SET007 Axioms: SET007+234.ax


%------------------------------------------------------------------------------
% File     : SET007+234 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Lattice of Real Numbers. The Lattice of Real Functions
% 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    : real_lat [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   68 (  23 unit)
%            Number of atoms       :  253 (  70 equality)
%            Maximal formula depth :   14 (   5 average)
%            Number of connectives :  219 (  34 ~  ;   0  |;  75  &)
%                                         (   4 <=>; 106 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   21 (   1 propositional; 0-4 arity)
%            Number of functors    :   18 (   4 constant; 0-6 arity)
%            Number of variables   :  107 (   0 singleton; 107 !;   0 ?)
%            Maximal term depth    :    4 (   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(cc1_real_lat,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_real_lat))
     => v1_xreal_0(A) ) )).

fof(fc1_real_lat,axiom,
    ( ~ v3_struct_0(k3_real_lat)
    & v3_lattices(k3_real_lat) )).

fof(fc2_real_lat,axiom,
    ( ~ v3_struct_0(k3_real_lat)
    & v3_lattices(k3_real_lat)
    & v4_lattices(k3_real_lat)
    & v5_lattices(k3_real_lat)
    & v6_lattices(k3_real_lat)
    & v7_lattices(k3_real_lat)
    & v8_lattices(k3_real_lat)
    & v9_lattices(k3_real_lat)
    & v10_lattices(k3_real_lat) )).

fof(fc3_real_lat,axiom,
    ( ~ v3_struct_0(k3_real_lat)
    & v3_lattices(k3_real_lat)
    & v4_lattices(k3_real_lat)
    & v5_lattices(k3_real_lat)
    & v6_lattices(k3_real_lat)
    & v7_lattices(k3_real_lat)
    & v8_lattices(k3_real_lat)
    & v9_lattices(k3_real_lat)
    & v10_lattices(k3_real_lat)
    & v11_lattices(k3_real_lat)
    & v12_lattices(k3_real_lat) )).

fof(d1_real_lat,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
     => ( A = k1_real_lat
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k3_square_1(B,C) ) ) ) ) )).

fof(d2_real_lat,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
     => ( A = k2_real_lat
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k4_square_1(B,C) ) ) ) ) )).

fof(d3_real_lat,axiom,(
    $true )).

fof(d4_real_lat,axiom,(
    k3_real_lat = g3_lattices(k1_numbers,k2_real_lat,k1_real_lat) )).

fof(t1_real_lat,axiom,(
    $true )).

fof(t2_real_lat,axiom,(
    $true )).

fof(t3_real_lat,axiom,(
    $true )).

fof(t4_real_lat,axiom,(
    $true )).

fof(t5_real_lat,axiom,(
    $true )).

fof(t6_real_lat,axiom,(
    $true )).

fof(t7_real_lat,axiom,(
    $true )).

fof(t8_real_lat,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_real_lat))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_real_lat))
         => k1_binop_1(k2_real_lat,A,B) = k1_binop_1(k2_real_lat,B,A) ) ) )).

fof(t9_real_lat,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_real_lat))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_real_lat))
         => k1_binop_1(k1_real_lat,A,B) = k1_binop_1(k1_real_lat,B,A) ) ) )).

fof(t10_real_lat,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_real_lat))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_real_lat))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k3_real_lat))
             => ( k1_binop_1(k2_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k2_real_lat,B,C),A)
                & k1_binop_1(k2_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k2_real_lat,A,B),C)
                & k1_binop_1(k2_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k2_real_lat,B,A),C)
                & k1_binop_1(k2_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k2_real_lat,C,A),B)
                & k1_binop_1(k2_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k2_real_lat,C,B),A)
                & k1_binop_1(k2_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k2_real_lat,A,C),B) ) ) ) ) )).

