% Mizar problem: t113_xboole_1,xboole_1,1322,31 
fof(t113_xboole_1,conjecture,(
    ! [A,B,C,D] : k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D) = k2_xboole_0(A,k2_xboole_0(k2_xboole_0(B,C),D)) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xboole_0,dt_k2_xboole_0,idempotence_k2_xboole_0,t4_xboole_1]),
    [file(xboole_1,t113_xboole_1)]).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(t4_xboole_1,axiom,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_1),
    []).