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  Ding scored at least a half-century in every frame he won as he extended his first-session lead from 6-2 to 10-2.
  Williams, who had to play with a new tip after splitting his old one on Monday, managed to pot just two balls before the mid-session interval.
  The Welshman did take frame 13, but China's Ding powered to victory.
  Two-time Crucible champion Williams only made two half-centuries, but said he was destined to lose from the moment he split his old tip.
  "I got beat easily and, to be honest, deep down I knew I would so I cannot really grumble," said Williams, 41.
  "I was playing, and feeling, brilliant. With the players left in, it was probably my best chance of winning the World Championship.
  "But as soon as my tip split the night before I knew then that my chances were gone. It was almost impossible. It didn't matter who I played.
  "He played good but in the first session, I feel, if I had my normal tip I would have been in front."
  Ding still had to take his opportunities and he did so in devastating style.
  Williams was so accustomed to sitting in his chair during a one-sided start to the evening session, that Ding had to remind his opponent to get up and go in for a break.
  The Welshman then joked that he had Ding "rattled" and his "head had gone" when he tweeted during the interlude.
  Ding, who last reached the semi-finals in 2011, has dropped down to 17 in the world and had to qualify for this year's tournament.
  But the 29-year-old looked to be reaping the reward of so much time in play during a one-sided morning session where he was sharp and fluent in taking six from seven frames after Williams won the opener.
  And he sealed victory with little fuss, grabbing his 11th score of more than 50 on his way.
  "I got some easy chances in the match because Mark had a lot of bad kicks," Ding said. "And every player has a big problem if they have a new tip.
  "I controlled the game, took my chances and made some good breaks. I was confident. Every time I saw a chance I thought I could go for it and pot it."
  In the evening's other match, world number one Mark Selby maintained his four-frame advantage over gutsy qualifier Kyren Wilson to lead 10-6 with a session to play.
  Wilson, who beat top-10 seeds Joe Perry and Mark Allen to reach the last eight, had chances in the first three frames but lost them all as the 2014 champion Selby built a 6-0 lead.
  The Kettering man responded by taking the next two and then won a scrappy ninth frame of a disjointed match to get to within three.
  But Selby's famed matchplay saw him keep his rival at bay and he won a tense final frame to avoid his lead being reduced to two frames.
  Wilson and Selby return to finish their match on Wednesday morning.
target: Ding Junhui thrashed Mark Williams 13-3 inside two sessions to become the first man into this year's World Championship semi-finals.