SET007 Axioms: SET007+106.ax


%------------------------------------------------------------------------------
% File     : SET007+106 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Real Function Continuity
% 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    : fcont_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   57 (   3 unit)
%            Number of atoms       :  407 (  29 equality)
%            Maximal formula depth :   23 (   9 average)
%            Number of connectives :  375 (  25 ~  ;   6  |; 160  &)
%                                         (  10 <=>; 174 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   24 (   1 propositional; 0-4 arity)
%            Number of functors    :   38 (   4 constant; 0-6 arity)
%            Number of variables   :  162 (   0 singleton; 158 !;   4 ?)
%            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_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_fcont_1(A,B)
          <=> ( r2_hidden(B,k4_relset_1(k1_numbers,k1_numbers,A))
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ( ( r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,A))
                      & v4_seq_2(C)
                      & k2_seq_2(C) = B )
                   => ( v4_seq_2(k2_rfunct_2(A,C))
                      & k2_seq_1(k1_numbers,k1_numbers,A,B) = k2_seq_2(k2_rfunct_2(A,C)) ) ) ) ) ) ) ) )).

fof(t1_fcont_1,axiom,(
    $true )).

fof(t2_fcont_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( r1_fcont_1(B,A)
          <=> ( r2_hidden(A,k4_relset_1(k1_numbers,k1_numbers,B))
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ( ( r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,B))
                      & v4_seq_2(C)
                      & k2_seq_2(C) = A
                      & ! [D] :
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => k2_seq_1(k5_numbers,k1_numbers,C,D) != A ) )
                   => ( v4_seq_2(k2_rfunct_2(B,C))
                      & k2_seq_1(k1_numbers,k1_numbers,B,A) = k2_seq_2(k2_rfunct_2(B,C)) ) ) ) ) ) ) ) )).

fof(t3_fcont_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( r1_fcont_1(B,A)
          <=> ( r2_hidden(A,k4_relset_1(k1_numbers,k1_numbers,B))
              & ! [C] :
                  ( v1_xreal_0(C)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & ! [D] :
                          ( v1_xreal_0(D)
                         => ~ ( ~ r1_xreal_0(D,np__0)
                              & ! [E] :
                                  ( v1_xreal_0(E)
                                 => ~ ( r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,B))
                                      & ~ r1_xreal_0(D,k18_complex1(k6_xcmplx_0(E,A)))
                                      & r1_xreal_0(C,k18_complex1(k5_real_1(k2_seq_1(k1_numbers,k1_numbers,B,E),k2_seq_1(k1_numbers,k1_numbers,B,A)))) ) ) ) ) ) ) ) ) ) ) )).

fof(t4_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_fcont_1(A,B)
          <=> ( r2_hidden(B,k4_relset_1(k1_numbers,k1_numbers,A))
              & ! [C] :
                  ( m1_rcomp_1(C,k2_seq_1(k1_numbers,k1_numbers,A,B))
                 => ? [D] :
                      ( m1_rcomp_1(D,B)
                      & ! [E] :
                          ( v1_xreal_0(E)
                         => ( ( r2_hidden(E,k4_relset_1(k1_numbers,k1_numbers,A))
                              & r2_hidden(E,D) )
                           => r2_hidden(k2_seq_1(k1_numbers,k1_numbers,A,E),C) ) ) ) ) ) ) ) ) )).

fof(t5_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_fcont_1(A,B)
          <=> ( r2_hidden(B,k4_relset_1(k1_numbers,k1_numbers,A))
              & ! [C] :
                  ( m1_rcomp_1(C,k2_seq_1(k1_numbers,k1_numbers,A,B))
                 => ? [D] :
                      ( m1_rcomp_1(D,B)
                      & r1_tarski(k10_relset_1(k1_numbers,k1_numbers,A,D),C) ) ) ) ) ) ) )).

fof(t6_fcont_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( r2_hidden(A,k4_relset_1(k1_numbers,k1_numbers,B))
           => ( ! [C] :
                  ( m1_rcomp_1(C,A)
                 => k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),C) != k1_seq_4(A) )
              | r1_fcont_1(B,A) ) ) ) ) )).

fof(t7_fcont_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_fcont_1(B,A)
                  & r1_fcont_1(C,A) )
               => ( r1_fcont_1(k6_seq_1(k1_numbers,k1_numbers,B,C),A)
                  & r1_fcont_1(k7_seq_1(k1_numbers,k1_numbers,B,C),A)
                  & r1_fcont_1(k8_seq_1(k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).

