Consider the following premises. exists y: T(y) -> P_4(y). forall y: S(y) -> ~P_4(y). forall y: T(y). Can we infer exists y: ~S(y) from them? If possible, name the inference rules being used at each step.
 From exists y: T(y) -> P_4(y), forall y: T(y) we can infer exists y: P_4(y) via existential modus ponens. Finally, from forall y: S(y) -> ~P_4(y), exists y: P_4(y) we can infer exists y: ~S(y) via existential modus tollens. Therefore, the answer is yes.