x1=c1=k1 is separate from / not with x2=c2=k2 in state/condition/enterprise x3=k3; x1 is individual / alone / separate.
A fu'ivla synonym variant of kancau, specialized for the purpose of specifying individuality and application of singular logic with lu'a'ei and denying/excluding massness (see loi) for this sumti or, similarly, plurality and application of plural logic (or visa versa with to'e (or no'e for either singular or plural)). «lu'a'ei karncau le prenu cu bevri le pipno» means ‘Each person individually carried the piano’, closer to pre-xorlo CLL lo - it may sound odd if the 3 persons carried the piano at the same time, since it was a statement with explicit individuality. «lu'a'au» makes a sumti individualistic, and is equivalent to «lu'a'ei karncau». For less rigorous shortcuts to express (non-)individuality, the modal koi'au can be used (e.g. «le koi'au prenu»), as well as terle'o to express ‘as individuals’ (see le'oi for more information on this idiom); karncau especially with lu'a'ei is meant to be fully explicit (alias: lu'a'au). See also: tolykarncau, norykarncau. Note: this word is a fu'ivla and not a lujvo in morphology, since ‘n’ would not be needed to hyphenate 2 rafsi ‘kar’ and ‘cau’.