Consider the following premises. forall x_1: S(x_1) <-> U_3(x_1). exists x_1: S(x_1) -> P(x_1). forall x_1: U_3(x_1) <-> S(x_1). Can we infer forall x_1: ~(U_3(x_1) -> P(x_1)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.