I would like to know if can be proven that NN for problems involving permutations can be as efficient as a SAT solver, less, or more efficient (e.g. if using th

I would like to know if can be proven that NN for problems involving permutations can be as efficient as a SAT solver, less, or more efficient (e.g. if using the training just as a acceleration avoid learning futile permutations works for saving training time, or if it is not noticeable)