Consider the following premises. forall z: ~W(z). forall z: T(z) -> R(z). forall z: R_1(z) <-> T(z). forall z: T(z) <-> W(z). exists z: R(z) -> R_1(z). Can we infer exists z: ~R_1(z) from them?
 From forall z: R_1(z) <-> T(z) we can infer forall z: R_1(z) -> T(z). From forall z: T(z) -> R(z), exists z: R(z) -> R_1(z) we can infer exists z: T(z) -> R_1(z). From forall z: T(z) <-> W(z), forall z: ~W(z) we can infer forall z: ~T(z). From exists z: T(z) -> R_1(z), forall z: R_1(z) -> T(z) we can infer exists z: T(z) <-> R_1(z). Finally, from exists z: T(z) <-> R_1(z), forall z: ~T(z) we can infer exists z: ~R_1(z). Therefore, the answer is yes.