that face you make

Barr did not lie in his summary letter and this was reported that Mueller found the summary letter to accurately reflect the findings of the investigation. This was reported by even left leaning sources like the Washington Post.

So this clearly debunks your first claim, because Barr having spoke with Mueller would not be aware of any frustration they had with his summary. Mueller was frustrated with the media's reporting around his report.

Initial reporting said that Mueller didn't object to Barr's summary.

But that reporting was wrong.

We know this now because of the letter that Mueller sent after that summary letter was released. As I quoted above and will quote again now, according to Mueller's letter to Barr, Barr's summary "did not fully capture the context, nature and substance"

Here is a link to Time's reporting that also contains a link to Mueller's letter: http://time.com/5581055/robert-mueller-william-barr-letter-transcript/

You can read it for yourself. Clearly, Mueller did not agree with Barr's summary.

Barr lied.

To Congress. To us.

After Barr received the letter, Barr called Mueller, and on that call Barr pressed Mueller as to whether he believed anything in his summary letter was inaccurate or wrong and Mueller said according to DOJ officials on the call "The officials said that Mueller did not describe Barr's letter as inaccurate but that he thought it was resulting in misleading news coverage about the report."

So, Barr did not lie. He called Mueller after receiving the letter, that call established that Mueller DID NOT believe the letter to be inaccurate.

That brings us to Barr's testimony. ”that it does not adequately or accurately, necessarily, portray the report's findings. Do you know what they're referencing with that?"

This is not a like, because the phone call didn't address this. The phone call, again after the letter, was about whether or not Barr's summary was inaccurate.

Barr says that's what was discussed during the phone conversation. A transcript of that call was taken. When senators asked if they could see that transcript, Barr said he would not release it.

Why would Barr keep that transcript hidden if Mueller agreed with him?

Mueller didn't agree with Barr's summary. Otherwise it would be the easiest thing to release that transcript- even a redacted form if things were discussed not suitable for the public eye. But no. He's not going to provide evidence to support his statement.

Which means he's lying.

False, his reluctancy to release the transcript does not prove he is lying. Your making that assumption.

A DOJ official recounted the conversation to the media.

Keep on deluding yourself.

Sorry, no. Barr doesn't get a "because you'll just have to believe me." free pass.

In April- AFTER the letter from Mueller was sent and after their conversation over the phone- he was asked if he knew if Mueller supported his summary.

He said: "I don't know whether Bob Mueller supported my conclusion."

By your "reasoning" that's a lie. Because he did know. He had the letter. He had spoken directly with Mueller.

Barr is a liar.