Garbage is garbage and failure to reason is failure to reason no matter the language. If your LLM can't translate your problem to a Prolog program that solves your problem- Prolog can't solve your problem.
Here's just one more observation: the problems where translating reasoning to Prolog will work best are problems where there are a lot of examples of Prolog to be found on the web, e.g. wolf-cabbage-goat problems and the like. With problems like that it is much easier for an LLM to generate a correct translation of the problem to Prolog and get a correct solution just because there's lots of examples. But if you choose a problem that's rarely attacked with Prolog code, like, I don't know, some mathematical problem that obtains in nuclear physics as a for instance, then an LLM will be much more likely to generate garbage Prolog, while e.g. Fortran would be a better target language. From what I can see, the papers linked in the article above concentrate on the Prolog-friendly kind of problem, like logical puzzles and the like. That smells like cherry picking to me, or just good, old confirmation bias.
Again, Prolog is not magick. The article above and the papers it links to seem to take this attitude of "just add Prolog" and that will make LLMs suddenly magickally reason with fairy dust on top. Ain't gonna happen.
https://arxiv.org/abs/2405.04776
Their argument is that CoT can only improve performance of LLMs in reasoning tasks when the prompter already knows the answer and can somehow embed it in their prompt. The paper I link above supports this intuition with empirical results, summarised in the abstract as follows:
While our problems are very simple, we only find meaningful performance improvements from chain of thought prompts when those prompts are exceedingly specific to their problem class, and that those improvements quickly deteriorate as the size n of the query-specified stack grows past the size of stacks shown in the examples. We also create scalable variants of three domains commonly studied in previous CoT papers and demonstrate the existence of similar failure modes. Our results hint that, contrary to previous claims in the literature, CoT's performance improvements do not stem from the model learning general algorithmic procedures via demonstrations but depend on carefully engineering highly problem specific prompts.
And if that's the case and I need to know the solution to a reasoning task before I can prompt an LLM to solve it- then why do I need to prompt an LLM to solve it? Or, if I'm just asking an LLM to generate the Prolog code I can write myself then what's the point of that? As I argue in another comment, an LLM will only do well in generating correct code if it has seen some sufficient number of examples of the code I'm asking it to generate anyway. So I don't think that CoT, used to generate Prolog, is really adding anything to my capability to solve problems by coding in Prolog.
I have no idea how o1 works internally and I prefer not to speculate but it doesn't seem to be some silver bullet that will make LLMs capable of reasoning.