% Mizar problem: t3_gate_4,gate_4,347,50 
fof(t3_gate_4,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1] : 
      ( v1_xboole_0(L1)
     => ( v1_xboole_0(A)
        | v1_xboole_0(M)
        | ( ~ v1_xboole_0(Z)
          & v1_xboole_0(k4_gate_1(M1,Y)) )
        | ( ~ v1_xboole_0(k4_gate_1(M1,Y))
          & v1_xboole_0(Z) )
        | ( ~ v1_xboole_0(A1)
          & v1_xboole_0(k4_gate_1(N,k2_gate_1(B,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(N,k2_gate_1(B,Z)))
          & v1_xboole_0(A1) )
        | ( ~ v1_xboole_0(B1)
          & v1_xboole_0(k4_gate_1(O,k2_gate_1(C,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(O,k2_gate_1(C,Z)))
          & v1_xboole_0(B1) )
        | ( ~ v1_xboole_0(C1)
          & v1_xboole_0(k4_gate_1(P,k2_gate_1(D,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(P,k2_gate_1(D,Z)))
          & v1_xboole_0(C1) )
        | ( ~ v1_xboole_0(D1)
          & v1_xboole_0(k4_gate_1(Q,k2_gate_1(E,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(Q,k2_gate_1(E,Z)))
          & v1_xboole_0(D1) )
        | ( ~ v1_xboole_0(E1)
          & v1_xboole_0(k4_gate_1(R,k2_gate_1(F,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(R,k2_gate_1(F,Z)))
          & v1_xboole_0(E1) )
        | ( ~ v1_xboole_0(F1)
          & v1_xboole_0(k4_gate_1(S,k2_gate_1(G,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(S,k2_gate_1(G,Z)))
          & v1_xboole_0(F1) )
        | ( ~ v1_xboole_0(G1)
          & v1_xboole_0(k4_gate_1(T,k2_gate_1(H,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(T,k2_gate_1(H,Z)))
          & v1_xboole_0(G1) )
        | ( ~ v1_xboole_0(H1)
          & v1_xboole_0(k4_gate_1(U,k2_gate_1(I,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(U,k2_gate_1(I,Z)))
          & v1_xboole_0(H1) )
        | ( ~ v1_xboole_0(I1)
          & v1_xboole_0(k4_gate_1(V,k2_gate_1(J,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(V,k2_gate_1(J,Z)))
          & v1_xboole_0(I1) )
        | ( ~ v1_xboole_0(J1)
          & v1_xboole_0(k4_gate_1(W,k2_gate_1(K,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(W,k2_gate_1(K,Z)))
          & v1_xboole_0(J1) )
        | ( ~ v1_xboole_0(K1)
          & v1_xboole_0(k4_gate_1(X,k2_gate_1(L,Z))) )
        | ( ~ v1_xboole_0(k4_gate_1(X,k2_gate_1(L,Z)))
          & v1_xboole_0(K1) )
        | ( ~ ( ~ v1_xboole_0(K1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(X,k2_gate_1(L,Y)),k4_gate_1(L1,k2_gate_1(L,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(X,k2_gate_1(L,Y)),k4_gate_1(L1,k2_gate_1(L,M1))))
              & v1_xboole_0(K1) )
          & ~ ( ~ v1_xboole_0(J1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(W,k2_gate_1(K,Y)),k4_gate_1(L1,k2_gate_1(K,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(W,k2_gate_1(K,Y)),k4_gate_1(L1,k2_gate_1(K,M1))))
              & v1_xboole_0(J1) )
          & ~ ( ~ v1_xboole_0(I1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(V,k2_gate_1(J,Y)),k4_gate_1(L1,k2_gate_1(J,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(V,k2_gate_1(J,Y)),k4_gate_1(L1,k2_gate_1(J,M1))))
              & v1_xboole_0(I1) )
