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BIG-Bench Extra Hard (BBEH) / In this question, assume each person either always tells the truth or always…

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input

In this question, assume each person either always tells the truth or always lies. Octavio says Mia lies. Madison says Owyn lies. Jamey says Phoebe lies. Raymond tells the truth. Tamika says Andree, Odell and Oakleigh all tell the truth. Oakleigh says Mariana lies. Maxim says Ophelia lies. Amberly says Jamey, Marina and Murray all tell the truth. Mavis says Margaret tells the truth. Odell says Mariana tells the truth. Omar says Murphy lies. Murphy says Omar lies. Phoebe says Helene tells the truth. Ozias says Maybelle tells the truth. Ka says Jerry tells the truth. Shaunda says exactly two of Willian, Olympia and Orlando tell the truth. Alejandro says only one of Audrie, Michelle and Maxim lies. Olympia says Orlando lies. Willian says only one of Conception, Micah and Hritik tells the truth. Micah says Oswin tells the truth. Margaret says Mavis tells the truth. Inga says either all three of Amberly, Margaret and Mavis lie, or two of them tell the truth. Helene says Ka lies. Marina says McKenzie tells the truth. Elanor says exactly one of Shaunda, Octavio and Mia tell the truth. Murray says McKenzie lies. Andree says Raymond tells the truth. Jerry says exactly one of Elanor, Madison and Owyn tells the truth.Hritik says Oswin lies. Mia says Octavio lies. Owyn says Madison lies. Michelle says Ophelia tells the truth. Conception says only one of Alejandro, Ozias and Miranda lies. Miranda says Maybelle lies. Orlando says Olympia lies. Audrie says exactly two of Tamika, Murphy and Omar tells the truth. Do Jamey, Helene, and Inga tell the truth? Your answer should be a list of three words separated by commas. Each of them must be either yes (if the person tells the truth), no (if the person lies), or unknown (if the person's truth cannot be determined). For example, <unknown, no, yes> or <yes, yes, yes>.

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