fof(t8_fcont_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( r1_fcont_1(C,A)
               => r1_fcont_1(k13_seq_1(k1_numbers,k1_numbers,C,B),A) ) ) ) ) )).

fof(t9_fcont_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( r1_fcont_1(B,A)
           => ( r1_fcont_1(k21_seq_1(k1_numbers,k1_numbers,B),A)
              & r1_fcont_1(k16_seq_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).

fof(t10_fcont_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( r1_fcont_1(B,A)
           => ( k2_seq_1(k1_numbers,k1_numbers,B,A) = np__0
              | r1_fcont_1(k4_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).

fof(t11_fcont_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_fcont_1(B,A)
                  & r1_fcont_1(C,A) )
               => ( k2_seq_1(k1_numbers,k1_numbers,B,A) = np__0
                  | r1_fcont_1(k2_rfunct_1(k1_numbers,k1_numbers,C,B),A) ) ) ) ) ) )).

fof(t12_fcont_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_fcont_1(B,A)
                  & r1_fcont_1(C,k2_seq_1(k1_numbers,k1_numbers,B,A)) )
               => r1_fcont_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(d2_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( r2_fcont_1(A,B)
        <=> ( r1_tarski(B,k4_relset_1(k1_numbers,k1_numbers,A))
            & ! [C] :
                ( v1_xreal_0(C)
               => ( r2_hidden(C,B)
                 => r1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,A,B),C) ) ) ) ) ) )).

fof(t13_fcont_1,axiom,(
    $true )).

fof(t14_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ( r2_fcont_1(B,A)
      <=> ( r1_tarski(A,k4_relset_1(k1_numbers,k1_numbers,B))
          & ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( ( r1_tarski(k1_rfunct_2(C),A)
                  & v4_seq_2(C)
                  & r2_hidden(k2_seq_2(C),A) )
               => ( v4_seq_2(k2_rfunct_2(B,C))
                  & k2_seq_1(k1_numbers,k1_numbers,B,k2_seq_2(C)) = k2_seq_2(k2_rfunct_2(B,C)) ) ) ) ) ) ) )).

fof(t15_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ( r2_fcont_1(B,A)
      <=> ( r1_tarski(A,k4_relset_1(k1_numbers,k1_numbers,B))
          & ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( r2_hidden(C,A)
                      & ~ r1_xreal_0(D,np__0)
                      & ! [E] :
                          ( v1_xreal_0(E)
                         => ~ ( ~ r1_xreal_0(E,np__0)
                              & ! [F] :
                                  ( v1_xreal_0(F)
                                 => ~ ( r2_hidden(F,A)
                                      & ~ r1_xreal_0(E,k18_complex1(k6_xcmplx_0(F,C)))
                                      & r1_xreal_0(D,k18_complex1(k5_real_1(k2_seq_1(k1_numbers,k1_numbers,B,F),k2_seq_1(k1_numbers,k1_numbers,B,C)))) ) ) ) ) ) ) ) ) ) ) )).

fof(t16_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ( r2_fcont_1(B,A)
      <=> r2_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A),A) ) ) )).

fof(t17_fcont_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,k1_numbers,k1_numbers) )
     => ( ( r2_fcont_1(C,A)
          & r1_tarski(B,A) )
       => r2_fcont_1(C,B) ) ) )).

fof(t18_fcont_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( r2_hidden(A,k4_relset_1(k1_numbers,k1_numbers,B))
           => r2_fcont_1(B,k1_seq_4(A)) ) ) ) )).

fof(t19_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,k1_numbers,k1_numbers) )
         => ( ( r2_fcont_1(B,A)
              & r2_fcont_1(C,A) )
           => ( r2_fcont_1(k6_seq_1(k1_numbers,k1_numbers,B,C),A)
              & r2_fcont_1(k7_seq_1(k1_numbers,k1_numbers,B,C),A)
              & r2_fcont_1(k8_seq_1(k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).

fof(t20_fcont_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,k1_numbers,k1_numbers) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,k1_numbers,k1_numbers) )
         => ( ( r2_fcont_1(C,A)
              & r2_fcont_1(D,B) )
           => ( r2_fcont_1(k6_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B))
              & r2_fcont_1(k7_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B))
              & r2_fcont_1(k8_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B)) ) ) ) ) )).

