Z3独特作业

时间：2012-09-13 12:42:25

标签： encoding z3

我有一个名为uniqueFunc的未解释函数。 现在，我想为每个索引0到16分配一个唯一的数字1到17。 所以我的代码是 - 

(declare-fun uniqueFunc (Int) Int)

(assert (and (> (uniqueFunc 0) 0) (< (uniqueFunc 0) 18)))
(assert (and (> (uniqueFunc 1) 0) (< (uniqueFunc 1) 18)))
(assert (and (> (uniqueFunc 2) 0) (< (uniqueFunc 2) 18)))
(assert (and (> (uniqueFunc 3) 0) (< (uniqueFunc 3) 18)))
(assert (and (> (uniqueFunc 4) 0) (< (uniqueFunc 4) 18)))
(assert (and (> (uniqueFunc 5) 0) (< (uniqueFunc 5) 18)))
(assert (and (> (uniqueFunc 6) 0) (< (uniqueFunc 6) 18)))
(assert (and (> (uniqueFunc 7) 0) (< (uniqueFunc 7) 18)))
(assert (and (> (uniqueFunc 8) 0) (< (uniqueFunc 8) 18)))
(assert (and (> (uniqueFunc 9) 0) (< (uniqueFunc 9) 18)))
(assert (and (> (uniqueFunc 10) 0) (< (uniqueFunc 10) 18)))
(assert (and (> (uniqueFunc 11) 0) (< (uniqueFunc 11) 18)))
(assert (and (> (uniqueFunc 12) 0) (< (uniqueFunc 12) 18)))
(assert (and (> (uniqueFunc 13) 0) (< (uniqueFunc 13) 18)))
(assert (and (> (uniqueFunc 14) 0) (< (uniqueFunc 14) 18)))
(assert (and (> (uniqueFunc 15) 0) (< (uniqueFunc 15) 18)))
(assert (and (> (uniqueFunc 16) 0) (< (uniqueFunc 16) 18)))

