diff --git a/src/sat/smt/arith_axioms.cpp b/src/sat/smt/arith_axioms.cpp index 875a65619..59b594907 100644 --- a/src/sat/smt/arith_axioms.cpp +++ b/src/sat/smt/arith_axioms.cpp @@ -170,7 +170,7 @@ namespace arith { // Add basic mod axiom for abs handling // (mod x y) = (mod x -y) when y != 0 - fundamental property for divisibility - expr_ref neg_q(a.mk_uminus(q), m); + expr_ref neg_q(a.mk_add(a.mk_int(-1), q), m); expr_ref mod_neg(a.mk_mod(p, neg_q), m); literal mod_eq_mod_neg = mk_literal(m.mk_eq(mod, mod_neg)); add_clause(eqz, mod_eq_mod_neg); @@ -210,32 +210,10 @@ namespace arith { // Add axiom: (mod x y) = (mod x -y) when y != 0 // This is needed for divisibility problems to work correctly with abs(y) - expr_ref neg_q(a.mk_uminus(q), m); + expr_ref neg_q(a.mk_add(a.mk_int(-1), q), m); expr_ref mod_neg(a.mk_mod(p, neg_q), m); literal mod_eq_mod_neg = mk_literal(m.mk_eq(mod, mod_neg)); add_clause(eqz, mod_eq_mod_neg); - - // Also add the axiom for abs: (mod x y) = (mod x abs(y)) when y != 0 - expr_ref abs_q(m.mk_ite(a.mk_ge(q, zero), q, a.mk_uminus(q)), m); - expr_ref mod_abs(a.mk_mod(p, abs_q), m); - literal mod_eq_mod_abs = mk_literal(m.mk_eq(mod, mod_abs)); - add_clause(eqz, mod_eq_mod_abs); - - // Add conditional axioms for the ite form that abs gets rewritten to - // (mod x (ite (>= y 0) y (-y))) should equal (mod x y) when y >= 0 - // (mod x (ite (>= y 0) y (-y))) should equal (mod x (-y)) when y < 0 - expr_ref q_ge_0(a.mk_ge(q, zero), m); - expr_ref ite_divisor(m.mk_ite(q_ge_0, q, neg_q), m); - expr_ref mod_ite(a.mk_mod(p, ite_divisor), m); - - // When y >= 0: mod(x, ite(...)) = mod(x, y) - literal q_ge_0_lit = mk_literal(q_ge_0); - literal mod_ite_eq_mod = mk_literal(m.mk_eq(mod_ite, mod)); - add_clause(eqz, ~q_ge_0_lit, mod_ite_eq_mod); - - // When y < 0: mod(x, ite(...)) = mod(x, -y) - literal mod_ite_eq_mod_neg = mk_literal(m.mk_eq(mod_ite, mod_neg)); - add_clause(eqz, q_ge_0_lit, mod_ite_eq_mod_neg); } diff --git a/src/smt/theory_arith_core.h b/src/smt/theory_arith_core.h index 8b941a3d8..05894dad5 100644 --- a/src/smt/theory_arith_core.h +++ b/src/smt/theory_arith_core.h @@ -584,7 +584,7 @@ namespace smt { // Add basic mod axioms for abs handling // (mod x y) = (mod x -y) when y != 0 - fundamental property for divisibility - expr_ref neg_divisor(m_util.mk_uminus(divisor), m); + expr_ref neg_divisor(m_util.mk_add(m_util.mk_int(-1), divisor), m); expr_ref mod_neg(m_util.mk_mod(dividend, neg_divisor), m); mk_axiom(eqz, m.mk_eq(mod, mod_neg)); @@ -621,27 +621,9 @@ namespace smt { // Add axiom: (mod x y) = (mod x -y) when y != 0 // This is needed for divisibility problems to work correctly with abs(y) - expr_ref neg_divisor(m_util.mk_uminus(divisor), m); + expr_ref neg_divisor(m_util.mk_add(m_util.mk_int(-1), divisor), m); expr_ref mod_neg(m_util.mk_mod(dividend, neg_divisor), m); mk_axiom(eqz, m.mk_eq(mod, mod_neg)); - - // Also add the axiom for abs: (mod x y) = (mod x abs(y)) when y != 0 - expr_ref abs_divisor(m.mk_ite(m_util.mk_ge(divisor, zero), divisor, m_util.mk_uminus(divisor)), m); - expr_ref mod_abs(m_util.mk_mod(dividend, abs_divisor), m); - mk_axiom(eqz, m.mk_eq(mod, mod_abs)); - - // Add conditional axioms for the ite form that abs gets rewritten to - expr_ref divisor_ge_0(m_util.mk_ge(divisor, zero), m); - expr_ref ite_divisor(m.mk_ite(divisor_ge_0, divisor, neg_divisor), m); - expr_ref mod_ite(m_util.mk_mod(dividend, ite_divisor), m); - - // When y >= 0: mod(x, ite(...)) = mod(x, y) - expr_ref ante1(m.mk_and(m.mk_not(eqz), divisor_ge_0), m); - mk_axiom(ante1, m.mk_eq(mod_ite, mod)); - - // When y < 0: mod(x, ite(...)) = mod(x, -y) - expr_ref ante2(m.mk_and(m.mk_not(eqz), m.mk_not(divisor_ge_0)), m); - mk_axiom(ante2, m.mk_eq(mod_ite, mod_neg)); } if (m_params.m_arith_enum_const_mod && m_util.is_numeral(divisor, k) &&