fof(t21_fcont_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,k1_numbers,k1_numbers) )
         => ( r2_fcont_1(C,B)
           => r2_fcont_1(k13_seq_1(k1_numbers,k1_numbers,C,A),B) ) ) ) )).

fof(t22_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ( r2_fcont_1(B,A)
       => ( r2_fcont_1(k21_seq_1(k1_numbers,k1_numbers,B),A)
          & r2_fcont_1(k16_seq_1(k1_numbers,k1_numbers,B),A) ) ) ) )).

fof(t23_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ( ( r2_fcont_1(B,A)
          & k3_funct_2(k1_numbers,k1_numbers,B,k1_seq_4(np__0)) = k1_xboole_0 )
       => r2_fcont_1(k4_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) )).

fof(t24_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ( ( r2_fcont_1(B,A)
          & k3_funct_2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,B,A),k1_seq_4(np__0)) = k1_xboole_0 )
       => r2_fcont_1(k4_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) )).

fof(t25_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,k1_numbers,k1_numbers) )
         => ( ( r2_fcont_1(B,A)
              & k3_funct_2(k1_numbers,k1_numbers,B,k1_seq_4(np__0)) = k1_xboole_0
              & r2_fcont_1(C,A) )
           => r2_fcont_1(k2_rfunct_1(k1_numbers,k1_numbers,C,B),A) ) ) ) )).

fof(t26_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,k1_numbers,k1_numbers) )
         => ( ( r2_fcont_1(B,A)
              & r2_fcont_1(C,k10_relset_1(k1_numbers,k1_numbers,B,A)) )
           => r2_fcont_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) )).

fof(t27_fcont_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,k1_numbers,k1_numbers) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,k1_numbers,k1_numbers) )
         => ( ( r2_fcont_1(C,A)
              & r2_fcont_1(D,B) )
           => r2_fcont_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,D),k3_xboole_0(A,k3_funct_2(k1_numbers,k1_numbers,C,B))) ) ) ) )).

fof(t28_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v1_partfun1(A,k1_numbers,k1_numbers)
          & ! [B] :
              ( v1_xreal_0(B)
             => ! [C] :
                  ( v1_xreal_0(C)
                 => k2_seq_1(k1_numbers,k1_numbers,A,k2_xcmplx_0(B,C)) = k3_real_1(k2_seq_1(k1_numbers,k1_numbers,A,B),k2_seq_1(k1_numbers,k1_numbers,A,C)) ) ) )
       => ( ! [B] :
              ( v1_xreal_0(B)
             => ~ r1_fcont_1(A,B) )
          | r2_fcont_1(A,k1_numbers) ) ) ) )).

fof(t29_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ( v1_rcomp_1(k4_relset_1(k1_numbers,k1_numbers,A))
          & r2_fcont_1(A,k4_relset_1(k1_numbers,k1_numbers,A)) )
       => v1_rcomp_1(k5_relset_1(k1_numbers,k1_numbers,A)) ) ) )).

fof(t30_fcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( r1_tarski(A,k4_relset_1(k1_numbers,k1_numbers,B))
              & v1_rcomp_1(A)
              & r2_fcont_1(B,A) )
           => v1_rcomp_1(k10_relset_1(k1_numbers,k1_numbers,B,A)) ) ) ) )).

fof(t31_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ~ ( k4_relset_1(k1_numbers,k1_numbers,A) != k1_xboole_0
          & v1_rcomp_1(k4_relset_1(k1_numbers,k1_numbers,A))
          & r2_fcont_1(A,k4_relset_1(k1_numbers,k1_numbers,A))
          & ! [B] :
              ( v1_xreal_0(B)
             => ! [C] :
                  ( v1_xreal_0(C)
                 => ~ ( r2_hidden(B,k4_relset_1(k1_numbers,k1_numbers,A))
                      & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A))
                      & k2_seq_1(k1_numbers,k1_numbers,A,B) = k4_seq_4(k5_relset_1(k1_numbers,k1_numbers,A))
                      & k2_seq_1(k1_numbers,k1_numbers,A,C) = k5_seq_4(k5_relset_1(k1_numbers,k1_numbers,A)) ) ) ) ) ) )).

