If Big Corp has a US patent and Inter Corp is infringing in the US then Big Corp can take them to a US court. If they win then either Inter desists in the US or pays a licence fee (or whatever the court decides).
The fact that Inter Corp is incorporated somewhere else is irrelevant as it's its operation in the US that will be brought to book. Outside of the US it's a different matter and will depend on what international patents Big Corp has, where Inter Corp is infringing etc.