I don't know if I answered your post via email or not.
There were two Conrad Muth 's in the 1880 Vanderburgh Co., Indiana census. I am descended through Conrad 1806-1884 and Catherine Hartman Muth 1808- 1899.
I would love to see a copy of the will. As far as I know, Conrad & Catherine (Spelled Katherine in census ) had only one son. John C Muth.The middle name could have been Conrad but I have not found anything else for John.