Consider the following premises. forall z_3: R_1(z_3) -> W(z_3). forall z_3: T_3(z_3) <-> W(z_3). forall z_3: W(z_3) -> R_1(z_3). forall z_3: ~R_1(z_3). Can we infer exists z_3: T_3(z_3) from them? If possible, name the inference rules being used at each step.
 From forall z_3: R_1(z_3) -> W(z_3), forall z_3: W(z_3) -> R_1(z_3) we can infer forall z_3: R_1(z_3) <-> W(z_3) via universal biconditional introduction. From forall z_3: R_1(z_3) <-> W(z_3), forall z_3: ~R_1(z_3) we can infer forall z_3: ~W(z_3) via universal biconditional elimination. Finally, from forall z_3: T_3(z_3) <-> W(z_3), forall z_3: ~W(z_3) we can infer forall z_3: ~T_3(z_3) via universal biconditional elimination, which contradicts exists z_3: T_3(z_3). Therefore, the answer is no.