fof(t11_real_lat,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_real_lat))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_real_lat))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k3_real_lat))
             => ( k1_binop_1(k1_real_lat,A,k1_binop_1(k1_real_lat,B,C)) = k1_binop_1(k1_real_lat,k1_binop_1(k1_real_lat,B,C),A)
                & k1_binop_1(k1_real_lat,A,k1_binop_1(k1_real_lat,B,C)) = k1_binop_1(k1_real_lat,k1_binop_1(k1_real_lat,A,B),C)
                & k1_binop_1(k1_real_lat,A,k1_binop_1(k1_real_lat,B,C)) = k1_binop_1(k1_real_lat,k1_binop_1(k1_real_lat,B,A),C)
                & k1_binop_1(k1_real_lat,A,k1_binop_1(k1_real_lat,B,C)) = k1_binop_1(k1_real_lat,k1_binop_1(k1_real_lat,C,A),B)
                & k1_binop_1(k1_real_lat,A,k1_binop_1(k1_real_lat,B,C)) = k1_binop_1(k1_real_lat,k1_binop_1(k1_real_lat,C,B),A)
                & k1_binop_1(k1_real_lat,A,k1_binop_1(k1_real_lat,B,C)) = k1_binop_1(k1_real_lat,k1_binop_1(k1_real_lat,A,C),B) ) ) ) ) )).

fof(t12_real_lat,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_real_lat))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_real_lat))
         => ( k1_binop_1(k2_real_lat,k1_binop_1(k1_real_lat,A,B),B) = B
            & k1_binop_1(k2_real_lat,B,k1_binop_1(k1_real_lat,A,B)) = B
            & k1_binop_1(k2_real_lat,B,k1_binop_1(k1_real_lat,B,A)) = B
            & k1_binop_1(k2_real_lat,k1_binop_1(k1_real_lat,B,A),B) = B ) ) ) )).

fof(t13_real_lat,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_real_lat))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_real_lat))
         => ( k1_binop_1(k1_real_lat,A,k1_binop_1(k2_real_lat,A,B)) = A
            & k1_binop_1(k1_real_lat,k1_binop_1(k2_real_lat,B,A),A) = A
            & k1_binop_1(k1_real_lat,A,k1_binop_1(k2_real_lat,B,A)) = A
            & k1_binop_1(k1_real_lat,k1_binop_1(k2_real_lat,A,B),A) = A ) ) ) )).

fof(t14_real_lat,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k3_real_lat))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k3_real_lat))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k3_real_lat))
             => k1_binop_1(k1_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k1_real_lat,A,B),k1_binop_1(k1_real_lat,A,C)) ) ) ) )).

fof(d5_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers))
            & m2_relset_1(B,k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) )
         => ( B = k4_real_lat(A)
          <=> ! [C] :
                ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
               => ! [D] :
                    ( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                   => k1_funcsdom(A,k1_numbers,B,C,D) = k4_funcsdom(k1_numbers,A,k2_real_lat,C,D) ) ) ) ) ) )).

fof(d6_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers))
            & m2_relset_1(B,k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) )
         => ( B = k5_real_lat(A)
          <=> ! [C] :
                ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
               => ! [D] :
                    ( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                   => k1_funcsdom(A,k1_numbers,B,C,D) = k4_funcsdom(k1_numbers,A,k1_real_lat,C,D) ) ) ) ) ) )).

fof(t15_real_lat,axiom,(
    $true )).

fof(t16_real_lat,axiom,(
    $true )).

fof(t17_real_lat,axiom,(
    $true )).

fof(t18_real_lat,axiom,(
    $true )).

fof(t19_real_lat,axiom,(
    $true )).

fof(t20_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,C) = k1_funcsdom(A,k1_numbers,k4_real_lat(A),C,B) ) ) ) )).

fof(t21_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,C) = k1_funcsdom(A,k1_numbers,k5_real_lat(A),C,B) ) ) ) )).

fof(t22_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => ! [D] :
                  ( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                 => k1_funcsdom(A,k1_numbers,k4_real_lat(A),k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,C),D) = k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,k1_funcsdom(A,k1_numbers,k4_real_lat(A),C,D)) ) ) ) ) )).

