Consider the following premises. forall z: U(z) -> T(z). forall z: T(z) -> ~P_2(z). exists z: T(z) -> U(z). forall z: P_2(z). Can we infer forall z: U(z) from them? If possible, name the inference rules being used at each step.
 From exists z: T(z) -> U(z), forall z: U(z) -> T(z) we can infer exists z: T(z) <-> U(z) via existential biconditional introduction. From forall z: T(z) -> ~P_2(z), forall z: P_2(z) we can infer forall z: ~T(z) via universal modus tollens. Finally, from exists z: T(z) <-> U(z), forall z: ~T(z) we can infer exists z: ~U(z) via existential biconditional elimination, which contradicts forall z: U(z). Therefore, the answer is no.