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ls_entail_ls2_01.sb.smt2
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/
ls_entail_ls2_01.sb.smt2
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(set-logic SHID)
(set-info :source | Songbird - https://songbird-prover.github.io/ |)
(set-info :smt-lib-version 2)
(set-info :category "crafted")
(set-info :status unsat)
;; singleton heap
(declare-sort Refnode 0)
(declare-datatypes
((node 0))
(((c_node (next Refnode)))))
(declare-heap (Refnode node))
;; heap predicates
(define-fun-rec ls ((x_2 Refnode) (y_3 Refnode)) Bool
(or
(and
(_ emp Refnode node)
(= x_2 y_3))
(exists
((u_4 Refnode))
(sep
(pto x_2 (c_node u_4))
(ls u_4 y_3)))))
;; heap predicates
(define-fun-rec ls2 ((x_5 Refnode) (y_6 Refnode)) Bool
(or
(and
(_ emp Refnode node)
(= x_5 y_6))
(exists
((u_7 Refnode))
(sep
(pto x_5 (c_node u_7))
(ls2 u_7 y_6)))
(exists
((u_8 Refnode) (v_9 Refnode))
(sep
(pto u_8 (c_node v_9))
(pto x_5 (c_node u_8))
(ls2 v_9 y_6)))))
(check-sat)
;; entailment: x1->node{x2} * ls(x,x1) * ls(x2,x3) |- (exists u. u->node{x3} * ls2(x,u))
(declare-const x1 Refnode)
(declare-const x2 Refnode)
(declare-const x Refnode)
(declare-const x3 Refnode)
(assert
(sep
(pto x1 (c_node x2))
(ls x x1)
(ls x2 x3)))
(assert
(not
(exists
((u Refnode))
(sep
(pto u (c_node x3))
(ls2 x u)))))
(check-sat)