SET007 Axioms: SET007+150.ax


%------------------------------------------------------------------------------
% File     : SET007+150 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Convergence and the Limit of Complex Sequences. Series
% 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    : comseq_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  119 (   1 unit)
%            Number of atoms       :  993 ( 108 equality)
%            Maximal formula depth :   16 (   8 average)
%            Number of connectives :  909 (  35 ~  ;   9  |; 549  &)
%                                         (  13 <=>; 303 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   29 (   1 propositional; 0-3 arity)
%            Number of functors    :   56 (   9 constant; 0-4 arity)
%            Number of variables   :  268 (   0 singleton; 250 !;  18 ?)
%            Maximal term depth    :    6 (   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(cc1_comseq_3,axiom,(
    ! [A] :
      ( m1_relset_1(A,k5_numbers,k1_numbers)
     => ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k1_numbers)
          & v1_series_1(A) )
       => ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k1_numbers)
          & v1_seq_1(A)
          & v4_seq_2(A) ) ) ) )).

fof(cc2_comseq_3,axiom,(
    ! [A] :
      ( m1_relset_1(A,k5_numbers,k1_numbers)
     => ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k1_numbers)
          & v2_series_1(A) )
       => ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k1_numbers)
          & v1_seq_1(A)
          & v4_seq_2(A)
          & v1_series_1(A) ) ) ) )).

fof(rc1_comseq_3,axiom,(
    ? [A] :
      ( m1_relset_1(A,k5_numbers,k1_numbers)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k1_numbers)
      & v1_seq_1(A)
      & v4_seq_2(A)
      & v1_series_1(A)
      & v2_series_1(A) ) )).

fof(fc1_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_relat_1(k1_series_1(k9_comseq_1(k5_numbers,A)))
        & v1_funct_1(k1_series_1(k9_comseq_1(k5_numbers,A)))
        & v1_funct_2(k1_series_1(k9_comseq_1(k5_numbers,A)),k5_numbers,k1_numbers)
        & v1_seq_1(k1_series_1(k9_comseq_1(k5_numbers,A)))
        & v3_seqm_3(k1_series_1(k9_comseq_1(k5_numbers,A))) ) ) )).

fof(fc2_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v2_comseq_2(A)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_relat_1(k3_comseq_3(A))
        & v1_funct_1(k3_comseq_3(A))
        & v1_funct_2(k3_comseq_3(A),k5_numbers,k1_numbers)
        & v1_seq_1(k3_comseq_3(A))
        & v4_seq_2(k3_comseq_3(A)) ) ) )).

fof(fc3_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v2_comseq_2(A)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_relat_1(k4_comseq_3(A))
        & v1_funct_1(k4_comseq_3(A))
        & v1_funct_2(k4_comseq_3(A),k5_numbers,k1_numbers)
        & v1_seq_1(k4_comseq_3(A))
        & v4_seq_2(k4_comseq_3(A)) ) ) )).

fof(rc2_comseq_3,axiom,(
    ? [A] :
      ( m1_relset_1(A,k5_numbers,k2_numbers)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k2_numbers)
      & v1_comseq_3(A) ) )).

fof(fc4_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v1_comseq_3(A)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ( ~ v1_xboole_0(k7_comseq_3(A))
        & v1_relat_1(k7_comseq_3(A))
        & v1_funct_1(k7_comseq_3(A))
        & v1_funct_2(k7_comseq_3(A),k5_numbers,k2_numbers)
        & v1_comseq_2(k7_comseq_3(A))
        & v2_comseq_2(k7_comseq_3(A))
        & v1_partfun1(k7_comseq_3(A),k5_numbers,k2_numbers) ) ) )).

fof(rc3_comseq_3,axiom,(
    ? [A] :
      ( m1_relset_1(A,k5_numbers,k2_numbers)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k2_numbers)
      & v2_comseq_3(A) ) )).

fof(fc5_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v2_comseq_3(A)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ( ~ v1_xboole_0(k9_comseq_1(k5_numbers,A))
        & v1_relat_1(k9_comseq_1(k5_numbers,A))
        & v1_funct_1(k9_comseq_1(k5_numbers,A))
        & v1_funct_2(k9_comseq_1(k5_numbers,A),k5_numbers,k1_numbers)
        & v1_seq_1(k9_comseq_1(k5_numbers,A))
        & v4_seq_2(k9_comseq_1(k5_numbers,A))
        & v1_series_1(k9_comseq_1(k5_numbers,A))
        & v1_partfun1(k9_comseq_1(k5_numbers,A),k5_numbers,k1_numbers) ) ) )).

fof(cc3_comseq_3,axiom,(
    ! [A] :
      ( m1_relset_1(A,k5_numbers,k2_numbers)
     => ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k2_numbers)
          & v1_comseq_3(A) )
       => ( ~ v1_xboole_0(A)
          & v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k2_numbers)
          & v1_comseq_2(A)
          & v2_comseq_2(A)
          & v1_partfun1(A,k5_numbers,k2_numbers) ) ) ) )).

