Consider the following premises. exists x_9: P_9(x_9) <-> U(x_9). forall x_9: P_9(x_9) <-> Q_3(x_9). Can we infer forall x_9: ~(U(x_9) -> Q_3(x_9)) from them? If possible, name the inference rules being used at each step.
 From exists x_9: P_9(x_9) <-> U(x_9) we can infer exists x_9: U(x_9) -> P_9(x_9) via existential biconditional elimination. Finally, from forall x_9: P_9(x_9) <-> Q_3(x_9) we can infer forall x_9: P_9(x_9) -> Q_3(x_9) via universal biconditional elimination, which contradicts forall x_9: ~(U(x_9) -> Q_3(x_9)). Therefore, the answer is no.