Consider the following premises. ~R_1(i_2). forall z: T(z) -> R_1(z). forall z: R_1(z) -> T(z). Can we infer ~T(i_2) from them? If possible, name the inference rules being used at each step.
 From forall z: R_1(z) -> T(z), forall z: T(z) -> R_1(z) we can infer forall z: R_1(z) <-> T(z) via universal biconditional introduction. From forall z: R_1(z) <-> T(z) we can infer R_1(i_2) <-> T(i_2) via universal instantiation. Finally, from R_1(i_2) <-> T(i_2), ~R_1(i_2) we can infer ~T(i_2) via biconditional elimination. Therefore, the answer is yes.