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