Consider the following premises. forall x_11: S_3(x_11) -> ~T_1(x_11). exists x_11: ~P_11(x_11) or U(x_11). forall x_11: P_11(x_11) or S_3(x_11). forall x_11: T_1(x_11) and Q_7(x_11). Can we infer forall x_11: ~U(x_11) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) or S_3(x_11), exists x_11: ~P_11(x_11) or U(x_11) we can infer exists x_11: S_3(x_11) or U(x_11) via existential resolution. From forall x_11: T_1(x_11) and Q_7(x_11) we can infer forall x_11: T_1(x_11) via universal simplification. From forall x_11: S_3(x_11) -> ~T_1(x_11), forall x_11: T_1(x_11) we can infer forall x_11: ~S_3(x_11) via universal modus tollens. Finally, from exists x_11: S_3(x_11) or U(x_11), forall x_11: ~S_3(x_11) we can infer exists x_11: U(x_11) via existential disjunctive syllogism, which contradicts forall x_11: ~U(x_11). Therefore, the answer is no.