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Boolean satisfiability (SAT) solvers have been successfully applied to a wide variety of difficult combinatorial problems. Many further problems can be solved by SAT Modulo Theory (SMT) solvers, which extend SAT solvers to handle additional types of constraints. However, building efficient SMT solvers is often very difficult. In this paper, we define the concept of a Boolean monotonic theory and show how to easily build efficient SMT solvers, including effective theory propagation and clausedoi:10.1609/aaai.v29i1.9755 fatcat:ezcflwu74bhfxoczd6h53itp7q