Consider the following premises. forall x_2: ~U_2(x_2). forall x_2: ~P_2(x_2) or R_2(x_2). forall x_2: P_2(x_2) or U_2(x_2). Can we infer exists x_2: ~R_2(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 R_2(x_2) we can infer forall x_2: U_2(x_2) or R_2(x_2) via universal resolution. Finally, from forall x_2: U_2(x_2) or R_2(x_2), forall x_2: ~U_2(x_2) we can infer forall x_2: R_2(x_2) via universal disjunctive syllogism, which contradicts exists x_2: ~R_2(x_2). Therefore, the answer is no.