When the time for probating and registering claims has elapsed, the court shall cause notice to be inserted for three successive weeks in some newspaper published in the county that at a time fixed the claims will be taken up for examination and adjudication by the court or by the clerk in vacation, as the order may designate, that all claims not required by law to be probated and registered must be filed with the clerk by the day named in the notice, and that all creditors may attend. At the time appointed the court shall examine into the validity of each claim which has been probated and registered and such other claims as may have been filed with the clerk. The executor or administrator or any creditor may object to any claim, and the court shall hear evidence in support of the objection, shall allow any claim that should be allowed, and shall reject in whole or in part any which is in whole or in part not well founded. It shall not be necessary for any creditor to refile with the clerk any claim which has been duly probated and registered within the time and in the manner required by law. All other claims, unless filed with the clerk by the day named in the notice, shall not be allowed; but lawful claims, not required to be probated and registered, which are not filed with the clerk by the day named in the notice shall not be barred as to any surplus that remains after paying in full all claims allowed by the court at the examination and adjudication named in the notice. Provided, however, that in cases where the executor or administrator shall have, prior to the adjudication of insolvency, paid any claim or claims, whether probated and registered or not, such executor or administrator shall have the right by the day named in the notice, to file with the clerk a verified itemized statement of the amount which has been paid thereon, and obtain allowance therefor in the same amount to which the creditor or creditors, whose claim or claims had been so paid, would have been entitled had such creditor filed the claim.