Consider the following premises. r_2 <-> T_4(j). forall z: ~T_4(z). Can we infer r_2 from them? If possible, name the inference rules being used at each step.
 From forall z: ~T_4(z) we can infer ~T_4(j) via universal instantiation. Finally, from r_2 <-> T_4(j), ~T_4(j) we can infer ~r_2 via biconditional elimination, which contradicts r_2. Therefore, the answer is no.