% Mizar problem: t51_boolealg,boolealg,492,28 
fof(t51_boolealg,conjecture,(
    ! [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)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_lattices,cc2_lattices,cc3_lattices,cc4_lattices,cc5_lattices,cc6_lattices,cc7_lattices,commutativity_k4_lattices,d1_boolealg,d7_lattices,dt_k1_boolealg,dt_k2_lattices,dt_k4_lattices,dt_k5_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_r1_boolealg,reflexivity_r1_boolealg,symmetry_r1_boolealg,t40_lattices,t47_lattices]),
    [file(boolealg,t51_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(cc3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v13_lattices(A)
          & v14_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v15_lattices(A) ) ) ) ),
    file(lattices,cc3_lattices),
    []).

fof(cc4_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v15_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v13_lattices(A)
          & v14_lattices(A) ) ) ) ),
    file(lattices,cc4_lattices),
    []).

fof(cc5_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v17_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v11_lattices(A)
          & v13_lattices(A)
          & v14_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A) ) ) ) ),
    file(lattices,cc5_lattices),
    []).

fof(cc6_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v11_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v17_lattices(A) ) ) ) ),
    file(lattices,cc6_lattices),
    []).

fof(cc7_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v11_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v12_lattices(A) ) ) ) ),
    file(lattices,cc7_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(d7_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A) )
     => ( v7_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))
                   => k2_lattices(A,B,k2_lattices(A,C,D)) = k2_lattices(A,k2_lattices(A,B,C),D) ) ) ) ) ) ),
    file(lattices,d7_lattices),
    []).

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_k5_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A) )
     => m1_subset_1(k5_lattices(A),u1_struct_0(A)) ) ),
    file(lattices,k5_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_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 ) ) ),
    file(boolealg,r1_boolealg),
    []).

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) ) ),
    file(boolealg,r1_boolealg),
    []).

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) ) ) ),
    file(boolealg,r1_boolealg),
    []).

fof(t40_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_lattices(A,k5_lattices(A),B) = k5_lattices(A) ) ) ),
    file(lattices,t40_lattices),
    []).

fof(t47_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_lattices(A,k7_lattices(A,B),B) = k5_lattices(A) ) ) ),
    file(lattices,t47_lattices),
    []).