Consider the following premises. exists z: S_4(z) <-> W(z). forall z: S_4(z) -> W(z). forall z: ~W(z). Can we infer forall z: S_4(z) from them?
 From exists z: S_4(z) <-> W(z) we can infer exists z: W(z) -> S_4(z). From forall z: S_4(z) -> W(z), exists z: W(z) -> S_4(z) we can infer exists z: S_4(z) <-> W(z). Finally, from exists z: S_4(z) <-> W(z), forall z: ~W(z) we can infer exists z: ~S_4(z), which contradicts forall z: S_4(z). Therefore, the answer is no.