Consider the following premises. forall z_1: ~W(z_1). forall z_1: R(z_1) -> T(z_1). exists z_1: R_3(z_1) <-> T(z_1). forall z_1: W(z_1) or R(z_1). Can we infer forall z_1: ~T(z_1) from them? If possible, name the inference rules being used at each step.
 From forall z_1: W(z_1) or R(z_1), forall z_1: ~W(z_1) we can infer forall z_1: R(z_1) via universal disjunctive syllogism. From forall z_1: R(z_1) we can infer forall z_1: R(z_1) or R_3(z_1) via universal addition. From exists z_1: R_3(z_1) <-> T(z_1) we can infer exists z_1: R_3(z_1) -> T(z_1) via existential biconditional elimination. Finally, from forall z_1: R(z_1) -> T(z_1), exists z_1: R_3(z_1) -> T(z_1), forall z_1: R(z_1) or R_3(z_1) we can infer exists z_1: T(z_1) via existential disjunction elimination, which contradicts forall z_1: ~T(z_1). Therefore, the answer is no.