[sacado2]

It's often a modeling issue. Modeling languages are so abstract and general they give up a part of the problem's structure.

The most famous example is the pigeonhole problem, when given to SAT solvers. Definition of the problem is: I have n pigeons and m pigeonholes, with n = m + 1. Can I put all n pigeons in a different pigeonhole? The answer is obvious to a human. If I have 20 pigeons and only 19 pigeonholes, I won't make it. But even state of the art SAT solvers will fail at solving this in a reasonable amount of time. Because of the way the problem is represented (a conjunction of boolean clauses). With just a slightly more expressive modeling language (such as pseudo-boolean representation / reasoning), you solve it with the blink of an eye.

We humans are efficient because we recognize the underlying structure of the problem. You'll solve the pigeonhole problem in a split second. But if I encode the problem in CNF (the language of SAT solvers) and give it to you without more information, you won't be able to do it anymore.