Consider the following premises. forall x_2: P_2(x_2) or U_2(x_2). exists x_2: ~U_2(x_2). forall x_2: ~P_2(x_2) or T(x_2). Can we infer forall x_2: ~T(x_2) from them? If possible, name the inference rules being used at each step.
 From forall x_2: P_2(x_2) or U_2(x_2), forall x_2: ~P_2(x_2) or T(x_2) we can infer forall x_2: U_2(x_2) or T(x_2) via universal resolution. Finally, from forall x_2: U_2(x_2) or T(x_2), exists x_2: ~U_2(x_2) we can infer exists x_2: T(x_2) via existential disjunctive syllogism, which contradicts forall x_2: ~T(x_2). Therefore, the answer is no.