SET007 Axioms: SET007+147.ax


%------------------------------------------------------------------------------
% File     : SET007+147 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Hilbert Positive Propositional Calculus
% 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    : hilbert1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   76 (   6 unit)
%            Number of atoms       :  308 (   8 equality)
%            Maximal formula depth :   18 (   6 average)
%            Number of connectives :  236 (   4 ~  ;   0  |;  56  &)
%                                         (  12 <=>; 164 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   18 (   1 propositional; 0-3 arity)
%            Number of functors    :   18 (   9 constant; 0-2 arity)
%            Number of variables   :  159 (   0 singleton; 158 !;   1 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_hilbert1,axiom,(
    ! [A] :
      ( v5_hilbert1(A)
     => ( ~ v1_xboole_0(A)
        & v1_hilbert1(A)
        & v2_hilbert1(A)
        & v3_hilbert1(A)
        & v4_hilbert1(A) ) ) )).

fof(cc2_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k13_finseq_1(k5_numbers)))
     => ( ( v1_hilbert1(A)
          & v2_hilbert1(A)
          & v3_hilbert1(A)
          & v4_hilbert1(A) )
       => v5_hilbert1(A) ) ) )).

fof(fc1_hilbert1,axiom,
    ( ~ v1_xboole_0(k1_hilbert1)
    & v1_hilbert1(k1_hilbert1)
    & v2_hilbert1(k1_hilbert1)
    & v3_hilbert1(k1_hilbert1)
    & v4_hilbert1(k1_hilbert1)
    & v5_hilbert1(k1_hilbert1) )).

fof(rc1_hilbert1,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_hilbert1(A)
      & v2_hilbert1(A)
      & v3_hilbert1(A)
      & v4_hilbert1(A)
      & v5_hilbert1(A) ) )).

fof(fc2_hilbert1,axiom,
    ( ~ v1_xboole_0(k1_hilbert1)
    & v1_fraenkel(k1_hilbert1)
    & v1_hilbert1(k1_hilbert1)
    & v2_hilbert1(k1_hilbert1)
    & v3_hilbert1(k1_hilbert1)
    & v4_hilbert1(k1_hilbert1)
    & v5_hilbert1(k1_hilbert1) )).

fof(cc3_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v1_finseq_1(A) ) ) )).

fof(fc3_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => v6_hilbert1(k5_hilbert1(A)) ) )).

fof(fc4_hilbert1,axiom,(
    v6_hilbert1(k6_hilbert1) )).

fof(d1_hilbert1,axiom,(
    ! [A] :
      ( v1_hilbert1(A)
    <=> r2_hidden(k12_finseq_1(k5_numbers,np__0),A) ) )).

fof(d2_hilbert1,axiom,(
    ! [A] :
      ( v2_hilbert1(A)
    <=> ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( r2_hidden(B,A)
                  & r2_hidden(C,A) )
               => r2_hidden(k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__1),B),C),A) ) ) ) ) )).

fof(d3_hilbert1,axiom,(
    ! [A] :
      ( v3_hilbert1(A)
    <=> ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( r2_hidden(B,A)
                  & r2_hidden(C,A) )
               => r2_hidden(k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__2),B),C),A) ) ) ) ) )).

fof(d4_hilbert1,axiom,(
    ! [A] :
      ( v4_hilbert1(A)
    <=> ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r2_hidden(k12_finseq_1(k5_numbers,k1_nat_1(np__3,B)),A) ) ) )).

fof(d5_hilbert1,axiom,(
    ! [A] :
      ( v5_hilbert1(A)
    <=> ( r1_tarski(A,k13_finseq_1(k5_numbers))
        & v1_hilbert1(A)
        & v2_hilbert1(A)
        & v3_hilbert1(A)
        & v4_hilbert1(A) ) ) )).

fof(d6_hilbert1,axiom,(
    ! [A] :
      ( A = k1_hilbert1
    <=> ( v5_hilbert1(A)
        & ! [B] :
            ( v5_hilbert1(B)
           => r1_tarski(A,B) ) ) ) )).