fof(fc6_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v1_comseq_3(A)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_relat_1(k3_comseq_3(A))
        & v1_funct_1(k3_comseq_3(A))
        & v1_funct_2(k3_comseq_3(A),k5_numbers,k1_numbers)
        & v1_seq_1(k3_comseq_3(A))
        & v4_seq_2(k3_comseq_3(A))
        & v1_series_1(k3_comseq_3(A)) ) ) )).

fof(fc7_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v1_comseq_3(A)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_relat_1(k4_comseq_3(A))
        & v1_funct_1(k4_comseq_3(A))
        & v1_funct_2(k4_comseq_3(A),k5_numbers,k1_numbers)
        & v1_seq_1(k4_comseq_3(A))
        & v4_seq_2(k4_comseq_3(A))
        & v1_series_1(k4_comseq_3(A)) ) ) )).

fof(fc8_comseq_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v1_comseq_3(A)
        & m1_relset_1(A,k5_numbers,k2_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_numbers)
        & v1_comseq_3(B)
        & m1_relset_1(B,k5_numbers,k2_numbers) )
     => ( ~ v1_xboole_0(k2_comseq_1(k5_numbers,A,B))
        & v1_relat_1(k2_comseq_1(k5_numbers,A,B))
        & v1_funct_1(k2_comseq_1(k5_numbers,A,B))
        & v1_funct_2(k2_comseq_1(k5_numbers,A,B),k5_numbers,k2_numbers)
        & v1_comseq_2(k2_comseq_1(k5_numbers,A,B))
        & v2_comseq_2(k2_comseq_1(k5_numbers,A,B))
        & v1_partfun1(k2_comseq_1(k5_numbers,A,B),k5_numbers,k2_numbers)
        & v1_comseq_3(k2_comseq_1(k5_numbers,A,B)) ) ) )).

fof(fc9_comseq_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v1_comseq_3(A)
        & m1_relset_1(A,k5_numbers,k2_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_numbers)
        & v1_comseq_3(B)
        & m1_relset_1(B,k5_numbers,k2_numbers) )
     => ( ~ v1_xboole_0(k6_comseq_1(k5_numbers,A,B))
        & v1_relat_1(k6_comseq_1(k5_numbers,A,B))
        & v1_funct_1(k6_comseq_1(k5_numbers,A,B))
        & v1_funct_2(k6_comseq_1(k5_numbers,A,B),k5_numbers,k2_numbers)
        & v1_comseq_2(k6_comseq_1(k5_numbers,A,B))
        & v2_comseq_2(k6_comseq_1(k5_numbers,A,B))
        & v1_partfun1(k6_comseq_1(k5_numbers,A,B),k5_numbers,k2_numbers)
        & v1_comseq_3(k6_comseq_1(k5_numbers,A,B)) ) ) )).

fof(fc10_comseq_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_numbers)
        & v1_comseq_3(B)
        & m1_relset_1(B,k5_numbers,k2_numbers) )
     => ( ~ v1_xboole_0(k4_comseq_1(k5_numbers,B,A))
        & v1_relat_1(k4_comseq_1(k5_numbers,B,A))
        & v1_funct_1(k4_comseq_1(k5_numbers,B,A))
        & v1_funct_2(k4_comseq_1(k5_numbers,B,A),k5_numbers,k2_numbers)
        & v1_comseq_2(k4_comseq_1(k5_numbers,B,A))
        & v2_comseq_2(k4_comseq_1(k5_numbers,B,A))
        & v1_partfun1(k4_comseq_1(k5_numbers,B,A),k5_numbers,k2_numbers)
        & v1_comseq_3(k4_comseq_1(k5_numbers,B,A)) ) ) )).

fof(fc11_comseq_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v1_comseq_3(A)
        & m1_relset_1(A,k5_numbers,k2_numbers)
        & m1_subset_1(B,k5_numbers) )
     => ( ~ v1_xboole_0(k6_comseq_3(A,B))
        & v1_relat_1(k6_comseq_3(A,B))
        & v1_funct_1(k6_comseq_3(A,B))
        & v1_funct_2(k6_comseq_3(A,B),k5_numbers,k2_numbers)
        & v1_comseq_2(k6_comseq_3(A,B))
        & v2_comseq_2(k6_comseq_3(A,B))
        & v1_partfun1(k6_comseq_3(A,B),k5_numbers,k2_numbers)
        & v1_comseq_3(k6_comseq_3(A,B)) ) ) )).

fof(fc12_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v2_comseq_3(A)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_relat_1(k1_series_1(k9_comseq_1(k5_numbers,A)))
        & v1_funct_1(k1_series_1(k9_comseq_1(k5_numbers,A)))
        & v1_funct_2(k1_series_1(k9_comseq_1(k5_numbers,A)),k5_numbers,k1_numbers)
        & v1_seq_1(k1_series_1(k9_comseq_1(k5_numbers,A)))
        & v1_seq_2(k1_series_1(k9_comseq_1(k5_numbers,A)))
        & v3_seqm_3(k1_series_1(k9_comseq_1(k5_numbers,A))) ) ) )).

