SET007 Axioms: SET007+143.ax


%------------------------------------------------------------------------------
% File     : SET007+143 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Property of Complex Functions
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : cfunct_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  101 (  12 unit)
%            Number of atoms       :  645 (  93 equality)
%            Maximal formula depth :   14 (   8 average)
%            Number of connectives :  636 (  92 ~  ;   0  |; 223  &)
%                                         (   9 <=>; 312 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   17 (   1 propositional; 0-4 arity)
%            Number of functors    :   33 (   5 constant; 0-4 arity)
%            Number of variables   :  311 (   0 singleton; 310 !;   1 ?)
%            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(d1_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => ( D = k1_cfunct_1(A,B,C)
                  <=> ( k4_relset_1(A,k2_numbers,D) = k5_subset_1(A,k4_relset_1(A,k2_numbers,B),k6_subset_1(A,k4_relset_1(A,k2_numbers,C),k11_relset_1(A,k2_numbers,C,k1_tarski(np__0))))
                      & ! [E] :
                          ( m1_subset_1(E,A)
                         => ( r2_hidden(E,k4_relset_1(A,k2_numbers,D))
                           => k4_finseq_4(A,k2_numbers,D,E) = k9_complex1(k4_finseq_4(A,k2_numbers,B,E),k12_complex1(k4_finseq_4(A,k2_numbers,C,E))) ) ) ) ) ) ) ) ) )).

fof(d2_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ( C = k2_cfunct_1(A,B)
              <=> ( k4_relset_1(A,k2_numbers,C) = k6_subset_1(A,k4_relset_1(A,k2_numbers,B),k11_relset_1(A,k2_numbers,B,k1_tarski(np__0)))
                  & ! [D] :
                      ( m1_subset_1(D,A)
                     => ( r2_hidden(D,k4_relset_1(A,k2_numbers,C))
                       => k4_finseq_4(A,k2_numbers,C,D) = k12_complex1(k4_finseq_4(A,k2_numbers,B,D)) ) ) ) ) ) ) ) )).

fof(t1_cfunct_1,axiom,(
    $true )).

fof(t2_cfunct_1,axiom,(
    $true )).

fof(t3_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ( k4_relset_1(A,k2_numbers,k2_comseq_1(A,B,C)) = k5_subset_1(A,k4_relset_1(A,k2_numbers,B),k4_relset_1(A,k2_numbers,C))
                & ! [D] :
                    ( m1_subset_1(D,A)
                   => ( r2_hidden(D,k4_relset_1(A,k2_numbers,k2_comseq_1(A,B,C)))
                     => k4_finseq_4(A,k2_numbers,k2_comseq_1(A,B,C),D) = k8_complex1(k4_finseq_4(A,k2_numbers,B,D),k4_finseq_4(A,k2_numbers,C,D)) ) ) ) ) ) ) )).

fof(t4_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ( k4_relset_1(A,k2_numbers,k6_comseq_1(A,B,C)) = k5_subset_1(A,k4_relset_1(A,k2_numbers,B),k4_relset_1(A,k2_numbers,C))
                & ! [D] :
                    ( m1_subset_1(D,A)
                   => ( r2_hidden(D,k4_relset_1(A,k2_numbers,k6_comseq_1(A,B,C)))
                     => k4_finseq_4(A,k2_numbers,k6_comseq_1(A,B,C),D) = k11_complex1(k4_finseq_4(A,k2_numbers,B,D),k4_finseq_4(A,k2_numbers,C,D)) ) ) ) ) ) ) )).

fof(t5_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ( k4_relset_1(A,k2_numbers,k3_comseq_1(A,B,C)) = k5_subset_1(A,k4_relset_1(A,k2_numbers,B),k4_relset_1(A,k2_numbers,C))
                & ! [D] :
                    ( m1_subset_1(D,A)
                   => ( r2_hidden(D,k4_relset_1(A,k2_numbers,k3_comseq_1(A,B,C)))
                     => k4_finseq_4(A,k2_numbers,k3_comseq_1(A,B,C),D) = k9_complex1(k4_finseq_4(A,k2_numbers,B,D),k4_finseq_4(A,k2_numbers,C,D)) ) ) ) ) ) ) )).

fof(t6_cfunct_1,axiom,(
    $true )).

fof(t7_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k2_numbers)
             => ( k4_relset_1(A,k2_numbers,k4_comseq_1(A,B,C)) = k4_relset_1(A,k2_numbers,B)
                & ! [D] :
                    ( m1_subset_1(D,A)
                   => ( r2_hidden(D,k4_relset_1(A,k2_numbers,k4_comseq_1(A,B,C)))
                     => k4_finseq_4(A,k2_numbers,k4_comseq_1(A,B,C),D) = k9_complex1(C,k4_finseq_4(A,k2_numbers,B,D)) ) ) ) ) ) ) )).

fof(t8_cfunct_1,axiom,(
    $true )).

fof(t9_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ( k4_relset_1(A,k2_numbers,k5_comseq_1(A,B)) = k4_relset_1(A,k2_numbers,B)
            & ! [C] :
                ( m1_subset_1(C,A)
               => ( r2_hidden(C,k4_relset_1(A,k2_numbers,k5_comseq_1(A,B)))
                 => k4_finseq_4(A,k2_numbers,k5_comseq_1(A,B),C) = k10_complex1(k4_finseq_4(A,k2_numbers,B,C)) ) ) ) ) ) )).

fof(t10_cfunct_1,axiom,(
    $true )).

fof(t11_cfunct_1,axiom,(
    $true )).

fof(t12_cfunct_1,axiom,(
    $true )).

fof(t13_cfunct_1,axiom,(
    $true )).

fof(t14_cfunct_1,axiom,(
    $true )).

fof(t15_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ( r1_tarski(k4_relset_1(A,k2_numbers,k2_cfunct_1(A,B)),k4_relset_1(A,k2_numbers,B))
            & k5_subset_1(A,k4_relset_1(A,k2_numbers,B),k6_subset_1(A,k4_relset_1(A,k2_numbers,B),k11_relset_1(A,k2_numbers,B,k1_tarski(np__0)))) = k6_subset_1(A,k4_relset_1(A,k2_numbers,B),k11_relset_1(A,k2_numbers,B,k1_tarski(np__0))) ) ) ) )).

fof(t16_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => k6_subset_1(A,k4_relset_1(A,k2_numbers,k3_comseq_1(A,B,C)),k11_relset_1(A,k2_numbers,k3_comseq_1(A,B,C),k1_tarski(np__0))) = k5_subset_1(A,k6_subset_1(A,k4_relset_1(A,k2_numbers,B),k11_relset_1(A,k2_numbers,B,k1_tarski(np__0))),k6_subset_1(A,k4_relset_1(A,k2_numbers,C),k11_relset_1(A,k2_numbers,C,k1_tarski(np__0)))) ) ) ) )).

fof(t17_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ~ ( r2_hidden(B,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,C)))
                  & k4_finseq_4(A,k2_numbers,C,B) = np__0 ) ) ) ) )).

fof(t18_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => k11_relset_1(A,k2_numbers,k2_cfunct_1(A,B),k1_tarski(np__0)) = k1_xboole_0 ) ) )).

fof(t19_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ( k11_relset_1(A,k1_numbers,k9_comseq_1(A,B),k1_tarski(np__0)) = k11_relset_1(A,k2_numbers,B,k1_tarski(np__0))
            & k11_relset_1(A,k2_numbers,k5_comseq_1(A,B),k1_tarski(np__0)) = k11_relset_1(A,k2_numbers,B,k1_tarski(np__0)) ) ) ) )).

fof(t20_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => k4_relset_1(A,k2_numbers,k2_cfunct_1(A,k2_cfunct_1(A,B))) = k4_relset_1(A,k2_numbers,k2_partfun1(A,k2_numbers,B,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,B)))) ) ) )).

