You are right, I completely missed that, to me internal version of Codex meant the harness, but I was wrong.

Not necessarily, it's plausible that GPT-5.6 Sol could also find this disproof, as neither of us has enough information to make a conclusive case.

Public GPT is certainly capable, it was able to reverse-engineer the counterexample into a short proof: https://x.com/davikrehalt/status/2079175065695035442

I still suspect Fable 6 found the counterexample, mostly because Anthropic has been silent about this achievement. This is a huge accomplishment, and companies don't usually stay quiet when they hit a breakthrough like this. The lack of a press release or blog post is very suspicious.