Consider the following premises. exists x_3: ~T_4(x_3) or U(x_3). forall x_3: P_3(x_3). forall x_3: P_3(x_3) -> T_4(x_3). Can we infer exists x_3: T(x_3) or U(x_3) from them? If possible, name the inference rules being used at each step.
 From forall x_3: P_3(x_3) -> T_4(x_3), forall x_3: P_3(x_3) we can infer forall x_3: T_4(x_3) via universal modus ponens. From forall x_3: T_4(x_3) we can infer forall x_3: T_4(x_3) or T(x_3) via universal addition. Finally, from forall x_3: T_4(x_3) or T(x_3), exists x_3: ~T_4(x_3) or U(x_3) we can infer exists x_3: T(x_3) or U(x_3) via existential resolution. Therefore, the answer is yes.