crash due to not checking for dead rows.
non-termination due to solving div and mod separately.
To ensure termination one needs to at least process them simultaneously, otherwise the metric of number-of-terms x under number of mod/div does not decrease. Substituting in K*y + z under either a mod or div increases the number of terms under a mod/div when eliminating only one of the kinds.
Currently handling divides constraints separately because pre-existing solution uses the model to determine z as a constant between 0 and K-1. The treatment of mod/div is supposed to be more general and use a variable while at the same time reducing the mod/div terms where the eliminated variable is used (the variable z is not added under the mod/div terms, but instead the model is used to determine cut-offs to calculate mod/div directly.
elimination of mod/div should be applied to all occurrences of x under mod/div at the same time. It affects performance and termination to perform elimination on each occurrence since substituting in two new variables for eliminated x doubles the number of variables under other occurrences.
Also generalize inequality resolution to use div.
The new features are still disabled.
This update changes the handling of mod and adds support for nested div terms.
Simple use cases that are handled using small results are given below.
```
(declare-const x Int)
(declare-const y Int)
(declare-const z Int)
(assert (exists ((x Int)) (and (<= y (* 10 x)) (<= (* 10 x) z))))
(apply qe2)
(reset)
(declare-const y Int)
(assert (exists ((x Int)) (and (> x 0) (= (div x 41) y))))
(apply qe2)
(reset)
(declare-const y Int)
(assert (exists ((x Int)) (= (mod x 41) y)))
(apply qe2)
(reset)
```
The main idea is to introduce definition rows for mod/div terms.
Elimination of variables under mod/div is defined by rewriting the variable to multiples of the mod/divisior and remainder.
The functionality is disabled in this push.
strict inequality (over reals) require solving for least-upper/greatest-lower bounds that may coincide with non-strict inequalities (be epsilon stronger). Instead of using the coefficient 'a' to turn the inequality into an equality, add the slack value as a constant.
The contract is that users of mb-skolem ensure that
interface equalities are preserved (by adding a
sufficient set of disequalities, such as a chain
x1 < x2 < x3 .., to force that solutions for
x_i does not clash).
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
