Is the 20th Busy Beaver number independent of set theory?

Prediction market on manifold. This resolves according to the resolution of conjecture 11 from this paper: Conjecture 11: ZF does not prove the value of BB(20). This question resolves when the conjecture is resolved, YES or NO according to whether the conjecture is true or false.

Liquidity: $1,000. Resolves: 12/31/9999.