unsat
(check
 ;; Declarations
(% a (term Bool)
(% b (term Bool)
(% c (term Bool)
(% A1 (th_holds (not (impl (and (impl (p_app a) (p_app b)) (impl (p_app b) (p_app c))) (impl (p_app a) (p_app c)))))
 ;; Proof of empty clause follows
(: (holds cln)
 ;; Preprocessing 
 ;; Clauses
(decl_atom (p_app b) (\ var3 (\ atom3
(decl_atom (p_app a) (\ var2 (\ atom2
(satlem _ _ (asf _ _ _ atom3 (\ lit6 (ast _ _ _ atom2 (\ lit5 (clausify_false (contra _ (or_elim_1 _ _ (not_not_intro _ lit5) (impl_elim _ _ (and_elim_1 _ _ (and_elim_1 _ _ (not_impl_elim _ _ A1))))) lit6)))))) (\ pb2
(decl_atom (p_app c) (\ var4 (\ atom4
(satlem _ _ (asf _ _ _ atom4 (\ lit8 (ast _ _ _ atom3 (\ lit7 (clausify_false (contra _ (or_elim_1 _ _ (not_not_intro _ lit7) (impl_elim _ _ (and_elim_2 _ _ (and_elim_1 _ _ (not_impl_elim _ _ A1))))) lit8)))))) (\ pb3
(satlem _ _ (asf _ _ _ atom2 (\ lit4 (clausify_false (contra _ (and_elim_1 _ _ (not_impl_elim _ _ (and_elim_2 _ _ (not_impl_elim _ _ A1)))) lit4)))) (\ pb4
(satlem _ _ (ast _ _ _ atom4 (\ lit9 (clausify_false (contra _ lit9 (and_elim_2 _ _ (not_impl_elim _ _ (and_elim_2 _ _ (not_impl_elim _ _ A1)))))))) (\ pb5
 ;; Theory Lemmas
(satlem_simplify _ _ _ (Q _ _ pb2 pb4 var2) (\cl6
(satlem_simplify _ _ _ (Q _ _ pb3 cl6 var3) (\cl7
(satlem_simplify _ _ _ (Q _ _ pb5 cl7 var4) (\empty empty)))))))))))))))))))))))))))))
;;