Consider the following premises. forall x: Q(x) -> W(x). forall x: W_3(x) -> Q(x). forall x: W_3(x) or ~W(x). Can we infer exists x: ~(W(x) -> W_3(x)) from them?
 From forall x: W_3(x) -> Q(x), forall x: Q(x) -> W(x) we can infer forall x: W_3(x) -> W(x). From forall x: W_3(x) or ~W(x) we can infer forall x: W(x) -> W_3(x). From forall x: W_3(x) -> W(x), forall x: W(x) -> W_3(x) we can infer forall x: W_3(x) <-> W(x). Finally, from forall x: W_3(x) <-> W(x) we can infer forall x: W(x) -> W_3(x), which contradicts exists x: ~(W(x) -> W_3(x)). Therefore, the answer is no.