% Mizar problem: t11_e_siec,e_siec,176,37 
fof(t11_e_siec,conjecture,(
    ! [A] : 
      ( u1_struct_0(k3_e_siec(A)) = A
      & u1_e_siec(k3_e_siec(A)) = k6_relat_1(A)
      & u2_e_siec(k3_e_siec(A)) = k6_relat_1(A) ) ),
    inference(mizar_bg_added,[status(thm)],[free_g1_e_siec,abstractness_v1_e_siec,existence_l1_e_siec,existence_l1_struct_0,dt_g1_e_siec,dt_l1_e_siec,dt_l1_struct_0,rc1_e_siec,rc2_e_siec,rc3_e_siec,rc4_e_siec,dt_k3_e_siec,dt_k6_relat_1,dt_u1_e_siec,dt_u1_struct_0,dt_u2_e_siec,d5_e_siec]),
    [file(e_siec,t11_e_siec)]).

fof(free_g1_e_siec,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(B)
        & v1_relat_1(C) )
     => ! [D,E,F] : 
          ( g1_e_siec(A,B,C) = g1_e_siec(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(e_siec,g1_e_siec),
    []).

fof(abstractness_v1_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => ( v1_e_siec(A)
       => A = g1_e_siec(u1_struct_0(A),u1_e_siec(A),u2_e_siec(A)) ) ) ),
    file(e_siec,v1_e_siec),
    []).

fof(existence_l1_e_siec,axiom,(
    ? [A] : l1_e_siec(A) ),
    file(e_siec,l1_e_siec),
    []).

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

fof(dt_g1_e_siec,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(B)
        & v1_relat_1(C) )
     => ( v1_e_siec(g1_e_siec(A,B,C))
        & l1_e_siec(g1_e_siec(A,B,C)) ) ) ),
    file(e_siec,g1_e_siec),
    []).

fof(dt_l1_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => l1_struct_0(A) ) ),
    file(e_siec,l1_e_siec),
    []).

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

fof(rc1_e_siec,axiom,(
    ? [A] : 
      ( l1_e_siec(A)
      & v1_e_siec(A) ) ),
    file(e_siec,rc1_e_siec),
    []).

fof(rc2_e_siec,axiom,(
    ? [A] : 
      ( l1_e_siec(A)
      & v2_e_siec(A) ) ),
    file(e_siec,rc2_e_siec),
    []).

fof(rc3_e_siec,axiom,(
    ? [A] : 
      ( l1_e_siec(A)
      & v3_e_siec(A) ) ),
    file(e_siec,rc3_e_siec),
    []).

fof(rc4_e_siec,axiom,(
    ? [A] : 
      ( l1_e_siec(A)
      & v1_e_siec(A)
      & v2_e_siec(A)
      & v3_e_siec(A) ) ),
    file(e_siec,rc4_e_siec),
    []).

fof(dt_k3_e_siec,axiom,(
    ! [A] : 
      ( v1_e_siec(k3_e_siec(A))
      & v2_e_siec(k3_e_siec(A))
      & v3_e_siec(k3_e_siec(A))
      & l1_e_siec(k3_e_siec(A)) ) ),
    file(e_siec,k3_e_siec),
    []).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    []).

fof(dt_u1_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => v1_relat_1(u1_e_siec(A)) ) ),
    file(e_siec,u1_e_siec),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u2_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => v1_relat_1(u2_e_siec(A)) ) ),
    file(e_siec,u2_e_siec),
    []).

fof(d5_e_siec,axiom,(
    ! [A] : k3_e_siec(A) = g1_e_siec(A,k6_relat_1(A),k6_relat_1(A)) ),
    file(e_siec,d5_e_siec),
    []).