fof(cc4_comseq_3,axiom,(
    ! [A] :
      ( m1_relset_1(A,k5_numbers,k2_numbers)
     => ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k2_numbers)
          & v2_comseq_3(A) )
       => ( ~ v1_xboole_0(A)
          & v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k2_numbers)
          & v1_comseq_2(A)
          & v2_comseq_2(A)
          & v1_partfun1(A,k5_numbers,k2_numbers)
          & v1_comseq_3(A) ) ) ) )).

fof(rc4_comseq_3,axiom,(
    ? [A] :
      ( m1_relset_1(A,k5_numbers,k2_numbers)
      & ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k2_numbers)
      & v1_comseq_2(A)
      & v2_comseq_2(A)
      & v1_partfun1(A,k5_numbers,k2_numbers)
      & v1_comseq_3(A)
      & v2_comseq_3(A) ) )).

fof(t1_comseq_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( k1_nat_1(A,np__1) != k5_complex1
        & k3_xcmplx_0(k1_nat_1(A,np__1),k7_complex1) != k5_complex1 ) ) )).

fof(t2_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k2_seq_1(k5_numbers,k1_numbers,A,B) = np__0 )
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k22_seq_1(A)),B) = np__0 ) ) ) )).

fof(t3_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k2_seq_1(k5_numbers,k1_numbers,A,B) = np__0 )
       => v2_series_1(A) ) ) )).

fof(t4_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v4_seq_2(A)
       => ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ~ ( ~ r1_xreal_0(B,np__0)
                & ! [C] :
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => ? [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & ? [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                            & r1_xreal_0(C,D)
                            & r1_xreal_0(C,E)
                            & r1_xreal_0(B,k18_complex1(k5_real_1(k2_seq_1(k5_numbers,k1_numbers,A,D),k2_seq_1(k5_numbers,k1_numbers,A,E)))) ) ) ) ) ) ) ) )).

fof(t5_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),B) )
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => r1_xreal_0(k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),k1_nat_1(C,D)),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),C)),k4_real_1(B,D)) ) ) ) ) ) )).

fof(t6_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),B) )
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),C),k4_real_1(B,k1_nat_1(C,np__1))) ) ) ) ) )).

fof(t7_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( r1_xreal_0(E,C)
                         => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,E),k4_real_1(D,k2_seq_1(k5_numbers,k1_numbers,B,E))) ) )
                   => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),C),k4_real_1(D,k2_seq_1(k5_numbers,k1_numbers,k1_series_1(B),C))) ) ) ) ) ) )).

fof(t8_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ( ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( r1_xreal_0(E,C)
                         => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,E),k4_real_1(D,k2_seq_1(k5_numbers,k1_numbers,B,E))) ) )
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( r1_xreal_0(E,C)
                         => ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( r1_xreal_0(k1_nat_1(E,F),C)
                               => r1_xreal_0(k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),k1_nat_1(E,F)),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),E)),k4_real_1(D,k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(B),k1_nat_1(E,F)),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(B),E)))) ) ) ) ) ) ) ) ) ) )).

fof(t9_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,A,B)) )
       => ( ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(B,C)
                   => k18_complex1(k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),C),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),B))) = k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),C),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),B)) ) ) )
          & ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => k18_complex1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),B)) = k2_seq_1(k5_numbers,k1_numbers,k1_series_1(A),B) ) ) ) ) )).

fof(t10_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( ( v2_comseq_2(A)
              & v2_comseq_2(B)
              & k2_comseq_2(k6_comseq_1(k5_numbers,A,B)) = k5_complex1 )
           => k2_comseq_2(A) = k2_comseq_2(B) ) ) ) )).

fof(d1_comseq_3,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( B = k1_comseq_3(A)
          <=> ( k1_comseq_1(B,np__0) = k6_complex1
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k1_comseq_1(B,k1_nat_1(C,np__1)) = k3_xcmplx_0(k1_comseq_1(B,C),A) ) ) ) ) ) )).

fof(d2_comseq_3,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v4_ordinal2(B)
         => k2_comseq_3(A,B) = k1_funct_1(k1_comseq_3(A),B) ) ) )).

fof(t11_comseq_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => k2_comseq_3(A,np__0) = k6_complex1 ) )).

fof(d3_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( B = k3_comseq_3(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_seq_1(k5_numbers,k1_numbers,B,C) = k3_complex1(k1_comseq_1(A,C)) ) ) ) ) )).

fof(d4_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( B = k4_comseq_3(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_seq_1(k5_numbers,k1_numbers,B,C) = k4_complex1(k1_comseq_1(A,C)) ) ) ) ) )).

fof(t12_comseq_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => r1_xreal_0(k17_complex1(A),k3_real_1(k18_complex1(k3_complex1(A)),k18_complex1(k4_complex1(A)))) ) )).

fof(t13_comseq_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ( r1_xreal_0(k18_complex1(k3_complex1(A)),k17_complex1(A))
        & r1_xreal_0(k18_complex1(k4_complex1(A)),k17_complex1(A)) ) ) )).

