"That film wasn't too successful, but then 'WarGames,' which was successful, came out right when I won the Tony for 'Brighton Beach' in 1983.
The person later won an award for WarGames.
This statement fit into the neither category, because while we know this person won an award for Brighton Beach, we do not know if they won anything for WarGames. The system may not have made that differentiation. 
( z1 win :ARG0 ( z2 person ) :ARG1 ( z3 award :ARG3 ( z4 game :name ( z5 name :op "WarGames" ) ) ) :time ( z6 after ) )