SET007 Axioms: SET007+270.ax


%------------------------------------------------------------------------------
% File     : SET007+270 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Algebra of Normal Forms
% 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    : normform [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  129 (  38 unit)
%            Number of atoms       :  599 (  64 equality)
%            Maximal formula depth :   17 (   7 average)
%            Number of connectives :  561 (  91 ~  ;   0  |; 210  &)
%                                         (  10 <=>; 250 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   1 propositional; 0-4 arity)
%            Number of functors    :   41 (   1 constant; 0-6 arity)
%            Number of variables   :  342 (   0 singleton; 337 !;   5 ?)
%            Maximal term depth    :    5 (   2 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(fc1_normform,axiom,(
    ! [A] :
      ( v1_relat_1(k5_normform(A))
      & v1_funct_1(k5_normform(A))
      & v1_funct_2(k5_normform(A),k2_zfmisc_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
      & v1_binop_1(k5_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
      & v2_binop_1(k5_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
      & v3_binop_1(k5_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) ) )).

fof(fc2_normform,axiom,(
    ! [A] :
      ( v1_relat_1(k7_normform(A))
      & ~ v1_xboole_0(k7_normform(A)) ) )).

fof(fc3_normform,axiom,(
    ! [A] : ~ v1_xboole_0(k8_normform(A)) )).

fof(fc4_normform,axiom,(
    ! [A] :
      ( ~ v3_struct_0(k12_normform(A))
      & v3_lattices(k12_normform(A)) ) )).

fof(fc5_normform,axiom,(
    ! [A] :
      ( ~ v3_struct_0(k12_normform(A))
      & v3_lattices(k12_normform(A))
      & v4_lattices(k12_normform(A))
      & v5_lattices(k12_normform(A))
      & v6_lattices(k12_normform(A))
      & v7_lattices(k12_normform(A))
      & v8_lattices(k12_normform(A))
      & v9_lattices(k12_normform(A))
      & v10_lattices(k12_normform(A)) ) )).

fof(fc6_normform,axiom,(
    ! [A] :
      ( ~ v3_struct_0(k12_normform(A))
      & v3_lattices(k12_normform(A))
      & v4_lattices(k12_normform(A))
      & v5_lattices(k12_normform(A))
      & v6_lattices(k12_normform(A))
      & v7_lattices(k12_normform(A))
      & v8_lattices(k12_normform(A))
      & v9_lattices(k12_normform(A))
      & v10_lattices(k12_normform(A))
      & v11_lattices(k12_normform(A))
      & v12_lattices(k12_normform(A))
      & v13_lattices(k12_normform(A)) ) )).

fof(d1_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ( r1_normform(A,B,C,D)
                  <=> ( r1_tarski(k2_domain_1(A,B,C),k2_domain_1(A,B,D))
                      & r1_tarski(k3_domain_1(A,B,C),k3_domain_1(A,B,D)) ) ) ) ) ) ) )).

fof(d2_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => k1_normform(A,B,C,D) = k1_domain_1(A,B,k1_finsub_1(A,k2_domain_1(A,B,C),k2_domain_1(A,B,D)),k1_finsub_1(B,k3_domain_1(A,B,C),k3_domain_1(A,B,D))) ) ) ) ) )).

fof(d3_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => k2_normform(A,B,C,D) = k1_domain_1(A,B,k3_finsub_1(A,k2_domain_1(A,B,C),k2_domain_1(A,B,D)),k3_finsub_1(B,k3_domain_1(A,B,C),k3_domain_1(A,B,D))) ) ) ) ) )).

fof(d4_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => k3_normform(A,B,C,D) = k1_domain_1(A,B,k2_finsub_1(A,k2_domain_1(A,B,C),k2_domain_1(A,B,D)),k2_finsub_1(B,k3_domain_1(A,B,C),k3_domain_1(A,B,D))) ) ) ) ) )).

fof(d5_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => k4_normform(A,B,C,D) = k1_domain_1(A,B,k4_finsub_1(A,k2_domain_1(A,B,C),k2_domain_1(A,B,D)),k4_finsub_1(B,k3_domain_1(A,B,C),k3_domain_1(A,B,D))) ) ) ) ) )).

fof(t1_normform,axiom,(
    $true )).

