Collaboration on a suggested project - problem with a colleague
I will come at from the other direction. I will assume that your summary is correct, and that this person truly did nothing other than point you to a question that had already been posed in published work. In this case, you are under no obligation to work with him. You must be careful to cite his work appropriately, and probably acknowledge him in the acknowledgment section as having suggested this line of research, but I don't think he has a legitimate case for co-authorship.
That said, he could still create a messy, public confrontation. So, I would send a note like this:

John,
Some time ago, we discussed collaborating on an effort to prove [blah] as an extension of your work in [blah]. So far I don't think either of us has made much progress, so I wanted to reach out with you about resurrecting this work.
At this point, I think it would be best if I tackled this on my own. If successful, I will write up a paper that cites your paper, and will acknowledge you in the acknowledgments. What do you think?*
-Name

Depending on whether you are willing to consider working with this guy, you could also replace the last sentence with:

If you would prefer to collaborate on this paper as a co-author, we can discuss, but I am hoping to publish in the next ~6 months, so we should meet ASAP to discuss what you will contribute and when it will be ready.

Then there are a few possible outcomes:

If he ignores you, or says &quot;good&quot;, then all is okay.
If he claims to be interested in collaborating with you, you will have to discuss this with him.

You may need to be fairly aggressive in telling him that you don't think collaborating will be feasible, but better to have this argument now and in private, rather than after publishing without him.
If you are willing to give him a chance, you can try to define his contributions and the deadlines now, and let him know that if doesn't have satisfactory material by the deadline, you will publish your results without him. If he is serious about working with you, then this is reasonable; if he is lazy as you say, he may withdraw his objections.


If you cannot come to terms, or if he reacts very poorly, then you can decide whether you want to risk a nasty, public fight over authorship, or whether you want to drop the line of research.