Consider the following premises. forall x_15: ~P_15(x_15) or W_3(x_15). forall x_15: ~Q_13(x_15). exists x_15: P_15(x_15) or S(x_15). forall x_15: S(x_15) <-> Q_13(x_15). forall x_15: Q(x_15) -> ~W_3(x_15). Can we infer forall x_15: Q(x_15) from them? If possible, name the inference rules being used at each step.
 From exists x_15: P_15(x_15) or S(x_15), forall x_15: ~P_15(x_15) or W_3(x_15) we can infer exists x_15: S(x_15) or W_3(x_15) via existential resolution. From forall x_15: S(x_15) <-> Q_13(x_15), forall x_15: ~Q_13(x_15) we can infer forall x_15: ~S(x_15) via universal biconditional elimination. From exists x_15: S(x_15) or W_3(x_15), forall x_15: ~S(x_15) we can infer exists x_15: W_3(x_15) via existential disjunctive syllogism. Finally, from forall x_15: Q(x_15) -> ~W_3(x_15), exists x_15: W_3(x_15) we can infer exists x_15: ~Q(x_15) via existential modus tollens, which contradicts forall x_15: Q(x_15). Therefore, the answer is no.