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