Consider the following premises. forall y_4: T(y_4) and P(y_4). forall y_4: U(y_4) or ~T(y_4). exists y_4: U(y_4) -> S_4(y_4). Can we infer exists y_4: S_4(y_4) from them?
 From forall y_4: U(y_4) or ~T(y_4) we can infer forall y_4: T(y_4) -> U(y_4). From forall y_4: T(y_4) -> U(y_4), exists y_4: U(y_4) -> S_4(y_4) we can infer exists y_4: T(y_4) -> S_4(y_4). From forall y_4: T(y_4) and P(y_4) we can infer forall y_4: T(y_4). Finally, from exists y_4: T(y_4) -> S_4(y_4), forall y_4: T(y_4) we can infer exists y_4: S_4(y_4). Therefore, the answer is yes.