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