Consider the following premises. exists x_11: R(x_11) -> Q_11(x_11). forall x_11: U_2(x_11) -> R(x_11). forall x_11: ~R(x_11). forall x_11: U_2(x_11) <-> Q_11(x_11). Can we infer forall x_11: U_2(x_11) from them? If possible, name the inference rules being used at each step.
 From forall x_11: U_2(x_11) <-> Q_11(x_11) we can infer forall x_11: Q_11(x_11) -> U_2(x_11) via universal biconditional elimination. From exists x_11: R(x_11) -> Q_11(x_11), forall x_11: Q_11(x_11) -> U_2(x_11) we can infer exists x_11: R(x_11) -> U_2(x_11) via existential transitivity. From forall x_11: U_2(x_11) -> R(x_11), exists x_11: R(x_11) -> U_2(x_11) we can infer exists x_11: U_2(x_11) <-> R(x_11) via existential biconditional introduction. Finally, from exists x_11: U_2(x_11) <-> R(x_11), forall x_11: ~R(x_11) we can infer exists x_11: ~U_2(x_11) via existential biconditional elimination, which contradicts forall x_11: U_2(x_11). Therefore, the answer is no.