Davis–Putnam algorithm

The Davis–Putnam algorithm is a systematic method for determining if a logical statement (or set of statements) can be true at the same time. It works by breaking down the problem into smaller parts, repeatedly picking a variable and testing both possibilities—true or false—while simplifying the statements accordingly. If a contradiction appears or all options are exhausted without a consistent solution, the statements cannot all be true together. Conversely, if a consistent assignment is found, the statements are satisfiable. This process helps in automated reasoning, such as verifying whether a set of logical rules can coexist without conflict.