Consider the following premises. forall y: T(y) -> S_3(y). forall y: T(y) <-> S_3(y). exists y: ~R(y). forall y: T(y) <-> R(y). Can we infer forall y: S_3(y) from them?
 From forall y: T(y) <-> S_3(y) we can infer forall y: S_3(y) -> T(y). From forall y: T(y) <-> R(y), exists y: ~R(y) we can infer exists y: ~T(y). From forall y: T(y) -> S_3(y), forall y: S_3(y) -> T(y) we can infer forall y: T(y) <-> S_3(y). Finally, from forall y: T(y) <-> S_3(y), exists y: ~T(y) we can infer exists y: ~S_3(y), which contradicts forall y: S_3(y). Therefore, the answer is no.