fof(d7_hilbert1,axiom,(
    k2_hilbert1 = k12_finseq_1(k5_numbers,np__0) )).

fof(d8_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => k3_hilbert1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__1),A),B) ) ) )).

fof(d9_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => k4_hilbert1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__2),A),B) ) ) )).

fof(d10_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ( v6_hilbert1(A)
      <=> ( r2_hidden(k2_hilbert1,A)
          & ! [B] :
              ( m1_subset_1(B,k1_hilbert1)
             => ! [C] :
                  ( m1_subset_1(C,k1_hilbert1)
                 => ! [D] :
                      ( m1_subset_1(D,k1_hilbert1)
                     => ( r2_hidden(k3_hilbert1(B,k3_hilbert1(C,B)),A)
                        & r2_hidden(k3_hilbert1(k3_hilbert1(B,k3_hilbert1(C,D)),k3_hilbert1(k3_hilbert1(B,C),k3_hilbert1(B,D))),A)
                        & r2_hidden(k3_hilbert1(k4_hilbert1(B,C),B),A)
                        & r2_hidden(k3_hilbert1(k4_hilbert1(B,C),C),A)
                        & r2_hidden(k3_hilbert1(B,k3_hilbert1(C,k4_hilbert1(B,C))),A)
                        & ( ( r2_hidden(B,A)
                            & r2_hidden(k3_hilbert1(B,C),A) )
                         => r2_hidden(C,A) ) ) ) ) ) ) ) ) )).

fof(d11_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1))
         => ( B = k5_hilbert1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_hilbert1)
               => ( r2_hidden(C,B)
                <=> ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(k1_hilbert1))
                     => ( ( v6_hilbert1(D)
                          & r1_tarski(A,D) )
                       => r2_hidden(C,D) ) ) ) ) ) ) ) )).

fof(d12_hilbert1,axiom,(
    k6_hilbert1 = k5_hilbert1(k1_subset_1(k1_hilbert1)) )).

fof(t1_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => r2_hidden(k2_hilbert1,k5_hilbert1(A)) ) )).

fof(t2_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(B,k3_hilbert1(C,k4_hilbert1(B,C))),k5_hilbert1(A)) ) ) ) )).

fof(t3_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => ! [D] :
                  ( m1_subset_1(D,k1_hilbert1)
                 => r2_hidden(k3_hilbert1(k3_hilbert1(B,k3_hilbert1(C,D)),k3_hilbert1(k3_hilbert1(B,C),k3_hilbert1(B,D))),k5_hilbert1(A)) ) ) ) ) )).

fof(t4_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(B,k3_hilbert1(C,B)),k5_hilbert1(A)) ) ) ) )).

fof(t5_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k4_hilbert1(B,C),B),k5_hilbert1(A)) ) ) ) )).

fof(t6_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k4_hilbert1(B,C),C),k5_hilbert1(A)) ) ) ) )).

fof(t7_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => ( ( r2_hidden(B,k5_hilbert1(A))
                  & r2_hidden(k3_hilbert1(B,C),k5_hilbert1(A)) )
               => r2_hidden(C,k5_hilbert1(A)) ) ) ) ) )).

fof(t8_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1))
         => ( ( v6_hilbert1(A)
              & r1_tarski(B,A) )
           => r1_tarski(k5_hilbert1(B),A) ) ) ) )).

fof(t9_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => r1_tarski(A,k5_hilbert1(A)) ) )).

fof(t10_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1))
         => ( r1_tarski(A,B)
           => r1_tarski(k5_hilbert1(A),k5_hilbert1(B)) ) ) ) )).

fof(t11_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => k5_hilbert1(k5_hilbert1(A)) = k5_hilbert1(A) ) )).

fof(t12_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ( v6_hilbert1(A)
      <=> k5_hilbert1(A) = A ) ) )).

fof(t13_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => ( v6_hilbert1(A)
       => r1_tarski(k6_hilbert1,A) ) ) )).

