Consider the following premises. forall x_8: P_8(x_8) or Q_8(x_8). forall x_8: P_8(x_8) -> R_8(x_8). forall x_8: Q_8(x_8) -> R_8(x_8). forall x_8: P_1(x_8) -> Q(x_8). forall x_8: P_1(x_8). Can we infer forall x_8: Q(x_8) and R_8(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) -> R_8(x_8), forall x_8: Q_8(x_8) -> R_8(x_8), forall x_8: P_8(x_8) or Q_8(x_8) we can infer forall x_8: R_8(x_8) via universal disjunction elimination. From forall x_8: P_1(x_8) -> Q(x_8), forall x_8: P_1(x_8) we can infer forall x_8: Q(x_8) via universal modus ponens. Finally, from forall x_8: Q(x_8), forall x_8: R_8(x_8) we can infer forall x_8: Q(x_8) and R_8(x_8) via universal conjunction. Therefore, the answer is yes.