Residential Tenancy Agreement

Keep animals (including birds, poultry, fish, mammals and reptiles) in or on premises

What does that mean exactly ..
Having a fight debate my roommates cats being allowed inside the house.

technically, you arent pets allowed anywhere on the property, so that is both inside and outside.

Where on Earth you rent from? All countries of the world has rental agreements?

This means that you must keep your pets in the area that is leased to you .. (Yes, that includes inside the house.)