What does Oedipus discover in his search to find the murderer of Laius?

In his search for the murderer of Laius, Oedipus unwittingly discovers that he himself is the killer. Through a series of revelations and encounters, Oedipus uncovers the truth about his past and his relationship with Laius. Here's a summary of the key discoveries that lead Oedipus to this realization:

1. Oracles and Prophecies: Oedipus learns that the oracle of Delphi had predicted that he would kill his father and marry his mother. Initially, he believes this prophecy applies to his adoptive parents, Polybus and Merope, so he leaves Corinth to avoid fulfilling it.

2. Fateful Journey: During his journey, Oedipus encounters a group of travelers and gets into an argument with an old man. In the heat of the moment, Oedipus strikes the old man, unaware that it is Laius. He kills Laius and his companions at a crossroads, but this incident remains unsolved in Oedipus's mind.

3. Investigating Laius's Murder: When Oedipus arrives in Thebes and solves the riddle of the Sphinx, he becomes the new king and inherits the unresolved case of Laius's murder. Determined to find the truth, Oedipus launches an investigation.

4. Teiresias's Prophecy: Oedipus consults the blind seer Teiresias, who reluctantly reveals the shocking truth: Oedipus is fated to kill his own father and have children with his mother. Teiresias also hints that Oedipus has already committed these acts without knowing it.

5. Messenger from Corinth: Oedipus receives a messenger from Corinth with news of Polybus's death and an offer to return to Corinth as the new king. This news initially eases Oedipus's worries about the prophecy but unwittingly provides more clues to his true identity.

6. Jocasta's Story: Oedipus's wife and mother, Jocasta, reveals her own traumatic past and the story of a son who was abandoned due to a prophecy similar to Oedipus's. As Oedipus pieces together the details, he realizes that he is the abandoned child.

7. Discovery of the Truth: Jocasta recognizes the truth and begs Oedipus to stop searching, but Oedipus is determined to uncover the full extent of his fate. The truth ultimately becomes inescapable as more evidence emerges, leading Oedipus to a profound revelation about his identity and his tragic actions.

In the end, Oedipus discovers the horrifying truth that he inadvertently fulfilled the oracle's prophecy, unknowingly killing his biological father, Laius, and marrying his biological mother, Jocasta. This leads to his downfall and the events that unfold in Sophocles' tragedies "Oedipus Rex" and "Oedipus at Colonus."