Consider the following premises. ~p_4 -> q. p_4 -> P_2(a_14). forall x_3: ~P_2(x_3). Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From forall x_3: ~P_2(x_3) we can infer ~P_2(a_14) via universal instantiation. From p_4 -> P_2(a_14), ~P_2(a_14) we can infer ~p_4 via modus tollens. Finally, from ~p_4 -> q, ~p_4 we can infer q via modus ponens, which contradicts ~q. Therefore, the answer is no.