Consider the following premises. forall x_4: T(x_4) -> S_1(x_4). forall x_4: T(x_4) -> P(x_4). forall x_4: ~P(x_4). exists x_4: T(x_4) -> S_1(x_4). forall x_4: S_1(x_4) -> T(x_4). Can we infer forall x_4: S_1(x_4) from them?
 From forall x_4: T(x_4) -> S_1(x_4), forall x_4: S_1(x_4) -> T(x_4) we can infer forall x_4: T(x_4) <-> S_1(x_4). From forall x_4: T(x_4) -> P(x_4), forall x_4: ~P(x_4) we can infer forall x_4: ~T(x_4). From forall x_4: T(x_4) <-> S_1(x_4) we can infer forall x_4: S_1(x_4) -> T(x_4). From exists x_4: T(x_4) -> S_1(x_4), forall x_4: S_1(x_4) -> T(x_4) we can infer exists x_4: T(x_4) <-> S_1(x_4). Finally, from exists x_4: T(x_4) <-> S_1(x_4), forall x_4: ~T(x_4) we can infer exists x_4: ~S_1(x_4), which contradicts forall x_4: S_1(x_4). Therefore, the answer is no.