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|
(check
(% s sort
(% a (term s)
(% b (term s)
(% c (term s)
(% f (term (arrow s s))
; -------------------- declaration of input formula -----------------------------------
(% A1 (th_holds (= s a b))
(% A2 (th_holds (= s b c))
(% A3 (th_holds (not (= s a c)))
; ------------------- specify that the following is a proof of the empty clause -----------------
(: (holds cln)
; ---------- use atoms (a1, a2, a3) to map theory literals to boolean literals (v1, v2, v3) ------
(decl_atom (= s a b) (\ v1 (\ a1
(decl_atom (= s b c) (\ v2 (\ a2
(decl_atom (= s a c) (\ v3 (\ a3
; --------------------------- proof of theory lemma ---------------------------------------------
(satlem _ _ (ast _ _ _ a1 (\ l1 (ast _ _ _ a2 (\ l2 (asf _ _ _ a3 (\ l3 (clausify_false (contra _ (trans _ _ _ _ l1 l2) l3)))))))) (\ CT1
; -------------------- clausification of input formulas -----------------------------------------
(satlem _ _
(asf _ _ _ a1 (\ l1
(clausify_false
(contra _ A1 l1)
))) (\ C1
; C1 is the clause ( v1 )
(satlem _ _
(asf _ _ _ a2 (\ l2
(clausify_false
(contra _ A2 l2)
))) (\ C2
; C2 is the clause ( v2 )
(satlem _ _
(ast _ _ _ a3 (\ l3
(clausify_false
(contra _ l3 A3)
))) (\ C3
; C3 is the clause ( ~v3 )
; -------------------- resolution proof ------------------------------------------------------------
(satlem_simplify _ _ _
(R _ _
(R _ _ C2
(R _ _ C1 CT1 v1) v2) C3 v3)
(\ x x))
)))))))))))))))))))))))))))
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