Here you have two predicates on words P: Sigma* -> N and T: Sigma* -> N. The question is give a list of words w such that for all w, P(w) and T(w) are both true

Here you have two predicates on words P: Sigma* -> N and T: Sigma* -> N. The question is give a list of words w such that for all w, P(w) and T(w) are both true. It has access to the correct values for P(w) and T(w), so there is a simple algorithm that can produce all words, you just enumerate them each one and verify that the word satisfies both predicates. An intelligent agent should be able to understand this without any understanding of the underlying domain. If I try to reformulate your answer, this is like words are a different domain than what GPT has been trained on (which is tokens), and so it is not unexpected that GPT cannot generalize to this other domain. Is that a correct interpretation of your statement? In my view failing to see the similarity in the relationship between class objects is a sign of a lack of 'intelligence', whatever that may be in a very precise sense.