clpfd - Can someone explain why this prolog query evaluates to false? -

i trying write predicate pythagorean(x,y,z,w) can generate triples such x^2 + y^2 = z^2, w >= x,y,z > 0.

this wrote:

pyth(x,y,z,w) :-    x > 0,     y > 0,    z > 0,    s1 x*x + y*y,    s2 z*z,     s1 == s2,    w  @> z. 

use clpfd!

:- use_module(library(clpfd)). 

we define pytri/2 based on fd-constraints sum/3, chain/2, (#=)/2, , (#<)/2:

pytri(zs,perimeter) :-    zs = [a,b,c],    maplist(#<(1),zs),    sum(zs,#=,perimeter),    chain(zs,#<),    a^2 + b^2 #= c^2. 

let's find 17 pythagorean triples (16 primitive + 1 non-primitive) having perimeter ≤ 100:

?- pytri([x,y,z],perimeter), perimeter #=< 100, labeling([],[z,y,x]).   perimeter = 12, x =  3, y =  4, z =  5 ; perimeter = 24, x =  6, y =  8, z = 10 ; perimeter = 30, x =  5, y = 12, z = 13 ; perimeter = 36, x =  9, y = 12, z = 15 ; perimeter = 40, x =  8, y = 15, z = 17 ; perimeter = 48, x = 12, y = 16, z = 20 ; perimeter = 60, x = 15, y = 20, z = 25 ; perimeter = 56, x =  7, y = 24, z = 25 ; perimeter = 60, x = 10, y = 24, z = 26 ; perimeter = 70, x = 20, y = 21, z = 29 ; perimeter = 72, x = 18, y = 24, z = 30 ; perimeter = 80, x = 16, y = 30, z = 34 ; perimeter = 84, x = 21, y = 28, z = 35 ; perimeter = 84, x = 12, y = 35, z = 37 ; perimeter = 90, x = 15, y = 36, z = 39 ; perimeter = 96, x = 24, y = 32, z = 40 ; perimeter = 90, x =  9, y = 40, z = 41 ; false.                                   % terminates universally