The Rocket, 48, is bidding to win a record eighth Crucible title in Sheffield this year.
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But he made a slow start to his last-eight match as Bingham took a 3-1 lead into the mid-session interval.
O’Sullivan responded in impressive fashion, claiming the next three frames to edge in front.
But it was 2015 champion Bingham who finished the day the stronger of the two as he ensured the pair went in level at four frames each.
And O’Sullivan was keen to leave the stage as quickly as possible as he rapidly headed for the exit.
When Bingham missed a red having already clinched the frame, the seven-time champion was straight out of his seat.
He went straight up to his opponent to give him and the referee fist-bumps, before he walked straight out of shot towards the dressing room.
And the Eurosport commentator said: “O’Sullivan’s had enough of the frame, of the afternoon in general.”
O’Sullivan’s hopes of an eighth world title received a boost ahead of his second session against Bingham on Wednesday.
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Inside Ronnie’s colourful career
FROM his lightning breaks to blasts at officials, Ronnie O’Sullivan has fired snooker into the spotlight.
The pre-tournament’s second favourite Judd Trump, who was set to meet O’Sullivan in a blockbuster semi-final, saw his Crucible hopes ended as he suffered a 13-9 defeat to Welsh qualifier Jak Jones.
Victory for O’Sullivan over Bingham would see him book his place in a record-extending 14th world championship semi-final.
If he was then to beat Jones, he would be looking to make it eight wins from nine Crucible finals.
His only defeat in a world championship final came in 2014 when he lost 18-14 to Mark Selby.