fof(t2_normform,axiom,(
    $true )).

fof(t3_normform,axiom,(
    $true )).

fof(t4_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ( ( r1_normform(A,B,C,D)
                      & r1_normform(A,B,D,C) )
                   => C = D ) ) ) ) ) )).

fof(t5_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,k2_zfmisc_1(A,B))
                     => ( ( r1_normform(A,B,C,D)
                          & r1_normform(A,B,D,E) )
                       => r1_normform(A,B,C,E) ) ) ) ) ) ) )).

fof(t6_normform,axiom,(
    $true )).

fof(t7_normform,axiom,(
    $true )).

fof(t8_normform,axiom,(
    $true )).

fof(t9_normform,axiom,(
    $true )).

fof(t10_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ( k2_domain_1(A,B,k1_normform(A,B,C,D)) = k1_finsub_1(A,k2_domain_1(A,B,C),k2_domain_1(A,B,D))
                    & k3_domain_1(A,B,k1_normform(A,B,C,D)) = k1_finsub_1(B,k3_domain_1(A,B,C),k3_domain_1(A,B,D)) ) ) ) ) ) )).

fof(t11_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ( k2_domain_1(A,B,k2_normform(A,B,C,D)) = k3_finsub_1(A,k2_domain_1(A,B,C),k2_domain_1(A,B,D))
                    & k3_domain_1(A,B,k2_normform(A,B,C,D)) = k3_finsub_1(B,k3_domain_1(A,B,C),k3_domain_1(A,B,D)) ) ) ) ) ) )).

fof(t12_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ( k2_domain_1(A,B,k3_normform(A,B,C,D)) = k2_finsub_1(A,k2_domain_1(A,B,C),k2_domain_1(A,B,D))
                    & k3_domain_1(A,B,k3_normform(A,B,C,D)) = k2_finsub_1(B,k3_domain_1(A,B,C),k3_domain_1(A,B,D)) ) ) ) ) ) )).

fof(t13_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ( k2_domain_1(A,B,k4_normform(A,B,C,D)) = k4_finsub_1(A,k2_domain_1(A,B,C),k2_domain_1(A,B,D))
                    & k3_domain_1(A,B,k4_normform(A,B,C,D)) = k4_finsub_1(B,k3_domain_1(A,B,C),k3_domain_1(A,B,D)) ) ) ) ) ) )).

fof(t14_normform,axiom,(
    $true )).

fof(t15_normform,axiom,(
    $true )).

fof(t16_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,k2_zfmisc_1(A,B))
                     => k1_normform(A,B,k1_normform(A,B,C,D),E) = k1_normform(A,B,C,k1_normform(A,B,D,E)) ) ) ) ) ) )).

fof(t17_normform,axiom,(
    $true )).

fof(t18_normform,axiom,(
    $true )).

fof(t19_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,k2_zfmisc_1(A,B))
                     => k2_normform(A,B,k2_normform(A,B,C,D),E) = k2_normform(A,B,C,k2_normform(A,B,D,E)) ) ) ) ) ) )).

fof(t20_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,k2_zfmisc_1(A,B))
                     => k2_normform(A,B,C,k1_normform(A,B,D,E)) = k1_normform(A,B,k2_normform(A,B,C,D),k2_normform(A,B,C,E)) ) ) ) ) ) )).

fof(t21_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => k1_normform(A,B,C,k2_normform(A,B,D,C)) = C ) ) ) ) )).

fof(t22_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => k2_normform(A,B,C,k1_normform(A,B,D,C)) = C ) ) ) ) )).

fof(t23_normform,axiom,(
    $true )).

fof(t24_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,k2_zfmisc_1(A,B))
                     => k1_normform(A,B,C,k2_normform(A,B,D,E)) = k2_normform(A,B,k1_normform(A,B,C,D),k1_normform(A,B,C,E)) ) ) ) ) ) )).

fof(t25_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,k2_zfmisc_1(A,B))
                     => ( ( r1_normform(A,B,C,D)
                          & r1_normform(A,B,E,D) )
                       => r1_normform(A,B,k1_normform(A,B,C,E),D) ) ) ) ) ) ) )).

fof(t26_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ( r1_normform(A,B,C,k1_normform(A,B,C,D))
                    & r1_normform(A,B,D,k1_normform(A,B,C,D)) ) ) ) ) ) )).

