Consider the following premises. forall y: S(y) and W_4(y). Can we infer exists y: ~(S(y) or P(y)) from them?
 From forall y: S(y) and W_4(y) we can infer forall y: S(y). Finally, from forall y: S(y) we can infer forall y: S(y) or P(y), which contradicts exists y: ~(S(y) or P(y)). Therefore, the answer is no.