AllWays Moving and Storage AllWays refuses to pay damages even after driver explicitely said to list them on the contract Phoenix Arizona

Allways Moving and Storage delivered (most) of our property to our new home, and there were many damages to very expensive items including: rip in leather sofa, broken/crushed wood door on kitchen hutch, broken leg on entertainment center, broken leg on dresser, broken portion of hand carved roman column, tv base pulled off and missing. stole our dolly, stole our metal trash can!, crushed the wicker hamper. 

The driver said to call the company in the morning and they would handle it through their insurance. Then during the "All CASH" transaction, I signed the contract to complete the move process.  When my husband called this morning, the woman on the phone claimed that since their driver had not signed the contract (which listed on ly some of the damages), then the insurance was null and void.  My husband said, I guess we'll have to sue you then.  The woman responded "see you in court" and hung up.  Nice.