SET007 Axioms: SET007+392.ax


%------------------------------------------------------------------------------
% File     : SET007+392 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Boolean Properties of Lattices
% 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    : boolealg [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  102 (  10 unit)
%            Number of atoms       :  737 (   7 equality)
%            Maximal formula depth :   16 (   8 average)
%            Number of connectives :  746 ( 111 ~  ;   6  |; 303  &)
%                                         (  12 <=>; 314 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   14 (   1 propositional; 0-3 arity)
%            Number of functors    :    8 (   0 constant; 1-3 arity)
%            Number of variables   :  305 (   0 singleton; 305 !;   0 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(d1_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_boolealg(A,B,C) = k4_lattices(A,B,k7_lattices(A,C)) ) ) ) )).

fof(d2_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_boolealg(A,B,C) = k3_lattices(A,k1_boolealg(A,B,C),k1_boolealg(A,C,B)) ) ) ) )).

fof(d3_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_boolealg(A,B,C)
              <=> ( r3_lattices(A,B,C)
                  & r3_lattices(A,C,B) ) ) ) ) ) )).

fof(d4_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_boolealg(A,B,C)
              <=> k4_lattices(A,B,C) != k5_lattices(A) ) ) ) ) )).

fof(t1_boolealg,axiom,(
    $true )).

fof(t2_boolealg,axiom,(
    $true )).

fof(t3_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_lattices(A,k3_lattices(A,B,C),D)
                   => ( r3_lattices(A,B,D)
                      & r3_lattices(A,C,D) ) ) ) ) ) ) )).

fof(t4_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r3_lattices(A,k4_lattices(A,B,C),k3_lattices(A,B,D)) ) ) ) ) )).

fof(t5_boolealg,axiom,(
    $true )).

fof(t6_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_lattices(A,B,C)
                   => r3_lattices(A,k1_boolealg(A,B,D),C) ) ) ) ) ) )).

fof(t7_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_lattices(A,B,C)
                   => r3_lattices(A,k1_boolealg(A,B,D),k1_boolealg(A,C,D)) ) ) ) ) ) )).

fof(t8_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r3_lattices(A,k1_boolealg(A,B,C),B) ) ) ) )).

fof(t9_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r3_lattices(A,k1_boolealg(A,B,C),k2_boolealg(A,B,C)) ) ) ) )).

fof(t10_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r3_lattices(A,k1_boolealg(A,B,C),D)
                      & r3_lattices(A,k1_boolealg(A,C,B),D) )
                   => r3_lattices(A,k2_boolealg(A,B,C),D) ) ) ) ) ) )).

fof(t11_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_boolealg(A,B,k3_lattices(A,C,D))
                  <=> ( r3_lattices(A,C,B)
                      & r3_lattices(A,D,B)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r3_lattices(A,C,E)
                              & r3_lattices(A,D,E) )
                           => r3_lattices(A,B,E) ) ) ) ) ) ) ) ) )).

fof(t12_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_boolealg(A,B,k4_lattices(A,C,D))
                  <=> ( r3_lattices(A,B,C)
                      & r3_lattices(A,B,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r3_lattices(A,E,C)
                              & r3_lattices(A,E,D) )
                           => r3_lattices(A,E,B) ) ) ) ) ) ) ) ) )).

fof(t13_boolealg,axiom,(
    $true )).

fof(t14_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_boolealg(A,k4_lattices(A,B,k1_boolealg(A,C,D)),k1_boolealg(A,k4_lattices(A,B,C),D)) ) ) ) ) )).

fof(t15_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_boolealg(A,B,C)
               => r2_boolealg(A,C,B) ) ) ) ) )).

fof(t16_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r2_boolealg(A,B,B)
          <=> B != k5_lattices(A) ) ) ) )).

fof(t17_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k2_boolealg(A,B,C),k2_boolealg(A,C,B)) ) ) ) )).

fof(t18_boolealg,axiom,(
    $true )).

fof(t19_boolealg,axiom,(
    $true )).

fof(t20_boolealg,axiom,(
    $true )).

fof(t21_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v12_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( ~ r2_boolealg(A,B,C)
                  & r2_boolealg(A,C,B) ) ) ) ) )).

fof(t22_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v11_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_boolealg(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,B,D)),B)
                   => r3_lattices(A,B,k3_lattices(A,C,D)) ) ) ) ) ) )).

fof(t23_boolealg,axiom,(
    $true )).

fof(t24_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v11_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_boolealg(A,k1_boolealg(A,k3_lattices(A,B,C),D),k3_lattices(A,k1_boolealg(A,B,D),k1_boolealg(A,C,D))) ) ) ) ) )).

