Going nowhere fast

I thought earlier this week that I was finally cracking a problem I've been trying to solve—that, in fact, I thought I'd solved late last year, only I'd overlooked something "minor". I had managed to solve a special case, and I was making rapid progress on another special case that, I was sure, would reveal how the rest of the cases should work out.

The theorems looked beautiful. The trouble was, they looked too beautiful. In fact, they contradicted well-known facts. I realized that I had to examine more carefully what was going on. Digging into it, I finally saw that I had operated under an assumption that, instead of being a valid assumption, was more akin to a delusion.

Since then, I've explored a number of options for fixing the problem, or even approaching it from a different point of view, and I've found that I'm getting absolutely nowhere. I'm having zero success at all. The most avenues that look promising lead quickly to dead ends infested with criminal gangs, so to speak, while the avenues that look like deads ends infested with criminal gangs—well, they don't get any better. The problem is starting to look impossible to resolve.

I reckon it's time to abandon this problem for a while. For a long, long while. That puts me in a very bad position, but I don't see any other way to progress at the moment.