Discourse Representation Theory (DRT) distinguishes itself from other semantic representation frameworks by its ability to model complex semantic and discourse phenomena through structural nesting and variable binding. While seq2seq models hold the state of the art on DRT parsing, their accuracy degrades with the complexity of the sentence, and they sometimes struggle to produce well-formed DRT representations. We introduce the AMS parser, a compositional, neurosymbolic semantic parser for DRT. It rests on a novel mechanism for predicting quantifier scope. We show that the AMS parser reliably produces well-formed outputs and performs well on DRT parsing, especially on complex sentences.