% Mizar problem: t9_yellow_5,yellow_5,129,30 
fof(t9_yellow_5,conjecture,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(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_orders_2(A,B,D)
                      & r3_orders_2(A,C,D) )
                   => r3_orders_2(A,k13_lattice3(A,B,C),D) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_lattice3,commutativity_k13_lattice3,dt_k10_lattice3,dt_k13_lattice3,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,redefinition_k13_lattice3,redefinition_r3_orders_2,reflexivity_r3_orders_2,t7_yellow_5,t8_yellow_5]),
    [file(yellow_5,t9_yellow_5)]).

fof(cc1_lattice3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_lattice3(A)
       => ~ v3_struct_0(A) ) ) ),
    file(lattice3,cc1_lattice3),
    []).

fof(commutativity_k13_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k13_lattice3(A,B,C) = k13_lattice3(A,C,B) ) ),
    file(lattice3,k13_lattice3),
    []).

fof(dt_k10_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k10_lattice3(A,B,C),u1_struct_0(A)) ) ),
    file(lattice3,k10_lattice3),
    []).

fof(dt_k13_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k13_lattice3(A,B,C),u1_struct_0(A)) ) ),
    file(lattice3,k13_lattice3),
    []).

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(redefinition_k13_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k13_lattice3(A,B,C) = k10_lattice3(A,B,C) ) ),
    file(lattice3,k13_lattice3),
    []).

fof(redefinition_r3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r3_orders_2(A,B,C)
      <=> r1_orders_2(A,B,C) ) ) ),
    file(orders_2,r3_orders_2),
    []).

fof(reflexivity_r3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r3_orders_2(A,B,B) ) ),
    file(orders_2,r3_orders_2),
    []).

fof(t7_yellow_5,axiom,(
    ! [A] : 
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(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_orders_2(A,B,C)
                   => r1_orders_2(A,k13_lattice3(A,B,D),k13_lattice3(A,C,D)) ) ) ) ) ) ),
    file(yellow_5,t7_yellow_5),
    []).

fof(t8_yellow_5,axiom,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,B,C)
               => k13_lattice3(A,B,C) = C ) ) ) ) ),
    file(yellow_5,t8_yellow_5),
    []).