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• Fraig

Ipasir-check-aignet-equivalence

Signature

(ipasir-check-aignet-equivalence 
     lit1 lit2 config aignet aignet-refcounts 
     sat-lits ipasir fraig-stats) 
 
  → 
(mv status new-sat-lits new-ipasir new-fraig-stats)

Arguments

lit1 — Guard (litp lit1).

lit2 — Guard (litp lit2).

config — Guard (fraig-config-p config).

Returns

status — Type (or (equal status :failed) (equal status :unsat) (equal status :sat)) .

Definitions and Theorems

Function: ipasir-check-aignet-equivalence

(defun ipasir-check-aignet-equivalence
       (lit1 lit2 config aignet aignet-refcounts
             sat-lits ipasir fraig-stats)
 (declare (xargs :stobjs (aignet aignet-refcounts
                                 sat-lits ipasir fraig-stats)))
 (declare (xargs :guard (and (litp lit1)
                             (litp lit2)
                             (fraig-config-p config))))
 (declare
  (xargs
     :guard
     (and (fanin-litp lit1 aignet)
          (fanin-litp lit2 aignet)
          (sat-lits-wfp sat-lits aignet)
          (< (lit-id lit1)
             (u32-length aignet-refcounts))
          (< (lit-id lit2)
             (u32-length aignet-refcounts))
          (non-exec (and (not (eq (ipasir$a->status ipasir) :undef))
                         (not (ipasir$a->new-clause ipasir))
                         (not (ipasir$a->assumption ipasir)))))))
 (let ((__function__ 'ipasir-check-aignet-equivalence))
   (declare (ignorable __function__))
   (b*
     ((lit1 (lit-fix lit1))
      (lit2 (lit-fix lit2))
      ((mv sat-lits ipasir fraig-stats)
       (ipasir-maybe-recycle config sat-lits ipasir fraig-stats))
      ((mv sat-lits ipasir)
       (aignet-lit->ipasir lit1 t aignet-refcounts
                           sat-lits aignet ipasir))
      ((mv sat-lits ipasir)
       (aignet-lit->ipasir lit2 t aignet-refcounts
                           sat-lits aignet ipasir))
      (sat-lit1 (aignet-lit->sat-lit lit1 sat-lits))
      (sat-lit2 (aignet-lit->sat-lit lit2 sat-lits))
      ((mv status ipasir)
       (ipasir-check-equivalence ipasir sat-lit1 sat-lit2))
      (fraig-stats (fraig-stats-count-sat-call status fraig-stats)))
     (mv status sat-lits ipasir fraig-stats))))

Theorem: return-type-of-ipasir-check-aignet-equivalence.status

(defthm return-type-of-ipasir-check-aignet-equivalence.status
  (b* (((mv ?status ?new-sat-lits
            ?new-ipasir ?new-fraig-stats)
        (ipasir-check-aignet-equivalence
             lit1 lit2 config aignet aignet-refcounts
             sat-lits ipasir fraig-stats)))
    (or (equal status :failed)
        (equal status :unsat)
        (equal status :sat)))
  :rule-classes
  ((:forward-chaining
        :trigger-terms
        ((mv-nth 0
                 (ipasir-check-aignet-equivalence
                      lit1 lit2 config aignet aignet-refcounts
                      sat-lits ipasir fraig-stats))))))

Theorem: ipasir-check-aignet-equivalence-ipasir-status

(defthm ipasir-check-aignet-equivalence-ipasir-status
  (b* (((mv ?status ?new-sat-lits
            ?new-ipasir ?new-fraig-stats)
        (ipasir-check-aignet-equivalence
             lit1 lit2 config aignet aignet-refcounts
             sat-lits ipasir fraig-stats)))
    (equal (ipasir$a->status new-ipasir)
           (case status
             (:sat :sat)
             (:unsat :unsat)
             (otherwise :input)))))

Theorem: ipasir-check-aignet-equivalence-new-clause

(defthm ipasir-check-aignet-equivalence-new-clause
  (b* (((mv ?status ?new-sat-lits
            ?new-ipasir ?new-fraig-stats)
        (ipasir-check-aignet-equivalence
             lit1 lit2 config aignet aignet-refcounts
             sat-lits ipasir fraig-stats)))
    (equal (ipasir$a->new-clause new-ipasir)
           nil)))

