This is an ordinary defenum.
Function:
(defun ipasir-status-p (x) (declare (xargs :guard t)) (or (eq x ':undef) (eq x ':input) (eq x ':unsat) (eq x ':sat)))
Theorem: type-when-ipasir-status-p
(defthm type-when-ipasir-status-p (implies (ipasir-status-p x) (if (symbolp x) (if (not (equal x 't)) (not (equal x 'nil)) 'nil) 'nil)) :rule-classes :compound-recognizer)