Consider the following premises. forall z: ~W(z). forall z: T_4(z) -> R(z). exists z: W(z) or ~R(z). forall z: W(z) -> T_4(z). Can we infer forall z: T_4(z) from them? If possible, name the inference rules being used at each step.
 From exists z: W(z) or ~R(z) we can infer exists z: R(z) -> W(z) via existential rewriting. From forall z: T_4(z) -> R(z), exists z: R(z) -> W(z) we can infer exists z: T_4(z) -> W(z) via existential transitivity. From exists z: T_4(z) -> W(z), forall z: W(z) -> T_4(z) we can infer exists z: T_4(z) <-> W(z) via existential biconditional introduction. Finally, from exists z: T_4(z) <-> W(z), forall z: ~W(z) we can infer exists z: ~T_4(z) via existential biconditional elimination, which contradicts forall z: T_4(z). Therefore, the answer is no.