Мидраш к Мелахим А 3:27

R. Elazar said: "At three places the Holy spirit appeared: At the court of Shem, in the court of the prophet Samuel, and in the court of King Solomon. At the court of Shem, as it is written (Gen. 38, 26) And Juda acknowledged them and said, She hath been more righteous than I. And whence did he know? Perhaps just as he was with her, so was some one else. Therefore a Heavenly voice was heard: I have decided that so is it to be. In the court of Samuel, as it is written (I. Sam. 12, 5) And he answered, He is witness. Why He? It ought to be they! Hence a Heavenly voice was heard, I witness that so it is. And in the court of King Solomon, as it is written (I. Kin. 3, 17) The king then answered and said, Give her the living child and do not slay it; She is its mother. And whence do we know that it really was so, perhaps she deceived him? Hence the last words, she is its mother, were said by a Heavenly voice." Said Raba: "If it were based merely upon the Scripture, all of them could be objected to, but this is shown by tradition."

“Woe is you, land, whose king is a lad, and your princes dine in the morning. Happy are you, land, that your king is a free man, and your princes dine at the proper time, in valor and not in drunkenness” (Ecclesiastes 10:16–17).
“Woe is you, land, whose king is a lad” – it is written: “Then, two women who were prostitutes came” (I Kings 3:16).⁷¹They each had a baby and one of the babies died. Each claimed the live one was hers, and they came before King Solomon for adjudication. See I Kings 3:16–28. Who were they? Rabbi Meir says: They were spirits. The Rabbis say: They were women awaiting levirate marriage.⁷²If a man dies without children, his widow is subject to the law of levirate marriage. The husbands of these women died without children but while their wives were pregnant, and the women subsequently gave birth. However, a child who dies within the first thirty days does not exempt the mother from levirate marriage, and therefore an outcome of the case would be the determination of which woman would be subject to levirate marriage (Midrash HaMevo’ar). Rabbi Simon in the name of Rabbi Yehoshua says: They were actual prostitutes, and he issued their verdict without witnesses and forewarning. “The one woman said: Please, my lord…it was on the third day after I gave birth…the son of this woman died” (I Kings 3:17–19) because she rolled upon him. “She arose during the night.… I arose in the morning to nurse my son.… The woman said: No, but…. The king said: This one says…” (I Kings 3:20–23). Rabbi Pinḥas and Rabbi Yirmeya [said] in the name of Rabbi Ḥiyya bar Abba and Rabbi Beivai, and some tend to cite it in the name of Rabbi Pedat: The procedure of the judgment is as follows: The judge sits, the judged stand, the mediator decides between them,⁷³Some commentaries suggest that the phrase “the mediator decides between them” is mistaken and should not appear (see Rabbi David Luria). the plaintiff lodges his complaint, the defendant responds, and the judge decides between them. Rabbi Simon said: From here it is derived that the judge must reiterate their claims, from this verse: “[The king said:] This one says: This is my son that lives [and your son is the dead], and that one says: [No, your son is the dead and my son is the living]” (I Kings 3:23).
“The king said: Bring me a sword.… The king said: Cut the living child.… The woman whose child was the living one…” (I Kings 3:24–26) – Rabbi Yehuda said that Rabbi Ilai said: Had I been there, I would have wrapped soft wool around his neck,⁷⁴Around Solomon’s neck, as a judge who issues a false judgment is executed by strangulation. as when he said: “Bring me a sword,” had [the mother] not been overcome by mercy for him [her child], he would have been killed. Regarding that moment, it says: “Woe is you, land, whose king is a lad.” At that moment, he began spouting wisdom; he said: Was it for nothing that the Holy One blessed be He created in this person two eyes, two ears, two feet, two hands? It was because the Holy One blessed be He foresaw that this judgment is destined to transpire.⁷⁵The Holy One blessed be He created man proportionally so it would be possible to cut the child lengthwise into two equal parts. [Ultimately] he did not do so, but rather he said: “Give her the living child, and do not kill him” (I Kings 3:27). Regarding that moment, it says: “Happy are you, land, that your king is a free man and your princes dine at the proper time” – at the time of the World to Come; “and not in drunkenness [vashti]” – in his strength and not in his weakness [bitshisho]. “The king answered and said: Give her the living child.” The Divine Spirit was shouting and saying: She is certainly his mother.
Rabbi Shmuel bar Naḥmani said: In three places, the attribute of justice shouted: In the court of Shem, in the court of Samuel, and in the court of Solomon. In the court of Shem, from where is it derived? It is as it is stated: “Judah recognized and said: She is more righteous than I” (Genesis 38:26), and the Divine Spirit shouted and said: All of these matters originated with Me.⁷⁶The events leading up to the trial (see Genesis, chap. 38) were a result of Divine providence. In the court of Samuel, from where is it derived? It is as it is stated: “Here I am; testify against me before the Lord.… He said to them: The Lord is witness for you, and His anointed is witness” (I Samuel 12:3–5). It is not written here, “they said…witness,” but rather, “he said…witness.” Who said “witness”? The Divine Spirit said: ‘You will testify regarding the revealed, and I will testify regarding the concealed.’ In the court of Solomon, from where is it derived? It is as it is stated: “The king answered and said: Give her the living child” (I Kings 3:27). The Divine Spirit shouted and said: She is certainly his mother.
Another matter: “Woe is you, land, whose king is a lad” – these are the kings of Israel; “happy are you, land, that your king is a free man” – these are the kings of Judah. “And your princes dine in the morning” – these are the kings of Israel; “and your princes dine at the proper time” – these are the kings of Judah.⁷⁷The kings of Israel were wicked, and therefore consumed in this world all goodness they will receive. Many of the kings of Judah were righteous, and have a share in the World to Come.