Agent-Skills.md

Agent Skills: Counterexample Generator

Automated search for counterexamples to mathematical conjectures

theorem-provingID: a5c-ai/babysitter/counterexample-generator

Repository

a5c-ai/babysitter
a5c-aiLicense: MIT
244

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pnpm dlx add-skill https://github.com/a5c-ai/babysitter/tree/HEAD/plugins/babysitter/skills/babysit/process/specializations/domains/science/mathematics/skills/counterexample-generator

Skill Files

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plugins/babysitter/skills/babysit/process/specializations/domains/science/mathematics/skills/counterexample-generator/SKILL.md

Skill Metadata

Name
counterexample-generator
Description
Automated search for counterexamples to mathematical conjectures

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