Consider the following premises. forall z: T(z). R(a_3) -> p_1. T(a_3) -> p_1. Can we infer ~p_1 from them? If possible, name the inference rules being used at each step.
 From forall z: T(z) we can infer forall z: T(z) or R(z) via universal addition. From forall z: T(z) or R(z) we can infer T(a_3) or R(a_3) via universal instantiation. Finally, from T(a_3) -> p_1, R(a_3) -> p_1, T(a_3) or R(a_3) we can infer p_1 via disjunction elimination, which contradicts ~p_1. Therefore, the answer is no.