Consider the following premises. forall x_7: Q_7(x_7). w -> P_7(h_2). forall x_7: P_7(x_7) -> ~Q_7(x_7). Can we infer ~w 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(h_2) via universal instantiation. Finally, from w -> P_7(h_2), ~P_7(h_2) we can infer ~w via modus tollens. Therefore, the answer is yes.