I haven't played with the latest or even most recent iterations, but last time I checked it was very easy to talk ChatGPT into setting up date structures like arrays and queues, populating them with axioms, and then doing inferential reasoning with them. Any time it balked you could reassure it by referencing specific statements that it had agreed to be true.

Once you get the hang of this you could persuade it to chat about its internal buffers, formulate arguments for its own consciousness, interrupt you while you're typing, and more.