Consider the following premises. exists z: Q(z) or ~T_3(z). forall z: T(z) -> T_3(z). forall z: Q(z) -> T(z). forall z: ~T_3(z). Can we infer exists z: ~Q(z) from them? If possible, name the inference rules being used at each step.
 From exists z: Q(z) or ~T_3(z) we can infer exists z: T_3(z) -> Q(z) via existential rewriting. From forall z: Q(z) -> T(z), forall z: T(z) -> T_3(z) we can infer forall z: Q(z) -> T_3(z) via universal transitivity. From exists z: T_3(z) -> Q(z), forall z: Q(z) -> T_3(z) we can infer exists z: T_3(z) <-> Q(z) via existential biconditional introduction. Finally, from exists z: T_3(z) <-> Q(z), forall z: ~T_3(z) we can infer exists z: ~Q(z) via existential biconditional elimination. Therefore, the answer is yes.