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Add symbolic-modulus congruence rule to nla_divisions (#10119)

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Implement check_mod_congruence in nla_divisions: for two mod-atoms
sharing a (possibly symbolic) divisor y, emit the model-guided tautology
div(x,y) - div(s,y) = delta => mod(x,y) - mod(s,y) = (x - s) - delta*y.
This discharges linear congruences over a symbolic modulus that the
nonlinear core did not otherwise isolate. Thread the div(x,y) variable
through add_divisibility (nla_core/nla_solver/nla_divisions) and
register it in theory_lra for symbolic-divisor mod terms.

Solves FStar.BitVector-1 (0.7s) and FStar.Matrix-1 (1.6s), previously
300s timeouts; all 92 unit tests pass.


Copilot-Session: 726c4e71-03ff-45f6-8322-5253254e1d7e

---------

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
This commit is contained in:
Nikolaj Bjorner 2026-07-14 12:31:17 -07:00 • committed by GitHub
parent 82a0d42970
commit 2f48e355d8
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6 changed files with 74 additions and 13 deletions
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6
src/smt/theory_lra.cpp
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@ -489,13 +489,17 @@ class theory_lra::imp {
// register mod(x, y) with variable divisor for divisibility reasoning
ensure_nla();
if (m_nla) {
app_ref div(a.mk_idiv(n1, n2), m);
ctx().internalize(div, false);
internalize_term(to_app(div));
internalize_term(to_app(n1));
internalize_term(to_app(n2));
internalize_term(t);
theory_var d = mk_var(div);
theory_var x = mk_var(n1);
theory_var y = mk_var(n2);
theory_var rv = mk_var(n);
m_nla->add_divisibility(register_theory_var_in_lar_solver(rv), register_theory_var_in_lar_solver(x), register_theory_var_in_lar_solver(y));
m_nla->add_divisibility(register_theory_var_in_lar_solver(rv), register_theory_var_in_lar_solver(x), register_theory_var_in_lar_solver(y), register_theory_var_in_lar_solver(d));
}
}
}