Consider the following premises. exists x: T_2(x) -> P_3(x). forall x: ~R_3(x). forall x: P_3(x) <-> R_3(x). Can we infer exists x: ~T_2(x) from them? If possible, name the inference rules being used at each step.
 From forall x: P_3(x) <-> R_3(x) we can infer forall x: P_3(x) -> R_3(x) via universal biconditional elimination. From exists x: T_2(x) -> P_3(x), forall x: P_3(x) -> R_3(x) we can infer exists x: T_2(x) -> R_3(x) via existential transitivity. Finally, from exists x: T_2(x) -> R_3(x), forall x: ~R_3(x) we can infer exists x: ~T_2(x) via existential modus tollens. Therefore, the answer is yes.