SET007 Axioms: SET007+154.ax


%------------------------------------------------------------------------------
% File     : SET007+154 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Property of Complex Sequence and Continuity of Complex Function
% 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    : cfcont_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   82 (   3 unit)
%            Number of atoms       :  674 (  69 equality)
%            Maximal formula depth :   23 (   8 average)
%            Number of connectives :  620 (  28 ~  ;  10  |; 321  &)
%                                         (  15 <=>; 246 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   22 (   1 propositional; 0-3 arity)
%            Number of functors    :   41 (   6 constant; 0-4 arity)
%            Number of variables   :  216 (   0 singleton; 208 !;   8 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(d1_cfcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k2_numbers,k2_numbers) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,A))
           => k1_cfcont_1(A,B) = k5_relat_1(B,A) ) ) ) )).

fof(d2_cfcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k2_numbers,k2_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k2_numbers)
         => ( r1_cfcont_1(A,B)
          <=> ( r2_hidden(B,k4_relset_1(k2_numbers,k2_numbers,A))
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k2_numbers)
                    & m2_relset_1(C,k5_numbers,k2_numbers) )
                 => ( ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,C),k4_relset_1(k2_numbers,k2_numbers,A))
                      & v2_comseq_2(C)
                      & k2_comseq_2(C) = B )
                   => ( v2_comseq_2(k1_cfcont_1(A,C))
                      & k4_finseq_4(k2_numbers,k2_numbers,A,B) = k2_comseq_2(k1_cfcont_1(A,C)) ) ) ) ) ) ) ) )).

fof(t1_cfcont_1,axiom,(
    $true )).

fof(t2_cfcont_1,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) )
             => ( A = k6_comseq_1(k5_numbers,B,C)
              <=> ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k1_comseq_1(A,D) = k11_complex1(k1_comseq_1(B,D),k1_comseq_1(C,D)) ) ) ) ) ) )).

fof(t3_cfcont_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => r1_tarski(k5_relset_1(k5_numbers,k2_numbers,k6_comseq_3(B,A)),k5_relset_1(k5_numbers,k2_numbers,B)) ) ) )).

fof(t4_cfcont_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_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)
                & m2_relset_1(C,k2_numbers,k2_numbers) )
             => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,C))
               => r2_hidden(k1_comseq_1(B,A),k4_relset_1(k2_numbers,k2_numbers,C)) ) ) ) ) )).

fof(t5_cfcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_numbers)
        & m2_relset_1(B,k5_numbers,k2_numbers) )
     => ( r2_hidden(A,k5_relset_1(k5_numbers,k2_numbers,B))
      <=> ? [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = k1_comseq_1(B,C) ) ) ) )).

fof(t6_cfcont_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => r2_hidden(k1_comseq_1(B,A),k5_relset_1(k5_numbers,k2_numbers,B)) ) ) )).

fof(t7_cfcont_1,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)
           => r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k5_relset_1(k5_numbers,k2_numbers,B)) ) ) ) )).

fof(t8_cfcont_1,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)
              & v1_comseq_1(B) )
           => v1_comseq_1(A) ) ) ) )).

fof(t9_cfcont_1,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,k1_numbers)
                & v1_seqm_3(C)
                & v7_seqm_3(C)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( k5_comseq_3(C,k2_comseq_1(k5_numbers,A,B)) = k2_comseq_1(k5_numbers,k5_comseq_3(C,A),k5_comseq_3(C,B))
                & k5_comseq_3(C,k6_comseq_1(k5_numbers,A,B)) = k6_comseq_1(k5_numbers,k5_comseq_3(C,A),k5_comseq_3(C,B))
                & k5_comseq_3(C,k3_comseq_1(k5_numbers,A,B)) = k3_comseq_1(k5_numbers,k5_comseq_3(C,A),k5_comseq_3(C,B)) ) ) ) ) )).

fof(t10_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,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,k1_numbers)
                & v1_seqm_3(C)
                & v7_seqm_3(C)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => k5_comseq_3(C,k4_comseq_1(k5_numbers,B,A)) = k4_comseq_1(k5_numbers,k5_comseq_3(C,B),A) ) ) ) )).

