On completing three cyclically generated transversals to a latin square

Let P   be a partial latin square of prime order p>7p>7 consisting of three cyclically generated transversals. Specifically, let P be a partial latin square of the form:P={(i,c+i,s+i),(i,c′+i,s′+i),(i,c″+i,s″+i)|0⩽i7p>7, every partial transversal of size 3 in the addition table for the integers modulo p can be completed to a full transversal.