Theorem: ipasir-check-aignet-equivalence-assumption

(defthm ipasir-check-aignet-equivalence-assumption
  (b* (((mv ?status ?new-sat-lits
            ?new-ipasir ?new-fraig-stats)
        (ipasir-check-aignet-equivalence
             lit1 lit2 config aignet aignet-refcounts
             sat-lits ipasir fraig-stats)))
    (equal (ipasir$a->assumption new-ipasir)
           nil)))

Theorem: sat-lits-wfp-of-ipasir-check-aignet-equivalence

(defthm sat-lits-wfp-of-ipasir-check-aignet-equivalence
  (b* (((mv ?status ?new-sat-lits
            ?new-ipasir ?new-fraig-stats)
        (ipasir-check-aignet-equivalence
             lit1 lit2 config aignet aignet-refcounts
             sat-lits ipasir fraig-stats)))
    (implies (and (sat-lits-wfp sat-lits aignet))
             (sat-lits-wfp new-sat-lits aignet))))

Theorem: ipasir-formula-wfp-of-ipasir-check-aignet-equivalence

(defthm ipasir-formula-wfp-of-ipasir-check-aignet-equivalence
  (b* (((mv ?status ?new-sat-lits
            ?new-ipasir ?new-fraig-stats)
        (ipasir-check-aignet-equivalence
             lit1 lit2 config aignet aignet-refcounts
             sat-lits ipasir fraig-stats)))
    (implies (and (sat-lits-wfp sat-lits aignet)
                  (aignet-litp lit1 aignet)
                  (aignet-litp lit2 aignet)
                  (sat-lit-list-listp (ipasir$a->formula ipasir)
                                      sat-lits))
             (sat-lit-list-listp (ipasir$a->formula new-ipasir)
                                 new-sat-lits))))

Theorem: cnf-for-aignet-of-ipasir-check-aignet-equivalence

(defthm cnf-for-aignet-of-ipasir-check-aignet-equivalence
  (b* (((mv ?status ?new-sat-lits
            ?new-ipasir ?new-fraig-stats)
        (ipasir-check-aignet-equivalence
             lit1 lit2 config aignet aignet-refcounts
             sat-lits ipasir fraig-stats)))
    (implies (and (cnf-for-aignet aignet (ipasir$a->formula ipasir)
                                  sat-lits)
                  (sat-lits-wfp sat-lits aignet)
                  (aignet-litp lit1 aignet)
                  (aignet-litp lit2 aignet)
                  (sat-lit-list-listp (ipasir$a->formula ipasir)
                                      sat-lits))
             (cnf-for-aignet aignet (ipasir$a->formula new-ipasir)
                             new-sat-lits))))

Theorem: ipasir-check-aignet-equivalence-unsat

(defthm ipasir-check-aignet-equivalence-unsat
 (b* (((mv ?status ?new-sat-lits
           ?new-ipasir ?new-fraig-stats)
       (ipasir-check-aignet-equivalence
            lit1 lit2 config aignet aignet-refcounts
            sat-lits ipasir fraig-stats)))
  (implies
   (and (cnf-for-aignet aignet (ipasir$a->formula ipasir)
                        sat-lits)
        (sat-lits-wfp sat-lits aignet)
        (aignet-litp lit1 aignet)
        (aignet-litp lit2 aignet)
        (sat-lit-list-listp (ipasir$a->formula ipasir)
                            sat-lits))
   (equal
     (equal status :unsat)
     (and (hide (equal status :unsat))
          (aignet-lits-comb-equivalent lit1 aignet lit2 aignet))))))

Theorem: ipasir-check-aignet-equivalence-lit1-has-sat-vars

(defthm ipasir-check-aignet-equivalence-lit1-has-sat-vars
  (b* (((mv ?status ?new-sat-lits
            ?new-ipasir ?new-fraig-stats)
        (ipasir-check-aignet-equivalence
             lit1 lit2 config aignet aignet-refcounts
             sat-lits ipasir fraig-stats)))
    (implies (and (sat-lits-wfp sat-lits aignet)
                  (equal id (lit-id lit1))
                  (aignet-litp lit1 aignet))
             (aignet-id-has-sat-var id new-sat-lits))))

