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.
\brief convert p == 0 into a solved form v == r, such that
v has bounds [lo, oo) iff r has bounds [lo', oo)
v has bounds (oo,hi] iff r has bounds (oo,hi']
The solved form allows the Grobner solver identify more bounds conflicts.
A bad leading term can miss bounds conflicts.
For example for x + y + z == 0 where x, y : [0, oo) and z : (oo,0]
we prefer to solve z == -x - y instead of x == -z - y
because the solution -z - y has neither an upper, nor a lower bound.
The Grobner solver is augmented with a notion of a substitution that is applied before the solver is run.