fof(t11_cfcont_1,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) )
         => ( k5_comseq_3(B,k5_comseq_1(k5_numbers,A)) = k5_comseq_1(k5_numbers,k5_comseq_3(B,A))
            & k3_seqm_3(B,k9_comseq_1(k5_numbers,A)) = k9_comseq_1(k5_numbers,k5_comseq_3(B,A)) ) ) ) )).

fof(t12_cfcont_1,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) )
         => k7_comseq_1(k5_comseq_3(B,A)) = k5_comseq_3(B,k7_comseq_1(A)) ) ) )).

fof(t13_cfcont_1,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,k1_numbers)
                & v1_seqm_3(C)
                & v7_seqm_3(C)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => k5_comseq_3(C,k8_comseq_1(A,B)) = k8_comseq_1(k5_comseq_3(C,A),k5_comseq_3(C,B)) ) ) ) )).

fof(t14_cfcont_1,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_zfmisc_1(k2_numbers))
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r2_hidden(k1_comseq_1(A,C),B) )
           => r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),B) ) ) ) )).

fof(t15_cfcont_1,axiom,(
    $true )).

fof(t16_cfcont_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_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)
                & m2_relset_1(C,k2_numbers,k2_numbers) )
             => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,C))
               => k1_comseq_1(k1_cfcont_1(C,B),A) = k4_finseq_4(k2_numbers,k2_numbers,C,k1_comseq_1(B,A)) ) ) ) ) )).

fof(t17_cfcont_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_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)
                & m2_relset_1(C,k2_numbers,k2_numbers) )
             => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,C))
               => k6_comseq_3(k1_cfcont_1(C,B),A) = k1_cfcont_1(C,k6_comseq_3(B,A)) ) ) ) ) )).

fof(t18_cfcont_1,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)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k2_numbers,k2_numbers) )
             => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k5_subset_1(k2_numbers,k4_relset_1(k2_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,C)))
               => ( k1_cfcont_1(k2_comseq_1(k2_numbers,B,C),A) = k2_comseq_1(k5_numbers,k1_cfcont_1(B,A),k1_cfcont_1(C,A))
                  & k1_cfcont_1(k6_comseq_1(k2_numbers,B,C),A) = k6_comseq_1(k5_numbers,k1_cfcont_1(B,A),k1_cfcont_1(C,A))
                  & k1_cfcont_1(k3_comseq_1(k2_numbers,B,C),A) = k3_comseq_1(k5_numbers,k1_cfcont_1(B,A),k1_cfcont_1(C,A)) ) ) ) ) ) )).

fof(t19_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,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)
                & m2_relset_1(C,k2_numbers,k2_numbers) )
             => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,C))
               => k1_cfcont_1(k4_comseq_1(k2_numbers,C,A),B) = k4_comseq_1(k5_numbers,k1_cfcont_1(C,B),A) ) ) ) ) )).

fof(t20_cfcont_1,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)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,B))
           => k5_comseq_1(k5_numbers,k1_cfcont_1(B,A)) = k1_cfcont_1(k5_comseq_1(k2_numbers,B),A) ) ) ) )).

fof(t21_cfcont_1,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)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,k2_cfunct_1(k2_numbers,B)))
           => v1_comseq_1(k1_cfcont_1(B,A)) ) ) ) )).

fof(t22_cfcont_1,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)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,k2_cfunct_1(k2_numbers,B)))
           => k1_cfcont_1(k2_cfunct_1(k2_numbers,B),A) = k7_comseq_1(k1_cfcont_1(B,A)) ) ) ) )).

fof(t23_cfcont_1,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)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ! [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) )
             => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,B))
               => k3_comseq_3(k5_comseq_3(C,k1_cfcont_1(B,A))) = k3_comseq_3(k1_cfcont_1(B,k5_comseq_3(C,A))) ) ) ) ) )).

