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tseitin rule checking - wip

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Unit test

```
(set-option :sat.euf true)
(set-option :sat.smt.proof tseitinproof.smt2)

(declare-const a1 Bool)
(declare-const a2 Bool)
(declare-const a3 Bool)
(declare-const a4 Bool)
(declare-const a5 Bool)
(declare-const a6 Bool)
(declare-const a7 Bool)
(declare-const a8 Bool)
(declare-const a9 Bool)

(declare-const a10 Bool)
(declare-const a11 Bool)
(declare-const a12 Bool)
(declare-const a13 Bool)
(declare-const a14 Bool)
(declare-const a15 Bool)
(declare-const a16 Bool)
(declare-const a17 Bool)
(declare-const a18 Bool)
(declare-const a19 Bool)

(declare-const x1 Bool)
(declare-const x2 Bool)
(declare-const x3 Bool)
(declare-const x4 Bool)
(declare-const x5 Bool)
(declare-const x6 Bool)
(declare-const x7 Bool)
(declare-const x8 Bool)
(declare-const x9 Bool)

(assert (= x1 (and a1 a2)))
(assert (= x2 (or a3 a4)))
(assert (= x3 (=> a5 a6)))
(assert (= x4 (=  a7 a8)))
(assert (= x5 (if a9 a10 a11)))
(assert (= x6 (=> a12 a13)))

(check-sat)
```

Output proof

```
(declare-fun a1 () Bool)
(declare-fun a2 () Bool)
(define-const $26 Bool (and a1 a2))
(declare-fun tseitin (Bool Bool) Proof)
(define-const $60 Bool (not $26))
(define-const $61 Proof (tseitin $60 a1))
(infer a1 (not $26) $61)
(define-const $62 Proof (tseitin $60 a2))
(infer a2 (not $26) $62)
(declare-fun tseitin (Bool Bool Bool) Proof)
(define-const $64 Bool (not a2))
(define-const $63 Bool (not a1))
(define-const $65 Proof (tseitin $63 $64 $26))
(infer (not a1) (not a2) $26 $65)
(declare-fun x1 () Bool)
(assume (not x1) $26)
(assume x1 (not $26))
(declare-fun a3 () Bool)
(declare-fun a4 () Bool)
(define-const $31 Bool (or a3 a4))
(define-const $66 Bool (not a3))
(define-const $67 Proof (tseitin $66 $31))
(infer (not a3) $31 $67)
(define-const $68 Bool (not a4))
(define-const $69 Proof (tseitin $68 $31))
(infer (not a4) $31 $69)
(define-const $70 Bool (not $31))
(define-const $71 Proof (tseitin a3 a4 $70))
(infer a3 a4 (not $31) $71)
(declare-fun x2 () Bool)
(assume (not x2) $31)
(assume x2 (not $31))
(declare-fun a6 () Bool)
(declare-fun a5 () Bool)
(define-const $38 Bool (not a5))
(define-const $39 Bool (or a6 $38))
(define-const $72 Bool (not a6))
(define-const $73 Proof (tseitin $72 $39))
(infer (not a6) $39 $73)
(define-const $74 Proof (tseitin a5 $39))
(infer a5 $39 $74)
(define-const $75 Bool (not $39))
(define-const $76 Proof (tseitin a6 $38 $75))
(infer a6 (not a5) (not $39) $76)
(declare-fun x3 () Bool)
(assume (not x3) $39)
(assume x3 (not $39))
(declare-fun a7 () Bool)
(declare-fun a8 () Bool)
(define-const $44 Bool (= a7 a8))
(define-const $78 Bool (not a7))
(define-const $77 Bool (not $44))
(define-const $79 Proof (tseitin $77 a8 $78))
(infer (not a7) a8 (not $44) $79)
(define-const $80 Bool (not a8))
(define-const $81 Proof (tseitin $77 $80 a7))
(infer a7 (not a8) (not $44) $81)
(define-const $82 Proof (tseitin $44 a8 a7))
(infer a7 a8 $44 $82)
(define-const $83 Proof (tseitin $44 $80 $78))
(infer (not a7) (not a8) $44 $83)
(declare-fun x4 () Bool)
(assume (not x4) $44)
(assume x4 (not $44))
(declare-fun a9 () Bool)
(declare-fun a10 () Bool)
(declare-fun a11 () Bool)
(define-const $50 Bool (ite a9 a10 a11))
(define-const $85 Bool (not a9))
(define-const $84 Bool (not $50))
(define-const $86 Proof (tseitin $84 $85 a10))
(infer (not a9) a10 (not $50) $86)
(define-const $87 Proof (tseitin $84 a9 a11))
(infer a9 a11 (not $50) $87)
(define-const $88 Bool (not a10))
(define-const $89 Proof (tseitin $50 $85 $88))
(infer (not a9) (not a10) $50 $89)
(define-const $90 Bool (not a11))
(define-const $91 Proof (tseitin $50 a9 $90))
(infer a9 (not a11) $50 $91)
(define-const $92 Proof (tseitin $88 $90 $50))
(infer (not a10) (not a11) $50 $92)
(define-const $93 Proof (tseitin a10 a11 $84))
(infer a10 a11 (not $50) $93)
(declare-fun x5 () Bool)
(assume (not x5) $50)
(assume x5 (not $50))
(declare-fun a13 () Bool)
(declare-fun a12 () Bool)
(define-const $57 Bool (not a12))
(define-const $58 Bool (or a13 $57))
(define-const $94 Bool (not a13))
(define-const $95 Proof (tseitin $94 $58))
(infer (not a13) $58 $95)
(define-const $96 Proof (tseitin a12 $58))
(infer a12 $58 $96)
(define-const $97 Bool (not $58))
(define-const $98 Proof (tseitin a13 $57 $97))
(infer a13 (not a12) (not $58) $98)
(declare-fun x6 () Bool)
(assume (not x6) $58)
(assume x6 (not $58))

