Consider the following premises. p. forall x_2: ~W(x_2). forall x_2: W(x_2) or P(x_2). Can we infer p and P(f) from them? If possible, name the inference rules being used at each step.
 From forall x_2: W(x_2) or P(x_2), forall x_2: ~W(x_2) we can infer forall x_2: P(x_2) via universal disjunctive syllogism. From forall x_2: P(x_2) we can infer P(f) via universal instantiation. Finally, from p, P(f) we can infer p and P(f) via conjunction. Therefore, the answer is yes.