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