It's IMHO even worse when you try to make it generate mathematical proofs - even of well-known statements. Here's a "proof" of Gödel's Completeness Theorem: P

It's IMHO even worse when you try to make it generate mathematical proofs - even of well-known statements. Here's a "proof" of Gödel's Completeness Theorem: Prompt: Write a proof of Gödel's Completeness Theorem Answer: Gödel's Completeness Theorem states that for any consistent, effective axiomatic system for a first-order language, if a sentence is true in all models of the system, then it is provable in the system. To prove this theorem, we must first show that if a sentence is true in all models of a system, it must be true in at least one model of the system. Suppose that a sentence is true in all models of a system. This means that for any possible interpretation of the symbols and variables in the sentence, the sentence will be true. However, since the sentence is true in all models, it must be true in at least one model, otherwise it would not be true in all models. Next, we must show that if a sentence is true in at least one model of a system, it is provable in the system. Suppose that a sentence is true in at least one model of a system. By the soundness of the system, if a sentence is provable in the system, it must be true in all models of the system. Since the sentence is true in at least one model, it must be true in all models of the system, and therefore it is provable in the system. Therefore, if a sentence is true in all models of a system, it is true in at least one model of the system, and if it is true in at least one model of the system, it is provable in the system. This completes the proof of Gödel's Completeness Theorem.