fof(t27_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ( C = k1_normform(A,B,C,D)
                   => r1_normform(A,B,D,C) ) ) ) ) ) )).

fof(t28_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,k2_zfmisc_1(A,B))
                     => ( r1_normform(A,B,C,D)
                       => ( r1_normform(A,B,k1_normform(A,B,E,C),k1_normform(A,B,E,D))
                          & r1_normform(A,B,k1_normform(A,B,C,E),k1_normform(A,B,D,E)) ) ) ) ) ) ) ) )).

fof(t29_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => k1_normform(A,B,k3_normform(A,B,C,D),D) = k1_normform(A,B,C,D) ) ) ) ) )).

fof(t30_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,k2_zfmisc_1(A,B))
                     => ( r1_normform(A,B,k3_normform(A,B,C,D),E)
                       => r1_normform(A,B,C,k1_normform(A,B,D,E)) ) ) ) ) ) ) )).

fof(t31_normform,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] :
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,k2_zfmisc_1(A,B))
                     => ( r1_normform(A,B,C,k1_normform(A,B,D,E))
                       => r1_normform(A,B,k3_normform(A,B,C,E),D) ) ) ) ) ) ) )).

fof(d6_normform,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
        & m2_relset_1(B,k2_zfmisc_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) )
     => ( B = k5_normform(A)
      <=> ! [C] :
            ( m1_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
           => ! [D] :
                ( m1_subset_1(D,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
               => k2_binop_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),B,C,D) = k1_normform(k5_finsub_1(A),k5_finsub_1(A),C,D) ) ) ) ) )).

fof(d7_normform,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C] :
          ( m1_subset_1(C,k5_finsub_1(A))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)))
                & m2_relset_1(D,A,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B))) )
             => k6_normform(A,B,C,D) = k7_setwiseo(A,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k5_normform(B),C,D) ) ) ) )).

fof(t32_normform,axiom,(
    $true )).

fof(t33_normform,axiom,(
    $true )).

fof(t34_normform,axiom,(
    $true )).

fof(t35_normform,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
            & m2_relset_1(C,B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) )
         => ! [D] :
              ( m1_subset_1(D,k5_finsub_1(B))
             => ! [E] :
                  ( m1_subset_1(E,B)
                 => ( r2_hidden(E,D)
                   => r1_normform(k5_finsub_1(A),k5_finsub_1(A),k8_funct_2(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),C,E),k6_normform(B,A,D,C)) ) ) ) ) ) )).

fof(t36_normform,axiom,(
    ! [A] : r3_binop_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k1_domain_1(k5_finsub_1(A),k5_finsub_1(A),k1_setwiseo(A),k1_setwiseo(A)),k5_normform(A)) )).

fof(t37_normform,axiom,(
    ! [A] : v1_setwiseo(k5_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) )).

fof(t38_normform,axiom,(
    ! [A] : k3_binop_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_normform(A)) = k1_domain_1(k5_finsub_1(A),k5_finsub_1(A),k1_setwiseo(A),k1_setwiseo(A)) )).

fof(t39_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
     => r1_normform(k5_finsub_1(A),k5_finsub_1(A),k3_binop_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_normform(A)),B) ) )).

fof(t40_normform,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
            & m2_relset_1(C,B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) )
         => ! [D] :
              ( m1_subset_1(D,k5_finsub_1(B))
             => ! [E] :
                  ( m1_subset_1(E,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
                 => ( ! [F] :
                        ( m1_subset_1(F,B)
                       => ( r2_hidden(F,D)
                         => r1_normform(k5_finsub_1(A),k5_finsub_1(A),k8_funct_2(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),C,F),E) ) )
                   => r1_normform(k5_finsub_1(A),k5_finsub_1(A),k6_normform(B,A,D,C),E) ) ) ) ) ) )).

fof(t41_normform,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(B))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
                & m2_relset_1(D,B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
                    & m2_relset_1(E,B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) )
                 => ( k7_relat_1(D,C) = k7_relat_1(E,C)
                   => k6_normform(B,A,C,D) = k6_normform(B,A,C,E) ) ) ) ) ) )).