```
This commit is contained in:
Nikolaj Bjorner 2022-10-10 23:44:03 +02:00
parent fceedf60dc
commit cd8b8b603a
3 changed files with 131 additions and 28 deletions
Download patch file Download diff file Expand all files Collapse all files

38
src/sat/tactic/goal2sat.cpp
View file

@ -124,6 +124,14 @@ struct goal2sat::imp : public sat::sat_internalizer {
return nullptr;
}
euf::th_proof_hint* mk_tseitin(sat::literal a, sat::literal b, sat::literal c) {
if (m_euf && ensure_euf()->use_drat()) {
sat::literal lits[3] = { a, b, c };
return ensure_euf()->mk_smt_hint(m_tseitin, 3, lits);
}
return nullptr;
}
sat::status mk_status(euf::th_proof_hint* ph = nullptr) const {
return sat::status::th(m_is_redundant, m.get_basic_family_id(), ph);
}
@ -522,13 +530,13 @@ struct goal2sat::imp : public sat::sat_internalizer {
sat::bool_var k = add_var(false, n);
sat::literal l(k, false);
cache(n, l);
mk_clause(~l, ~c, t);
mk_clause(~l, c, e);
mk_clause(l, ~c, ~t);
mk_clause(l, c, ~e);
mk_clause(~l, ~c, t, mk_tseitin(~l, ~c, t));
mk_clause(~l, c, e, mk_tseitin(~l, c, e));
mk_clause(l, ~c, ~t, mk_tseitin(l, ~c, ~t));
mk_clause(l, c, ~e, mk_tseitin(l, c, ~e));
if (m_ite_extra) {
mk_clause(~t, ~e, l);
mk_clause(t, e, ~l);
mk_clause(~t, ~e, l, mk_tseitin(~t, ~e, l));
mk_clause(t, e, ~l, mk_tseitin(t, e, ~l));
}
if (aig()) aig()->add_ite(l, c, t, e);
if (sign)
@ -555,8 +563,8 @@ struct goal2sat::imp : public sat::sat_internalizer {
sat::literal l(k, false);
cache(t, l);
// l <=> ~lit
mk_clause(lit, l);
mk_clause(~lit, ~l);
mk_clause(lit, l, mk_tseitin(lit, l));
mk_clause(~lit, ~l, mk_tseitin(~lit, ~l));
if (sign)
l.neg();
m_result_stack.push_back(l);
@ -587,9 +595,9 @@ struct goal2sat::imp : public sat::sat_internalizer {
sat::literal l(k, false);
cache(t, l);
// l <=> (l1 => l2)
mk_clause(~l, ~l1, l2);
mk_clause(l1, l);
mk_clause(~l2, l);
mk_clause(~l, ~l1, l2, mk_tseitin(~l, ~l1, l2));
mk_clause(l1, l, mk_tseitin(l1, l));
mk_clause(~l2, l, mk_tseitin(~l2, l));
if (sign)
l.neg();
m_result_stack.push_back(l);
@ -625,10 +633,10 @@ struct goal2sat::imp : public sat::sat_internalizer {
sat::literal l(k, false);
if (m.is_xor(t))
l1.neg();
mk_clause(~l, l1, ~l2);
mk_clause(~l, ~l1, l2);
mk_clause(l, l1, l2);
mk_clause(l, ~l1, ~l2);
mk_clause(~l, l1, ~l2, mk_tseitin(~l, l1, ~l2));
mk_clause(~l, ~l1, l2, mk_tseitin(~l, ~l1, l2));
mk_clause(l, l1, l2, mk_tseitin(l, l1, l2));
mk_clause(l, ~l1, ~l2, mk_tseitin(l, ~l1, ~l2));
if (aig()) aig()->add_iff(l, l1, l2);
cache(t, l);