Consider the following premises. forall y: U(y) -> P_1(y). forall y: S(y). forall y: S(y) -> U(y). Can we infer P_1(c) from them?
 From forall y: S(y) -> U(y), forall y: U(y) -> P_1(y) we can infer forall y: S(y) -> P_1(y). From forall y: S(y) -> P_1(y), forall y: S(y) we can infer forall y: P_1(y). Finally, from forall y: P_1(y) we can infer P_1(c). Therefore, the answer is yes.