I’ve been working on that on and off since 2012. I picked it up again about a month ago and have made dramatic speed improvements to my search, but exhausting the whole space I’m searching will still take my computer an estimated 70 years.
If it were just a matter of a few thousand dollars of computer time (say, less than $5000) the money would already be spent and I’d have an answer.
We’ll see, I may build the tooling to distribute the search and enlist help from others interested.
It’s only been about 2 weeks since I was able to drop the runtime from “age of the universe” levels to just decades.
I think it's an extraordinarily hard problem computationally, even with exceptional theoretical backing.
Where people may be able to beat me is if no solution exists-- there may be some highly nontrivial, but findable unsatisfiability argument.