数独4*4補助ルール付き

グループ内(2*2,3*3などの正方マス)には同一数字は入らない、
というルールを付け加えて、前回のものと速度を比較した。

sig Cell {
	x:Int,
	y:Int,
	v:Int
} {
	x >= 0 and x <= 3 
	y >= 0 and y <= 3 
	v >= 1 and v <= 4
}

fact AllCellsPosition {
	no disj c1,c2:Cell | c1.x == c2.x and c1.y == c2.y
	no disj c1,c2:Cell | c1.x == c2.x and c1.v == c2.v
	no disj c1,c2:Cell | c1.y == c2.y and c1.v == c2.v
}

fact SubRule1 {
	some disj c1,c2,c3,c4:Cell |
		c1.x == 0 and c1.y == 0 and
		c2.x == 0 and c2.y == 1 and
		c3.x == 1 and c3.y == 0 and
		c4.x == 1 and c4.y == 1 and
		c1.v != c2.v and c1.v != c3.v and c1.v != c4.v and
		c2.v != c3.v and c2.v != c4.v and
		c3.v != c4.v
}

fact SubRule2 {
	some disj c1,c2,c3,c4:Cell |
		c1.x == 2 and c1.y == 0 and
		c2.x == 2 and c2.y == 1 and
		c3.x == 3 and c3.y == 0 and
		c4.x == 3 and c4.y == 1 and
		c1.v != c2.v and c1.v != c3.v and c1.v != c4.v and
		c2.v != c3.v and c2.v != c4.v and
		c3.v != c4.v
}

fact SubRule3 {
	some disj c1,c2,c3,c4:Cell |
		c1.x == 0 and c1.y == 2 and
		c2.x == 0 and c2.y == 3 and
		c3.x == 1 and c3.y == 2 and
		c4.x == 1 and c4.y == 3 and
		c1.v != c2.v and c1.v != c3.v and c1.v != c4.v and
		c2.v != c3.v and c2.v != c4.v and
		c3.v != c4.v
}

fact SubRule4 {
	some disj c1,c2,c3,c4:Cell |
		c1.x == 2 and c1.y == 2 and
		c2.x == 2 and c2.y == 3 and
		c3.x == 3 and c3.y == 2 and
		c4.x == 3 and c4.y == 3 and
		c1.v != c2.v and c1.v != c3.v and c1.v != c4.v and
		c2.v != c3.v and c2.v != c4.v and
		c3.v != c4.v
}

fact Values {
	one c:Cell | c.x == 3 and c.y == 0 and c.v == 4

	one c:Cell | c.x == 2 and c.y == 1 and c.v == 1
	one c:Cell | c.x == 3 and c.y == 1 and c.v == 2

	one c:Cell | c.x == 1 and c.y == 2 and c.v == 1
	one c:Cell | c.x == 2 and c.y == 2 and c.v == 4
	one c:Cell | c.x == 3 and c.y == 2 and c.v == 3

	one c:Cell | c.x == 0 and c.y == 3 and c.v == 4
	one c:Cell | c.x == 1 and c.y == 3 and c.v == 3
	one c:Cell | c.x == 2 and c.y == 3 and c.v == 2
	one c:Cell | c.x == 3 and c.y == 3 and c.v == 1
}

run {} for exactly 16 Cell 

実行速度は、私のマシンでは、補助ルールなしで3.5秒、
補助ルールありで19秒。
最低限のルールでしばってある方が速いわけですかそうですか。
書き方にもコツがありそうな気がする。