alt Hacker NewsI think incompleteness theorem means that you can't guarantee the agents will always be able to converge on a proof, since you can't have both completeness and soundness (and we obviously need soundness since that's the whole point of a theorem prover).
But most real-world programs are maybe not that "expressive" since we don't even want them to be capable of infinite loops (since those would often be denial of service vectors). So you should usually be able to prove that they halt (and presumably other properties as well), especially when you allow agents to rewrite things to pull out invariants that make proofs easier (as they did).
And for cases where getting clean invariants are difficult, I imagine you can just hack it by having some cutoff which trivially ensures things always halt. (Not sure what the equivalent would be for "no bug" proofs, probably rejecting things that are technically valid input per spec but seem unusual?)
While I completely agree with 3uru, where it can get stuck is if your system contains a pseudorandom generator or some other cryptographic shenanigans. These are programs deliberately made difficult to analyze and reason about.
I would say, in practice, you are more likely to encounter complexity barrier (we don't know how to decide some NP-hard problem fast enough) to proving things about your program than you're to encounter a true undecidability barrier (Rice theorem).