fof(t24_cfcont_1,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)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ! [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) )
             => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,B))
               => k4_comseq_3(k5_comseq_3(C,k1_cfcont_1(B,A))) = k4_comseq_3(k1_cfcont_1(B,k5_comseq_3(C,A))) ) ) ) ) )).

fof(t25_cfcont_1,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)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ! [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) )
             => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,B))
               => k5_comseq_3(C,k1_cfcont_1(B,A)) = k1_cfcont_1(B,k5_comseq_3(C,A)) ) ) ) ) )).

fof(t26_cfcont_1,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)
                & m2_relset_1(C,k2_numbers,k2_numbers) )
             => ( ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,A),k4_relset_1(k2_numbers,k2_numbers,C))
                  & m1_comseq_3(B,A) )
               => m1_comseq_3(k1_cfcont_1(C,B),k1_cfcont_1(C,A)) ) ) ) ) )).

fof(t27_cfcont_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_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)
                & m2_relset_1(C,k2_numbers,k2_numbers) )
             => ( v1_partfun1(C,k2_numbers,k2_numbers)
               => k1_comseq_1(k1_cfcont_1(C,B),A) = k4_finseq_4(k2_numbers,k2_numbers,C,k1_comseq_1(B,A)) ) ) ) ) )).

fof(t28_cfcont_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_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)
                & m2_relset_1(C,k2_numbers,k2_numbers) )
             => ( v1_partfun1(C,k2_numbers,k2_numbers)
               => k1_cfcont_1(C,k6_comseq_3(B,A)) = k6_comseq_3(k1_cfcont_1(C,B),A) ) ) ) ) )).

fof(t29_cfcont_1,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)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k2_numbers,k2_numbers) )
             => ( ( v1_partfun1(B,k2_numbers,k2_numbers)
                  & v1_partfun1(C,k2_numbers,k2_numbers) )
               => ( k1_cfcont_1(k2_comseq_1(k2_numbers,B,C),A) = k2_comseq_1(k5_numbers,k1_cfcont_1(B,A),k1_cfcont_1(C,A))
                  & k1_cfcont_1(k6_comseq_1(k2_numbers,B,C),A) = k6_comseq_1(k5_numbers,k1_cfcont_1(B,A),k1_cfcont_1(C,A))
                  & k1_cfcont_1(k3_comseq_1(k2_numbers,B,C),A) = k3_comseq_1(k5_numbers,k1_cfcont_1(B,A),k1_cfcont_1(C,A)) ) ) ) ) ) )).

fof(t30_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,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)
                & m2_relset_1(C,k2_numbers,k2_numbers) )
             => ( v1_partfun1(C,k2_numbers,k2_numbers)
               => k1_cfcont_1(k4_comseq_1(k2_numbers,C,A),B) = k4_comseq_1(k5_numbers,k1_cfcont_1(C,B),A) ) ) ) ) )).

fof(t31_cfcont_1,axiom,(
    ! [A,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)
            & m2_relset_1(C,k2_numbers,k2_numbers) )
         => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,k8_relset_1(k2_numbers,k2_numbers,C,A)))
           => k1_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,C,A),B) = k1_cfcont_1(C,B) ) ) ) )).

fof(t32_cfcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_numbers)
        & m2_relset_1(B,k5_numbers,k2_numbers) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k2_numbers))
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,k2_numbers,k2_numbers) )
             => ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,k8_relset_1(k2_numbers,k2_numbers,D,A)))
               => ( ( ~ r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,k8_relset_1(k2_numbers,k2_numbers,D,C)))
                    & ~ r1_tarski(A,C) )
                  | k1_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,D,A),B) = k1_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,D,C),B) ) ) ) ) ) )).

fof(t33_cfcont_1,axiom,(
    ! [A,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)
            & m2_relset_1(C,k2_numbers,k2_numbers) )
         => ( ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),k4_relset_1(k2_numbers,k2_numbers,k8_relset_1(k2_numbers,k2_numbers,C,A)))
              & k11_relset_1(k2_numbers,k2_numbers,C,k1_tarski(np__0)) = k1_xboole_0 )
           => k1_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,k2_cfunct_1(k2_numbers,C),A),B) = k7_comseq_1(k1_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,C,A),B)) ) ) ) )).

