Consider the following premises. forall x_13: Q_9(x_13) -> U_4(x_13). forall x_13: P_13(x_13). forall x_13: P_13(x_13) -> Q_9(x_13). forall x_13: Q_13(x_13). Can we infer forall x_13: U_4(x_13) or Q_1(x_13) from them? If possible, name the inference rules being used at each step.
 From forall x_13: P_13(x_13), forall x_13: Q_13(x_13) we can infer forall x_13: P_13(x_13) and Q_13(x_13) via universal conjunction. From forall x_13: P_13(x_13) -> Q_9(x_13), forall x_13: Q_9(x_13) -> U_4(x_13) we can infer forall x_13: P_13(x_13) -> U_4(x_13) via universal transitivity. From forall x_13: P_13(x_13) and Q_13(x_13) we can infer forall x_13: P_13(x_13) via universal simplification. From forall x_13: P_13(x_13) -> U_4(x_13), forall x_13: P_13(x_13) we can infer forall x_13: U_4(x_13) via universal modus ponens. Finally, from forall x_13: U_4(x_13) we can infer forall x_13: U_4(x_13) or Q_1(x_13) via universal addition. Therefore, the answer is yes.