Consider the following premises. forall x_16: Q_9(x_16) -> S_2(x_16). forall x_16: R(x_16). forall x_16: R_16(x_16) -> Q_9(x_16). forall x_16: Q_16(x_16) -> R_16(x_16). forall x_16: S_2(x_16) -> Q(x_16). forall x_16: P_16(x_16) -> R_16(x_16). forall x_16: P_16(x_16) or Q_16(x_16). Can we infer forall x_16: R(x_16) and Q(x_16) from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) -> R_16(x_16), forall x_16: Q_16(x_16) -> R_16(x_16), forall x_16: P_16(x_16) or Q_16(x_16) we can infer forall x_16: R_16(x_16) via universal disjunction elimination. From forall x_16: R_16(x_16) -> Q_9(x_16), forall x_16: R_16(x_16) we can infer forall x_16: Q_9(x_16) via universal modus ponens. From forall x_16: Q_9(x_16) -> S_2(x_16), forall x_16: Q_9(x_16) we can infer forall x_16: S_2(x_16) via universal modus ponens. From forall x_16: S_2(x_16) -> Q(x_16), forall x_16: S_2(x_16) we can infer forall x_16: Q(x_16) via universal modus ponens. Finally, from forall x_16: R(x_16), forall x_16: Q(x_16) we can infer forall x_16: R(x_16) and Q(x_16) via universal conjunction. Therefore, the answer is yes.