SET007 Axioms: SET007+67.ax


%------------------------------------------------------------------------------
% File     : SET007+67 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Koenig's Theorem
% 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    : card_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   87 (  29 unit)
%            Number of atoms       :  334 (  59 equality)
%            Maximal formula depth :   17 (   5 average)
%            Number of connectives :  261 (  14 ~  ;   4  |; 131  &)
%                                         (  12 <=>; 100 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   1 propositional; 0-3 arity)
%            Number of functors    :   40 (  10 constant; 0-2 arity)
%            Number of variables   :  155 (   0 singleton; 148 !;   7 ?)
%            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(rc1_card_3,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_card_3(A) ) )).

fof(fc1_card_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B))
        & v1_card_3(k7_relat_1(A,B)) ) ) )).

fof(fc2_card_3,axiom,(
    ! [A,B] :
      ( v1_card_1(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v1_ordinal2(k2_funcop_1(A,B))
        & v1_card_3(k2_funcop_1(A,B)) ) ) )).

fof(fc3_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => v1_fraenkel(k4_card_3(A)) ) )).

fof(fc4_card_3,axiom,(
    ! [A,B,C] :
      ( ( v1_setfam_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => ( ~ v1_xboole_0(k4_card_3(C))
        & v1_fraenkel(k4_card_3(C)) ) ) )).

fof(fc5_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => ( ~ v1_xboole_0(k4_card_3(A))
        & v1_fraenkel(k4_card_3(A)) ) ) )).

fof(d1_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_card_3(A)
      <=> ! [B] :
            ( r2_hidden(B,k1_relat_1(A))
           => v1_card_1(k1_funct_1(A,B)) ) ) ) )).

fof(t1_card_3,axiom,(
    $true )).

fof(t2_card_3,axiom,(
    $true )).

fof(t3_card_3,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v1_card_3(k1_xboole_0) )).

fof(d2_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( B = k1_card_3(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] :
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(B,C) = k1_card_1(k1_funct_1(A,C)) ) ) ) ) ) )).

fof(d3_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k2_card_3(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] :
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(B,C) = k2_zfmisc_1(k1_funct_1(A,C),k1_tarski(C)) ) ) ) ) ) )).

fof(d4_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k3_card_3(A) = k3_tarski(k2_relat_1(A)) ) )).

fof(d5_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( B = k4_card_3(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ? [D] :
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & C = D
                  & k1_relat_1(D) = k1_relat_1(A)
                  & ! [E] :
                      ( r2_hidden(E,k1_relat_1(A))
                     => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) )).

fof(t4_card_3,axiom,(
    $true )).

fof(t5_card_3,axiom,(
    $true )).

fof(t6_card_3,axiom,(
    $true )).

fof(t7_card_3,axiom,(
    $true )).

fof(t8_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => k1_card_3(A) = A ) )).

fof(t9_card_3,axiom,(
    k1_card_3(k1_xboole_0) = k1_xboole_0 )).

fof(t10_card_3,axiom,(
    ! [A,B] : k1_card_3(k2_funcop_1(A,B)) = k2_funcop_1(A,k1_card_1(B)) )).

fof(t11_card_3,axiom,(
    k2_card_3(k1_xboole_0) = k1_xboole_0 )).

fof(t12_card_3,axiom,(
    ! [A,B] : k2_card_3(k2_funcop_1(k1_tarski(A),B)) = k2_funcop_1(k1_tarski(A),k2_zfmisc_1(B,k1_tarski(A))) )).

fof(t13_card_3,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(A,k1_relat_1(C))
          & r2_hidden(B,k1_relat_1(C)) )
       => ( A = B
          | r1_xboole_0(k1_funct_1(k2_card_3(C),A),k1_funct_1(k2_card_3(C),B)) ) ) ) )).

fof(t14_card_3,axiom,(
    k3_card_3(k1_xboole_0) = k1_xboole_0 )).