(assert (and (not (= (uniqueFunc 0) (uniqueFunc 1)))
     (not (= (uniqueFunc 0) (uniqueFunc 2)))
     (not (= (uniqueFunc 0) (uniqueFunc 3)))
     (not (= (uniqueFunc 0) (uniqueFunc 4)))
     (not (= (uniqueFunc 0) (uniqueFunc 5)))
     (not (= (uniqueFunc 0) (uniqueFunc 6)))
     (not (= (uniqueFunc 0) (uniqueFunc 7)))
     (not (= (uniqueFunc 0) (uniqueFunc 8)))
     (not (= (uniqueFunc 0) (uniqueFunc 9)))
     (not (= (uniqueFunc 0) (uniqueFunc 10)))
     (not (= (uniqueFunc 0) (uniqueFunc 11)))
     (not (= (uniqueFunc 0) (uniqueFunc 12)))
     (not (= (uniqueFunc 0) (uniqueFunc 13)))
     (not (= (uniqueFunc 0) (uniqueFunc 14)))
     (not (= (uniqueFunc 0) (uniqueFunc 15)))
     (not (= (uniqueFunc 0) (uniqueFunc 16)))
     (not (= (uniqueFunc 1) (uniqueFunc 2)))
     (not (= (uniqueFunc 1) (uniqueFunc 3)))
     (not (= (uniqueFunc 1) (uniqueFunc 4)))
     (not (= (uniqueFunc 1) (uniqueFunc 5)))
     (not (= (uniqueFunc 1) (uniqueFunc 6)))
     (not (= (uniqueFunc 1) (uniqueFunc 7)))
     (not (= (uniqueFunc 1) (uniqueFunc 8)))
     (not (= (uniqueFunc 1) (uniqueFunc 9)))
     (not (= (uniqueFunc 1) (uniqueFunc 10)))
     (not (= (uniqueFunc 1) (uniqueFunc 11)))
     (not (= (uniqueFunc 1) (uniqueFunc 12)))
     (not (= (uniqueFunc 1) (uniqueFunc 13)))
     (not (= (uniqueFunc 1) (uniqueFunc 14)))
     (not (= (uniqueFunc 1) (uniqueFunc 15)))
     (not (= (uniqueFunc 1) (uniqueFunc 16)))
     (not (= (uniqueFunc 2) (uniqueFunc 3)))
     (not (= (uniqueFunc 2) (uniqueFunc 4)))
     (not (= (uniqueFunc 2) (uniqueFunc 5)))
     (not (= (uniqueFunc 2) (uniqueFunc 6)))
     (not (= (uniqueFunc 2) (uniqueFunc 7)))
     (not (= (uniqueFunc 2) (uniqueFunc 8)))
     (not (= (uniqueFunc 2) (uniqueFunc 9)))
     (not (= (uniqueFunc 2) (uniqueFunc 10)))
     (not (= (uniqueFunc 2) (uniqueFunc 11)))
     (not (= (uniqueFunc 2) (uniqueFunc 12)))
     (not (= (uniqueFunc 2) (uniqueFunc 13)))
     (not (= (uniqueFunc 2) (uniqueFunc 14)))
     (not (= (uniqueFunc 2) (uniqueFunc 15)))
     (not (= (uniqueFunc 2) (uniqueFunc 16)))
     (not (= (uniqueFunc 3) (uniqueFunc 4)))
     (not (= (uniqueFunc 3) (uniqueFunc 5)))
     (not (= (uniqueFunc 3) (uniqueFunc 6)))
     (not (= (uniqueFunc 3) (uniqueFunc 7)))
     (not (= (uniqueFunc 3) (uniqueFunc 8)))
     (not (= (uniqueFunc 3) (uniqueFunc 9)))
     (not (= (uniqueFunc 3) (uniqueFunc 10)))
     (not (= (uniqueFunc 3) (uniqueFunc 11)))
     (not (= (uniqueFunc 3) (uniqueFunc 12)))
     (not (= (uniqueFunc 3) (uniqueFunc 13)))
     (not (= (uniqueFunc 3) (uniqueFunc 14)))
     (not (= (uniqueFunc 3) (uniqueFunc 15)))
     (not (= (uniqueFunc 3) (uniqueFunc 16)))
     (not (= (uniqueFunc 4) (uniqueFunc 5)))
     (not (= (uniqueFunc 4) (uniqueFunc 6)))
     (not (= (uniqueFunc 4) (uniqueFunc 7)))
     (not (= (uniqueFunc 4) (uniqueFunc 8)))
     (not (= (uniqueFunc 4) (uniqueFunc 9)))
     (not (= (uniqueFunc 4) (uniqueFunc 10)))
     (not (= (uniqueFunc 4) (uniqueFunc 11)))
     (not (= (uniqueFunc 4) (uniqueFunc 12)))
     (not (= (uniqueFunc 4) (uniqueFunc 13)))
     (not (= (uniqueFunc 4) (uniqueFunc 14)))
     (not (= (uniqueFunc 4) (uniqueFunc 15)))
     (not (= (uniqueFunc 4) (uniqueFunc 16)))
     (not (= (uniqueFunc 5) (uniqueFunc 6)))
     (not (= (uniqueFunc 5) (uniqueFunc 7)))
     (not (= (uniqueFunc 5) (uniqueFunc 8)))
     (not (= (uniqueFunc 5) (uniqueFunc 9)))
