Consider the following premises. forall y: U(y) -> P_1(y). forall y: R(y) -> U(y). forall y: ~P_1(y). forall y: P_1(y) -> R(y). Can we infer exists y: U(y) from them?
 From forall y: P_1(y) -> R(y), forall y: R(y) -> U(y) we can infer forall y: P_1(y) -> U(y). From forall y: U(y) -> P_1(y), forall y: P_1(y) -> U(y) we can infer forall y: U(y) <-> P_1(y). Finally, from forall y: U(y) <-> P_1(y), forall y: ~P_1(y) we can infer forall y: ~U(y), which contradicts exists y: U(y). Therefore, the answer is no.