The conjecture that the quasivariety of odd antilattices is not a variety

An antilattice is an algebra with two binary operations, usually denoted by $\land$ and $\lor$, satisfying the identities defining antilattices. An antilattice is odd if it has no subantilattice with $2$ elements. The class of all odd antilattices is a quasivariety.

Odd-antlattice quasivariety conjecture. The quasivariety of odd antilattices is proper; that is, it is not a variety.

The preceding result gives a quasi-equational axiomatization of odd antilattices. The conjecture asks whether those quasi-identities can be replaced by identities; a positive answer would make odd antilattices a variety, whereas this conjecture predicts that they cannot.