Consider the following premises. exists z_1: S_4(z_1) -> P(z_1). forall z_1: S_4(z_1) or ~W(z_1). forall z_1: P(z_1) <-> U(z_1). Can we infer exists z_1: W(z_1) -> U(z_1) from them? If possible, name the inference rules being used at each step.
 From forall z_1: P(z_1) <-> U(z_1) we can infer forall z_1: P(z_1) -> U(z_1) via universal biconditional elimination. From exists z_1: S_4(z_1) -> P(z_1), forall z_1: P(z_1) -> U(z_1) we can infer exists z_1: S_4(z_1) -> U(z_1) via existential transitivity. From forall z_1: S_4(z_1) or ~W(z_1) we can infer forall z_1: W(z_1) -> S_4(z_1) via universal rewriting. Finally, from forall z_1: W(z_1) -> S_4(z_1), exists z_1: S_4(z_1) -> U(z_1) we can infer exists z_1: W(z_1) -> U(z_1) via existential transitivity. Therefore, the answer is yes.