Question

我正在尝试使用Z3求解器定义一个抽象的半环，但是，每当我尝试使用该环执行任何操作时，求解器似乎就会永远运行。

目前，我有以下Z3 smt代码：

; declare the ring elements
(declare-sort R)

(declare-fun add (R R) R)
(declare-fun mul (R R) R)

(declare-fun one () R)
(declare-fun zero () R)

; the add properties
(assert (forall ((a R)) (= (add a zero) a)))
(assert (forall ((a R) (b R)) (= (add a b) (add b a))))
(assert (forall ((a R) (b R) (c R)) (= (add (add a b) c) (add a (add b c)))))

; the multiply properties
(assert (forall ((a R)) (= (mul a one) a)))
(assert (forall ((a R)) (= (mul a zero) zero)))
(assert (forall ((a R) (b R)) (= (mul a b) (mul b a))))
(assert (forall ((a R) (b R) (c R)) (= (mul (mul a b) c) (mul a (mul b c)))))

; distributive
(assert (forall ((a R) (b R) (c R)) (= (mul a (add b c)) (add (mul a b) (mul a c)))))

; different elements
(assert (distinct zero one))

; Either of the following blocks on their own cause the solver to run seemingly forever
(declare-fun fubar () R)
(assert (= fubar (mul fubar one)))

(assert (= zero (mul zero one)))



(set-option :timeout 100000)
(check-sat)
(get-model)

Answer 1

由于大量使用量词，我非常怀疑Z3是否适合此类问题。有限的模型查找和电子匹配并不容易。好的旧定理证明也许在这里是更好的选择，或者至少对基数非常明确，因此可以删除量化。（诚然，这仅适用于小型域。）

Z3解算器使用抽象环超时

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