J solution (~0.2s runtime on my machine)
Nats =: '0123456789'&(i. ".@:{ ' ' ,~ [)
Claim =: ,"0/&((+ i.@])/)
claims =. |:@(2 2 $ }.)@Nats;._2 fread 'input'
claimed =. <@,@(1000 #:inv Claim)/"2 claims
echo # overlaps =. (~.@#~ -.@~:) ; claimed NB. Part 1