Consider the following premises. forall z_2: T(z_2) -> U(z_2). exists z_2: T(z_2) or ~U(z_2). Can we infer forall z_2: ~(U(z_2) <-> T(z_2)) from them? If possible, name the inference rules being used at each step.
 From exists z_2: T(z_2) or ~U(z_2) we can infer exists z_2: U(z_2) -> T(z_2) via existential rewriting. Finally, from exists z_2: U(z_2) -> T(z_2), forall z_2: T(z_2) -> U(z_2) we can infer exists z_2: U(z_2) <-> T(z_2) via existential biconditional introduction, which contradicts forall z_2: ~(U(z_2) <-> T(z_2)). Therefore, the answer is no.