Consider the following premises. forall z: S(z). exists z: T_4(z). forall z: T(z) <-> S(z). Can we infer forall z: ~(T_4(z) and T(z)) from them? If possible, name the inference rules being used at each step.
 From forall z: T(z) <-> S(z) we can infer forall z: S(z) -> T(z) via universal biconditional elimination. From forall z: S(z) -> T(z), forall z: S(z) we can infer forall z: T(z) via universal modus ponens. Finally, from exists z: T_4(z), forall z: T(z) we can infer exists z: T_4(z) and T(z) via existential conjunction, which contradicts forall z: ~(T_4(z) and T(z)). Therefore, the answer is no.