Consider the following premises. forall x_9: ~P_9(x_9). forall x_9: P_9(x_9) -> Q(x_9). forall x_9: W(x_9) -> Q_1(x_9). forall x_9: Q(x_9) -> P_9(x_9). forall x_9: Q_1(x_9) -> Q(x_9). Can we infer exists x_9: W(x_9) from them?
 From forall x_9: P_9(x_9) -> Q(x_9), forall x_9: Q(x_9) -> P_9(x_9) we can infer forall x_9: P_9(x_9) <-> Q(x_9). From forall x_9: P_9(x_9) <-> Q(x_9), forall x_9: ~P_9(x_9) we can infer forall x_9: ~Q(x_9). From forall x_9: W(x_9) -> Q_1(x_9), forall x_9: Q_1(x_9) -> Q(x_9) we can infer forall x_9: W(x_9) -> Q(x_9). Finally, from forall x_9: W(x_9) -> Q(x_9), forall x_9: ~Q(x_9) we can infer forall x_9: ~W(x_9), which contradicts exists x_9: W(x_9). Therefore, the answer is no.