Finitely presented left orderable monsters

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