fof(t21_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k2_numbers)
             => ( C != np__0
               => k11_relset_1(A,k2_numbers,k4_comseq_1(A,B,C),k1_tarski(np__0)) = k11_relset_1(A,k2_numbers,B,k1_tarski(np__0)) ) ) ) ) )).

fof(t22_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => k2_comseq_1(A,k2_comseq_1(A,B,C),D) = k2_comseq_1(A,B,k2_comseq_1(A,C,D)) ) ) ) ) )).

fof(t23_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => k3_comseq_1(A,k3_comseq_1(A,B,C),D) = k3_comseq_1(A,B,k3_comseq_1(A,C,D)) ) ) ) ) )).

fof(t24_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => k3_comseq_1(A,k2_comseq_1(A,B,C),D) = k2_comseq_1(A,k3_comseq_1(A,B,D),k3_comseq_1(A,C,D)) ) ) ) ) )).

fof(t25_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => k3_comseq_1(A,B,k2_comseq_1(A,C,D)) = k2_comseq_1(A,k3_comseq_1(A,B,C),k3_comseq_1(A,B,D)) ) ) ) ) )).

fof(t26_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => k4_comseq_1(A,k3_comseq_1(A,B,C),D) = k3_comseq_1(A,k4_comseq_1(A,B,D),C) ) ) ) ) )).

fof(t27_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => k4_comseq_1(A,k3_comseq_1(A,B,C),D) = k3_comseq_1(A,B,k4_comseq_1(A,C,D)) ) ) ) ) )).

fof(t28_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => k3_comseq_1(A,k6_comseq_1(A,B,C),D) = k6_comseq_1(A,k3_comseq_1(A,B,D),k3_comseq_1(A,C,D)) ) ) ) ) )).

fof(t29_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => k6_comseq_1(A,k3_comseq_1(A,B,C),k3_comseq_1(A,B,D)) = k3_comseq_1(A,B,k6_comseq_1(A,C,D)) ) ) ) ) )).

fof(t30_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => k4_comseq_1(A,k2_comseq_1(A,B,C),D) = k2_comseq_1(A,k4_comseq_1(A,B,D),k4_comseq_1(A,C,D)) ) ) ) ) )).

fof(t31_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k2_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => k4_comseq_1(A,B,k9_complex1(C,D)) = k4_comseq_1(A,k4_comseq_1(A,B,D),C) ) ) ) ) )).

fof(t32_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => k4_comseq_1(A,k6_comseq_1(A,B,C),D) = k6_comseq_1(A,k4_comseq_1(A,B,D),k4_comseq_1(A,C,D)) ) ) ) ) )).

fof(t33_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => k6_comseq_1(A,B,C) = k4_comseq_1(A,k6_comseq_1(A,C,B),k10_complex1(k6_complex1)) ) ) ) )).

fof(t34_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => k6_comseq_1(A,B,k2_comseq_1(A,C,D)) = k6_comseq_1(A,k6_comseq_1(A,B,C),D) ) ) ) ) )).

fof(t35_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => k4_comseq_1(A,B,k6_complex1) = B ) ) )).

fof(t36_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => k6_comseq_1(A,B,k6_comseq_1(A,C,D)) = k2_comseq_1(A,k6_comseq_1(A,B,C),D) ) ) ) ) )).

fof(t37_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => k2_comseq_1(A,B,k6_comseq_1(A,C,D)) = k6_comseq_1(A,k2_comseq_1(A,B,C),D) ) ) ) ) )).

fof(t38_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => k9_comseq_1(A,k3_comseq_1(A,B,C)) = k8_seq_1(A,k1_numbers,k9_comseq_1(A,B),k9_comseq_1(A,C)) ) ) ) )).