fof(d3_cfcont_1,axiom,(
    $true )).

fof(d4_cfcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v5_seqm_3(A)
      <=> ? [B] :
            ( m1_subset_1(B,k2_numbers)
            & ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k1_comseq_1(A,C) = B ) ) ) ) )).

fof(t34_cfcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v5_seqm_3(A)
      <=> ? [B] :
            ( m1_subset_1(B,k2_numbers)
            & k5_relset_1(k5_numbers,k2_numbers,A) = k1_tarski(B) ) ) ) )).

fof(t35_cfcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v5_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k1_comseq_1(A,B) = k1_comseq_1(A,k1_nat_1(B,np__1)) ) ) ) )).

fof(t36_cfcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v5_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k1_comseq_1(A,B) = k1_comseq_1(A,k1_nat_1(B,C)) ) ) ) ) )).

fof(t37_cfcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v5_seqm_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k1_comseq_1(A,B) = k1_comseq_1(A,C) ) ) ) ) )).

fof(t38_cfcont_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_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(k6_comseq_3(B,A),B) ) ) )).

fof(t39_cfcont_1,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)
              & v2_comseq_2(B) )
           => v2_comseq_2(A) ) ) ) )).

fof(t40_cfcont_1,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)
              & v2_comseq_2(B) )
           => k2_comseq_2(A) = k2_comseq_2(B) ) ) ) )).

fof(t41_cfcont_1,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)
           => ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ? [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                      & r1_xreal_0(C,D)
                      & k1_comseq_1(B,D) != k1_comseq_1(A,D) ) )
              | v2_comseq_2(B) ) ) ) ) )).

fof(t42_cfcont_1,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)
           => ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ? [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                      & r1_xreal_0(C,D)
                      & k1_comseq_1(B,D) != k1_comseq_1(A,D) ) )
              | k2_comseq_2(A) = k2_comseq_2(B) ) ) ) ) )).

fof(t43_cfcont_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_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(B)
           => ( v2_comseq_2(k6_comseq_3(B,A))
              & k2_comseq_2(k6_comseq_3(B,A)) = k2_comseq_2(B) ) ) ) ) )).

fof(t44_cfcont_1,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)
           => ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => A != k6_comseq_3(B,C) )
              | v2_comseq_2(B) ) ) ) ) )).

fof(t45_cfcont_1,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)
           => ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => A != k6_comseq_3(B,C) )
              | k2_comseq_2(B) = k2_comseq_2(A) ) ) ) ) )).

fof(t46_cfcont_1,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)
          & k2_comseq_2(A) != np__0
          & ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ~ v1_comseq_1(k6_comseq_3(A,B)) ) ) ) )).

fof(t47_cfcont_1,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)
          & k2_comseq_2(A) != np__0
          & ! [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)
                  & v1_comseq_1(B) ) ) ) ) )).

fof(t48_cfcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v5_seqm_3(A)
       => v2_comseq_2(A) ) ) )).

fof(t49_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ( ( ( v5_seqm_3(B)
                & r2_hidden(A,k5_relset_1(k5_numbers,k2_numbers,B)) )
              | ( v5_seqm_3(B)
                & ? [C] :
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                    & k1_comseq_1(B,C) = A ) ) )
           => k2_comseq_2(B) = A ) ) ) )).

fof(t50_cfcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k2_numbers)
        & m2_relset_1(A,k5_numbers,k2_numbers) )
     => ( v5_seqm_3(A)
       => ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k2_comseq_2(A) = k1_comseq_1(A,B) ) ) ) )).

fof(t51_cfcont_1,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)
       => ( k2_comseq_2(A) = np__0
          | ! [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)
                  & v1_comseq_1(B) )
               => k2_comseq_2(k7_comseq_1(B)) = k12_complex1(k2_comseq_2(A)) ) ) ) ) ) )).

