Consider the following premises. forall x: W(x) or W_4(x). exists x: W(x) -> P(x). forall x: ~P(x). Can we infer exists x: W_4(x) from them? If possible, name the inference rules being used at each step.
 From exists x: W(x) -> P(x), forall x: ~P(x) we can infer exists x: ~W(x) via existential modus tollens. Finally, from forall x: W(x) or W_4(x), exists x: ~W(x) we can infer exists x: W_4(x) via existential disjunctive syllogism. Therefore, the answer is yes.