Consider the following premises. s_2 -> T_4(a). s_2 or T_3(a). forall z: T_3(z) -> T_4(z). Can we infer ~T_4(a) from them? If possible, name the inference rules being used at each step.
 From forall z: T_3(z) -> T_4(z) we can infer T_3(a) -> T_4(a) via universal instantiation. Finally, from s_2 -> T_4(a), T_3(a) -> T_4(a), s_2 or T_3(a) we can infer T_4(a) via disjunction elimination, which contradicts ~T_4(a). Therefore, the answer is no.