fof(t14_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( ( k3_comseq_3(A) = k3_comseq_3(B)
              & k4_comseq_3(A) = k4_comseq_3(B) )
           => A = B ) ) ) )).

fof(t15_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( k9_seq_1(k3_comseq_3(A),k3_comseq_3(B)) = k3_comseq_3(k2_comseq_1(k5_numbers,A,B))
            & k9_seq_1(k4_comseq_3(A),k4_comseq_3(B)) = k4_comseq_3(k2_comseq_1(k5_numbers,A,B)) ) ) ) )).

fof(t16_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( k17_seq_1(k3_comseq_3(A)) = k3_comseq_3(k5_comseq_1(k5_numbers,A))
        & k17_seq_1(k4_comseq_3(A)) = k4_comseq_3(k5_comseq_1(k5_numbers,A)) ) ) )).

fof(t17_comseq_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k2_numbers)
         => ( k4_real_1(A,k3_complex1(B)) = k3_complex1(k3_xcmplx_0(A,B))
            & k4_real_1(A,k4_complex1(B)) = k4_complex1(k3_xcmplx_0(A,B)) ) ) ) )).

fof(t18_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( k10_seq_1(k3_comseq_3(A),k3_comseq_3(B)) = k3_comseq_3(k6_comseq_1(k5_numbers,A,B))
            & k10_seq_1(k4_comseq_3(A),k4_comseq_3(B)) = k4_comseq_3(k6_comseq_1(k5_numbers,A,B)) ) ) ) )).

fof(t19_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( k14_seq_1(k3_comseq_3(A),B) = k3_comseq_3(k4_comseq_1(k5_numbers,A,B))
            & k14_seq_1(k4_comseq_3(A),B) = k4_comseq_3(k4_comseq_1(k5_numbers,A,B)) ) ) ) )).

fof(t20_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k2_numbers)
         => ( k3_comseq_3(k4_comseq_1(k5_numbers,A,B)) = k10_seq_1(k14_seq_1(k3_comseq_3(A),k3_complex1(B)),k14_seq_1(k4_comseq_3(A),k4_complex1(B)))
            & k4_comseq_3(k4_comseq_1(k5_numbers,A,B)) = k9_seq_1(k14_seq_1(k4_comseq_3(A),k3_complex1(B)),k14_seq_1(k3_comseq_3(A),k4_complex1(B))) ) ) ) )).

fof(t21_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( k3_comseq_3(k3_comseq_1(k5_numbers,A,B)) = k10_seq_1(k11_seq_1(k3_comseq_3(A),k3_comseq_3(B)),k11_seq_1(k4_comseq_3(A),k4_comseq_3(B)))
            & k4_comseq_3(k3_comseq_1(k5_numbers,A,B)) = k9_seq_1(k11_seq_1(k3_comseq_3(A),k4_comseq_3(B)),k11_seq_1(k4_comseq_3(A),k3_comseq_3(B))) ) ) ) )).

fof(t22_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & v1_seqm_3(B)
            & v7_seqm_3(B)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( k3_comseq_3(k5_comseq_3(B,A)) = k3_seqm_3(B,k3_comseq_3(A))
            & k4_comseq_3(k5_comseq_3(B,A)) = k3_seqm_3(B,k4_comseq_3(A)) ) ) ) )).

fof(d5_comseq_3,axiom,(
    $true )).

fof(d6_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k2_numbers)
                & m2_relset_1(C,k5_numbers,k2_numbers) )
             => ( C = k6_comseq_3(A,B)
              <=> ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k1_comseq_1(C,D) = k1_comseq_1(A,k1_nat_1(D,B)) ) ) ) ) ) )).

fof(t23_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k1_seqm_3(k3_comseq_3(A),B) = k3_comseq_3(k6_comseq_3(A,B))
            & k1_seqm_3(k4_comseq_3(A),B) = k4_comseq_3(k6_comseq_3(A,B)) ) ) ) )).

fof(d7_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( B = k7_comseq_3(A)
          <=> ( k1_comseq_1(B,np__0) = k1_comseq_1(A,np__0)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k1_comseq_1(B,k1_nat_1(C,np__1)) = k8_complex1(k1_comseq_1(B,C),k1_comseq_1(A,k1_nat_1(C,np__1))) ) ) ) ) ) )).

fof(d8_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => k8_comseq_3(A) = k2_comseq_2(k7_comseq_3(A)) ) )).

fof(t24_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k1_comseq_1(A,B) = k5_complex1 )
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k1_comseq_1(k7_comseq_3(A),B) = k5_complex1 ) ) ) )).

fof(t25_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k1_comseq_1(A,B) = k5_complex1 )
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k9_comseq_1(k5_numbers,A)),B) = np__0 ) ) ) )).

fof(t26_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( k1_series_1(k3_comseq_3(A)) = k3_comseq_3(k7_comseq_3(A))
        & k1_series_1(k4_comseq_3(A)) = k4_comseq_3(k7_comseq_3(A)) ) ) )).

