Z3 – Make a model under Tseitin encoding

(set-logic QF_UF)< br />(
 set-option
 :produce-models
 true
)

; ------ snip ----- --
;
; declarations, 
; and assert statement
; of "original" formula
; here.
;
;- ----- snap -------

(
 apply
 (
 then
 (
 !
 simplify
 :elim-and
 true
 )
 tseitin-cnf
 )
)

(goals
(goal

; ------ snip -------
; 
; Lot's of lines here
 ;
; ------ snap -------

 :precision precise :depth 2)
)

(apply 
 (then (! simplify :elim-and true)
 tseitin-cnf))

I used the following code snippet in z3 4.0 to convert the formula to CNF.

(set-logic QF_UF)
(
 set-option
 :produce-models
 true
)

; ------ snip -------
; 
; declarations, 
; and assert statement
; of "original" formula
; here.
;
; ------ snap- ------

(
 apply
 (
 then
 (
 !
 simplify
: elim-and
 true
 )
 tseitin-cnf
 )
)

I get something like the following:

(goals
(goal

; ------ snip - -----
 ;
; Lot's of lines here
 ;
; ------ snap -------

 :precision precise :depth 2)
)

I assume that every expression after the target is a clause of CNF, i.e. all these expressions should be combined to produce the actual formula. I call this conjunction the “coding” formula.

Obviously, the original formula and the coding formula are not equivalent, because the coding formula contains a new variable k! 0,k! 1,…Tseitin coding. However, I expect them to be completely satisfied, or in fact they are satisfied with the same model (when ignoring the k!i variable).

That is, I expect ( Encoding formula) AND (non-original formula) is not satisfiable. Unfortunately, this does not seem to be the case; I have a counter-example, this check actually returns sat.

This is an error in z3, and I use it Is it wrong, or is any of my assumptions invalid?

This is a bug in the new tseitin-cnf tactics. I fixed the bug and the fix will be provided in the next version (Z3 4.1). In In the meantime, you can solve this problem by using simplified rounds.
That is, use

(apply 
 (then (! simplify :elim-and true)
 (! simplify :elim-and true)
 tseitin-cnf))

Replace

(apply 
 (then (! simplify :elim-and true)
 tseitin-cnf))