Consider the following premises. forall x_9: Q_9(x_9) -> R_1(x_9). exists x_9: P_9(x_9) <-> Q_9(x_9). forall x_9: R_1(x_9) -> P_9(x_9). Can we infer forall x_9: ~(P_9(x_9) <-> R_1(x_9)) from them?
 From exists x_9: P_9(x_9) <-> Q_9(x_9) we can infer exists x_9: P_9(x_9) -> Q_9(x_9). From exists x_9: P_9(x_9) -> Q_9(x_9), forall x_9: Q_9(x_9) -> R_1(x_9) we can infer exists x_9: P_9(x_9) -> R_1(x_9). Finally, from exists x_9: P_9(x_9) -> R_1(x_9), forall x_9: R_1(x_9) -> P_9(x_9) we can infer exists x_9: P_9(x_9) <-> R_1(x_9), which contradicts forall x_9: ~(P_9(x_9) <-> R_1(x_9)). Therefore, the answer is no.