Construct Counterexamples

Q: What is a Claude Code skill and how does the Construct Counterexamples skill fit in?

A Claude Code skill is a SKILL.md file that lives under ~/.claude/skills/<name>/ and tells the Claude Code CLI agent how to perform a specific task (instructions, prompts, allowed tools). Skills are auto-discovered at session start. Construct Counterexamples is one of 67,000+ skills indexed in the open ClaudSkills catalog, classified under the General category. Learn more at https://claudskills.com/learn/what-is-skill-md/.

Category: General · Sub-category: general-misc · Last updated: 2026-06-13

Construct candidate counterexamples to test a proposed conjecture, lemma, or intermediate claim by keeping the assumptions true while making the claimed conclusion fail. Use when you are stuck in reasoning and want to see where the assumptions take effect and gain intuition, when a proposed conjecture/claim feels fragile or unproved, or when you want to test whether the assumptions can hold while the claimed conclusion fails.

From the source SKILL.md

Actively falsify proposed conjectures or intermediate claims by finding examples that satisfy the assumptions but violate the claimed conclusion.

What this skill does

Construct Counterexamples is a community-contributed Claude Code skill in the general-misc sub-category. It ships as a SKILL.md file that Claude Code auto-discovers under ~/.claude/skills/construct-counterexamples/ and loads when your prompt matches the skill's trigger.

When to invoke it: Use when you are stuck in reasoning and want to see where the assumptions take effect and gain intuition, when a proposed conjecture/claim feels fragile or unproved, or when you want to test whether the assumptions can hold while the claimed conclusion fails.

Who uses this skill

The Construct Counterexamples Claude Code skill is built for Claude Code users and developers across all disciplines looking for general-purpose AI assistance. It's part of ClaudSkills (also referred to as Claude Skills or Claude Code Skills) — the open community-curated registry of 119,000+ SKILL.md files for Anthropic's Claude Code agent and the wider Claude ecosystem (Claude API, Claude Agent SDK).

How to install

Free

Manual install (2 steps)

mkdir -p ~/.claude/skills/construct-counterexamples
curl -L https://claudskills.com/skills/construct-counterexamples/SKILL.md \
  -o ~/.claude/skills/construct-counterexamples/SKILL.md

Or just download SKILL.md directly and drop it into ~/.claude/skills/construct-counterexamples/. Claude Code auto-discovers it on next session.

Skills live at ~/.claude/skills/construct-counterexamples/SKILL.md on macOS/Linux, or %USERPROFILE%\.claude\skills\construct-counterexamples\SKILL.md on Windows. See the full install guide for step-by-step instructions.

📱 Install from your phone or desktop Telegram

Open @claudskills_bot on Telegram, tap Open Desktop App, and the desktop app installs this skill for you. Or share the bot link with a colleague — they get the same one-tap install. Learn more →

Pro

One-click install via the desktop app

The ClaudSkills desktop app installs any skill directly into ~/.claude/skills/ with one click — no terminal required. Pro starts at $9/mo or $149 lifetime.

Pro

For the full experience including quality scoring and one-click install features for each skill — upgrade to Pro.

See pricing → Download desktop app

Frequently asked questions

How do I install the Construct Counterexamples Claude Code skill?

Install via the ClaudSkills desktop app (one click) or copy SKILL.md from the source repository to ~/.claude/skills/construct-counterexamples/SKILL.md and restart Claude Code. Both flows are detailed at claudskills.com/install/.

What does the Construct Counterexamples skill do?

Is this skill free to install?

Yes. ClaudSkills is an open registry — every skill keeps its source repository's license, and manual install via copy is free. ClaudSkills Pro ($9/mo, $79/yr, or $149 one-time) adds one-click install via the desktop app and a multi-signal Quality Score.

When should I use the Construct Counterexamples skill?

Use Construct Counterexamples when your Claude Code task falls under the General category — specifically in the general misc area. Claude Code auto-discovers installed skills and invokes the right one based on the task description, so you can also ask Claude directly (e.g. "use Construct Counterexamples" or describe the task and let Claude pick). Browse related skills at /category/general/.

What is a Claude Code skill and how does the Construct Counterexamples skill fit in?

A Claude Code skill is a SKILL.md file that lives under ~/.claude/skills/<name>/ and tells the Claude Code CLI agent how to perform a specific task (instructions, prompts, allowed tools). Skills are auto-discovered at session start. Construct Counterexamples is one of 67,000+ skills indexed in the open ClaudSkills catalog, classified under the General category. Learn more at /learn/what-is-a-claude-skill/.

Attribution & license

Source: https://github.com/frenzymath/Rethlas/blob/974b82ccfbcb07c405a233886e6e8d1d4db84828/agents/generation/.agents/skills/construct-counterexamples/SKILL.md
License: Apache-2.0
Author: frenzymath

Cite this skill

If you reference this skill in a blog post, paper, or documentation, you can cite it as:

APA

frenzymath. (2026). Construct Counterexamples [Claude Code skill]. ClaudSkills. https://claudskills.com/skills/construct-counterexamples/

BibTeX

@misc{construct-counterexamples-2026,
  author    = {frenzymath},
  title     = {Construct Counterexamples [Claude Code skill]},
  year      = {2026},
  publisher = {ClaudSkills},
  url       = {https://claudskills.com/skills/construct-counterexamples/}
}

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