z3錯誤地說UNSAT

Question

對於下面的問題，解決方案存在，但Z3說UNSAT。

(set-logic QF_UFNRA) 
(declare-fun a() Real) 
(declare-fun b() Real) 
(declare-fun c() Real) 
(declare-fun d() Real) 
(declare-fun e() Real) 
(declare-fun f() Real) 
(declare-fun g() Real) 
(declare-fun h() Real) 
(assert (and (<= a 1.0) (> a 0.0))) 
(assert (and (<= b 1.0) (> b 0.0))) 
(assert (and (<= c 1.0) (> c 0.0))) 
(assert (and (<= d 1.0) (> d 0.0))) 
(assert (and (<= e 1.0) (>= e 0.0))) 
(assert (and (<= f 1.0) (>= f 0.0))) 
(assert (and (<= g 1.0) (>= g 0.0))) 
(assert (and (<= h 1.0) (>= h 0.0))) 
(assert (= (* (+ a b) (+ a c)) a)) 
(assert (= (* (+ a b) (+ b d)) b)) 
(assert (= (* (+ a c) (+ c d)) c)) 
(assert (= (* (+ b d) (+ c d)) d)) 
(assert (= (+ a b c d e f g h) 1.0)) 
(check-sat) 

有效的解決方案：

a = 1/12, b = 1/4, c = 1/6, d = 1/2, e = f = g = h = 0 

我無法弄清楚爲什麼Z3表示不飽和度

z3版本是z3-4.3.0-x64。

Answer 1

我不知道什麼是rise4fun上的z3版本（http://rise4fun.com/z3）。我只是測試它，它說SAT。它會返回您提供的模型。