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