Consider the following premises. forall y: ~P_4(y). forall y: S(y) <-> R_3(y). S(a_5) or q. forall y: R_3(y) <-> P_4(y). Can we infer q from them? If possible, name the inference rules being used at each step.
 From forall y: R_3(y) <-> P_4(y), forall y: ~P_4(y) we can infer forall y: ~R_3(y) via universal biconditional elimination. From forall y: S(y) <-> R_3(y), forall y: ~R_3(y) we can infer forall y: ~S(y) via universal biconditional elimination. From forall y: ~S(y) we can infer ~S(a_5) via universal instantiation. Finally, from S(a_5) or q, ~S(a_5) we can infer q via disjunctive syllogism. Therefore, the answer is yes.