If you have signed a contract that states that "all intellectual property you produce during your employment belongs to $COMPANY", it would be a harder argument

If you have signed a contract that states that "all intellectual property you produce during your employment belongs to $COMPANY", it would be a harder argument, I think. I have had contracts changed to carve out the "on my time, on my kit" exception (and, yes, I am quite antsy having to involve any of my own equipment in anything work-related).