Consider the following premises. forall x_2: P_2(x_2) or ~P(x_2). exists x_2: ~P_2(x_2). Can we infer exists x_2: ~P(x_2) from them? If possible, name the inference rules being used at each step.
 From forall x_2: P_2(x_2) or ~P(x_2) we can infer forall x_2: P(x_2) -> P_2(x_2) via universal rewriting. Finally, from forall x_2: P(x_2) -> P_2(x_2), exists x_2: ~P_2(x_2) we can infer exists x_2: ~P(x_2) via existential modus tollens. Therefore, the answer is yes.