Consider the following premises. exists x_6: T_2(x_6). forall x_6: Q_6(x_6) -> R_4(x_6). forall x_6: ~P_6(x_6) or R_6(x_6). forall x_6: R_6(x_6) -> R_4(x_6). forall x_6: P_6(x_6) or Q_6(x_6). Can we infer exists x_6: T_2(x_6) and R_4(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) or Q_6(x_6), forall x_6: ~P_6(x_6) or R_6(x_6) we can infer forall x_6: Q_6(x_6) or R_6(x_6) via universal resolution. From forall x_6: Q_6(x_6) -> R_4(x_6), forall x_6: R_6(x_6) -> R_4(x_6), forall x_6: Q_6(x_6) or R_6(x_6) we can infer forall x_6: R_4(x_6) via universal disjunction elimination. Finally, from exists x_6: T_2(x_6), forall x_6: R_4(x_6) we can infer exists x_6: T_2(x_6) and R_4(x_6) via existential conjunction. Therefore, the answer is yes.