fof(t52_cfcont_1,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) )
         => ( ( v5_seqm_3(A)
              & v2_comseq_2(B) )
           => ( k2_comseq_2(k2_comseq_1(k5_numbers,A,B)) = k8_complex1(k1_comseq_1(A,np__0),k2_comseq_2(B))
              & k2_comseq_2(k6_comseq_1(k5_numbers,A,B)) = k11_complex1(k1_comseq_1(A,np__0),k2_comseq_2(B))
              & k2_comseq_2(k6_comseq_1(k5_numbers,B,A)) = k11_complex1(k2_comseq_2(B),k1_comseq_1(A,np__0))
              & k2_comseq_2(k3_comseq_1(k5_numbers,A,B)) = k9_complex1(k1_comseq_1(A,np__0),k2_comseq_2(B)) ) ) ) ) )).

fof(t53_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ( r1_cfcont_1(B,A)
          <=> ( r2_hidden(A,k4_relset_1(k2_numbers,k2_numbers,B))
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k2_numbers)
                    & m2_relset_1(C,k5_numbers,k2_numbers) )
                 => ( ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,C),k4_relset_1(k2_numbers,k2_numbers,B))
                      & v2_comseq_2(C)
                      & k2_comseq_2(C) = A
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => k1_comseq_1(C,D) != A ) )
                   => ( v2_comseq_2(k1_cfcont_1(B,C))
                      & k4_finseq_4(k2_numbers,k2_numbers,B,A) = k2_comseq_2(k1_cfcont_1(B,C)) ) ) ) ) ) ) ) )).

fof(t54_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ( r1_cfcont_1(B,A)
          <=> ( r2_hidden(A,k4_relset_1(k2_numbers,k2_numbers,B))
              & ! [C] :
                  ( m1_subset_1(C,k1_numbers)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & ! [D] :
                          ( m1_subset_1(D,k1_numbers)
                         => ~ ( ~ r1_xreal_0(D,np__0)
                              & ! [E] :
                                  ( m1_subset_1(E,k2_numbers)
                                 => ~ ( r2_hidden(E,k4_relset_1(k2_numbers,k2_numbers,B))
                                      & ~ r1_xreal_0(D,k17_complex1(k11_complex1(E,A)))
                                      & r1_xreal_0(C,k17_complex1(k11_complex1(k4_finseq_4(k2_numbers,k2_numbers,B,E),k4_finseq_4(k2_numbers,k2_numbers,B,A)))) ) ) ) ) ) ) ) ) ) ) )).

fof(t55_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k2_numbers,k2_numbers) )
             => ( ( r1_cfcont_1(B,A)
                  & r1_cfcont_1(C,A) )
               => ( r1_cfcont_1(k2_comseq_1(k2_numbers,B,C),A)
                  & r1_cfcont_1(k6_comseq_1(k2_numbers,B,C),A)
                  & r1_cfcont_1(k3_comseq_1(k2_numbers,B,C),A) ) ) ) ) ) )).

fof(t56_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ! [B] :
          ( m1_subset_1(B,k2_numbers)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k2_numbers,k2_numbers) )
             => ( r1_cfcont_1(C,A)
               => r1_cfcont_1(k4_comseq_1(k2_numbers,C,B),A) ) ) ) ) )).

fof(t57_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ( r1_cfcont_1(B,A)
           => r1_cfcont_1(k5_comseq_1(k2_numbers,B),A) ) ) ) )).

fof(t58_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ( r1_cfcont_1(B,A)
           => ( k4_finseq_4(k2_numbers,k2_numbers,B,A) = np__0
              | r1_cfcont_1(k2_cfunct_1(k2_numbers,B),A) ) ) ) ) )).

fof(t59_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k2_numbers,k2_numbers) )
             => ( ( r1_cfcont_1(B,A)
                  & r1_cfcont_1(C,A) )
               => ( k4_finseq_4(k2_numbers,k2_numbers,B,A) = np__0
                  | r1_cfcont_1(k1_cfunct_1(k2_numbers,C,B),A) ) ) ) ) ) )).

fof(d5_cfcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k2_numbers,k2_numbers) )
     => ! [B] :
          ( r2_cfcont_1(A,B)
        <=> ( r1_tarski(B,k4_relset_1(k2_numbers,k2_numbers,A))
            & ! [C] :
                ( m1_subset_1(C,k2_numbers)
               => ( r2_hidden(C,B)
                 => r1_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,A,B),C) ) ) ) ) ) )).

