# Z3 — High-Performance SMT Solver by Microsoft Research

> Z3 is a theorem prover and satisfiability modulo theories (SMT) solver used for software verification, constraint solving, and formal methods research.

## Install

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# Z3 — High-Performance SMT Solver by Microsoft Research

## Quick Use
```bash
pip install z3-solver
```
```python
from z3 import *
x, y = Ints('x y')
s = Solver()
s.add(x + y == 10, x - y == 4)
print(s.check())   # sat
print(s.model())   # [x = 7, y = 3]
```

## Introduction
Z3 is an SMT (Satisfiability Modulo Theories) solver developed by Microsoft Research. It decides the satisfiability of logical formulas over integers, bit-vectors, arrays, floating-point numbers, and other data types. Z3 is widely used in program verification, symbolic execution, test generation, and constraint-based synthesis.

## What Z3 Does
- Solves satisfiability problems over arithmetic, bit-vectors, arrays, and strings
- Powers program verification tools like Dafny, KLEE, and Seahorn
- Supports optimization objectives (MaxSMT) for constrained optimization
- Provides proof generation and unsatisfiable core extraction
- Offers bindings for Python, C, C++, Java, .NET, and OCaml

## Architecture Overview
Z3 implements a DPLL(T) architecture combining a SAT solver core with theory solvers for linear arithmetic, non-linear arithmetic, bit-vectors, arrays, datatypes, sequences, and floating-point. Theories communicate through an equality graph, and the solver supports incremental solving with push/pop scopes. The fixedpoint engine adds Datalog and CHC (constrained Horn clause) solving.

## Self-Hosting & Configuration
- Install the Python binding: `pip install z3-solver`
- Pre-built binaries available for Linux, macOS, and Windows
- Build from source with CMake for custom configurations
- No external dependencies beyond a C++ compiler for source builds
- Embeddable as a library via the C API in any application

## Key Features
- One of the fastest and most widely adopted SMT solvers in the world
- Incremental solving for interactive verification workflows
- Supports quantifiers with pattern-based and MBQI instantiation
- Parallel solving mode for multi-core utilization
- Extensive documentation and an active research community

## Comparison with Similar Tools
- **CVC5** — competitive SMT solver; Z3 has broader industry adoption
- **Yices 2** — lightweight and fast for specific theories; Z3 covers more theory combinations
- **MathSAT** — strong on interpolation; Z3 has wider language bindings
- **STP** — specialized for bit-vector/array; Z3 is more general-purpose

## FAQ
**Q: Is Z3 suitable for production use?**
A: Yes. Z3 is used in production by Microsoft, Amazon, and others for verification, security analysis, and network configuration validation.

**Q: Can Z3 solve optimization problems?**
A: Yes. Z3 supports optimization via its Optimize class, handling both hard constraints and soft objectives with priorities.

**Q: What is the difference between SAT and SMT?**
A: SAT solves Boolean satisfiability. SMT extends SAT with theories like arithmetic and arrays, letting you reason about richer domains.

**Q: Does Z3 support non-linear arithmetic?**
A: Yes, Z3 has a dedicated nlsat solver for non-linear real arithmetic and heuristic support for non-linear integer arithmetic.

## Sources
- https://github.com/Z3Prover/z3
- https://z3prover.github.io/

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