  A left orderable monster is a finitely generated left orderable group all of
whose fixpoint-free actions on the line are proximal: the action is
semiconjugate to a minimal action so that for every bounded interval $I$ and
open interval $J$, there is a group element that sends $I$ into $J$. In his
2018 ICM address, Navas asked about the existence of left orderable monsters.
By now there are several examples, all of which are finitely generated but not
finitely presentable. We provide the first examples of left orderable monsters
that are finitely presentable, and even of type $F_\infty$. The construction
itself is elementary, and these groups satisfy several additional properties
separating them from the previous examples: they are not simple, they act
minimally on the circle, and they have an infinite-dimensional space of
homogeneous quasimorphisms. Our construction is flexible enough that it
produces infinitely many isomorphism classes of finitely presented (and type
$F_{\infty}$) left orderable monsters.
