Consider the following premises. forall z_1: U(z_1) or ~W(z_1). forall z_1: P_1(z_1) -> W(z_1). Can we infer forall z_1: P_1(z_1) -> U(z_1) from them? If possible, name the inference rules being used at each step.
 From forall z_1: U(z_1) or ~W(z_1) we can infer forall z_1: W(z_1) -> U(z_1) via universal rewriting. Finally, from forall z_1: P_1(z_1) -> W(z_1), forall z_1: W(z_1) -> U(z_1) we can infer forall z_1: P_1(z_1) -> U(z_1) via universal transitivity. Therefore, the answer is yes.