fof(t32_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ~ ( B != k1_xboole_0
              & r1_tarski(B,k4_relset_1(k1_numbers,k1_numbers,A))
              & v1_rcomp_1(B)
              & r2_fcont_1(A,B)
              & ! [C] :
                  ( v1_xreal_0(C)
                 => ! [D] :
                      ( v1_xreal_0(D)
                     => ~ ( r2_hidden(C,B)
                          & r2_hidden(D,B)
                          & k2_seq_1(k1_numbers,k1_numbers,A,C) = k4_seq_4(k10_relset_1(k1_numbers,k1_numbers,A,B))
                          & k2_seq_1(k1_numbers,k1_numbers,A,D) = k5_seq_4(k10_relset_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) ) ) )).

fof(d3_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ! [B] :
          ( r3_fcont_1(A,B)
        <=> ( r1_tarski(B,k4_relset_1(k1_numbers,k1_numbers,A))
            & ? [C] :
                ( v1_xreal_0(C)
                & ~ r1_xreal_0(C,np__0)
                & ! [D] :
                    ( v1_xreal_0(D)
                   => ! [E] :
                        ( v1_xreal_0(E)
                       => ( ( r2_hidden(D,B)
                            & r2_hidden(E,B) )
                         => r1_xreal_0(k18_complex1(k5_real_1(k2_seq_1(k1_numbers,k1_numbers,A,D),k2_seq_1(k1_numbers,k1_numbers,A,E))),k3_xcmplx_0(C,k18_complex1(k6_xcmplx_0(D,E)))) ) ) ) ) ) ) ) )).

fof(t33_fcont_1,axiom,(
    $true )).

fof(t34_fcont_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,k1_numbers,k1_numbers) )
     => ( ( r3_fcont_1(C,A)
          & r1_tarski(B,A) )
       => r3_fcont_1(C,B) ) ) )).

fof(t35_fcont_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,k1_numbers,k1_numbers) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,k1_numbers,k1_numbers) )
         => ( ( r3_fcont_1(C,A)
              & r3_fcont_1(D,B) )
           => r3_fcont_1(k6_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B)) ) ) ) )).

fof(t36_fcont_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & m2_relset_1(C,k1_numbers,k1_numbers) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & m2_relset_1(D,k1_numbers,k1_numbers) )
         => ( ( r3_fcont_1(C,A)
              & r3_fcont_1(D,B) )
           => r3_fcont_1(k7_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B)) ) ) ) )).

fof(t37_fcont_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_funct_1(E)
        & m2_relset_1(E,k1_numbers,k1_numbers) )
     => ! [F] :
          ( ( v1_funct_1(F)
            & m2_relset_1(F,k1_numbers,k1_numbers) )
         => ( ( r3_fcont_1(E,A)
              & r3_fcont_1(F,B)
              & r3_rfunct_1(E,C)
              & r3_rfunct_1(F,D) )
           => r3_fcont_1(k8_seq_1(k1_numbers,k1_numbers,E,F),k3_xboole_0(k3_xboole_0(k3_xboole_0(A,C),B),D)) ) ) ) )).

fof(t38_fcont_1,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,k1_numbers,k1_numbers) )
         => ( r3_fcont_1(C,A)
           => r3_fcont_1(k13_seq_1(k1_numbers,k1_numbers,C,B),A) ) ) ) )).

fof(t39_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ( r3_fcont_1(B,A)
       => ( r3_fcont_1(k16_seq_1(k1_numbers,k1_numbers,B),A)
          & r3_fcont_1(k21_seq_1(k1_numbers,k1_numbers,B),A) ) ) ) )).

fof(t40_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ( ( r1_tarski(A,k4_relset_1(k1_numbers,k1_numbers,B))
          & r1_partfun2(k1_numbers,k1_numbers,B,A) )
       => r3_fcont_1(B,A) ) ) )).

fof(t41_fcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => r3_fcont_1(k1_partfun2(k1_numbers,A),A) ) )).

fof(t42_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ( r3_fcont_1(B,A)
       => r2_fcont_1(B,A) ) ) )).

fof(t43_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ? [B] :
            ( v1_xreal_0(B)
            & k5_relset_1(k1_numbers,k1_numbers,A) = k1_seq_4(B) )
       => r2_fcont_1(A,k4_relset_1(k1_numbers,k1_numbers,A)) ) ) )).