fof(t27_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => k2_comseq_1(k5_numbers,k7_comseq_3(A),k7_comseq_3(B)) = k7_comseq_3(k2_comseq_1(k5_numbers,A,B)) ) ) )).

fof(t28_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => k6_comseq_1(k5_numbers,k7_comseq_3(A),k7_comseq_3(B)) = k7_comseq_3(k6_comseq_1(k5_numbers,A,B)) ) ) )).

fof(t29_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k2_numbers)
         => k7_comseq_3(k4_comseq_1(k5_numbers,A,B)) = k4_comseq_1(k5_numbers,k7_comseq_3(A),B) ) ) )).

fof(t30_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r1_xreal_0(k17_complex1(k1_comseq_1(k7_comseq_3(A),B)),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k9_comseq_1(k5_numbers,A)),B)) ) ) )).

fof(t31_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => r1_xreal_0(k17_complex1(k11_complex1(k1_comseq_1(k7_comseq_3(A),B),k1_comseq_1(k7_comseq_3(A),C))),k18_complex1(k5_real_1(k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k9_comseq_1(k5_numbers,A)),B),k2_seq_1(k5_numbers,k1_numbers,k1_series_1(k9_comseq_1(k5_numbers,A)),C)))) ) ) ) )).

fof(t32_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k1_seqm_3(k1_series_1(k3_comseq_3(A)),B) = k3_comseq_3(k6_comseq_3(k7_comseq_3(A),B))
            & k1_seqm_3(k1_series_1(k4_comseq_3(A)),B) = k4_comseq_3(k6_comseq_3(k7_comseq_3(A),B)) ) ) ) )).

fof(t33_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k1_comseq_1(A,C) = k1_comseq_1(B,np__0) )
           => k7_comseq_3(k6_comseq_3(B,np__1)) = k6_comseq_1(k5_numbers,k6_comseq_3(k7_comseq_3(B),np__1),A) ) ) ) )).

fof(t34_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => v3_seqm_3(k1_series_1(k9_comseq_1(k5_numbers,A))) ) )).

fof(t35_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_xreal_0(D,C)
                     => k1_comseq_1(A,D) = k1_comseq_1(B,D) ) )
               => k1_comseq_1(k7_comseq_3(A),C) = k1_comseq_1(k7_comseq_3(B),C) ) ) ) ) )).

fof(t36_comseq_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ( k6_complex1 != A
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k1_comseq_1(k7_comseq_3(k1_comseq_3(A)),B) = k13_complex1(k11_complex1(k6_complex1,k2_comseq_3(A,k1_nat_1(B,np__1))),k11_complex1(k6_complex1,A)) ) ) ) )).

fof(t37_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k2_numbers)
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k1_comseq_1(A,k1_nat_1(C,np__1)) = k9_complex1(B,k1_comseq_1(A,C)) )
           => ( B = k6_complex1
              | ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k1_comseq_1(k7_comseq_3(A),C) = k9_complex1(k1_comseq_1(A,np__0),k13_complex1(k11_complex1(k6_complex1,k2_comseq_3(B,k1_nat_1(C,np__1))),k11_complex1(k6_complex1,B))) ) ) ) ) ) )).

fof(t38_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k2_numbers)
                & m2_relset_1(C,k5_numbers,k2_numbers) )
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( k3_complex1(k1_comseq_1(C,D)) = k2_seq_1(k5_numbers,k1_numbers,A,D)
                      & k4_complex1(k1_comseq_1(C,D)) = k2_seq_1(k5_numbers,k1_numbers,B,D) ) )
               => ( ( v4_seq_2(A)
                    & v4_seq_2(B) )
                <=> v2_comseq_2(C) ) ) ) ) ) )).

fof(t39_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v4_seq_2(A)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & v4_seq_2(B)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k2_numbers)
                & m2_relset_1(C,k5_numbers,k2_numbers) )
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( k3_complex1(k1_comseq_1(C,D)) = k2_seq_1(k5_numbers,k1_numbers,A,D)
                      & k4_complex1(k1_comseq_1(C,D)) = k2_seq_1(k5_numbers,k1_numbers,B,D) ) )
               => ( v2_comseq_2(C)
                  & k2_comseq_2(C) = k2_xcmplx_0(k2_seq_2(A),k3_xcmplx_0(k2_seq_2(B),k7_complex1)) ) ) ) ) ) )).

fof(t40_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k2_numbers)
                & v2_comseq_2(C)
                & m2_relset_1(C,k5_numbers,k2_numbers) )
             => ( ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( k3_complex1(k1_comseq_1(C,D)) = k2_seq_1(k5_numbers,k1_numbers,A,D)
                      & k4_complex1(k1_comseq_1(C,D)) = k2_seq_1(k5_numbers,k1_numbers,B,D) ) )
               => ( v4_seq_2(A)
                  & v4_seq_2(B)
                  & k2_seq_2(A) = k3_complex1(k2_comseq_2(C))
                  & k2_seq_2(B) = k4_complex1(k2_comseq_2(C)) ) ) ) ) ) )).

