The connective 'not' is unary, not binary, so "1 'or' (1 'not' 1)" does not look right. Perhaps what is meant is 'and not'.

Though this has to be always double-checked, usually 'and' (an analog of multiplication) binds tighter than 'or' (an analog of addition), and unary 'not' binds tighter than both of them. So "1 'or' 1 'and not' 1" would be interpreted as "1 'or' (1 'and not' 1)".