Consider the following premises. forall x_5: T(x_5) -> W(x_5). exists x_5: W(x_5) -> T(x_5). forall x_5: ~P_3(x_5). forall x_5: P_3(x_5) <-> T(x_5). Can we infer forall x_5: W(x_5) from them? If possible, name the inference rules being used at each step.
 From exists x_5: W(x_5) -> T(x_5), forall x_5: T(x_5) -> W(x_5) we can infer exists x_5: W(x_5) <-> T(x_5) via existential biconditional introduction. From forall x_5: P_3(x_5) <-> T(x_5), forall x_5: ~P_3(x_5) we can infer forall x_5: ~T(x_5) via universal biconditional elimination. Finally, from exists x_5: W(x_5) <-> T(x_5), forall x_5: ~T(x_5) we can infer exists x_5: ~W(x_5) via existential biconditional elimination, which contradicts forall x_5: W(x_5). Therefore, the answer is no.