theory-counterexample

Identify minimal counterexamples that violate assumptions in mathematical claims.

7|1|Updated Mar 19, 2026

Search Tags:#mathematics #logic #assumptions #critical-thinking #counterexample #proof-analysis #theory-testing

Ready to run

npx skills add https://github.com/Shiien/Self-Evolved-Research-Framework --skill theory-counterexample

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: theory-counterexample
Source: https://github.com/Shiien/Self-Evolved-Research-Framework/tree/main/skills/theory-counterexample
Command: npx skills add https://github.com/Shiien/Self-Evolved-Research-Framework --skill theory-counterexample

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

This skill helps you systematically test mathematical claims by constructing counterexamples, highlighting where assumptions fail and guiding refinement.

Core Features & Use Cases

Generate degenerate, boundary, and pathological counterexamples to reveal weaknesses in a claim.
Report minimal counterexamples and specify which assumption is violated, with suggested strengthened conditions.
Applicable to mathematical proofs, logic, and theoretical computer science conjectures; useful for proof critique, research brainstorming, and hypothesis refinement.

Quick Start

State a claim with explicit assumptions and ask the system to produce a counterexample or verify the claim.

Frequently Asked Questions about theory-counterexample

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I find a counterexample to disprove a mathematical conjecture?▼

Identify a counterexample by testing the claim's explicit assumptions using degenerate cases, boundary conditions, and known pathological examples across domains like algebra and analysis to disprove or challenge the mathematical claim.

What is a minimal counterexample in proof analysis?▼

A minimal counterexample in proof analysis is the simplest specific case that demonstrates a mathematical claim fails by violating its stated assumptions, helping researchers identify exactly where the proof breaks down and suggests stronger conditions.

How do I test mathematical claims using boundary conditions and pathological examples?▼

Test mathematical claims by applying boundary conditions and pathological examples across algebra, analysis, and logic. This process challenges the stated assumptions and verifies robustness for typical cases or isolates failures to refine the hypothesis.

Can I use this to critique theoretical computer science conjectures and logic proofs?▼

Yes, you can critique theoretical computer science conjectures and logic proofs. The system constructs counterexamples to reveal weaknesses in assumptions, providing outputs that specify the violated condition and suggest stronger constraints or a formal proof.

What do I need to provide to generate a counterexample for a mathematical claim?▼

You need to state the mathematical claim with explicit assumptions. The system then processes this input to output a clear minimal counterexample, the specific violated assumption, and suggestions for stronger conditions or a formal proof.

When should I not rely on a counterexample to test a mathematical hypothesis?▼

You should not rely solely on a counterexample when verification of robustness for typical cases is required without identifying specific assumption failures, as the system focuses on challenging claims and refining hypotheses rather than proving universal validity.