For a sentence like "Kủq rào kôı jí na ru kảqsı jí bũ", I'd ideally like to assign it something like the following interpretation (with some details removed for simplicity):
∃e. kuq(e) ∧ (∃e1. koı(e1, J) ∧ rao(e, e1)) ∧ (¬∃e1. kaqsı(e1, J) ∧ rao(e, e1))
But there are a couple of big disconnects between this and the actual structure of the Toaq sentence. First, the rao seems to have been split in two by the presence of ru inside the t5 clause, and it's also been pushed underneath the bu in the second conjunct. It has to be this way though - if the rao were placed outside the existential quantifiers, it would not be able to access the event variables that it's supposed to operate on, and if the negation were moved under the quantifier, it just wouldn't have the right meaning.
Just looking at the Toaq though, it would be really nice if the sentence could turn out to have the form
∃e. kuq(e) ∧ rao*(e, ???)