Consider the following premises. w or ~S_17(a_17). forall x_17: S_3(x_17) or S_17(x_17). S_3(a_17) -> w. Can we infer w or q from them? If possible, name the inference rules being used at each step.
 From forall x_17: S_3(x_17) or S_17(x_17) we can infer S_3(a_17) or S_17(a_17) via universal instantiation. From w or ~S_17(a_17) we can infer S_17(a_17) -> w via rewriting. From S_3(a_17) -> w, S_17(a_17) -> w, S_3(a_17) or S_17(a_17) we can infer w via disjunction elimination. Finally, from w we can infer w or q via addition. Therefore, the answer is yes.