Consider the following premises. forall x_1: W(x_1). forall x_1: T(x_1) -> W_4(x_1). forall x_1: W(x_1) -> T(x_1). Can we infer forall x_1: W_4(x_1) or S(x_1) from them? If possible, name the inference rules being used at each step.
 From forall x_1: W(x_1) -> T(x_1), forall x_1: T(x_1) -> W_4(x_1) we can infer forall x_1: W(x_1) -> W_4(x_1) via universal transitivity. From forall x_1: W(x_1) -> W_4(x_1), forall x_1: W(x_1) we can infer forall x_1: W_4(x_1) via universal modus ponens. Finally, from forall x_1: W_4(x_1) we can infer forall x_1: W_4(x_1) or S(x_1) via universal addition. Therefore, the answer is yes.