% Mizar problem: t49_yellow_5,yellow_5,809,50 
fof(t49_yellow_5,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(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,k13_lattice3(A,C,D))
                      & k12_lattice3(A,B,D) = k3_yellow_0(A) )
                   => r3_orders_2(A,B,C) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc10_waybel_1,cc1_lattice3,cc2_lattice3,cc5_waybel_1,cc6_waybel_1,cc7_waybel_1,cc8_waybel_1,cc9_waybel_1,commutativity_k12_lattice3,commutativity_k13_lattice3,d3_waybel_1,dt_k10_lattice3,dt_k11_lattice3,dt_k12_lattice3,dt_k13_lattice3,dt_k3_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,redefinition_k12_lattice3,redefinition_k13_lattice3,redefinition_r3_orders_2,reflexivity_r3_orders_2,t10_yellow_5,t23_yellow_0,t4_waybel_1]),
    [file(yellow_5,t49_yellow_5)]).

fof(cc10_waybel_1,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v11_waybel_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v2_yellow_0(A)
          & v2_waybel_1(A)
          & v9_waybel_1(A) ) ) ) ),
    file(waybel_1,cc10_waybel_1),
    []).

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

fof(cc2_lattice3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v2_lattice3(A)
       => ~ v3_struct_0(A) ) ) ),
    file(lattice3,cc2_lattice3),
    []).

fof(cc5_waybel_1,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v9_waybel_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A) ) ) ) ),
    file(waybel_1,cc5_waybel_1),
    []).

fof(cc6_waybel_1,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v9_waybel_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_waybel_1(A) ) ) ) ),
    file(waybel_1,cc6_waybel_1),
    []).

fof(cc7_waybel_1,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v9_waybel_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_yellow_0(A) ) ) ) ),
    file(waybel_1,cc7_waybel_1),
    []).

fof(cc8_waybel_1,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v11_waybel_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v1_yellow_0(A)
          & v2_yellow_0(A)
          & v3_yellow_0(A)
          & v2_waybel_1(A)
          & v10_waybel_1(A) ) ) ) ),
    file(waybel_1,cc8_waybel_1),
    []).

fof(cc9_waybel_1,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_yellow_0(A)
          & v2_waybel_1(A)
          & v10_waybel_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v1_yellow_0(A)
          & v2_yellow_0(A)
          & v3_yellow_0(A)
          & v2_waybel_1(A)
          & v10_waybel_1(A)
          & v11_waybel_1(A) ) ) ) ),
    file(waybel_1,cc9_waybel_1),
    []).

fof(commutativity_k12_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k12_lattice3(A,B,C) = k12_lattice3(A,C,B) ) ),
    file(lattice3,k12_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(d3_waybel_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v2_waybel_1(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))
                   => k11_lattice3(A,B,k10_lattice3(A,C,D)) = k10_lattice3(A,k11_lattice3(A,B,C),k11_lattice3(A,B,D)) ) ) ) ) ) ),
    file(waybel_1,d3_waybel_1),
    []).

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_k11_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(k11_lattice3(A,B,C),u1_struct_0(A)) ) ),
    file(lattice3,k11_lattice3),
    []).

fof(dt_k12_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v2_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(k12_lattice3(A,B,C),u1_struct_0(A)) ) ),
    file(lattice3,k12_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_k3_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => m1_subset_1(k3_yellow_0(A),u1_struct_0(A)) ) ),
    file(yellow_0,k3_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(redefinition_k12_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k12_lattice3(A,B,C) = k11_lattice3(A,B,C) ) ),
    file(lattice3,k12_lattice3),
    []).

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(t10_yellow_5,axiom,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_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,C,B)
               => k12_lattice3(A,B,C) = C ) ) ) ) ),
    file(yellow_5,t10_yellow_5),
    []).

fof(t23_yellow_0,axiom,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & v2_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))
                 => ( D = k12_lattice3(A,B,C)
                  <=> ( r1_orders_2(A,D,B)
                      & r1_orders_2(A,D,C)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r1_orders_2(A,E,B)
                              & r1_orders_2(A,E,C) )
                           => r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) ),
    file(yellow_0,t23_yellow_0),
    []).

fof(t4_waybel_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( v2_lattice3(A)
             => k11_lattice3(A,k3_yellow_0(A),B) = k3_yellow_0(A) )
            & ( ( v1_lattice3(A)
                & v2_orders_2(A)
                & v3_orders_2(A) )
             => k10_lattice3(A,k3_yellow_0(A),B) = B ) ) ) ) ),
    file(waybel_1,t4_waybel_1),
    []).