Consider the following premises. ~Q(a_3) or s. forall x_6: P_6(x_6) -> Q(x_6). forall x_6: P_6(x_6). Can we infer Q_4(a_3) or s from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) -> Q(x_6), forall x_6: P_6(x_6) we can infer forall x_6: Q(x_6) via universal modus ponens. From forall x_6: Q(x_6) we can infer forall x_6: Q(x_6) or Q_4(x_6) via universal addition. From forall x_6: Q(x_6) or Q_4(x_6) we can infer Q(a_3) or Q_4(a_3) via universal instantiation. Finally, from Q(a_3) or Q_4(a_3), ~Q(a_3) or s we can infer Q_4(a_3) or s via resolution. Therefore, the answer is yes.