Consider the following premises. forall x: ~P(x). exists x: S(x) or ~U(x). forall x: P(x) or U(x). Can we infer forall x: ~S(x) from them?
 From exists x: S(x) or ~U(x) we can infer exists x: U(x) -> S(x). From forall x: P(x) or U(x), forall x: ~P(x) we can infer forall x: U(x). Finally, from exists x: U(x) -> S(x), forall x: U(x) we can infer exists x: S(x), which contradicts forall x: ~S(x). Therefore, the answer is no.