Consider the following premises. forall y_4: Q(y_4) -> T(y_4). forall y_4: T(y_4) -> W(y_4). forall y_4: W(y_4) -> Q(y_4). forall y_4: W(y_4) or ~T(y_4). Can we infer exists y_4: ~(T(y_4) <-> W(y_4)) from them?
 From forall y_4: W(y_4) or ~T(y_4) we can infer forall y_4: T(y_4) -> W(y_4). From forall y_4: W(y_4) -> Q(y_4), forall y_4: Q(y_4) -> T(y_4) we can infer forall y_4: W(y_4) -> T(y_4). From forall y_4: W(y_4) -> T(y_4), forall y_4: T(y_4) -> W(y_4) we can infer forall y_4: W(y_4) <-> T(y_4). From forall y_4: W(y_4) <-> T(y_4) we can infer forall y_4: W(y_4) -> T(y_4). Finally, from forall y_4: T(y_4) -> W(y_4), forall y_4: W(y_4) -> T(y_4) we can infer forall y_4: T(y_4) <-> W(y_4), which contradicts exists y_4: ~(T(y_4) <-> W(y_4)). Therefore, the answer is no.