Consider the following premises. exists z: W_2(z) <-> T(z). forall z: ~R(z). forall z: R(z) <-> W(z). forall z: W(z) <-> W_2(z). Can we infer forall z: T(z) from them? If possible, name the inference rules being used at each step.
 From forall z: R(z) <-> W(z), forall z: ~R(z) we can infer forall z: ~W(z) via universal biconditional elimination. From forall z: W(z) <-> W_2(z), forall z: ~W(z) we can infer forall z: ~W_2(z) via universal biconditional elimination. Finally, from exists z: W_2(z) <-> T(z), forall z: ~W_2(z) we can infer exists z: ~T(z) via existential biconditional elimination, which contradicts forall z: T(z). Therefore, the answer is no.