% Mizar problem: t56_xboole_1,xboole_1,741,33 
fof(t56_xboole_1,conjecture,(
    ! [A,B,C] : 
      ( ( r2_xboole_0(A,B)
        & r2_xboole_0(B,C) )
     => r2_xboole_0(A,C) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_xboole_0,d8_xboole_0,irreflexivity_r2_xboole_0,l58_xboole_1,reflexivity_r1_tarski]),
    [file(xboole_1,t56_xboole_1)]).

fof(antisymmetry_r2_xboole_0,axiom,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
     => ~ r2_xboole_0(B,A) ) ),
    file(xboole_0,r2_xboole_0),
    []).

fof(d8_xboole_0,axiom,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        & A != B ) ) ),
    file(xboole_0,d8_xboole_0),
    []).

fof(irreflexivity_r2_xboole_0,axiom,(
    ! [A,B] : ~ r2_xboole_0(A,A) ),
    file(xboole_0,r2_xboole_0),
    []).

fof(l58_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r2_xboole_0(B,C) )
     => r2_xboole_0(A,C) ) ),
    file(xboole_1,l58_xboole_1),
    []).

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