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In Sophocles' "Oedipus Rex" all the things you are looking for, character, irony, and conflict can all be boiled down to one simple statement: Oedipus, the protagonist, inadvertently kills his father and marries his mother.
The irony is that his father had learned from an oracle that his son was destined to kill him, so he decides to literally take fate into his own hands by abandoning his infant son and leaving the boy to die.
But Oedipus does not die. He if found, and grows up strong and healthy. One day, he encounters his father (whom he does not know is his father). An argument ensues, and Oedipus kills the man. Not much later, he ends up marrying his mother, the now widow of his father, again, of course, not knowing that she is his mother.
Fate has not been avoided, thus the irony and conflict, all rolled up into one.