Consider the following premises. exists y_4: Q(y_4) -> S(y_4). forall y_4: U(y_4) -> Q_2(y_4). forall y_4: Q(y_4) <-> Q_2(y_4). Can we infer forall y_4: ~(U(y_4) -> S(y_4)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.