Consider the following premises. exists z: ~S(z). forall z: S(z) or ~R(z). forall z: R(z) or ~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: R(z) or ~S(z) we can infer forall z: S(z) -> R(z) via universal rewriting. From forall z: S(z) or ~R(z) we can infer forall z: R(z) -> S(z) via universal rewriting. From forall z: S(z) -> R(z), forall z: R(z) -> S(z) we can infer forall z: S(z) <-> R(z) via universal biconditional introduction. Finally, from forall z: S(z) <-> R(z), exists 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.