fof(t41_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & v2_comseq_2(A)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v4_seq_2(k3_comseq_3(A))
        & v4_seq_2(k4_comseq_3(A))
        & k2_seq_2(k3_comseq_3(A)) = k3_complex1(k2_comseq_2(A))
        & k2_seq_2(k4_comseq_3(A)) = k4_complex1(k2_comseq_2(A)) ) ) )).

fof(t42_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( ( v4_seq_2(k3_comseq_3(A))
          & v4_seq_2(k4_comseq_3(A)) )
       => ( v2_comseq_2(A)
          & k3_complex1(k2_comseq_2(A)) = k2_seq_2(k3_comseq_3(A))
          & k4_complex1(k2_comseq_2(A)) = k2_seq_2(k4_comseq_3(A)) ) ) ) )).

fof(t43_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k2_numbers)
         => ( ( k1_comseq_1(A,np__0) = B
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k1_comseq_1(A,k1_nat_1(C,np__1)) = k9_complex1(k1_comseq_1(A,C),B) ) )
           => ( r1_xreal_0(k17_complex1(B),np__0)
              | r1_xreal_0(np__1,k17_complex1(B))
              | ( v2_comseq_2(A)
                & k2_comseq_2(A) = k5_complex1 ) ) ) ) ) )).

fof(t44_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k2_numbers)
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k1_comseq_1(A,C) = k2_comseq_3(B,k1_nat_1(C,np__1)) )
           => ( r1_xreal_0(np__1,k17_complex1(B))
              | ( v2_comseq_2(A)
                & k2_comseq_2(A) = k5_complex1 ) ) ) ) ) )).

fof(t45_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ~ ( ~ r1_xreal_0(B,np__0)
              & ? [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(C,D)
                       => r1_xreal_0(B,k17_complex1(k1_comseq_1(A,D))) ) ) )
              & v4_seq_2(k9_comseq_1(k5_numbers,A))
              & k2_seq_2(k9_comseq_1(k5_numbers,A)) = np__0 ) ) ) )).

fof(t46_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v2_comseq_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ~ ( ~ r1_xreal_0(B,np__0)
                & ! [C] :
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => ? [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & r1_xreal_0(C,D)
                        & r1_xreal_0(B,k17_complex1(k11_complex1(k1_comseq_1(A,D),k1_comseq_1(A,C)))) ) ) ) ) ) ) )).

fof(t47_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v2_comseq_2(A)
       => ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ~ ( ~ r1_xreal_0(B,np__0)
                & ! [C] :
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => ? [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & ? [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                            & r1_xreal_0(C,D)
                            & r1_xreal_0(C,E)
                            & r1_xreal_0(B,k17_complex1(k11_complex1(k1_comseq_1(A,D),k1_comseq_1(A,E)))) ) ) ) ) ) ) ) )).

fof(t48_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r1_xreal_0(k17_complex1(k1_comseq_1(B,C)),k2_seq_1(k5_numbers,k1_numbers,A,C)) )
              & v4_seq_2(A)
              & k2_seq_2(A) = np__0 )
           => ( v2_comseq_2(B)
              & k2_comseq_2(B) = k5_complex1 ) ) ) ) )).

fof(d9_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( m1_comseq_3(B,A)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & v1_seqm_3(C)
                & v7_seqm_3(C)
                & m2_relset_1(C,k5_numbers,k1_numbers)
                & B = k5_comseq_3(C,A) ) ) ) ) )).

fof(t49_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( m1_comseq_3(A,B)
           => ( m1_seqm_3(k3_comseq_3(A),k3_comseq_3(B))
              & m1_seqm_3(k4_comseq_3(A),k4_comseq_3(B)) ) ) ) ) )).

fof(t50_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k2_numbers)
                & m2_relset_1(C,k5_numbers,k2_numbers) )
             => ( ( m1_comseq_3(A,B)
                  & m1_comseq_3(B,C) )
               => m1_comseq_3(A,C) ) ) ) ) )).

fof(t51_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ~ ( v1_comseq_2(A)
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k2_numbers)
                & m2_relset_1(B,k5_numbers,k2_numbers) )
             => ~ ( m1_comseq_3(B,A)
                  & v2_comseq_2(B) ) ) ) ) )).

fof(d10_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_comseq_3(A)
      <=> v2_comseq_2(k7_comseq_3(A)) ) ) )).

fof(d11_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v2_comseq_3(A)
      <=> v1_series_1(k9_comseq_1(k5_numbers,A)) ) ) )).

fof(t52_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k1_comseq_1(A,B) = k5_complex1 )
       => v2_comseq_3(A) ) ) )).

fof(t53_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_comseq_3(A)
       => ( v2_comseq_2(A)
          & k2_comseq_2(A) = k5_complex1 ) ) ) )).

