User:Ascii/Coprime Relation for Integers is Non-transitive

Theorem
The relation "is coprime to" on the integers is not non-transitive.

That is, it is neither transitive:


 * $\neg \, \forall m, n, p \in \Z: m \perp n \land n \perp p \implies m \perp p$

nor antitransitive:


 * $\neg \, \forall m, n, p \in \Z: m \perp n \land n \perp p \implies m \not \perp p$

where $\perp$ denotes "is coprime to".