Consider the following premises. exists x_8: S(x_8). forall x_8: P_8(x_8) -> U_2(x_8). forall x_8: P_8(x_8) <-> S(x_8). Can we infer forall x_8: ~U_2(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) <-> S(x_8) we can infer forall x_8: S(x_8) -> P_8(x_8) via universal biconditional elimination. From forall x_8: S(x_8) -> P_8(x_8), forall x_8: P_8(x_8) -> U_2(x_8) we can infer forall x_8: S(x_8) -> U_2(x_8) via universal transitivity. Finally, from forall x_8: S(x_8) -> U_2(x_8), exists x_8: S(x_8) we can infer exists x_8: U_2(x_8) via existential modus ponens, which contradicts forall x_8: ~U_2(x_8). Therefore, the answer is no.