Derivations with power central values on Lie ideals in prime rings

Let R be a prime ring of char R not equal 2 with a nonzero derivation d and let U be its noncentral Lie ideal. If for some fixed integers n(1) >= 0, n(2) >= 0, n(3) >= 0, (u(n1)[d(u), u]u(n2))(n3) epsilon Z(R) for all u epsilon U, then R satisfies S-4, the standard identity in four variables.