% Mizar problem: t98_xboole_1,xboole_1,1188,24 
fof(t98_xboole_1,conjecture,(
    ! [A,B] : k2_xboole_0(A,B) = k5_xboole_0(A,k4_xboole_0(B,A)) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xboole_0,commutativity_k3_xboole_0,commutativity_k5_xboole_0,d6_xboole_0,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_xboole_0,dt_k5_xboole_0,idempotence_k2_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,t12_xboole_1,t36_xboole_1,t39_xboole_1,t41_xboole_1,t52_xboole_1]),
    [file(xboole_1,t98_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(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(commutativity_k5_xboole_0,axiom,(
    ! [A,B] : k5_xboole_0(A,B) = k5_xboole_0(B,A) ),
    file(xboole_0,k5_xboole_0),
    []).

fof(d6_xboole_0,axiom,(
    ! [A,B] : k5_xboole_0(A,B) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) ),
    file(xboole_0,d6_xboole_0),
    []).

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

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

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

fof(dt_k5_xboole_0,axiom,(
    $true ),
    file(xboole_0,k5_xboole_0),
    []).

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

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t12_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ) ),
    file(xboole_1,t12_xboole_1),
    []).

fof(t36_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    []).

fof(t39_xboole_1,axiom,(
    ! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B) ),
    file(xboole_1,t39_xboole_1),
    []).

fof(t41_xboole_1,axiom,(
    ! [A,B,C] : k4_xboole_0(k4_xboole_0(A,B),C) = k4_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t41_xboole_1),
    []).

fof(t52_xboole_1,axiom,(
    ! [A,B,C] : k4_xboole_0(A,k4_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,C)) ),
    file(xboole_1,t52_xboole_1),
    []).