Consider the following premises. forall x_6: P_6(x_6) -> Q_6(x_6). forall x_6: ~Q_6(x_6). P_6(i_3) or p. Can we infer ~p from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) -> Q_6(x_6), forall x_6: ~Q_6(x_6) we can infer forall x_6: ~P_6(x_6) via universal modus tollens. From forall x_6: ~P_6(x_6) we can infer ~P_6(i_3) via universal instantiation. Finally, from P_6(i_3) or p, ~P_6(i_3) we can infer p via disjunctive syllogism, which contradicts ~p. Therefore, the answer is no.