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overhaul of proof format for new solver

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This commit overhauls the proof format (in development) for the new core.

NOTE: this functionality is work in progress with a long way to go.
It is shielded by the sat.euf option, which is off by default and in pre-release state.
It is too early to fuzz or use it. It is pushed into master to shed light on road-map for certifying inferences of sat.euf.

It retires the ad-hoc extension of DRUP used by the SAT solver.
Instead it relies on SMT with ad-hoc extensions for proof terms.
It adds the following commands (consumed by proof_cmds.cpp):

- assume  - for input clauses
- learn   - when a clause is learned (or redundant clause is added)
- del     - when a clause is deleted.

The commands take a list of expressions of type Bool and the
last argument can optionally be of type Proof.
When the last argument is of type Proof it is provided as a hint
to justify the learned clause.

Proof hints can be checked using a self-contained proof
checker. The sat/smt/euf_proof_checker.h class provides
a plugin dispatcher for checkers.
It is instantiated with a checker for arithmetic lemmas,
so far for Farkas proofs.

Use example:
```
(set-option :sat.euf true)
(set-option :tactic.default_tactic smt)
(set-option :sat.smt.proof f.proof)
(declare-const x Int)
(declare-const y Int)
(declare-const z Int)
(declare-const u Int)
(assert (< x y))
(assert (< y z))
(assert (< z x))
(check-sat)
```

Run z3 on a file with above content.
Then run z3 on f.proof

```
(verified-smt)
(verified-smt)
(verified-smt)
(verified-farkas)
(verified-smt)
```
This commit is contained in:
Nikolaj Bjorner 2022-08-28 17:44:33 -07:00
parent 9922c766b9
commit e2f4fc2307
37 changed files with 809 additions and 1078 deletions
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21
src/sat/smt/arith_solver.cpp
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@ -39,8 +39,6 @@ namespace arith {
lp().settings().set_random_seed(get_config().m_random_seed);
m_lia = alloc(lp::int_solver, *m_solver.get());
m_farkas2.m_ty = sat::hint_type::farkas_h;
m_farkas2.m_literals.resize(2);
}
solver::~solver() {
@ -197,11 +195,12 @@ namespace arith {
reset_evidence();
m_core.push_back(lit1);
TRACE("arith", tout << lit2 << " <- " << m_core << "\n";);
sat::proof_hint* ph = nullptr;
arith_proof_hint* ph = nullptr;
if (ctx.use_drat()) {
ph = &m_farkas2;
m_farkas2.m_literals[0] = std::make_pair(rational(1), lit1);
m_farkas2.m_literals[1] = std::make_pair(rational(1), ~lit2);
m_arith_hint.set_type(ctx, hint_type::farkas_h);
m_arith_hint.add_lit(rational(1), lit1);
m_arith_hint.add_lit(rational(1), ~lit2);
ph = m_arith_hint.mk(ctx);
}
assign(lit2, m_core, m_eqs, ph);
++m_stats.m_bounds_propagations;
@ -262,7 +261,7 @@ namespace arith {
TRACE("arith", for (auto lit : m_core) tout << lit << ": " << s().value(lit) << "\n";);
DEBUG_CODE(for (auto lit : m_core) { VERIFY(s().value(lit) == l_true); });
++m_stats.m_bound_propagations1;
assign(lit, m_core, m_eqs, explain(sat::hint_type::bound_h, lit));
assign(lit, m_core, m_eqs, explain(hint_type::bound_h, lit));
}
if (should_refine_bounds() && first)
@ -378,7 +377,7 @@ namespace arith {
reset_evidence();
m_explanation.clear();
lp().explain_implied_bound(be, m_bp);
assign(bound, m_core, m_eqs, explain(sat::hint_type::farkas_h, bound));
assign(bound, m_core, m_eqs, explain(hint_type::farkas_h, bound));
}
@ -1178,7 +1177,7 @@ namespace arith {
app_ref b = mk_bound(m_lia->get_term(), m_lia->get_offset(), !m_lia->is_upper());
IF_VERBOSE(4, verbose_stream() << "cut " << b << "\n");
literal lit = expr2literal(b);
assign(lit, m_core, m_eqs, explain(sat::hint_type::bound_h, lit));
assign(lit, m_core, m_eqs, explain(hint_type::bound_h, lit));
lia_check = l_false;
break;
}
@ -1200,7 +1199,7 @@ namespace arith {
return lia_check;
}
void solver::assign(literal lit, literal_vector const& core, svector<enode_pair> const& eqs, sat::proof_hint const* pma) {
void solver::assign(literal lit, literal_vector const& core, svector<enode_pair> const& eqs, euf::th_proof_hint const* pma) {
if (core.size() < small_lemma_size() && eqs.empty()) {
m_core2.reset();
for (auto const& c : core)
@ -1247,7 +1246,7 @@ namespace arith {
for (literal& c : m_core)
c.neg();
add_clause(m_core, explain(sat::hint_type::farkas_h));
add_clause(m_core, explain(hint_type::farkas_h));
}
bool solver::is_infeasible() const {