What is the ruling on using a washing machine in the dwelling without the owner's permission, given that there is a contract stating that it is not to be used due to the availability of a communal washing machine at a monthly cost?

"The contract is the law of the contracting parties," and it must be adhered to, as Allah Almighty says: "O you who have believed, fulfill [all] contracts." It is not permissible to use the aforementioned washing machine without the owner's permission, and one must absolve oneself of this by paying him his due or seeking his forgiveness.