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