Theorem: ipasir-check-aignet-equivalence-lit2-has-sat-vars

(defthm ipasir-check-aignet-equivalence-lit2-has-sat-vars
  (b* (((mv ?status ?new-sat-lits
            ?new-ipasir ?new-fraig-stats)
        (ipasir-check-aignet-equivalence
             lit1 lit2 config aignet aignet-refcounts
             sat-lits ipasir fraig-stats)))
    (implies (and (sat-lits-wfp sat-lits aignet)
                  (equal id (lit-id lit2))
                  (aignet-litp lit2 aignet))
             (aignet-id-has-sat-var id new-sat-lits))))

Theorem: ipasir-check-aignet-equivalence-of-lit-fix-lit1

(defthm ipasir-check-aignet-equivalence-of-lit-fix-lit1
  (equal (ipasir-check-aignet-equivalence
              (lit-fix lit1)
              lit2 config aignet aignet-refcounts
              sat-lits ipasir fraig-stats)
         (ipasir-check-aignet-equivalence
              lit1 lit2 config aignet aignet-refcounts
              sat-lits ipasir fraig-stats)))

Theorem: ipasir-check-aignet-equivalence-lit-equiv-congruence-on-lit1

(defthm ipasir-check-aignet-equivalence-lit-equiv-congruence-on-lit1
  (implies (lit-equiv lit1 lit1-equiv)
           (equal (ipasir-check-aignet-equivalence
                       lit1 lit2 config aignet aignet-refcounts
                       sat-lits ipasir fraig-stats)
                  (ipasir-check-aignet-equivalence
                       lit1-equiv
                       lit2 config aignet aignet-refcounts
                       sat-lits ipasir fraig-stats)))
  :rule-classes :congruence)

Theorem: ipasir-check-aignet-equivalence-of-lit-fix-lit2

(defthm ipasir-check-aignet-equivalence-of-lit-fix-lit2
 (equal
     (ipasir-check-aignet-equivalence lit1 (lit-fix lit2)
                                      config aignet aignet-refcounts
                                      sat-lits ipasir fraig-stats)
     (ipasir-check-aignet-equivalence
          lit1 lit2 config aignet aignet-refcounts
          sat-lits ipasir fraig-stats)))

Theorem: ipasir-check-aignet-equivalence-lit-equiv-congruence-on-lit2

(defthm ipasir-check-aignet-equivalence-lit-equiv-congruence-on-lit2
 (implies
  (lit-equiv lit2 lit2-equiv)
  (equal
     (ipasir-check-aignet-equivalence
          lit1 lit2 config aignet aignet-refcounts
          sat-lits ipasir fraig-stats)
     (ipasir-check-aignet-equivalence lit1 lit2-equiv
                                      config aignet aignet-refcounts
                                      sat-lits ipasir fraig-stats)))
 :rule-classes :congruence)

Theorem: ipasir-check-aignet-equivalence-of-fraig-config-fix-config

(defthm ipasir-check-aignet-equivalence-of-fraig-config-fix-config
  (equal (ipasir-check-aignet-equivalence
              lit1 lit2 (fraig-config-fix config)
              aignet aignet-refcounts
              sat-lits ipasir fraig-stats)
         (ipasir-check-aignet-equivalence
              lit1 lit2 config aignet aignet-refcounts
              sat-lits ipasir fraig-stats)))

Theorem: ipasir-check-aignet-equivalence-fraig-config-equiv-congruence-on-config

(defthm
 ipasir-check-aignet-equivalence-fraig-config-equiv-congruence-on-config
 (implies (fraig-config-equiv config config-equiv)
          (equal (ipasir-check-aignet-equivalence
                      lit1 lit2 config aignet aignet-refcounts
                      sat-lits ipasir fraig-stats)
                 (ipasir-check-aignet-equivalence
                      lit1 lit2
                      config-equiv aignet aignet-refcounts
                      sat-lits ipasir fraig-stats)))
 :rule-classes :congruence)