fof(t15_card_3,axiom,(
    ! [A,B] : r1_tarski(k3_card_3(k2_funcop_1(A,B)),B) )).

fof(t16_card_3,axiom,(
    ! [A,B] :
      ( A != k1_xboole_0
     => k3_card_3(k2_funcop_1(A,B)) = B ) )).

fof(t17_card_3,axiom,(
    ! [A,B] : k3_card_3(k2_funcop_1(k1_tarski(A),B)) = B )).

fof(t18_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k4_card_3(B))
          <=> ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] :
                  ( r2_hidden(C,k1_relat_1(B))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) )).

fof(t19_card_3,axiom,(
    k4_card_3(k1_xboole_0) = k1_tarski(k1_xboole_0) )).

fof(t20_card_3,axiom,(
    ! [A,B] : k1_funct_2(A,B) = k4_card_3(k2_funcop_1(A,B)) )).

fof(d6_card_3,axiom,(
    ! [A,B,C] :
      ( C = k5_card_3(A,B)
    <=> ! [D] :
          ( r2_hidden(D,C)
        <=> ? [E] :
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & r2_hidden(E,B)
              & D = k1_funct_1(E,A) ) ) ) )).

fof(t21_card_3,axiom,(
    $true )).

fof(t22_card_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k1_relat_1(B))
       => ( k4_card_3(B) = k1_xboole_0
          | k5_card_3(A,k4_card_3(B)) = k1_funct_1(B,A) ) ) ) )).

fof(t23_card_3,axiom,(
    $true )).

fof(t24_card_3,axiom,(
    ! [A] : k5_card_3(A,k1_xboole_0) = k1_xboole_0 )).

fof(t25_card_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => k5_card_3(A,k1_tarski(B)) = k1_tarski(k1_funct_1(B,A)) ) )).

fof(t26_card_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => k5_card_3(A,k2_tarski(B,C)) = k2_tarski(k1_funct_1(B,A),k1_funct_1(C,A)) ) ) )).

fof(t27_card_3,axiom,(
    ! [A,B,C] : k5_card_3(C,k2_xboole_0(A,B)) = k2_xboole_0(k5_card_3(C,A),k5_card_3(C,B)) )).

fof(t28_card_3,axiom,(
    ! [A,B,C] : r1_tarski(k5_card_3(C,k3_xboole_0(A,B)),k3_xboole_0(k5_card_3(C,A),k5_card_3(C,B))) )).

fof(t29_card_3,axiom,(
    ! [A,B,C] : r1_tarski(k4_xboole_0(k5_card_3(B,A),k5_card_3(B,C)),k5_card_3(B,k4_xboole_0(A,C))) )).

fof(t30_card_3,axiom,(
    ! [A,B,C] : r1_tarski(k5_xboole_0(k5_card_3(B,A),k5_card_3(B,C)),k5_card_3(B,k5_xboole_0(A,C))) )).

fof(t31_card_3,axiom,(
    ! [A,B] : r1_tarski(k1_card_1(k5_card_3(B,A)),k1_card_1(A)) )).

fof(t32_card_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ~ ( r2_hidden(A,k3_card_3(k2_card_3(B)))
          & ! [C,D] : A != k4_tarski(C,D) ) ) )).

fof(t33_card_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k3_card_3(k2_card_3(B)))
      <=> ( r2_hidden(k2_mcart_1(A),k1_relat_1(B))
          & r2_hidden(k1_mcart_1(A),k1_funct_1(B,k2_mcart_1(A)))
          & A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) ) ) ) )).

fof(t34_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
           => r1_tarski(k2_card_3(A),k2_card_3(B)) ) ) ) )).

fof(t35_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
           => r1_tarski(k3_card_3(A),k3_card_3(B)) ) ) ) )).

fof(t36_card_3,axiom,(
    ! [A,B] : k3_card_3(k2_card_3(k2_funcop_1(A,B))) = k2_zfmisc_1(B,A) )).

