Purpose-To carry out a prospective analysis of the experience of the Supreme Federal Court (STF) and the Colombian Constitutional Court (CCC) with Artificial Intelligence (AI). Methodology-In terms of methodology, we use the qualitative approach, where the data analysis technique is discourse analysis and the unit of analysis are official documents and reports related to disruptive technologies for judicial use, emphasizing those dedicated to "experience"Colombian with the Pretoria AI. Findings-In Latin America, AI Systems, such as Victor and PretorIA, are automation tools supporting synthesis and prediction tasks in the supreme courts in Brazil and Colombia. However, they are not magic solutions to solve judicial congestion, although the 4th Industrial Revolution bring progress for positive changes. The significant challenges, however, are also in law theory through an ethical framework for the development, design, and operational work of AI. Nevertheless, our comprehension of those systems remains limited. For this reason, supreme courts must observe positive law and ethics to avoid a tyranny of the code, avoiding their impact over law sources', preventing an algorithm from "deciding"the criteria for applying the law. Thus, supreme courts need to calibrate and influence its design, preventing its obsolescence, but, above all, preventing human dignity obsolescence, human labor, and power of deliberation. All these are essential for shaping version 4.0 of the Social Rule of Law. Practical implications-Promote the engagement of magistrates and citizenship in design and programming of AI Systems for supreme courts' use, within an ethical framework that prevents human beings, their values, and their rights' obsolescence. Originality-This paper analyzes AI Systems used to solve supreme courts' problems in Brazil and Colombia, studying how they work, but also its additional features considering theories that allow affirming that programming and design are subject to the Rule of Law rules and a Human Rights oriented ethical framework. © 2021 The Author(s).