Small BCK algebras of order 4.4

Help for the posets applet
list:=[
[# 1
[ 1, 2, 3, 4 ],
[ 1, 1, 3, 4 ],
[ 1, 2, 1, 4 ],
[ 1, 2, 3, 1 ]
]
];

Computed by Peter Jipsen using GAP 3.4 (this list can be copied and read into GAP)