C) = k15_seq_1(C) ) )).

fof(dt_k12_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B)) )
     => m2_rfunct_3(k12_rfunct_3(A,B,C),A,k1_numbers,k4_rfunct_3(A,k1_numbers)) ) )).

fof(redefinition_k12_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B)) )
     => k12_rfunct_3(A,B,C) = k3_rfunct_1(C) ) )).

fof(dt_k13_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B))
        & v1_xreal_0(D) )
     => m2_rfunct_3(k13_rfunct_3(A,B,C,D),A,k1_numbers,k4_rfunct_3(A,k1_numbers)) ) )).

fof(redefinition_k13_rfunct_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_membered(B)
        & m1_subset_1(C,k4_rfunct_3(A,B))
        & v1_xreal_0(D) )
     => k13_rfunct_3(A,B,C,D) = k12_seq_1(C,D) ) )).

fof(dt_k14_rfunct_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v1_funct_1(k14_rfunct_3(A))
        & v1_funct_2(k14_rfunct_3(A),k2_zfmisc_1(k4_rfunct_3(A,k1_numbers),k4_rfunct_3(A,k1_numbers)),k4_rfunct_3(A,k1_numbers))
        & m2_relset_1(k14_rfunct_3(A),k2_zfmisc_1(k4_rfunct_3(A,k1_numbers),k4_rfunct_3(A,k1_numbers)),k4_rfunct_3(A,k1_numbers)) ) ) )).

fof(dt_k15_rfunct_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,k4_rfunct_3(A,k1_numbers)) )
     => m2_rfunct_3(k15_rfunct_3(A,B),A,k1_numbers,k4_rfunct_3(A,k1_numbers)) ) )).

fof(dt_k16_rfunct_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => m2_finseq_1(k16_rfunct_3(A,B),k4_rfunct_3(A,k1_numbers)) ) )).

fof(dt_k17_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,k4_rfunct_3(A,k1_numbers))
        & m1_finseq_1(C,k1_numbers) )
     => m2_finseq_1(k17_rfunct_3(A,B,C),k4_rfunct_3(A,k1_numbers)) ) )).

fof(dt_k18_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,k4_rfunct_3(A,k1_numbers))
        & m1_subset_1(C,A) )
     => m2_finseq_1(k18_rfunct_3(A,B,C),k1_numbers) ) )).

fof(dt_k19_rfunct_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => ( v1_funct_1(k19_rfunct_3(A,B))
        & m2_relset_1(k19_rfunct_3(A,B),A,k1_numbers) ) ) )).

fof(dt_k20_rfunct_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => ( v1_funct_1(k20_rfunct_3(A,B))
        & m2_relset_1(k20_rfunct_3(A,B),A,k1_numbers) ) ) )).

fof(dt_k21_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers)
        & m1_subset_1(C,k1_numbers) )
     => ( v1_funct_1(k21_rfunct_3(A,B,C))
        & m2_relset_1(k21_rfunct_3(A,B,C),A,k1_numbers) ) ) )).

fof(dt_k22_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => ( v1_rfinseq(k22_rfunct_3(A,B,C))
        & m2_finseq_1(k22_rfunct_3(A,B,C),k1_numbers) ) ) )).

fof(dt_k23_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers)
        & v1_finset_1(C) )
     => ( v1_funct_1(k23_rfunct_3(A,B,C))
        & v1_finset_1(k23_rfunct_3(A,B,C))
        & m2_relset_1(k23_rfunct_3(A,B,C),A,k1_numbers) ) ) )).

fof(redefinition_k23_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers)
        & v1_finset_1(C) )
     => k23_rfunct_3(A,B,C) = k7_relat_1(B,C) ) )).

fof(dt_k24_rfunct_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k1_numbers) )
     => m1_subset_1(k24_rfunct_3(A,B,C),k1_numbers) ) )).
%------------------------------------------------------------------------------