Consider the following premises. forall z: U(z) -> P(z). forall z: Q_3(z) <-> P(z). exists z: U(z) or ~Q_3(z). Can we infer forall z: ~(P(z) <-> Q_3(z)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.