Ill is a synonym of Wrong. Wrong is a synonym of False. False is the opposite of Prove. Prove is related to Math. 
Early is related to Record. Record is related to Statement. Thing is a type of Statement. 
Ill <--Synonym--> Wrong <--Synonym--> False <--Antonym--> Prove <--RelatedTo--> Math 
Early <--RelatedTo--> Record <--RelatedTo--> Statement <--IsA-- Thing 