fof(t39_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k2_numbers)
             => k9_comseq_1(A,k4_comseq_1(A,B,C)) = k13_seq_1(A,k1_numbers,k9_comseq_1(A,B),k17_complex1(C)) ) ) ) )).

fof(t40_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => k5_comseq_1(A,B) = k4_comseq_1(A,B,k10_complex1(k6_complex1)) ) ) )).

fof(t41_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => k5_comseq_1(A,k5_comseq_1(A,B)) = B ) ) )).

fof(t42_cfunct_1,axiom,(
    $true )).

fof(t43_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => k6_comseq_1(A,B,k5_comseq_1(A,C)) = k2_comseq_1(A,B,C) ) ) ) )).

fof(t44_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => k2_cfunct_1(A,k2_cfunct_1(A,B)) = k2_partfun1(A,k2_numbers,B,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,B))) ) ) )).

fof(t45_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => k2_cfunct_1(A,k3_comseq_1(A,B,C)) = k3_comseq_1(A,k2_cfunct_1(A,B),k2_cfunct_1(A,C)) ) ) ) )).

fof(t46_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k2_numbers)
             => ( C != np__0
               => k2_cfunct_1(A,k4_comseq_1(A,B,C)) = k4_comseq_1(A,k2_cfunct_1(A,B),k12_complex1(C)) ) ) ) ) )).

fof(t47_cfunct_1,axiom,(
    $true )).

fof(t48_cfunct_1,axiom,(
    $true )).

fof(t49_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => k2_cfunct_1(A,k5_comseq_1(A,B)) = k4_comseq_1(A,k2_cfunct_1(A,B),k10_complex1(k6_complex1)) ) ) )).

fof(t50_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => k4_rfunct_1(A,k1_numbers,k9_comseq_1(A,B)) = k9_comseq_1(A,k2_cfunct_1(A,B)) ) ) )).

fof(t51_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => k1_cfunct_1(A,B,C) = k3_comseq_1(A,B,k2_cfunct_1(A,C)) ) ) ) )).

fof(t52_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => k4_comseq_1(A,k1_cfunct_1(A,B,C),D) = k1_cfunct_1(A,k4_comseq_1(A,B,D),C) ) ) ) ) )).

fof(t53_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => k3_comseq_1(A,k1_cfunct_1(A,B,C),C) = k2_partfun1(A,k2_numbers,B,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,C))) ) ) ) )).

fof(t54_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k2_numbers) )
                     => k3_comseq_1(A,k1_cfunct_1(A,B,C),k1_cfunct_1(A,D,E)) = k1_cfunct_1(A,k3_comseq_1(A,B,D),k3_comseq_1(A,C,E)) ) ) ) ) ) )).

fof(t55_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => k2_cfunct_1(A,k1_cfunct_1(A,B,C)) = k1_cfunct_1(A,k2_partfun1(A,k2_numbers,C,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,C))),B) ) ) ) )).

fof(t56_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => k3_comseq_1(A,B,k1_cfunct_1(A,C,D)) = k1_cfunct_1(A,k3_comseq_1(A,B,C),D) ) ) ) ) )).

fof(t57_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => k1_cfunct_1(A,B,k1_cfunct_1(A,C,D)) = k1_cfunct_1(A,k3_comseq_1(A,B,k2_partfun1(A,k2_numbers,D,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,D)))),C) ) ) ) ) )).

fof(t58_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ( k5_comseq_1(A,k1_cfunct_1(A,B,C)) = k1_cfunct_1(A,k5_comseq_1(A,B),C)
                & k1_cfunct_1(A,B,k5_comseq_1(A,C)) = k5_comseq_1(A,k1_cfunct_1(A,B,C)) ) ) ) ) )).

fof(t59_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => ( k2_comseq_1(A,k1_cfunct_1(A,B,C),k1_cfunct_1(A,D,C)) = k1_cfunct_1(A,k2_comseq_1(A,B,D),C)
                    & k6_comseq_1(A,k1_cfunct_1(A,B,C),k1_cfunct_1(A,D,C)) = k1_cfunct_1(A,k6_comseq_1(A,B,D),C) ) ) ) ) ) )).

