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