What is the ruling regarding a judge's refusal to hear the testimony of witnesses because they did not say, "I bear witness by Allah the Almighty," even though their testimony was established under oath?

The issue of administering an oath to witnesses is a matter of disagreement among scholars. The majority hold that witnesses are not obligated to swear an oath, and it is not a condition for the acceptance of their testimony. Some scholars, however, believe that a witness swearing an oath invalidates their testimony because it implies an accusation against them. Yet, some scholars, such as Ibn Waddah and the Qadi al-Jama'a of Cordoba, Muhammad ibn Bishr, advocate for administering an oath to them due to the corruption of the times. Ibn al-Qayyim did not consider this far-fetched. Accordingly, the swearing of an oath by witnesses is not a condition for the acceptance of their testimony according to the majority of scholars. And if they do not swear an oath during testimony, there is no one who has stated that their testimony is invalid.