fof(t23_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => ! [D] :
                  ( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                 => k1_funcsdom(A,k1_numbers,k5_real_lat(A),k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,C),D) = k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,k1_funcsdom(A,k1_numbers,k5_real_lat(A),C,D)) ) ) ) ) )).

fof(t24_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,C)) = B ) ) ) )).

fof(t25_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => k1_funcsdom(A,k1_numbers,k4_real_lat(A),k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,C),B) = B ) ) ) )).

fof(t26_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => k1_funcsdom(A,k1_numbers,k4_real_lat(A),k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,C),C) = C ) ) ) )).

fof(t27_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,k1_funcsdom(A,k1_numbers,k5_real_lat(A),C,B)) = B ) ) ) )).

fof(t28_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,C)) = B ) ) ) )).

fof(t29_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,k1_funcsdom(A,k1_numbers,k4_real_lat(A),C,B)) = B ) ) ) )).

fof(t30_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => k1_funcsdom(A,k1_numbers,k5_real_lat(A),k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,C),C) = C ) ) ) )).

fof(t31_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => k1_funcsdom(A,k1_numbers,k5_real_lat(A),k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,C),B) = B ) ) ) )).

fof(t32_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
         => ! [C] :
              ( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
             => ! [D] :
                  ( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
                 => k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,k1_funcsdom(A,k1_numbers,k4_real_lat(A),C,D)) = k1_funcsdom(A,k1_numbers,k4_real_lat(A),k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,C),k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,D)) ) ) ) ) )).

fof(d7_real_lat,axiom,(
    $true )).

fof(d8_real_lat,axiom,(
    $true )).

fof(d9_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(g3_lattices(k1_fraenkel(A,k1_numbers),k4_real_lat(A),k5_real_lat(A))))
         => k6_real_lat(A,B) = B ) ) )).

fof(d10_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k7_real_lat(A) = g3_lattices(k1_fraenkel(A,k1_numbers),k4_real_lat(A),k5_real_lat(A)) ) )).

fof(t33_real_lat,axiom,(
    $true )).

fof(t34_real_lat,axiom,(
    $true )).

fof(t35_real_lat,axiom,(
    $true )).

fof(t36_real_lat,axiom,(
    $true )).

fof(t37_real_lat,axiom,(
    $true )).

fof(t38_real_lat,axiom,(
    $true )).

fof(t39_real_lat,axiom,(
    $true )).

fof(t40_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
             => k1_binop_1(k4_real_lat(A),B,C) = k1_binop_1(k4_real_lat(A),C,B) ) ) ) )).

fof(t41_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
             => k1_binop_1(k5_real_lat(A),B,C) = k1_binop_1(k5_real_lat(A),C,B) ) ) ) )).

fof(t42_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k7_real_lat(A)))
                 => ( k1_binop_1(k4_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k4_real_lat(A),C,D),B)
                    & k1_binop_1(k4_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k4_real_lat(A),B,C),D)
                    & k1_binop_1(k4_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k4_real_lat(A),C,B),D)
                    & k1_binop_1(k4_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k4_real_lat(A),D,B),C)
                    & k1_binop_1(k4_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k4_real_lat(A),D,C),B)
                    & k1_binop_1(k4_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k4_real_lat(A),B,D),C) ) ) ) ) ) )).

