Consider the following premises. forall x_12: W(x_12) -> S_3(x_12). forall x_12: W(x_12) <-> Q(x_12). forall x_12: S_3(x_12) -> W(x_12). forall x_12: P_8(x_12) or S_3(x_12). exists x_12: ~P_8(x_12) or Q(x_12). Can we infer forall x_12: ~W(x_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: W(x_12) <-> Q(x_12) we can infer forall x_12: Q(x_12) -> W(x_12) via universal biconditional elimination. From forall x_12: P_8(x_12) or S_3(x_12), exists x_12: ~P_8(x_12) or Q(x_12) we can infer exists x_12: S_3(x_12) or Q(x_12) via existential resolution. From forall x_12: W(x_12) -> S_3(x_12), forall x_12: S_3(x_12) -> W(x_12) we can infer forall x_12: W(x_12) <-> S_3(x_12) via universal biconditional introduction. From forall x_12: W(x_12) <-> S_3(x_12) we can infer forall x_12: S_3(x_12) -> W(x_12) via universal biconditional elimination. Finally, from forall x_12: S_3(x_12) -> W(x_12), forall x_12: Q(x_12) -> W(x_12), exists x_12: S_3(x_12) or Q(x_12) we can infer exists x_12: W(x_12) via existential disjunction elimination, which contradicts forall x_12: ~W(x_12). Therefore, the answer is no.