Existing is related to Be. Be is a synonym of Follow. Follow is related to Leading. 
you are likely to find Hotel in/at/on Town. Town is related to Reading. Reading is a different concept from Math. Math is the opposite of Problem. 
Existing <--RelatedTo--> Be <--Synonym--> Follow <--RelatedTo--> Leading 
Hotel --AtLocation--> Town <--RelatedTo--> Reading <--DistinctFrom--> Math <--Antonym--> Problem 