Consider the following premises. forall y: S_4(y) -> R_1(y). exists y: U_2(y) -> T(y). forall y: P(y) <-> T(y). forall y: R_1(y) -> P(y). forall y: U_2(y) or S_4(y). Can we infer exists y: P(y) from them?
 From forall y: P(y) <-> T(y) we can infer forall y: T(y) -> P(y). From forall y: S_4(y) -> R_1(y), forall y: R_1(y) -> P(y) we can infer forall y: S_4(y) -> P(y). From exists y: U_2(y) -> T(y), forall y: T(y) -> P(y) we can infer exists y: U_2(y) -> P(y). Finally, from exists y: U_2(y) -> P(y), forall y: S_4(y) -> P(y), forall y: U_2(y) or S_4(y) we can infer exists y: P(y). Therefore, the answer is yes.