Consider the following premises. forall x_2: ~P_2(x_2) or R_3(x_2). exists x_2: P_2(x_2) or W_3(x_2). forall x_2: R_3(x_2) -> R(x_2). forall x_2: W_3(x_2) -> R(x_2). Can we infer exists x_2: R(x_2) from them? If possible, name the inference rules being used at each step.
 From exists x_2: P_2(x_2) or W_3(x_2), forall x_2: ~P_2(x_2) or R_3(x_2) we can infer exists x_2: W_3(x_2) or R_3(x_2) via existential resolution. Finally, from forall x_2: W_3(x_2) -> R(x_2), forall x_2: R_3(x_2) -> R(x_2), exists x_2: W_3(x_2) or R_3(x_2) we can infer exists x_2: R(x_2) via existential disjunction elimination. Therefore, the answer is yes.