Consider the following premises. exists z: U(z) <-> Q_2(z). forall z: Q_2(z) <-> U(z). Can we infer forall z: ~(U(z) -> Q_2(z)) from them? If possible, name the inference rules being used at each step.
 From exists z: U(z) <-> Q_2(z) we can infer exists z: Q_2(z) -> U(z) via existential biconditional elimination. Finally, from forall z: Q_2(z) <-> U(z) we can infer forall z: U(z) -> Q_2(z) via universal biconditional elimination, which contradicts forall z: ~(U(z) -> Q_2(z)). Therefore, the answer is no.