fof(t60_cfcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k2_numbers,k2_numbers) )
     => ( r2_cfcont_1(B,A)
      <=> ( r1_tarski(A,k4_relset_1(k2_numbers,k2_numbers,B))
          & ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k2_numbers)
                & m2_relset_1(C,k5_numbers,k2_numbers) )
             => ( ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,C),A)
                  & v2_comseq_2(C)
                  & r2_hidden(k2_comseq_2(C),A) )
               => ( v2_comseq_2(k1_cfcont_1(B,C))
                  & k4_finseq_4(k2_numbers,k2_numbers,B,k2_comseq_2(C)) = k2_comseq_2(k1_cfcont_1(B,C)) ) ) ) ) ) ) )).

fof(t61_cfcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k2_numbers,k2_numbers) )
     => ( r2_cfcont_1(B,A)
      <=> ( r1_tarski(A,k4_relset_1(k2_numbers,k2_numbers,B))
          & ! [C] :
              ( m1_subset_1(C,k2_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ~ ( r2_hidden(C,A)
                      & ~ r1_xreal_0(D,np__0)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ~ ( ~ r1_xreal_0(E,np__0)
                              & ! [F] :
                                  ( m1_subset_1(F,k2_numbers)
                                 => ~ ( r2_hidden(F,A)
                                      & ~ r1_xreal_0(E,k17_complex1(k11_complex1(F,C)))
                                      & r1_xreal_0(D,k17_complex1(k11_complex1(k4_finseq_4(k2_numbers,k2_numbers,B,F),k4_finseq_4(k2_numbers,k2_numbers,B,C)))) ) ) ) ) ) ) ) ) ) ) )).

fof(t62_cfcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k2_numbers,k2_numbers) )
     => ( r2_cfcont_1(B,A)
      <=> r2_cfcont_1(k8_relset_1(k2_numbers,k2_numbers,B,A),A) ) ) )).

fof(t63_cfcont_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,k2_numbers,k2_numbers) )
     => ( ( r2_cfcont_1(C,A)
          & r1_tarski(B,A) )
       => r2_cfcont_1(C,B) ) ) )).

fof(t64_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ( r2_hidden(A,k4_relset_1(k2_numbers,k2_numbers,B))
           => r2_cfcont_1(B,k1_tarski(A)) ) ) ) )).

fof(t65_cfcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k2_numbers,k2_numbers) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,k2_numbers,k2_numbers) )
         => ( ( r2_cfcont_1(B,A)
              & r2_cfcont_1(C,A) )
           => ( r2_cfcont_1(k2_comseq_1(k2_numbers,B,C),A)
              & r2_cfcont_1(k6_comseq_1(k2_numbers,B,C),A)
              & r2_cfcont_1(k3_comseq_1(k2_numbers,B,C),A) ) ) ) ) )).

fof(t66_cfcont_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,k2_numbers,k2_numbers) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,k2_numbers,k2_numbers) )
         => ( ( r2_cfcont_1(C,A)
              & r2_cfcont_1(D,B) )
           => ( r2_cfcont_1(k2_comseq_1(k2_numbers,C,D),k3_xboole_0(A,B))
              & r2_cfcont_1(k6_comseq_1(k2_numbers,C,D),k3_xboole_0(A,B))
              & r2_cfcont_1(k3_comseq_1(k2_numbers,C,D),k3_xboole_0(A,B)) ) ) ) ) )).

fof(t67_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,k2_numbers,k2_numbers) )
         => ( r2_cfcont_1(C,B)
           => r2_cfcont_1(k4_comseq_1(k2_numbers,C,A),B) ) ) ) )).

fof(t68_cfcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k2_numbers,k2_numbers) )
     => ( r2_cfcont_1(B,A)
       => r2_cfcont_1(k5_comseq_1(k2_numbers,B),A) ) ) )).

