Consider the following premises. forall x_5: ~Q_5(x_5). forall x_5: U_1(x_5) -> Q_5(x_5). forall x_5: U_3(x_5) -> ~W(x_5). forall x_5: U_1(x_5) or W(x_5). Can we infer forall x_5: ~U_3(x_5) from them? If possible, name the inference rules being used at each step.
 From forall x_5: U_1(x_5) -> Q_5(x_5), forall x_5: ~Q_5(x_5) we can infer forall x_5: ~U_1(x_5) via universal modus tollens. From forall x_5: U_1(x_5) or W(x_5), forall x_5: ~U_1(x_5) we can infer forall x_5: W(x_5) via universal disjunctive syllogism. Finally, from forall x_5: U_3(x_5) -> ~W(x_5), forall x_5: W(x_5) we can infer forall x_5: ~U_3(x_5) via universal modus tollens. Therefore, the answer is yes.