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; Copyright (C) 2017, Regents of the University of Texas
; Marijn Heule, Warren A. Hunt, Jr., and Matt Kaufmann
; License: A 3-clause BSD license. See the LICENSE file distributed with ACL2.
; See ../README.
(in-package "LRAT")
(include-book "incremental")
(deflabel soundness-start)
(in-theory (theory 'ground-zero))
(defthm ordered-formula-p-forward-to-true-listp
(implies (ordered-formula-p formula)
(true-listp formula))
:hints (("Goal" :in-theory (enable ordered-formula-p)))
:rule-classes :forward-chaining)
(defun proved-formula (cnf-file clrat-file chunk-size debug incomplete-okp ctx
state)
(declare (xargs :stobjs state
:guard-hints
(("Goal" :in-theory (enable incl-valid-proofp$-top
acl2::error1-logic)))))
(mv-let (erp val/formula state)
(incl-valid-proofp$-top cnf-file clrat-file
incomplete-okp
chunk-size debug ctx state)
(value (and (null erp)
(consp val/formula)
(eq (car val/formula) t)
; The formula returned by incl-valid-proofp$-top is in reverse order. We
; prefer to return a formula that we expect to agree with the formula
; represented in the input cnf-file.
(reverse (cdr val/formula))))))
(in-theory (disable reverse))
(encapsulate
()
(local (include-book "soundness-main"))
(set-enforce-redundancy t)
(defthm soundness-main
(implies
(and (equal (car (incl-valid-proofp$-top-rec formula
clrat-file posn chunk-size
clrat-file-length
old-suffix debug max-var a$ ctx
state))
:complete)
(formula-p formula)
(a$p a$)
(equal (a$ptr a$) 0)
(integerp max-var)
(<= (formula-max-var formula 0) max-var))
(not (satisfiable formula)))))
(defthm a$p-initial-a$
(a$p (resize-a$arr 2 (create-a$)))
:hints (("Goal" :in-theory (current-theory 'soundness-start))))
(defthm a$ptr-initial-a$
(equal (a$ptr (resize-a$arr 2 (create-a$)))
0)
:hints (("Goal" :in-theory (current-theory 'soundness-start))))
(defthm soundness-helper-1
(implies
(and (formula-p formula)
(posp clrat-file-length)
(equal (car (incl-valid-proofp$-top-rec formula
clrat-file 0 chunk-size
clrat-file-length
"" debug
(formula-max-var formula 0)
(resize-a$arr 2 (create-a$))
ctx state))
:complete))
(not (satisfiable formula)))
:hints (("Goal" :in-theory (enable natp-formula-max-var))))
(encapsulate ; Prove satisfiable-reverse.
()
(local
(progn ; Prove hons-assoc-equal-reverse.
(defthm hons-assoc-equal-revappend-lemma-1
(implies (and (ordered-formula-p1 formula i)
(natp i)
(natp j)
(<= i j))
(equal (hons-assoc-equal j (revappend formula acc))
(hons-assoc-equal j acc)))
:hints (("Goal"
:in-theory (enable ordered-formula-p1))))
(defthm hons-assoc-equal-revappend-lemma-2
(implies (and (ordered-formula-p1 formula i)
(natp i)
(natp j)
(<= i j))
(equal (hons-assoc-equal j formula)
nil))
:hints (("Goal"
:in-theory (enable ordered-formula-p1))))
(defthm hons-assoc-equal-revappend
(implies (ordered-formula-p1 formula start)
(equal (hons-assoc-equal index (revappend formula acc))
(or (hons-assoc-equal index formula)
(hons-assoc-equal index acc))))
:hints (("Goal"
:in-theory (enable ordered-formula-p1))))
(defthm hons-assoc-equal-reverse
(implies (ordered-formula-p formula)
(equal (hons-assoc-equal index (reverse formula))
(hons-assoc-equal index formula)))
:hints (("Goal" :in-theory (enable reverse ordered-formula-p))))))
(local
(defthm solution-p-reverse-implies-solution-p
(implies (and (ordered-formula-p formula)
(solution-p assignment (reverse formula)))
(solution-p assignment formula))
:hints (("Goal"
:in-theory (enable formula-truep-necc solution-p)
:restrict ((formula-truep-necc
((index (formula-truep-witness formula assignment)))))
:expand ((formula-truep formula assignment))))))
(defthm satisfiable-reverse
(implies (and (ordered-formula-p formula)
(not (satisfiable formula)))
(not (satisfiable (reverse formula))))
:hints (("Goal"
:in-theory (enable satisfiable-suff)
:restrict ((satisfiable-suff
((assignment (satisfiable-witness (reverse formula))))))
:expand ((satisfiable (reverse formula)))))))
(defthm soundness-helper-2
(implies (mv-let (erp val/formula state)
(incl-valid-proofp$-top cnf-file clrat-file nil
chunk-size debug ctx state)
(declare (ignore state))
(and (not erp)
(equal formula (reverse (cdr val/formula)))
(car val/formula)))
(not (satisfiable formula)))
:hints (("Goal"
:in-theory (enable incl-valid-proofp$-top
acl2::error1-logic
incl-valid-proofp$-top-aux
ordered-formula-p-implies-formula-p))))
(defthm soundness
(let ((formula (mv-nth 1
(proved-formula cnf-file clrat-file chunk-size debug
nil ; incomplete-okp
ctx state))))
(implies formula
(not (satisfiable formula))))
:hints (("Goal" :restrict ((soundness-helper-2
((state state)
(ctx ctx)
(debug debug)
(chunk-size chunk-size)
(clrat-file clrat-file)
(cnf-file cnf-file)))))))
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