Consider the following premises. ~U_3(e). forall z: U_3(z) -> S(z). forall z: W_4(z) or ~S(z). forall z: W_4(z) -> U_3(z). Can we infer S(e) from them? If possible, name the inference rules being used at each step.
 From forall z: W_4(z) or ~S(z) we can infer forall z: S(z) -> W_4(z) via universal rewriting. From forall z: S(z) -> W_4(z), forall z: W_4(z) -> U_3(z) we can infer forall z: S(z) -> U_3(z) via universal transitivity. From forall z: U_3(z) -> S(z), forall z: S(z) -> U_3(z) we can infer forall z: U_3(z) <-> S(z) via universal biconditional introduction. From forall z: U_3(z) <-> S(z) we can infer U_3(e) <-> S(e) via universal instantiation. Finally, from U_3(e) <-> S(e), ~U_3(e) we can infer ~S(e) via biconditional elimination, which contradicts S(e). Therefore, the answer is no.