Consider the following premises. exists z_2: T(z_2) -> R_4(z_2). forall z_2: R_4(z_2) -> T(z_2). forall z_2: T(z_2). Can we infer forall z_2: ~R_4(z_2) from them? If possible, name the inference rules being used at each step.
 From forall z_2: R_4(z_2) -> T(z_2), exists z_2: T(z_2) -> R_4(z_2) we can infer exists z_2: R_4(z_2) <-> T(z_2) via existential biconditional introduction. From exists z_2: R_4(z_2) <-> T(z_2) we can infer exists z_2: T(z_2) -> R_4(z_2) via existential biconditional elimination. Finally, from exists z_2: T(z_2) -> R_4(z_2), forall z_2: T(z_2) we can infer exists z_2: R_4(z_2) via existential modus ponens, which contradicts forall z_2: ~R_4(z_2). Therefore, the answer is no.