Assumptions in Z3 or Z3Py

Question

is there a way to express assumptions in Z3 (I am using the Z3Py library) such that the engine does not check their validity but takes them as underlying theories, just like in theorem proving?

For example, lets say that I have two unary functions with argument of type Real. I would like to tell the Z3 engine that for all input values, f1(t) is equal to f2(t).

Encoded in Z3Py that would look something like the following:
t = Real("t")
assumption1 = ForAll(t, f1(t) = f2(t)).

The problem with the presented code is that my assertion set is quite big and I use quantifiers (I am trying to prove satisfiability of a real-time system). If I add the above assertion to the set of the other assertions the checking procedure does not terminate.

Answer 1

is there a way to express assumptions in Z3 (I am using the Z3Py library) such that the engine does not check their validity but takes them as underlying theories, just like in theorem proving?

In fact, all assertions you add to Z3 are treated as what you call assumptions. Z3 checks satisfiability of the assertions, it does not check validity. To check validity of a formula F, you assert (not F), and check for satisfiability of (not F). If (not F) is unsat, then F is valid. If you have background axioms, you are essentially checking validity of Background => F, so you can check satisifiability of Background & (not F).

Whether Z3 terminates on your query depends on which combination of theories and quantifiers you use. The more features your queries combine the tougher it is. For formulas over pure linear arithmetic or polynomial real arithmetic, these are called LRA, LIA and NRA in the SMT-LIB classification (see smtlib.org) Z3 uses specialized decision procedures that have recently been added.

Answer 2

Yes, that's possible just as you describe it, but you will end up with quantifiers, which does of course mean that you're solving a harder problem and Z3 will behave differently (it's possible you end up using completely different solvers that don't even share much source code).

For the particular example given, it's possible to eliminate the quantifier cheaply because it has the form of a function definition (ForAll x . f(x) = ...), ie, we can just replace all occurrences of f with the right hand side and then the quantifier is trivially satisfied. In Z3, this is done by the macro finder, which may be applied as a tactic (with name "macro-finder"), or if you are using the "smt" tactic (implicitly via others or directly), then you can set smt.macro_finder=true.