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