Automated search for counterexamples to mathematical conjectures
Scanned 9/2/2026
Install to Claude Code
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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]
---
# 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
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