King Solomon faces a complete legal dead end. Two women present contradictory claims over a living infant, and there is absolutely no evidence to prove who is telling the truth. To resolve the dispute, the king issues a command that initially seems like a cold compromise. He gives the order to physically cut the living child in two [מצודת ציון]. The apparent logic behind this instruction is that since neither side can provide proof, the disputed infant should be divided so that each woman receives an equal half [ביאור שטיינזלץ].
However, this command is never intended to be an actual verdict. Instead, it is a calculated psychological test. The king has already used his wisdom to deduce which woman is speaking the truth and which one stole the child, simply by listening to their words. The true purpose of ordering the child to be cut is to stage a public examination. This is designed to expose the truth and prove to everyone present in the courtroom exactly what the king has already figured out [מצודת דוד].