Consider the following premises. forall x_20: P_16(x_20) -> ~Q_20(x_20). p_2 -> P_16(a). forall x_20: ~P_20(x_20). forall x_20: P_20(x_20) or Q_20(x_20). Can we infer p_2 from them? If possible, name the inference rules being used at each step.
 From forall x_20: P_20(x_20) or Q_20(x_20), forall x_20: ~P_20(x_20) we can infer forall x_20: Q_20(x_20) via universal disjunctive syllogism. From forall x_20: P_16(x_20) -> ~Q_20(x_20), forall x_20: Q_20(x_20) we can infer forall x_20: ~P_16(x_20) via universal modus tollens. From forall x_20: ~P_16(x_20) we can infer ~P_16(a) via universal instantiation. Finally, from p_2 -> P_16(a), ~P_16(a) we can infer ~p_2 via modus tollens, which contradicts p_2. Therefore, the answer is no.