19, 13, 30 @ -2,  1, -2
18, 19, 22 @ -1, -1, -2
20, 25, 34 @ -2, -2, -4
12, 31, 28 @ -1, -2, -1
20, 19, 15 @  1, -5, -3

Using first 3 rays

x + a*t1 = 19 - 2t1, y + b*t1 = 13 + t1, z + c*t1 = 30 - 2t1,
x + a*t2 = 18 - t2, y + b*t2 = 19 - t2, z + c*t2 = 22 - 2t2,
x + a*t3 = 20 - 2t3, y + b*t3 = 25 - 2t3, z + c*t3 = 34 - 4t3
9 eqs, 9 unks, thus solution in 3 points.
--> a = -3, b = 1, c = 2, t1 = 5, t2 = 3, t3 = 4, x = 24, y = 13, z = 10

x+a*t1 == 320870677764563-40*t1, y+b*t1 == 335750934489987-24*t1, z+c*t1 == 282502845957937+10*t1,
x+a*t2 == 219235623600942+127*t2, y+b*t2 == 408022798608755-45*t2, z+c*t2 == 245679379684914+66*t2,
x+a*t3 == 171834827764229-122*t3, y+b*t3 == 225154401936948-521*t3, z+c*t3 == 232302441670972+95*t3

sage: x, y, z, a, b, c, t1, t2, t3 = var('x, y, z, a, b, c, t1, t2, t3')
sage: solve([
....:     x+a*t1 == 320870677764563-40*t1, y+b*t1 == 335750934489987-24*t1, z+c*t1 == 282502845957937+10*t1,
....:     x+a*t2 == 219235623600942+127*t2, y+b*t2 == 408022798608755-45*t2, z+c*t2 == 245679379684914+66*t2,
....:     x+a*t3 == 171834827764229-122*t3, y+b*t3 == 225154401936948-521*t3, z+c*t3 == 232302441670972+95*t3],
....:   x,y,z,a,b,c,t1,t2,t3)
[[x == 149412455352770, y == 174964385672289, z == 233413147425100, a == 201, b == 202, c == 79, t1 == 711444906273, t2 == 943556327678, t3 == 69419109633]]
sage: 149412455352770+174964385672289+233413147425100
557789988450159