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Balance

Supergate-has-contradiction

Signature
(supergate-has-contradiction x) → contradictionp
Arguments: x — literal-sorted.
Guard (lit-listp x).

Definitions and Theorems

Function: supergate-has-contradiction

(defun supergate-has-contradiction (x)
  (declare (xargs :guard (lit-listp x)))
  (declare (xargs :guard (consp x)))
  (let ((__function__ 'supergate-has-contradiction))
    (declare (ignorable __function__))
    (or (and (mbt (consp x))
             (eql (lit-fix (car x)) 0))
        (and (consp (cdr x))
             (or (eql (lit-fix (car x))
                      (lit-negate (cadr x)))
                 (supergate-has-contradiction (cdr x)))))))

Theorem: supergate-has-contradiction-correct

(defthm supergate-has-contradiction-correct
 (b* nil
   (implies (supergate-has-contradiction x)
            (equal (aignet-eval-conjunction x invals regvals aignet)
                   0))))

Theorem: supergate-has-contradiction-of-lit-list-fix-x

(defthm supergate-has-contradiction-of-lit-list-fix-x
  (equal (supergate-has-contradiction (lit-list-fix x))
         (supergate-has-contradiction x)))

Theorem: supergate-has-contradiction-lit-list-equiv-congruence-on-x

(defthm supergate-has-contradiction-lit-list-equiv-congruence-on-x
  (implies (satlink::lit-list-equiv x x-equiv)
           (equal (supergate-has-contradiction x)
                  (supergate-has-contradiction x-equiv)))
  :rule-classes :congruence)