% Mizar problem: t22_e_siec,e_siec,379,36 
fof(t22_e_siec,conjecture,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => r1_xboole_0(k8_e_siec(A),k9_e_siec(A)) ) ),
    inference(mizar_bg_added,[status(thm)],[fc3_relat_1,existence_l1_struct_0,dt_k2_relat_1,dt_l1_struct_0,dt_u1_e_siec,dt_u1_struct_0,symmetry_r1_xboole_0,existence_l1_e_siec,dt_k4_xboole_0,dt_k8_e_siec,dt_k9_e_siec,dt_l1_e_siec,rc2_e_siec,rc3_e_siec,d10_e_siec,d11_e_siec,t79_xboole_1]),
    [file(e_siec,t22_e_siec)]).

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

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

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(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

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

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

fof(dt_k8_e_siec,axiom,(
    $true ),
    file(e_siec,k8_e_siec),
    []).

fof(dt_k9_e_siec,axiom,(
    $true ),
    file(e_siec,k9_e_siec),
    []).

fof(dt_l1_e_siec,axiom,(
    ! [A] : 
      ( l1_e_siec(A)
     => l1_struct_0(A) ) ),
    file(e_siec,l1_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(d10_e_siec,axiom,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k8_e_siec(A) = k2_relat_1(u1_e_siec(A)) ) ),
    file(e_siec,d10_e_siec),
    []).

fof(d11_e_siec,axiom,(
    ! [A] : 
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k9_e_siec(A) = k4_xboole_0(u1_struct_0(A),k8_e_siec(A)) ) ),
    file(e_siec,d11_e_siec),
    []).

fof(t79_xboole_1,axiom,(
    ! [A,B] : r1_xboole_0(k4_xboole_0(A,B),B) ),
    file(xboole_1,t79_xboole_1),
    []).