Z3 is an efficient Satisfiability Modulo Theories (SMT) solver developed by Microsoft Research. It is designed to solve logical first-order formulas with respect to various background theories such as arithmetic, bit-vectors, arrays, and uninterpreted functions. Z3 has been widely used in software verification and analysis applications, including Spec\#/Boogie, Pex, HAVOC, Vigilante, a verifying C compiler (VCC), and Yogi. The solver integrates a modern DPLL-based SAT solver, a core theory solver for equalities and uninterpreted functions, satellite solvers for arithmetic and arrays, and an E-matching abstract machine for quantifiers. Z3 uses novel algorithms for quantifier instantiation and theory combination, achieving significant performance improvements over existing SMT solvers. It supports multiple input formats and APIs, making it versatile for different applications. The system architecture includes a simplifier, compiler, congruence closure core, theory combination, SAT solver, clause deletion, relevancy propagation, and model generation. Z3 has been successfully applied in extended static checking, test case generation, and predicate abstraction.Z3 is an efficient Satisfiability Modulo Theories (SMT) solver developed by Microsoft Research. It is designed to solve logical first-order formulas with respect to various background theories such as arithmetic, bit-vectors, arrays, and uninterpreted functions. Z3 has been widely used in software verification and analysis applications, including Spec\#/Boogie, Pex, HAVOC, Vigilante, a verifying C compiler (VCC), and Yogi. The solver integrates a modern DPLL-based SAT solver, a core theory solver for equalities and uninterpreted functions, satellite solvers for arithmetic and arrays, and an E-matching abstract machine for quantifiers. Z3 uses novel algorithms for quantifier instantiation and theory combination, achieving significant performance improvements over existing SMT solvers. It supports multiple input formats and APIs, making it versatile for different applications. The system architecture includes a simplifier, compiler, congruence closure core, theory combination, SAT solver, clause deletion, relevancy propagation, and model generation. Z3 has been successfully applied in extended static checking, test case generation, and predicate abstraction.