fof(t37_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k4_card_3(A) = k1_xboole_0
      <=> r2_hidden(k1_xboole_0,k2_relat_1(A)) ) ) )).

fof(t38_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] :
                  ( r2_hidden(C,k1_relat_1(A))
                 => r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r1_tarski(k4_card_3(A),k4_card_3(B)) ) ) ) )).

fof(t39_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] :
          ( r2_hidden(B,k1_relat_1(A))
         => k1_card_1(k1_funct_1(A,B)) = k1_funct_1(A,B) ) ) )).

fof(t40_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] :
          ( r2_hidden(B,k1_relat_1(A))
         => k1_card_1(k1_funct_1(k2_card_3(A),B)) = k1_funct_1(A,B) ) ) )).

fof(d7_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => k6_card_3(A) = k1_card_1(k3_card_3(k2_card_3(A))) ) )).

fof(d8_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => k7_card_3(A) = k1_card_1(k4_card_3(A)) ) )).

fof(t41_card_3,axiom,(
    $true )).

fof(t42_card_3,axiom,(
    $true )).

fof(t43_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] :
                  ( r2_hidden(C,k1_relat_1(A))
                 => r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r1_tarski(k6_card_3(A),k6_card_3(B)) ) ) ) )).

fof(t44_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ( r2_hidden(k1_xboole_0,k2_relat_1(A))
      <=> k7_card_3(A) = np__0 ) ) )).

fof(t45_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] :
                  ( r2_hidden(C,k1_relat_1(A))
                 => r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r1_tarski(k7_card_3(A),k7_card_3(B)) ) ) ) )).

fof(t46_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( r1_tarski(A,B)
           => r1_tarski(k6_card_3(A),k6_card_3(B)) ) ) ) )).

fof(t47_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( r1_tarski(A,B)
           => ( r2_hidden(np__0,k2_relat_1(B))
              | r1_tarski(k7_card_3(A),k7_card_3(B)) ) ) ) ) )).

fof(t48_card_3,axiom,(
    ! [A] :
      ( v1_card_1(A)
     => k6_card_3(k2_funcop_1(k1_xboole_0,A)) = np__0 ) )).

fof(t49_card_3,axiom,(
    ! [A] :
      ( v1_card_1(A)
     => k7_card_3(k2_funcop_1(k1_xboole_0,A)) = np__1 ) )).

fof(t50_card_3,axiom,(
    ! [A] :
      ( v1_card_1(A)
     => ! [B] : k6_card_3(k2_funcop_1(k1_tarski(B),A)) = A ) )).

fof(t51_card_3,axiom,(
    ! [A] :
      ( v1_card_1(A)
     => ! [B] : k7_card_3(k2_funcop_1(k1_tarski(B),A)) = A ) )).

fof(t52_card_3,axiom,(
    ! [A] :
      ( v1_card_1(A)
     => ! [B] :
          ( v1_card_1(B)
         => k6_card_3(k2_funcop_1(A,B)) = k2_card_2(A,B) ) ) )).

fof(t53_card_3,axiom,(
    ! [A] :
      ( v1_card_1(A)
     => ! [B] :
          ( v1_card_1(B)
         => k7_card_3(k2_funcop_1(A,B)) = k3_card_2(B,A) ) ) )).

fof(t54_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(k1_card_3(A))) ) )).

fof(t55_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(A)) ) )).

fof(t56_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_card_3(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] :
                  ( r2_hidden(C,k1_relat_1(A))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) )
           => r2_hidden(k6_card_3(A),k7_card_3(B)) ) ) ) )).

fof(t57_card_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => v1_finset_1(k4_classes1(A)) ) )).

fof(t58_card_3,axiom,(
    ! [A] :
      ( v1_finset_1(A)
     => r2_hidden(k1_card_1(A),k1_card_1(k5_ordinal2)) ) )).

