Nothing But The Truth was implemented entirely by me, so if you have issues with that one complain to either myself or the writer. ^_^
We put a bunch of different checks and balances into it in case you simply don't want to do the trial part or figure out the evidence; you can take the corruption path immediately and just not bother trying to refute François's testimony; you can intentionally present the wrong thing 4 times and just end the trial with the "bad" outcome; you could have gotten a lifeline from Marie by blackmailing her with the affair evidence, which gives you an extra chance if you lose your lives.
The intended path for the non-vice route though is:
1. Press François's line "That left everyone but Anthelme and Lorraine accounted for downstairs as they went up."
2. Present either Laval's Affair or Marie's Ledger against the line "Of course, Marie has no reason to lie, so my alibi remains as strong as ever." (if you blackmailed her and present the affair, you'll get a confirmation prompt since it loses you her support for the lifeline)
3. Present the Sleeping Formula against the line "While I was alone with Marie due to his nap, there's no way I could have known he would be asleep."
4. Press Marie's line "He did say as he left that he had 'something he had to do'."
5. Present Letters to Lorraine against Lorraine's line "I was sick of weathering his barbs in silence, so I was going to demand he stop."
6. Present Laval's Diary against François's line "In any case, nothing this 'true heir' can do would actually prove their provenance."
7. Present the Missing Will against the line "You know nothing about this supposed heir. Perhaps you intend to scour all of Verdeaux?"
Note that there's currently a bug where if you have the *full* version of the Missing Will from having both the scrap of paper and having talked to Camille about it, it doesn't work when you present it against the testimony line. This has been fixed for the next release.
The path for the vice route is the same up until the post-recess if you chose not to cross-examine François. It's then:
1. Present Letters to Lorraine against Lorraine's statement "I knew nothing of it being with Laval; nothing has changed between us two."
2. Present the Marked Article against the line "Anthelme told me to go see Laval first after we talked a bit in the study."
From this point, the choices are vice-based and you're told which evidence will be used.
Point 2 is the one I think has the weakest logical connection in the trial overall and I'm going to talk to Absurdity about perhaps revisiting it; there is a hint if you press that statement but I still think it needs something more.