fof(t14_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => r2_hidden(k3_hilbert1(A,A),k6_hilbert1) ) )).

fof(t15_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ( r2_hidden(A,k6_hilbert1)
           => r2_hidden(k3_hilbert1(B,A),k6_hilbert1) ) ) ) )).

fof(t16_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => r2_hidden(k3_hilbert1(A,k2_hilbert1),k6_hilbert1) ) )).

fof(t17_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => r2_hidden(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(A,A)),k6_hilbert1) ) ) )).

fof(t18_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => r2_hidden(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(B,B)),k6_hilbert1) ) ) )).

fof(t19_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(k3_hilbert1(C,A),k3_hilbert1(C,B))),k6_hilbert1) ) ) ) )).

fof(t20_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => ( r2_hidden(k3_hilbert1(A,k3_hilbert1(B,C)),k6_hilbert1)
               => r2_hidden(k3_hilbert1(B,k3_hilbert1(A,C)),k6_hilbert1) ) ) ) ) )).

fof(t21_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(k3_hilbert1(B,C),k3_hilbert1(A,C))),k6_hilbert1) ) ) ) )).

fof(t22_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => ( r2_hidden(k3_hilbert1(A,B),k6_hilbert1)
               => r2_hidden(k3_hilbert1(k3_hilbert1(B,C),k3_hilbert1(A,C)),k6_hilbert1) ) ) ) ) )).

fof(t23_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => ( ( r2_hidden(k3_hilbert1(A,B),k6_hilbert1)
                  & r2_hidden(k3_hilbert1(B,C),k6_hilbert1) )
               => r2_hidden(k3_hilbert1(A,C),k6_hilbert1) ) ) ) ) )).

fof(t24_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => ! [D] :
                  ( m1_subset_1(D,k1_hilbert1)
                 => r2_hidden(k3_hilbert1(k3_hilbert1(A,k3_hilbert1(B,C)),k3_hilbert1(k3_hilbert1(D,B),k3_hilbert1(A,k3_hilbert1(D,C)))),k6_hilbert1) ) ) ) ) )).

fof(t25_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k3_hilbert1(k3_hilbert1(A,B),C),k3_hilbert1(B,C)),k6_hilbert1) ) ) ) )).

fof(t26_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k3_hilbert1(A,k3_hilbert1(B,C)),k3_hilbert1(B,k3_hilbert1(A,C))),k6_hilbert1) ) ) ) )).

fof(t27_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => r2_hidden(k3_hilbert1(k3_hilbert1(A,k3_hilbert1(A,B)),k3_hilbert1(A,B)),k6_hilbert1) ) ) )).

fof(t28_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => r2_hidden(k3_hilbert1(A,k3_hilbert1(k3_hilbert1(A,B),B)),k6_hilbert1) ) ) )).

fof(t29_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => ( ( r2_hidden(k3_hilbert1(A,k3_hilbert1(B,C)),k6_hilbert1)
                  & r2_hidden(B,k6_hilbert1) )
               => r2_hidden(k3_hilbert1(A,C),k6_hilbert1) ) ) ) ) )).

fof(t30_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => r2_hidden(k3_hilbert1(A,k4_hilbert1(A,A)),k6_hilbert1) ) )).

fof(t31_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ( r2_hidden(k4_hilbert1(A,B),k6_hilbert1)
          <=> ( r2_hidden(A,k6_hilbert1)
              & r2_hidden(B,k6_hilbert1) ) ) ) ) )).

fof(t32_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ( r2_hidden(k4_hilbert1(A,B),k6_hilbert1)
          <=> r2_hidden(k4_hilbert1(B,A),k6_hilbert1) ) ) ) )).

fof(t33_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k3_hilbert1(k4_hilbert1(A,B),C),k3_hilbert1(A,k3_hilbert1(B,C))),k6_hilbert1) ) ) ) )).

