Consider the following premises. P_7(a_5) or s. forall x_7: Q_7(x_7). forall x_7: P_7(x_7) -> ~Q_7(x_7). Can we infer s from them? If possible, name the inference rules being used at each step.
 From forall x_7: P_7(x_7) -> ~Q_7(x_7), forall x_7: Q_7(x_7) we can infer forall x_7: ~P_7(x_7) via universal modus tollens. From forall x_7: ~P_7(x_7) we can infer ~P_7(a_5) via universal instantiation. Finally, from P_7(a_5) or s, ~P_7(a_5) we can infer s via disjunctive syllogism. Therefore, the answer is yes.