Si es posible, me gustaría una segunda opinión sobre mi código.

Las limitaciones del problema son:

a,b,c,d,e,f son enteros distintos de ceros1 = [a,b,c] ys2 = [d,e,f] son conjuntosLa sumas1_i + s2_j parai,j = 0..2 tiene que ser un cuadrado perfecto

No entiendo por qué, pero mi código devuelve un modelo no disponible. Además, al comentar las siguientes líneas:

(assert (and (> sqrtx4 1) (= x4 (* sqrtx4 sqrtx4))))
(assert (and (> sqrtx5 1) (= x5 (* sqrtx5 sqrtx5))))
(assert (and (> sqrtx6 1) (= x6 (* sqrtx6 sqrtx6))))

(assert (and (> sqrtx7 1) (= x7 (* sqrtx7 sqrtx7))))
(assert (and (> sqrtx8 1) (= x8 (* sqrtx8 sqrtx8))))
(assert (and (> sqrtx9 1) (= x9 (* sqrtx9 sqrtx9))))

Los valores para d, e, f son negativos. No hay ninguna restricción que les obligue a hacerlo. Me pregunto si quizás hay algunas restricciones ocultas que se colaron y estropearon el modelo.

Una solución esperada válida sería:

a = 3
b = 168
c = 483
d = 1
e = 193
f = 673

Edita: insertando(assert (= a 3)) y(assert (= b 168)) da como resultado que el solucionador encuentre los valores correctos. Esto solo me desconcierta aún más.

Código completo:

(declare-fun sqrtx1 () Int)
(declare-fun sqrtx2 () Int)
(declare-fun sqrtx3 () Int)
(declare-fun sqrtx4 () Int)
(declare-fun sqrtx5 () Int)
(declare-fun sqrtx6 () Int)
(declare-fun sqrtx7 () Int)
(declare-fun sqrtx8 () Int)
(declare-fun sqrtx9 () Int)

(declare-fun a     () Int)
(declare-fun b     () Int)
(declare-fun c     () Int)
(declare-fun d     () Int)
(declare-fun e     () Int)
(declare-fun f     () Int)

(declare-fun x1     () Int)
(declare-fun x2     () Int)
(declare-fun x3     () Int)
(declare-fun x4     () Int)
(declare-fun x5     () Int)
(declare-fun x6     () Int)
(declare-fun x7     () Int)
(declare-fun x8     () Int)
(declare-fun x9     () Int)


;all numbers are non-zero integers
(assert (not (= a 0)))
(assert (not (= b 0)))
(assert (not (= c 0)))
(assert (not (= d 0)))
(assert (not (= e 0)))
(assert (not (= f 0)))

;both arrays need to be sets
(assert (not (= a b)))
(assert (not (= a c)))
(assert (not (= b c)))

(assert (not (= d e)))
(assert (not (= d f)))
(assert (not (= e f)))



(assert (and (> sqrtx1 1) (= x1 (* sqrtx1 sqrtx1))))
(assert (and (> sqrtx2 1) (= x2 (* sqrtx2 sqrtx2))))
(assert (and (> sqrtx3 1) (= x3 (* sqrtx3 sqrtx3))))


(assert (and (> sqrtx4 1) (= x4 (* sqrtx4 sqrtx4))))
(assert (and (> sqrtx5 1) (= x5 (* sqrtx5 sqrtx5))))
(assert (and (> sqrtx6 1) (= x6 (* sqrtx6 sqrtx6))))

(assert (and (> sqrtx7 1) (= x7 (* sqrtx7 sqrtx7))))
(assert (and (> sqrtx8 1) (= x8 (* sqrtx8 sqrtx8))))
(assert (and (> sqrtx9 1) (= x9 (* sqrtx9 sqrtx9))))

;all combinations of sums need to be squared
(assert (= (+ a d) x1))
(assert (= (+ a e) x2))
(assert (= (+ a f) x3)) 

(assert (= (+ b d) x4))
(assert (= (+ b e) x5))
(assert (= (+ b f) x6))

(assert (= (+ c d) x7))
(assert (= (+ c e) x8))
(assert (= (+ c f) x9))


(check-sat-using (then simplify solve-eqs smt))
(get-model)
(get-value (a))
(get-value (b))
(get-value (c))
(get-value (d))
(get-value (e))
(get-value (f))