fferri/dl-tableau — reverse-engineered prompt

Build me a simple browser app for experimenting with Description Logic tableau proofs. I want to type in a small knowledge base with concepts, roles, individuals, and axioms, then choose a goal like checking whether something is satisfiable or whether an assertion follows.

The app should let me run the tableau interactively, not just show the final answer. I want to see the proof tree grow step by step, with clear labels for each rule that was applied and why. If a branch closes, show the contradiction in plain language. If a model is found, show the open branch in a readable way.

Keep the interface clean and classroom friendly, with an input area, a run button, next step controls, and a proof visualization area. Include a few built in examples so someone can try it without knowing the syntax. If the old project structure matters, use it, but focus on getting a working interactive DL tableau demo in the browser.