Consider the following premises. forall x_4: S(x_4) or ~R(x_4). forall x_4: Q_2(x_4) -> R(x_4). forall x_4: P(x_4) -> Q_2(x_4). Can we infer forall x_4: P(x_4) -> S(x_4) from them? If possible, name the inference rules being used at each step.
 From forall x_4: P(x_4) -> Q_2(x_4), forall x_4: Q_2(x_4) -> R(x_4) we can infer forall x_4: P(x_4) -> R(x_4) via universal transitivity. From forall x_4: S(x_4) or ~R(x_4) we can infer forall x_4: R(x_4) -> S(x_4) via universal rewriting. Finally, from forall x_4: P(x_4) -> R(x_4), forall x_4: R(x_4) -> S(x_4) we can infer forall x_4: P(x_4) -> S(x_4) via universal transitivity. Therefore, the answer is yes.