Lets start with the statement, “The kernel of the group homomorphism is a normal subgroup.” Lets try to use chatGPT to prove it?

Here is the first prompt where I tried Prolog first before the theoretical proof of Predicate Logic on which Prolog is based.

“Using prolog prove subgroup of an abelian group is abelian”

Here is a snippet of proof:

Similarly, we generated the prolog code for “Using prolog prove kernel of a group homomorphism is a normal subgroup”

But we need theoretical and mathematical proof.

Here is ChatGPT with the prompt “To prove that every subgroup of an abelian group is abelian, we will formalize the proof using predicate logic.”

Now, we prove, The kernel of the group homomorphism is a normal subgroup.

Can LLM and chatGPT prove more theorems using predicate logic?

Summary:

Using existential and universal quantifiers helps in theorem proving, but LLMs somehow can’t write full proofs using these quantifiers.

Till what we tested more data regarding predicate logic must be provided to LLMs in a way that machines can comprehend in a semi-supervised manner.

More to come…

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Warm regards