The reviewer who skimmed your paper and then filed false claims is not a mystery to solve. They are a fact of the review process, and the way you respond will determine whether you walk away with a strong paper or a wounded ego. Your instinct to reach out to the program chair is understandable, but it should be a last resort, not a first move. The PC is not a referee for hurt feelings; they are there to manage the process, not to police every lazy read. What you can do, and what you should do, is treat the rebuttal as a targeted exercise in clarity and evidence.
When a reviewer says something is "not explored" and the paper clearly shows it is, the fault is rarely with the reviewer alone. It is a signal that your presentation of that work is not landing with the intended audience. You have two options: you can assume the reviewer is malicious, or you can assume they are rushed, tired, and reading at 2 a.m. The productive path is to assume the latter. In your rebuttal, point directly to the section, figure, or table where the work appears. Quote your own sentence back at them. Then explain, in one or two plain lines, why their claim is incorrect. Do not argue. Do not condescend. Just show the receipt.
The citation demand is a separate issue, and here you have more room to maneuver. The reviewer is angry that you did not cite a particular work and is asking for extra experiments on it, even though that violates IJCAI policy. You are right that this is a bad look. But you do not need to fight the policy battle in your rebuttal. You can acknowledge the work you missed, thank the reviewer for bringing it to your attention, and then note that per the conference guidelines, additional experiments are outside the scope of the rebuttal. You can also offer to incorporate the citation and any relevant discussion into the camera-ready version. That does not make you a pushover. It makes you a professional who knows the difference between a substantive critique and a power play.
Here is the concrete move: draft your rebuttal as if you are explaining the paper to a smart colleague who has not read it. Use the reviewer's own language to structure your response. For every false claim, give a one-sentence correction with a reference. For the citation, acknowledge, contextualize, and defer to policy. Then, and this is the part most people skip, re-read your own rebuttal the way the reviewer will. Is it defensive? Does it sound like you are making excuses? If so, rewrite. The goal is not to win the reviewer over. The goal is to make it easy for the PC to see that the review is not accurate. Do that, and you have done your job. The rest is out of your hands.