% Mizar problem: t34_e_siec,e_siec,817,52 
fof(t34_e_siec,conjecture,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k4_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))),k4_relat_1(k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u2_e_siec(A)))))) = k4_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))))
        & k5_relat_1(k4_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))),k4_relat_1(k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u1_e_siec(A)))))) = k4_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_k2_relat_1,dt_k4_relat_1,dt_k4_xboole_0,dt_k5_relat_1,dt_k6_relat_1,dt_l1_e_siec,dt_l1_struct_0,dt_u1_e_siec,dt_u1_struct_0,dt_u2_e_siec,existence_l1_e_siec,existence_l1_struct_0,fc3_relat_1,involutiveness_k4_relat_1,rc2_e_siec,rc3_e_siec,t31_e_siec,t54_relat_1]),
    [file(e_siec,t34_e_siec)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v1_relat_1(k4_relat_1(A)) ) ),
    file(relat_1,k4_relat_1),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

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

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(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(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(fc3_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k4_xboole_0(A,B)) ) ),
    file(relat_1,fc3_relat_1),
    []).

fof(involutiveness_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k4_relat_1(k4_relat_1(A)) = A ) ),
    file(relat_1,k4_relat_1),
    []).

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(t31_e_siec,axiom,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u2_e_siec(A)))),k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))
        & k5_relat_1(k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u1_e_siec(A)))),k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))) ) ) ),
    file(e_siec,t31_e_siec),
    []).

fof(t54_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => k4_relat_1(k5_relat_1(A,B)) = k5_relat_1(k4_relat_1(B),k4_relat_1(A)) ) ) ),
    file(relat_1,t54_relat_1),
    []).