Consider the following premises. forall x_4: ~S_1(x_4) or U_1(x_4). forall x_4: P_4(x_4) or Q_4(x_4). forall x_4: ~P_4(x_4) or S_1(x_4). forall x_4: ~Q_4(x_4) or P(x_4). Can we infer forall x_4: P(x_4) or U_1(x_4) from them? If possible, name the inference rules being used at each step.
 From forall x_4: P_4(x_4) or Q_4(x_4), forall x_4: ~P_4(x_4) or S_1(x_4) we can infer forall x_4: Q_4(x_4) or S_1(x_4) via universal resolution. From forall x_4: Q_4(x_4) or S_1(x_4), forall x_4: ~Q_4(x_4) or P(x_4) we can infer forall x_4: S_1(x_4) or P(x_4) via universal resolution. Finally, from forall x_4: S_1(x_4) or P(x_4), forall x_4: ~S_1(x_4) or U_1(x_4) we can infer forall x_4: P(x_4) or U_1(x_4) via universal resolution. Therefore, the answer is yes.