A method to prove the safety (e.g., value-alignment) and other properties of artificial intelligence systems possessing general and/or super-human intelligence (together, AGI). The method uses probabilistic proofs in Interactive proof systems (IPS), in which a Verifier queries a computationally more powerful Prover and reduces the probability of the Prover deceiving the Verifier to any specified low probability (e.g., 2−100) IPS-based procedures can be used to test AGI behavior control systems that incorporate hard-coded ethics or valuelearning methods. An embodiment of the method, mapping the axioms and transformation rules of a behavior control system to a finite set of prime numbers, makes it possible to validate safe behavior via IPS number-theoretic methods. Other IPS embodiments can prove an unlimited number of AGI properties. Multi-prover IPS, program-checking IPS, and probabilistically checkable proofs extend the power of the paradigm. The method applies to value-alignment between future AGI generations of disparate power.