Consider the following premises. p -> ~Q_11(c_2). forall x_11: ~P_11(x_11). forall x_11: P_11(x_11) or 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) or Q_11(x_11), forall x_11: ~P_11(x_11) we can infer forall x_11: Q_11(x_11) via universal disjunctive syllogism. From forall x_11: Q_11(x_11) we can infer Q_11(c_2) via universal instantiation. Finally, from p -> ~Q_11(c_2), Q_11(c_2) we can infer ~p via modus tollens. Therefore, the answer is yes.