Consider the following premises. exists z: T_2(z) <-> S_4(z). forall z: Q(z) -> T_2(z). forall z: ~T(z) or Q(z). forall z: T(z) or S_4(z). Can we infer exists z: T_2(z) from them? If possible, name the inference rules being used at each step.
 From exists z: T_2(z) <-> S_4(z) we can infer exists z: S_4(z) -> T_2(z) via existential biconditional elimination. From forall z: T(z) or S_4(z), forall z: ~T(z) or Q(z) we can infer forall z: S_4(z) or Q(z) via universal resolution. Finally, from exists z: S_4(z) -> T_2(z), forall z: Q(z) -> T_2(z), forall z: S_4(z) or Q(z) we can infer exists z: T_2(z) via existential disjunction elimination. Therefore, the answer is yes.