In Sophocles' Oedipus Rex, when does Oedipus begin to think that he himself is the murderer of Laius—what details lead him to this conclusion?

In Sophocles' Oedipus Rex, details
from Tiresias and Jocasta are what finally convince Oedipus that he has murdered the
former King of Thebes.

Creon has learned that the kingdom
of Thebes is cursed because the lawful King of the city was murdered. Oedipus, trying to
help his people by bringing an end to the outbreak of plague, the loss of their crops
and death of their animals, calls for Tiresias (the prophet) and asks for his help.
Tiresias argues extensively with Oedipus, desperate to leave and say nothing. It is not
until the King accuses the prophet of treachery that Tiresias tells Oedipus what he
demands to hear.

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…I say to you: Abide by that
decree

you made earlier, and from this day address
(370)

neither these men here nor me, since
you

are the unholy polluter of this
land.

In essence, Tiresias
tells Oedipus that he is the murderer, the cause of all the
suffering in Thebes. Almost in riddles, Tiresias continues, half-explaining that Oedipus
has done more evil than he can even imagine. (Here he alludes to
Oedipus' sinful marriage to his mother and to the children he has fathered with his
mother—his children are actually his siblings...but still Oedipus does not yet
understand the significance of what Tiresias has struggled to keep
secret.)

Oedipus sends Tiresias away, angry at his veiled
accusations. He fights with Creon as well, accusing him of
conspiring to take his throne from him. When Oedipus and Jocasta are finally alone, she
tells him a story to show that the gods will reveal what prophets and seers sometimes do
not. She believes the oracle that prophesied her husband's death at the hands of their
son was wrong; however, as she speaks to Oedipus, her words strike a chord of horror in
his heart.

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JOCASTA:

A
prophecy came to Laius once…

that death would come to him
from his child,

whoever was born to him from me. But
then,

just as the report is, some foreign
brigands

slew him where the three wagon-roads
meet.

Yet three days had not passed from the birth of my
child, (745)

when that man, binding his ankles
together,

sent him in another’s hands into the
wild

of the mountain. And so Apollo brought
about

neither that he slay his father nor that
Laius

suffer the terrible thing he feared from his
child.(750)

In hearing what
Jocasta has said, especially about Laius being killed where three roads met, Oedipus
asks her questions as to the town where her husband died, what he looked like and who
was with him. All the details lead Oedipus, tragically, to believe that without knowing
it, he did in fact kill his father. (Still Jocasta knows nothing of
this.)

When Oedipus asks how she knew of any of the details
of Laius' death, she reveals that there was one survivor, and Oedipus, looking for the
final damning piece of evidence, asks his wife to summon this man who has left the city
to become a shepherd once more.

Meanwhile, a messenger
arrives from Corinth to tell Oedipus that his "father" is dead, but
reveals...

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...Polybus is nothing to you by birth!
 (1043)

Oedipus had fled his
father's house for fear of killing him, only to end up where he
would kill his biological father. The messenger and the shepherd
meet, and it is discovered that the shepherd gave Oedipus to the messenger (a shepherd
then) to save the baby's life. All that Tiresias inferred was true, and Oedipus knows
that the prophecies were not false: he is the monster the prophet accused him of being,
cursed from his birth.