I have installed Z3 version 4.1 and I attempt to use it programmatically in a java application. My application is communicating with the Z3 via ProcessBuilder. The version of Z3 is verified as 4.1 by using the /version command line argument.
However, Z3 does not accept negative constants as part of expressions. When I attempt to provide a negative integers I get the following message:
(error "line 4 column 31: unknown constant -1")
This is the input I provide to Z3:
(push)
(declare-fun y () Int )
(define-fun x () Int y )
(assert (and (<= y 1000) (>= y -1) ) )
(assert (= x 42) )
(check-sat)
(pop)
I am using the following arguments to instantiate the Z3:
Z3 /smt2 /in /t:2
Any help is appreciated. Thank you in advance.
Try (- 1). See bottom of page 38 in http://smtlib.cs.uiowa.edu/papers/smt-lib-reference-v2.6-r2017-07-18.pdf
Related
I'm currently trying to write an SMT script using define-fun-rec. I've tested with both Z3, version 4.4.2, and CVC4, version 1.4. As far as I can tell, these are the most recent versions of both, and both support the feature*. However, both do not seem to recognize the command.
(I made some changes to this based on Nikolaj's reply. It still gives the error messages.) Specifically, given:
(define-fun-rec
fac ((x Int)) Int
(
ite (<= x 1)
1
(* x (fac (- x 1)))
)
)
(assert (= (fac 4) 24))
(check-sat)
Z3 outputs:
unsupported
; define-fun-rec
(error "line 10 column 17: unknown function/constant fac")
sat
And CVC4 outputs:
(error "Parse Error: fac.smt2:1.15: expected SMT-LIBv2 command, got `define-fun-rec'.
(define-fun-rec
^
")
My best guess is that there is some sort of flag I need to set or I need to be using some specific logic, but I've had a lot of trouble finding any sort of detailed instructions or examples with define-fun-rec. Any advice would be appreciated. Thanks!
*Z3 has support: How to deal with recursive function in Z3?
CVC4 has support: http://lara.epfl.ch/~reynolds/pres-smt15.pdf
The latest version of CVC4 can be downloaded under "Development versions" (on the right hand side) of:
http://cvc4.cs.nyu.edu/downloads/
The latest development version has support for recursive function definitions. You can use the cvc4 command line option "--fmf-fun" to enable a technique that finds small models for problems involving recursive function applications, assuming definitions are admissible.
(Although, unfortunately your example with factorial also requires non-linear arithmetic, which CVC4 does not yet support.)
Don't set the logic to LIA. This is not in the LIA fragment and Z3 will use the wrong tactic to solve the problem.Just remove the set-logic line.
It helps to not use an undefined function "f" inside the definition of "fib".
I would suggest that you call the function "fac" and not "fib" since you are defining a factorial function.
Thus,
(define-fun-rec
fac ((x Int)) Int
(
ite (<= x 1)
1
(* x (fac (- x 1)))
)
)
(assert (= (fac 4) 24))
(check-sat)
z3 -version
Z3 version 4.4.2
z3 fac.smt2
sat
If you change 24 to 25 you get unsat.
I need to add the following assertion
assert(x=y^2)
is it required to define a function or any syntax is available to add it directly
.Please help me.
Z3 has a built-in power operator, ^. If you're using the SMT-LIB interface it would be (assert (= x (^ y 2))). You'd probably be better off using (assert (= x (* y y))) if the power is always 2, though.
Running Z3 on the following sequence of propositions
(declare-const x Real)
(assert (= 1 (^ x (/ 1 2))))
(check-sat-using qfnra-nlsat)
(get-model)
(eval (= x (^ x (/ 1 2))))
produces
sat
(model
(define-fun x () Real
(- 1.0))
)
Z3(5, 25): ERROR: even root of negative number is not real
Note that the final line simply evaluates the equation from line 2 on the proposed solution for x, so Z3 seems to contradict itself. Is this a bug or am I missing something?
This example exposes some bugs in the facilities dealing with root objects. A fix has been checked into the master branch (Z3 now returns unknown for this tactic).
I have a test.smt2 file:
(set-logic QF_IDL)
(declare-const a Int)
(declare-const b Int)
(declare-const c Int)
(assert (or (< a 2) (< b 2 )) )
(check-sat)
(get-model)
(exit)
Is there anyway to tell Z3 to only output a=1 (or b=1)? Because when a is 1, b's value does not matter any more.
I executed z3 smt.relevancy=2 -smt2 test.smt2
(following How do I get Z3 to return minimal model?, although smt.relevancy seems has default value 2), but it still outputs:
sat
(model
(define-fun b () Int
2)
(define-fun a () Int
1)
)
Thank you!
The example given in the answer to the question referred to is slightly out of date. A Solver() will pick a suitable tactic to solve the problem, and it appears that it picks a different one now. We can still get that behavior by using a SimpleSolver() (at a possibly significant performance loss). Here's an updated example:
from z3 import *
x, y = Bools('x y')
s = SimpleSolver()
s.set(auto_config=False,relevancy=2)
s.add(Or(x, y))
print s.check()
print s.model()
Note that the (check-sat) command will not execute the same tactic as the SimpleSolver(); to get the same behavior when solving SMT2 files, we need to use the smt tactic, i.e., use (check-sat-using smt). In many cases it will be beneficial to additionally run the simplifier on the problem first which we can achieve by constructing a custom tactic, e.g., (check-sat-using (then simplify smt))
I was trying to represent a real number with two integer numbers as using them as the numerator and the denominator of the real number. I wrote the following program:
(declare-const a Int)
(declare-const b Int)
(declare-const f Real)
(assert (= f (/ a b)))
(assert (= f 0.5))
(assert (> b 2))
(assert (> b a))
(check-sat)
(get-model)
The program returned SAT result as follows:
sat
(model
(define-fun f () Real
(/ 1.0 2.0))
(define-fun b () Int
4)
(define-fun a () Int
2)
)
However, if I write '(assert (= f (div a b)))' instead of '(assert (= f (/ a b)))', then the result is UNSAT. Why does not div return the same result?
Moreover, and the main concern for me, I did not find a way to use operator '/' in z3 .Net API. I can see only function MkDiv, which actually for operator 'div'. Is there a way so that I can apply operator '/' in the case of z3 .Net API? Thank you in advance.
Strictly speaking neither of these formulas is SMT-LIB2 compliant, because / is a function that takes two Real inputs and produces a Real output, whereas div is a function that takes two Int inputs and produces an Int (see SMT-LIB Theories). Z3 is more relaxed and automatically converts those objects. If we enable the option smtlib2_compliant=true then it will indeed report an error in both cases.
The reason for the div version being unsatisfiable is that there is indeed no solution where f is an integer according to (= f (/ a b)), but there is indeed no integer that satisfies (= f 0.5)