fof(t42_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
     => ( r2_hidden(B,k7_normform(A))
      <=> r1_xboole_0(k2_domain_1(k5_finsub_1(A),k5_finsub_1(A),B),k3_domain_1(k5_finsub_1(A),k5_finsub_1(A),B)) ) ) )).

fof(t43_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
     => ! [C] :
          ( m1_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
         => ( ( r2_hidden(B,k7_normform(A))
              & r2_hidden(C,k7_normform(A)) )
           => ( r2_hidden(k1_normform(k5_finsub_1(A),k5_finsub_1(A),B,C),k7_normform(A))
            <=> k5_setwiseo(A,k3_finsub_1(k5_finsub_1(A),k2_domain_1(k5_finsub_1(A),k5_finsub_1(A),B),k3_domain_1(k5_finsub_1(A),k5_finsub_1(A),C)),k3_finsub_1(k5_finsub_1(A),k2_domain_1(k5_finsub_1(A),k5_finsub_1(A),C),k3_domain_1(k5_finsub_1(A),k5_finsub_1(A),B))) = k1_xboole_0 ) ) ) ) )).

fof(t44_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => r1_xboole_0(k2_domain_1(k5_finsub_1(A),k5_finsub_1(A),B),k3_domain_1(k5_finsub_1(A),k5_finsub_1(A),B)) ) )).

fof(t45_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
     => ! [C] :
          ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
         => ( r1_normform(k5_finsub_1(A),k5_finsub_1(A),B,C)
           => m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) ) ) ) )).

fof(t46_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C] :
          ~ ( r2_hidden(C,k2_domain_1(k5_finsub_1(A),k5_finsub_1(A),B))
            & r2_hidden(C,k3_domain_1(k5_finsub_1(A),k5_finsub_1(A),B)) ) ) )).

fof(t47_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C] :
          ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
         => ~ ( ~ r2_hidden(k1_normform(k5_finsub_1(A),k5_finsub_1(A),B,C),k7_normform(A))
              & ! [D] :
                  ( m1_subset_1(D,A)
                 => ( ~ ( r2_hidden(D,k2_domain_1(k5_finsub_1(A),k5_finsub_1(A),B))
                        & r2_hidden(D,k3_domain_1(k5_finsub_1(A),k5_finsub_1(A),C)) )
                    & ~ ( r2_hidden(D,k2_domain_1(k5_finsub_1(A),k5_finsub_1(A),C))
                        & r2_hidden(D,k3_domain_1(k5_finsub_1(A),k5_finsub_1(A),B)) ) ) ) ) ) ) )).

fof(t48_normform,axiom,(
    $true )).

fof(t49_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
     => ( r1_xboole_0(k2_domain_1(k5_finsub_1(A),k5_finsub_1(A),B),k3_domain_1(k5_finsub_1(A),k5_finsub_1(A),B))
       => m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) ) ) )).

fof(t50_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C,D] :
          ( ( r1_tarski(C,k2_domain_1(k5_finsub_1(A),k5_finsub_1(A),B))
            & r1_tarski(D,k3_domain_1(k5_finsub_1(A),k5_finsub_1(A),B)) )
         => m2_subset_1(k4_tarski(C,D),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) ) ) )).

fof(t51_normform,axiom,(
    ! [A] : r2_hidden(k1_xboole_0,k8_normform(A)) )).

fof(t52_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C] :
          ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
         => ! [D] :
              ( m1_subset_1(D,k5_finsub_1(k7_normform(A)))
             => ( ( r2_hidden(D,k8_normform(A))
                  & r2_hidden(B,D)
                  & r2_hidden(C,D)
                  & r1_normform(k5_finsub_1(A),k5_finsub_1(A),B,C) )
               => B = C ) ) ) ) )).

fof(t53_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ( ! [C] :
            ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
           => ! [D] :
                ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
               => ( ( r2_hidden(C,B)
                    & r2_hidden(D,B)
                    & r1_normform(k5_finsub_1(A),k5_finsub_1(A),C,D) )
                 => C = D ) ) )
       => r2_hidden(B,k8_normform(A)) ) ) )).

fof(t54_normform,axiom,(
    $true )).

