Consider the following premises. forall y_4: Q(y_4) <-> S_2(y_4). S_2(e_1) -> T_1(e_1). forall y_4: T_1(y_4) -> Q(y_4). Can we infer ~(T_1(e_1) <-> S_2(e_1)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.