% Mizar problem: t114_xboole_1,xboole_1,1332,6 
fof(t114_xboole_1,conjecture,(
    ! [A,B,C,D] : 
      ( ( r1_xboole_0(A,D)
        & r1_xboole_0(B,D)
        & r1_xboole_0(C,D) )
     => r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xboole_0,dt_k2_xboole_0,idempotence_k2_xboole_0,symmetry_r1_xboole_0,t70_xboole_1]),
    [file(xboole_1,t114_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(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t70_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ~ ( ~ r1_xboole_0(A,k2_xboole_0(B,C))
          & r1_xboole_0(A,B)
          & r1_xboole_0(A,C) )
      & ~ ( ~ ( r1_xboole_0(A,B)
              & r1_xboole_0(A,C) )
          & r1_xboole_0(A,k2_xboole_0(B,C)) ) ) ),
    file(xboole_1,t70_xboole_1),
    []).