Counterexample to the conjecture

Here is what Art Drisko showed about the conjecture.

12345
21534
34251
45123
53412



This has 3 1-transversals, each containing the 1 in row 2 (call it the pivot).

No 2-transversal for the net above can split, since only one of the pieces could contain the pivot. The following set of entries is a 3-transversal, but since it doesn't contain the pivot, it can't split into a 1-transversal and a 2-transversal.

1_3_5
2__34
_425_
451__
_3_12






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