Counterexample Generator

Purpose

Provides automated search capabilities for finding counterexamples to mathematical conjectures and validating proof attempts.

Capabilities

• Random testing with intelligent sampling
• SMT-based counterexample search
• Quickcheck-style property testing
• Boundary case enumeration
• Finite model finding (Nitpick, Quickcheck)

Usage Guidelines

1. Property Specification: Define testable properties formally
2. Sampling Strategy: Choose appropriate random distributions
3. Constraint Solving: Use SMT for structured search
4. Boundary Testing: Exhaustively check small cases

Tools/Libraries

• Z3
• CVC5
• Quickcheck
• Nitpick