% Mizar problem: t98_sheffer2,sheffer2,992,61 
fof(t98_sheffer2,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_sheffer1(A)
        & v11_sheffer1(A)
        & v12_sheffer1(A)
        & l1_sheffer1(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))
                 => k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),C),k5_sheffer1(A,k5_sheffer1(A,B,B),C)),k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,D,B)),k5_sheffer1(A,C,k5_sheffer1(A,D,B)))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),k5_sheffer1(A,k5_sheffer1(A,D,D),C)),k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,k5_sheffer1(A,D,D),C))) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d15_sheffer1,dt_k5_sheffer1,dt_l1_sheffer1,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_sheffer1,existence_l1_struct_0,existence_m1_subset_1,rc5_sheffer1]),
    [file(sheffer2,t98_sheffer2)]).

fof(d15_sheffer1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_sheffer1(A) )
     => ( v12_sheffer1(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))
                   => k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,B,k5_sheffer1(A,C,D))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),B),k5_sheffer1(A,k5_sheffer1(A,D,D),B)) ) ) ) ) ) ),
    file(sheffer1,d15_sheffer1),
    []).

fof(dt_k5_sheffer1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_sheffer1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k5_sheffer1(A,B,C),u1_struct_0(A)) ) ),
    file(sheffer1,k5_sheffer1),
    []).

fof(dt_l1_sheffer1,axiom,(
    ! [A] : 
      ( l1_sheffer1(A)
     => l1_struct_0(A) ) ),
    file(sheffer1,l1_sheffer1),
    []).

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

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_sheffer1,axiom,(
    ? [A] : l1_sheffer1(A) ),
    file(sheffer1,l1_sheffer1),
    []).

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

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

fof(rc5_sheffer1,axiom,(
    ? [A] : 
      ( l1_sheffer1(A)
      & ~ v3_struct_0(A) ) ),
    file(sheffer1,rc5_sheffer1),
    []).