Can infertile tortoises lay eggs?

by Ryan
(England)

Just now I was walking along, and crack. I step in something. I look down and theres a small white (smashed) egg in the middle of the floor. The yolk, the normal yellow, and there appears to be nothing else in the egg.
There are two possibilities that i can think of: Either my cat brought it in, or my Hermann's tortoise laid it.
My tortoise is currently five years old and female, and has never been introduced to a male as far I know. Looking at her bum, and i can see that its looks slightly slimy, like she has just done a very clean poo.
Do tortoises sometimes lay infertile eggs? Or has my cat just brought it in, and im being paranoid?