fof(t25_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r3_lattices(A,B,k5_lattices(A))
           => r1_boolealg(A,B,k5_lattices(A)) ) ) ) )).

fof(t26_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r3_lattices(A,B,C)
                      & r3_lattices(A,B,D)
                      & r1_boolealg(A,k4_lattices(A,C,D),k5_lattices(A)) )
                   => r1_boolealg(A,B,k5_lattices(A)) ) ) ) ) ) )).

fof(t27_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_boolealg(A,k3_lattices(A,B,C),k5_lattices(A))
              <=> ( r1_boolealg(A,B,k5_lattices(A))
                  & r1_boolealg(A,C,k5_lattices(A)) ) ) ) ) ) )).

fof(t28_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r3_lattices(A,B,C)
                      & r1_boolealg(A,k4_lattices(A,C,D),k5_lattices(A)) )
                   => r1_boolealg(A,k4_lattices(A,B,D),k5_lattices(A)) ) ) ) ) ) )).

fof(t29_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_boolealg(A,k1_boolealg(A,k5_lattices(A),B),k5_lattices(A)) ) ) )).

fof(t30_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r3_boolealg(A,B,C)
                      & r3_lattices(A,C,D) )
                   => r3_boolealg(A,B,D) ) ) ) ) ) )).

fof(t31_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_boolealg(A,B,k4_lattices(A,C,D))
                   => ( r3_boolealg(A,B,C)
                      & r3_boolealg(A,B,D) ) ) ) ) ) ) )).

fof(t32_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_boolealg(A,B,k1_boolealg(A,C,D))
                   => r3_boolealg(A,B,C) ) ) ) ) ) )).

fof(t33_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ r2_boolealg(A,B,k5_lattices(A)) ) ) )).

fof(t34_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( ~ r2_boolealg(A,B,C)
                      & r3_lattices(A,D,C)
                      & r2_boolealg(A,B,D) ) ) ) ) ) )).

fof(t35_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( ~ ( r2_boolealg(A,B,C)
                          & r2_boolealg(A,B,D) )
                      & r2_boolealg(A,B,k4_lattices(A,C,D)) ) ) ) ) ) )).

fof(t36_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r3_lattices(A,B,C)
                      & r3_lattices(A,B,D) )
                   => ( r2_boolealg(A,C,D)
                      | r1_boolealg(A,B,k5_lattices(A)) ) ) ) ) ) ) )).

fof(t37_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ~ r2_boolealg(A,B,C)
                   => ( ~ r2_boolealg(A,k4_lattices(A,D,B),k4_lattices(A,D,C))
                      & ~ r2_boolealg(A,k4_lattices(A,B,D),k4_lattices(A,C,D)) ) ) ) ) ) ) )).

fof(t38_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_lattices(A,k1_boolealg(A,B,C),D)
                   => r3_lattices(A,B,k3_lattices(A,C,D)) ) ) ) ) ) )).

fof(t39_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_lattices(A,B,C)
                   => r3_lattices(A,k1_boolealg(A,D,C),k1_boolealg(A,D,B)) ) ) ) ) ) )).

fof(t40_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r3_lattices(A,B,C)
                          & r3_lattices(A,D,E) )
                       => r3_lattices(A,k1_boolealg(A,B,E),k1_boolealg(A,C,D)) ) ) ) ) ) ) )).

fof(t41_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_lattices(A,B,k3_lattices(A,C,D))
                   => ( r3_lattices(A,k1_boolealg(A,B,C),D)
                      & r3_lattices(A,k1_boolealg(A,B,D),C) ) ) ) ) ) ) )).

fof(t42_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,k7_lattices(A,B),k7_lattices(A,k4_lattices(A,B,C)))
                & r3_lattices(A,k7_lattices(A,C),k7_lattices(A,k4_lattices(A,B,C))) ) ) ) ) )).

fof(t43_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,k7_lattices(A,k3_lattices(A,B,C)),k7_lattices(A,B))
                & r3_lattices(A,k7_lattices(A,k3_lattices(A,B,C)),k7_lattices(A,C)) ) ) ) ) )).

fof(t44_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,B,k1_boolealg(A,C,B))
               => r1_boolealg(A,B,k5_lattices(A)) ) ) ) ) )).

fof(t45_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,B,C)
               => r1_boolealg(A,C,k3_lattices(A,B,k1_boolealg(A,C,B))) ) ) ) ) )).

fof(t46_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_boolealg(A,k1_boolealg(A,B,C),k5_lattices(A))
              <=> r3_lattices(A,B,C) ) ) ) ) )).

