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