Consider the following premises. forall x_14: R_1(x_14). P_1(a_1). forall x_14: Q_14(x_14). Can we infer exists x_14: P_1(x_14) and R_1(x_14) from them? If possible, name the inference rules being used at each step.
 From forall x_14: R_1(x_14), forall x_14: Q_14(x_14) we can infer forall x_14: R_1(x_14) and Q_14(x_14) via universal conjunction. From forall x_14: R_1(x_14) and Q_14(x_14) we can infer forall x_14: R_1(x_14) via universal simplification. From P_1(a_1) we can infer exists x_14: P_1(x_14) via existential generalization. Finally, from exists x_14: P_1(x_14), forall x_14: R_1(x_14) we can infer exists x_14: P_1(x_14) and R_1(x_14) via existential conjunction. Therefore, the answer is yes.