Consider the following premises. exists z: Q_1(z) -> R_4(z). forall z: Q(z) <-> R_4(z). forall z: Q_1(z) <-> Q(z). Can we infer forall z: ~(Q(z) -> R_4(z)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.