% Mizar problem: t31_yellow_0,yellow_0,985,56 
fof(t31_yellow_0,conjecture,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( ( B = k2_yellow_0(A,C)
                  & r2_yellow_0(A,C) )
               => ( r1_lattice3(A,C,B)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r1_lattice3(A,C,D)
                       => r1_orders_2(A,D,B) ) ) ) )
              & ( ( r1_lattice3(A,C,B)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r1_lattice3(A,C,D)
                       => r1_orders_2(A,D,B) ) ) )
               => ( B = k2_yellow_0(A,C)
                  & r2_yellow_0(A,C) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d10_yellow_0,dt_k2_yellow_0,dt_l1_orders_2,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_subset_1,t16_yellow_0]),
    [file(yellow_0,t31_yellow_0)]).

fof(d10_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r2_yellow_0(A,B)
           => ( C = k2_yellow_0(A,B)
            <=> ( r1_lattice3(A,B,C)
                & ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_lattice3(A,B,D)
                     => r1_orders_2(A,D,C) ) ) ) ) ) ) ) ),
    file(yellow_0,d10_yellow_0),
    []).

fof(dt_k2_yellow_0,axiom,(
    ! [A,B] : 
      ( l1_orders_2(A)
     => m1_subset_1(k2_yellow_0(A,B),u1_struct_0(A)) ) ),
    file(yellow_0,k2_yellow_0),
    []).

fof(dt_l1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => l1_struct_0(A) ) ),
    file(orders_2,l1_orders_2),
    []).

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_orders_2,axiom,(
    ? [A] : l1_orders_2(A) ),
    file(orders_2,l1_orders_2),
    []).

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(t16_yellow_0,axiom,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( r2_yellow_0(A,B)
        <=> ? [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
              & r1_lattice3(A,B,C)
              & ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_lattice3(A,B,D)
                   => r1_orders_2(A,D,C) ) ) ) ) ) ),
    file(yellow_0,t16_yellow_0),
    []).