fof(t47_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r3_lattices(A,B,k3_lattices(A,C,D))
                      & r1_boolealg(A,k4_lattices(A,B,D),k5_lattices(A)) )
                   => r3_lattices(A,B,C) ) ) ) ) ) )).

fof(t48_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k3_lattices(A,B,C),k3_lattices(A,k1_boolealg(A,B,C),C)) ) ) ) )).

fof(t49_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k1_boolealg(A,B,k3_lattices(A,B,C)),k5_lattices(A)) ) ) ) )).

fof(t50_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_boolealg(A,k1_boolealg(A,B,k4_lattices(A,B,C)),k1_boolealg(A,B,C))
                & r1_boolealg(A,k1_boolealg(A,B,k4_lattices(A,C,B)),k1_boolealg(A,B,C)) ) ) ) ) )).

fof(t51_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k4_lattices(A,k1_boolealg(A,B,C),C),k5_lattices(A)) ) ) ) )).

fof(t52_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_boolealg(A,k3_lattices(A,B,k1_boolealg(A,C,B)),k3_lattices(A,B,C))
                & r1_boolealg(A,k3_lattices(A,k1_boolealg(A,C,B),B),k3_lattices(A,C,B)) ) ) ) ) )).

fof(t53_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k3_lattices(A,k4_lattices(A,B,C),k1_boolealg(A,B,C)),B) ) ) ) )).

fof(t54_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_boolealg(A,k1_boolealg(A,B,k1_boolealg(A,C,D)),k3_lattices(A,k1_boolealg(A,B,C),k4_lattices(A,B,D))) ) ) ) ) )).

fof(t55_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k1_boolealg(A,B,k1_boolealg(A,B,C)),k4_lattices(A,B,C)) ) ) ) )).

fof(t56_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k1_boolealg(A,k3_lattices(A,B,C),C),k1_boolealg(A,B,C)) ) ) ) )).

fof(t57_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_boolealg(A,k4_lattices(A,B,C),k5_lattices(A))
              <=> r1_boolealg(A,k1_boolealg(A,B,C),B) ) ) ) ) )).

fof(t58_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_boolealg(A,k1_boolealg(A,B,k3_lattices(A,C,D)),k4_lattices(A,k1_boolealg(A,B,C),k1_boolealg(A,B,D))) ) ) ) ) )).

fof(t59_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_boolealg(A,k1_boolealg(A,B,k4_lattices(A,C,D)),k3_lattices(A,k1_boolealg(A,B,C),k1_boolealg(A,B,D))) ) ) ) ) )).

fof(t60_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_boolealg(A,k4_lattices(A,B,k1_boolealg(A,C,D)),k1_boolealg(A,k4_lattices(A,B,C),k4_lattices(A,B,D)))
                    & r1_boolealg(A,k4_lattices(A,k1_boolealg(A,C,D),B),k1_boolealg(A,k4_lattices(A,C,B),k4_lattices(A,D,B))) ) ) ) ) ) )).

fof(t61_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k1_boolealg(A,k3_lattices(A,B,C),k4_lattices(A,B,C)),k3_lattices(A,k1_boolealg(A,B,C),k1_boolealg(A,C,B))) ) ) ) )).

fof(t62_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_boolealg(A,k1_boolealg(A,k1_boolealg(A,B,C),D),k1_boolealg(A,B,k3_lattices(A,C,D))) ) ) ) ) )).

fof(t63_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_boolealg(A,k1_boolealg(A,B,C),k1_boolealg(A,C,B))
               => r1_boolealg(A,B,C) ) ) ) ) )).

fof(t64_boolealg,axiom,(
    $true )).

fof(t65_boolealg,axiom,(
    $true )).

fof(t66_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_boolealg(A,k1_boolealg(A,B,B),k5_lattices(A)) ) ) )).

fof(t67_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_boolealg(A,k1_boolealg(A,B,k5_lattices(A)),B) ) ) )).

fof(t68_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k7_lattices(A,k1_boolealg(A,B,C)),k3_lattices(A,k7_lattices(A,B),C)) ) ) ) )).

fof(t69_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_boolealg(A,B,k3_lattices(A,C,D))
                  <=> ( r3_boolealg(A,B,C)
                      | r3_boolealg(A,B,D) ) ) ) ) ) ) )).

fof(t70_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ r2_boolealg(A,k4_lattices(A,B,C),k1_boolealg(A,B,C)) ) ) ) )).

fof(t71_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ~ r2_boolealg(A,B,k3_lattices(A,C,D))
                  <=> ( ~ r2_boolealg(A,B,C)
                      & ~ r2_boolealg(A,B,D) ) ) ) ) ) ) )).

fof(t72_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ r2_boolealg(A,k1_boolealg(A,B,C),C) ) ) ) )).

