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hey good morning everyone um lets get started with uh for day four and today we are very pleased to have Randy Bryant talking about the power of external resolution and explore it thank you so its been an interesting uh series of talks Ive learned a lot and um but Ive come at this really as an engineer who wants to build tools uh and the one tool Ive discovered recently and Ill talk about is extended resolution Ill Ill describe more about what I mean by that but my career a large part of my career has been spent doing what I call formal verification and this is just a subset of the titles of some of my papers um and the word formal verification shows up a lot but the honest truth is and so you can think of the general principle of what this is is you have some mathematical description of a system and you make some statements about Its Behavior and you want to be able to formally verify thats correct but the truth is that the tools that my students and I have developed over the