Consider the following premises. exists x_2: ~W_1(x_2). forall x_2: ~P_2(x_2) or U_3(x_2). forall x_2: P_2(x_2) or W_1(x_2). Can we infer exists x_2: U_3(x_2) from them? If possible, name the inference rules being used at each step.
 From forall x_2: P_2(x_2) or W_1(x_2), forall x_2: ~P_2(x_2) or U_3(x_2) we can infer forall x_2: W_1(x_2) or U_3(x_2) via universal resolution. Finally, from forall x_2: W_1(x_2) or U_3(x_2), exists x_2: ~W_1(x_2) we can infer exists x_2: U_3(x_2) via existential disjunctive syllogism. Therefore, the answer is yes.