Consider the following premises. forall z_1: ~S_1(z_1). exists z_1: W(z_1) <-> S_1(z_1). Can we infer forall z_1: W(z_1) from them?
 From exists z_1: W(z_1) <-> S_1(z_1) we can infer exists z_1: W(z_1) -> S_1(z_1). Finally, from exists z_1: W(z_1) -> S_1(z_1), forall z_1: ~S_1(z_1) we can infer exists z_1: ~W(z_1), which contradicts forall z_1: W(z_1). Therefore, the answer is no.