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; to check, run : lfsc sat.plf smt.plf th_base.plf example.plf
; --------------------------------------------------------------------------------
; literals :
; L1 : forall x. x != x
; L2 : t = t
; input :
; L1
; (instantiation) lemma :
; L1 => L2
; theory conflicts :
; ~L2
; With the theory lemma, the input is unsatisfiable.
; --------------------------------------------------------------------------------
; (0) -------------------- term declarations -----------------------------------
(check
(% s sort
(% t (term s)
; (1) -------------------- input formula -----------------------------------
(% x (term s)
(% A1 (th_holds (forall _ x (not (= _ x x))))
; (2) ------------------- specify that the following is a proof of the empty clause -----------------
(: (holds cln)
; (3) -------------------- theory lemmas prior to rewriting/preprocess/CNF -----------------
; --- these should introduce (th_holds ...)
; instantiation lemma
(inst _ _ _ t (not (= _ t t)) A1 (\ A2
; (4) -------------------- map theory literals to boolean variables
; --- maps all theory literals involved in proof to boolean literals
(decl_atom (forall _ x (not (= _ x x))) (\ v1 (\ a1
(decl_atom (= _ t t) (\ v2 (\ a2
; (5) -------------------- theory conflicts ---------------------------------------------
; --- these should introduce (holds ...)
(satlem _ _
(asf _ _ _ a2 (\ l2
(clausify_false
(contra _ (refl _ t) l2)
))) (\ CT1
; CT1 is the clause ( v2 )
; (6) -------------------- clausification -----------------------------------------
; --- these should introduce (holds ...)
(satlem _ _
(ast _ _ _ a2 (\ l2
(clausify_false
(contra _ l2 A2)
))) (\ C1
; C1 is the clause ( ~v2 )
; (7) -------------------- resolution proof ------------------------------------------------------------
(satlem_simplify _ _ _
(R _ _ CT1 C1 v2)
(\ x x))
))))))))))))))))))
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