Consider the following premises. forall x_17: P(x_17) -> W(x_17). forall x_17: W(x_17) or ~Q_17(x_17). S_2(g). forall x_17: ~P_6(x_17) or Q_17(x_17). forall x_17: P_6(x_17) or P(x_17). Can we infer exists x_17: S_2(x_17) and W(x_17) from them? If possible, name the inference rules being used at each step.
 From forall x_17: W(x_17) or ~Q_17(x_17) we can infer forall x_17: Q_17(x_17) -> W(x_17) via universal rewriting. From S_2(g) we can infer exists x_17: S_2(x_17) via existential generalization. From forall x_17: P_6(x_17) or P(x_17), forall x_17: ~P_6(x_17) or Q_17(x_17) we can infer forall x_17: P(x_17) or Q_17(x_17) via universal resolution. From forall x_17: P(x_17) -> W(x_17), forall x_17: Q_17(x_17) -> W(x_17), forall x_17: P(x_17) or Q_17(x_17) we can infer forall x_17: W(x_17) via universal disjunction elimination. Finally, from exists x_17: S_2(x_17), forall x_17: W(x_17) we can infer exists x_17: S_2(x_17) and W(x_17) via existential conjunction. Therefore, the answer is yes.