问题：
[多选题]A borrowed from a bank, A, B and the Bank signed a mortgage agreement, under which B provided the mortgage guaranteeing the repayment. B handed over the property ownership certificate to the Bank, but the Bank did not complete the title registration of estate under the mortgage due to the registration department’s problem. B reported the loss of the property ownership certificate to the registration department and got a new one. Thereafter, B sold this property to C who knew everything, and finished the title transfer procedure. A did not pay back the loan on due date.
About the loan, house mortgage, sales and purchase, which of the following is true?
A、B should assume the liability for the breach of contract to the bank.
B、C should pay back to the bank.
C、If C pays back to the bank, he could claim the repayment from A.
D、Due to the fact that the registration department failed to complete the mortgage registration, the bank occupies the property ownership certificate, thus acquiring the mortgage.
