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Fix Z3 Euclidean division for rationals and reals - #1025
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Round the quotient according to the divisor sign so that the remainder is nonnegative. Keep division by zero uninterpreted and declare its auxiliary functions when exporting to SMT-LIB or Z3 API calls. Add satisfiable and unsatisfiable unit checks for fractional operands, sign combinations, exact division and zero divisors, with integer controls. Closes vprover#994
quickbeam123
approved these changes
Oct 20, 2026
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Closes #994.
The Z3 backend translates rational and real
$quotient_eas ordinary division, which can refute satisfiable inputs. Round down for positive divisors and up for negative divisors;$remainder_ethen uses the corrected quotient. Keep zero-divisor results uninterpreted and declare the auxiliary functions in exported problems.Checks:
GaveUp; the direct Z3 unit tests return SAT.