z3 错误地说 UNSAT

Question

对于以下问题，解决方案存在，但 z3 显示为 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)

有效解决方案：

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

我不明白为什么 z3 说 unsat。

z3 版本是 z3-4.3.0-x64。

Answer 1

我不知道rise4fun (http://rise4fun.com/z3) 上的z3 版本是什么。我刚刚测试了它，它说的是SAT。它返回您提供的模型。