Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add ArabelaTso/Skills-4-SE --skill counterexample-debuggergit clone --depth 1 https://github.com/ArabelaTso/Skills-4-SEWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/arabelatso/skills-4-se/counterexample-debugger)<a href="https://agentmods.dev/skills/arabelatso/skills-4-se/counterexample-debugger"><img src="https://agentmods.dev/badge/skills/arabelatso/skills-4-se/counterexample-debugger.svg" alt="Measured on agentmods" height="20"></a>- NVIDIA SkillSpector pass
What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00127 | $0.01759 |
| Opus 5 | $0.00063 | $0.00879 |
| Sonnet 5 | $0.00025 | $0.00352 |
| Haiku 4.5 | $0.00013 | $0.00176 |
Grade A, and why
counterexample-debugger scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 9d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 292 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Counterexample-Guided Proof Debugger
Analyze counterexamples from Nitpick or QuickChick to explain proof failures and suggest corrections to specifications or proofs.
Workflow
1. Receive Counterexample Information
Identify what information is provided:
- Counterexample output: From Nitpick or QuickChick
- Failed theorem: The statement that couldn't be proven
- Proof attempt: Any partial proof or tactics tried
- Context: Definitions and lemmas involved
2. Choose Target System
Determine which proof assistant is being used:
- Isabelle/HOL with Nitpick: Finite model finder
- Coq with QuickChick: Property-based testing
- Both: Provide analysis for both systems
3. Analyze the Counterexample
Examine the counterexample systematically:
Verify the counterexample:
- Manually compute the result for the given values
- Confirm it actually violates the theorem
- Check if it's a genuine counterexample or tool limitation
Identify the violation:
- Which part of the theorem fails?
- What values cause the failure?
- Is it an edge case or fundamental issue?
Determine the root cause:
- Missing precondition?
- Incorrect specification?
- Wrong quantifier order?
- Implementation bug?
- Off-by-one error?
- Type constraint issue?
4. Explain the Failure
Provide clear explanation:
What went wrong:
- Describe why the counterexample violates the theorem
- Show the computation step-by-step
- Highlight the specific point of failure
Why it happened:
- Explain the underlying cause
- Identify the conceptual error
- Note any common patterns (empty list, boundary values, etc.)
Impact assessment:
- Is the theorem fundamentally wrong?
- Does it need preconditions?
- Is the specification incomplete?
5. Suggest Corrections
Provide actionable fixes based on the root cause:
For missing preconditions:
(* Before *)
lemma "hd xs ∈ set xs"
(* After *)
lemma "xs ≠ [] ⟹ hd xs ∈ set xs"
For incorrect specifications:
(* Before: uses < instead of <= *)
x < y && is_sorted (y :: ys)
(* After *)
x <= y && is_sorted (y :: ys)
What ships with it
3 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 9d ago First seen · 292 lines · 127 tokens per session scan A 1669bb68ac1b
counterexample-debugger is a skill published in the GitHub repository ArabelaTso/Skills-4-SE (251 stars, last pushed 18d ago), licensed Apache-2.0. It adds 127 tokens to every session and 1,759 once invoked, about $0.0006 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.
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