Consider the following premises. exists z_4: R_3(z_4) or R(z_4). forall z_4: ~R_3(z_4) or T_1(z_4). forall z_4: Q(z_4) <-> T_1(z_4). forall z_4: R(z_4) <-> Q(z_4). Can we infer exists z_4: Q(z_4) from them? If possible, name the inference rules being used at each step.
 From exists z_4: R_3(z_4) or R(z_4), forall z_4: ~R_3(z_4) or T_1(z_4) we can infer exists z_4: R(z_4) or T_1(z_4) via existential resolution. From forall z_4: R(z_4) <-> Q(z_4) we can infer forall z_4: R(z_4) -> Q(z_4) via universal biconditional elimination. From forall z_4: Q(z_4) <-> T_1(z_4) we can infer forall z_4: T_1(z_4) -> Q(z_4) via universal biconditional elimination. Finally, from forall z_4: R(z_4) -> Q(z_4), forall z_4: T_1(z_4) -> Q(z_4), exists z_4: R(z_4) or T_1(z_4) we can infer exists z_4: Q(z_4) via existential disjunction elimination. Therefore, the answer is yes.