No, you cannot.
I rarely do anything with LMs [1], but if I do I ask them to code "blocked clause decomposition" [2] in Haskell. Blocked clause decomposition is very, very simple as far as algorithm's implementation complexity goes and Haskell is just an unusual but simple implementation language.
[1] https://arxiv.org/pdf/2403.07183.pdf
[2] https://www.cs.utexas.edu/~marijn/publications/bcd.pdf
I tried that on one less known model (my son sent me a link) and on Phind two times.The Phind's responces were very illuminating ones.
On a first try, it tried to make me code that myself by pointing to a paper that does not contain any blocked clause decomposition algorithm(s), just worthless combinations of them and references to other papers. Of course, I read that paper before. When I specifically asked to provide me with code, it did not even provided me with the correct type of blocked clause, which should be a pair of a CNF clause and a literal that blocks it.
On a second try I could not even pass through bullshitting phase - I just was not able to persuade a LM to write any code. The second try I attempted after I saw an advert here on HN about Phind's new and updated LM, better at coding.
Try that youself with your unusual but known problem of choice.
And this is exactly a problem of collapse of knowledge: you can't ask an LM to code you a problem it hasn't seen several dozen of times during training. You just cannot, you will not get a satisfying answer.