Consider the following premises. forall x_5: Q_4(x_5) -> U_2(x_5). forall x_5: R_2(x_5) or Q_4(x_5). exists x_5: U_2(x_5) <-> R_2(x_5). Can we infer forall x_5: ~U_2(x_5) from them? If possible, name the inference rules being used at each step.
 From exists x_5: U_2(x_5) <-> R_2(x_5) we can infer exists x_5: R_2(x_5) -> U_2(x_5) via existential biconditional elimination. Finally, from exists x_5: R_2(x_5) -> U_2(x_5), forall x_5: Q_4(x_5) -> U_2(x_5), forall x_5: R_2(x_5) or Q_4(x_5) we can infer exists x_5: U_2(x_5) via existential disjunction elimination, which contradicts forall x_5: ~U_2(x_5). Therefore, the answer is no.