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