fof(t73_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ~ r2_boolealg(A,B,C)
               => ( r1_boolealg(A,k1_boolealg(A,k3_lattices(A,B,C),C),B)
                  & r1_boolealg(A,k1_boolealg(A,k3_lattices(A,B,C),B),C) ) ) ) ) ) )).

fof(t74_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_boolealg(A,k3_lattices(A,k7_lattices(A,B),k7_lattices(A,C)),k3_lattices(A,B,C))
               => ( r2_boolealg(A,B,k7_lattices(A,B))
                  | r2_boolealg(A,C,k7_lattices(A,C))
                  | ( r1_boolealg(A,B,k7_lattices(A,C))
                    & r1_boolealg(A,C,k7_lattices(A,B)) ) ) ) ) ) ) )).

fof(t75_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_boolealg(A,k3_lattices(A,k7_lattices(A,B),k7_lattices(A,C)),k3_lattices(A,B,C))
               => ( r2_boolealg(A,C,k7_lattices(A,B))
                  | r2_boolealg(A,B,k7_lattices(A,C))
                  | ( r1_boolealg(A,B,k7_lattices(A,B))
                    & r1_boolealg(A,C,k7_lattices(A,C)) ) ) ) ) ) ) )).

fof(t76_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_boolealg(A,k3_boolealg(A,B,k5_lattices(A)),B) ) ) )).

fof(t77_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_boolealg(A,k3_boolealg(A,B,B),k5_lattices(A)) ) ) )).

fof(t78_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ r2_boolealg(A,k4_lattices(A,B,C),k3_boolealg(A,B,C)) ) ) ) )).

fof(t79_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k3_lattices(A,B,C),k3_boolealg(A,B,k1_boolealg(A,C,B))) ) ) ) )).

fof(t80_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k3_boolealg(A,B,k4_lattices(A,B,C)),k1_boolealg(A,B,C)) ) ) ) )).

fof(t81_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k3_lattices(A,B,C),k3_lattices(A,k3_boolealg(A,B,C),k4_lattices(A,B,C))) ) ) ) )).

fof(t82_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k3_boolealg(A,k3_boolealg(A,B,C),k4_lattices(A,B,C)),k3_lattices(A,B,C)) ) ) ) )).

fof(t83_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k3_boolealg(A,k3_boolealg(A,B,C),k3_lattices(A,B,C)),k4_lattices(A,B,C)) ) ) ) )).

fof(t84_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k3_boolealg(A,B,C),k1_boolealg(A,k3_lattices(A,B,C),k4_lattices(A,B,C))) ) ) ) )).

fof(t85_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_boolealg(A,k1_boolealg(A,k3_boolealg(A,B,C),D),k3_lattices(A,k1_boolealg(A,B,k3_lattices(A,C,D)),k1_boolealg(A,C,k3_lattices(A,B,D)))) ) ) ) ) )).

fof(t86_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_boolealg(A,k1_boolealg(A,B,k3_boolealg(A,C,D)),k3_lattices(A,k1_boolealg(A,B,k3_lattices(A,C,D)),k4_lattices(A,k4_lattices(A,B,C),D))) ) ) ) ) )).

fof(t87_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => r1_boolealg(A,k3_boolealg(A,k3_boolealg(A,B,C),D),k3_boolealg(A,B,k3_boolealg(A,C,D))) ) ) ) ) )).

fof(t88_boolealg,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_boolealg(A,k7_lattices(A,k3_boolealg(A,B,C)),k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C)))) ) ) ) )).

fof(symmetry_r1_boolealg,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r1_boolealg(A,B,C)
       => r1_boolealg(A,C,B) ) ) )).

fof(reflexivity_r1_boolealg,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r1_boolealg(A,B,B) ) )).

fof(redefinition_r1_boolealg,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r1_boolealg(A,B,C)
      <=> B = C ) ) )).

fof(symmetry_r3_boolealg,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r3_boolealg(A,B,C)
       => r3_boolealg(A,C,B) ) ) )).

fof(redefinition_r3_boolealg,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r3_boolealg(A,B,C)
      <=> r2_boolealg(A,B,C) ) ) )).

fof(dt_k1_boolealg,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_boolealg(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k2_boolealg,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_boolealg(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k3_boolealg,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k3_boolealg(A,B,C),u1_struct_0(A)) ) )).

fof(commutativity_k3_boolealg,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k3_boolealg(A,B,C) = k3_boolealg(A,C,B) ) )).

fof(redefinition_k3_boolealg,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k3_boolealg(A,B,C) = k2_boolealg(A,B,C) ) )).
%------------------------------------------------------------------------------