The overarching conflict of the play is, as others have already mentioned, that between Oedipus and himself. But in the course of this conflict playing out, a number of other important conflicts are generated as a result. Oedipus's overriding desire to find Laius' murderer (himself) leads him into direct conflict with the blind seer-prophet Tiresias.
At first, Tiresias is reluctant to reveal the identity of Laius's killer—not surprisingly, when you consider that he's actually standing right in front of him. Tiresias's reluctance to divulge this crucial information leads Oedipus to accuse him of being the murderer. Tiresias is then left with no choice: he must tell the truth.
But Oedipus simply cannot believe his ears. And so we're introduced to another conflict related to Oedipus vs himself: Oedipus vs the truth. Oedipus has pledged to get at the truth, to find out who killed Laius no matter what, but when all the sordid details of what really happened are revealed to him, he instantly...
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