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