Consider the following premises. forall x_13: Q_13(x_13) -> R_13(x_13). forall x_13: P_13(x_13) -> R_13(x_13). forall x_13: P_13(x_13) or Q_13(x_13). forall x_13: P_7(x_13) -> ~R_13(x_13). P_7(a_5) or p_1. Can we infer p_1 from them? If possible, name the inference rules being used at each step.
 From forall x_13: P_13(x_13) -> R_13(x_13), forall x_13: Q_13(x_13) -> R_13(x_13), forall x_13: P_13(x_13) or Q_13(x_13) we can infer forall x_13: R_13(x_13) via universal disjunction elimination. From forall x_13: P_7(x_13) -> ~R_13(x_13), forall x_13: R_13(x_13) we can infer forall x_13: ~P_7(x_13) via universal modus tollens. From forall x_13: ~P_7(x_13) we can infer ~P_7(a_5) via universal instantiation. Finally, from P_7(a_5) or p_1, ~P_7(a_5) we can infer p_1 via disjunctive syllogism. Therefore, the answer is yes.