Consider the following premises. forall x_6: Q_2(x_6). exists x_6: P_6(x_6) or U(x_6). forall x_6: ~P_6(x_6) or S_3(x_6). forall x_6: U(x_6) -> ~Q_2(x_6). Can we infer forall x_6: ~S_3(x_6) from them? If possible, name the inference rules being used at each step.
 From exists x_6: P_6(x_6) or U(x_6), forall x_6: ~P_6(x_6) or S_3(x_6) we can infer exists x_6: U(x_6) or S_3(x_6) via existential resolution. From forall x_6: U(x_6) -> ~Q_2(x_6), forall x_6: Q_2(x_6) we can infer forall x_6: ~U(x_6) via universal modus tollens. Finally, from exists x_6: U(x_6) or S_3(x_6), forall x_6: ~U(x_6) we can infer exists x_6: S_3(x_6) via existential disjunctive syllogism, which contradicts forall x_6: ~S_3(x_6). Therefore, the answer is no.