%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG044+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n019.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Thu Jul 14 18:29:04 EDT 2022 % Result : Theorem 0.42s 0.60s % Output : Proof 0.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : ALG044+1 : TPTP v8.1.0. Released v2.7.0. % 0.12/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Wed Jun 8 01:09:40 EDT 2022 % 0.12/0.34 % CPUTime : % 0.42/0.60 (* PROOF-FOUND *) % 0.42/0.60 % SZS status Theorem % 0.42/0.60 (* BEGIN-PROOF *) % 0.42/0.60 % SZS output start Proof % 0.42/0.60 Theorem co1 : ((~((((op (e0) (e0)) = (e0))/\(((op (e1) (e1)) = (e0))/\(((op (e2) (e2)) = (e0))/\((op (e3) (e3)) = (e0)))))\/((((op (e0) (e0)) = (e1))/\(((op (e1) (e1)) = (e1))/\(((op (e2) (e2)) = (e1))/\((op (e3) (e3)) = (e1)))))\/((((op (e0) (e0)) = (e2))/\(((op (e1) (e1)) = (e2))/\(((op (e2) (e2)) = (e2))/\((op (e3) (e3)) = (e2)))))\/(((op (e0) (e0)) = (e3))/\(((op (e1) (e1)) = (e3))/\(((op (e2) (e2)) = (e3))/\((op (e3) (e3)) = (e3)))))))))/\((((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3)))))/\((((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3)))))/\((((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3)))))/\((((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3)))))/\((((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3)))))/\((((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3)))))/\((((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3)))))/\((((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3)))))/\((((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3)))))/\((((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3)))))/\((((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3)))))/\((((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3)))))/\((((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3)))))/\((((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3)))))/\((((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3)))))/\((((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3)))))/\(((op (unit) (e0)) = (e0))/\(((op (e0) (unit)) = (e0))/\(((op (unit) (e1)) = (e1))/\(((op (e1) (unit)) = (e1))/\(((op (unit) (e2)) = (e2))/\(((op (e2) (unit)) = (e2))/\(((op (unit) (e3)) = (e3))/\(((op (e3) (unit)) = (e3))/\((((unit) = (e0))\/(((unit) = (e1))\/(((unit) = (e2))\/((unit) = (e3)))))/\((((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0)))))/\((((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0)))))/\((((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1)))))/\((((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1)))))/\((((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2)))))/\((((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2)))))/\((((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3)))))/\((((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3)))))/\((((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0)))))/\((((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0)))))/\((((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1)))))/\((((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1)))))/\((((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2)))))/\((((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2)))))/\((((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3)))))/\((((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3)))))/\((((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0)))))/\((((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0)))))/\((((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1)))))/\((((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1)))))/\((((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2)))))/\((((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2)))))/\((((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3)))))/\((((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3)))))/\((((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0)))))/\((((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0)))))/\((((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1)))))/\((((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1)))))/\((((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2)))))/\((((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2)))))/\((((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3)))))/\(((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). % 0.42/0.60 Proof. % 0.42/0.60 assert (zenon_L1_ : (~((e3) = (e3))) -> False). % 0.42/0.60 do 0 intro. intros zenon_H4. % 0.42/0.60 apply zenon_H4. apply refl_equal. % 0.42/0.60 (* end of lemma zenon_L1_ *) % 0.42/0.60 assert (zenon_L2_ : (~((e0) = (e0))) -> False). % 0.42/0.60 do 0 intro. intros zenon_H5. % 0.42/0.60 apply zenon_H5. apply refl_equal. % 0.42/0.60 (* end of lemma zenon_L2_ *) % 0.42/0.60 assert (zenon_L3_ : (~((unit) = (e0))) -> False). % 0.42/0.60 do 0 intro. intros zenon_H6. % 0.42/0.60 exact (zenon_H6 ax3). % 0.42/0.60 (* end of lemma zenon_L3_ *) % 0.42/0.60 assert (zenon_L4_ : (~((e1) = (e1))) -> False). % 0.42/0.60 do 0 intro. intros zenon_H7. % 0.42/0.60 apply zenon_H7. apply refl_equal. % 0.42/0.60 (* end of lemma zenon_L4_ *) % 0.42/0.60 assert (zenon_L5_ : (~((e2) = (e2))) -> False). % 0.42/0.60 do 0 intro. intros zenon_H8. % 0.42/0.60 apply zenon_H8. apply refl_equal. % 0.42/0.60 (* end of lemma zenon_L5_ *) % 0.42/0.60 apply NNPP. intro zenon_G. % 0.42/0.60 apply (zenon_and_s _ _ ax1). zenon_intro zenon_Ha. zenon_intro zenon_H9. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H9). zenon_intro zenon_Hc. zenon_intro zenon_Hb. % 0.42/0.60 apply (zenon_and_s _ _ zenon_Hb). zenon_intro zenon_He. zenon_intro zenon_Hd. % 0.42/0.60 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H10. zenon_intro zenon_Hf. % 0.42/0.60 apply (zenon_and_s _ _ zenon_Hf). zenon_intro zenon_H12. zenon_intro zenon_H11. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H11). zenon_intro zenon_H14. zenon_intro zenon_H13. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H13). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H15). zenon_intro zenon_H18. zenon_intro zenon_H17. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H17). zenon_intro zenon_H1a. zenon_intro zenon_H19. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H1e. zenon_intro zenon_H1d. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H20. zenon_intro zenon_H1f. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H22. zenon_intro zenon_H21. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H24. zenon_intro zenon_H23. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H28. zenon_intro zenon_H27. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H2c. zenon_intro zenon_H2b. % 0.42/0.60 apply (zenon_notand_s _ _ zenon_G); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 0.42/0.60 apply zenon_H2e. zenon_intro zenon_H2f. % 0.42/0.60 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H10. zenon_intro zenon_H32. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H35. zenon_intro zenon_H2b. % 0.42/0.60 cut (((op (e2) (e2)) = (e3)) = ((e0) = (e3))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_He. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H24. % 0.42/0.60 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4]. % 0.42/0.60 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H36]. % 0.42/0.60 congruence. % 0.42/0.60 exact (zenon_H36 zenon_H35). % 0.42/0.60 apply zenon_H4. apply refl_equal. % 0.42/0.60 apply (zenon_or_s _ _ zenon_H30); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H38). zenon_intro zenon_H3a. zenon_intro zenon_H39. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3e. zenon_intro zenon_H3d. % 0.42/0.60 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H3f | zenon_intro zenon_H7 ]. % 0.42/0.60 cut (((e1) = (e1)) = ((e0) = (e1))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Ha. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H3f. % 0.42/0.60 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 0.42/0.60 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 0.42/0.60 congruence. % 0.42/0.60 cut (((op (e3) (e3)) = (e0)) = ((e1) = (e0))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_H40. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H2b. % 0.42/0.60 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H5]. % 0.42/0.60 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 0.42/0.60 congruence. % 0.42/0.60 exact (zenon_H41 zenon_H3d). % 0.42/0.60 apply zenon_H5. apply refl_equal. % 0.42/0.60 apply zenon_H7. apply refl_equal. % 0.42/0.60 apply zenon_H7. apply refl_equal. % 0.42/0.60 apply (zenon_or_s _ _ zenon_H37); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H45. zenon_intro zenon_H44. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H47. zenon_intro zenon_H46. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.42/0.60 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H4a | zenon_intro zenon_H8 ]. % 0.42/0.60 cut (((e2) = (e2)) = ((e0) = (e2))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Hc. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H4a. % 0.42/0.60 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8]. % 0.42/0.60 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 0.42/0.60 congruence. % 0.42/0.60 cut (((op (e3) (e3)) = (e0)) = ((e2) = (e0))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_H4b. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H2b. % 0.42/0.60 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H5]. % 0.42/0.60 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 0.42/0.60 congruence. % 0.42/0.60 exact (zenon_H4c zenon_H48). % 0.42/0.60 apply zenon_H5. apply refl_equal. % 0.42/0.60 apply zenon_H8. apply refl_equal. % 0.42/0.60 apply zenon_H8. apply refl_equal. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H1a. zenon_intro zenon_H4f. % 0.42/0.60 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H24. zenon_intro zenon_H50. % 0.42/0.60 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H51 | zenon_intro zenon_H4 ]. % 0.42/0.60 cut (((e3) = (e3)) = ((e0) = (e3))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_He. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H51. % 0.42/0.60 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4]. % 0.42/0.60 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 0.42/0.60 congruence. % 0.42/0.60 cut (((op (e3) (e3)) = (e0)) = ((e3) = (e0))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_H52. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H2b. % 0.42/0.60 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H5]. % 0.42/0.60 cut (((op (e3) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 0.42/0.60 congruence. % 0.42/0.60 exact (zenon_H53 zenon_H50). % 0.42/0.60 apply zenon_H5. apply refl_equal. % 0.42/0.60 apply zenon_H4. apply refl_equal. % 0.42/0.60 apply zenon_H4. apply refl_equal. % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H55). zenon_intro zenon_H57. zenon_intro zenon_H56. % 0.42/0.60 exact (zenon_H57 zenon_H10). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H59). zenon_intro zenon_H5b. zenon_intro zenon_H5a. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H5a). zenon_intro zenon_H5d. zenon_intro zenon_H5c. % 0.42/0.60 exact (zenon_H5d zenon_H12). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H58); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H5f). zenon_intro zenon_H61. zenon_intro zenon_H60. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H60). zenon_intro zenon_H63. zenon_intro zenon_H62. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H62). zenon_intro zenon_H65. zenon_intro zenon_H64. % 0.42/0.60 exact (zenon_H65 zenon_H14). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H5e); [ zenon_intro zenon_H67 | zenon_intro zenon_H66 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H67). zenon_intro zenon_H69. zenon_intro zenon_H68. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H68). zenon_intro zenon_H6b. zenon_intro zenon_H6a. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H6a). zenon_intro zenon_H6d. zenon_intro zenon_H6c. % 0.42/0.60 exact (zenon_H6c zenon_H16). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H66); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H6f). zenon_intro zenon_H71. zenon_intro zenon_H70. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72. % 0.42/0.60 exact (zenon_H73 zenon_H18). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H75). zenon_intro zenon_H77. zenon_intro zenon_H76. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H76). zenon_intro zenon_H79. zenon_intro zenon_H78. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H78). zenon_intro zenon_H7b. zenon_intro zenon_H7a. % 0.42/0.60 exact (zenon_H7a zenon_H1a). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H74); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H7d). zenon_intro zenon_H7f. zenon_intro zenon_H7e. % 0.42/0.60 exact (zenon_H7f zenon_H1c). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H7c); [ zenon_intro zenon_H81 | zenon_intro zenon_H80 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H81). zenon_intro zenon_H83. zenon_intro zenon_H82. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H82). zenon_intro zenon_H85. zenon_intro zenon_H84. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H84). zenon_intro zenon_H87. zenon_intro zenon_H86. % 0.42/0.60 exact (zenon_H87 zenon_H1e). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H80); [ zenon_intro zenon_H89 | zenon_intro zenon_H88 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H8a). zenon_intro zenon_H8d. zenon_intro zenon_H8c. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H8c). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 0.42/0.60 exact (zenon_H8f zenon_H20). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H88); [ zenon_intro zenon_H91 | zenon_intro zenon_H90 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H91). zenon_intro zenon_H93. zenon_intro zenon_H92. % 0.42/0.60 exact (zenon_H93 zenon_H22). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H90); [ zenon_intro zenon_H95 | zenon_intro zenon_H94 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H95). zenon_intro zenon_H36. zenon_intro zenon_H96. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H96). zenon_intro zenon_H98. zenon_intro zenon_H97. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H97). zenon_intro zenon_H9a. zenon_intro zenon_H99. % 0.42/0.60 exact (zenon_H99 zenon_H24). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H94); [ zenon_intro zenon_H9c | zenon_intro zenon_H9b ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H9d. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H9d). zenon_intro zenon_Ha0. zenon_intro zenon_H9f. % 0.42/0.60 exact (zenon_Ha0 zenon_H26). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H9b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha1 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Ha2). zenon_intro zenon_Ha4. zenon_intro zenon_Ha3. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Ha3). zenon_intro zenon_Ha6. zenon_intro zenon_Ha5. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Ha5). zenon_intro zenon_Ha8. zenon_intro zenon_Ha7. % 0.42/0.60 exact (zenon_Ha7 zenon_H28). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Ha1); [ zenon_intro zenon_Haa | zenon_intro zenon_Ha9 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Haa). zenon_intro zenon_Hac. zenon_intro zenon_Hab. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Hab). zenon_intro zenon_Hae. zenon_intro zenon_Had. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Had). zenon_intro zenon_Hb0. zenon_intro zenon_Haf. % 0.42/0.60 exact (zenon_Hb0 zenon_H2a). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Ha9); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb1 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Hb2). zenon_intro zenon_Hb4. zenon_intro zenon_Hb3. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Hb3). zenon_intro zenon_Hb6. zenon_intro zenon_Hb5. % 0.42/0.60 exact (zenon_Hb6 zenon_H2c). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hb1); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hb7 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Hb8). zenon_intro zenon_Hba. zenon_intro zenon_Hb9. % 0.42/0.60 exact (zenon_Hba zenon_H2b). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hb7); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hbb ]. % 0.42/0.60 cut (((op (e0) (e0)) = (e0)) = ((op (unit) (e0)) = (e0))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Hbc. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H10. % 0.42/0.60 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H5]. % 0.42/0.60 cut (((op (e0) (e0)) = (op (unit) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 0.42/0.60 congruence. % 0.42/0.60 elim (classic ((op (unit) (e0)) = (op (unit) (e0)))); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hbf ]. % 0.42/0.60 cut (((op (unit) (e0)) = (op (unit) (e0))) = ((op (e0) (e0)) = (op (unit) (e0)))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Hbd. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_Hbe. % 0.42/0.60 cut (((op (unit) (e0)) = (op (unit) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 0.42/0.60 cut (((op (unit) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 0.42/0.60 congruence. % 0.42/0.60 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H5]. % 0.42/0.60 cut (((unit) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 0.42/0.60 congruence. % 0.42/0.60 exact (zenon_H6 ax3). % 0.42/0.60 apply zenon_H5. apply refl_equal. % 0.42/0.60 apply zenon_Hbf. apply refl_equal. % 0.42/0.60 apply zenon_Hbf. apply refl_equal. % 0.42/0.60 apply zenon_H5. apply refl_equal. % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_Hc2 | zenon_intro zenon_Hc1 ]. % 0.42/0.60 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (unit)) = (e0))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Hc2. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H10. % 0.42/0.60 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H5]. % 0.42/0.60 cut (((op (e0) (e0)) = (op (e0) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 0.42/0.60 congruence. % 0.42/0.60 elim (classic ((op (e0) (unit)) = (op (e0) (unit)))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 0.42/0.60 cut (((op (e0) (unit)) = (op (e0) (unit))) = ((op (e0) (e0)) = (op (e0) (unit)))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Hc3. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_Hc4. % 0.42/0.60 cut (((op (e0) (unit)) = (op (e0) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 0.42/0.60 cut (((op (e0) (unit)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 0.42/0.60 congruence. % 0.42/0.60 cut (((unit) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 0.42/0.60 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H5]. % 0.42/0.60 congruence. % 0.42/0.60 apply zenon_H5. apply refl_equal. % 0.42/0.60 exact (zenon_H6 ax3). % 0.42/0.60 apply zenon_Hc5. apply refl_equal. % 0.42/0.60 apply zenon_Hc5. apply refl_equal. % 0.42/0.60 apply zenon_H5. apply refl_equal. % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc7 ]. % 0.42/0.60 cut (((op (e0) (e1)) = (e1)) = ((op (unit) (e1)) = (e1))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Hc8. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H12. % 0.42/0.60 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 0.42/0.60 cut (((op (e0) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 0.42/0.60 congruence. % 0.42/0.60 elim (classic ((op (unit) (e1)) = (op (unit) (e1)))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ]. % 0.42/0.60 cut (((op (unit) (e1)) = (op (unit) (e1))) = ((op (e0) (e1)) = (op (unit) (e1)))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Hc9. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_Hca. % 0.42/0.60 cut (((op (unit) (e1)) = (op (unit) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 0.42/0.60 cut (((op (unit) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 0.42/0.60 congruence. % 0.42/0.60 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 0.42/0.60 cut (((unit) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 0.42/0.60 congruence. % 0.42/0.60 exact (zenon_H6 ax3). % 0.42/0.60 apply zenon_H7. apply refl_equal. % 0.42/0.60 apply zenon_Hcb. apply refl_equal. % 0.42/0.60 apply zenon_Hcb. apply refl_equal. % 0.42/0.60 apply zenon_H7. apply refl_equal. % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hc7); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcd ]. % 0.42/0.60 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (unit)) = (e1))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Hce. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H18. % 0.42/0.60 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 0.42/0.60 cut (((op (e1) (e0)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 0.42/0.60 congruence. % 0.42/0.60 elim (classic ((op (e1) (unit)) = (op (e1) (unit)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 0.42/0.60 cut (((op (e1) (unit)) = (op (e1) (unit))) = ((op (e1) (e0)) = (op (e1) (unit)))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Hcf. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_Hd0. % 0.42/0.60 cut (((op (e1) (unit)) = (op (e1) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 0.42/0.60 cut (((op (e1) (unit)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 0.42/0.60 congruence. % 0.42/0.60 cut (((unit) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 0.42/0.60 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 0.42/0.60 congruence. % 0.42/0.60 apply zenon_H7. apply refl_equal. % 0.42/0.60 exact (zenon_H6 ax3). % 0.42/0.60 apply zenon_Hd1. apply refl_equal. % 0.42/0.60 apply zenon_Hd1. apply refl_equal. % 0.42/0.60 apply zenon_H7. apply refl_equal. % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hcd); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 0.42/0.60 cut (((op (e0) (e2)) = (e2)) = ((op (unit) (e2)) = (e2))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Hd4. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H14. % 0.42/0.60 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8]. % 0.42/0.60 cut (((op (e0) (e2)) = (op (unit) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 0.42/0.60 congruence. % 0.42/0.60 elim (classic ((op (unit) (e2)) = (op (unit) (e2)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 0.42/0.60 cut (((op (unit) (e2)) = (op (unit) (e2))) = ((op (e0) (e2)) = (op (unit) (e2)))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Hd5. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_Hd6. % 0.42/0.60 cut (((op (unit) (e2)) = (op (unit) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 0.42/0.60 cut (((op (unit) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 0.42/0.60 congruence. % 0.42/0.60 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8]. % 0.42/0.60 cut (((unit) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 0.42/0.60 congruence. % 0.42/0.60 exact (zenon_H6 ax3). % 0.42/0.60 apply zenon_H8. apply refl_equal. % 0.42/0.60 apply zenon_Hd7. apply refl_equal. % 0.42/0.60 apply zenon_Hd7. apply refl_equal. % 0.42/0.60 apply zenon_H8. apply refl_equal. % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hd3); [ zenon_intro zenon_Hda | zenon_intro zenon_Hd9 ]. % 0.42/0.60 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (unit)) = (e2))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Hda. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H20. % 0.42/0.60 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8]. % 0.42/0.60 cut (((op (e2) (e0)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 0.42/0.60 congruence. % 0.42/0.60 elim (classic ((op (e2) (unit)) = (op (e2) (unit)))); [ zenon_intro zenon_Hdc | zenon_intro zenon_Hdd ]. % 0.42/0.60 cut (((op (e2) (unit)) = (op (e2) (unit))) = ((op (e2) (e0)) = (op (e2) (unit)))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_Hdb. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_Hdc. % 0.42/0.60 cut (((op (e2) (unit)) = (op (e2) (unit)))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 0.42/0.60 cut (((op (e2) (unit)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 0.42/0.60 congruence. % 0.42/0.60 cut (((unit) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 0.42/0.60 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8]. % 0.42/0.60 congruence. % 0.42/0.60 apply zenon_H8. apply refl_equal. % 0.42/0.60 exact (zenon_H6 ax3). % 0.42/0.60 apply zenon_Hdd. apply refl_equal. % 0.42/0.60 apply zenon_Hdd. apply refl_equal. % 0.42/0.60 apply zenon_H8. apply refl_equal. % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hd9); [ zenon_intro zenon_He0 | zenon_intro zenon_Hdf ]. % 0.42/0.60 cut (((op (e0) (e3)) = (e3)) = ((op (unit) (e3)) = (e3))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_He0. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H16. % 0.42/0.60 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4]. % 0.42/0.60 cut (((op (e0) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 0.42/0.60 congruence. % 0.42/0.60 elim (classic ((op (unit) (e3)) = (op (unit) (e3)))); [ zenon_intro zenon_He2 | zenon_intro zenon_He3 ]. % 0.42/0.60 cut (((op (unit) (e3)) = (op (unit) (e3))) = ((op (e0) (e3)) = (op (unit) (e3)))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_He1. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_He2. % 0.42/0.60 cut (((op (unit) (e3)) = (op (unit) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 0.42/0.60 cut (((op (unit) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 0.42/0.60 congruence. % 0.42/0.60 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4]. % 0.42/0.60 cut (((unit) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 0.42/0.60 congruence. % 0.42/0.60 exact (zenon_H6 ax3). % 0.42/0.60 apply zenon_H4. apply refl_equal. % 0.42/0.60 apply zenon_He3. apply refl_equal. % 0.42/0.60 apply zenon_He3. apply refl_equal. % 0.42/0.60 apply zenon_H4. apply refl_equal. % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hdf); [ zenon_intro zenon_He6 | zenon_intro zenon_He5 ]. % 0.42/0.60 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (unit)) = (e3))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_He6. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_H28. % 0.42/0.60 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4]. % 0.42/0.60 cut (((op (e3) (e0)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 0.42/0.60 congruence. % 0.42/0.60 elim (classic ((op (e3) (unit)) = (op (e3) (unit)))); [ zenon_intro zenon_He8 | zenon_intro zenon_He9 ]. % 0.42/0.60 cut (((op (e3) (unit)) = (op (e3) (unit))) = ((op (e3) (e0)) = (op (e3) (unit)))). % 0.42/0.60 intro zenon_D_pnotp. % 0.42/0.60 apply zenon_He7. % 0.42/0.60 rewrite <- zenon_D_pnotp. % 0.42/0.60 exact zenon_He8. % 0.42/0.60 cut (((op (e3) (unit)) = (op (e3) (unit)))); [idtac | apply NNPP; zenon_intro zenon_He9]. % 0.42/0.60 cut (((op (e3) (unit)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 0.42/0.60 congruence. % 0.42/0.60 cut (((unit) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 0.42/0.60 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4]. % 0.42/0.60 congruence. % 0.42/0.60 apply zenon_H4. apply refl_equal. % 0.42/0.60 exact (zenon_H6 ax3). % 0.42/0.60 apply zenon_He9. apply refl_equal. % 0.42/0.60 apply zenon_He9. apply refl_equal. % 0.42/0.60 apply zenon_H4. apply refl_equal. % 0.42/0.60 apply (zenon_notand_s _ _ zenon_He5); [ zenon_intro zenon_Hec | zenon_intro zenon_Heb ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Hec). zenon_intro zenon_H6. zenon_intro zenon_Hed. % 0.42/0.60 exact (zenon_H6 ax3). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Heb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hee ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Hef). zenon_intro zenon_H57. zenon_intro zenon_Hf0. % 0.42/0.60 exact (zenon_H57 zenon_H10). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hee); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf1 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Hf2). zenon_intro zenon_H57. zenon_intro zenon_Hf3. % 0.42/0.60 exact (zenon_H57 zenon_H10). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf4 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Hf5). zenon_intro zenon_Hf7. zenon_intro zenon_Hf6. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Hf6). zenon_intro zenon_H5d. zenon_intro zenon_Hf8. % 0.42/0.60 exact (zenon_H5d zenon_H12). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hf4); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hf9 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Hfa). zenon_intro zenon_Hf7. zenon_intro zenon_Hfb. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Hfb). zenon_intro zenon_H73. zenon_intro zenon_Hfc. % 0.42/0.60 exact (zenon_H73 zenon_H18). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfe | zenon_intro zenon_Hfd ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Hfe). zenon_intro zenon_H100. zenon_intro zenon_Hff. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_Hff). zenon_intro zenon_H102. zenon_intro zenon_H101. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H101). zenon_intro zenon_H65. zenon_intro zenon_H6d. % 0.42/0.60 exact (zenon_H65 zenon_H14). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H104). zenon_intro zenon_H100. zenon_intro zenon_H105. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H105). zenon_intro zenon_H107. zenon_intro zenon_H106. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H106). zenon_intro zenon_H8f. zenon_intro zenon_Ha8. % 0.42/0.60 exact (zenon_H8f zenon_H20). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H103); [ zenon_intro zenon_H109 | zenon_intro zenon_H108 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H109). zenon_intro zenon_H10b. zenon_intro zenon_H10a. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H10a). zenon_intro zenon_H10d. zenon_intro zenon_H10c. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H10c). zenon_intro zenon_H64. zenon_intro zenon_H6c. % 0.42/0.60 exact (zenon_H6c zenon_H16). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H108); [ zenon_intro zenon_H10f | zenon_intro zenon_H10e ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H10f). zenon_intro zenon_H10b. zenon_intro zenon_H110. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H110). zenon_intro zenon_H112. zenon_intro zenon_H111. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H111). zenon_intro zenon_H8e. zenon_intro zenon_Ha7. % 0.42/0.60 exact (zenon_Ha7 zenon_H28). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H10e); [ zenon_intro zenon_H114 | zenon_intro zenon_H113 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H114). zenon_intro zenon_H71. zenon_intro zenon_H115. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H115). zenon_intro zenon_H77. zenon_intro zenon_H116. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H116). zenon_intro zenon_H7f. zenon_intro zenon_H83. % 0.42/0.60 exact (zenon_H7f zenon_H1c). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H113); [ zenon_intro zenon_H118 | zenon_intro zenon_H117 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H118). zenon_intro zenon_H5b. zenon_intro zenon_H119. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H119). zenon_intro zenon_H77. zenon_intro zenon_H11a. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H11a). zenon_intro zenon_H93. zenon_intro zenon_Hac. % 0.42/0.60 exact (zenon_H93 zenon_H22). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H117); [ zenon_intro zenon_H11c | zenon_intro zenon_H11b ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H11c). zenon_intro zenon_H73. zenon_intro zenon_H11d. % 0.42/0.60 exact (zenon_H73 zenon_H18). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H11b); [ zenon_intro zenon_H11f | zenon_intro zenon_H11e ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H11f). zenon_intro zenon_H5d. zenon_intro zenon_H120. % 0.42/0.60 exact (zenon_H5d zenon_H12). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H11e); [ zenon_intro zenon_H122 | zenon_intro zenon_H121 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H122). zenon_intro zenon_H107. zenon_intro zenon_H123. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H123). zenon_intro zenon_H7b. zenon_intro zenon_H124. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H124). zenon_intro zenon_H125. zenon_intro zenon_H87. % 0.42/0.60 exact (zenon_H87 zenon_H1e). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H121); [ zenon_intro zenon_H127 | zenon_intro zenon_H126 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H127). zenon_intro zenon_H102. zenon_intro zenon_H128. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H128). zenon_intro zenon_H7b. zenon_intro zenon_H129. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H129). zenon_intro zenon_H12a. zenon_intro zenon_Hb0. % 0.42/0.60 exact (zenon_Hb0 zenon_H2a). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H126); [ zenon_intro zenon_H12c | zenon_intro zenon_H12b ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H12c). zenon_intro zenon_H112. zenon_intro zenon_H12d. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H12d). zenon_intro zenon_H7a. zenon_intro zenon_H12e. % 0.42/0.60 exact (zenon_H7a zenon_H1a). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H12b); [ zenon_intro zenon_H130 | zenon_intro zenon_H12f ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H130). zenon_intro zenon_H10d. zenon_intro zenon_H131. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H131). zenon_intro zenon_H7a. zenon_intro zenon_H132. % 0.42/0.60 exact (zenon_H7a zenon_H1a). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H12f); [ zenon_intro zenon_H134 | zenon_intro zenon_H133 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H134). zenon_intro zenon_H8b. zenon_intro zenon_H135. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H135). zenon_intro zenon_H93. zenon_intro zenon_H136. % 0.42/0.60 exact (zenon_H93 zenon_H22). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H133); [ zenon_intro zenon_H138 | zenon_intro zenon_H137 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H138). zenon_intro zenon_H61. zenon_intro zenon_H139. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H139). zenon_intro zenon_H7f. zenon_intro zenon_H13a. % 0.42/0.60 exact (zenon_H7f zenon_H1c). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H137); [ zenon_intro zenon_H13c | zenon_intro zenon_H13b ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H13c). zenon_intro zenon_H8d. zenon_intro zenon_H13d. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H13e). zenon_intro zenon_H98. zenon_intro zenon_Ha0. % 0.42/0.60 exact (zenon_Ha0 zenon_H26). