Consider the following premises. forall x_8: Q_2(x_8). exists x_8: U(x_8) <-> P(x_8). forall x_8: P(x_8) -> ~Q_2(x_8). Can we infer forall x_8: U(x_8) from them? If possible, name the inference rules being used at each step.
 From exists x_8: U(x_8) <-> P(x_8) we can infer exists x_8: U(x_8) -> P(x_8) via existential biconditional elimination. From forall x_8: P(x_8) -> ~Q_2(x_8), forall x_8: Q_2(x_8) we can infer forall x_8: ~P(x_8) via universal modus tollens. Finally, from exists x_8: U(x_8) -> P(x_8), forall x_8: ~P(x_8) we can infer exists x_8: ~U(x_8) via existential modus tollens, which contradicts forall x_8: U(x_8). Therefore, the answer is no.