Consider the following premises. forall x_9: ~R_4(x_9) or P_1(x_9). forall x_9: ~Q_9(x_9). exists x_9: T_2(x_9) <-> Q_9(x_9). forall x_9: R_4(x_9) or T_2(x_9). Can we infer exists x_9: P_1(x_9) from them? If possible, name the inference rules being used at each step.
 From exists x_9: T_2(x_9) <-> Q_9(x_9), forall x_9: ~Q_9(x_9) we can infer exists x_9: ~T_2(x_9) via existential biconditional elimination. From forall x_9: R_4(x_9) or T_2(x_9), forall x_9: ~R_4(x_9) or P_1(x_9) we can infer forall x_9: T_2(x_9) or P_1(x_9) via universal resolution. Finally, from forall x_9: T_2(x_9) or P_1(x_9), exists x_9: ~T_2(x_9) we can infer exists x_9: P_1(x_9) via existential disjunctive syllogism. Therefore, the answer is yes.