fof(t60_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k2_numbers) )
                     => k2_comseq_1(A,k1_cfunct_1(A,B,C),k1_cfunct_1(A,D,E)) = k1_cfunct_1(A,k2_comseq_1(A,k3_comseq_1(A,B,E),k3_comseq_1(A,D,C)),k3_comseq_1(A,C,E)) ) ) ) ) ) )).

fof(t61_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k2_numbers) )
                     => k1_cfunct_1(A,k1_cfunct_1(A,B,C),k1_cfunct_1(A,D,E)) = k1_cfunct_1(A,k3_comseq_1(A,B,k2_partfun1(A,k2_numbers,E,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,E)))),k3_comseq_1(A,C,D)) ) ) ) ) ) )).

fof(t62_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,A,k2_numbers) )
                     => k6_comseq_1(A,k1_cfunct_1(A,B,C),k1_cfunct_1(A,D,E)) = k1_cfunct_1(A,k6_comseq_1(A,k3_comseq_1(A,B,E),k3_comseq_1(A,D,C)),k3_comseq_1(A,C,E)) ) ) ) ) ) )).

fof(t63_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => k9_comseq_1(A,k1_cfunct_1(A,B,C)) = k2_rfunct_1(A,k1_numbers,k9_comseq_1(A,B),k9_comseq_1(A,C)) ) ) ) )).

fof(t64_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,B,k2_numbers) )
             => ( k2_partfun1(B,k2_numbers,k2_comseq_1(B,C,D),A) = k2_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),k2_partfun1(B,k2_numbers,D,A))
                & k2_partfun1(B,k2_numbers,k2_comseq_1(B,C,D),A) = k2_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),D)
                & k2_partfun1(B,k2_numbers,k2_comseq_1(B,C,D),A) = k2_comseq_1(B,C,k2_partfun1(B,k2_numbers,D,A)) ) ) ) ) )).

fof(t65_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,B,k2_numbers) )
             => ( k2_partfun1(B,k2_numbers,k3_comseq_1(B,C,D),A) = k3_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),k2_partfun1(B,k2_numbers,D,A))
                & k2_partfun1(B,k2_numbers,k3_comseq_1(B,C,D),A) = k3_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),D)
                & k2_partfun1(B,k2_numbers,k3_comseq_1(B,C,D),A) = k3_comseq_1(B,C,k2_partfun1(B,k2_numbers,D,A)) ) ) ) ) )).

fof(t66_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ( k2_partfun1(B,k2_numbers,k5_comseq_1(B,C),A) = k5_comseq_1(B,k2_partfun1(B,k2_numbers,C,A))
            & k2_partfun1(B,k2_numbers,k2_cfunct_1(B,C),A) = k2_cfunct_1(B,k2_partfun1(B,k2_numbers,C,A))
            & k2_partfun1(B,k1_numbers,k9_comseq_1(B,C),A) = k9_comseq_1(B,k2_partfun1(B,k2_numbers,C,A)) ) ) ) )).

fof(t67_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,B,k2_numbers) )
             => ( k2_partfun1(B,k2_numbers,k6_comseq_1(B,C,D),A) = k6_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),k2_partfun1(B,k2_numbers,D,A))
                & k2_partfun1(B,k2_numbers,k6_comseq_1(B,C,D),A) = k6_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),D)
                & k2_partfun1(B,k2_numbers,k6_comseq_1(B,C,D),A) = k6_comseq_1(B,C,k2_partfun1(B,k2_numbers,D,A)) ) ) ) ) )).

fof(t68_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,B,k2_numbers) )
             => ( k2_partfun1(B,k2_numbers,k1_cfunct_1(B,C,D),A) = k1_cfunct_1(B,k2_partfun1(B,k2_numbers,C,A),k2_partfun1(B,k2_numbers,D,A))
                & k2_partfun1(B,k2_numbers,k1_cfunct_1(B,C,D),A) = k1_cfunct_1(B,k2_partfun1(B,k2_numbers,C,A),D)
                & k2_partfun1(B,k2_numbers,k1_cfunct_1(B,C,D),A) = k1_cfunct_1(B,C,k2_partfun1(B,k2_numbers,D,A)) ) ) ) ) )).

fof(t69_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ! [D] :
              ( m1_subset_1(D,k2_numbers)
             => k2_partfun1(B,k2_numbers,k4_comseq_1(B,C,D),A) = k4_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),D) ) ) ) )).

fof(t70_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ( ( ( v1_partfun1(B,A,k2_numbers)
                    & v1_partfun1(C,A,k2_numbers) )
                 => v1_partfun1(k2_comseq_1(A,B,C),A,k2_numbers) )
                & ( v1_partfun1(k2_comseq_1(A,B,C),A,k2_numbers)
                 => ( v1_partfun1(B,A,k2_numbers)
                    & v1_partfun1(C,A,k2_numbers) ) )
                & ( ( v1_partfun1(B,A,k2_numbers)
                    & v1_partfun1(C,A,k2_numbers) )
                 => v1_partfun1(k6_comseq_1(A,B,C),A,k2_numbers) )
                & ( v1_partfun1(k6_comseq_1(A,B,C),A,k2_numbers)
                 => ( v1_partfun1(B,A,k2_numbers)
                    & v1_partfun1(C,A,k2_numbers) ) )
                & ( ( v1_partfun1(B,A,k2_numbers)
                    & v1_partfun1(C,A,k2_numbers) )
                 => v1_partfun1(k3_comseq_1(A,B,C),A,k2_numbers) )
                & ( v1_partfun1(k3_comseq_1(A,B,C),A,k2_numbers)
                 => ( v1_partfun1(B,A,k2_numbers)
                    & v1_partfun1(C,A,k2_numbers) ) ) ) ) ) ) )).

fof(t71_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k2_numbers)
             => ( v1_partfun1(B,A,k2_numbers)
              <=> v1_partfun1(k4_comseq_1(A,B,C),A,k2_numbers) ) ) ) ) )).

fof(t72_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ( v1_partfun1(B,A,k2_numbers)
          <=> v1_partfun1(k5_comseq_1(A,B),A,k2_numbers) ) ) ) )).

fof(t73_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ( v1_partfun1(B,A,k2_numbers)
          <=> v1_partfun1(k9_comseq_1(A,B),A,k1_numbers) ) ) ) )).

fof(t74_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ( v1_partfun1(k2_cfunct_1(A,B),A,k2_numbers)
          <=> ( k11_relset_1(A,k2_numbers,B,k1_tarski(np__0)) = k1_xboole_0
              & v1_partfun1(B,A,k2_numbers) ) ) ) ) )).

fof(t75_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ( ( v1_partfun1(B,A,k2_numbers)
                  & k11_relset_1(A,k2_numbers,C,k1_tarski(np__0)) = k1_xboole_0
                  & v1_partfun1(C,A,k2_numbers) )
              <=> v1_partfun1(k1_cfunct_1(A,B,C),A,k2_numbers) ) ) ) ) )).

fof(t76_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => ( ( v1_partfun1(C,A,k2_numbers)
                      & v1_partfun1(D,A,k2_numbers) )
                   => ( k4_finseq_4(A,k2_numbers,k2_comseq_1(A,C,D),B) = k8_complex1(k4_finseq_4(A,k2_numbers,C,B),k4_finseq_4(A,k2_numbers,D,B))
                      & k4_finseq_4(A,k2_numbers,k6_comseq_1(A,C,D),B) = k11_complex1(k4_finseq_4(A,k2_numbers,C,B),k4_finseq_4(A,k2_numbers,D,B))
                      & k4_finseq_4(A,k2_numbers,k3_comseq_1(A,C,D),B) = k9_complex1(k4_finseq_4(A,k2_numbers,C,B),k4_finseq_4(A,k2_numbers,D,B)) ) ) ) ) ) ) )).

