Z3 Theorem Prover

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Z3 Theorem Prover
Z3 Theorem Prover Logo 329x329.jpg
Original author(s)Microsoft Research
Initial release2012; 9 years ago (2012)
Stable release
z3-4.8.10 / January 20, 2021; 3 months ago (2021-01-20)[1]
Written inC++
Operating systemWindows, FreeBSD, Linux (Debian, Ubuntu), macOS
PlatformIA-32, x86-64
TypeTheorem prover
LicenseMIT License

Z3 Theorem Prover is a cross-platform satisfiability modulo theories (SMT) solver by Microsoft.[2]


Z3 was developed in the Research in Software Engineering (RiSE) group at Microsoft Research and is targeted at solving problems that arise in software verification and software analysis. Z3 supports arithmetic, fixed-size bit-vectors, extensional arrays, datatypes, uninterpreted functions, and quantifiers. Its main applications are extended static checking, test case generation, and predicate abstraction.

In 2015, it received the Programming Languages Software Award from ACM SIGPLAN.[3][4] In 2018, Z3 received the Test of Time Award from the European Joint Conferences on Theory and Practice of Software (ETAPS).[5] Microsoft researchers Nikolaj Bjørner and Leonardo de Moura received the 2019 Herbrand Award for Distinguished Contributions to Automated Reasoning in recognition of their work in advancing theorem proving with Z3.[6][7]

Z3 was open sourced in the beginning of 2015.[8] The source code is licensed under MIT License and hosted on GitHub.[9] The solver can be built using Visual Studio, a Makefile or using CMake and runs on Windows, FreeBSD, Linux, and macOS.

It has bindings for various programming languages including C, C++, Java, Haskell, OCaml, Python, WebAssembly, and .NET/Mono. The default input format is SMTLIB2.


Propositional and predicate logic[edit]

In this example propositional logic assertions are checked using functions to represent the propositions a and b. The following Z3 script checks to see if ¬(a ∧ b ) ≡ (¬ a ∨ ¬ b):

(declare-fun a () Bool)
(declare-fun b () Bool)
(assert (not (= (not (and a b)) (or (not a)(not b)))))



Note that the script asserts the negation of the proposition of interest. The unsat result means that the negated proposition is not satisfiable, thus proving the desired result (De Morgan's laws).

Solving equations[edit]

The following script solves the two given equations, finding suitable values for the variables a and b:

(declare-const a Int)
(declare-const b Int)
(assert (= (+ a b) 20))
(assert (= (+ a (* 2 b)) 10))


  (define-fun b () Int
  (define-fun a () Int

See also[edit]


  1. ^ https://github.com/Z3Prover/z3/releases/tag/z3-4.8.10
  2. ^ http://lim.univ-reunion.fr/staff/fred/Enseignement/AlgoAvancee/Exos/Z3-exercises.pdf
  3. ^ "Programming Languages Software Award". www.sigplan.org.
  4. ^ Microsoft Z3 Theorem Prover Wins Award
  5. ^ ETAPS 2018 Test of Time Award
  6. ^ The inner magic behind the Z3 theorem prover - Microsoft Research
  7. ^ Herbrand Award
  8. ^ "Microsoft's Visual Studio timeline and Z3 Theorem Prover, Google Cloud Launcher, Facebook's Fresco—SD Times news digest: March 27, 2015". March 27, 2015.
  9. ^ "GitHub - Z3Prover/z3: The Z3 Theorem Prover". December 1, 2019 – via GitHub.

Further reading[edit]

  • Leonardo De Moura, Nikolaj Bjørner (2008). "Z3: an efficient SMT solver". Tools and Algorithms for the Construction and Analysis of Systems. 4963: 337–340.CS1 maint: uses authors parameter (link)
  • Dennis Yurichev - SAT/SMT by Example - With many examples using Z3Py.

External links[edit]