# Counterexamples and domain eligibility

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Counterexamples and domain eligibility](https://ocme.evemisslab.com/en/atlas/atlas-counterexample/)

A counterexample must belong to the claimed domain and falsify the universal predicate. An outside value or failure to find a counterexample does not by itself prove the original statement.

atlas-counterexample · canonical_mko

[Counterexamples and domain eligibility](https://ocme.evemisslab.com/en/mko/mko-counterexample/)

## Prerequisite nodes


- [Quantifiers and explicit domains](https://ocme.evemisslab.com/en/atlas/atlas-quantifier/)
- [Mathematical proof](https://ocme.evemisslab.com/en/atlas/atlas-proof/)