Consider the following premises. q -> R_17(a_17). forall x_17: R_17(x_17) -> S_17(x_17). S_17(a_17) -> q. S_17(a_17). Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From forall x_17: R_17(x_17) -> S_17(x_17) we can infer R_17(a_17) -> S_17(a_17) via universal instantiation. From q -> R_17(a_17), R_17(a_17) -> S_17(a_17) we can infer q -> S_17(a_17) via transitivity. From S_17(a_17) -> q, q -> S_17(a_17) we can infer S_17(a_17) <-> q via biconditional introduction. From S_17(a_17) <-> q we can infer S_17(a_17) -> q via biconditional elimination. Finally, from S_17(a_17) -> q, S_17(a_17) we can infer q via modus ponens, which contradicts ~q. Therefore, the answer is no.