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