fof(t43_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k7_real_lat(A)))
                 => ( k1_binop_1(k5_real_lat(A),B,k1_binop_1(k5_real_lat(A),C,D)) = k1_binop_1(k5_real_lat(A),k1_binop_1(k5_real_lat(A),C,D),B)
                    & k1_binop_1(k5_real_lat(A),B,k1_binop_1(k5_real_lat(A),C,D)) = k1_binop_1(k5_real_lat(A),k1_binop_1(k5_real_lat(A),B,C),D)
                    & k1_binop_1(k5_real_lat(A),B,k1_binop_1(k5_real_lat(A),C,D)) = k1_binop_1(k5_real_lat(A),k1_binop_1(k5_real_lat(A),C,B),D)
                    & k1_binop_1(k5_real_lat(A),B,k1_binop_1(k5_real_lat(A),C,D)) = k1_binop_1(k5_real_lat(A),k1_binop_1(k5_real_lat(A),D,B),C)
                    & k1_binop_1(k5_real_lat(A),B,k1_binop_1(k5_real_lat(A),C,D)) = k1_binop_1(k5_real_lat(A),k1_binop_1(k5_real_lat(A),D,C),B)
                    & k1_binop_1(k5_real_lat(A),B,k1_binop_1(k5_real_lat(A),C,D)) = k1_binop_1(k5_real_lat(A),k1_binop_1(k5_real_lat(A),B,D),C) ) ) ) ) ) )).

fof(t44_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
             => ( k1_binop_1(k4_real_lat(A),k1_binop_1(k5_real_lat(A),B,C),C) = C
                & k1_binop_1(k4_real_lat(A),C,k1_binop_1(k5_real_lat(A),B,C)) = C
                & k1_binop_1(k4_real_lat(A),C,k1_binop_1(k5_real_lat(A),C,B)) = C
                & k1_binop_1(k4_real_lat(A),k1_binop_1(k5_real_lat(A),C,B),C) = C ) ) ) ) )).

fof(t45_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
             => ( k1_binop_1(k5_real_lat(A),B,k1_binop_1(k4_real_lat(A),B,C)) = B
                & k1_binop_1(k5_real_lat(A),k1_binop_1(k4_real_lat(A),C,B),B) = B
                & k1_binop_1(k5_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,B)) = B
                & k1_binop_1(k5_real_lat(A),k1_binop_1(k4_real_lat(A),B,C),B) = B ) ) ) ) )).

fof(t46_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k7_real_lat(A)))
                 => k1_binop_1(k5_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k5_real_lat(A),B,C),k1_binop_1(k5_real_lat(A),B,D)) ) ) ) ) )).

fof(t47_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ~ v3_struct_0(k7_real_lat(A))
        & v10_lattices(k7_real_lat(A))
        & v11_lattices(k7_real_lat(A))
        & l3_lattices(k7_real_lat(A)) ) ) )).

fof(dt_k1_real_lat,axiom,
    ( v1_funct_1(k1_real_lat)
    & v1_funct_2(k1_real_lat,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
    & m2_relset_1(k1_real_lat,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )).

fof(dt_k2_real_lat,axiom,
    ( v1_funct_1(k2_real_lat)
    & v1_funct_2(k2_real_lat,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
    & m2_relset_1(k2_real_lat,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )).

fof(dt_k3_real_lat,axiom,
    ( v3_lattices(k3_real_lat)
    & l3_lattices(k3_real_lat) )).

fof(dt_k4_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v1_funct_1(k4_real_lat(A))
        & v1_funct_2(k4_real_lat(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers))
        & m2_relset_1(k4_real_lat(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) ) ) )).

fof(dt_k5_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v1_funct_1(k5_real_lat(A))
        & v1_funct_2(k5_real_lat(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers))
        & m2_relset_1(k5_real_lat(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) ) ) )).

fof(dt_k6_real_lat,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,u1_struct_0(g3_lattices(k1_fraenkel(A,k1_numbers),k4_real_lat(A),k5_real_lat(A)))) )
     => m2_fraenkel(k6_real_lat(A,B),A,k1_numbers,k1_fraenkel(A,k1_numbers)) ) )).

fof(dt_k7_real_lat,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ~ v3_struct_0(k7_real_lat(A))
        & v3_lattices(k7_real_lat(A))
        & v10_lattices(k7_real_lat(A))
        & l3_lattices(k7_real_lat(A)) ) ) )).
%------------------------------------------------------------------------------