% Mizar problem: t14_necklace,necklace,569,22 
fof(t14_necklace,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ( ( r4_necklace(A,B)
                  & r4_necklace(B,C) )
               => r4_necklace(A,C) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_orders_3,d3_necklace,dt_l1_orders_2,dt_l1_struct_0,existence_l1_orders_2,existence_l1_struct_0,rc3_struct_0,redefinition_r3_necklace,reflexivity_r3_necklace,reflexivity_r4_necklace,symmetry_r4_necklace,t13_necklace]),
    [file(necklace,t14_necklace)]).

fof(cc1_orders_3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v3_struct_0(A)
       => v1_orders_3(A) ) ) ),
    file(orders_3,cc1_orders_3),
    []).

fof(d3_necklace,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ( r4_necklace(A,B)
          <=> ( r3_necklace(B,A)
              & r3_necklace(A,B) ) ) ) ) ),
    file(necklace,d3_necklace),
    []).

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(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(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(redefinition_r3_necklace,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ( r3_necklace(A,B)
      <=> r2_necklace(A,B) ) ) ),
    file(necklace,r3_necklace),
    []).

fof(reflexivity_r3_necklace,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => r3_necklace(B,B) ) ),
    file(necklace,r3_necklace),
    []).

fof(reflexivity_r4_necklace,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => r4_necklace(A,A) ) ),
    file(necklace,r4_necklace),
    []).

fof(symmetry_r4_necklace,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ( r4_necklace(A,B)
       => r4_necklace(B,A) ) ) ),
    file(necklace,r4_necklace),
    []).

fof(t13_necklace,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ( ( r3_necklace(B,A)
                  & r3_necklace(C,B) )
               => r3_necklace(C,A) ) ) ) ) ),
    file(necklace,t13_necklace),
    []).