Consider the following premises. forall x_6: W(x_6) <-> P_4(x_6). exists x_6: ~Q_6(x_6). forall x_6: W(x_6) -> Q_6(x_6). Can we infer forall x_6: P_4(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: W(x_6) -> Q_6(x_6), exists x_6: ~Q_6(x_6) we can infer exists x_6: ~W(x_6) via existential modus tollens. From forall x_6: W(x_6) <-> P_4(x_6) we can infer forall x_6: P_4(x_6) -> W(x_6) via universal biconditional elimination. Finally, from forall x_6: P_4(x_6) -> W(x_6), exists x_6: ~W(x_6) we can infer exists x_6: ~P_4(x_6) via existential modus tollens, which contradicts forall x_6: P_4(x_6). Therefore, the answer is no.