It took a few months of work to get the enumeration program to seemingly handle this case. Runtime was a couple of weeks to generate an output file of 147GB. This contains a lot of duplication as filtering by the generation program is minimal.

I use an offline program to filter the output and cut it down by removing overlaps etc. I decided to split it down such that I process all the 6-bit numbers followed by the 7-bit and so on through 32-bit numbers.

If the number of convex sets can be gotten to a reasonable number in each bucket, they can be exhaustively tested against the available data.

Any 6-bit number can be generated with 5 small steps via the binary method. So that case is trivial:

// 24745

1 6 6 @(a)+@(b)+@(c)+@(d)+@(e)+@(f)

So far, I have only managed to prune down the 7-12-bit and 14-bit numbers: