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