Consider the following premises. forall z: U_4(z) -> S(z). forall z: S(z) -> U_4(z). forall z: U_4(z). Can we infer forall z: S(z) from them? If possible, name the inference rules being used at each step.
 From forall z: U_4(z) -> S(z), forall z: S(z) -> U_4(z) we can infer forall z: U_4(z) <-> S(z) via universal biconditional introduction. From forall z: U_4(z) <-> S(z) we can infer forall z: U_4(z) -> S(z) via universal biconditional elimination. Finally, from forall z: U_4(z) -> S(z), forall z: U_4(z) we can infer forall z: S(z) via universal modus ponens. Therefore, the answer is yes.