Consider the following premises. forall z: P(z) -> U(z). forall z: U(z) <-> T_1(z). forall z: P(z) <-> T_1(z). Can we infer exists z: ~(T_1(z) -> U(z)) from them?
 From forall z: P(z) <-> T_1(z) we can infer forall z: T_1(z) -> P(z). From forall z: T_1(z) -> P(z), forall z: P(z) -> U(z) we can infer forall z: T_1(z) -> U(z). From forall z: U(z) <-> T_1(z) we can infer forall z: U(z) -> T_1(z). From forall z: U(z) -> T_1(z), forall z: T_1(z) -> U(z) we can infer forall z: U(z) <-> T_1(z). Finally, from forall z: U(z) <-> T_1(z) we can infer forall z: T_1(z) -> U(z), which contradicts exists z: ~(T_1(z) -> U(z)). Therefore, the answer is no.