fof(t55_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => ! [D] :
              ( m1_subset_1(D,k5_finsub_1(k7_normform(A)))
             => ~ ( r2_hidden(B,k10_normform(A,C,D))
                  & ! [E] :
                      ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
                     => ! [F] :
                          ( m2_subset_1(F,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
                         => ~ ( r2_hidden(E,C)
                              & r2_hidden(F,D)
                              & B = k1_normform(k5_finsub_1(A),k5_finsub_1(A),E,F) ) ) ) ) ) ) ) )).

fof(t56_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C] :
          ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
         => ! [D] :
              ( m1_subset_1(D,k5_finsub_1(k7_normform(A)))
             => ! [E] :
                  ( m1_subset_1(E,k5_finsub_1(k7_normform(A)))
                 => ( ( r2_hidden(B,D)
                      & r2_hidden(C,E)
                      & r2_hidden(k1_normform(k5_finsub_1(A),k5_finsub_1(A),B,C),k7_normform(A)) )
                   => r2_hidden(k1_normform(k5_finsub_1(A),k5_finsub_1(A),B,C),k10_normform(A,D,E)) ) ) ) ) ) )).

fof(t57_normform,axiom,(
    $true )).

fof(t58_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C] :
          ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
         => ! [D] :
              ( m1_subset_1(D,k5_finsub_1(k7_normform(A)))
             => ( r2_hidden(B,k9_normform(A,D))
               => ( r2_hidden(B,D)
                  & ( ( r2_hidden(C,D)
                      & r1_normform(k5_finsub_1(A),k5_finsub_1(A),C,B) )
                   => C = B ) ) ) ) ) ) )).

fof(t59_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => ( r2_hidden(B,k9_normform(A,C))
           => r2_hidden(B,C) ) ) ) )).

fof(t60_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C] :
          ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
         => ! [D] :
              ( m1_subset_1(D,k5_finsub_1(k7_normform(A)))
             => ( ( r2_hidden(B,k9_normform(A,D))
                  & r2_hidden(C,D)
                  & r1_normform(k5_finsub_1(A),k5_finsub_1(A),C,B) )
               => C = B ) ) ) ) )).

fof(t61_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => ( ( r2_hidden(B,C)
              & ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
                 => ( ( r2_hidden(D,C)
                      & r1_normform(k5_finsub_1(A),k5_finsub_1(A),D,B) )
                   => D = B ) ) )
           => r2_hidden(B,k9_normform(A,C)) ) ) ) )).

fof(t62_normform,axiom,(
    $true )).

fof(t63_normform,axiom,(
    $true )).

fof(t64_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => r1_tarski(k9_normform(A,B),B) ) )).

fof(t65_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => ~ ( r2_hidden(B,C)
              & ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
                 => ~ ( r1_normform(k5_finsub_1(A),k5_finsub_1(A),D,B)
                      & r2_hidden(D,k9_normform(A,C)) ) ) ) ) ) )).

fof(t66_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A))
     => k9_normform(A,B) = B ) )).

fof(t67_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => r1_tarski(k9_normform(A,k5_setwiseo(k7_normform(A),B,C)),k5_setwiseo(k7_normform(A),k9_normform(A,B),C)) ) ) )).

fof(t68_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => k9_normform(A,k5_setwiseo(k7_normform(A),k9_normform(A,B),C)) = k9_normform(A,k5_setwiseo(k7_normform(A),B,C)) ) ) )).

fof(t69_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => k9_normform(A,k5_setwiseo(k7_normform(A),B,k9_normform(A,C))) = k9_normform(A,k5_setwiseo(k7_normform(A),B,C)) ) ) )).

fof(t70_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => ! [D] :
              ( m1_subset_1(D,k5_finsub_1(k7_normform(A)))
             => ( r1_tarski(B,C)
               => r1_tarski(k10_normform(A,B,D),k10_normform(A,C,D)) ) ) ) ) )).

fof(t71_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => r1_tarski(k9_normform(A,k10_normform(A,B,C)),k10_normform(A,k9_normform(A,B),C)) ) ) )).

fof(t72_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => k10_normform(A,B,C) = k10_normform(A,C,B) ) ) )).

fof(t73_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => ! [D] :
              ( m1_subset_1(D,k5_finsub_1(k7_normform(A)))
             => ( r1_tarski(B,C)
               => r1_tarski(k10_normform(A,D,B),k10_normform(A,D,C)) ) ) ) ) )).

