Consider the following premises. exists z_1: U_1(z_1) <-> P(z_1). forall z_1: P(z_1) or ~U_1(z_1). Can we infer forall z_1: ~(U_1(z_1) -> P(z_1)) from them?
 From exists z_1: U_1(z_1) <-> P(z_1) we can infer exists z_1: P(z_1) -> U_1(z_1). Finally, from forall z_1: P(z_1) or ~U_1(z_1) we can infer forall z_1: U_1(z_1) -> P(z_1), which contradicts forall z_1: ~(U_1(z_1) -> P(z_1)). Therefore, the answer is no.