Consider the following premises. forall x: S_3(x) -> W(x). forall x: W(x) -> S_3(x). forall x: S_3(x) or ~Q(x). forall x: R_4(x) -> Q(x). Can we infer forall x: R_4(x) -> W(x) from them? If possible, name the inference rules being used at each step.
 From forall x: W(x) -> S_3(x), forall x: S_3(x) -> W(x) we can infer forall x: W(x) <-> S_3(x) via universal biconditional introduction. From forall x: W(x) <-> S_3(x) we can infer forall x: S_3(x) -> W(x) via universal biconditional elimination. From forall x: S_3(x) or ~Q(x) we can infer forall x: Q(x) -> S_3(x) via universal rewriting. From forall x: R_4(x) -> Q(x), forall x: Q(x) -> S_3(x) we can infer forall x: R_4(x) -> S_3(x) via universal transitivity. Finally, from forall x: R_4(x) -> S_3(x), forall x: S_3(x) -> W(x) we can infer forall x: R_4(x) -> W(x) via universal transitivity. Therefore, the answer is yes.