fof(t74_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => k9_normform(A,k10_normform(A,k9_normform(A,B),C)) = k9_normform(A,k10_normform(A,B,C)) ) ) )).

fof(t75_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => k9_normform(A,k10_normform(A,B,k9_normform(A,C))) = k9_normform(A,k10_normform(A,B,C)) ) ) )).

fof(t76_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A))
     => ! [C] :
          ( m2_subset_1(C,k5_finsub_1(k7_normform(A)),k8_normform(A))
         => ! [D] :
              ( m2_subset_1(D,k5_finsub_1(k7_normform(A)),k8_normform(A))
             => k10_normform(A,B,k10_normform(A,C,D)) = k10_normform(A,k10_normform(A,B,C),D) ) ) ) )).

fof(t77_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A))
     => ! [C] :
          ( m2_subset_1(C,k5_finsub_1(k7_normform(A)),k8_normform(A))
         => ! [D] :
              ( m2_subset_1(D,k5_finsub_1(k7_normform(A)),k8_normform(A))
             => k10_normform(A,B,k5_setwiseo(k7_normform(A),C,D)) = k5_setwiseo(k7_normform(A),k10_normform(A,B,C),k10_normform(A,B,D)) ) ) ) )).

fof(t78_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => r1_tarski(B,k10_normform(A,B,B)) ) )).

fof(t79_normform,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A))
     => k9_normform(A,k10_normform(A,B,B)) = k9_normform(A,B) ) )).

fof(d12_normform,axiom,(
    $true )).

fof(d13_normform,axiom,(
    $true )).

fof(d14_normform,axiom,(
    ! [A,B] :
      ( ( v3_lattices(B)
        & l3_lattices(B) )
     => ( B = k12_normform(A)
      <=> ( u1_struct_0(B) = k8_normform(A)
          & ! [C] :
              ( m2_subset_1(C,k5_finsub_1(k7_normform(A)),k8_normform(A))
             => ! [D] :
                  ( m2_subset_1(D,k5_finsub_1(k7_normform(A)),k8_normform(A))
                 => ( k1_binop_1(u2_lattices(B),C,D) = k9_normform(A,k5_setwiseo(k7_normform(A),C,D))
                    & k1_binop_1(u1_lattices(B),C,D) = k9_normform(A,k10_normform(A,C,D)) ) ) ) ) ) ) )).

fof(t80_normform,axiom,(
    $true )).

fof(t81_normform,axiom,(
    $true )).

fof(t82_normform,axiom,(
    $true )).

fof(t83_normform,axiom,(
    $true )).

fof(t84_normform,axiom,(
    $true )).

fof(t85_normform,axiom,(
    ! [A] : m1_subset_1(k1_xboole_0,u1_struct_0(k12_normform(A))) )).

fof(t86_normform,axiom,(
    ! [A] : k5_lattices(k12_normform(A)) = k1_xboole_0 )).

fof(reflexivity_r1_normform,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => r1_normform(A,B,C,C) ) )).

fof(dt_k1_normform,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => m1_subset_1(k1_normform(A,B,C,D),k2_zfmisc_1(A,B)) ) )).

fof(commutativity_k1_normform,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => k1_normform(A,B,C,D) = k1_normform(A,B,D,C) ) )).

fof(idempotence_k1_normform,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => k1_normform(A,B,C,C) = C ) )).

fof(dt_k2_normform,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => m1_subset_1(k2_normform(A,B,C,D),k2_zfmisc_1(A,B)) ) )).

fof(commutativity_k2_normform,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => k2_normform(A,B,C,D) = k2_normform(A,B,D,C) ) )).

fof(idempotence_k2_normform,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => k2_normform(A,B,C,C) = C ) )).

fof(dt_k3_normform,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => m1_subset_1(k3_normform(A,B,C,D),k2_zfmisc_1(A,B)) ) )).

fof(dt_k4_normform,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => m1_subset_1(k4_normform(A,B,C,D),k2_zfmisc_1(A,B)) ) )).

fof(commutativity_k4_normform,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => k4_normform(A,B,C,D) = k4_normform(A,B,D,C) ) )).

fof(dt_k5_normform,axiom,(
    ! [A] :
      ( v1_funct_1(k5_normform(A))
      & v1_funct_2(k5_normform(A),k2_zfmisc_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
      & m2_relset_1(k5_normform(A),k2_zfmisc_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) ) )).

