Consider the following premises. forall x_9: P_9(x_9) -> U_2(x_9). forall x_9: Q_9(x_9) -> U_2(x_9). forall x_9: R(x_9). exists x_9: P_9(x_9) or Q_9(x_9). Can we infer exists x_9: R(x_9) and U_2(x_9) from them? If possible, name the inference rules being used at each step.
 From forall x_9: P_9(x_9) -> U_2(x_9), forall x_9: Q_9(x_9) -> U_2(x_9), exists x_9: P_9(x_9) or Q_9(x_9) we can infer exists x_9: U_2(x_9) via existential disjunction elimination. Finally, from forall x_9: R(x_9), exists x_9: U_2(x_9) we can infer exists x_9: R(x_9) and U_2(x_9) via existential conjunction. Therefore, the answer is yes.