Consider the following premises. forall x_2: ~P_2(x_2). forall x_2: P_2(x_2) or U(x_2). forall x_2: U(x_2) -> S_1(x_2). Can we infer forall x_2: S_1(x_2) from them? If possible, name the inference rules being used at each step.
 From forall x_2: P_2(x_2) or U(x_2), forall x_2: ~P_2(x_2) we can infer forall x_2: U(x_2) via universal disjunctive syllogism. Finally, from forall x_2: U(x_2) -> S_1(x_2), forall x_2: U(x_2) we can infer forall x_2: S_1(x_2) via universal modus ponens. Therefore, the answer is yes.