Consider the following premises. forall x: ~T(x). forall x: S(x) -> T(x). forall x: S(x) <-> P(x). Can we infer forall x: ~P(x) from them?
 From forall x: S(x) <-> P(x) we can infer forall x: P(x) -> S(x). From forall x: P(x) -> S(x), forall x: S(x) -> T(x) we can infer forall x: P(x) -> T(x). Finally, from forall x: P(x) -> T(x), forall x: ~T(x) we can infer forall x: ~P(x). Therefore, the answer is yes.