Consider the following premises. forall x_14: W(x_14) -> Q_8(x_14). forall x_14: ~S_1(x_14). exists x_14: Q_8(x_14) -> P(x_14). forall x_14: W(x_14) <-> S_1(x_14). forall x_14: P(x_14) <-> W(x_14). Can we infer forall x_14: P(x_14) from them? If possible, name the inference rules being used at each step.
 From forall x_14: P(x_14) <-> W(x_14) we can infer forall x_14: P(x_14) -> W(x_14) via universal biconditional elimination. From forall x_14: W(x_14) -> Q_8(x_14), exists x_14: Q_8(x_14) -> P(x_14) we can infer exists x_14: W(x_14) -> P(x_14) via existential transitivity. From forall x_14: W(x_14) <-> S_1(x_14), forall x_14: ~S_1(x_14) we can infer forall x_14: ~W(x_14) via universal biconditional elimination. From exists x_14: W(x_14) -> P(x_14), forall x_14: P(x_14) -> W(x_14) we can infer exists x_14: W(x_14) <-> P(x_14) via existential biconditional introduction. Finally, from exists x_14: W(x_14) <-> P(x_14), forall x_14: ~W(x_14) we can infer exists x_14: ~P(x_14) via existential biconditional elimination, which contradicts forall x_14: P(x_14). Therefore, the answer is no.