Trust the Proof Checker?

You’ve got an AI proof-checker, “ProofBot”, that rules each proof VALID or INVALID. Each task shows a claim, ProofBot’s confident ruling, and a % sure. But ProofBot is JAGGED, like real AI: it can rubber-stamp a genuinely hard, correct proof — that √2 is irrational, or that the odd numbers sum to a perfect square — yet confidently approve a proof with a first-week flaw: a rule that doesn’t exist, an argument that assumes its own conclusion, a hidden divide-by-zero. For each one, decide: TRUST ProofBot’s ruling, or CHECK THE LOGIC YOURSELF. You do well by catching the confident misses, because an AI sounding certain is not the same as reasoning validly — and how hard the proof looks tells you nothing about whether the bot judged it right. In proof, you can always check: find a counterexample, spot the circular step, catch the illegal move.