Consider the following premises. exists z: ~R_1(z). forall z: Q(z) <-> T_3(z). forall z: R_1(z) <-> Q(z). Can we infer exists z: ~T_3(z) from them? If possible, name the inference rules being used at each step.
 From forall z: R_1(z) <-> Q(z), exists z: ~R_1(z) we can infer exists z: ~Q(z) via existential biconditional elimination. From forall z: Q(z) <-> T_3(z) we can infer forall z: T_3(z) -> Q(z) via universal biconditional elimination. Finally, from forall z: T_3(z) -> Q(z), exists z: ~Q(z) we can infer exists z: ~T_3(z) via existential modus tollens. Therefore, the answer is yes.