Your ruleset is basically right, except it's a set, not a string, and order does not matter. I sorted it and made it into a string for convenience because perl regex operate on strings, and there is a substring function, but not a subset function. I repeat back what you wrote with updated wording:

I want to run through the set and select four characters from it. After I've taken those four out, I want to go back and get four more from what's left, and so on, until I can't form any more tuples. The rules for selecting 4-tuples are that they must all be the same letter (quantity of at least 4), or they must be one letter from each of four consecutive letters.

I have tried your program, and it does only very little. I do not understand that big regex. I will explain what is missing. For the first data line, the remainder after taking out the same-tuples is ADEFFGMMSSTV. It should be split this way: ADEF;FGMS;MSTV. For the second data line, after taking out the same-tuples the remainder is ADEFFGGMMSTV. From this, no solution can be found anymore, as no matter how you turn it, there are only at most two 4-tuples left that satisfy the second condition and the last 4 are not consecutive. For the third data line, the program says nothing, it correctly recognises this set has no solution, but shouldn't it at least try to remove the obvious 4-tuples ADEF or DEFG?