fof(t77_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => ( v1_partfun1(C,A,k2_numbers)
                   => k4_finseq_4(A,k2_numbers,k4_comseq_1(A,C,D),B) = k9_complex1(D,k4_finseq_4(A,k2_numbers,C,B)) ) ) ) ) ) )).

fof(t78_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ( v1_partfun1(C,A,k2_numbers)
               => ( k4_finseq_4(A,k2_numbers,k5_comseq_1(A,C),B) = k10_complex1(k4_finseq_4(A,k2_numbers,C,B))
                  & k2_seq_1(A,k1_numbers,k9_comseq_1(A,C),B) = k17_complex1(k4_finseq_4(A,k2_numbers,C,B)) ) ) ) ) ) )).

fof(t79_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ( v1_partfun1(k2_cfunct_1(A,C),A,k2_numbers)
               => k4_finseq_4(A,k2_numbers,k2_cfunct_1(A,C),B) = k12_complex1(k4_finseq_4(A,k2_numbers,C,B)) ) ) ) ) )).

fof(t80_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,k2_numbers) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,k2_numbers) )
                 => ( ( v1_partfun1(C,A,k2_numbers)
                      & v1_partfun1(k2_cfunct_1(A,D),A,k2_numbers) )
                   => k4_finseq_4(A,k2_numbers,k1_cfunct_1(A,C,D),B) = k9_complex1(k4_finseq_4(A,k2_numbers,C,B),k12_complex1(k4_finseq_4(A,k2_numbers,D,B))) ) ) ) ) ) )).

fof(d3_cfunct_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,A,k2_numbers) )
         => ! [C] :
              ( r1_cfunct_1(A,B,C)
            <=> r3_rfunct_1(k9_comseq_1(A,B),C) ) ) ) )).

fof(t81_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ( r1_cfunct_1(B,C,A)
          <=> ? [D] :
                ( v1_xreal_0(D)
                & ! [E] :
                    ( m1_subset_1(E,B)
                   => ( r2_hidden(E,k3_xboole_0(A,k4_relset_1(B,k2_numbers,C)))
                     => r1_xreal_0(k17_complex1(k4_finseq_4(B,k2_numbers,C,E)),D) ) ) ) ) ) ) )).

fof(t82_cfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,C,k2_numbers) )
         => ( ( r1_tarski(A,B)
              & r1_cfunct_1(C,D,B) )
           => r1_cfunct_1(C,D,A) ) ) ) )).

fof(t83_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ( r1_xboole_0(A,k4_relset_1(B,k2_numbers,C))
           => r1_cfunct_1(B,C,A) ) ) ) )).

fof(t84_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ! [D] :
              ( m1_subset_1(D,k2_numbers)
             => ( r1_cfunct_1(B,C,A)
               => r1_cfunct_1(B,k4_comseq_1(B,C,D),A) ) ) ) ) )).

fof(t85_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => r2_rfunct_1(k9_comseq_1(B,C),A) ) ) )).

fof(t86_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ( r1_cfunct_1(B,C,A)
           => ( r3_rfunct_1(k9_comseq_1(B,C),A)
              & r1_cfunct_1(B,k5_comseq_1(B,C),A) ) ) ) ) )).

fof(t87_cfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,C,k2_numbers) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,k2_numbers) )
             => ( ( r1_cfunct_1(C,D,A)
                  & r1_cfunct_1(C,E,B) )
               => r1_cfunct_1(C,k2_comseq_1(C,D,E),k3_xboole_0(A,B)) ) ) ) ) )).

fof(t88_cfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,C,k2_numbers) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,k2_numbers) )
             => ( ( r1_cfunct_1(C,D,A)
                  & r1_cfunct_1(C,E,B) )
               => ( r1_cfunct_1(C,k3_comseq_1(C,D,E),k3_xboole_0(A,B))
                  & r1_cfunct_1(C,k6_comseq_1(C,D,E),k3_xboole_0(A,B)) ) ) ) ) ) )).

fof(t89_cfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,C,k2_numbers) )
         => ( ( r1_cfunct_1(C,D,A)
              & r1_cfunct_1(C,D,B) )
           => r1_cfunct_1(C,D,k2_xboole_0(A,B)) ) ) ) )).

fof(t90_cfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,C,k2_numbers) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,k2_numbers) )
             => ( ( r1_partfun2(C,k2_numbers,D,A)
                  & r1_partfun2(C,k2_numbers,E,B) )
               => ( r1_partfun2(C,k2_numbers,k2_comseq_1(C,D,E),k3_xboole_0(A,B))
                  & r1_partfun2(C,k2_numbers,k6_comseq_1(C,D,E),k3_xboole_0(A,B))
                  & r1_partfun2(C,k2_numbers,k3_comseq_1(C,D,E),k3_xboole_0(A,B)) ) ) ) ) ) )).

fof(t91_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ! [D] :
              ( m1_subset_1(D,k2_numbers)
             => ( r1_partfun2(B,k2_numbers,C,A)
               => r1_partfun2(B,k2_numbers,k4_comseq_1(B,C,D),A) ) ) ) ) )).

fof(t92_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ( r1_partfun2(B,k2_numbers,C,A)
           => ( r1_partfun2(B,k1_numbers,k9_comseq_1(B,C),A)
              & r1_partfun2(B,k2_numbers,k5_comseq_1(B,C),A) ) ) ) ) )).

fof(t93_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ( r1_partfun2(B,k2_numbers,C,A)
           => r1_cfunct_1(B,C,A) ) ) ) )).

fof(t94_cfunct_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,B,k2_numbers) )
         => ( r1_partfun2(B,k2_numbers,C,A)
           => ( ! [D] :
                  ( m1_subset_1(D,k2_numbers)
                 => r1_cfunct_1(B,k4_comseq_1(B,C,D),A) )
              & r1_cfunct_1(B,k5_comseq_1(B,C),A)
              & r3_rfunct_1(k9_comseq_1(B,C),A) ) ) ) ) )).

fof(t95_cfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,C,k2_numbers) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,k2_numbers) )
             => ( ( r1_cfunct_1(C,D,A)
                  & r1_partfun2(C,k2_numbers,E,B) )
               => r1_cfunct_1(C,k2_comseq_1(C,D,E),k3_xboole_0(A,B)) ) ) ) ) )).

fof(t96_cfunct_1,axiom,(
    ! [A,B,C] :
      ( ~ v1_xboole_0(C)
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,C,k2_numbers) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & m2_relset_1(E,C,k2_numbers) )
             => ( ( r1_cfunct_1(C,D,A)
                  & r1_partfun2(C,k2_numbers,E,B) )
               => ( r1_cfunct_1(C,k6_comseq_1(C,D,E),k3_xboole_0(A,B))
                  & r1_cfunct_1(C,k6_comseq_1(C,E,D),k3_xboole_0(A,B))
                  & r1_cfunct_1(C,k3_comseq_1(C,D,E),k3_xboole_0(A,B)) ) ) ) ) ) )).

fof(dt_k1_cfunct_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k2_numbers)
        & v1_funct_1(C)
        & m1_relset_1(C,A,k2_numbers) )
     => ( v1_funct_1(k1_cfunct_1(A,B,C))
        & m2_relset_1(k1_cfunct_1(A,B,C),A,k2_numbers) ) ) )).

fof(dt_k2_cfunct_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & m1_relset_1(B,A,k2_numbers) )
     => ( v1_funct_1(k2_cfunct_1(A,B))
        & m2_relset_1(k2_cfunct_1(A,B),A,k2_numbers) ) ) )).
%------------------------------------------------------------------------------