Consider the following premises. exists y: ~P_4(y). forall y: U(y) <-> S(y). forall y: S(y) -> P_4(y). forall y: P_4(y) -> S(y). Can we infer forall y: P_4(y) -> S(y) from them? If possible, name the inference rules being used at each step.
That is one of the premises. Therefore, the answer is yes.