% Mizar problem: t18_xboole_1,xboole_1,199,29 
fof(t18_xboole_1,conjecture,(
    ! [A,B,C] : 
      ( r1_tarski(A,k3_xboole_0(B,C))
     => r1_tarski(A,B) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k3_xboole_0,dt_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,t17_xboole_1,t1_xboole_1]),
    [file(xboole_1,t18_xboole_1)]).

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(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_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(t17_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    []).

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).