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