Consider the following premises. forall z: W(z) -> R_4(z). exists z: S_2(z) or ~S_4(z). forall z: R_4(z) <-> S_4(z). Can we infer exists z: W(z) -> S_2(z) from them?
 From forall z: R_4(z) <-> S_4(z) we can infer forall z: R_4(z) -> S_4(z). From exists z: S_2(z) or ~S_4(z) we can infer exists z: S_4(z) -> S_2(z). From forall z: R_4(z) -> S_4(z), exists z: S_4(z) -> S_2(z) we can infer exists z: R_4(z) -> S_2(z). Finally, from forall z: W(z) -> R_4(z), exists z: R_4(z) -> S_2(z) we can infer exists z: W(z) -> S_2(z). Therefore, the answer is yes.