Consider the following premises. forall x_7: P_7(x_7) <-> T(x_7). forall x_7: P_4(x_7) or P_7(x_7). forall x_7: P_4(x_7) -> T(x_7). exists x_7: S(x_7). Can we infer exists x_7: S(x_7) and T(x_7) from them? If possible, name the inference rules being used at each step.
 From forall x_7: P_7(x_7) <-> T(x_7) we can infer forall x_7: P_7(x_7) -> T(x_7) via universal biconditional elimination. From forall x_7: P_4(x_7) -> T(x_7), forall x_7: P_7(x_7) -> T(x_7), forall x_7: P_4(x_7) or P_7(x_7) we can infer forall x_7: T(x_7) via universal disjunction elimination. Finally, from exists x_7: S(x_7), forall x_7: T(x_7) we can infer exists x_7: S(x_7) and T(x_7) via existential conjunction. Therefore, the answer is yes.