Consider the following premises. forall z: R_2(z) -> R(z). exists z: R_2(z) <-> R(z). Can we infer forall z: ~(R(z) <-> R_2(z)) from them? If possible, name the inference rules being used at each step.
 From exists z: R_2(z) <-> R(z) we can infer exists z: R(z) -> R_2(z) via existential biconditional elimination. Finally, from exists z: R(z) -> R_2(z), forall z: R_2(z) -> R(z) we can infer exists z: R(z) <-> R_2(z) via existential biconditional introduction, which contradicts forall z: ~(R(z) <-> R_2(z)). Therefore, the answer is no.