Consider the following premises. forall x_11: S_2(x_11) <-> P_11(x_11). forall x_11: P_11(x_11) -> ~Q_11(x_11). p -> S_2(a_5). forall x_11: Q_11(x_11). Can we infer ~p from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) -> ~Q_11(x_11), forall x_11: Q_11(x_11) we can infer forall x_11: ~P_11(x_11) via universal modus tollens. From forall x_11: S_2(x_11) <-> P_11(x_11), forall x_11: ~P_11(x_11) we can infer forall x_11: ~S_2(x_11) via universal biconditional elimination. From forall x_11: ~S_2(x_11) we can infer ~S_2(a_5) via universal instantiation. Finally, from p -> S_2(a_5), ~S_2(a_5) we can infer ~p via modus tollens. Therefore, the answer is yes.