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name: counterexample-generator description: Automated search for counterexamples to mathematical conjectures allowed-tools:

• Bash
• Read
• Write
• Edit
• Glob
• Grep metadata: specialization: mathematics domain: science category: theorem-proving phase: 6 graph: domains: [domain:mathematics] specializations: [specialization:computational-mathematics] skillAreas: [skill-area:mathematical-reasoning, skill-area:computational-geometry, skill-area:graph-algorithms] workflows: [workflow:experiment-design] roles: [role:computational-scientist, role:research-scientist]

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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