Identities related to a pair of generalized skew derivations on Lie ideals

Let S be a prime ring with char(S) not equal 2, Q(r) its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of S, F and G two generalized skew derivations of S. If F(tau s) +/- G(s)G(tau) +/- s tau = 0, for any tau, s is an element of L, then one of the following holds: (1) F = 0 and there exists lambda is an element of C such that G(tau) =lambda tau, for any tau is an element of S, with lambda(2) + 1 = 0; (2) S satisfies the standard polynomial identity s(4)(tau(1),..., tau(4)).