Consider the following premises. forall x_15: P_15(x_15) <-> Q_15(x_15). exists x_15: ~P_15(x_15). forall x_15: Q_15(x_15) or W(x_15). forall x_15: Q(x_15) -> ~W(x_15). Can we infer exists x_15: ~Q(x_15) from them? If possible, name the inference rules being used at each step.
 From forall x_15: P_15(x_15) <-> Q_15(x_15), exists x_15: ~P_15(x_15) we can infer exists x_15: ~Q_15(x_15) via existential biconditional elimination. From forall x_15: Q_15(x_15) or W(x_15), exists x_15: ~Q_15(x_15) we can infer exists x_15: W(x_15) via existential disjunctive syllogism. Finally, from forall x_15: Q(x_15) -> ~W(x_15), exists x_15: W(x_15) we can infer exists x_15: ~Q(x_15) via existential modus tollens. Therefore, the answer is yes.