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