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. ~R_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) we can infer q -> R_17(a_17) via biconditional elimination. From R_17(a_17) -> S_17(a_17), S_17(a_17) -> q we can infer R_17(a_17) -> q via transitivity. From q -> R_17(a_17), R_17(a_17) -> q we can infer q <-> R_17(a_17) via biconditional introduction. Finally, from q <-> R_17(a_17), ~R_17(a_17) we can infer ~q via biconditional elimination. Therefore, the answer is yes.