fof(dt_k6_normform,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,k5_finsub_1(A))
        & v1_funct_1(D)
        & v1_funct_2(D,A,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)))
        & m1_relset_1(D,A,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B))) )
     => m1_subset_1(k6_normform(A,B,C,D),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B))) ) )).

fof(dt_k7_normform,axiom,(
    ! [A] : m1_subset_1(k7_normform(A),k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))) )).

fof(dt_k8_normform,axiom,(
    ! [A] : m1_subset_1(k8_normform(A),k1_zfmisc_1(k5_finsub_1(k7_normform(A)))) )).

fof(dt_k9_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => m2_subset_1(k9_normform(A,B),k5_finsub_1(k7_normform(A)),k8_normform(A)) ) )).

fof(dt_k10_normform,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
        & m1_subset_1(C,k5_finsub_1(k7_normform(A))) )
     => m1_subset_1(k10_normform(A,B,C),k5_finsub_1(k7_normform(A))) ) )).

fof(dt_k11_normform,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A))
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & m1_subset_1(D,B)
        & m1_subset_1(E,B) )
     => m2_subset_1(k11_normform(A,B,C,D,E),A,B) ) )).

fof(redefinition_k11_normform,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A))
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & m1_subset_1(D,B)
        & m1_subset_1(E,B) )
     => k11_normform(A,B,C,D,E) = k1_binop_1(C,D,E) ) )).

fof(dt_k12_normform,axiom,(
    ! [A] :
      ( v3_lattices(k12_normform(A))
      & l3_lattices(k12_normform(A)) ) )).

fof(d8_normform,axiom,(
    ! [A] : k7_normform(A) = a_1_0_normform(A) )).

fof(d9_normform,axiom,(
    ! [A] : k8_normform(A) = a_1_1_normform(A) )).

fof(d10_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => k9_normform(A,B) = a_2_0_normform(A,B) ) )).

fof(d11_normform,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => k10_normform(A,B,C) = k3_xboole_0(k7_normform(A),a_3_0_normform(A,B,C)) ) ) )).

fof(fraenkel_a_1_0_normform,axiom,(
    ! [A,B] :
      ( r2_hidden(A,a_1_0_normform(B))
    <=> ? [C] :
          ( m1_subset_1(C,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)))
          & A = C
          & r1_xboole_0(k2_domain_1(k5_finsub_1(B),k5_finsub_1(B),C),k3_domain_1(k5_finsub_1(B),k5_finsub_1(B),C)) ) ) )).

fof(fraenkel_a_1_1_normform,axiom,(
    ! [A,B] :
      ( r2_hidden(A,a_1_1_normform(B))
    <=> ? [C] :
          ( m1_subset_1(C,k5_finsub_1(k7_normform(B)))
          & A = C
          & ! [D] :
              ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
             => ! [E] :
                  ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
                 => ( ( r2_hidden(D,C)
                      & r2_hidden(E,C)
                      & r1_normform(k5_finsub_1(B),k5_finsub_1(B),D,E) )
                   => D = E ) ) ) ) ) )).

fof(fraenkel_a_2_0_normform,axiom,(
    ! [A,B,C] :
      ( m1_subset_1(C,k5_finsub_1(k7_normform(B)))
     => ( r2_hidden(A,a_2_0_normform(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
            & A = D
            & ! [E] :
                ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
               => ( ( r2_hidden(E,C)
                    & r1_normform(k5_finsub_1(B),k5_finsub_1(B),E,D) )
                <=> E = D ) ) ) ) ) )).

fof(fraenkel_a_3_0_normform,axiom,(
    ! [A,B,C,D] :
      ( ( m1_subset_1(C,k5_finsub_1(k7_normform(B)))
        & m1_subset_1(D,k5_finsub_1(k7_normform(B))) )
     => ( r2_hidden(A,a_3_0_normform(B,C,D))
      <=> ? [E,F] :
            ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
            & m2_subset_1(F,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
            & A = k1_normform(k5_finsub_1(B),k5_finsub_1(B),E,F)
            & r2_hidden(E,C)
            & r2_hidden(F,D) ) ) ) )).
%------------------------------------------------------------------------------