Consider the following premises. exists x_6: P(x_6) -> T(x_6). forall x_6: ~S(x_6). forall x_6: P(x_6) -> S(x_6). forall x_6: T(x_6) -> P(x_6). Can we infer exists x_6: P(x_6) -> T(x_6) from them?
That is one of the premises. Therefore, the answer is yes.