Consider the following premises. forall z: W(z) -> U(z). forall z: U(z) or P(z). forall z: U(z) -> W(z). forall z: W(z) <-> P(z). Can we infer exists z: ~W(z) from them?
 From forall z: U(z) -> W(z), forall z: W(z) -> U(z) we can infer forall z: U(z) <-> W(z). From forall z: W(z) <-> P(z) we can infer forall z: P(z) -> W(z). From forall z: U(z) <-> W(z) we can infer forall z: U(z) -> W(z). Finally, from forall z: U(z) -> W(z), forall z: P(z) -> W(z), forall z: U(z) or P(z) we can infer forall z: W(z), which contradicts exists z: ~W(z). Therefore, the answer is no.