Consider the following premises. ~P(a_7). P(a_7) -> U(a_7). forall z_1: U(z_1) <-> P(z_1). Can we infer ~U(a_7) from them?
 From forall z_1: U(z_1) <-> P(z_1) we can infer forall z_1: U(z_1) -> P(z_1). From forall z_1: U(z_1) -> P(z_1) we can infer U(a_7) -> P(a_7). From U(a_7) -> P(a_7), P(a_7) -> U(a_7) we can infer U(a_7) <-> P(a_7). Finally, from U(a_7) <-> P(a_7), ~P(a_7) we can infer ~U(a_7). Therefore, the answer is yes.