Consider the following premises. exists y_4: T(y_4) -> W(y_4). forall y_4: T(y_4) <-> W(y_4). forall y_4: ~T(y_4). Can we infer exists y_4: ~W(y_4) from them?
 From forall y_4: T(y_4) <-> W(y_4) we can infer forall y_4: W(y_4) -> T(y_4). From exists y_4: T(y_4) -> W(y_4), forall y_4: W(y_4) -> T(y_4) we can infer exists y_4: T(y_4) <-> W(y_4). Finally, from exists y_4: T(y_4) <-> W(y_4), forall y_4: ~T(y_4) we can infer exists y_4: ~W(y_4). Therefore, the answer is yes.