% Mizar problem: t6_boolealg,boolealg,82,23 
fof(t6_boolealg,conjecture,(
    ! [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) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_lattices,cc2_lattices,commutativity_k4_lattices,d1_boolealg,dt_k1_boolealg,dt_k2_lattices,dt_k4_lattices,dt_k7_lattices,dt_l1_lattices,dt_l1_struct_0,dt_l2_lattices,dt_l3_lattices,dt_m1_subset_1,dt_u1_struct_0,existence_l1_lattices,existence_l1_struct_0,existence_l2_lattices,existence_l3_lattices,existence_m1_subset_1,redefinition_k4_lattices,redefinition_r3_lattices,reflexivity_r3_lattices,t23_lattices,t25_lattices,t27_lattices]),
    [file(boolealg,t6_boolealg)]).

fof(cc1_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A) ) ) ) ),
    file(lattices,cc1_lattices),
    []).

fof(cc2_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v10_lattices(A) ) ) ) ),
    file(lattices,cc2_lattices),
    []).

fof(commutativity_k4_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_lattices(A,B,C) = k4_lattices(A,C,B) ) ),
    file(lattices,k4_lattices),
    []).

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)) ) ) ) ),
    file(boolealg,d1_boolealg),
    []).

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)) ) ),
    file(boolealg,k1_boolealg),
    []).

fof(dt_k2_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_lattices(A,B,C),u1_struct_0(A)) ) ),
    file(lattices,k2_lattices),
    []).

fof(dt_k4_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)) ) ),
    file(lattices,k4_lattices),
    []).

fof(dt_k7_lattices,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k7_lattices(A,B),u1_struct_0(A)) ) ),
    file(lattices,k7_lattices),
    []).

fof(dt_l1_lattices,axiom,(
    ! [A] : 
      ( l1_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l1_lattices),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l2_lattices,axiom,(
    ! [A] : 
      ( l2_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l2_lattices),
    []).

fof(dt_l3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( l1_lattices(A)
        & l2_lattices(A) ) ) ),
    file(lattices,l3_lattices),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_lattices,axiom,(
    ? [A] : l1_lattices(A) ),
    file(lattices,l1_lattices),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l2_lattices,axiom,(
    ? [A] : l2_lattices(A) ),
    file(lattices,l2_lattices),
    []).

fof(existence_l3_lattices,axiom,(
    ? [A] : l3_lattices(A) ),
    file(lattices,l3_lattices),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(redefinition_k4_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_lattices(A,B,C) = k2_lattices(A,B,C) ) ),
    file(lattices,k4_lattices),
    []).

fof(redefinition_r3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r3_lattices(A,B,C)
      <=> r1_lattices(A,B,C) ) ) ),
    file(lattices,r3_lattices),
    []).

fof(reflexivity_r3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r3_lattices(A,B,B) ) ),
    file(lattices,r3_lattices),
    []).

fof(t23_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_lattices(A,k4_lattices(A,B,C),B) ) ) ) ),
    file(lattices,t23_lattices),
    []).

fof(t25_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v5_lattices(A)
        & l2_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_lattices(A,B,C)
                      & r1_lattices(A,C,D) )
                   => r1_lattices(A,B,D) ) ) ) ) ) ),
    file(lattices,t25_lattices),
    []).

fof(t27_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v7_lattices(A)
        & v8_lattices(A)
        & v9_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_lattices(A,B,C)
                   => r1_lattices(A,k2_lattices(A,B,D),k2_lattices(A,C,D)) ) ) ) ) ) ),
    file(lattices,t27_lattices),
    []).