fof(t59_card_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( v3_ordinal1(B)
         => ( r2_hidden(k1_card_1(A),k1_card_1(B))
           => r2_hidden(A,B) ) ) ) )).

fof(t60_card_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( v1_card_1(B)
         => ( r2_hidden(k1_card_1(A),B)
           => r2_hidden(A,B) ) ) ) )).

fof(t61_card_3,axiom,(
    ! [A] :
      ~ ( v6_ordinal1(A)
        & ! [B] :
            ~ ( r1_tarski(B,A)
              & k3_tarski(B) = k3_tarski(A)
              & ! [C] :
                  ~ ( r1_tarski(C,B)
                    & C != k1_xboole_0
                    & ! [D] :
                        ~ ( r2_hidden(D,C)
                          & ! [E] :
                              ( r2_hidden(E,C)
                             => r1_tarski(D,E) ) ) ) ) ) )).

fof(t62_card_3,axiom,(
    ! [A] :
      ( v1_card_1(A)
     => ! [B] :
          ( ( ! [C] :
                ( r2_hidden(C,B)
               => r2_hidden(k1_card_1(C),A) )
            & v6_ordinal1(B) )
         => r1_tarski(k1_card_1(k3_tarski(B)),A) ) ) )).

fof(s1_card_3,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_card_3(A)
      & k1_relat_1(A) = f1_s1_card_3
      & ! [B] :
          ( r2_hidden(B,f1_s1_card_3)
         => k1_funct_1(A,B) = f2_s1_card_3(B) ) ) )).

fof(s2_card_3,axiom,
    ( ( f1_s2_card_3 != k1_xboole_0
      & ! [A,B] :
          ( ( p1_s2_card_3(A,B)
            & p1_s2_card_3(B,A) )
         => A = B )
      & ! [A,B,C] :
          ( ( p1_s2_card_3(A,B)
            & p1_s2_card_3(B,C) )
         => p1_s2_card_3(A,C) ) )
   => ? [A] :
        ( r2_hidden(A,f1_s2_card_3)
        & ! [B] :
            ~ ( r2_hidden(B,f1_s2_card_3)
              & B != A
              & p1_s2_card_3(B,A) ) ) )).

fof(s3_card_3,axiom,
    ( ( f1_s3_card_3 != k1_xboole_0
      & ! [A,B] :
          ( p1_s3_card_3(A,B)
          | p1_s3_card_3(B,A) )
      & ! [A,B,C] :
          ( ( p1_s3_card_3(A,B)
            & p1_s3_card_3(B,C) )
         => p1_s3_card_3(A,C) ) )
   => ? [A] :
        ( r2_hidden(A,f1_s3_card_3)
        & ! [B] :
            ( r2_hidden(B,f1_s3_card_3)
           => p1_s3_card_3(A,B) ) ) )).

fof(s4_card_3,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s4_card_3
      & ! [B] :
          ( r2_hidden(B,f1_s4_card_3)
         => ! [C] :
              ( r2_hidden(C,k1_funct_1(A,B))
            <=> ( r2_hidden(C,f2_s4_card_3(B))
                & p1_s4_card_3(B,C) ) ) ) ) )).

fof(dt_k1_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k1_card_3(A))
        & v1_funct_1(k1_card_3(A))
        & v1_card_3(k1_card_3(A)) ) ) )).

fof(dt_k2_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_card_3(A))
        & v1_funct_1(k2_card_3(A)) ) ) )).

fof(dt_k3_card_3,axiom,(
    $true )).

fof(dt_k4_card_3,axiom,(
    $true )).

fof(dt_k5_card_3,axiom,(
    $true )).

fof(dt_k6_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => v1_card_1(k6_card_3(A)) ) )).

fof(dt_k7_card_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_card_3(A) )
     => v1_card_1(k7_card_3(A)) ) )).
%------------------------------------------------------------------------------