Consider the following premises. exists x_15: Q_15(x_15) -> W(x_15). forall x_15: Q(x_15) <-> W(x_15). forall x_15: U(x_15) -> Q_15(x_15). forall x_15: U(x_15). Can we infer forall x_15: ~Q(x_15) from them? If possible, name the inference rules being used at each step.
 From forall x_15: U(x_15) -> Q_15(x_15), exists x_15: Q_15(x_15) -> W(x_15) we can infer exists x_15: U(x_15) -> W(x_15) via existential transitivity. From forall x_15: Q(x_15) <-> W(x_15) we can infer forall x_15: W(x_15) -> Q(x_15) via universal biconditional elimination. From exists x_15: U(x_15) -> W(x_15), forall x_15: U(x_15) we can infer exists x_15: W(x_15) via existential modus ponens. Finally, from forall x_15: W(x_15) -> Q(x_15), exists x_15: W(x_15) we can infer exists x_15: Q(x_15) via existential modus ponens, which contradicts forall x_15: ~Q(x_15). Therefore, the answer is no.