Consider the following premises. forall x_15: ~Q_15(x_15). forall x_15: T_2(x_15) or U_3(x_15). forall x_15: P_15(x_15) <-> T_2(x_15). exists x_15: P_15(x_15) <-> Q_15(x_15). Can we infer forall x_15: ~U_3(x_15) from them? If possible, name the inference rules being used at each step.
 From exists x_15: P_15(x_15) <-> Q_15(x_15), forall x_15: ~Q_15(x_15) we can infer exists x_15: ~P_15(x_15) via existential biconditional elimination. From forall x_15: P_15(x_15) <-> T_2(x_15), exists x_15: ~P_15(x_15) we can infer exists x_15: ~T_2(x_15) via existential biconditional elimination. Finally, from forall x_15: T_2(x_15) or U_3(x_15), exists x_15: ~T_2(x_15) we can infer exists x_15: U_3(x_15) via existential disjunctive syllogism, which contradicts forall x_15: ~U_3(x_15). Therefore, the answer is no.