Higher-dimensional cNTV spacetimes refute the two-light-line axiom

Let $n \geq 3$ and let $M$ be a cNTV $n$-dimensional spacetime. Write \langle M, \mathrel{\scalebox{0.85}{\oldalpha}} \rangle for its frame with the causal relation \mathrel{\scalebox{0.85}{\oldalpha}}. Higher-dimensional cNTV conjecture.

\langle M, \mathrel{\scalebox{0.85}{$\oldalpha$}} \rangle \not\models a \mathrel{\scalebox{0.85}{$\oldalpha$}}_2 f,

or, equivalently, \mathbf{D4da_2} \nsubseteq \mathcal{L}(\langle M, \mathrel{\scalebox{0.85}{\oldalpha}} \rangle). The conjecture would separate the logic of two-dimensional spacetimes from that of higher-dimensional cNTV spacetimes; proving it requires showing that every such spacetime has at least three distinct light lines through a point that is irreflexive in \mathrel{\scalebox{0.85}{\oldalpha}}.