Consider the following premises. forall x_13: ~Q_5(x_13). exists x_13: R_2(x_13) <-> U(x_13). forall x_13: S_1(x_13) -> Q_5(x_13). forall x_13: S_1(x_13) <-> R_2(x_13). Can we infer forall x_13: U(x_13) from them? If possible, name the inference rules being used at each step.
 From exists x_13: R_2(x_13) <-> U(x_13) we can infer exists x_13: U(x_13) -> R_2(x_13) via existential biconditional elimination. From forall x_13: S_1(x_13) -> Q_5(x_13), forall x_13: ~Q_5(x_13) we can infer forall x_13: ~S_1(x_13) via universal modus tollens. From forall x_13: S_1(x_13) <-> R_2(x_13), forall x_13: ~S_1(x_13) we can infer forall x_13: ~R_2(x_13) via universal biconditional elimination. Finally, from exists x_13: U(x_13) -> R_2(x_13), forall x_13: ~R_2(x_13) we can infer exists x_13: ~U(x_13) via existential modus tollens, which contradicts forall x_13: U(x_13). Therefore, the answer is no.