Consider the following premises. forall x_6: ~Q_6(x_6). forall x_6: S(x_6) -> U_2(x_6). forall x_6: S(x_6) <-> Q_6(x_6). exists x_6: U_2(x_6) -> S(x_6). Can we infer forall x_6: U_2(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: S(x_6) <-> Q_6(x_6), forall x_6: ~Q_6(x_6) we can infer forall x_6: ~S(x_6) via universal biconditional elimination. From exists x_6: U_2(x_6) -> S(x_6), forall x_6: S(x_6) -> U_2(x_6) we can infer exists x_6: U_2(x_6) <-> S(x_6) via existential biconditional introduction. Finally, from exists x_6: U_2(x_6) <-> S(x_6), forall x_6: ~S(x_6) we can infer exists x_6: ~U_2(x_6) via existential biconditional elimination, which contradicts forall x_6: U_2(x_6). Therefore, the answer is no.