fof(t34_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k3_hilbert1(A,k3_hilbert1(B,C)),k3_hilbert1(k4_hilbert1(A,B),C)),k6_hilbert1) ) ) ) )).

fof(t35_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(k3_hilbert1(A,C),k3_hilbert1(A,k4_hilbert1(B,C)))),k6_hilbert1) ) ) ) )).

fof(t36_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => r2_hidden(k3_hilbert1(k4_hilbert1(k3_hilbert1(A,B),A),B),k6_hilbert1) ) ) )).

fof(t37_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k4_hilbert1(k4_hilbert1(k3_hilbert1(A,B),A),C),B),k6_hilbert1) ) ) ) )).

fof(t38_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(k4_hilbert1(C,A),B)),k6_hilbert1) ) ) ) )).

fof(t39_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(k4_hilbert1(A,C),B)),k6_hilbert1) ) ) ) )).

fof(t40_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k3_hilbert1(k4_hilbert1(A,B),C),k3_hilbert1(k4_hilbert1(A,B),k4_hilbert1(C,B))),k6_hilbert1) ) ) ) )).

fof(t41_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(k4_hilbert1(A,C),k4_hilbert1(B,C))),k6_hilbert1) ) ) ) )).

fof(t42_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k4_hilbert1(k3_hilbert1(A,B),k4_hilbert1(A,C)),k4_hilbert1(B,C)),k6_hilbert1) ) ) ) )).

fof(t43_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => r2_hidden(k3_hilbert1(k4_hilbert1(A,B),k4_hilbert1(B,A)),k6_hilbert1) ) ) )).

fof(t44_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k4_hilbert1(k3_hilbert1(A,B),k4_hilbert1(A,C)),k4_hilbert1(C,B)),k6_hilbert1) ) ) ) )).

fof(t45_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(k4_hilbert1(A,C),k4_hilbert1(C,B))),k6_hilbert1) ) ) ) )).

fof(t46_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(k4_hilbert1(C,A),k4_hilbert1(C,B))),k6_hilbert1) ) ) ) )).

fof(t47_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k4_hilbert1(A,k4_hilbert1(B,C)),k4_hilbert1(A,k4_hilbert1(C,B))),k6_hilbert1) ) ) ) )).

fof(t48_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k4_hilbert1(k3_hilbert1(A,B),k3_hilbert1(A,C)),k3_hilbert1(A,k4_hilbert1(B,C))),k6_hilbert1) ) ) ) )).

fof(t49_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k4_hilbert1(k4_hilbert1(A,B),C),k4_hilbert1(A,k4_hilbert1(B,C))),k6_hilbert1) ) ) ) )).

fof(t50_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_hilbert1)
     => ! [B] :
          ( m1_subset_1(B,k1_hilbert1)
         => ! [C] :
              ( m1_subset_1(C,k1_hilbert1)
             => r2_hidden(k3_hilbert1(k4_hilbert1(A,k4_hilbert1(B,C)),k4_hilbert1(k4_hilbert1(A,B),C)),k6_hilbert1) ) ) ) )).

fof(dt_k1_hilbert1,axiom,(
    $true )).

fof(dt_k2_hilbert1,axiom,(
    m1_subset_1(k2_hilbert1,k1_hilbert1) )).

fof(dt_k3_hilbert1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_hilbert1)
        & m1_subset_1(B,k1_hilbert1) )
     => m1_subset_1(k3_hilbert1(A,B),k1_hilbert1) ) )).

fof(dt_k4_hilbert1,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_hilbert1)
        & m1_subset_1(B,k1_hilbert1) )
     => m1_subset_1(k4_hilbert1(A,B),k1_hilbert1) ) )).

fof(dt_k5_hilbert1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1))
     => m1_subset_1(k5_hilbert1(A),k1_zfmisc_1(k1_hilbert1)) ) )).

fof(dt_k6_hilbert1,axiom,(
    m1_subset_1(k6_hilbert1,k1_zfmisc_1(k1_hilbert1)) )).
%------------------------------------------------------------------------------