fof(t54_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_comseq_3(A)
       => ( v1_series_1(k3_comseq_3(A))
          & v1_series_1(k4_comseq_3(A))
          & k8_comseq_3(A) = k2_xcmplx_0(k2_series_1(k3_comseq_3(A)),k3_xcmplx_0(k2_series_1(k4_comseq_3(A)),k7_complex1)) ) ) ) )).

fof(t55_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( ( v1_comseq_3(A)
              & v1_comseq_3(B) )
           => ( v1_comseq_3(k2_comseq_1(k5_numbers,A,B))
              & k8_comseq_3(k2_comseq_1(k5_numbers,A,B)) = k8_complex1(k8_comseq_3(A),k8_comseq_3(B)) ) ) ) ) )).

fof(t56_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( ( v1_comseq_3(A)
              & v1_comseq_3(B) )
           => ( v1_comseq_3(k6_comseq_1(k5_numbers,A,B))
              & k8_comseq_3(k6_comseq_1(k5_numbers,A,B)) = k11_complex1(k8_comseq_3(A),k8_comseq_3(B)) ) ) ) ) )).

fof(t57_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k2_numbers)
         => ( v1_comseq_3(A)
           => ( v1_comseq_3(k4_comseq_1(k5_numbers,A,B))
              & k8_comseq_3(k4_comseq_1(k5_numbers,A,B)) = k9_complex1(B,k8_comseq_3(A)) ) ) ) ) )).

fof(t58_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( ( v1_series_1(k3_comseq_3(A))
          & v1_series_1(k4_comseq_3(A)) )
       => ( v1_comseq_3(A)
          & k8_comseq_3(A) = k2_xcmplx_0(k2_series_1(k3_comseq_3(A)),k3_xcmplx_0(k2_series_1(k4_comseq_3(A)),k7_complex1)) ) ) ) )).

fof(t59_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_comseq_3(A)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => v1_comseq_3(k6_comseq_3(A,B)) ) ) ) )).

fof(t60_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( ? [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & v1_comseq_3(k6_comseq_3(A,B)) )
       => v1_comseq_3(A) ) ) )).

fof(t61_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_comseq_3(A)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k8_comseq_3(A) = k8_complex1(k1_comseq_1(k7_comseq_3(A),B),k8_comseq_3(k6_comseq_3(A,k1_nat_1(B,np__1)))) ) ) ) )).

fof(t62_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_seq_2(k1_series_1(k9_comseq_1(k5_numbers,A)))
      <=> v2_comseq_3(A) ) ) )).

fof(t63_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_comseq_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ~ ( ~ r1_xreal_0(B,np__0)
                & ! [C] :
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => ? [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                        & r1_xreal_0(C,D)
                        & r1_xreal_0(B,k17_complex1(k11_complex1(k1_comseq_1(k7_comseq_3(A),D),k1_comseq_1(k7_comseq_3(A),C)))) ) ) ) ) ) ) )).

fof(t64_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v2_comseq_3(A)
       => v1_comseq_3(A) ) ) )).

fof(t65_comseq_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ( ~ r1_xreal_0(np__1,k17_complex1(A))
       => ( v1_comseq_3(k1_comseq_3(A))
          & k8_comseq_3(k1_comseq_3(A)) = k13_complex1(k6_complex1,k11_complex1(k6_complex1,A)) ) ) ) )).

fof(t66_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k2_numbers)
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k1_comseq_1(A,k1_nat_1(C,np__1)) = k9_complex1(B,k1_comseq_1(A,C)) )
           => ( r1_xreal_0(np__1,k17_complex1(B))
              | ( v1_comseq_3(A)
                & k8_comseq_3(A) = k13_complex1(k1_comseq_1(A,np__0),k11_complex1(k6_complex1,B)) ) ) ) ) ) )).

fof(t67_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( v1_series_1(A)
           => ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ? [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                      & r1_xreal_0(C,D)
                      & ~ r1_xreal_0(k17_complex1(k1_comseq_1(B,D)),k2_seq_1(k5_numbers,k1_numbers,A,D)) ) )
              | v2_comseq_3(B) ) ) ) ) )).

fof(t68_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),C))
                    & r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),C),k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),C)) ) )
              & v2_comseq_3(B) )
           => ( v2_comseq_3(A)
              & r1_xreal_0(k2_series_1(k9_comseq_1(k5_numbers,A)),k2_series_1(k9_comseq_1(k5_numbers,B))) ) ) ) ) )).

fof(t69_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ~ ( ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),B),np__0) )
          & ? [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(B,C)
                   => r1_xreal_0(np__1,k6_real_1(k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),k1_nat_1(C,np__1)),k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),C))) ) ) )
          & v2_comseq_3(A) ) ) )).

fof(t70_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k2_seq_1(k5_numbers,k1_numbers,A,C) = k2_power(C,k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),C)) )
              & v4_seq_2(A) )
           => ( r1_xreal_0(np__1,k2_seq_2(A))
              | v2_comseq_3(B) ) ) ) ) )).

