Consider the following premises. q -> T_4(i). forall x: R_4(x) -> T_4(x). q or p_1. p_1 -> R_4(i). Can we infer ~T_4(i) from them? If possible, name the inference rules being used at each step.
 From forall x: R_4(x) -> T_4(x) we can infer R_4(i) -> T_4(i) via universal instantiation. From p_1 -> R_4(i), R_4(i) -> T_4(i) we can infer p_1 -> T_4(i) via transitivity. Finally, from q -> T_4(i), p_1 -> T_4(i), q or p_1 we can infer T_4(i) via disjunction elimination, which contradicts ~T_4(i). Therefore, the answer is no.