Consider the following premises. forall x_9: P_9(x_9) or Q_9(x_9). forall x_9: ~Q_9(x_9). forall x_9: ~P_9(x_9) or R_9(x_9). forall x_9: P_3(x_9). Can we infer P_3(e_2) from them? If possible, name the inference rules being used at each step.
 From forall x_9: P_9(x_9) or Q_9(x_9), forall x_9: ~P_9(x_9) or R_9(x_9) we can infer forall x_9: Q_9(x_9) or R_9(x_9) via universal resolution. From forall x_9: Q_9(x_9) or R_9(x_9), forall x_9: ~Q_9(x_9) we can infer forall x_9: R_9(x_9) via universal disjunctive syllogism. From forall x_9: P_3(x_9), forall x_9: R_9(x_9) we can infer forall x_9: P_3(x_9) and R_9(x_9) via universal conjunction. From forall x_9: P_3(x_9) and R_9(x_9) we can infer P_3(e_2) and R_9(e_2) via universal instantiation. Finally, from P_3(e_2) and R_9(e_2) we can infer P_3(e_2) via simplification. Therefore, the answer is yes.