fof(t69_cfcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k2_numbers,k2_numbers) )
     => ( ( r2_cfcont_1(B,A)
          & k11_relset_1(k2_numbers,k2_numbers,B,k1_tarski(np__0)) = k1_xboole_0 )
       => r2_cfcont_1(k2_cfunct_1(k2_numbers,B),A) ) ) )).

fof(t70_cfcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k2_numbers,k2_numbers) )
     => ( ( r2_cfcont_1(B,A)
          & k11_relset_1(k2_numbers,k2_numbers,k8_relset_1(k2_numbers,k2_numbers,B,A),k1_tarski(np__0)) = k1_xboole_0 )
       => r2_cfcont_1(k2_cfunct_1(k2_numbers,B),A) ) ) )).

fof(t71_cfcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k2_numbers,k2_numbers) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,k2_numbers,k2_numbers) )
         => ( ( r2_cfcont_1(B,A)
              & k11_relset_1(k2_numbers,k2_numbers,B,k1_tarski(np__0)) = k1_xboole_0
              & r2_cfcont_1(C,A) )
           => r2_cfcont_1(k1_cfunct_1(k2_numbers,C,B),A) ) ) ) )).

fof(t72_cfcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k2_numbers,k2_numbers) )
     => ( ( v1_partfun1(A,k2_numbers,k2_numbers)
          & ! [B] :
              ( m1_subset_1(B,k2_numbers)
             => ! [C] :
                  ( m1_subset_1(C,k2_numbers)
                 => k4_finseq_4(k2_numbers,k2_numbers,A,k8_complex1(B,C)) = k8_complex1(k4_finseq_4(k2_numbers,k2_numbers,A,B),k4_finseq_4(k2_numbers,k2_numbers,A,C)) ) ) )
       => ( ! [B] :
              ( m1_subset_1(B,k2_numbers)
             => ~ r1_cfcont_1(A,B) )
          | r2_cfcont_1(A,k2_numbers) ) ) ) )).

fof(d6_cfcont_1,axiom,(
    ! [A] :
      ( v1_cfcont_1(A)
    <=> ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k2_numbers)
            & m2_relset_1(B,k5_numbers,k2_numbers) )
         => ~ ( r1_tarski(k5_relset_1(k5_numbers,k2_numbers,B),A)
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k2_numbers)
                    & m2_relset_1(C,k5_numbers,k2_numbers) )
                 => ~ ( m1_comseq_3(C,B)
                      & v2_comseq_2(C)
                      & r2_hidden(k2_comseq_2(C),A) ) ) ) ) ) )).

fof(t73_cfcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k2_numbers,k2_numbers) )
     => ( ( v1_cfcont_1(k4_relset_1(k2_numbers,k2_numbers,A))
          & r2_cfcont_1(A,k4_relset_1(k2_numbers,k2_numbers,A)) )
       => v1_cfcont_1(k5_relset_1(k2_numbers,k2_numbers,A)) ) ) )).

fof(t74_cfcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k2_numbers))
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k2_numbers,k2_numbers) )
         => ( ( r1_tarski(A,k4_relset_1(k2_numbers,k2_numbers,B))
              & v1_cfcont_1(A)
              & r2_cfcont_1(B,A) )
           => v1_cfcont_1(k10_relset_1(k2_numbers,k2_numbers,B,A)) ) ) ) )).

fof(s1_cfcont_1,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ? [B] :
            ( m1_subset_1(B,k2_numbers)
            & p1_s1_cfcont_1(A,B) ) )
   => ? [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)
           => p1_s1_cfcont_1(B,k1_comseq_1(A,B)) ) ) )).

fof(dt_k1_cfcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(A)
        & m1_relset_1(A,k2_numbers,k2_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k2_numbers)
        & m1_relset_1(B,k5_numbers,k2_numbers) )
     => ( v1_funct_1(k1_cfcont_1(A,B))
        & v1_funct_2(k1_cfcont_1(A,B),k5_numbers,k2_numbers)
        & m2_relset_1(k1_cfcont_1(A,B),k5_numbers,k2_numbers) ) ) )).
%------------------------------------------------------------------------------