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