Consider the following premises. T(h) -> p_2. p_2 or ~P_1(h). forall z: U_4(z) or P_1(z). forall z: ~U_4(z) or T(z). Can we infer p_2 from them? If possible, name the inference rules being used at each step.
 From forall z: U_4(z) or P_1(z), forall z: ~U_4(z) or T(z) we can infer forall z: P_1(z) or T(z) via universal resolution. From forall z: P_1(z) or T(z) we can infer P_1(h) or T(h) via universal instantiation. From p_2 or ~P_1(h) we can infer P_1(h) -> p_2 via rewriting. Finally, from P_1(h) -> p_2, T(h) -> p_2, P_1(h) or T(h) we can infer p_2 via disjunction elimination. Therefore, the answer is yes.