Consider the following premises. forall z: S_1(z) -> T_1(z). exists z: S_1(z) <-> U(z). forall z: T_1(z) -> S_1(z). forall z: ~T_1(z). Can we infer forall z: U(z) from them? If possible, name the inference rules being used at each step.
 From forall z: T_1(z) -> S_1(z), forall z: S_1(z) -> T_1(z) we can infer forall z: T_1(z) <-> S_1(z) via universal biconditional introduction. From forall z: T_1(z) <-> S_1(z), forall z: ~T_1(z) we can infer forall z: ~S_1(z) via universal biconditional elimination. Finally, from exists z: S_1(z) <-> U(z), forall z: ~S_1(z) we can infer exists z: ~U(z) via existential biconditional elimination, which contradicts forall z: U(z). Therefore, the answer is no.