Consider the following premises. forall x: S(x) <-> W(x). forall x: Q_3(x) -> W(x). exists x: T_1(x) -> Q_3(x). Can we infer forall x: ~(T_1(x) -> S(x)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.