          & ~ ( ~ v1_xboole_0(H1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(U,k2_gate_1(I,Y)),k4_gate_1(L1,k2_gate_1(I,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(U,k2_gate_1(I,Y)),k4_gate_1(L1,k2_gate_1(I,M1))))
              & v1_xboole_0(H1) )
          & ~ ( ~ v1_xboole_0(G1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(T,k2_gate_1(H,Y)),k4_gate_1(L1,k2_gate_1(H,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(T,k2_gate_1(H,Y)),k4_gate_1(L1,k2_gate_1(H,M1))))
              & v1_xboole_0(G1) )
          & ~ ( ~ v1_xboole_0(F1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(S,k2_gate_1(G,Y)),k4_gate_1(L1,k2_gate_1(G,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(S,k2_gate_1(G,Y)),k4_gate_1(L1,k2_gate_1(G,M1))))
              & v1_xboole_0(F1) )
          & ~ ( ~ v1_xboole_0(E1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(R,k2_gate_1(F,Y)),k4_gate_1(L1,k2_gate_1(F,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(R,k2_gate_1(F,Y)),k4_gate_1(L1,k2_gate_1(F,M1))))
              & v1_xboole_0(E1) )
          & ~ ( ~ v1_xboole_0(D1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(Q,k2_gate_1(E,Y)),k4_gate_1(L1,k2_gate_1(E,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(Q,k2_gate_1(E,Y)),k4_gate_1(L1,k2_gate_1(E,M1))))
              & v1_xboole_0(D1) )
          & ~ ( ~ v1_xboole_0(C1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(P,k2_gate_1(D,Y)),k4_gate_1(L1,k2_gate_1(D,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(P,k2_gate_1(D,Y)),k4_gate_1(L1,k2_gate_1(D,M1))))
              & v1_xboole_0(C1) )
          & ~ ( ~ v1_xboole_0(B1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(O,k2_gate_1(C,Y)),k4_gate_1(L1,k2_gate_1(C,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(O,k2_gate_1(C,Y)),k4_gate_1(L1,k2_gate_1(C,M1))))
              & v1_xboole_0(B1) )
          & ~ ( ~ v1_xboole_0(A1)
              & v1_xboole_0(k4_gate_1(k4_gate_1(N,k2_gate_1(B,Y)),k4_gate_1(L1,k2_gate_1(B,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(N,k2_gate_1(B,Y)),k4_gate_1(L1,k2_gate_1(B,M1))))
              & v1_xboole_0(A1) )
          & ~ ( ~ v1_xboole_0(Z)
              & v1_xboole_0(k4_gate_1(k4_gate_1(L1,k2_gate_1(A,Y)),k4_gate_1(L1,k2_gate_1(A,M1)))) )
          & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(L1,k2_gate_1(A,Y)),k4_gate_1(L1,k2_gate_1(A,M1))))
              & v1_xboole_0(Z) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_k2_gate_1,dt_k4_gate_1,t6_gate_1,t8_gate_1]),
    [file(gate_4,t3_gate_4)]).

fof(dt_k2_gate_1,axiom,(
    $true ),
    file(gate_1,k2_gate_1),
    []).

fof(dt_k4_gate_1,axiom,(
    $true ),
    file(gate_1,k4_gate_1),
    []).

fof(t6_gate_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_gate_1(A,B))
    <=> ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) ) ) ),
    file(gate_1,t6_gate_1),
    []).

fof(t8_gate_1,axiom,(
    ! [A,B] : 
      ( ~ ( ~ v1_xboole_0(k4_gate_1(A,B))
          & ~ ( ~ v1_xboole_0(A)
              & v1_xboole_0(B) )
          & ~ ( v1_xboole_0(A)
              & ~ v1_xboole_0(B) ) )
      & ~ ( ( ( ~ v1_xboole_0(A)
              & v1_xboole_0(B) )
            | ( v1_xboole_0(A)
              & ~ v1_xboole_0(B) ) )
          & v1_xboole_0(k4_gate_1(A,B)) ) ) ),
    file(gate_1,t8_gate_1),
    []).