     (not (= (uniqueFunc 5) (uniqueFunc 10)))
     (not (= (uniqueFunc 5) (uniqueFunc 11)))
     (not (= (uniqueFunc 5) (uniqueFunc 12)))
     (not (= (uniqueFunc 5) (uniqueFunc 13)))
     (not (= (uniqueFunc 5) (uniqueFunc 14)))
     (not (= (uniqueFunc 5) (uniqueFunc 15)))
     (not (= (uniqueFunc 5) (uniqueFunc 16)))
     (not (= (uniqueFunc 6) (uniqueFunc 7)))
     (not (= (uniqueFunc 6) (uniqueFunc 8)))
     (not (= (uniqueFunc 6) (uniqueFunc 9)))
     (not (= (uniqueFunc 6) (uniqueFunc 10)))
     (not (= (uniqueFunc 6) (uniqueFunc 11)))
     (not (= (uniqueFunc 6) (uniqueFunc 12)))
     (not (= (uniqueFunc 6) (uniqueFunc 13)))
     (not (= (uniqueFunc 6) (uniqueFunc 14)))
     (not (= (uniqueFunc 6) (uniqueFunc 15)))
     (not (= (uniqueFunc 6) (uniqueFunc 16)))
     (not (= (uniqueFunc 7) (uniqueFunc 8)))
     (not (= (uniqueFunc 7) (uniqueFunc 9)))
     (not (= (uniqueFunc 7) (uniqueFunc 10)))
     (not (= (uniqueFunc 7) (uniqueFunc 11)))
     (not (= (uniqueFunc 7) (uniqueFunc 12)))
     (not (= (uniqueFunc 7) (uniqueFunc 13)))
     (not (= (uniqueFunc 7) (uniqueFunc 14)))
     (not (= (uniqueFunc 7) (uniqueFunc 15)))
     (not (= (uniqueFunc 7) (uniqueFunc 16)))
     (not (= (uniqueFunc 8) (uniqueFunc 9)))
     (not (= (uniqueFunc 8) (uniqueFunc 10)))
     (not (= (uniqueFunc 8) (uniqueFunc 11)))
     (not (= (uniqueFunc 8) (uniqueFunc 12)))
     (not (= (uniqueFunc 8) (uniqueFunc 13)))
     (not (= (uniqueFunc 8) (uniqueFunc 14)))
     (not (= (uniqueFunc 8) (uniqueFunc 15)))
     (not (= (uniqueFunc 8) (uniqueFunc 16)))
     (not (= (uniqueFunc 9) (uniqueFunc 10)))
     (not (= (uniqueFunc 9) (uniqueFunc 11)))
     (not (= (uniqueFunc 9) (uniqueFunc 12)))
     (not (= (uniqueFunc 9) (uniqueFunc 13)))
     (not (= (uniqueFunc 9) (uniqueFunc 14)))
     (not (= (uniqueFunc 9) (uniqueFunc 15)))
     (not (= (uniqueFunc 9) (uniqueFunc 16)))
     (not (= (uniqueFunc 10) (uniqueFunc 11)))
     (not (= (uniqueFunc 10) (uniqueFunc 12)))
     (not (= (uniqueFunc 10) (uniqueFunc 13)))
     (not (= (uniqueFunc 10) (uniqueFunc 14)))
     (not (= (uniqueFunc 10) (uniqueFunc 15)))
     (not (= (uniqueFunc 10) (uniqueFunc 16)))
     (not (= (uniqueFunc 11) (uniqueFunc 12)))
     (not (= (uniqueFunc 11) (uniqueFunc 13)))
     (not (= (uniqueFunc 11) (uniqueFunc 14)))
     (not (= (uniqueFunc 11) (uniqueFunc 15)))
     (not (= (uniqueFunc 11) (uniqueFunc 16)))
     (not (= (uniqueFunc 12) (uniqueFunc 13)))
     (not (= (uniqueFunc 12) (uniqueFunc 14)))
     (not (= (uniqueFunc 12) (uniqueFunc 15)))
     (not (= (uniqueFunc 12) (uniqueFunc 16)))
     (not (= (uniqueFunc 13) (uniqueFunc 14)))
     (not (= (uniqueFunc 13) (uniqueFunc 15)))
     (not (= (uniqueFunc 13) (uniqueFunc 16)))
     (not (= (uniqueFunc 14) (uniqueFunc 15)))
     (not (= (uniqueFunc 14) (uniqueFunc 16)))
     (not (= (uniqueFunc 15) (uniqueFunc 16)))))

有更好的方法吗？

谢谢， Pranav

1 个答案:

答案 0 :(得分：1)

是的，Z3有一个distinct表达式。这将为您做所有不相等的排列。这是API描述：

http://research.microsoft.com/en-us/um/redmond/projects/z3/ml/z3.html#VALmk_distinct

对于你的例子：

(assert (distinct (uniqueFunc 0) (uniqueFunc 1) (uniqueFunc 2) (uniqueFunc 3) (uniqueFunc 4) (uniqueFunc 5) (uniqueFunc 6) (uniqueFunc 7) (uniqueFunc 8) (uniqueFunc 9) (uniqueFunc 10) (uniqueFunc 11) (uniqueFunc 12) (uniqueFunc 13) (uniqueFunc 14) (uniqueFunc 15) (uniqueFunc 16)))

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