Consider the following premises. forall x_8: ~Q_8(x_8) or R_5(x_8). forall x_8: P_8(x_8) -> Q_8(x_8). ~Q_6(a_3). forall x_8: P_8(x_8). Can we infer R_5(a_3) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) -> Q_8(x_8), forall x_8: P_8(x_8) we can infer forall x_8: Q_8(x_8) via universal modus ponens. From forall x_8: Q_8(x_8) we can infer forall x_8: Q_8(x_8) or Q_6(x_8) via universal addition. From forall x_8: Q_8(x_8) or Q_6(x_8), forall x_8: ~Q_8(x_8) or R_5(x_8) we can infer forall x_8: Q_6(x_8) or R_5(x_8) via universal resolution. From forall x_8: Q_6(x_8) or R_5(x_8) we can infer Q_6(a_3) or R_5(a_3) via universal instantiation. Finally, from Q_6(a_3) or R_5(a_3), ~Q_6(a_3) we can infer R_5(a_3) via disjunctive syllogism. Therefore, the answer is yes.