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H13b); [ zenon_intro zenon_H141 | zenon_intro zenon_H140 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H141). zenon_intro zenon_H63. zenon_intro zenon_H142. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H142). zenon_intro zenon_H144. zenon_intro zenon_H143. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H143). zenon_intro zenon_H98. zenon_intro zenon_Hb6. % 0.42/0.60 exact (zenon_Hb6 zenon_H2c). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H140); [ zenon_intro zenon_H146 | zenon_intro zenon_H145 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H146). zenon_intro zenon_H8f. zenon_intro zenon_H147. % 0.42/0.60 exact (zenon_H8f zenon_H20). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H145); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H149). zenon_intro zenon_H65. zenon_intro zenon_H14a. % 0.42/0.60 exact (zenon_H65 zenon_H14). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H148); [ zenon_intro zenon_H14c | zenon_intro zenon_H14b ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H14c). zenon_intro zenon_H8e. zenon_intro zenon_H14d. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H14d). zenon_intro zenon_H14f. zenon_intro zenon_H14e. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H14e). zenon_intro zenon_H99. zenon_intro zenon_H150. % 0.42/0.60 exact (zenon_H99 zenon_H24). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H14b); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H152). zenon_intro zenon_H64. zenon_intro zenon_H153. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H153). zenon_intro zenon_H155. zenon_intro zenon_H154. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H154). zenon_intro zenon_H99. zenon_intro zenon_H156. % 0.42/0.60 exact (zenon_H99 zenon_H24). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H151); [ zenon_intro zenon_H158 | zenon_intro zenon_H157 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H158). zenon_intro zenon_Ha4. zenon_intro zenon_H159. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H159). zenon_intro zenon_Hac. zenon_intro zenon_H15a. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H15a). zenon_intro zenon_Hb4. zenon_intro zenon_Hba. % 0.42/0.60 exact (zenon_Hba zenon_H2b). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H157); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H15c). zenon_intro zenon_H69. zenon_intro zenon_H15d. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H15d). zenon_intro zenon_H83. zenon_intro zenon_H15e. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H15e). zenon_intro zenon_H9e. zenon_intro zenon_Hba. % 0.42/0.60 exact (zenon_Hba zenon_H2b). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H15b); [ zenon_intro zenon_H160 | zenon_intro zenon_H15f ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H160). zenon_intro zenon_Ha6. zenon_intro zenon_H161. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H161). zenon_intro zenon_Hae. zenon_intro zenon_H162. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H162). zenon_intro zenon_Hb6. zenon_intro zenon_H41. % 0.42/0.60 exact (zenon_Hb6 zenon_H2c). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H15f); [ zenon_intro zenon_H164 | zenon_intro zenon_H163 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H164). zenon_intro zenon_H6b. zenon_intro zenon_H165. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H165). zenon_intro zenon_H85. zenon_intro zenon_H166. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H166). zenon_intro zenon_Ha0. zenon_intro zenon_H41. % 0.42/0.60 exact (zenon_Ha0 zenon_H26). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H163); [ zenon_intro zenon_H168 | zenon_intro zenon_H167 ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H168). zenon_intro zenon_Ha8. zenon_intro zenon_H169. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H169). zenon_intro zenon_Hb0. zenon_intro zenon_H16a. % 0.42/0.60 exact (zenon_Hb0 zenon_H2a). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H167); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H16c). zenon_intro zenon_H6d. zenon_intro zenon_H16d. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H16d). zenon_intro zenon_H87. zenon_intro zenon_H16e. % 0.42/0.60 exact (zenon_H87 zenon_H1e). % 0.42/0.60 apply (zenon_notand_s _ _ zenon_H16b); [ zenon_intro zenon_H170 | zenon_intro zenon_H16f ]. % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H170). zenon_intro zenon_Ha7. zenon_intro zenon_H171. % 0.42/0.60 exact (zenon_Ha7 zenon_H28). % 0.42/0.60 apply (zenon_notor_s _ _ zenon_H16f). zenon_intro zenon_H6c. zenon_intro zenon_H172. % 0.42/0.60 exact (zenon_H6c zenon_H16). % 0.42/0.60 Qed. % 0.42/0.60 % SZS output end Proof % 0.42/0.60 (* END-PROOF *) % 0.42/0.60 nodes searched: 575 % 0.42/0.60 max branch formulas: 80 % 0.42/0.60 proof nodes created: 137 % 0.42/0.60 formulas created: 3764 % 0.42/0.60 %------------------------------------------------------------------------------