fof(t44_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ( ( r1_tarski(A,k4_relset_1(k1_numbers,k1_numbers,B))
          & r1_partfun2(k1_numbers,k1_numbers,B,A) )
       => r2_fcont_1(B,A) ) ) )).

fof(t45_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ! [B] :
            ( v1_xreal_0(B)
           => ( r2_hidden(B,k4_relset_1(k1_numbers,k1_numbers,A))
             => k2_seq_1(k1_numbers,k1_numbers,A,B) = B ) )
       => r2_fcont_1(A,k4_relset_1(k1_numbers,k1_numbers,A)) ) ) )).

fof(t46_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( A = k1_partfun2(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,A))
       => r2_fcont_1(A,k4_relset_1(k1_numbers,k1_numbers,A)) ) ) )).

fof(t47_fcont_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( ( r1_tarski(A,k4_relset_1(k1_numbers,k1_numbers,B))
              & k2_partfun1(k1_numbers,k1_numbers,B,A) = k1_partfun2(k1_numbers,A) )
           => r2_fcont_1(B,A) ) ) ) )).

fof(t48_fcont_1,axiom,(
    ! [A,B] :
      ( v1_xreal_0(B)
     => ! [C] :
          ( v1_xreal_0(C)
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,k1_numbers,k1_numbers) )
             => ( ( r1_tarski(A,k4_relset_1(k1_numbers,k1_numbers,D))
                  & ! [E] :
                      ( v1_xreal_0(E)
                     => ( r2_hidden(E,A)
                       => k2_seq_1(k1_numbers,k1_numbers,D,E) = k2_xcmplx_0(k3_xcmplx_0(B,E),C) ) ) )
               => r2_fcont_1(D,A) ) ) ) ) )).

fof(t49_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ! [B] :
            ( v1_xreal_0(B)
           => ( r2_hidden(B,k4_relset_1(k1_numbers,k1_numbers,A))
             => k2_seq_1(k1_numbers,k1_numbers,A,B) = k5_square_1(B) ) )
       => r2_fcont_1(A,k4_relset_1(k1_numbers,k1_numbers,A)) ) ) )).

fof(t50_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ( ( r1_tarski(A,k4_relset_1(k1_numbers,k1_numbers,B))
          & ! [C] :
              ( v1_xreal_0(C)
             => ( r2_hidden(C,A)
               => k2_seq_1(k1_numbers,k1_numbers,B,C) = k5_square_1(C) ) ) )
       => r2_fcont_1(B,A) ) ) )).

fof(t51_fcont_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( ! [B] :
            ( v1_xreal_0(B)
           => ( r2_hidden(B,k4_relset_1(k1_numbers,k1_numbers,A))
             => k2_seq_1(k1_numbers,k1_numbers,A,B) = k18_complex1(B) ) )
       => r2_fcont_1(A,k4_relset_1(k1_numbers,k1_numbers,A)) ) ) )).

fof(t52_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ( ( r1_tarski(A,k4_relset_1(k1_numbers,k1_numbers,B))
          & ! [C] :
              ( v1_xreal_0(C)
             => ( r2_hidden(C,A)
               => k2_seq_1(k1_numbers,k1_numbers,B,C) = k18_complex1(C) ) ) )
       => r2_fcont_1(B,A) ) ) )).

fof(t53_fcont_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_numbers,k1_numbers) )
     => ( ( r1_tarski(A,k4_relset_1(k1_numbers,k1_numbers,B))
          & r5_rfunct_2(B,A) )
       => ( ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( r1_xreal_0(C,D)
                      & k10_relset_1(k1_numbers,k1_numbers,B,A) = k1_rcomp_1(C,D) ) ) )
          | r2_fcont_1(B,A) ) ) ) )).

fof(t54_fcont_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v2_funct_1(C)
                & m2_relset_1(C,k1_numbers,k1_numbers) )
             => ( ( r1_xreal_0(A,B)
                  & r1_tarski(k1_rcomp_1(A,B),k4_relset_1(k1_numbers,k1_numbers,C)) )
               => ( ( ~ r1_rfunct_2(C,k1_rcomp_1(A,B))
                    & ~ r2_rfunct_2(C,k1_rcomp_1(A,B)) )
                  | r2_fcont_1(k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(A,B))),k10_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(A,B))) ) ) ) ) ) )).
%------------------------------------------------------------------------------