Consider the following premises. exists x_12: P_2(x_12) -> Q_2(x_12). forall x_12: P_2(x_12). forall x_12: R(x_12) and Q_12(x_12). Can we infer exists x_12: R(x_12) and Q_2(x_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: R(x_12) and Q_12(x_12) we can infer forall x_12: R(x_12) via universal simplification. From exists x_12: P_2(x_12) -> Q_2(x_12), forall x_12: P_2(x_12) we can infer exists x_12: Q_2(x_12) via existential modus ponens. Finally, from forall x_12: R(x_12), exists x_12: Q_2(x_12) we can infer exists x_12: R(x_12) and Q_2(x_12) via existential conjunction. Therefore, the answer is yes.