Consider the following premises. forall x_7: ~Q_7(x_7). forall x_7: Q(x_7) <-> Q_7(x_7). forall x_7: P_3(x_7) or Q(x_7). exists x_7: ~P_3(x_7) or U_1(x_7). Can we infer forall x_7: ~U_1(x_7) from them? If possible, name the inference rules being used at each step.
 From forall x_7: Q(x_7) <-> Q_7(x_7), forall x_7: ~Q_7(x_7) we can infer forall x_7: ~Q(x_7) via universal biconditional elimination. From forall x_7: P_3(x_7) or Q(x_7), exists x_7: ~P_3(x_7) or U_1(x_7) we can infer exists x_7: Q(x_7) or U_1(x_7) via existential resolution. Finally, from exists x_7: Q(x_7) or U_1(x_7), forall x_7: ~Q(x_7) we can infer exists x_7: U_1(x_7) via existential disjunctive syllogism, which contradicts forall x_7: ~U_1(x_7). Therefore, the answer is no.