I have the following simple example for which Z3 times out:
(set-option :produce-models true)
(define-fun T_0 (($in1 Real) ($in2 Real)
($out Real) ($assms Bool) ($prop Bool)) Bool
(and (= $assms (< $in1 $in2))
(= $prop (=> $assms (and (< $in1 $out) (< $out $in2))))))
(declare-fun $in1$0 () Real)
(declare-fun $in2$0 () Real)
(declare-fun $out$0 () Real)
(declare-fun $assms$0 () Bool)
(assert (forall (($out$0 Real) ($assms$0 Bool))
(not (and (T_0 $in1$0 $in2$0 $out$0 $assms$0 true)))))
(check-sat)
Now, if we simplify the assertion, propagating the equality, z3 immediately returns UNSAT (as expected):
(define-fun T_1 (($in1 Real) ($in2 Real)
($out Real) ($prop Bool)) Bool
(and (= $prop (=> (< $in1 $in2) (and (< $in1 $out) (< $out $in2))))))
(declare-fun $in1$0 () Real)
(declare-fun $in2$0 () Real)
(declare-fun $out$0 () Real)
(assert (forall (($out$0 Real) ($assms$0 Bool))
(not (and (T_1 $in1$0 $in2$0 $out$0 true)))))
(check-sat)
This example seems to show that Z3 does not propagate equalities under quantifiers. For example, the following assertion works (yields UNSAT):
(assert (forall (($out$0 Real))
(and (not (= true (=> (< $in1$0 $in2$0)
(and (< $in1$0 $out$0) (< $out$0 $in2$0))))))))
Is there any way to get z3 to propagate equalities, or to choose another search strategy that uses the equation?
