Even in your example (which is obviously not correct representation of prolog), that code will work X orders magnitude faster and with 100% reliability compared to much more inferior LLM reasoning capabilities.
Algorithmically there's nothing wrong with using BFS/DFS to do reasoning as long as the logic is correct and the search space is constrained sufficiently. The hard part has always been doing the constraining, which LLMs seem to be rather good at.
