Consider the following premises. exists x_6: P_6(x_6) -> T_4(x_6). forall x_6: T_4(x_6) -> P_6(x_6). forall x_6: ~P_6(x_6). Can we infer forall x_6: T_4(x_6) from them? If possible, name the inference rules being used at each step.
 From exists x_6: P_6(x_6) -> T_4(x_6), forall x_6: T_4(x_6) -> P_6(x_6) we can infer exists x_6: P_6(x_6) <-> T_4(x_6) via existential biconditional introduction. From exists x_6: P_6(x_6) <-> T_4(x_6) we can infer exists x_6: T_4(x_6) -> P_6(x_6) via existential biconditional elimination. Finally, from exists x_6: T_4(x_6) -> P_6(x_6), forall x_6: ~P_6(x_6) we can infer exists x_6: ~T_4(x_6) via existential modus tollens, which contradicts forall x_6: T_4(x_6). Therefore, the answer is no.