fof(t71_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ~ ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k2_seq_1(k5_numbers,k1_numbers,A,C) = k2_power(C,k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),C)) )
              & ? [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(C,D)
                       => r1_xreal_0(np__1,k2_seq_1(k5_numbers,k1_numbers,A,D)) ) ) )
              & v1_series_1(k9_comseq_1(k5_numbers,B)) ) ) ) )).

fof(t72_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ~ ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k2_seq_1(k5_numbers,k1_numbers,A,C) = k2_power(C,k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),C)) )
              & v4_seq_2(A)
              & ~ r1_xreal_0(k2_seq_2(A),np__1)
              & v2_comseq_3(B) ) ) ) )).

fof(t73_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( ( v4_seqm_3(k9_comseq_1(k5_numbers,B))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => k2_seq_1(k5_numbers,k1_numbers,A,C) = k4_real_1(k4_power(np__2,C),k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),k4_power(np__2,C))) ) )
           => ( v2_comseq_3(B)
            <=> v1_series_1(A) ) ) ) ) )).

fof(t74_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r1_xreal_0(np__1,C)
                 => k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),C) = k6_real_1(np__1,k4_power(C,B)) ) )
           => ( r1_xreal_0(B,np__1)
              | v2_comseq_3(A) ) ) ) ) )).

fof(t75_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ~ ( r1_xreal_0(B,np__1)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(np__1,C)
                   => k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),C) = k6_real_1(np__1,k4_power(C,B)) ) )
              & v2_comseq_3(A) ) ) ) )).

fof(t76_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( k1_comseq_1(B,C) != k5_complex1
                    & k2_seq_1(k5_numbers,k1_numbers,A,C) = k6_real_1(k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),k1_nat_1(C,np__1)),k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,B),C)) ) )
              & v4_seq_2(A) )
           => ( r1_xreal_0(np__1,k2_seq_2(A))
              | v2_comseq_3(B) ) ) ) ) )).

fof(t77_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ~ ( ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => k1_comseq_1(A,B) != k5_complex1 )
          & ? [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(B,C)
                   => r1_xreal_0(np__1,k6_real_1(k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),k1_nat_1(C,np__1)),k2_seq_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A),C))) ) ) )
          & v2_comseq_3(A) ) ) )).

fof(dt_m1_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ! [B] :
          ( m1_comseq_3(B,A)
         => ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) ) ) ) )).

fof(existence_m1_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ? [B] : m1_comseq_3(B,A) ) )).

fof(dt_k1_comseq_3,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ( v1_funct_1(k1_comseq_3(A))
        & v1_funct_2(k1_comseq_3(A),k5_numbers,k2_numbers)
        & m2_relset_1(k1_comseq_3(A),k5_numbers,k2_numbers) ) ) )).

fof(dt_k2_comseq_3,axiom,(
    ! [A,B] :
      ( ( v1_xcmplx_0(A)
        & v4_ordinal2(B) )
     => m1_subset_1(k2_comseq_3(A,B),k2_numbers) ) )).

fof(dt_k3_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_funct_1(k3_comseq_3(A))
        & v1_funct_2(k3_comseq_3(A),k5_numbers,k1_numbers)
        & m2_relset_1(k3_comseq_3(A),k5_numbers,k1_numbers) ) ) )).

fof(dt_k4_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_funct_1(k4_comseq_3(A))
        & v1_funct_2(k4_comseq_3(A),k5_numbers,k1_numbers)
        & m2_relset_1(k4_comseq_3(A),k5_numbers,k1_numbers) ) ) )).

fof(dt_k5_comseq_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v1_seqm_3(A)
        & v7_seqm_3(A)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_numbers)
        & m1_relset_1(B,k5_numbers,k2_numbers) )
     => ( v1_funct_1(k5_comseq_3(A,B))
        & v1_funct_2(k5_comseq_3(A,B),k5_numbers,k2_numbers)
        & m2_relset_1(k5_comseq_3(A,B),k5_numbers,k2_numbers) ) ) )).

fof(redefinition_k5_comseq_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v1_seqm_3(A)
        & v7_seqm_3(A)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_numbers)
        & m1_relset_1(B,k5_numbers,k2_numbers) )
     => k5_comseq_3(A,B) = k5_relat_1(A,B) ) )).

fof(dt_k6_comseq_3,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m1_relset_1(A,k5_numbers,k2_numbers)
        & m1_subset_1(B,k5_numbers) )
     => ( v1_funct_1(k6_comseq_3(A,B))
        & v1_funct_2(k6_comseq_3(A,B),k5_numbers,k2_numbers)
        & m2_relset_1(k6_comseq_3(A,B),k5_numbers,k2_numbers) ) ) )).

fof(dt_k7_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => ( v1_funct_1(k7_comseq_3(A))
        & v1_funct_2(k7_comseq_3(A),k5_numbers,k2_numbers)
        & m2_relset_1(k7_comseq_3(A),k5_numbers,k2_numbers) ) ) )).

fof(dt_k8_comseq_3,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m1_relset_1(A,k5_numbers,k2_numbers) )
     => m1_subset_1(k8_comseq_3(A),k2_numbers) ) )).
%------------------------------------------------------------------------------