Consider the following premises. forall x_8: ~P_2(x_8) or R_2(x_8). forall x_8: P_2(x_8) or S_2(x_8). exists x_8: ~P_8(x_8). forall x_8: P_8(x_8) <-> S_2(x_8). Can we infer exists x_8: R_2(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) <-> S_2(x_8), exists x_8: ~P_8(x_8) we can infer exists x_8: ~S_2(x_8) via existential biconditional elimination. From forall x_8: P_2(x_8) or S_2(x_8), forall x_8: ~P_2(x_8) or R_2(x_8) we can infer forall x_8: S_2(x_8) or R_2(x_8) via universal resolution. Finally, from forall x_8: S_2(x_8) or R_2(x_8), exists x_8: ~S_2(x_8) we can infer exists x_8: R_2(x_8) via existential disjunctive syllogism. Therefore, the answer is yes.