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