Consider the following premises. forall z: T_4(z) or ~T_1(z). forall z: T_1(z) or ~T_4(z). Can we infer T_4(a_2) -> T_1(a_2) from them? If possible, name the inference rules being used at each step.
 From forall z: T_1(z) or ~T_4(z) we can infer forall z: T_4(z) -> T_1(z) via universal rewriting. From forall z: T_4(z) or ~T_1(z) we can infer forall z: T_1(z) -> T_4(z) via universal rewriting. From forall z: T_4(z) -> T_1(z), forall z: T_1(z) -> T_4(z) we can infer forall z: T_4(z) <-> T_1(z) via universal biconditional introduction. From forall z: T_4(z) <-> T_1(z) we can infer T_4(a_2) <-> T_1(a_2) via universal instantiation. Finally, from T_4(a_2) <-> T_1(a_2) we can infer T_4(a_2) -> T_1(a_2) via biconditional elimination. Therefore, the answer is yes.